<?xml version="1.0"?>
<div class="add">

<b>let </b><font color="Maroon">c<sub>47</sub></font> be   <a href="ami_1.html#NM4">State</a> of <a href="scmpds_2.html#K1">SCMPDS</a> ;<br/><b>let </b><font color="Maroon">c<sub>48</sub></font>, <font color="Maroon">c<sub>49</sub></font> be   <a href="nat_1.html#NM1">Nat</a>;<br/>



<b>reconsider </b><font color="Maroon">c<sub>50</sub></font> =  <a href="scpqsort.html#K1" target="_self">Partition</a>  as  <a href="scmpds_4.html#V3">shiftable</a> <a href="scmpds_5.html#V3">No-StopCode</a> <a href="scmpds_4.html#NM1">Program-block</a> ;<br/>
<b>set </b><font color="Maroon">c<sub>51</sub></font> = <font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font>;<br/>
<b>set </b><font color="Maroon">c<sub>52</sub></font> = <a href="scmp_gcd.html#K2">GBP</a> ,2 <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span>;<br/>
<b>set </b><font color="Maroon">c<sub>53</sub></font> =  <a href="scmpds_2.html#K14">SubFrom</a> <a href="scmp_gcd.html#K2">GBP</a> ,2,<a href="scmp_gcd.html#K3">SBP</a> ,<span class="p1">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span>;<br/>
<b>set </b><font color="Maroon">c<sub>54</sub></font> = <a href="scmp_gcd.html#K2">GBP</a> ,2 <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p1">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span>;<br/>
<b>set </b><font color="Maroon">c<sub>55</sub></font> = <a href="scmp_gcd.html#K2">GBP</a> ,4 <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span>;<br/>
<b>set </b><font color="Maroon">c<sub>56</sub></font> = <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 3</span>)</span> <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span>;<br/>
<b>set </b><font color="Maroon">c<sub>57</sub></font> = <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span> <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K2">GBP</a> ,4;<br/>
<b>set </b><font color="Maroon">c<sub>58</sub></font> = <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 2</span>)</span> <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K2">GBP</a> ,4;<br/>
<b>set </b><font color="Maroon">c<sub>59</sub></font> =  <a href="scmpds_2.html#K12">AddTo</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span>,<span class="p1">(<span class="default"><a href="xcmplx_0.html#K4">-</a> 1</span>)</span>;<br/>
<b>set </b><font color="Maroon">c<sub>60</sub></font> =  <a href="scmpds_2.html#K12">AddTo</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 2</span>)</span>,1;<br/>
<b>set </b><font color="Maroon">c<sub>61</sub></font> =  <a href="scmpds_2.html#K12">AddTo</a> <a href="scmp_gcd.html#K2">GBP</a> ,1,2;<br/>
<b>set </b><font color="Maroon">c<sub>62</sub></font> =  <a href="scmpds_4.html#K1">Load</a> <span class="p1">(<span class="default"><a href="scmpds_2.html#K12">AddTo</a> <a href="scmp_gcd.html#K2">GBP</a> ,1,<span class="p2">(<span class="default"><a href="xcmplx_0.html#K4">-</a> 2</span>)</span></span>)</span>;<br/>
<b>set </b><font color="Maroon">c<sub>63</sub></font> = <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a> ,<span class="p0">(<span class="default"><span class="p1">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 3</span>)</span> <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p0">(<span class="default"><span class="p1">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p5">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a> ,<span class="p0">(<span class="default"><span class="p1">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span> <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K2">GBP</a> ,4</span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p4">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a> ,<span class="p5">(<span class="default"><span class="p0">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 2</span>)</span> <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K2">GBP</a> ,4</span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p3">(<span class="default"><a href="scmpds_2.html#K12">AddTo</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p4">(<span class="default"><span class="p5">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span>,<span class="p4">(<span class="default"><a href="xcmplx_0.html#K4">-</a> 1</span>)</span></span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p2">(<span class="default"><a href="scmpds_2.html#K12">AddTo</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 2</span>)</span>,1</span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p1">(<span class="default"><a href="scmpds_2.html#K12">AddTo</a> <a href="scmp_gcd.html#K2">GBP</a> ,1,2</span>)</span>;<br/>
<b>set </b><font color="Maroon">c<sub>64</sub></font> = <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a> ,2 <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p4">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span></span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p3">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a> ,4 <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p4">(<span class="default"><span class="p5">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span> <a href="scmpds_4.html#K3">';'</a> <font color="Maroon">c<sub>50</sub></font></span>)</span> <a href="scmpds_4.html#K3">';'</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><span class="p0">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a> ,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 3</span>)</span> <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p0">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a> ,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span> <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K2">GBP</a> ,4</span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p5">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a> ,<span class="p0">(<span class="default"><span class="p1">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 2</span>)</span> <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K2">GBP</a> ,4</span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p4">(<span class="default"><a href="scmpds_2.html#K12">AddTo</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p5">(<span class="default"><span class="p0">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span>,<span class="p5">(<span class="default"><a href="xcmplx_0.html#K4">-</a> 1</span>)</span></span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p3">(<span class="default"><a href="scmpds_2.html#K12">AddTo</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p4">(<span class="default"><span class="p5">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 2</span>)</span>,1</span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p2">(<span class="default"><a href="scmpds_2.html#K12">AddTo</a> <a href="scmp_gcd.html#K2">GBP</a> ,1,2</span>)</span></span>)</span>;<br/>
<b>set </b><font color="Maroon">c<sub>65</sub></font> =  <a href="scmpds_6.html#K3">if&gt;0</a> <a href="scmp_gcd.html#K2">GBP</a> ,2,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a> ,2 <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p5">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span></span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p4">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a> ,4 <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p5">(<span class="default"><span class="p0">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span> <a href="scmpds_4.html#K3">';'</a> <font color="Maroon">c<sub>50</sub></font></span>)</span> <a href="scmpds_4.html#K3">';'</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><span class="p0">(<span class="default"><span class="p1">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a> ,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 3</span>)</span> <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p1">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a> ,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span> <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K2">GBP</a> ,4</span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p0">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a> ,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 2</span>)</span> <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K2">GBP</a> ,4</span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p5">(<span class="default"><a href="scmpds_2.html#K12">AddTo</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p0">(<span class="default"><span class="p1">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span>,<span class="p0">(<span class="default"><a href="xcmplx_0.html#K4">-</a> 1</span>)</span></span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p4">(<span class="default"><a href="scmpds_2.html#K12">AddTo</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p5">(<span class="default"><span class="p0">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 2</span>)</span>,1</span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p3">(<span class="default"><a href="scmpds_2.html#K12">AddTo</a> <a href="scmp_gcd.html#K2">GBP</a> ,1,2</span>)</span></span>)</span></span>)</span>,<span class="p1">(<span class="default"><a href="scmpds_4.html#K1">Load</a> <span class="p2">(<span class="default"><a href="scmpds_2.html#K12">AddTo</a> <a href="scmp_gcd.html#K2">GBP</a> ,1,<span class="p3">(<span class="default"><a href="xcmplx_0.html#K4">-</a> 2</span>)</span></span>)</span></span>)</span>;<br/>
<b>set </b><font color="Maroon">c<sub>66</sub></font> = <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a> ,2 <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p2">(<span class="default"><a href="scmpds_2.html#K14">SubFrom</a> <a href="scmp_gcd.html#K2">GBP</a> ,2,<a href="scmp_gcd.html#K3">SBP</a> ,<span class="p3">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span></span>)</span></span>)</span> <a href="scmpds_4.html#K3">';'</a> <span class="p1">(<span class="default"><a href="scmpds_6.html#K3">if&gt;0</a> <a href="scmp_gcd.html#K2">GBP</a> ,2,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a> ,2 <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p0">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span></span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p5">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a> ,4 <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p0">(<span class="default"><span class="p1">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span> <a href="scmpds_4.html#K3">';'</a> <font color="Maroon">c<sub>50</sub></font></span>)</span> <a href="scmpds_4.html#K3">';'</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><span class="p0">(<span class="default"><span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a> ,<span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 3</span>)</span> <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p2">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a> ,<span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span> <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K2">GBP</a> ,4</span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p1">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a> ,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 2</span>)</span> <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K2">GBP</a> ,4</span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p0">(<span class="default"><a href="scmpds_2.html#K12">AddTo</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span>,<span class="p1">(<span class="default"><a href="xcmplx_0.html#K4">-</a> 1</span>)</span></span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p5">(<span class="default"><a href="scmpds_2.html#K12">AddTo</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p0">(<span class="default"><span class="p1">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 2</span>)</span>,1</span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p4">(<span class="default"><a href="scmpds_2.html#K12">AddTo</a> <a href="scmp_gcd.html#K2">GBP</a> ,1,2</span>)</span></span>)</span></span>)</span>,<span class="p2">(<span class="default"><a href="scmpds_4.html#K1">Load</a> <span class="p3">(<span class="default"><a href="scmpds_2.html#K12">AddTo</a> <a href="scmp_gcd.html#K2">GBP</a> ,1,<span class="p4">(<span class="default"><a href="xcmplx_0.html#K4">-</a> 2</span>)</span></span>)</span></span>)</span></span>)</span>;<br/>
<b>set </b><font color="Maroon">c<sub>67</sub></font> =  <a href="scmpds_8.html#K3">while&gt;0</a> <a href="scmp_gcd.html#K2">GBP</a> ,1,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a> ,2 <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p4">(<span class="default"><span class="p5">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p3">(<span class="default"><a href="scmpds_2.html#K14">SubFrom</a> <a href="scmp_gcd.html#K2">GBP</a> ,2,<a href="scmp_gcd.html#K3">SBP</a> ,<span class="p4">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span></span>)</span></span>)</span> <a href="scmpds_4.html#K3">';'</a> <span class="p2">(<span class="default"><a href="scmpds_6.html#K3">if&gt;0</a> <a href="scmp_gcd.html#K2">GBP</a> ,2,<span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><span class="p0">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a> ,2 <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p1">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span></span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p0">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a> ,4 <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span> <a href="scmpds_4.html#K3">';'</a> <font color="Maroon">c<sub>50</sub></font></span>)</span> <a href="scmpds_4.html#K3">';'</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><span class="p0">(<span class="default"><span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a> ,<span class="p4">(<span class="default"><span class="p5">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 3</span>)</span> <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p4">(<span class="default"><span class="p5">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p3">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a> ,<span class="p4">(<span class="default"><span class="p5">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span> <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K2">GBP</a> ,4</span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p2">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a> ,<span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 2</span>)</span> <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K2">GBP</a> ,4</span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p1">(<span class="default"><a href="scmpds_2.html#K12">AddTo</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span>,<span class="p2">(<span class="default"><a href="xcmplx_0.html#K4">-</a> 1</span>)</span></span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p0">(<span class="default"><a href="scmpds_2.html#K12">AddTo</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 2</span>)</span>,1</span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p5">(<span class="default"><a href="scmpds_2.html#K12">AddTo</a> <a href="scmp_gcd.html#K2">GBP</a> ,1,2</span>)</span></span>)</span></span>)</span>,<span class="p3">(<span class="default"><a href="scmpds_4.html#K1">Load</a> <span class="p4">(<span class="default"><a href="scmpds_2.html#K12">AddTo</a> <a href="scmp_gcd.html#K2">GBP</a> ,1,<span class="p5">(<span class="default"><a href="xcmplx_0.html#K4">-</a> 2</span>)</span></span>)</span></span>)</span></span>)</span></span>)</span>;<br/>
<i><font color="Green">E44</font></i>:  <a href="card_1.html#K4">card</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><span class="p0">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a> ,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 3</span>)</span> <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p0">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a> ,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span> <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K2">GBP</a> ,4</span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p5">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a> ,<span class="p0">(<span class="default"><span class="p1">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 2</span>)</span> <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K2">GBP</a> ,4</span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p4">(<span class="default"><a href="scmpds_2.html#K12">AddTo</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p5">(<span class="default"><span class="p0">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span>,<span class="p5">(<span class="default"><a href="xcmplx_0.html#K4">-</a> 1</span>)</span></span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p3">(<span class="default"><a href="scmpds_2.html#K12">AddTo</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p4">(<span class="default"><span class="p5">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 2</span>)</span>,1</span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p2">(<span class="default"><a href="scmpds_2.html#K12">AddTo</a> <a href="scmp_gcd.html#K2">GBP</a> ,1,2</span>)</span></span>)</span> = 
<span class="p1">(<span class="default"><a href="card_1.html#K4">card</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><span class="p0">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a> ,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 3</span>)</span> <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p0">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a> ,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span> <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K2">GBP</a> ,4</span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p5">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a> ,<span class="p0">(<span class="default"><span class="p1">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 2</span>)</span> <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K2">GBP</a> ,4</span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p4">(<span class="default"><a href="scmpds_2.html#K12">AddTo</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p5">(<span class="default"><span class="p0">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span>,<span class="p5">(<span class="default"><a href="xcmplx_0.html#K4">-</a> 1</span>)</span></span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p3">(<span class="default"><a href="scmpds_2.html#K12">AddTo</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p4">(<span class="default"><span class="p5">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 2</span>)</span>,1</span>)</span></span>)</span></span>)</span> <a href="nat_1.html#K1">+</a> 1
<b>by </b><i><a class="ref" href="scmp_gcd.html#T8">SCMP_GCD:8</a></i>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="card_1.html#K4">card</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><span class="p0">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a> ,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 3</span>)</span> <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p0">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a> ,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span> <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K2">GBP</a> ,4</span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p5">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a> ,<span class="p0">(<span class="default"><span class="p1">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 2</span>)</span> <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K2">GBP</a> ,4</span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p4">(<span class="default"><a href="scmpds_2.html#K12">AddTo</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p5">(<span class="default"><span class="p0">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span>,<span class="p5">(<span class="default"><a href="xcmplx_0.html#K4">-</a> 1</span>)</span></span>)</span></span>)</span></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span> <a href="nat_1.html#K1">+</a> 1
<b>by </b><i><a class="ref" href="scmp_gcd.html#T8">SCMP_GCD:8</a></i>
<br/>.= 
<span class="p1">(<span class="default">4 <a href="nat_1.html#K1">+</a> 1</span>)</span> <a href="nat_1.html#K1">+</a> 1
<b>by </b><i><a class="ref" href="scpqsort.html#T4" target="_self">Th4</a></i>
;<br/>
<i><font color="Green">E45</font></i>:  <a href="card_1.html#K4">card</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a> ,2 <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p4">(<span class="default"><span class="p5">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p3">(<span class="default"><a href="scmpds_2.html#K14">SubFrom</a> <a href="scmp_gcd.html#K2">GBP</a> ,2,<a href="scmp_gcd.html#K3">SBP</a> ,<span class="p4">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span></span>)</span></span>)</span> <a href="scmpds_4.html#K3">';'</a> <span class="p2">(<span class="default"><a href="scmpds_6.html#K3">if&gt;0</a> <a href="scmp_gcd.html#K2">GBP</a> ,2,<span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><span class="p0">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a> ,2 <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p1">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span></span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p0">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a> ,4 <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span> <a href="scmpds_4.html#K3">';'</a> <font color="Maroon">c<sub>50</sub></font></span>)</span> <a href="scmpds_4.html#K3">';'</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><span class="p0">(<span class="default"><span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a> ,<span class="p4">(<span class="default"><span class="p5">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 3</span>)</span> <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p4">(<span class="default"><span class="p5">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p3">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a> ,<span class="p4">(<span class="default"><span class="p5">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span> <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K2">GBP</a> ,4</span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p2">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a> ,<span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 2</span>)</span> <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K2">GBP</a> ,4</span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p1">(<span class="default"><a href="scmpds_2.html#K12">AddTo</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span>,<span class="p2">(<span class="default"><a href="xcmplx_0.html#K4">-</a> 1</span>)</span></span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p0">(<span class="default"><a href="scmpds_2.html#K12">AddTo</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 2</span>)</span>,1</span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p5">(<span class="default"><a href="scmpds_2.html#K12">AddTo</a> <a href="scmp_gcd.html#K2">GBP</a> ,1,2</span>)</span></span>)</span></span>)</span>,<span class="p3">(<span class="default"><a href="scmpds_4.html#K1">Load</a> <span class="p4">(<span class="default"><a href="scmpds_2.html#K12">AddTo</a> <a href="scmp_gcd.html#K2">GBP</a> ,1,<span class="p5">(<span class="default"><a href="xcmplx_0.html#K4">-</a> 2</span>)</span></span>)</span></span>)</span></span>)</span></span>)</span> = 
<span class="p1">(<span class="default"><a href="card_1.html#K4">card</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a> ,2 <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p4">(<span class="default"><span class="p5">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p3">(<span class="default"><a href="scmpds_2.html#K14">SubFrom</a> <a href="scmp_gcd.html#K2">GBP</a> ,2,<a href="scmp_gcd.html#K3">SBP</a> ,<span class="p4">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span></span>)</span></span>)</span></span>)</span> <a href="nat_1.html#K1">+</a> <span class="p1">(<span class="default"><a href="card_1.html#K4">card</a> <span class="p2">(<span class="default"><a href="scmpds_6.html#K3">if&gt;0</a> <a href="scmp_gcd.html#K2">GBP</a> ,2,<span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><span class="p0">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a> ,2 <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p1">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span></span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p0">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a> ,4 <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span> <a href="scmpds_4.html#K3">';'</a> <font color="Maroon">c<sub>50</sub></font></span>)</span> <a href="scmpds_4.html#K3">';'</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><span class="p0">(<span class="default"><span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a> ,<span class="p4">(<span class="default"><span class="p5">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 3</span>)</span> <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p4">(<span class="default"><span class="p5">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p3">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a> ,<span class="p4">(<span class="default"><span class="p5">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span> <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K2">GBP</a> ,4</span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p2">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a> ,<span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 2</span>)</span> <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K2">GBP</a> ,4</span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p1">(<span class="default"><a href="scmpds_2.html#K12">AddTo</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span>,<span class="p2">(<span class="default"><a href="xcmplx_0.html#K4">-</a> 1</span>)</span></span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p0">(<span class="default"><a href="scmpds_2.html#K12">AddTo</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 2</span>)</span>,1</span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p5">(<span class="default"><a href="scmpds_2.html#K12">AddTo</a> <a href="scmp_gcd.html#K2">GBP</a> ,1,2</span>)</span></span>)</span></span>)</span>,<span class="p3">(<span class="default"><a href="scmpds_4.html#K1">Load</a> <span class="p4">(<span class="default"><a href="scmpds_2.html#K12">AddTo</a> <a href="scmp_gcd.html#K2">GBP</a> ,1,<span class="p5">(<span class="default"><a href="xcmplx_0.html#K4">-</a> 2</span>)</span></span>)</span></span>)</span></span>)</span></span>)</span>
<b>by </b><i><a class="ref" href="scmpds_4.html#T45">SCMPDS_4:45</a></i>
<br/>.= 
2 <a href="nat_1.html#K1">+</a> <span class="p1">(<span class="default"><a href="card_1.html#K4">card</a> <span class="p2">(<span class="default"><a href="scmpds_6.html#K3">if&gt;0</a> <a href="scmp_gcd.html#K2">GBP</a> ,2,<span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><span class="p0">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a> ,2 <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p1">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span></span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p0">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a> ,4 <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span> <a href="scmpds_4.html#K3">';'</a> <font color="Maroon">c<sub>50</sub></font></span>)</span> <a href="scmpds_4.html#K3">';'</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><span class="p0">(<span class="default"><span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a> ,<span class="p4">(<span class="default"><span class="p5">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 3</span>)</span> <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p4">(<span class="default"><span class="p5">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p3">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a> ,<span class="p4">(<span class="default"><span class="p5">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span> <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K2">GBP</a> ,4</span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p2">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a> ,<span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 2</span>)</span> <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K2">GBP</a> ,4</span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p1">(<span class="default"><a href="scmpds_2.html#K12">AddTo</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span>,<span class="p2">(<span class="default"><a href="xcmplx_0.html#K4">-</a> 1</span>)</span></span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p0">(<span class="default"><a href="scmpds_2.html#K12">AddTo</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 2</span>)</span>,1</span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p5">(<span class="default"><a href="scmpds_2.html#K12">AddTo</a> <a href="scmp_gcd.html#K2">GBP</a> ,1,2</span>)</span></span>)</span></span>)</span>,<span class="p3">(<span class="default"><a href="scmpds_4.html#K1">Load</a> <span class="p4">(<span class="default"><a href="scmpds_2.html#K12">AddTo</a> <a href="scmp_gcd.html#K2">GBP</a> ,1,<span class="p5">(<span class="default"><a href="xcmplx_0.html#K4">-</a> 2</span>)</span></span>)</span></span>)</span></span>)</span></span>)</span>
<b>by </b><i><a class="ref" href="scmp_gcd.html#T9">SCMP_GCD:9</a></i>
<br/>.= 
2 <a href="nat_1.html#K1">+</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="card_1.html#K4">card</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><span class="p0">(<span class="default"><span class="p1">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a> ,2 <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p2">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span></span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p1">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a> ,4 <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span> <a href="scmpds_4.html#K3">';'</a> <font color="Maroon">c<sub>50</sub></font></span>)</span> <a href="scmpds_4.html#K3">';'</a> <span class="p5">(<span class="default"><span class="p0">(<span class="default"><span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a> ,<span class="p5">(<span class="default"><span class="p0">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 3</span>)</span> <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p5">(<span class="default"><span class="p0">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p4">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a> ,<span class="p5">(<span class="default"><span class="p0">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span> <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K2">GBP</a> ,4</span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p3">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a> ,<span class="p4">(<span class="default"><span class="p5">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 2</span>)</span> <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K2">GBP</a> ,4</span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p2">(<span class="default"><a href="scmpds_2.html#K12">AddTo</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span>,<span class="p3">(<span class="default"><a href="xcmplx_0.html#K4">-</a> 1</span>)</span></span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p1">(<span class="default"><a href="scmpds_2.html#K12">AddTo</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 2</span>)</span>,1</span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p0">(<span class="default"><a href="scmpds_2.html#K12">AddTo</a> <a href="scmp_gcd.html#K2">GBP</a> ,1,2</span>)</span></span>)</span></span>)</span></span>)</span> <a href="nat_1.html#K1">+</a> <span class="p3">(<span class="default"><a href="card_1.html#K4">card</a> <span class="p4">(<span class="default"><a href="scmpds_4.html#K1">Load</a> <span class="p5">(<span class="default"><a href="scmpds_2.html#K12">AddTo</a> <a href="scmp_gcd.html#K2">GBP</a> ,1,<span class="p0">(<span class="default"><a href="xcmplx_0.html#K4">-</a> 2</span>)</span></span>)</span></span>)</span></span>)</span></span>)</span> <a href="nat_1.html#K1">+</a> 2</span>)</span>
<b>by </b><i><a class="ref" href="scmpds_6.html#T79">SCMPDS_6:79</a></i>
<br/>.= 
2 <a href="nat_1.html#K1">+</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="card_1.html#K4">card</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><span class="p0">(<span class="default"><span class="p1">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a> ,2 <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p2">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span></span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p1">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a> ,4 <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span> <a href="scmpds_4.html#K3">';'</a> <font color="Maroon">c<sub>50</sub></font></span>)</span> <a href="scmpds_4.html#K3">';'</a> <span class="p5">(<span class="default"><span class="p0">(<span class="default"><span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a> ,<span class="p5">(<span class="default"><span class="p0">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 3</span>)</span> <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p5">(<span class="default"><span class="p0">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p4">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a> ,<span class="p5">(<span class="default"><span class="p0">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span> <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K2">GBP</a> ,4</span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p3">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a> ,<span class="p4">(<span class="default"><span class="p5">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 2</span>)</span> <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K2">GBP</a> ,4</span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p2">(<span class="default"><a href="scmpds_2.html#K12">AddTo</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span>,<span class="p3">(<span class="default"><a href="xcmplx_0.html#K4">-</a> 1</span>)</span></span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p1">(<span class="default"><a href="scmpds_2.html#K12">AddTo</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 2</span>)</span>,1</span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p0">(<span class="default"><a href="scmpds_2.html#K12">AddTo</a> <a href="scmp_gcd.html#K2">GBP</a> ,1,2</span>)</span></span>)</span></span>)</span></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span> <a href="nat_1.html#K1">+</a> 2</span>)</span>
<b>by </b><i><a class="ref" href="scmpds_5.html#T6">SCMPDS_5:6</a></i>
<br/>.= 
2 <a href="nat_1.html#K1">+</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="card_1.html#K4">card</a> <span class="p5">(<span class="default"><span class="p0">(<span class="default"><span class="p1">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a> ,2 <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p2">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span></span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p1">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a> ,4 <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span> <a href="scmpds_4.html#K3">';'</a> <a href="scpqsort.html#K1" target="_self">Partition</a> </span>)</span></span>)</span> <a href="nat_1.html#K1">+</a> <span class="p4">(<span class="default"><a href="card_1.html#K4">card</a> <span class="p5">(<span class="default"><span class="p0">(<span class="default"><span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a> ,<span class="p5">(<span class="default"><span class="p0">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 3</span>)</span> <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p5">(<span class="default"><span class="p0">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p4">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a> ,<span class="p5">(<span class="default"><span class="p0">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span> <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K2">GBP</a> ,4</span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p3">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a> ,<span class="p4">(<span class="default"><span class="p5">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 2</span>)</span> <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K2">GBP</a> ,4</span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p2">(<span class="default"><a href="scmpds_2.html#K12">AddTo</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span>,<span class="p3">(<span class="default"><a href="xcmplx_0.html#K4">-</a> 1</span>)</span></span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p1">(<span class="default"><a href="scmpds_2.html#K12">AddTo</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 2</span>)</span>,1</span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p0">(<span class="default"><a href="scmpds_2.html#K12">AddTo</a> <a href="scmp_gcd.html#K2">GBP</a> ,1,2</span>)</span></span>)</span></span>)</span></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span> <a href="nat_1.html#K1">+</a> 2</span>)</span>
<b>by </b><i><a class="ref" href="scmpds_4.html#T45">SCMPDS_4:45</a></i>
<br/>.= 
2 <a href="nat_1.html#K1">+</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="card_1.html#K4">card</a> <span class="p0">(<span class="default"><span class="p1">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a> ,2 <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p2">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span></span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p1">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a> ,4 <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span></span>)</span> <a href="nat_1.html#K1">+</a> <span class="p5">(<span class="default"><a href="card_1.html#K4">card</a> <a href="scpqsort.html#K1" target="_self">Partition</a> </span>)</span></span>)</span> <a href="nat_1.html#K1">+</a> <span class="p4">(<span class="default"><a href="card_1.html#K4">card</a> <span class="p5">(<span class="default"><span class="p0">(<span class="default"><span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a> ,<span class="p5">(<span class="default"><span class="p0">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 3</span>)</span> <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p5">(<span class="default"><span class="p0">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p4">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a> ,<span class="p5">(<span class="default"><span class="p0">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span> <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K2">GBP</a> ,4</span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p3">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a> ,<span class="p4">(<span class="default"><span class="p5">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 2</span>)</span> <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K2">GBP</a> ,4</span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p2">(<span class="default"><a href="scmpds_2.html#K12">AddTo</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span>,<span class="p3">(<span class="default"><a href="xcmplx_0.html#K4">-</a> 1</span>)</span></span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p1">(<span class="default"><a href="scmpds_2.html#K12">AddTo</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 2</span>)</span>,1</span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p0">(<span class="default"><a href="scmpds_2.html#K12">AddTo</a> <a href="scmp_gcd.html#K2">GBP</a> ,1,2</span>)</span></span>)</span></span>)</span></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span> <a href="nat_1.html#K1">+</a> 2</span>)</span>
<b>by </b><i><a class="ref" href="scmpds_4.html#T45">SCMPDS_4:45</a></i>
<br/>.= 
2 <a href="nat_1.html#K1">+</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default">2 <a href="nat_1.html#K1">+</a> 38</span>)</span> <a href="nat_1.html#K1">+</a> <span class="p4">(<span class="default"><a href="card_1.html#K4">card</a> <span class="p5">(<span class="default"><span class="p0">(<span class="default"><span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a> ,<span class="p5">(<span class="default"><span class="p0">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 3</span>)</span> <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p5">(<span class="default"><span class="p0">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p4">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a> ,<span class="p5">(<span class="default"><span class="p0">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span> <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K2">GBP</a> ,4</span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p3">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a> ,<span class="p4">(<span class="default"><span class="p5">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 2</span>)</span> <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K2">GBP</a> ,4</span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p2">(<span class="default"><a href="scmpds_2.html#K12">AddTo</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span>,<span class="p3">(<span class="default"><a href="xcmplx_0.html#K4">-</a> 1</span>)</span></span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p1">(<span class="default"><a href="scmpds_2.html#K12">AddTo</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 2</span>)</span>,1</span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p0">(<span class="default"><a href="scmpds_2.html#K12">AddTo</a> <a href="scmp_gcd.html#K2">GBP</a> ,1,2</span>)</span></span>)</span></span>)</span></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span> <a href="nat_1.html#K1">+</a> 2</span>)</span>
<b>by </b><i><a class="ref" href="scpqsort.html#T12" target="_self">Th12</a>, <a class="ref" href="scmp_gcd.html#T9">SCMP_GCD:9</a></i>
<br/>.= 
51
<b>by </b><i><a class="txt" href="scpqsort.html#E2:46"><i><font color="Green">E44</font></i></a></i>
;<br/>
<b>set </b><font color="Maroon">c<sub>68</sub></font> = <a href="scmp_gcd.html#K2">GBP</a>  <a href="scmpds_2.html#K6">:=</a> 0;<br/>
<b>set </b><font color="Maroon">c<sub>69</sub></font> = <a href="scmp_gcd.html#K3">SBP</a>  <a href="scmpds_2.html#K6">:=</a> 1;<br/>
<b>set </b><font color="Maroon">c<sub>70</sub></font> = <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p1">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="scmpds_2.html#K11">:=</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span>;<br/>
<b>set </b><font color="Maroon">c<sub>71</sub></font> = <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span> <a href="scmpds_2.html#K11">:=</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span>;<br/>
<b>set </b><font color="Maroon">c<sub>72</sub></font> = <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a>  <a href="scmpds_2.html#K6">:=</a> 0</span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p3">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a>  <a href="scmpds_2.html#K6">:=</a> 1</span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p2">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a> ,<span class="p3">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="scmpds_2.html#K11">:=</a> <span class="p3">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p1">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a> ,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span> <a href="scmpds_2.html#K11">:=</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span></span>)</span>;<br/>
<b>thus </b> <a href="card_1.html#K4">card</a> <span class="p1">(<span class="default"><a href="scpqsort.html#K2" target="_self">QuickSort</a> <font color="Maroon">c<sub>49</sub></font>,<font color="Maroon">c<sub>48</sub></font></span>)</span> = 
 <a href="card_1.html#K4">card</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a>  <a href="scmpds_2.html#K6">:=</a> 0</span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p5">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a>  <a href="scmpds_2.html#K6">:=</a> 1</span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p4">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a> ,<span class="p5">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="scmpds_2.html#K11">:=</a> <span class="p5">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p3">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a> ,<span class="p4">(<span class="default"><span class="p5">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span> <a href="scmpds_2.html#K11">:=</a> <span class="p4">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span></span>)</span></span>)</span> <a href="scmpds_4.html#K3">';'</a> <span class="p2">(<span class="default"><a href="scmpds_8.html#K3">while&gt;0</a> <a href="scmp_gcd.html#K2">GBP</a> ,1,<span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a> ,2 <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p0">(<span class="default"><span class="p1">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p5">(<span class="default"><a href="scmpds_2.html#K14">SubFrom</a> <a href="scmp_gcd.html#K2">GBP</a> ,2,<a href="scmp_gcd.html#K3">SBP</a> ,<span class="p0">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span></span>)</span></span>)</span> <a href="scmpds_4.html#K3">';'</a> <span class="p4">(<span class="default"><a href="scmpds_6.html#K3">if&gt;0</a> <a href="scmp_gcd.html#K2">GBP</a> ,2,<span class="p5">(<span class="default"><span class="p0">(<span class="default"><span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a> ,2 <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p3">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span></span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p2">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a> ,4 <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span> <a href="scmpds_4.html#K3">';'</a> <font color="Maroon">c<sub>50</sub></font></span>)</span> <a href="scmpds_4.html#K3">';'</a> <span class="p0">(<span class="default"><span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a> ,<span class="p0">(<span class="default"><span class="p1">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 3</span>)</span> <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p0">(<span class="default"><span class="p1">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p5">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a> ,<span class="p0">(<span class="default"><span class="p1">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span> <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K2">GBP</a> ,4</span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p4">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a> ,<span class="p5">(<span class="default"><span class="p0">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 2</span>)</span> <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K2">GBP</a> ,4</span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p3">(<span class="default"><a href="scmpds_2.html#K12">AddTo</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p4">(<span class="default"><span class="p5">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span>,<span class="p4">(<span class="default"><a href="xcmplx_0.html#K4">-</a> 1</span>)</span></span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p2">(<span class="default"><a href="scmpds_2.html#K12">AddTo</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 2</span>)</span>,1</span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p1">(<span class="default"><a href="scmpds_2.html#K12">AddTo</a> <a href="scmp_gcd.html#K2">GBP</a> ,1,2</span>)</span></span>)</span></span>)</span>,<span class="p5">(<span class="default"><a href="scmpds_4.html#K1">Load</a> <span class="p0">(<span class="default"><a href="scmpds_2.html#K12">AddTo</a> <a href="scmp_gcd.html#K2">GBP</a> ,1,<span class="p1">(<span class="default"><a href="xcmplx_0.html#K4">-</a> 2</span>)</span></span>)</span></span>)</span></span>)</span></span>)</span></span>)</span></span>)</span>

<br/>.= 
<span class="p1">(<span class="default"><a href="card_1.html#K4">card</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a>  <a href="scmpds_2.html#K6">:=</a> 0</span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p5">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a>  <a href="scmpds_2.html#K6">:=</a> 1</span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p4">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a> ,<span class="p5">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="scmpds_2.html#K11">:=</a> <span class="p5">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p3">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a> ,<span class="p4">(<span class="default"><span class="p5">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span> <a href="scmpds_2.html#K11">:=</a> <span class="p4">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span></span>)</span></span>)</span></span>)</span> <a href="nat_1.html#K1">+</a> <span class="p1">(<span class="default"><a href="card_1.html#K4">card</a> <span class="p2">(<span class="default"><a href="scmpds_8.html#K3">while&gt;0</a> <a href="scmp_gcd.html#K2">GBP</a> ,1,<span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a> ,2 <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p0">(<span class="default"><span class="p1">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p5">(<span class="default"><a href="scmpds_2.html#K14">SubFrom</a> <a href="scmp_gcd.html#K2">GBP</a> ,2,<a href="scmp_gcd.html#K3">SBP</a> ,<span class="p0">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span></span>)</span></span>)</span> <a href="scmpds_4.html#K3">';'</a> <span class="p4">(<span class="default"><a href="scmpds_6.html#K3">if&gt;0</a> <a href="scmp_gcd.html#K2">GBP</a> ,2,<span class="p5">(<span class="default"><span class="p0">(<span class="default"><span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a> ,2 <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p3">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span></span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p2">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a> ,4 <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span> <a href="scmpds_4.html#K3">';'</a> <font color="Maroon">c<sub>50</sub></font></span>)</span> <a href="scmpds_4.html#K3">';'</a> <span class="p0">(<span class="default"><span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a> ,<span class="p0">(<span class="default"><span class="p1">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 3</span>)</span> <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p0">(<span class="default"><span class="p1">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p5">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a> ,<span class="p0">(<span class="default"><span class="p1">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span> <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K2">GBP</a> ,4</span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p4">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a> ,<span class="p5">(<span class="default"><span class="p0">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 2</span>)</span> <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K2">GBP</a> ,4</span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p3">(<span class="default"><a href="scmpds_2.html#K12">AddTo</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p4">(<span class="default"><span class="p5">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span>,<span class="p4">(<span class="default"><a href="xcmplx_0.html#K4">-</a> 1</span>)</span></span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p2">(<span class="default"><a href="scmpds_2.html#K12">AddTo</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 2</span>)</span>,1</span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p1">(<span class="default"><a href="scmpds_2.html#K12">AddTo</a> <a href="scmp_gcd.html#K2">GBP</a> ,1,2</span>)</span></span>)</span></span>)</span>,<span class="p5">(<span class="default"><a href="scmpds_4.html#K1">Load</a> <span class="p0">(<span class="default"><a href="scmpds_2.html#K12">AddTo</a> <a href="scmp_gcd.html#K2">GBP</a> ,1,<span class="p1">(<span class="default"><a href="xcmplx_0.html#K4">-</a> 2</span>)</span></span>)</span></span>)</span></span>)</span></span>)</span></span>)</span></span>)</span>
<b>by </b><i><a class="ref" href="scmpds_4.html#T45">SCMPDS_4:45</a></i>
<br/>.= 
4 <a href="nat_1.html#K1">+</a> <span class="p1">(<span class="default"><a href="card_1.html#K4">card</a> <span class="p2">(<span class="default"><a href="scmpds_8.html#K3">while&gt;0</a> <a href="scmp_gcd.html#K2">GBP</a> ,1,<span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a> ,2 <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p0">(<span class="default"><span class="p1">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p5">(<span class="default"><a href="scmpds_2.html#K14">SubFrom</a> <a href="scmp_gcd.html#K2">GBP</a> ,2,<a href="scmp_gcd.html#K3">SBP</a> ,<span class="p0">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span></span>)</span></span>)</span> <a href="scmpds_4.html#K3">';'</a> <span class="p4">(<span class="default"><a href="scmpds_6.html#K3">if&gt;0</a> <a href="scmp_gcd.html#K2">GBP</a> ,2,<span class="p5">(<span class="default"><span class="p0">(<span class="default"><span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a> ,2 <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p3">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span></span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p2">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a> ,4 <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span> <a href="scmpds_4.html#K3">';'</a> <font color="Maroon">c<sub>50</sub></font></span>)</span> <a href="scmpds_4.html#K3">';'</a> <span class="p0">(<span class="default"><span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a> ,<span class="p0">(<span class="default"><span class="p1">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 3</span>)</span> <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p0">(<span class="default"><span class="p1">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p5">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a> ,<span class="p0">(<span class="default"><span class="p1">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span> <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K2">GBP</a> ,4</span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p4">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a> ,<span class="p5">(<span class="default"><span class="p0">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 2</span>)</span> <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K2">GBP</a> ,4</span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p3">(<span class="default"><a href="scmpds_2.html#K12">AddTo</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p4">(<span class="default"><span class="p5">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span>,<span class="p4">(<span class="default"><a href="xcmplx_0.html#K4">-</a> 1</span>)</span></span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p2">(<span class="default"><a href="scmpds_2.html#K12">AddTo</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 2</span>)</span>,1</span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p1">(<span class="default"><a href="scmpds_2.html#K12">AddTo</a> <a href="scmp_gcd.html#K2">GBP</a> ,1,2</span>)</span></span>)</span></span>)</span>,<span class="p5">(<span class="default"><a href="scmpds_4.html#K1">Load</a> <span class="p0">(<span class="default"><a href="scmpds_2.html#K12">AddTo</a> <a href="scmp_gcd.html#K2">GBP</a> ,1,<span class="p1">(<span class="default"><a href="xcmplx_0.html#K4">-</a> 2</span>)</span></span>)</span></span>)</span></span>)</span></span>)</span></span>)</span></span>)</span>
<b>by </b><i><a class="ref" href="scpqsort.html#T4" target="_self">Th4</a></i>
<br/>.= 
4 <a href="nat_1.html#K1">+</a> <span class="p1">(<span class="default">51 <a href="nat_1.html#K1">+</a> 2</span>)</span>
<b>by </b><i><a class="txt" href="scpqsort.html#E3:46"><i><font color="Green">E45</font></i></a>, <a class="ref" href="scmpds_8.html#T17">SCMPDS_8:17</a></i>
<br/>.= 
57

;<br/>

<b>assume </b><a NAME="E5:46"/><i><font color="Green">E46</font></i>: 
<font color="Maroon">c<sub>48</sub></font> <a href="xxreal_0.html#NR2" target="_self">&gt;=</a> 7
 ;<br/>

<b>set </b><font color="Maroon">c<sub>73</sub></font> =  <a href="scmpds_4.html#K9">IExec</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a>  <a href="scmpds_2.html#K6">:=</a> 0</span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p4">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a>  <a href="scmpds_2.html#K6">:=</a> 1</span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p3">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a> ,<span class="p4">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="scmpds_2.html#K11">:=</a> <span class="p4">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p2">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a> ,<span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span> <a href="scmpds_2.html#K11">:=</a> <span class="p3">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span></span>)</span></span>)</span>,<font color="Maroon">c<sub>47</sub></font>;<br/>
<b>set </b><font color="Maroon">c<sub>74</sub></font> =  <a href="scmp_gcd.html#K2">GBP</a> ;<br/>
<a NAME="E6:46"/><i><font color="Green">E47</font></i>: 
<font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font> <a href="xxreal_0.html#NR2" target="_self">&gt;=</a> 7 <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font>
 
<b>by </b><i><a class="txt" href="scpqsort.html#E5:46"><i><font color="Green">E46</font></i></a>, <a class="ref" href="xreal_1.html#T8">XREAL_1:8</a></i>;<br/>
<a NAME="E7:46"/>
7 <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font> <a href="xxreal_0.html#NR2" target="_self">&gt;=</a> 7
 
<b>by </b><i><a class="ref" href="nat_1.html#T29">NAT_1:29</a></i>;<br/>
<a NAME="E8:46"/><b>then </b><i><font color="Green">E48</font></i>: 
<font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font> <a href="xxreal_0.html#NR2" target="_self">&gt;=</a> 7
 
<b>by </b><i><a class="txt" href="scpqsort.html#E6:46"><i><font color="Green">E47</font></i></a>, <a class="ref" href="xreal_1.html#T2">XREAL_1:2</a></i>;<br/>
<a NAME="E9:46"/><b>then </b><i><font color="Green">E49</font></i>: 
<span class="p1">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 1 <a href="xxreal_0.html#NR2" target="_self">&gt;=</a> 7 <a href="nat_1.html#K1">+</a> 1
 
<b>by </b><i><a class="ref" href="xreal_1.html#T8">XREAL_1:8</a></i>;<br/>
<a NAME="E10:46"/><i><font color="Green">E50</font></i>: 
<span class="p1">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 2 <a href="xxreal_0.html#NR2" target="_self">&gt;=</a> 7 <a href="nat_1.html#K1">+</a> 2
 
<b>by </b><i><a class="txt" href="scpqsort.html#E8:46"><i><font color="Green">E48</font></i></a>, <a class="ref" href="xreal_1.html#T8">XREAL_1:8</a></i>;<br/>
<a NAME="E11:46"/><i><font color="Green">E51</font></i>: 
for <font color="Olive">b<sub>1</sub></font> being  <a href="ami_1.html#NM4">State</a> of <a href="scmpds_2.html#K1">SCMPDS</a> <br/>for <font color="Olive">b<sub>2</sub></font>, <font color="Olive">b<sub>3</sub></font> being  <a href="nat_1.html#NM1">Nat</a> st <font color="Olive">b<sub>1</sub></font> <a href="scmpds_2.html#K2">.</a> <a href="scmp_gcd.html#K2">GBP</a>  <a href="hidden.html#R1">=</a> 0 &amp; <font color="Olive">b<sub>1</sub></font> <a href="scmpds_2.html#K2">.</a> <a href="scmp_gcd.html#K3">SBP</a>  <a href="hidden.html#R1">=</a> <font color="Olive">b<sub>3</sub></font> &amp; <font color="Olive">b<sub>3</sub></font> <a href="hidden.html#R1">=</a> <font color="Olive">b<sub>2</sub></font> <a href="nat_1.html#K1">+</a> 1 holds <br/>( <span class="p1">(<span class="default"><a href="scmpds_4.html#K9">IExec</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><span class="p0">(<span class="default"><span class="p1">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a> ,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 3</span>)</span> <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p1">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a> ,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span> <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K2">GBP</a> ,4</span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p0">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a> ,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 2</span>)</span> <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K2">GBP</a> ,4</span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p5">(<span class="default"><a href="scmpds_2.html#K12">AddTo</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p0">(<span class="default"><span class="p1">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span>,<span class="p0">(<span class="default"><a href="xcmplx_0.html#K4">-</a> 1</span>)</span></span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p4">(<span class="default"><a href="scmpds_2.html#K12">AddTo</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p5">(<span class="default"><span class="p0">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 2</span>)</span>,1</span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p3">(<span class="default"><a href="scmpds_2.html#K12">AddTo</a> <a href="scmp_gcd.html#K2">GBP</a> ,1,2</span>)</span></span>)</span>,<font color="Olive">b<sub>1</sub></font></span>)</span> <a href="scmpds_2.html#K2">.</a> <a href="scmp_gcd.html#K2">GBP</a>  <a href="hidden.html#R1">=</a> 0 &amp; <span class="p1">(<span class="default"><a href="scmpds_4.html#K9">IExec</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><span class="p0">(<span class="default"><span class="p1">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a> ,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 3</span>)</span> <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p1">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a> ,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span> <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K2">GBP</a> ,4</span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p0">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a> ,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 2</span>)</span> <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K2">GBP</a> ,4</span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p5">(<span class="default"><a href="scmpds_2.html#K12">AddTo</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p0">(<span class="default"><span class="p1">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span>,<span class="p0">(<span class="default"><a href="xcmplx_0.html#K4">-</a> 1</span>)</span></span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p4">(<span class="default"><a href="scmpds_2.html#K12">AddTo</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p5">(<span class="default"><span class="p0">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 2</span>)</span>,1</span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p3">(<span class="default"><a href="scmpds_2.html#K12">AddTo</a> <a href="scmp_gcd.html#K2">GBP</a> ,1,2</span>)</span></span>)</span>,<font color="Olive">b<sub>1</sub></font></span>)</span> <a href="scmpds_2.html#K2">.</a> <a href="scmp_gcd.html#K3">SBP</a>  <a href="hidden.html#R1">=</a> <font color="Olive">b<sub>3</sub></font> <a href="nat_1.html#K1">+</a> 2 &amp; <span class="p1">(<span class="default"><a href="scmpds_4.html#K9">IExec</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><span class="p0">(<span class="default"><span class="p1">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a> ,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 3</span>)</span> <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p1">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a> ,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span> <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K2">GBP</a> ,4</span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p0">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a> ,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 2</span>)</span> <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K2">GBP</a> ,4</span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p5">(<span class="default"><a href="scmpds_2.html#K12">AddTo</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p0">(<span class="default"><span class="p1">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span>,<span class="p0">(<span class="default"><a href="xcmplx_0.html#K4">-</a> 1</span>)</span></span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p4">(<span class="default"><a href="scmpds_2.html#K12">AddTo</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p5">(<span class="default"><span class="p0">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 2</span>)</span>,1</span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p3">(<span class="default"><a href="scmpds_2.html#K12">AddTo</a> <a href="scmp_gcd.html#K2">GBP</a> ,1,2</span>)</span></span>)</span>,<font color="Olive">b<sub>1</sub></font></span>)</span> <a href="scmpds_2.html#K2">.</a> <span class="p1">(<span class="default"><a href="scmp_gcd.html#K1">intpos</a> <span class="p2">(<span class="default"><font color="Olive">b<sub>3</sub></font> <a href="nat_1.html#K1">+</a> <span class="p3">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span></span>)</span></span>)</span> <a href="hidden.html#R1">=</a> <font color="Olive">b<sub>1</sub></font> <a href="scmpds_2.html#K2">.</a> <span class="p1">(<span class="default"><a href="scmp_gcd.html#K1">intpos</a> <span class="p2">(<span class="default"><font color="Olive">b<sub>3</sub></font> <a href="nat_1.html#K1">+</a> <span class="p3">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span></span>)</span></span>)</span> &amp; <span class="p1">(<span class="default"><a href="scmpds_4.html#K9">IExec</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><span class="p0">(<span class="default"><span class="p1">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a> ,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 3</span>)</span> <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p1">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a> ,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span> <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K2">GBP</a> ,4</span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p0">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a> ,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 2</span>)</span> <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K2">GBP</a> ,4</span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p5">(<span class="default"><a href="scmpds_2.html#K12">AddTo</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p0">(<span class="default"><span class="p1">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span>,<span class="p0">(<span class="default"><a href="xcmplx_0.html#K4">-</a> 1</span>)</span></span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p4">(<span class="default"><a href="scmpds_2.html#K12">AddTo</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p5">(<span class="default"><span class="p0">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 2</span>)</span>,1</span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p3">(<span class="default"><a href="scmpds_2.html#K12">AddTo</a> <a href="scmp_gcd.html#K2">GBP</a> ,1,2</span>)</span></span>)</span>,<font color="Olive">b<sub>1</sub></font></span>)</span> <a href="scmpds_2.html#K2">.</a> <span class="p1">(<span class="default"><a href="scmp_gcd.html#K1">intpos</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Olive">b<sub>3</sub></font> <a href="nat_1.html#K1">+</a> <span class="p4">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><font color="Olive">b<sub>1</sub></font> <a href="scmpds_2.html#K2">.</a> <span class="p2">(<span class="default"><a href="scmp_gcd.html#K1">intpos</a> 4</span>)</span></span>)</span> <a href="xcmplx_0.html#K6">-</a> 1 &amp; <span class="p1">(<span class="default"><a href="scmpds_4.html#K9">IExec</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><span class="p0">(<span class="default"><span class="p1">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a> ,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 3</span>)</span> <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p1">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a> ,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span> <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K2">GBP</a> ,4</span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p0">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a> ,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 2</span>)</span> <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K2">GBP</a> ,4</span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p5">(<span class="default"><a href="scmpds_2.html#K12">AddTo</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p0">(<span class="default"><span class="p1">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span>,<span class="p0">(<span class="default"><a href="xcmplx_0.html#K4">-</a> 1</span>)</span></span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p4">(<span class="default"><a href="scmpds_2.html#K12">AddTo</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p5">(<span class="default"><span class="p0">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 2</span>)</span>,1</span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p3">(<span class="default"><a href="scmpds_2.html#K12">AddTo</a> <a href="scmp_gcd.html#K2">GBP</a> ,1,2</span>)</span></span>)</span>,<font color="Olive">b<sub>1</sub></font></span>)</span> <a href="scmpds_2.html#K2">.</a> <span class="p1">(<span class="default"><a href="scmp_gcd.html#K1">intpos</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Olive">b<sub>3</sub></font> <a href="nat_1.html#K1">+</a> <span class="p4">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span></span>)</span> <a href="nat_1.html#K1">+</a> 2</span>)</span></span>)</span> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><font color="Olive">b<sub>1</sub></font> <a href="scmpds_2.html#K2">.</a> <span class="p2">(<span class="default"><a href="scmp_gcd.html#K1">intpos</a> 4</span>)</span></span>)</span> <a href="xcmplx_0.html#K2">+</a> 1 &amp; <span class="p1">(<span class="default"><a href="scmpds_4.html#K9">IExec</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><span class="p0">(<span class="default"><span class="p1">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a> ,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 3</span>)</span> <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p1">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a> ,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span> <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K2">GBP</a> ,4</span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p0">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a> ,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 2</span>)</span> <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K2">GBP</a> ,4</span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p5">(<span class="default"><a href="scmpds_2.html#K12">AddTo</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p0">(<span class="default"><span class="p1">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span>,<span class="p0">(<span class="default"><a href="xcmplx_0.html#K4">-</a> 1</span>)</span></span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p4">(<span class="default"><a href="scmpds_2.html#K12">AddTo</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p5">(<span class="default"><span class="p0">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 2</span>)</span>,1</span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p3">(<span class="default"><a href="scmpds_2.html#K12">AddTo</a> <a href="scmp_gcd.html#K2">GBP</a> ,1,2</span>)</span></span>)</span>,<font color="Olive">b<sub>1</sub></font></span>)</span> <a href="scmpds_2.html#K2">.</a> <span class="p1">(<span class="default"><a href="scmp_gcd.html#K1">intpos</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Olive">b<sub>3</sub></font> <a href="nat_1.html#K1">+</a> <span class="p4">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span></span>)</span> <a href="nat_1.html#K1">+</a> 3</span>)</span></span>)</span> <a href="hidden.html#R1">=</a> <font color="Olive">b<sub>1</sub></font> <a href="scmpds_2.html#K2">.</a> <span class="p1">(<span class="default"><a href="scmp_gcd.html#K1">intpos</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Olive">b<sub>3</sub></font> <a href="nat_1.html#K1">+</a> <span class="p4">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> &amp; ( for <font color="Olive">b<sub>4</sub></font> being  <a href="nat_1.html#NM1">Nat</a> st <font color="Olive">b<sub>4</sub></font> <a href="xxreal_0.html#NR2" target="_self">&gt;=</a> 8 &amp; <font color="Olive">b<sub>4</sub></font> <a href="xxreal_0.html#NR3" target="_self">&lt;</a> <font color="Olive">b<sub>3</sub></font> <a href="nat_1.html#K1">+</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> holds <br/><span class="p1">(<span class="default"><a href="scmpds_4.html#K9">IExec</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><span class="p0">(<span class="default"><span class="p1">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a> ,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 3</span>)</span> <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p1">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a> ,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span> <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K2">GBP</a> ,4</span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p0">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a> ,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 2</span>)</span> <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K2">GBP</a> ,4</span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p5">(<span class="default"><a href="scmpds_2.html#K12">AddTo</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p0">(<span class="default"><span class="p1">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span>,<span class="p0">(<span class="default"><a href="xcmplx_0.html#K4">-</a> 1</span>)</span></span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p4">(<span class="default"><a href="scmpds_2.html#K12">AddTo</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p5">(<span class="default"><span class="p0">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 2</span>)</span>,1</span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p3">(<span class="default"><a href="scmpds_2.html#K12">AddTo</a> <a href="scmp_gcd.html#K2">GBP</a> ,1,2</span>)</span></span>)</span>,<font color="Olive">b<sub>1</sub></font></span>)</span> <a href="scmpds_2.html#K2">.</a> <span class="p1">(<span class="default"><a href="scmp_gcd.html#K1">intpos</a> <font color="Olive">b<sub>4</sub></font></span>)</span> <a href="hidden.html#R1">=</a> <font color="Olive">b<sub>1</sub></font> <a href="scmpds_2.html#K2">.</a> <span class="p1">(<span class="default"><a href="scmp_gcd.html#K1">intpos</a> <font color="Olive">b<sub>4</sub></font></span>)</span> ) )
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="46_4"><b>proof </b></a><div class="add">

<b>let </b><font color="Maroon">c<sub>75</sub></font> be   <a href="ami_1.html#NM4">State</a> of <a href="scmpds_2.html#K1">SCMPDS</a> ;<br/><b>let </b><font color="Maroon">c<sub>76</sub></font>, <font color="Maroon">c<sub>77</sub></font> be   <a href="nat_1.html#NM1">Nat</a>;<br/>



<b>assume </b><a NAME="E1:46_4"/><i><font color="Green">E52</font></i>: 
( <font color="Maroon">c<sub>75</sub></font> <a href="scmpds_2.html#K2">.</a> <a href="scmp_gcd.html#K2">GBP</a>  <a href="hidden.html#R1">=</a> 0 &amp; <font color="Maroon">c<sub>75</sub></font> <a href="scmpds_2.html#K2">.</a> <a href="scmp_gcd.html#K3">SBP</a>  <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>77</sub></font> &amp; <font color="Maroon">c<sub>77</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>76</sub></font> <a href="nat_1.html#K1">+</a> 1 )
 ;<br/>

<b>set </b><font color="Maroon">c<sub>78</sub></font> =  <a href="scmpds_5.html#K1">Initialized</a> <font color="Maroon">c<sub>75</sub></font>;<br/>
<b>set </b><font color="Maroon">c<sub>79</sub></font> =  <a href="scmpds_4.html#K9">IExec</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><span class="p0">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a> ,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 3</span>)</span> <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p0">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a> ,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span> <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K2">GBP</a> ,4</span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p5">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a> ,<span class="p0">(<span class="default"><span class="p1">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 2</span>)</span> <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K2">GBP</a> ,4</span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p4">(<span class="default"><a href="scmpds_2.html#K12">AddTo</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p5">(<span class="default"><span class="p0">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span>,<span class="p5">(<span class="default"><a href="xcmplx_0.html#K4">-</a> 1</span>)</span></span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p3">(<span class="default"><a href="scmpds_2.html#K12">AddTo</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p4">(<span class="default"><span class="p5">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 2</span>)</span>,1</span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p2">(<span class="default"><a href="scmpds_2.html#K12">AddTo</a> <a href="scmp_gcd.html#K2">GBP</a> ,1,2</span>)</span></span>)</span>,<font color="Maroon">c<sub>75</sub></font>;<br/>
<b>set </b><font color="Maroon">c<sub>80</sub></font> =  <a href="scmpds_4.html#K9">IExec</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a> ,<span class="p0">(<span class="default"><span class="p1">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 3</span>)</span> <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p0">(<span class="default"><span class="p1">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p5">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a> ,<span class="p0">(<span class="default"><span class="p1">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span> <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K2">GBP</a> ,4</span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p4">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a> ,<span class="p5">(<span class="default"><span class="p0">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 2</span>)</span> <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K2">GBP</a> ,4</span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p3">(<span class="default"><a href="scmpds_2.html#K12">AddTo</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p4">(<span class="default"><span class="p5">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span>,<span class="p4">(<span class="default"><a href="xcmplx_0.html#K4">-</a> 1</span>)</span></span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p2">(<span class="default"><a href="scmpds_2.html#K12">AddTo</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 2</span>)</span>,1</span>)</span></span>)</span>,<font color="Maroon">c<sub>75</sub></font>;<br/>
<b>set </b><font color="Maroon">c<sub>81</sub></font> =  <a href="scmpds_4.html#K9">IExec</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a> ,<span class="p5">(<span class="default"><span class="p0">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 3</span>)</span> <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p5">(<span class="default"><span class="p0">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p4">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a> ,<span class="p5">(<span class="default"><span class="p0">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span> <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K2">GBP</a> ,4</span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p3">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a> ,<span class="p4">(<span class="default"><span class="p5">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 2</span>)</span> <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K2">GBP</a> ,4</span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p2">(<span class="default"><a href="scmpds_2.html#K12">AddTo</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span>,<span class="p3">(<span class="default"><a href="xcmplx_0.html#K4">-</a> 1</span>)</span></span>)</span></span>)</span>,<font color="Maroon">c<sub>75</sub></font>;<br/>
<b>set </b><font color="Maroon">c<sub>82</sub></font> =  <a href="scmpds_4.html#K9">IExec</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a> ,<span class="p4">(<span class="default"><span class="p5">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 3</span>)</span> <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p4">(<span class="default"><span class="p5">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p3">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a> ,<span class="p4">(<span class="default"><span class="p5">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span> <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K2">GBP</a> ,4</span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p2">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a> ,<span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 2</span>)</span> <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K2">GBP</a> ,4</span>)</span></span>)</span>,<font color="Maroon">c<sub>75</sub></font>;<br/>
<b>set </b><font color="Maroon">c<sub>83</sub></font> =  <a href="scmpds_4.html#K9">IExec</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a> ,<span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 3</span>)</span> <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p2">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a> ,<span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span> <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K2">GBP</a> ,4</span>)</span></span>)</span>,<font color="Maroon">c<sub>75</sub></font>;<br/>
<b>set </b><font color="Maroon">c<sub>84</sub></font> =  <a href="ami_1.html#K4">Exec</a> <span class="p1">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a> ,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 3</span>)</span> <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span>,<span class="p1">(<span class="default"><a href="scmpds_5.html#K1">Initialized</a> <font color="Maroon">c<sub>75</sub></font></span>)</span>;<br/>
<b>set </b><font color="Maroon">c<sub>85</sub></font> = <font color="Maroon">c<sub>77</sub></font> <a href="nat_1.html#K1">+</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span>;<br/>
<a NAME="E2:46_4"/>
<font color="Maroon">c<sub>77</sub></font> <a href="xxreal_0.html#NR2" target="_self">&gt;=</a> 1
 
<b>by </b><i><a class="txt" href="scpqsort.html#E1:46_4"><i><font color="Green">E52</font></i></a>, <a class="ref" href="nat_1.html#T29">NAT_1:29</a></i>;<br/>
<a NAME="E3:46_4"/><b>then </b><i><font color="Green">E53</font></i>: 
<font color="Maroon">c<sub>77</sub></font> <a href="nat_1.html#K1">+</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="xxreal_0.html#NR2" target="_self">&gt;=</a> 1 <a href="nat_1.html#K1">+</a> 7
 
<b>by </b><i><a class="txt" href="scpqsort.html#E8:46"><i><font color="Green">E48</font></i></a>, <a class="ref" href="xreal_1.html#T9">XREAL_1:9</a></i>;<br/>
<a NAME="E4:46_4"/><b>then </b><i><font color="Green">E54</font></i>: 
<span class="p1">(<span class="default"><font color="Maroon">c<sub>77</sub></font> <a href="nat_1.html#K1">+</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span></span>)</span> <a href="nat_1.html#K1">+</a> 1 <a href="xxreal_0.html#NR2" target="_self">&gt;=</a> 8 <a href="nat_1.html#K1">+</a> 1
 
<b>by </b><i><a class="ref" href="xreal_1.html#T8">XREAL_1:8</a></i>;<br/>
<a NAME="E5:46_4"/><i><font color="Green">E55</font></i>: 
<span class="p1">(<span class="default"><font color="Maroon">c<sub>77</sub></font> <a href="nat_1.html#K1">+</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span></span>)</span> <a href="nat_1.html#K1">+</a> 2 <a href="xxreal_0.html#NR2" target="_self">&gt;=</a> 8 <a href="nat_1.html#K1">+</a> 2
 
<b>by </b><i><a class="txt" href="scpqsort.html#E3:46_4"><i><font color="Green">E53</font></i></a>, <a class="ref" href="xreal_1.html#T8">XREAL_1:8</a></i>;<br/>
<a NAME="E6:46_4"/><i><font color="Green">E56</font></i>: 
<span class="p1">(<span class="default"><font color="Maroon">c<sub>77</sub></font> <a href="nat_1.html#K1">+</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span></span>)</span> <a href="nat_1.html#K1">+</a> 3 <a href="xxreal_0.html#NR2" target="_self">&gt;=</a> 8 <a href="nat_1.html#K1">+</a> 3
 
<b>by </b><i><a class="txt" href="scpqsort.html#E3:46_4"><i><font color="Green">E53</font></i></a>, <a class="ref" href="xreal_1.html#T8">XREAL_1:8</a></i>;<br/>
<a NAME="E7:46_4"/><i><font color="Green">E57</font></i>: 
<span class="p1">(<span class="default"><a href="scmpds_5.html#K1">Initialized</a> <font color="Maroon">c<sub>75</sub></font></span>)</span> <a href="scmpds_2.html#K2">.</a> <a href="scmp_gcd.html#K3">SBP</a>  <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>77</sub></font>
 
<b>by </b><i><a class="txt" href="scpqsort.html#E1:46_4"><i><font color="Green">E52</font></i></a>, <a class="ref" href="scmpds_5.html#T40">SCMPDS_5:40</a></i>;<br/>
<b>then </b><i><font color="Green">E58</font></i>:  <a href="scmpds_2.html#K3">DataLoc</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="scmpds_5.html#K1">Initialized</a> <font color="Maroon">c<sub>75</sub></font></span>)</span> <a href="scmpds_2.html#K2">.</a> <a href="scmp_gcd.html#K3">SBP</a> </span>)</span>,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 3</span>)</span> = 
 <a href="scmp_gcd.html#K1">intpos</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>77</sub></font> <a href="nat_1.html#K1">+</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 3</span>)</span></span>)</span>
<b>by </b><i><a class="ref" href="scmp_gcd.html#T5">SCMP_GCD:5</a></i>
<br/>.= 
 <a href="scmp_gcd.html#K1">intpos</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>77</sub></font> <a href="nat_1.html#K1">+</a> <span class="p3">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span></span>)</span> <a href="nat_1.html#K1">+</a> 3</span>)</span>

;<br/>
<div><i><font color="Green">E59</font></i>: <a class="txt" onclick="hs2(this)" href="javascript:()" title="46_4_2"><b>now </b></a><div class="add"><b>let </b><font color="Maroon">c<sub>86</sub></font> be   <a href="nat_1.html#NM1">Nat</a>;<br/><b>assume </b><a NAME="E1:46_4_2"/>
<font color="Maroon">c<sub>86</sub></font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>77</sub></font> <a href="nat_1.html#K1">+</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span></span>)</span> <a href="nat_1.html#K1">+</a> 3
 ;<br/><a NAME="E2:46_4_2"/><b>then </b>
 <a href="scmp_gcd.html#K1">intpos</a> <font color="Maroon">c<sub>86</sub></font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a>  <a href="scmpds_2.html#K3">DataLoc</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="scmpds_5.html#K1">Initialized</a> <font color="Maroon">c<sub>75</sub></font></span>)</span> <a href="scmpds_2.html#K2">.</a> <a href="scmp_gcd.html#K3">SBP</a> </span>)</span>,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 3</span>)</span>
 <b>by </b><i><a class="txt" href="scpqsort.html#E8:46_4"><i><font color="Green">E58</font></i></a>, <a class="ref" href="scmp_gcd.html#T4">SCMP_GCD:4</a></i>;<br/><b>hence </b><span class="p1">(<span class="default"><a href="ami_1.html#K4">Exec</a> <span class="p2">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a> ,<span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 3</span>)</span> <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span>,<span class="p2">(<span class="default"><a href="scmpds_5.html#K1">Initialized</a> <font color="Maroon">c<sub>75</sub></font></span>)</span></span>)</span> <a href="scmpds_2.html#K2">.</a> <span class="p1">(<span class="default"><a href="scmp_gcd.html#K1">intpos</a> <font color="Maroon">c<sub>86</sub></font></span>)</span> = 
<span class="p1">(<span class="default"><a href="scmpds_5.html#K1">Initialized</a> <font color="Maroon">c<sub>75</sub></font></span>)</span> <a href="scmpds_2.html#K2">.</a> <span class="p1">(<span class="default"><a href="scmp_gcd.html#K1">intpos</a> <font color="Maroon">c<sub>86</sub></font></span>)</span>
<b>by </b><i><a class="ref" href="scmpds_2.html#T59">SCMPDS_2:59</a></i>
<br/>.= 
<font color="Maroon">c<sub>75</sub></font> <a href="scmpds_2.html#K2">.</a> <span class="p1">(<span class="default"><a href="scmp_gcd.html#K1">intpos</a> <font color="Maroon">c<sub>86</sub></font></span>)</span>
<b>by </b><i><a class="ref" href="scmpds_5.html#T40">SCMPDS_5:40</a></i>
;<br/><br/></div><b>end;</b></div>
<a NAME="E10:46_4"/><b>then </b><i><font color="Green">E60</font></i>: 
<span class="p1">(<span class="default"><a href="ami_1.html#K4">Exec</a> <span class="p2">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a> ,<span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 3</span>)</span> <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span>,<span class="p2">(<span class="default"><a href="scmpds_5.html#K1">Initialized</a> <font color="Maroon">c<sub>75</sub></font></span>)</span></span>)</span> <a href="scmpds_2.html#K2">.</a> <a href="scmp_gcd.html#K2">GBP</a>  <a href="hidden.html#R1">=</a> 0
 
<b>by </b><i><a class="txt" href="scpqsort.html#E1:46_4"><i><font color="Green">E52</font></i></a>, <a class="ref" href="scmp_gcd.html#D2">SCMP_GCD:def 2</a></i>;<br/>
<a NAME="E11:46_4"/>
<span class="p1">(<span class="default"><font color="Maroon">c<sub>77</sub></font> <a href="nat_1.html#K1">+</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span></span>)</span> <a href="nat_1.html#K1">+</a> 3 <a href="xxreal_0.html#NR4" target="_self">&gt;</a> 1
 
<b>by </b><i><a class="txt" href="scpqsort.html#E6:46_4"><i><font color="Green">E56</font></i></a>, <a class="ref" href="xreal_1.html#T2">XREAL_1:2</a></i>;<br/>
<a NAME="E12:46_4"/><b>then </b><i><font color="Green">E61</font></i>: 
<span class="p1">(<span class="default"><a href="ami_1.html#K4">Exec</a> <span class="p2">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a> ,<span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 3</span>)</span> <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span>,<span class="p2">(<span class="default"><a href="scmpds_5.html#K1">Initialized</a> <font color="Maroon">c<sub>75</sub></font></span>)</span></span>)</span> <a href="scmpds_2.html#K2">.</a> <a href="scmp_gcd.html#K3">SBP</a>  <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>77</sub></font>
 
<b>by </b><i><a class="txt" href="scpqsort.html#E1:46_4"><i><font color="Green">E52</font></i></a>, <a class="txt" href="scpqsort.html#E9:46_4"><i><font color="Green">E59</font></i></a>, <a class="ref" href="scmp_gcd.html#D3">SCMP_GCD:def 3</a></i>;<br/>
<a NAME="E13:46_4"/><i><font color="Green">E62</font></i>: 
<span class="p1">(<span class="default"><font color="Maroon">c<sub>77</sub></font> <a href="nat_1.html#K1">+</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span></span>)</span> <a href="nat_1.html#K1">+</a> 3 <a href="xxreal_0.html#NR4" target="_self">&gt;</a> 4
 
<b>by </b><i><a class="txt" href="scpqsort.html#E6:46_4"><i><font color="Green">E56</font></i></a>, <a class="ref" href="xreal_1.html#T2">XREAL_1:2</a></i>;<br/>
<a NAME="E14:46_4"/><b>then </b><i><font color="Green">E63</font></i>: 
<span class="p1">(<span class="default"><a href="ami_1.html#K4">Exec</a> <span class="p2">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a> ,<span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 3</span>)</span> <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span>,<span class="p2">(<span class="default"><a href="scmpds_5.html#K1">Initialized</a> <font color="Maroon">c<sub>75</sub></font></span>)</span></span>)</span> <a href="scmpds_2.html#K2">.</a> <span class="p1">(<span class="default"><a href="scmp_gcd.html#K1">intpos</a> 4</span>)</span> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>75</sub></font> <a href="scmpds_2.html#K2">.</a> <span class="p1">(<span class="default"><a href="scmp_gcd.html#K1">intpos</a> 4</span>)</span>
 
<b>by </b><i><a class="txt" href="scpqsort.html#E9:46_4"><i><font color="Green">E59</font></i></a></i>;<br/>
<a NAME="E15:46_4"/>
<span class="p1">(<span class="default"><font color="Maroon">c<sub>77</sub></font> <a href="nat_1.html#K1">+</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span></span>)</span> <a href="nat_1.html#K1">+</a> 0 <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>77</sub></font> <a href="nat_1.html#K1">+</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span></span>)</span> <a href="nat_1.html#K1">+</a> 3
 
;<br/>
<a NAME="E16:46_4"/><b>then </b><i><font color="Green">E64</font></i>: 
<span class="p1">(<span class="default"><a href="ami_1.html#K4">Exec</a> <span class="p2">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a> ,<span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 3</span>)</span> <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span>,<span class="p2">(<span class="default"><a href="scmpds_5.html#K1">Initialized</a> <font color="Maroon">c<sub>75</sub></font></span>)</span></span>)</span> <a href="scmpds_2.html#K2">.</a> <span class="p1">(<span class="default"><a href="scmp_gcd.html#K1">intpos</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>77</sub></font> <a href="nat_1.html#K1">+</a> <span class="p3">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span></span>)</span></span>)</span> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>75</sub></font> <a href="scmpds_2.html#K2">.</a> <span class="p1">(<span class="default"><a href="scmp_gcd.html#K1">intpos</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>77</sub></font> <a href="nat_1.html#K1">+</a> <span class="p3">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span></span>)</span></span>)</span>
 
<b>by </b><i><a class="txt" href="scpqsort.html#E9:46_4"><i><font color="Green">E59</font></i></a></i>;<br/>
<i><font color="Green">E65</font></i>: <span class="p1">(<span class="default"><a href="ami_1.html#K4">Exec</a> <span class="p2">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a> ,<span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 3</span>)</span> <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span>,<span class="p2">(<span class="default"><a href="scmpds_5.html#K1">Initialized</a> <font color="Maroon">c<sub>75</sub></font></span>)</span></span>)</span> <a href="scmpds_2.html#K2">.</a> <span class="p1">(<span class="default"><a href="scmp_gcd.html#K1">intpos</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">c<sub>77</sub></font> <a href="nat_1.html#K1">+</a> <span class="p4">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span></span>)</span> <a href="nat_1.html#K1">+</a> 3</span>)</span></span>)</span> = 
<span class="p1">(<span class="default"><a href="scmpds_5.html#K1">Initialized</a> <font color="Maroon">c<sub>75</sub></font></span>)</span> <a href="scmpds_2.html#K2">.</a> <span class="p1">(<span class="default"><a href="scmpds_2.html#K3">DataLoc</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="scmpds_5.html#K1">Initialized</a> <font color="Maroon">c<sub>75</sub></font></span>)</span> <a href="scmpds_2.html#K2">.</a> <a href="scmp_gcd.html#K3">SBP</a> </span>)</span>,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span>
<b>by </b><i><a class="txt" href="scpqsort.html#E8:46_4"><i><font color="Green">E58</font></i></a>, <a class="ref" href="scmpds_2.html#T59">SCMPDS_2:59</a></i>
<br/>.= 
<span class="p1">(<span class="default"><a href="scmpds_5.html#K1">Initialized</a> <font color="Maroon">c<sub>75</sub></font></span>)</span> <a href="scmpds_2.html#K2">.</a> <span class="p1">(<span class="default"><a href="scmp_gcd.html#K1">intpos</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>77</sub></font> <a href="nat_1.html#K1">+</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span>
<b>by </b><i><a class="txt" href="scpqsort.html#E7:46_4"><i><font color="Green">E57</font></i></a>, <a class="ref" href="scmp_gcd.html#T5">SCMP_GCD:5</a></i>
<br/>.= 
<font color="Maroon">c<sub>75</sub></font> <a href="scmpds_2.html#K2">.</a> <span class="p1">(<span class="default"><a href="scmp_gcd.html#K1">intpos</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">c<sub>77</sub></font> <a href="nat_1.html#K1">+</a> <span class="p4">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span>
<b>by </b><i><a class="ref" href="scmpds_5.html#T40">SCMPDS_5:40</a></i>
;<br/>
<i><font color="Green">E66</font></i>:  <a href="scmpds_2.html#K3">DataLoc</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K4">Exec</a> <span class="p3">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a> ,<span class="p4">(<span class="default"><span class="p5">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 3</span>)</span> <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p4">(<span class="default"><span class="p5">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span>,<span class="p3">(<span class="default"><a href="scmpds_5.html#K1">Initialized</a> <font color="Maroon">c<sub>75</sub></font></span>)</span></span>)</span> <a href="scmpds_2.html#K2">.</a> <a href="scmp_gcd.html#K3">SBP</a> </span>)</span>,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span> = 
 <a href="scmp_gcd.html#K1">intpos</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>77</sub></font> <a href="nat_1.html#K1">+</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span>
<b>by </b><i><a class="txt" href="scpqsort.html#E12:46_4"><i><font color="Green">E61</font></i></a>, <a class="ref" href="scmp_gcd.html#T5">SCMP_GCD:5</a></i>
<br/>.= 
 <a href="scmp_gcd.html#K1">intpos</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>77</sub></font> <a href="nat_1.html#K1">+</a> <span class="p3">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span>

;<br/>
<div><i><font color="Green">E67</font></i>: <a class="txt" onclick="hs2(this)" href="javascript:()" title="46_4_5"><b>now </b></a><div class="add"><b>let </b><font color="Maroon">c<sub>86</sub></font> be   <a href="nat_1.html#NM1">Nat</a>;<br/><b>assume </b><a NAME="E1:46_4_5"/>
<font color="Maroon">c<sub>86</sub></font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>77</sub></font> <a href="nat_1.html#K1">+</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span></span>)</span> <a href="nat_1.html#K1">+</a> 1
 ;<br/><a NAME="E2:46_4_5"/><b>then </b><i><font color="Green">E68</font></i>: 
 <a href="scmp_gcd.html#K1">intpos</a> <font color="Maroon">c<sub>86</sub></font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a>  <a href="scmpds_2.html#K3">DataLoc</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K4">Exec</a> <span class="p3">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a> ,<span class="p4">(<span class="default"><span class="p5">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 3</span>)</span> <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p4">(<span class="default"><span class="p5">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span>,<span class="p3">(<span class="default"><a href="scmpds_5.html#K1">Initialized</a> <font color="Maroon">c<sub>75</sub></font></span>)</span></span>)</span> <a href="scmpds_2.html#K2">.</a> <a href="scmp_gcd.html#K3">SBP</a> </span>)</span>,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span>
 <b>by </b><i><a class="txt" href="scpqsort.html#E18:46_4"><i><font color="Green">E66</font></i></a>, <a class="ref" href="scmp_gcd.html#T4">SCMP_GCD:4</a></i>;<br/><b>thus </b><span class="p1">(<span class="default"><a href="scmpds_4.html#K9">IExec</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a> ,<span class="p4">(<span class="default"><span class="p5">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 3</span>)</span> <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p4">(<span class="default"><span class="p5">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p3">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a> ,<span class="p4">(<span class="default"><span class="p5">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span> <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K2">GBP</a> ,4</span>)</span></span>)</span>,<font color="Maroon">c<sub>75</sub></font></span>)</span> <a href="scmpds_2.html#K2">.</a> <span class="p1">(<span class="default"><a href="scmp_gcd.html#K1">intpos</a> <font color="Maroon">c<sub>86</sub></font></span>)</span> = 
<span class="p1">(<span class="default"><a href="ami_1.html#K4">Exec</a> <span class="p2">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a> ,<span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span> <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K2">GBP</a> ,4</span>)</span>,<span class="p2">(<span class="default"><a href="ami_1.html#K4">Exec</a> <span class="p3">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a> ,<span class="p4">(<span class="default"><span class="p5">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 3</span>)</span> <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p4">(<span class="default"><span class="p5">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span>,<span class="p3">(<span class="default"><a href="scmpds_5.html#K1">Initialized</a> <font color="Maroon">c<sub>75</sub></font></span>)</span></span>)</span></span>)</span> <a href="scmpds_2.html#K2">.</a> <span class="p1">(<span class="default"><a href="scmp_gcd.html#K1">intpos</a> <font color="Maroon">c<sub>86</sub></font></span>)</span>
<b>by </b><i><a class="ref" href="scmpds_5.html#T47">SCMPDS_5:47</a></i>
<br/>.= 
<span class="p1">(<span class="default"><a href="ami_1.html#K4">Exec</a> <span class="p2">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a> ,<span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 3</span>)</span> <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span>,<span class="p2">(<span class="default"><a href="scmpds_5.html#K1">Initialized</a> <font color="Maroon">c<sub>75</sub></font></span>)</span></span>)</span> <a href="scmpds_2.html#K2">.</a> <span class="p1">(<span class="default"><a href="scmp_gcd.html#K1">intpos</a> <font color="Maroon">c<sub>86</sub></font></span>)</span>
<b>by </b><i><a class="txt" href="scpqsort.html#E2:46_4_5"><i><font color="Green">E68</font></i></a>, <a class="ref" href="scmpds_2.html#T59">SCMPDS_2:59</a></i>
;<br/></div><b>end;</b></div>
<a NAME="E20:46_4"/><b>then </b><i><font color="Green">E68</font></i>: 
<span class="p1">(<span class="default"><a href="scmpds_4.html#K9">IExec</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a> ,<span class="p4">(<span class="default"><span class="p5">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 3</span>)</span> <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p4">(<span class="default"><span class="p5">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p3">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a> ,<span class="p4">(<span class="default"><span class="p5">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span> <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K2">GBP</a> ,4</span>)</span></span>)</span>,<font color="Maroon">c<sub>75</sub></font></span>)</span> <a href="scmpds_2.html#K2">.</a> <a href="scmp_gcd.html#K2">GBP</a>  <a href="hidden.html#R1">=</a> 0
 
<b>by </b><i><a class="txt" href="scpqsort.html#E10:46_4"><i><font color="Green">E60</font></i></a>, <a class="ref" href="scmp_gcd.html#D2">SCMP_GCD:def 2</a></i>;<br/>
<a NAME="E21:46_4"/>
<span class="p1">(<span class="default"><font color="Maroon">c<sub>77</sub></font> <a href="nat_1.html#K1">+</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span></span>)</span> <a href="nat_1.html#K1">+</a> 1 <a href="xxreal_0.html#NR4" target="_self">&gt;</a> 1
 
<b>by </b><i><a class="txt" href="scpqsort.html#E4:46_4"><i><font color="Green">E54</font></i></a>, <a class="ref" href="xreal_1.html#T2">XREAL_1:2</a></i>;<br/>
<a NAME="E22:46_4"/><b>then </b><i><font color="Green">E69</font></i>: 
<span class="p1">(<span class="default"><a href="scmpds_4.html#K9">IExec</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a> ,<span class="p4">(<span class="default"><span class="p5">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 3</span>)</span> <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p4">(<span class="default"><span class="p5">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p3">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a> ,<span class="p4">(<span class="default"><span class="p5">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span> <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K2">GBP</a> ,4</span>)</span></span>)</span>,<font color="Maroon">c<sub>75</sub></font></span>)</span> <a href="scmpds_2.html#K2">.</a> <a href="scmp_gcd.html#K3">SBP</a>  <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>77</sub></font>
 
<b>by </b><i><a class="txt" href="scpqsort.html#E12:46_4"><i><font color="Green">E61</font></i></a>, <a class="txt" href="scpqsort.html#E19:46_4"><i><font color="Green">E67</font></i></a>, <a class="ref" href="scmp_gcd.html#D3">SCMP_GCD:def 3</a></i>;<br/>
<a NAME="E23:46_4"/><i><font color="Green">E70</font></i>: 
<span class="p1">(<span class="default"><font color="Maroon">c<sub>77</sub></font> <a href="nat_1.html#K1">+</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span></span>)</span> <a href="nat_1.html#K1">+</a> 1 <a href="xxreal_0.html#NR4" target="_self">&gt;</a> 4
 
<b>by </b><i><a class="txt" href="scpqsort.html#E4:46_4"><i><font color="Green">E54</font></i></a>, <a class="ref" href="xreal_1.html#T2">XREAL_1:2</a></i>;<br/>
<a NAME="E24:46_4"/>
<span class="p1">(<span class="default"><font color="Maroon">c<sub>77</sub></font> <a href="nat_1.html#K1">+</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span></span>)</span> <a href="nat_1.html#K1">+</a> 0 <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>77</sub></font> <a href="nat_1.html#K1">+</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span></span>)</span> <a href="nat_1.html#K1">+</a> 1
 
;<br/>
<a NAME="E25:46_4"/><b>then </b><i><font color="Green">E71</font></i>: 
<span class="p1">(<span class="default"><a href="scmpds_4.html#K9">IExec</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a> ,<span class="p4">(<span class="default"><span class="p5">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 3</span>)</span> <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p4">(<span class="default"><span class="p5">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p3">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a> ,<span class="p4">(<span class="default"><span class="p5">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span> <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K2">GBP</a> ,4</span>)</span></span>)</span>,<font color="Maroon">c<sub>75</sub></font></span>)</span> <a href="scmpds_2.html#K2">.</a> <span class="p1">(<span class="default"><a href="scmp_gcd.html#K1">intpos</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>77</sub></font> <a href="nat_1.html#K1">+</a> <span class="p3">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span></span>)</span></span>)</span> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>75</sub></font> <a href="scmpds_2.html#K2">.</a> <span class="p1">(<span class="default"><a href="scmp_gcd.html#K1">intpos</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>77</sub></font> <a href="nat_1.html#K1">+</a> <span class="p3">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span></span>)</span></span>)</span>
 
<b>by </b><i><a class="txt" href="scpqsort.html#E16:46_4"><i><font color="Green">E64</font></i></a>, <a class="txt" href="scpqsort.html#E19:46_4"><i><font color="Green">E67</font></i></a></i>;<br/>
<i><font color="Green">E72</font></i>: <span class="p1">(<span class="default"><a href="scmpds_4.html#K9">IExec</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a> ,<span class="p4">(<span class="default"><span class="p5">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 3</span>)</span> <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p4">(<span class="default"><span class="p5">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p3">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a> ,<span class="p4">(<span class="default"><span class="p5">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span> <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K2">GBP</a> ,4</span>)</span></span>)</span>,<font color="Maroon">c<sub>75</sub></font></span>)</span> <a href="scmpds_2.html#K2">.</a> <span class="p1">(<span class="default"><a href="scmp_gcd.html#K1">intpos</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">c<sub>77</sub></font> <a href="nat_1.html#K1">+</a> <span class="p4">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> = 
<span class="p1">(<span class="default"><a href="ami_1.html#K4">Exec</a> <span class="p2">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a> ,<span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span> <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K2">GBP</a> ,4</span>)</span>,<span class="p2">(<span class="default"><a href="ami_1.html#K4">Exec</a> <span class="p3">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a> ,<span class="p4">(<span class="default"><span class="p5">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 3</span>)</span> <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p4">(<span class="default"><span class="p5">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span>,<span class="p3">(<span class="default"><a href="scmpds_5.html#K1">Initialized</a> <font color="Maroon">c<sub>75</sub></font></span>)</span></span>)</span></span>)</span> <a href="scmpds_2.html#K2">.</a> <span class="p1">(<span class="default"><a href="scmp_gcd.html#K1">intpos</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">c<sub>77</sub></font> <a href="nat_1.html#K1">+</a> <span class="p4">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span>
<b>by </b><i><a class="ref" href="scmpds_5.html#T47">SCMPDS_5:47</a></i>
<br/>.= 
<span class="p1">(<span class="default"><a href="ami_1.html#K4">Exec</a> <span class="p2">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a> ,<span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 3</span>)</span> <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span>,<span class="p2">(<span class="default"><a href="scmpds_5.html#K1">Initialized</a> <font color="Maroon">c<sub>75</sub></font></span>)</span></span>)</span> <a href="scmpds_2.html#K2">.</a> <span class="p1">(<span class="default"><a href="scmpds_2.html#K3">DataLoc</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="ami_1.html#K4">Exec</a> <span class="p4">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a> ,<span class="p5">(<span class="default"><span class="p0">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 3</span>)</span> <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p5">(<span class="default"><span class="p0">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span>,<span class="p4">(<span class="default"><a href="scmpds_5.html#K1">Initialized</a> <font color="Maroon">c<sub>75</sub></font></span>)</span></span>)</span> <a href="scmpds_2.html#K2">.</a> <a href="scmp_gcd.html#K2">GBP</a> </span>)</span>,4</span>)</span>
<b>by </b><i><a class="txt" href="scpqsort.html#E18:46_4"><i><font color="Green">E66</font></i></a>, <a class="ref" href="scmpds_2.html#T59">SCMPDS_2:59</a></i>
<br/>.= 
<span class="p1">(<span class="default"><a href="ami_1.html#K4">Exec</a> <span class="p2">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a> ,<span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 3</span>)</span> <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span>,<span class="p2">(<span class="default"><a href="scmpds_5.html#K1">Initialized</a> <font color="Maroon">c<sub>75</sub></font></span>)</span></span>)</span> <a href="scmpds_2.html#K2">.</a> <span class="p1">(<span class="default"><a href="scmp_gcd.html#K1">intpos</a> <span class="p2">(<span class="default">0 <a href="nat_1.html#K1">+</a> 4</span>)</span></span>)</span>
<b>by </b><i><a class="txt" href="scpqsort.html#E10:46_4"><i><font color="Green">E60</font></i></a>, <a class="ref" href="scmp_gcd.html#T5">SCMP_GCD:5</a></i>
<br/>.= 
<font color="Maroon">c<sub>75</sub></font> <a href="scmpds_2.html#K2">.</a> <span class="p1">(<span class="default"><a href="scmp_gcd.html#K1">intpos</a> 4</span>)</span>
<b>by </b><i><a class="txt" href="scpqsort.html#E9:46_4"><i><font color="Green">E59</font></i></a>, <a class="txt" href="scpqsort.html#E13:46_4"><i><font color="Green">E62</font></i></a></i>
;<br/>
<a NAME="E27:46_4"/>
<span class="p1">(<span class="default"><font color="Maroon">c<sub>77</sub></font> <a href="nat_1.html#K1">+</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span></span>)</span> <a href="nat_1.html#K1">+</a> 3 <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>77</sub></font> <a href="nat_1.html#K1">+</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span></span>)</span> <a href="nat_1.html#K1">+</a> 1
 
;<br/>
<a NAME="E28:46_4"/><b>then </b><i><font color="Green">E73</font></i>: 
<span class="p1">(<span class="default"><a href="scmpds_4.html#K9">IExec</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a> ,<span class="p4">(<span class="default"><span class="p5">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 3</span>)</span> <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p4">(<span class="default"><span class="p5">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p3">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a> ,<span class="p4">(<span class="default"><span class="p5">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span> <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K2">GBP</a> ,4</span>)</span></span>)</span>,<font color="Maroon">c<sub>75</sub></font></span>)</span> <a href="scmpds_2.html#K2">.</a> <span class="p1">(<span class="default"><a href="scmp_gcd.html#K1">intpos</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">c<sub>77</sub></font> <a href="nat_1.html#K1">+</a> <span class="p4">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span></span>)</span> <a href="nat_1.html#K1">+</a> 3</span>)</span></span>)</span> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>75</sub></font> <a href="scmpds_2.html#K2">.</a> <span class="p1">(<span class="default"><a href="scmp_gcd.html#K1">intpos</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">c<sub>77</sub></font> <a href="nat_1.html#K1">+</a> <span class="p4">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span>
 
<b>by </b><i><a class="txt" href="scpqsort.html#E17:46_4"><i><font color="Green">E65</font></i></a>, <a class="txt" href="scpqsort.html#E19:46_4"><i><font color="Green">E67</font></i></a></i>;<br/>
<i><font color="Green">E74</font></i>:  <a href="scmpds_2.html#K3">DataLoc</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="scmpds_4.html#K9">IExec</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a> ,<span class="p5">(<span class="default"><span class="p0">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 3</span>)</span> <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p5">(<span class="default"><span class="p0">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p4">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a> ,<span class="p5">(<span class="default"><span class="p0">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span> <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K2">GBP</a> ,4</span>)</span></span>)</span>,<font color="Maroon">c<sub>75</sub></font></span>)</span> <a href="scmpds_2.html#K2">.</a> <a href="scmp_gcd.html#K3">SBP</a> </span>)</span>,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 2</span>)</span> = 
 <a href="scmp_gcd.html#K1">intpos</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>77</sub></font> <a href="nat_1.html#K1">+</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 2</span>)</span></span>)</span>
<b>by </b><i><a class="txt" href="scpqsort.html#E22:46_4"><i><font color="Green">E69</font></i></a>, <a class="ref" href="scmp_gcd.html#T5">SCMP_GCD:5</a></i>
<br/>.= 
 <a href="scmp_gcd.html#K1">intpos</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>77</sub></font> <a href="nat_1.html#K1">+</a> <span class="p3">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span></span>)</span> <a href="nat_1.html#K1">+</a> 2</span>)</span>

;<br/>
<div><i><font color="Green">E75</font></i>: <a class="txt" onclick="hs2(this)" href="javascript:()" title="46_4_8"><b>now </b></a><div class="add"><b>let </b><font color="Maroon">c<sub>86</sub></font> be   <a href="nat_1.html#NM1">Nat</a>;<br/><b>assume </b><a NAME="E1:46_4_8"/>
<font color="Maroon">c<sub>86</sub></font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>77</sub></font> <a href="nat_1.html#K1">+</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span></span>)</span> <a href="nat_1.html#K1">+</a> 2
 ;<br/><a NAME="E2:46_4_8"/><b>then </b><i><font color="Green">E76</font></i>: 
 <a href="scmp_gcd.html#K1">intpos</a> <font color="Maroon">c<sub>86</sub></font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a>  <a href="scmpds_2.html#K3">DataLoc</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="scmpds_4.html#K9">IExec</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a> ,<span class="p5">(<span class="default"><span class="p0">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 3</span>)</span> <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p5">(<span class="default"><span class="p0">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p4">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a> ,<span class="p5">(<span class="default"><span class="p0">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span> <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K2">GBP</a> ,4</span>)</span></span>)</span>,<font color="Maroon">c<sub>75</sub></font></span>)</span> <a href="scmpds_2.html#K2">.</a> <a href="scmp_gcd.html#K3">SBP</a> </span>)</span>,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 2</span>)</span>
 <b>by </b><i><a class="txt" href="scpqsort.html#E29:46_4"><i><font color="Green">E74</font></i></a>, <a class="ref" href="scmp_gcd.html#T4">SCMP_GCD:4</a></i>;<br/><b>thus </b><span class="p1">(<span class="default"><a href="scmpds_4.html#K9">IExec</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a> ,<span class="p5">(<span class="default"><span class="p0">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 3</span>)</span> <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p5">(<span class="default"><span class="p0">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p4">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a> ,<span class="p5">(<span class="default"><span class="p0">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span> <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K2">GBP</a> ,4</span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p3">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a> ,<span class="p4">(<span class="default"><span class="p5">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 2</span>)</span> <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K2">GBP</a> ,4</span>)</span></span>)</span>,<font color="Maroon">c<sub>75</sub></font></span>)</span> <a href="scmpds_2.html#K2">.</a> <span class="p1">(<span class="default"><a href="scmp_gcd.html#K1">intpos</a> <font color="Maroon">c<sub>86</sub></font></span>)</span> = 
<span class="p1">(<span class="default"><a href="ami_1.html#K4">Exec</a> <span class="p2">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a> ,<span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 2</span>)</span> <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K2">GBP</a> ,4</span>)</span>,<span class="p2">(<span class="default"><a href="scmpds_4.html#K9">IExec</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a> ,<span class="p5">(<span class="default"><span class="p0">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 3</span>)</span> <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p5">(<span class="default"><span class="p0">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p4">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a> ,<span class="p5">(<span class="default"><span class="p0">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span> <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K2">GBP</a> ,4</span>)</span></span>)</span>,<font color="Maroon">c<sub>75</sub></font></span>)</span></span>)</span> <a href="scmpds_2.html#K2">.</a> <span class="p1">(<span class="default"><a href="scmp_gcd.html#K1">intpos</a> <font color="Maroon">c<sub>86</sub></font></span>)</span>
<b>by </b><i><a class="ref" href="scmpds_5.html#T46">SCMPDS_5:46</a></i>
<br/>.= 
<span class="p1">(<span class="default"><a href="scmpds_4.html#K9">IExec</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a> ,<span class="p4">(<span class="default"><span class="p5">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 3</span>)</span> <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p4">(<span class="default"><span class="p5">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p3">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a> ,<span class="p4">(<span class="default"><span class="p5">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span> <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K2">GBP</a> ,4</span>)</span></span>)</span>,<font color="Maroon">c<sub>75</sub></font></span>)</span> <a href="scmpds_2.html#K2">.</a> <span class="p1">(<span class="default"><a href="scmp_gcd.html#K1">intpos</a> <font color="Maroon">c<sub>86</sub></font></span>)</span>
<b>by </b><i><a class="txt" href="scpqsort.html#E2:46_4_8"><i><font color="Green">E76</font></i></a>, <a class="ref" href="scmpds_2.html#T59">SCMPDS_2:59</a></i>
;<br/></div><b>end;</b></div>
<a NAME="E31:46_4"/><b>then </b><i><font color="Green">E76</font></i>: 
<span class="p1">(<span class="default"><a href="scmpds_4.html#K9">IExec</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a> ,<span class="p5">(<span class="default"><span class="p0">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 3</span>)</span> <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p5">(<span class="default"><span class="p0">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p4">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a> ,<span class="p5">(<span class="default"><span class="p0">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span> <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K2">GBP</a> ,4</span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p3">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a> ,<span class="p4">(<span class="default"><span class="p5">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 2</span>)</span> <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K2">GBP</a> ,4</span>)</span></span>)</span>,<font color="Maroon">c<sub>75</sub></font></span>)</span> <a href="scmpds_2.html#K2">.</a> <a href="scmp_gcd.html#K2">GBP</a>  <a href="hidden.html#R1">=</a> 0
 
<b>by </b><i><a class="txt" href="scpqsort.html#E20:46_4"><i><font color="Green">E68</font></i></a>, <a class="ref" href="scmp_gcd.html#D2">SCMP_GCD:def 2</a></i>;<br/>
<a NAME="E32:46_4"/>
<span class="p1">(<span class="default"><font color="Maroon">c<sub>77</sub></font> <a href="nat_1.html#K1">+</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span></span>)</span> <a href="nat_1.html#K1">+</a> 2 <a href="xxreal_0.html#NR4" target="_self">&gt;</a> 1
 
<b>by </b><i><a class="txt" href="scpqsort.html#E5:46_4"><i><font color="Green">E55</font></i></a>, <a class="ref" href="xreal_1.html#T2">XREAL_1:2</a></i>;<br/>
<a NAME="E33:46_4"/><b>then </b><i><font color="Green">E77</font></i>: 
<span class="p1">(<span class="default"><a href="scmpds_4.html#K9">IExec</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a> ,<span class="p5">(<span class="default"><span class="p0">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 3</span>)</span> <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p5">(<span class="default"><span class="p0">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p4">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a> ,<span class="p5">(<span class="default"><span class="p0">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span> <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K2">GBP</a> ,4</span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p3">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a> ,<span class="p4">(<span class="default"><span class="p5">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 2</span>)</span> <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K2">GBP</a> ,4</span>)</span></span>)</span>,<font color="Maroon">c<sub>75</sub></font></span>)</span> <a href="scmpds_2.html#K2">.</a> <a href="scmp_gcd.html#K3">SBP</a>  <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>77</sub></font>
 
<b>by </b><i><a class="txt" href="scpqsort.html#E22:46_4"><i><font color="Green">E69</font></i></a>, <a class="txt" href="scpqsort.html#E30:46_4"><i><font color="Green">E75</font></i></a>, <a class="ref" href="scmp_gcd.html#D3">SCMP_GCD:def 3</a></i>;<br/>
<a NAME="E34:46_4"/>
<span class="p1">(<span class="default"><font color="Maroon">c<sub>77</sub></font> <a href="nat_1.html#K1">+</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span></span>)</span> <a href="nat_1.html#K1">+</a> 0 <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>77</sub></font> <a href="nat_1.html#K1">+</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span></span>)</span> <a href="nat_1.html#K1">+</a> 2
 
;<br/>
<a NAME="E35:46_4"/><b>then </b><i><font color="Green">E78</font></i>: 
<span class="p1">(<span class="default"><a href="scmpds_4.html#K9">IExec</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a> ,<span class="p5">(<span class="default"><span class="p0">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 3</span>)</span> <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p5">(<span class="default"><span class="p0">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p4">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a> ,<span class="p5">(<span class="default"><span class="p0">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span> <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K2">GBP</a> ,4</span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p3">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a> ,<span class="p4">(<span class="default"><span class="p5">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 2</span>)</span> <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K2">GBP</a> ,4</span>)</span></span>)</span>,<font color="Maroon">c<sub>75</sub></font></span>)</span> <a href="scmpds_2.html#K2">.</a> <span class="p1">(<span class="default"><a href="scmp_gcd.html#K1">intpos</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>77</sub></font> <a href="nat_1.html#K1">+</a> <span class="p3">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span></span>)</span></span>)</span> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>75</sub></font> <a href="scmpds_2.html#K2">.</a> <span class="p1">(<span class="default"><a href="scmp_gcd.html#K1">intpos</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>77</sub></font> <a href="nat_1.html#K1">+</a> <span class="p3">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span></span>)</span></span>)</span>
 
<b>by </b><i><a class="txt" href="scpqsort.html#E25:46_4"><i><font color="Green">E71</font></i></a>, <a class="txt" href="scpqsort.html#E30:46_4"><i><font color="Green">E75</font></i></a></i>;<br/>
<a NAME="E36:46_4"/>
<span class="p1">(<span class="default"><font color="Maroon">c<sub>77</sub></font> <a href="nat_1.html#K1">+</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span></span>)</span> <a href="nat_1.html#K1">+</a> 1 <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>77</sub></font> <a href="nat_1.html#K1">+</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span></span>)</span> <a href="nat_1.html#K1">+</a> 2
 
;<br/>
<a NAME="E37:46_4"/><b>then </b><i><font color="Green">E79</font></i>: 
<span class="p1">(<span class="default"><a href="scmpds_4.html#K9">IExec</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a> ,<span class="p5">(<span class="default"><span class="p0">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 3</span>)</span> <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p5">(<span class="default"><span class="p0">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p4">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a> ,<span class="p5">(<span class="default"><span class="p0">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span> <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K2">GBP</a> ,4</span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p3">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a> ,<span class="p4">(<span class="default"><span class="p5">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 2</span>)</span> <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K2">GBP</a> ,4</span>)</span></span>)</span>,<font color="Maroon">c<sub>75</sub></font></span>)</span> <a href="scmpds_2.html#K2">.</a> <span class="p1">(<span class="default"><a href="scmp_gcd.html#K1">intpos</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">c<sub>77</sub></font> <a href="nat_1.html#K1">+</a> <span class="p4">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>75</sub></font> <a href="scmpds_2.html#K2">.</a> <span class="p1">(<span class="default"><a href="scmp_gcd.html#K1">intpos</a> 4</span>)</span>
 
<b>by </b><i><a class="txt" href="scpqsort.html#E26:46_4"><i><font color="Green">E72</font></i></a>, <a class="txt" href="scpqsort.html#E30:46_4"><i><font color="Green">E75</font></i></a></i>;<br/>
<i><font color="Green">E80</font></i>: <span class="p1">(<span class="default"><a href="scmpds_4.html#K9">IExec</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a> ,<span class="p5">(<span class="default"><span class="p0">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 3</span>)</span> <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p5">(<span class="default"><span class="p0">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p4">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a> ,<span class="p5">(<span class="default"><span class="p0">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span> <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K2">GBP</a> ,4</span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p3">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a> ,<span class="p4">(<span class="default"><span class="p5">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 2</span>)</span> <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K2">GBP</a> ,4</span>)</span></span>)</span>,<font color="Maroon">c<sub>75</sub></font></span>)</span> <a href="scmpds_2.html#K2">.</a> <span class="p1">(<span class="default"><a href="scmp_gcd.html#K1">intpos</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">c<sub>77</sub></font> <a href="nat_1.html#K1">+</a> <span class="p4">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span></span>)</span> <a href="nat_1.html#K1">+</a> 2</span>)</span></span>)</span> = 
<span class="p1">(<span class="default"><a href="ami_1.html#K4">Exec</a> <span class="p2">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a> ,<span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 2</span>)</span> <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K2">GBP</a> ,4</span>)</span>,<span class="p2">(<span class="default"><a href="scmpds_4.html#K9">IExec</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a> ,<span class="p5">(<span class="default"><span class="p0">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 3</span>)</span> <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p5">(<span class="default"><span class="p0">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p4">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a> ,<span class="p5">(<span class="default"><span class="p0">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span> <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K2">GBP</a> ,4</span>)</span></span>)</span>,<font color="Maroon">c<sub>75</sub></font></span>)</span></span>)</span> <a href="scmpds_2.html#K2">.</a> <span class="p1">(<span class="default"><a href="scmp_gcd.html#K1">intpos</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">c<sub>77</sub></font> <a href="nat_1.html#K1">+</a> <span class="p4">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span></span>)</span> <a href="nat_1.html#K1">+</a> 2</span>)</span></span>)</span>
<b>by </b><i><a class="ref" href="scmpds_5.html#T46">SCMPDS_5:46</a></i>
<br/>.= 
<span class="p1">(<span class="default"><a href="scmpds_4.html#K9">IExec</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a> ,<span class="p4">(<span class="default"><span class="p5">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 3</span>)</span> <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p4">(<span class="default"><span class="p5">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p3">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a> ,<span class="p4">(<span class="default"><span class="p5">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span> <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K2">GBP</a> ,4</span>)</span></span>)</span>,<font color="Maroon">c<sub>75</sub></font></span>)</span> <a href="scmpds_2.html#K2">.</a> <span class="p1">(<span class="default"><a href="scmpds_2.html#K3">DataLoc</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="scmpds_4.html#K9">IExec</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a> ,<span class="p0">(<span class="default"><span class="p1">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 3</span>)</span> <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p0">(<span class="default"><span class="p1">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p5">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a> ,<span class="p0">(<span class="default"><span class="p1">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span> <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K2">GBP</a> ,4</span>)</span></span>)</span>,<font color="Maroon">c<sub>75</sub></font></span>)</span> <a href="scmpds_2.html#K2">.</a> <a href="scmp_gcd.html#K2">GBP</a> </span>)</span>,4</span>)</span>
<b>by </b><i><a class="txt" href="scpqsort.html#E29:46_4"><i><font color="Green">E74</font></i></a>, <a class="ref" href="scmpds_2.html#T59">SCMPDS_2:59</a></i>
<br/>.= 
<span class="p1">(<span class="default"><a href="scmpds_4.html#K9">IExec</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a> ,<span class="p4">(<span class="default"><span class="p5">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 3</span>)</span> <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p4">(<span class="default"><span class="p5">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p3">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a> ,<span class="p4">(<span class="default"><span class="p5">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span> <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K2">GBP</a> ,4</span>)</span></span>)</span>,<font color="Maroon">c<sub>75</sub></font></span>)</span> <a href="scmpds_2.html#K2">.</a> <span class="p1">(<span class="default"><a href="scmp_gcd.html#K1">intpos</a> <span class="p2">(<span class="default">0 <a href="nat_1.html#K1">+</a> 4</span>)</span></span>)</span>
<b>by </b><i><a class="txt" href="scpqsort.html#E20:46_4"><i><font color="Green">E68</font></i></a>, <a class="ref" href="scmp_gcd.html#T5">SCMP_GCD:5</a></i>
<br/>.= 
<font color="Maroon">c<sub>75</sub></font> <a href="scmpds_2.html#K2">.</a> <span class="p1">(<span class="default"><a href="scmp_gcd.html#K1">intpos</a> 4</span>)</span>
<b>by </b><i><a class="txt" href="scpqsort.html#E14:46_4"><i><font color="Green">E63</font></i></a>, <a class="txt" href="scpqsort.html#E19:46_4"><i><font color="Green">E67</font></i></a>, <a class="txt" href="scpqsort.html#E23:46_4"><i><font color="Green">E70</font></i></a></i>
;<br/>
<a NAME="E39:46_4"/>
<span class="p1">(<span class="default"><font color="Maroon">c<sub>77</sub></font> <a href="nat_1.html#K1">+</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span></span>)</span> <a href="nat_1.html#K1">+</a> 3 <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>77</sub></font> <a href="nat_1.html#K1">+</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span></span>)</span> <a href="nat_1.html#K1">+</a> 2
 
;<br/>
<a NAME="E40:46_4"/><b>then </b><i><font color="Green">E81</font></i>: 
<span class="p1">(<span class="default"><a href="scmpds_4.html#K9">IExec</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a> ,<span class="p5">(<span class="default"><span class="p0">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 3</span>)</span> <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p5">(<span class="default"><span class="p0">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p4">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a> ,<span class="p5">(<span class="default"><span class="p0">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span> <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K2">GBP</a> ,4</span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p3">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a> ,<span class="p4">(<span class="default"><span class="p5">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 2</span>)</span> <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K2">GBP</a> ,4</span>)</span></span>)</span>,<font color="Maroon">c<sub>75</sub></font></span>)</span> <a href="scmpds_2.html#K2">.</a> <span class="p1">(<span class="default"><a href="scmp_gcd.html#K1">intpos</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">c<sub>77</sub></font> <a href="nat_1.html#K1">+</a> <span class="p4">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span></span>)</span> <a href="nat_1.html#K1">+</a> 3</span>)</span></span>)</span> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>75</sub></font> <a href="scmpds_2.html#K2">.</a> <span class="p1">(<span class="default"><a href="scmp_gcd.html#K1">intpos</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">c<sub>77</sub></font> <a href="nat_1.html#K1">+</a> <span class="p4">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span>
 
<b>by </b><i><a class="txt" href="scpqsort.html#E28:46_4"><i><font color="Green">E73</font></i></a>, <a class="txt" href="scpqsort.html#E30:46_4"><i><font color="Green">E75</font></i></a></i>;<br/>
<i><font color="Green">E82</font></i>:  <a href="scmpds_2.html#K3">DataLoc</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="scmpds_4.html#K9">IExec</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a> ,<span class="p0">(<span class="default"><span class="p1">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 3</span>)</span> <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p0">(<span class="default"><span class="p1">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p5">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a> ,<span class="p0">(<span class="default"><span class="p1">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span> <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K2">GBP</a> ,4</span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p4">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a> ,<span class="p5">(<span class="default"><span class="p0">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 2</span>)</span> <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K2">GBP</a> ,4</span>)</span></span>)</span>,<font color="Maroon">c<sub>75</sub></font></span>)</span> <a href="scmpds_2.html#K2">.</a> <a href="scmp_gcd.html#K3">SBP</a> </span>)</span>,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span> = 
 <a href="scmp_gcd.html#K1">intpos</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>77</sub></font> <a href="nat_1.html#K1">+</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span>
<b>by </b><i><a class="txt" href="scpqsort.html#E33:46_4"><i><font color="Green">E77</font></i></a>, <a class="ref" href="scmp_gcd.html#T5">SCMP_GCD:5</a></i>
<br/>.= 
 <a href="scmp_gcd.html#K1">intpos</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>77</sub></font> <a href="nat_1.html#K1">+</a> <span class="p3">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span>

;<br/>
<div><i><font color="Green">E83</font></i>: <a class="txt" onclick="hs2(this)" href="javascript:()" title="46_4_11"><b>now </b></a><div class="add"><b>let </b><font color="Maroon">c<sub>86</sub></font> be   <a href="nat_1.html#NM1">Nat</a>;<br/><b>assume </b><a NAME="E1:46_4_11"/>
<font color="Maroon">c<sub>86</sub></font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>77</sub></font> <a href="nat_1.html#K1">+</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span></span>)</span> <a href="nat_1.html#K1">+</a> 1
 ;<br/><a NAME="E2:46_4_11"/><b>then </b><i><font color="Green">E84</font></i>: 
 <a href="scmp_gcd.html#K1">intpos</a> <font color="Maroon">c<sub>86</sub></font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a>  <a href="scmpds_2.html#K3">DataLoc</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="scmpds_4.html#K9">IExec</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a> ,<span class="p0">(<span class="default"><span class="p1">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 3</span>)</span> <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p0">(<span class="default"><span class="p1">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p5">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a> ,<span class="p0">(<span class="default"><span class="p1">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span> <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K2">GBP</a> ,4</span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p4">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a> ,<span class="p5">(<span class="default"><span class="p0">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 2</span>)</span> <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K2">GBP</a> ,4</span>)</span></span>)</span>,<font color="Maroon">c<sub>75</sub></font></span>)</span> <a href="scmpds_2.html#K2">.</a> <a href="scmp_gcd.html#K3">SBP</a> </span>)</span>,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span>
 <b>by </b><i><a class="txt" href="scpqsort.html#E41:46_4"><i><font color="Green">E82</font></i></a>, <a class="ref" href="scmp_gcd.html#T4">SCMP_GCD:4</a></i>;<br/><b>thus </b><span class="p1">(<span class="default"><a href="scmpds_4.html#K9">IExec</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a> ,<span class="p0">(<span class="default"><span class="p1">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 3</span>)</span> <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p0">(<span class="default"><span class="p1">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p5">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a> ,<span class="p0">(<span class="default"><span class="p1">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span> <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K2">GBP</a> ,4</span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p4">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a> ,<span class="p5">(<span class="default"><span class="p0">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 2</span>)</span> <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K2">GBP</a> ,4</span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p3">(<span class="default"><a href="scmpds_2.html#K12">AddTo</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p4">(<span class="default"><span class="p5">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span>,<span class="p4">(<span class="default"><a href="xcmplx_0.html#K4">-</a> 1</span>)</span></span>)</span></span>)</span>,<font color="Maroon">c<sub>75</sub></font></span>)</span> <a href="scmpds_2.html#K2">.</a> <span class="p1">(<span class="default"><a href="scmp_gcd.html#K1">intpos</a> <font color="Maroon">c<sub>86</sub></font></span>)</span> = 
<span class="p1">(<span class="default"><a href="ami_1.html#K4">Exec</a> <span class="p2">(<span class="default"><a href="scmpds_2.html#K12">AddTo</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span>,<span class="p3">(<span class="default"><a href="xcmplx_0.html#K4">-</a> 1</span>)</span></span>)</span>,<span class="p2">(<span class="default"><a href="scmpds_4.html#K9">IExec</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a> ,<span class="p0">(<span class="default"><span class="p1">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 3</span>)</span> <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p0">(<span class="default"><span class="p1">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p5">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a> ,<span class="p0">(<span class="default"><span class="p1">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span> <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K2">GBP</a> ,4</span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p4">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a> ,<span class="p5">(<span class="default"><span class="p0">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 2</span>)</span> <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K2">GBP</a> ,4</span>)</span></span>)</span>,<font color="Maroon">c<sub>75</sub></font></span>)</span></span>)</span> <a href="scmpds_2.html#K2">.</a> <span class="p1">(<span class="default"><a href="scmp_gcd.html#K1">intpos</a> <font color="Maroon">c<sub>86</sub></font></span>)</span>
<b>by </b><i><a class="ref" href="scmpds_5.html#T46">SCMPDS_5:46</a></i>
<br/>.= 
<span class="p1">(<span class="default"><a href="scmpds_4.html#K9">IExec</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a> ,<span class="p5">(<span class="default"><span class="p0">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 3</span>)</span> <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p5">(<span class="default"><span class="p0">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p4">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a> ,<span class="p5">(<span class="default"><span class="p0">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span> <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K2">GBP</a> ,4</span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p3">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a> ,<span class="p4">(<span class="default"><span class="p5">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 2</span>)</span> <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K2">GBP</a> ,4</span>)</span></span>)</span>,<font color="Maroon">c<sub>75</sub></font></span>)</span> <a href="scmpds_2.html#K2">.</a> <span class="p1">(<span class="default"><a href="scmp_gcd.html#K1">intpos</a> <font color="Maroon">c<sub>86</sub></font></span>)</span>
<b>by </b><i><a class="txt" href="scpqsort.html#E2:46_4_11"><i><font color="Green">E84</font></i></a>, <a class="ref" href="scmpds_2.html#T60">SCMPDS_2:60</a></i>
;<br/></div><b>end;</b></div>
<a NAME="E43:46_4"/><b>then </b><i><font color="Green">E84</font></i>: 
<span class="p1">(<span class="default"><a href="scmpds_4.html#K9">IExec</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a> ,<span class="p0">(<span class="default"><span class="p1">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 3</span>)</span> <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p0">(<span class="default"><span class="p1">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p5">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a> ,<span class="p0">(<span class="default"><span class="p1">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span> <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K2">GBP</a> ,4</span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p4">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a> ,<span class="p5">(<span class="default"><span class="p0">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 2</span>)</span> <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K2">GBP</a> ,4</span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p3">(<span class="default"><a href="scmpds_2.html#K12">AddTo</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p4">(<span class="default"><span class="p5">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span>,<span class="p4">(<span class="default"><a href="xcmplx_0.html#K4">-</a> 1</span>)</span></span>)</span></span>)</span>,<font color="Maroon">c<sub>75</sub></font></span>)</span> <a href="scmpds_2.html#K2">.</a> <a href="scmp_gcd.html#K2">GBP</a>  <a href="hidden.html#R1">=</a> 0
 
<b>by </b><i><a class="txt" href="scpqsort.html#E31:46_4"><i><font color="Green">E76</font></i></a>, <a class="ref" href="scmp_gcd.html#D2">SCMP_GCD:def 2</a></i>;<br/>
<a NAME="E44:46_4"/>
<span class="p1">(<span class="default"><font color="Maroon">c<sub>77</sub></font> <a href="nat_1.html#K1">+</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span></span>)</span> <a href="nat_1.html#K1">+</a> 1 <a href="xxreal_0.html#NR4" target="_self">&gt;</a> 1
 
<b>by </b><i><a class="txt" href="scpqsort.html#E4:46_4"><i><font color="Green">E54</font></i></a>, <a class="ref" href="xreal_1.html#T2">XREAL_1:2</a></i>;<br/>
<a NAME="E45:46_4"/><b>then </b><i><font color="Green">E85</font></i>: 
<span class="p1">(<span class="default"><a href="scmpds_4.html#K9">IExec</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a> ,<span class="p0">(<span class="default"><span class="p1">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 3</span>)</span> <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p0">(<span class="default"><span class="p1">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p5">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a> ,<span class="p0">(<span class="default"><span class="p1">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span> <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K2">GBP</a> ,4</span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p4">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a> ,<span class="p5">(<span class="default"><span class="p0">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 2</span>)</span> <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K2">GBP</a> ,4</span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p3">(<span class="default"><a href="scmpds_2.html#K12">AddTo</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p4">(<span class="default"><span class="p5">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span>,<span class="p4">(<span class="default"><a href="xcmplx_0.html#K4">-</a> 1</span>)</span></span>)</span></span>)</span>,<font color="Maroon">c<sub>75</sub></font></span>)</span> <a href="scmpds_2.html#K2">.</a> <a href="scmp_gcd.html#K3">SBP</a>  <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>77</sub></font>
 
<b>by </b><i><a class="txt" href="scpqsort.html#E33:46_4"><i><font color="Green">E77</font></i></a>, <a class="txt" href="scpqsort.html#E42:46_4"><i><font color="Green">E83</font></i></a>, <a class="ref" href="scmp_gcd.html#D3">SCMP_GCD:def 3</a></i>;<br/>
<a NAME="E46:46_4"/>
<span class="p1">(<span class="default"><font color="Maroon">c<sub>77</sub></font> <a href="nat_1.html#K1">+</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span></span>)</span> <a href="nat_1.html#K1">+</a> 0 <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>77</sub></font> <a href="nat_1.html#K1">+</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span></span>)</span> <a href="nat_1.html#K1">+</a> 1
 
;<br/>
<a NAME="E47:46_4"/><b>then </b><i><font color="Green">E86</font></i>: 
<span class="p1">(<span class="default"><a href="scmpds_4.html#K9">IExec</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a> ,<span class="p0">(<span class="default"><span class="p1">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 3</span>)</span> <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p0">(<span class="default"><span class="p1">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p5">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a> ,<span class="p0">(<span class="default"><span class="p1">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span> <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K2">GBP</a> ,4</span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p4">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a> ,<span class="p5">(<span class="default"><span class="p0">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 2</span>)</span> <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K2">GBP</a> ,4</span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p3">(<span class="default"><a href="scmpds_2.html#K12">AddTo</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p4">(<span class="default"><span class="p5">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span>,<span class="p4">(<span class="default"><a href="xcmplx_0.html#K4">-</a> 1</span>)</span></span>)</span></span>)</span>,<font color="Maroon">c<sub>75</sub></font></span>)</span> <a href="scmpds_2.html#K2">.</a> <span class="p1">(<span class="default"><a href="scmp_gcd.html#K1">intpos</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>77</sub></font> <a href="nat_1.html#K1">+</a> <span class="p3">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span></span>)</span></span>)</span> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>75</sub></font> <a href="scmpds_2.html#K2">.</a> <span class="p1">(<span class="default"><a href="scmp_gcd.html#K1">intpos</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>77</sub></font> <a href="nat_1.html#K1">+</a> <span class="p3">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span></span>)</span></span>)</span>
 
<b>by </b><i><a class="txt" href="scpqsort.html#E35:46_4"><i><font color="Green">E78</font></i></a>, <a class="txt" href="scpqsort.html#E42:46_4"><i><font color="Green">E83</font></i></a></i>;<br/>
<i><font color="Green">E87</font></i>: <span class="p1">(<span class="default"><a href="scmpds_4.html#K9">IExec</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a> ,<span class="p0">(<span class="default"><span class="p1">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 3</span>)</span> <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p0">(<span class="default"><span class="p1">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p5">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a> ,<span class="p0">(<span class="default"><span class="p1">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span> <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K2">GBP</a> ,4</span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p4">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a> ,<span class="p5">(<span class="default"><span class="p0">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 2</span>)</span> <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K2">GBP</a> ,4</span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p3">(<span class="default"><a href="scmpds_2.html#K12">AddTo</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p4">(<span class="default"><span class="p5">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span>,<span class="p4">(<span class="default"><a href="xcmplx_0.html#K4">-</a> 1</span>)</span></span>)</span></span>)</span>,<font color="Maroon">c<sub>75</sub></font></span>)</span> <a href="scmpds_2.html#K2">.</a> <span class="p1">(<span class="default"><a href="scmp_gcd.html#K1">intpos</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">c<sub>77</sub></font> <a href="nat_1.html#K1">+</a> <span class="p4">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> = 
<span class="p1">(<span class="default"><a href="ami_1.html#K4">Exec</a> <span class="p2">(<span class="default"><a href="scmpds_2.html#K12">AddTo</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span>,<span class="p3">(<span class="default"><a href="xcmplx_0.html#K4">-</a> 1</span>)</span></span>)</span>,<span class="p2">(<span class="default"><a href="scmpds_4.html#K9">IExec</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a> ,<span class="p0">(<span class="default"><span class="p1">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 3</span>)</span> <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p0">(<span class="default"><span class="p1">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p5">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a> ,<span class="p0">(<span class="default"><span class="p1">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span> <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K2">GBP</a> ,4</span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p4">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a> ,<span class="p5">(<span class="default"><span class="p0">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 2</span>)</span> <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K2">GBP</a> ,4</span>)</span></span>)</span>,<font color="Maroon">c<sub>75</sub></font></span>)</span></span>)</span> <a href="scmpds_2.html#K2">.</a> <span class="p1">(<span class="default"><a href="scmp_gcd.html#K1">intpos</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">c<sub>77</sub></font> <a href="nat_1.html#K1">+</a> <span class="p4">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span>
<b>by </b><i><a class="ref" href="scmpds_5.html#T46">SCMPDS_5:46</a></i>
<br/>.= 
<span class="p1">(<span class="default"><font color="Maroon">c<sub>75</sub></font> <a href="scmpds_2.html#K2">.</a> <span class="p2">(<span class="default"><a href="scmp_gcd.html#K1">intpos</a> 4</span>)</span></span>)</span> <a href="xcmplx_0.html#K2">+</a> <span class="p1">(<span class="default"><a href="xcmplx_0.html#K4">-</a> 1</span>)</span>
<b>by </b><i><a class="txt" href="scpqsort.html#E37:46_4"><i><font color="Green">E79</font></i></a>, <a class="txt" href="scpqsort.html#E41:46_4"><i><font color="Green">E82</font></i></a>, <a class="ref" href="scmpds_2.html#T60">SCMPDS_2:60</a></i>
<br/>.= 
<span class="p1">(<span class="default"><font color="Maroon">c<sub>75</sub></font> <a href="scmpds_2.html#K2">.</a> <span class="p2">(<span class="default"><a href="scmp_gcd.html#K1">intpos</a> 4</span>)</span></span>)</span> <a href="xcmplx_0.html#K6">-</a> 1

;<br/>
<a NAME="E49:46_4"/>
<span class="p1">(<span class="default"><font color="Maroon">c<sub>77</sub></font> <a href="nat_1.html#K1">+</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span></span>)</span> <a href="nat_1.html#K1">+</a> 1 <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>77</sub></font> <a href="nat_1.html#K1">+</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span></span>)</span> <a href="nat_1.html#K1">+</a> 2
 
;<br/>
<a NAME="E50:46_4"/><b>then </b><i><font color="Green">E88</font></i>: 
<span class="p1">(<span class="default"><a href="scmpds_4.html#K9">IExec</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a> ,<span class="p0">(<span class="default"><span class="p1">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 3</span>)</span> <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p0">(<span class="default"><span class="p1">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p5">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a> ,<span class="p0">(<span class="default"><span class="p1">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span> <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K2">GBP</a> ,4</span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p4">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a> ,<span class="p5">(<span class="default"><span class="p0">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 2</span>)</span> <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K2">GBP</a> ,4</span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p3">(<span class="default"><a href="scmpds_2.html#K12">AddTo</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p4">(<span class="default"><span class="p5">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span>,<span class="p4">(<span class="default"><a href="xcmplx_0.html#K4">-</a> 1</span>)</span></span>)</span></span>)</span>,<font color="Maroon">c<sub>75</sub></font></span>)</span> <a href="scmpds_2.html#K2">.</a> <span class="p1">(<span class="default"><a href="scmp_gcd.html#K1">intpos</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">c<sub>77</sub></font> <a href="nat_1.html#K1">+</a> <span class="p4">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span></span>)</span> <a href="nat_1.html#K1">+</a> 2</span>)</span></span>)</span> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>75</sub></font> <a href="scmpds_2.html#K2">.</a> <span class="p1">(<span class="default"><a href="scmp_gcd.html#K1">intpos</a> 4</span>)</span>
 
<b>by </b><i><a class="txt" href="scpqsort.html#E38:46_4"><i><font color="Green">E80</font></i></a>, <a class="txt" href="scpqsort.html#E42:46_4"><i><font color="Green">E83</font></i></a></i>;<br/>
<a NAME="E51:46_4"/>
<span class="p1">(<span class="default"><font color="Maroon">c<sub>77</sub></font> <a href="nat_1.html#K1">+</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span></span>)</span> <a href="nat_1.html#K1">+</a> 3 <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>77</sub></font> <a href="nat_1.html#K1">+</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span></span>)</span> <a href="nat_1.html#K1">+</a> 1
 
;<br/>
<a NAME="E52:46_4"/><b>then </b><i><font color="Green">E89</font></i>: 
<span class="p1">(<span class="default"><a href="scmpds_4.html#K9">IExec</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a> ,<span class="p0">(<span class="default"><span class="p1">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 3</span>)</span> <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p0">(<span class="default"><span class="p1">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p5">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a> ,<span class="p0">(<span class="default"><span class="p1">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span> <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K2">GBP</a> ,4</span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p4">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a> ,<span class="p5">(<span class="default"><span class="p0">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 2</span>)</span> <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K2">GBP</a> ,4</span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p3">(<span class="default"><a href="scmpds_2.html#K12">AddTo</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p4">(<span class="default"><span class="p5">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span>,<span class="p4">(<span class="default"><a href="xcmplx_0.html#K4">-</a> 1</span>)</span></span>)</span></span>)</span>,<font color="Maroon">c<sub>75</sub></font></span>)</span> <a href="scmpds_2.html#K2">.</a> <span class="p1">(<span class="default"><a href="scmp_gcd.html#K1">intpos</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">c<sub>77</sub></font> <a href="nat_1.html#K1">+</a> <span class="p4">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span></span>)</span> <a href="nat_1.html#K1">+</a> 3</span>)</span></span>)</span> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>75</sub></font> <a href="scmpds_2.html#K2">.</a> <span class="p1">(<span class="default"><a href="scmp_gcd.html#K1">intpos</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">c<sub>77</sub></font> <a href="nat_1.html#K1">+</a> <span class="p4">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span>
 
<b>by </b><i><a class="txt" href="scpqsort.html#E40:46_4"><i><font color="Green">E81</font></i></a>, <a class="txt" href="scpqsort.html#E42:46_4"><i><font color="Green">E83</font></i></a></i>;<br/>
<i><font color="Green">E90</font></i>:  <a href="scmpds_2.html#K3">DataLoc</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="scmpds_4.html#K9">IExec</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><span class="p0">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a> ,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 3</span>)</span> <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p0">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a> ,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span> <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K2">GBP</a> ,4</span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p5">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a> ,<span class="p0">(<span class="default"><span class="p1">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 2</span>)</span> <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K2">GBP</a> ,4</span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p4">(<span class="default"><a href="scmpds_2.html#K12">AddTo</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p5">(<span class="default"><span class="p0">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span>,<span class="p5">(<span class="default"><a href="xcmplx_0.html#K4">-</a> 1</span>)</span></span>)</span></span>)</span>,<font color="Maroon">c<sub>75</sub></font></span>)</span> <a href="scmpds_2.html#K2">.</a> <a href="scmp_gcd.html#K3">SBP</a> </span>)</span>,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 2</span>)</span> = 
 <a href="scmp_gcd.html#K1">intpos</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>77</sub></font> <a href="nat_1.html#K1">+</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 2</span>)</span></span>)</span>
<b>by </b><i><a class="txt" href="scpqsort.html#E45:46_4"><i><font color="Green">E85</font></i></a>, <a class="ref" href="scmp_gcd.html#T5">SCMP_GCD:5</a></i>
<br/>.= 
 <a href="scmp_gcd.html#K1">intpos</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>77</sub></font> <a href="nat_1.html#K1">+</a> <span class="p3">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span></span>)</span> <a href="nat_1.html#K1">+</a> 2</span>)</span>

;<br/>
<div><i><font color="Green">E91</font></i>: <a class="txt" onclick="hs2(this)" href="javascript:()" title="46_4_14"><b>now </b></a><div class="add"><b>let </b><font color="Maroon">c<sub>86</sub></font> be   <a href="nat_1.html#NM1">Nat</a>;<br/><b>assume </b><a NAME="E1:46_4_14"/>
<font color="Maroon">c<sub>86</sub></font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>77</sub></font> <a href="nat_1.html#K1">+</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span></span>)</span> <a href="nat_1.html#K1">+</a> 2
 ;<br/><a NAME="E2:46_4_14"/><b>then </b><i><font color="Green">E92</font></i>: 
 <a href="scmp_gcd.html#K1">intpos</a> <font color="Maroon">c<sub>86</sub></font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a>  <a href="scmpds_2.html#K3">DataLoc</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="scmpds_4.html#K9">IExec</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><span class="p0">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a> ,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 3</span>)</span> <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p0">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a> ,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span> <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K2">GBP</a> ,4</span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p5">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a> ,<span class="p0">(<span class="default"><span class="p1">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 2</span>)</span> <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K2">GBP</a> ,4</span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p4">(<span class="default"><a href="scmpds_2.html#K12">AddTo</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p5">(<span class="default"><span class="p0">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span>,<span class="p5">(<span class="default"><a href="xcmplx_0.html#K4">-</a> 1</span>)</span></span>)</span></span>)</span>,<font color="Maroon">c<sub>75</sub></font></span>)</span> <a href="scmpds_2.html#K2">.</a> <a href="scmp_gcd.html#K3">SBP</a> </span>)</span>,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 2</span>)</span>
 <b>by </b><i><a class="txt" href="scpqsort.html#E53:46_4"><i><font color="Green">E90</font></i></a>, <a class="ref" href="scmp_gcd.html#T4">SCMP_GCD:4</a></i>;<br/><b>thus </b><span class="p1">(<span class="default"><a href="scmpds_4.html#K9">IExec</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><span class="p0">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a> ,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 3</span>)</span> <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p0">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a> ,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span> <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K2">GBP</a> ,4</span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p5">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a> ,<span class="p0">(<span class="default"><span class="p1">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 2</span>)</span> <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K2">GBP</a> ,4</span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p4">(<span class="default"><a href="scmpds_2.html#K12">AddTo</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p5">(<span class="default"><span class="p0">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span>,<span class="p5">(<span class="default"><a href="xcmplx_0.html#K4">-</a> 1</span>)</span></span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p3">(<span class="default"><a href="scmpds_2.html#K12">AddTo</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p4">(<span class="default"><span class="p5">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 2</span>)</span>,1</span>)</span></span>)</span>,<font color="Maroon">c<sub>75</sub></font></span>)</span> <a href="scmpds_2.html#K2">.</a> <span class="p1">(<span class="default"><a href="scmp_gcd.html#K1">intpos</a> <font color="Maroon">c<sub>86</sub></font></span>)</span> = 
<span class="p1">(<span class="default"><a href="ami_1.html#K4">Exec</a> <span class="p2">(<span class="default"><a href="scmpds_2.html#K12">AddTo</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 2</span>)</span>,1</span>)</span>,<span class="p2">(<span class="default"><a href="scmpds_4.html#K9">IExec</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><span class="p0">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a> ,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 3</span>)</span> <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p0">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a> ,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span> <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K2">GBP</a> ,4</span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p5">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a> ,<span class="p0">(<span class="default"><span class="p1">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 2</span>)</span> <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K2">GBP</a> ,4</span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p4">(<span class="default"><a href="scmpds_2.html#K12">AddTo</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p5">(<span class="default"><span class="p0">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span>,<span class="p5">(<span class="default"><a href="xcmplx_0.html#K4">-</a> 1</span>)</span></span>)</span></span>)</span>,<font color="Maroon">c<sub>75</sub></font></span>)</span></span>)</span> <a href="scmpds_2.html#K2">.</a> <span class="p1">(<span class="default"><a href="scmp_gcd.html#K1">intpos</a> <font color="Maroon">c<sub>86</sub></font></span>)</span>
<b>by </b><i><a class="ref" href="scmpds_5.html#T46">SCMPDS_5:46</a></i>
<br/>.= 
<span class="p1">(<span class="default"><a href="scmpds_4.html#K9">IExec</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a> ,<span class="p0">(<span class="default"><span class="p1">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 3</span>)</span> <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p0">(<span class="default"><span class="p1">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p5">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a> ,<span class="p0">(<span class="default"><span class="p1">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span> <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K2">GBP</a> ,4</span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p4">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a> ,<span class="p5">(<span class="default"><span class="p0">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 2</span>)</span> <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K2">GBP</a> ,4</span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p3">(<span class="default"><a href="scmpds_2.html#K12">AddTo</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p4">(<span class="default"><span class="p5">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span>,<span class="p4">(<span class="default"><a href="xcmplx_0.html#K4">-</a> 1</span>)</span></span>)</span></span>)</span>,<font color="Maroon">c<sub>75</sub></font></span>)</span> <a href="scmpds_2.html#K2">.</a> <span class="p1">(<span class="default"><a href="scmp_gcd.html#K1">intpos</a> <font color="Maroon">c<sub>86</sub></font></span>)</span>
<b>by </b><i><a class="txt" href="scpqsort.html#E2:46_4_14"><i><font color="Green">E92</font></i></a>, <a class="ref" href="scmpds_2.html#T60">SCMPDS_2:60</a></i>
;<br/></div><b>end;</b></div>
<a NAME="E55:46_4"/><b>then </b><i><font color="Green">E92</font></i>: 
<span class="p1">(<span class="default"><a href="scmpds_4.html#K9">IExec</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><span class="p0">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a> ,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 3</span>)</span> <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p0">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a> ,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span> <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K2">GBP</a> ,4</span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p5">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a> ,<span class="p0">(<span class="default"><span class="p1">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 2</span>)</span> <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K2">GBP</a> ,4</span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p4">(<span class="default"><a href="scmpds_2.html#K12">AddTo</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p5">(<span class="default"><span class="p0">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span>,<span class="p5">(<span class="default"><a href="xcmplx_0.html#K4">-</a> 1</span>)</span></span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p3">(<span class="default"><a href="scmpds_2.html#K12">AddTo</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p4">(<span class="default"><span class="p5">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 2</span>)</span>,1</span>)</span></span>)</span>,<font color="Maroon">c<sub>75</sub></font></span>)</span> <a href="scmpds_2.html#K2">.</a> <a href="scmp_gcd.html#K2">GBP</a>  <a href="hidden.html#R1">=</a> 0
 
<b>by </b><i><a class="txt" href="scpqsort.html#E43:46_4"><i><font color="Green">E84</font></i></a>, <a class="ref" href="scmp_gcd.html#D2">SCMP_GCD:def 2</a></i>;<br/>
<a NAME="E56:46_4"/>
<span class="p1">(<span class="default"><font color="Maroon">c<sub>77</sub></font> <a href="nat_1.html#K1">+</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span></span>)</span> <a href="nat_1.html#K1">+</a> 2 <a href="xxreal_0.html#NR4" target="_self">&gt;</a> 1
 
<b>by </b><i><a class="txt" href="scpqsort.html#E5:46_4"><i><font color="Green">E55</font></i></a>, <a class="ref" href="xreal_1.html#T2">XREAL_1:2</a></i>;<br/>
<a NAME="E57:46_4"/><b>then </b><i><font color="Green">E93</font></i>: 
<span class="p1">(<span class="default"><a href="scmpds_4.html#K9">IExec</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><span class="p0">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a> ,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 3</span>)</span> <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p0">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a> ,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span> <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K2">GBP</a> ,4</span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p5">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a> ,<span class="p0">(<span class="default"><span class="p1">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 2</span>)</span> <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K2">GBP</a> ,4</span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p4">(<span class="default"><a href="scmpds_2.html#K12">AddTo</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p5">(<span class="default"><span class="p0">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span>,<span class="p5">(<span class="default"><a href="xcmplx_0.html#K4">-</a> 1</span>)</span></span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p3">(<span class="default"><a href="scmpds_2.html#K12">AddTo</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p4">(<span class="default"><span class="p5">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 2</span>)</span>,1</span>)</span></span>)</span>,<font color="Maroon">c<sub>75</sub></font></span>)</span> <a href="scmpds_2.html#K2">.</a> <a href="scmp_gcd.html#K3">SBP</a>  <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>77</sub></font>
 
<b>by </b><i><a class="txt" href="scpqsort.html#E45:46_4"><i><font color="Green">E85</font></i></a>, <a class="txt" href="scpqsort.html#E54:46_4"><i><font color="Green">E91</font></i></a>, <a class="ref" href="scmp_gcd.html#D3">SCMP_GCD:def 3</a></i>;<br/>
<a NAME="E58:46_4"/>
<span class="p1">(<span class="default"><font color="Maroon">c<sub>77</sub></font> <a href="nat_1.html#K1">+</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span></span>)</span> <a href="nat_1.html#K1">+</a> 0 <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>77</sub></font> <a href="nat_1.html#K1">+</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span></span>)</span> <a href="nat_1.html#K1">+</a> 2
 
;<br/>
<a NAME="E59:46_4"/><b>then </b><i><font color="Green">E94</font></i>: 
<span class="p1">(<span class="default"><a href="scmpds_4.html#K9">IExec</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><span class="p0">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a> ,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 3</span>)</span> <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p0">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a> ,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span> <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K2">GBP</a> ,4</span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p5">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a> ,<span class="p0">(<span class="default"><span class="p1">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 2</span>)</span> <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K2">GBP</a> ,4</span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p4">(<span class="default"><a href="scmpds_2.html#K12">AddTo</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p5">(<span class="default"><span class="p0">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span>,<span class="p5">(<span class="default"><a href="xcmplx_0.html#K4">-</a> 1</span>)</span></span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p3">(<span class="default"><a href="scmpds_2.html#K12">AddTo</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p4">(<span class="default"><span class="p5">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 2</span>)</span>,1</span>)</span></span>)</span>,<font color="Maroon">c<sub>75</sub></font></span>)</span> <a href="scmpds_2.html#K2">.</a> <span class="p1">(<span class="default"><a href="scmp_gcd.html#K1">intpos</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>77</sub></font> <a href="nat_1.html#K1">+</a> <span class="p3">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span></span>)</span></span>)</span> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>75</sub></font> <a href="scmpds_2.html#K2">.</a> <span class="p1">(<span class="default"><a href="scmp_gcd.html#K1">intpos</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>77</sub></font> <a href="nat_1.html#K1">+</a> <span class="p3">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span></span>)</span></span>)</span>
 
<b>by </b><i><a class="txt" href="scpqsort.html#E47:46_4"><i><font color="Green">E86</font></i></a>, <a class="txt" href="scpqsort.html#E54:46_4"><i><font color="Green">E91</font></i></a></i>;<br/>
<a NAME="E60:46_4"/>
<span class="p1">(<span class="default"><font color="Maroon">c<sub>77</sub></font> <a href="nat_1.html#K1">+</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span></span>)</span> <a href="nat_1.html#K1">+</a> 1 <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>77</sub></font> <a href="nat_1.html#K1">+</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span></span>)</span> <a href="nat_1.html#K1">+</a> 2
 
;<br/>
<a NAME="E61:46_4"/><b>then </b><i><font color="Green">E95</font></i>: 
<span class="p1">(<span class="default"><a href="scmpds_4.html#K9">IExec</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><span class="p0">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a> ,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 3</span>)</span> <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p0">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a> ,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span> <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K2">GBP</a> ,4</span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p5">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a> ,<span class="p0">(<span class="default"><span class="p1">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 2</span>)</span> <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K2">GBP</a> ,4</span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p4">(<span class="default"><a href="scmpds_2.html#K12">AddTo</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p5">(<span class="default"><span class="p0">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span>,<span class="p5">(<span class="default"><a href="xcmplx_0.html#K4">-</a> 1</span>)</span></span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p3">(<span class="default"><a href="scmpds_2.html#K12">AddTo</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p4">(<span class="default"><span class="p5">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 2</span>)</span>,1</span>)</span></span>)</span>,<font color="Maroon">c<sub>75</sub></font></span>)</span> <a href="scmpds_2.html#K2">.</a> <span class="p1">(<span class="default"><a href="scmp_gcd.html#K1">intpos</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">c<sub>77</sub></font> <a href="nat_1.html#K1">+</a> <span class="p4">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>75</sub></font> <a href="scmpds_2.html#K2">.</a> <span class="p2">(<span class="default"><a href="scmp_gcd.html#K1">intpos</a> 4</span>)</span></span>)</span> <a href="xcmplx_0.html#K6">-</a> 1
 
<b>by </b><i><a class="txt" href="scpqsort.html#E48:46_4"><i><font color="Green">E87</font></i></a>, <a class="txt" href="scpqsort.html#E54:46_4"><i><font color="Green">E91</font></i></a></i>;<br/>
<i><font color="Green">E96</font></i>: <span class="p1">(<span class="default"><a href="scmpds_4.html#K9">IExec</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><span class="p0">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a> ,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 3</span>)</span> <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p0">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a> ,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span> <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K2">GBP</a> ,4</span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p5">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a> ,<span class="p0">(<span class="default"><span class="p1">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 2</span>)</span> <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K2">GBP</a> ,4</span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p4">(<span class="default"><a href="scmpds_2.html#K12">AddTo</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p5">(<span class="default"><span class="p0">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span>,<span class="p5">(<span class="default"><a href="xcmplx_0.html#K4">-</a> 1</span>)</span></span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p3">(<span class="default"><a href="scmpds_2.html#K12">AddTo</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p4">(<span class="default"><span class="p5">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 2</span>)</span>,1</span>)</span></span>)</span>,<font color="Maroon">c<sub>75</sub></font></span>)</span> <a href="scmpds_2.html#K2">.</a> <span class="p1">(<span class="default"><a href="scmp_gcd.html#K1">intpos</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">c<sub>77</sub></font> <a href="nat_1.html#K1">+</a> <span class="p4">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span></span>)</span> <a href="nat_1.html#K1">+</a> 2</span>)</span></span>)</span> = 
<span class="p1">(<span class="default"><a href="ami_1.html#K4">Exec</a> <span class="p2">(<span class="default"><a href="scmpds_2.html#K12">AddTo</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 2</span>)</span>,1</span>)</span>,<span class="p2">(<span class="default"><a href="scmpds_4.html#K9">IExec</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><span class="p0">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a> ,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 3</span>)</span> <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p0">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a> ,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span> <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K2">GBP</a> ,4</span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p5">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a> ,<span class="p0">(<span class="default"><span class="p1">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 2</span>)</span> <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K2">GBP</a> ,4</span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p4">(<span class="default"><a href="scmpds_2.html#K12">AddTo</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p5">(<span class="default"><span class="p0">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span>,<span class="p5">(<span class="default"><a href="xcmplx_0.html#K4">-</a> 1</span>)</span></span>)</span></span>)</span>,<font color="Maroon">c<sub>75</sub></font></span>)</span></span>)</span> <a href="scmpds_2.html#K2">.</a> <span class="p1">(<span class="default"><a href="scmp_gcd.html#K1">intpos</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">c<sub>77</sub></font> <a href="nat_1.html#K1">+</a> <span class="p4">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span></span>)</span> <a href="nat_1.html#K1">+</a> 2</span>)</span></span>)</span>
<b>by </b><i><a class="ref" href="scmpds_5.html#T46">SCMPDS_5:46</a></i>
<br/>.= 
<span class="p1">(<span class="default"><font color="Maroon">c<sub>75</sub></font> <a href="scmpds_2.html#K2">.</a> <span class="p2">(<span class="default"><a href="scmp_gcd.html#K1">intpos</a> 4</span>)</span></span>)</span> <a href="xcmplx_0.html#K2">+</a> 1
<b>by </b><i><a class="txt" href="scpqsort.html#E50:46_4"><i><font color="Green">E88</font></i></a>, <a class="txt" href="scpqsort.html#E53:46_4"><i><font color="Green">E90</font></i></a>, <a class="ref" href="scmpds_2.html#T60">SCMPDS_2:60</a></i>
;<br/>
<a NAME="E63:46_4"/>
<span class="p1">(<span class="default"><font color="Maroon">c<sub>77</sub></font> <a href="nat_1.html#K1">+</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span></span>)</span> <a href="nat_1.html#K1">+</a> 3 <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>77</sub></font> <a href="nat_1.html#K1">+</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span></span>)</span> <a href="nat_1.html#K1">+</a> 2
 
;<br/>
<a NAME="E64:46_4"/><b>then </b><i><font color="Green">E97</font></i>: 
<span class="p1">(<span class="default"><a href="scmpds_4.html#K9">IExec</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><span class="p0">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a> ,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 3</span>)</span> <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p0">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a> ,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span> <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K2">GBP</a> ,4</span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p5">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a> ,<span class="p0">(<span class="default"><span class="p1">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 2</span>)</span> <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K2">GBP</a> ,4</span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p4">(<span class="default"><a href="scmpds_2.html#K12">AddTo</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p5">(<span class="default"><span class="p0">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span>,<span class="p5">(<span class="default"><a href="xcmplx_0.html#K4">-</a> 1</span>)</span></span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p3">(<span class="default"><a href="scmpds_2.html#K12">AddTo</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p4">(<span class="default"><span class="p5">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 2</span>)</span>,1</span>)</span></span>)</span>,<font color="Maroon">c<sub>75</sub></font></span>)</span> <a href="scmpds_2.html#K2">.</a> <span class="p1">(<span class="default"><a href="scmp_gcd.html#K1">intpos</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">c<sub>77</sub></font> <a href="nat_1.html#K1">+</a> <span class="p4">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span></span>)</span> <a href="nat_1.html#K1">+</a> 3</span>)</span></span>)</span> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>75</sub></font> <a href="scmpds_2.html#K2">.</a> <span class="p1">(<span class="default"><a href="scmp_gcd.html#K1">intpos</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">c<sub>77</sub></font> <a href="nat_1.html#K1">+</a> <span class="p4">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span>
 
<b>by </b><i><a class="txt" href="scpqsort.html#E52:46_4"><i><font color="Green">E89</font></i></a>, <a class="txt" href="scpqsort.html#E54:46_4"><i><font color="Green">E91</font></i></a></i>;<br/>
<a NAME="E65:46_4"/><i><font color="Green">E98</font></i>: 
 <a href="scmpds_2.html#K3">DataLoc</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="scmpds_4.html#K9">IExec</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><span class="p0">(<span class="default"><span class="p1">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a> ,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 3</span>)</span> <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p1">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a> ,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span> <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K2">GBP</a> ,4</span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p0">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a> ,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 2</span>)</span> <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K2">GBP</a> ,4</span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p5">(<span class="default"><a href="scmpds_2.html#K12">AddTo</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p0">(<span class="default"><span class="p1">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span>,<span class="p0">(<span class="default"><a href="xcmplx_0.html#K4">-</a> 1</span>)</span></span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p4">(<span class="default"><a href="scmpds_2.html#K12">AddTo</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p5">(<span class="default"><span class="p0">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 2</span>)</span>,1</span>)</span></span>)</span>,<font color="Maroon">c<sub>75</sub></font></span>)</span> <a href="scmpds_2.html#K2">.</a> <a href="scmp_gcd.html#K2">GBP</a> </span>)</span>,1 <a href="hidden.html#R1">=</a>  <a href="scmp_gcd.html#K1">intpos</a> <span class="p1">(<span class="default">0 <a href="nat_1.html#K1">+</a> 1</span>)</span>
 
<b>by </b><i><a class="txt" href="scpqsort.html#E55:46_4"><i><font color="Green">E92</font></i></a>, <a class="ref" href="scmp_gcd.html#T5">SCMP_GCD:5</a></i>;<br/>
<div><i><font color="Green">E99</font></i>: <a class="txt" onclick="hs2(this)" href="javascript:()" title="46_4_16"><b>now </b></a><div class="add"><b>let </b><font color="Maroon">c<sub>86</sub></font> be   <a href="nat_1.html#NM1">Nat</a>;<br/><b>assume </b><a NAME="E1:46_4_16"/>
<font color="Maroon">c<sub>86</sub></font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> 1
 ;<br/><a NAME="E2:46_4_16"/><b>then </b><i><font color="Green">E100</font></i>: 
 <a href="scmp_gcd.html#K1">intpos</a> <font color="Maroon">c<sub>86</sub></font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a>  <a href="scmpds_2.html#K3">DataLoc</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="scmpds_4.html#K9">IExec</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><span class="p0">(<span class="default"><span class="p1">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a> ,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 3</span>)</span> <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p1">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a> ,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span> <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K2">GBP</a> ,4</span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p0">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a> ,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 2</span>)</span> <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K2">GBP</a> ,4</span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p5">(<span class="default"><a href="scmpds_2.html#K12">AddTo</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p0">(<span class="default"><span class="p1">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span>,<span class="p0">(<span class="default"><a href="xcmplx_0.html#K4">-</a> 1</span>)</span></span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p4">(<span class="default"><a href="scmpds_2.html#K12">AddTo</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p5">(<span class="default"><span class="p0">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 2</span>)</span>,1</span>)</span></span>)</span>,<font color="Maroon">c<sub>75</sub></font></span>)</span> <a href="scmpds_2.html#K2">.</a> <a href="scmp_gcd.html#K2">GBP</a> </span>)</span>,1
 <b>by </b><i><a class="txt" href="scpqsort.html#E65:46_4"><i><font color="Green">E98</font></i></a>, <a class="ref" href="scmp_gcd.html#T4">SCMP_GCD:4</a></i>;<br/><b>thus </b><span class="p1">(<span class="default"><a href="scmpds_4.html#K9">IExec</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><span class="p0">(<span class="default"><span class="p1">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a> ,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 3</span>)</span> <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p1">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a> ,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span> <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K2">GBP</a> ,4</span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p0">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a> ,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 2</span>)</span> <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K2">GBP</a> ,4</span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p5">(<span class="default"><a href="scmpds_2.html#K12">AddTo</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p0">(<span class="default"><span class="p1">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span>,<span class="p0">(<span class="default"><a href="xcmplx_0.html#K4">-</a> 1</span>)</span></span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p4">(<span class="default"><a href="scmpds_2.html#K12">AddTo</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p5">(<span class="default"><span class="p0">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 2</span>)</span>,1</span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p3">(<span class="default"><a href="scmpds_2.html#K12">AddTo</a> <a href="scmp_gcd.html#K2">GBP</a> ,1,2</span>)</span></span>)</span>,<font color="Maroon">c<sub>75</sub></font></span>)</span> <a href="scmpds_2.html#K2">.</a> <span class="p1">(<span class="default"><a href="scmp_gcd.html#K1">intpos</a> <font color="Maroon">c<sub>86</sub></font></span>)</span> = 
<span class="p1">(<span class="default"><a href="ami_1.html#K4">Exec</a> <span class="p2">(<span class="default"><a href="scmpds_2.html#K12">AddTo</a> <a href="scmp_gcd.html#K2">GBP</a> ,1,2</span>)</span>,<span class="p2">(<span class="default"><a href="scmpds_4.html#K9">IExec</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><span class="p0">(<span class="default"><span class="p1">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a> ,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 3</span>)</span> <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p1">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a> ,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span> <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K2">GBP</a> ,4</span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p0">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a> ,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 2</span>)</span> <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K2">GBP</a> ,4</span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p5">(<span class="default"><a href="scmpds_2.html#K12">AddTo</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p0">(<span class="default"><span class="p1">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span>,<span class="p0">(<span class="default"><a href="xcmplx_0.html#K4">-</a> 1</span>)</span></span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p4">(<span class="default"><a href="scmpds_2.html#K12">AddTo</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p5">(<span class="default"><span class="p0">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 2</span>)</span>,1</span>)</span></span>)</span>,<font color="Maroon">c<sub>75</sub></font></span>)</span></span>)</span> <a href="scmpds_2.html#K2">.</a> <span class="p1">(<span class="default"><a href="scmp_gcd.html#K1">intpos</a> <font color="Maroon">c<sub>86</sub></font></span>)</span>
<b>by </b><i><a class="ref" href="scmpds_5.html#T46">SCMPDS_5:46</a></i>
<br/>.= 
<span class="p1">(<span class="default"><a href="scmpds_4.html#K9">IExec</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><span class="p0">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a> ,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 3</span>)</span> <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p0">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a> ,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span> <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K2">GBP</a> ,4</span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p5">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a> ,<span class="p0">(<span class="default"><span class="p1">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 2</span>)</span> <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K2">GBP</a> ,4</span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p4">(<span class="default"><a href="scmpds_2.html#K12">AddTo</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p5">(<span class="default"><span class="p0">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span>,<span class="p5">(<span class="default"><a href="xcmplx_0.html#K4">-</a> 1</span>)</span></span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p3">(<span class="default"><a href="scmpds_2.html#K12">AddTo</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p4">(<span class="default"><span class="p5">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 2</span>)</span>,1</span>)</span></span>)</span>,<font color="Maroon">c<sub>75</sub></font></span>)</span> <a href="scmpds_2.html#K2">.</a> <span class="p1">(<span class="default"><a href="scmp_gcd.html#K1">intpos</a> <font color="Maroon">c<sub>86</sub></font></span>)</span>
<b>by </b><i><a class="txt" href="scpqsort.html#E2:46_4_16"><i><font color="Green">E100</font></i></a>, <a class="ref" href="scmpds_2.html#T60">SCMPDS_2:60</a></i>
;<br/></div><b>end;</b></div>
<b>hence </b><a NAME="E67:46_4"/>
<span class="p1">(<span class="default"><a href="scmpds_4.html#K9">IExec</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><span class="p0">(<span class="default"><span class="p1">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a> ,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 3</span>)</span> <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p1">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a> ,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span> <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K2">GBP</a> ,4</span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p0">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a> ,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 2</span>)</span> <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K2">GBP</a> ,4</span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p5">(<span class="default"><a href="scmpds_2.html#K12">AddTo</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p0">(<span class="default"><span class="p1">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span>,<span class="p0">(<span class="default"><a href="xcmplx_0.html#K4">-</a> 1</span>)</span></span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p4">(<span class="default"><a href="scmpds_2.html#K12">AddTo</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p5">(<span class="default"><span class="p0">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 2</span>)</span>,1</span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p3">(<span class="default"><a href="scmpds_2.html#K12">AddTo</a> <a href="scmp_gcd.html#K2">GBP</a> ,1,2</span>)</span></span>)</span>,<font color="Maroon">c<sub>75</sub></font></span>)</span> <a href="scmpds_2.html#K2">.</a> <a href="scmp_gcd.html#K2">GBP</a>  <a href="hidden.html#R1">=</a> 0
 <b>by </b><i><a class="txt" href="scpqsort.html#E55:46_4"><i><font color="Green">E92</font></i></a>, <a class="ref" href="scmp_gcd.html#D2">SCMP_GCD:def 2</a></i>;<br/>

<b>thus </b><span class="p1">(<span class="default"><a href="scmpds_4.html#K9">IExec</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><span class="p0">(<span class="default"><span class="p1">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a> ,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 3</span>)</span> <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p1">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a> ,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span> <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K2">GBP</a> ,4</span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p0">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a> ,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 2</span>)</span> <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K2">GBP</a> ,4</span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p5">(<span class="default"><a href="scmpds_2.html#K12">AddTo</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p0">(<span class="default"><span class="p1">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span>,<span class="p0">(<span class="default"><a href="xcmplx_0.html#K4">-</a> 1</span>)</span></span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p4">(<span class="default"><a href="scmpds_2.html#K12">AddTo</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p5">(<span class="default"><span class="p0">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 2</span>)</span>,1</span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p3">(<span class="default"><a href="scmpds_2.html#K12">AddTo</a> <a href="scmp_gcd.html#K2">GBP</a> ,1,2</span>)</span></span>)</span>,<font color="Maroon">c<sub>75</sub></font></span>)</span> <a href="scmpds_2.html#K2">.</a> <a href="scmp_gcd.html#K3">SBP</a>  = 
<span class="p1">(<span class="default"><a href="ami_1.html#K4">Exec</a> <span class="p2">(<span class="default"><a href="scmpds_2.html#K12">AddTo</a> <a href="scmp_gcd.html#K2">GBP</a> ,1,2</span>)</span>,<span class="p2">(<span class="default"><a href="scmpds_4.html#K9">IExec</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><span class="p0">(<span class="default"><span class="p1">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a> ,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 3</span>)</span> <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p1">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a> ,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span> <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K2">GBP</a> ,4</span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p0">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a> ,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 2</span>)</span> <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K2">GBP</a> ,4</span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p5">(<span class="default"><a href="scmpds_2.html#K12">AddTo</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p0">(<span class="default"><span class="p1">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span>,<span class="p0">(<span class="default"><a href="xcmplx_0.html#K4">-</a> 1</span>)</span></span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p4">(<span class="default"><a href="scmpds_2.html#K12">AddTo</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p5">(<span class="default"><span class="p0">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 2</span>)</span>,1</span>)</span></span>)</span>,<font color="Maroon">c<sub>75</sub></font></span>)</span></span>)</span> <a href="scmpds_2.html#K2">.</a> <a href="scmp_gcd.html#K3">SBP</a> 
<b>by </b><i><a class="ref" href="scmpds_5.html#T46">SCMPDS_5:46</a></i>
<br/>.= 
<font color="Maroon">c<sub>77</sub></font> <a href="nat_1.html#K1">+</a> 2
<b>by </b><i><a class="txt" href="scpqsort.html#E57:46_4"><i><font color="Green">E93</font></i></a>, <a class="txt" href="scpqsort.html#E65:46_4"><i><font color="Green">E98</font></i></a>, <a class="ref" href="scmpds_2.html#T60">SCMPDS_2:60</a>, <a class="ref" href="scmp_gcd.html#D3">SCMP_GCD:def 3</a></i>
;<br/>

<a NAME="E69:46_4"/>
<font color="Maroon">c<sub>77</sub></font> <a href="nat_1.html#K1">+</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="xxreal_0.html#NR4" target="_self">&gt;</a> 1
 
<b>by </b><i><a class="txt" href="scpqsort.html#E3:46_4"><i><font color="Green">E53</font></i></a>, <a class="ref" href="xreal_1.html#T2">XREAL_1:2</a></i>;<br/>
<b>hence </b><a NAME="E70:46_4"/>
<span class="p1">(<span class="default"><a href="scmpds_4.html#K9">IExec</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><span class="p0">(<span class="default"><span class="p1">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a> ,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 3</span>)</span> <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p1">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a> ,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span> <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K2">GBP</a> ,4</span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p0">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a> ,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 2</span>)</span> <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K2">GBP</a> ,4</span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p5">(<span class="default"><a href="scmpds_2.html#K12">AddTo</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p0">(<span class="default"><span class="p1">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span>,<span class="p0">(<span class="default"><a href="xcmplx_0.html#K4">-</a> 1</span>)</span></span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p4">(<span class="default"><a href="scmpds_2.html#K12">AddTo</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p5">(<span class="default"><span class="p0">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 2</span>)</span>,1</span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p3">(<span class="default"><a href="scmpds_2.html#K12">AddTo</a> <a href="scmp_gcd.html#K2">GBP</a> ,1,2</span>)</span></span>)</span>,<font color="Maroon">c<sub>75</sub></font></span>)</span> <a href="scmpds_2.html#K2">.</a> <span class="p1">(<span class="default"><a href="scmp_gcd.html#K1">intpos</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>77</sub></font> <a href="nat_1.html#K1">+</a> <span class="p3">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span></span>)</span></span>)</span> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>75</sub></font> <a href="scmpds_2.html#K2">.</a> <span class="p1">(<span class="default"><a href="scmp_gcd.html#K1">intpos</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>77</sub></font> <a href="nat_1.html#K1">+</a> <span class="p3">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span></span>)</span></span>)</span>
 <b>by </b><i><a class="txt" href="scpqsort.html#E59:46_4"><i><font color="Green">E94</font></i></a>, <a class="txt" href="scpqsort.html#E66:46_4"><i><font color="Green">E99</font></i></a></i>;<br/>

<a NAME="E71:46_4"/>
<span class="p1">(<span class="default"><font color="Maroon">c<sub>77</sub></font> <a href="nat_1.html#K1">+</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span></span>)</span> <a href="nat_1.html#K1">+</a> 1 <a href="xxreal_0.html#NR4" target="_self">&gt;</a> 1
 
<b>by </b><i><a class="txt" href="scpqsort.html#E4:46_4"><i><font color="Green">E54</font></i></a>, <a class="ref" href="xreal_1.html#T2">XREAL_1:2</a></i>;<br/>
<b>hence </b><a NAME="E72:46_4"/>
<span class="p1">(<span class="default"><a href="scmpds_4.html#K9">IExec</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><span class="p0">(<span class="default"><span class="p1">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a> ,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 3</span>)</span> <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p1">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a> ,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span> <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K2">GBP</a> ,4</span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p0">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a> ,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 2</span>)</span> <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K2">GBP</a> ,4</span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p5">(<span class="default"><a href="scmpds_2.html#K12">AddTo</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p0">(<span class="default"><span class="p1">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span>,<span class="p0">(<span class="default"><a href="xcmplx_0.html#K4">-</a> 1</span>)</span></span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p4">(<span class="default"><a href="scmpds_2.html#K12">AddTo</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p5">(<span class="default"><span class="p0">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 2</span>)</span>,1</span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p3">(<span class="default"><a href="scmpds_2.html#K12">AddTo</a> <a href="scmp_gcd.html#K2">GBP</a> ,1,2</span>)</span></span>)</span>,<font color="Maroon">c<sub>75</sub></font></span>)</span> <a href="scmpds_2.html#K2">.</a> <span class="p1">(<span class="default"><a href="scmp_gcd.html#K1">intpos</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">c<sub>77</sub></font> <a href="nat_1.html#K1">+</a> <span class="p4">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>75</sub></font> <a href="scmpds_2.html#K2">.</a> <span class="p2">(<span class="default"><a href="scmp_gcd.html#K1">intpos</a> 4</span>)</span></span>)</span> <a href="xcmplx_0.html#K6">-</a> 1
 <b>by </b><i><a class="txt" href="scpqsort.html#E61:46_4"><i><font color="Green">E95</font></i></a>, <a class="txt" href="scpqsort.html#E66:46_4"><i><font color="Green">E99</font></i></a></i>;<br/>

<a NAME="E73:46_4"/>
<span class="p1">(<span class="default"><font color="Maroon">c<sub>77</sub></font> <a href="nat_1.html#K1">+</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span></span>)</span> <a href="nat_1.html#K1">+</a> 2 <a href="xxreal_0.html#NR4" target="_self">&gt;</a> 1
 
<b>by </b><i><a class="txt" href="scpqsort.html#E5:46_4"><i><font color="Green">E55</font></i></a>, <a class="ref" href="xreal_1.html#T2">XREAL_1:2</a></i>;<br/>
<b>hence </b><a NAME="E74:46_4"/>
<span class="p1">(<span class="default"><a href="scmpds_4.html#K9">IExec</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><span class="p0">(<span class="default"><span class="p1">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a> ,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 3</span>)</span> <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p1">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a> ,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span> <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K2">GBP</a> ,4</span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p0">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a> ,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 2</span>)</span> <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K2">GBP</a> ,4</span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p5">(<span class="default"><a href="scmpds_2.html#K12">AddTo</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p0">(<span class="default"><span class="p1">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span>,<span class="p0">(<span class="default"><a href="xcmplx_0.html#K4">-</a> 1</span>)</span></span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p4">(<span class="default"><a href="scmpds_2.html#K12">AddTo</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p5">(<span class="default"><span class="p0">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 2</span>)</span>,1</span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p3">(<span class="default"><a href="scmpds_2.html#K12">AddTo</a> <a href="scmp_gcd.html#K2">GBP</a> ,1,2</span>)</span></span>)</span>,<font color="Maroon">c<sub>75</sub></font></span>)</span> <a href="scmpds_2.html#K2">.</a> <span class="p1">(<span class="default"><a href="scmp_gcd.html#K1">intpos</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">c<sub>77</sub></font> <a href="nat_1.html#K1">+</a> <span class="p4">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span></span>)</span> <a href="nat_1.html#K1">+</a> 2</span>)</span></span>)</span> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>75</sub></font> <a href="scmpds_2.html#K2">.</a> <span class="p2">(<span class="default"><a href="scmp_gcd.html#K1">intpos</a> 4</span>)</span></span>)</span> <a href="xcmplx_0.html#K2">+</a> 1
 <b>by </b><i><a class="txt" href="scpqsort.html#E62:46_4"><i><font color="Green">E96</font></i></a>, <a class="txt" href="scpqsort.html#E66:46_4"><i><font color="Green">E99</font></i></a></i>;<br/>

<a NAME="E75:46_4"/>
<span class="p1">(<span class="default"><font color="Maroon">c<sub>77</sub></font> <a href="nat_1.html#K1">+</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span></span>)</span> <a href="nat_1.html#K1">+</a> 3 <a href="xxreal_0.html#NR4" target="_self">&gt;</a> 1
 
<b>by </b><i><a class="txt" href="scpqsort.html#E6:46_4"><i><font color="Green">E56</font></i></a>, <a class="ref" href="xreal_1.html#T2">XREAL_1:2</a></i>;<br/>
<b>hence </b><a NAME="E76:46_4"/>
<span class="p1">(<span class="default"><a href="scmpds_4.html#K9">IExec</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><span class="p0">(<span class="default"><span class="p1">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a> ,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 3</span>)</span> <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p1">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a> ,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span> <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K2">GBP</a> ,4</span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p0">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a> ,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 2</span>)</span> <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K2">GBP</a> ,4</span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p5">(<span class="default"><a href="scmpds_2.html#K12">AddTo</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p0">(<span class="default"><span class="p1">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span>,<span class="p0">(<span class="default"><a href="xcmplx_0.html#K4">-</a> 1</span>)</span></span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p4">(<span class="default"><a href="scmpds_2.html#K12">AddTo</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p5">(<span class="default"><span class="p0">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 2</span>)</span>,1</span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p3">(<span class="default"><a href="scmpds_2.html#K12">AddTo</a> <a href="scmp_gcd.html#K2">GBP</a> ,1,2</span>)</span></span>)</span>,<font color="Maroon">c<sub>75</sub></font></span>)</span> <a href="scmpds_2.html#K2">.</a> <span class="p1">(<span class="default"><a href="scmp_gcd.html#K1">intpos</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">c<sub>77</sub></font> <a href="nat_1.html#K1">+</a> <span class="p4">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span></span>)</span> <a href="nat_1.html#K1">+</a> 3</span>)</span></span>)</span> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>75</sub></font> <a href="scmpds_2.html#K2">.</a> <span class="p1">(<span class="default"><a href="scmp_gcd.html#K1">intpos</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">c<sub>77</sub></font> <a href="nat_1.html#K1">+</a> <span class="p4">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span>
 <b>by </b><i><a class="txt" href="scpqsort.html#E64:46_4"><i><font color="Green">E97</font></i></a>, <a class="txt" href="scpqsort.html#E66:46_4"><i><font color="Green">E99</font></i></a></i>;<br/>

<div><b>hereby </b>
<div class="add"><b>let </b><font color="Maroon">c<sub>86</sub></font> be   <a href="nat_1.html#NM1">Nat</a>;<br/><b>assume </b><a NAME="E1:46_4_18"/><i><font color="Green">E100</font></i>: 
( <font color="Maroon">c<sub>86</sub></font> <a href="xxreal_0.html#NR2" target="_self">&gt;=</a> 8 &amp; <font color="Maroon">c<sub>86</sub></font> <a href="xxreal_0.html#NR3" target="_self">&lt;</a> <font color="Maroon">c<sub>77</sub></font> <a href="nat_1.html#K1">+</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> )
 ;<br/><a NAME="E2:46_4_18"/><b>then </b><i><font color="Green">E101</font></i>: 
<font color="Maroon">c<sub>86</sub></font> <a href="xxreal_0.html#NR4" target="_self">&gt;</a> 1
 <b>by </b><i><a class="ref" href="xreal_1.html#T2">XREAL_1:2</a></i>;<br/><a NAME="E3:46_4_18"/><i><font color="Green">E102</font></i>: 
<font color="Maroon">c<sub>77</sub></font> <a href="nat_1.html#K1">+</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="xxreal_0.html#R1">&lt;=</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>77</sub></font> <a href="nat_1.html#K1">+</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span></span>)</span> <a href="nat_1.html#K1">+</a> 2
 <b>by </b><i><a class="ref" href="nat_1.html#T29">NAT_1:29</a></i>;<br/><a NAME="E4:46_4_18"/><i><font color="Green">E103</font></i>: 
<font color="Maroon">c<sub>77</sub></font> <a href="nat_1.html#K1">+</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="xxreal_0.html#R1">&lt;=</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>77</sub></font> <a href="nat_1.html#K1">+</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span></span>)</span> <a href="nat_1.html#K1">+</a> 1
 <b>by </b><i><a class="ref" href="nat_1.html#T29">NAT_1:29</a></i>;<br/><a NAME="E5:46_4_18"/><i><font color="Green">E104</font></i>: 
<font color="Maroon">c<sub>77</sub></font> <a href="nat_1.html#K1">+</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="xxreal_0.html#R1">&lt;=</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>77</sub></font> <a href="nat_1.html#K1">+</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span></span>)</span> <a href="nat_1.html#K1">+</a> 3
 <b>by </b><i><a class="ref" href="nat_1.html#T29">NAT_1:29</a></i>;<br/><b>thus </b><span class="p1">(<span class="default"><a href="scmpds_4.html#K9">IExec</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><span class="p0">(<span class="default"><span class="p1">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a> ,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 3</span>)</span> <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p1">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a> ,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span> <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K2">GBP</a> ,4</span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p0">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a> ,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 2</span>)</span> <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K2">GBP</a> ,4</span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p5">(<span class="default"><a href="scmpds_2.html#K12">AddTo</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p0">(<span class="default"><span class="p1">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span>,<span class="p0">(<span class="default"><a href="xcmplx_0.html#K4">-</a> 1</span>)</span></span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p4">(<span class="default"><a href="scmpds_2.html#K12">AddTo</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p5">(<span class="default"><span class="p0">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 2</span>)</span>,1</span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p3">(<span class="default"><a href="scmpds_2.html#K12">AddTo</a> <a href="scmp_gcd.html#K2">GBP</a> ,1,2</span>)</span></span>)</span>,<font color="Maroon">c<sub>75</sub></font></span>)</span> <a href="scmpds_2.html#K2">.</a> <span class="p1">(<span class="default"><a href="scmp_gcd.html#K1">intpos</a> <font color="Maroon">c<sub>86</sub></font></span>)</span> = 
<span class="p1">(<span class="default"><a href="scmpds_4.html#K9">IExec</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><span class="p0">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a> ,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 3</span>)</span> <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p0">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a> ,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span> <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K2">GBP</a> ,4</span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p5">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a> ,<span class="p0">(<span class="default"><span class="p1">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 2</span>)</span> <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K2">GBP</a> ,4</span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p4">(<span class="default"><a href="scmpds_2.html#K12">AddTo</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p5">(<span class="default"><span class="p0">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span>,<span class="p5">(<span class="default"><a href="xcmplx_0.html#K4">-</a> 1</span>)</span></span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p3">(<span class="default"><a href="scmpds_2.html#K12">AddTo</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p4">(<span class="default"><span class="p5">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 2</span>)</span>,1</span>)</span></span>)</span>,<font color="Maroon">c<sub>75</sub></font></span>)</span> <a href="scmpds_2.html#K2">.</a> <span class="p1">(<span class="default"><a href="scmp_gcd.html#K1">intpos</a> <font color="Maroon">c<sub>86</sub></font></span>)</span>
<b>by </b><i><a class="txt" href="scpqsort.html#E66:46_4"><i><font color="Green">E99</font></i></a>, <a class="txt" href="scpqsort.html#E2:46_4_18"><i><font color="Green">E101</font></i></a></i>
<br/>.= 
<span class="p1">(<span class="default"><a href="scmpds_4.html#K9">IExec</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a> ,<span class="p0">(<span class="default"><span class="p1">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 3</span>)</span> <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p0">(<span class="default"><span class="p1">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p5">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a> ,<span class="p0">(<span class="default"><span class="p1">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span> <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K2">GBP</a> ,4</span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p4">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a> ,<span class="p5">(<span class="default"><span class="p0">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 2</span>)</span> <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K2">GBP</a> ,4</span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p3">(<span class="default"><a href="scmpds_2.html#K12">AddTo</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p4">(<span class="default"><span class="p5">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span>,<span class="p4">(<span class="default"><a href="xcmplx_0.html#K4">-</a> 1</span>)</span></span>)</span></span>)</span>,<font color="Maroon">c<sub>75</sub></font></span>)</span> <a href="scmpds_2.html#K2">.</a> <span class="p1">(<span class="default"><a href="scmp_gcd.html#K1">intpos</a> <font color="Maroon">c<sub>86</sub></font></span>)</span>
<b>by </b><i><a class="txt" href="scpqsort.html#E54:46_4"><i><font color="Green">E91</font></i></a>, <a class="txt" href="scpqsort.html#E1:46_4_18"><i><font color="Green">E100</font></i></a>, <a class="txt" href="scpqsort.html#E3:46_4_18"><i><font color="Green">E102</font></i></a></i>
<br/>.= 
<span class="p1">(<span class="default"><a href="scmpds_4.html#K9">IExec</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a> ,<span class="p5">(<span class="default"><span class="p0">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 3</span>)</span> <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p5">(<span class="default"><span class="p0">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p4">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a> ,<span class="p5">(<span class="default"><span class="p0">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span> <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K2">GBP</a> ,4</span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p3">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a> ,<span class="p4">(<span class="default"><span class="p5">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 2</span>)</span> <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K2">GBP</a> ,4</span>)</span></span>)</span>,<font color="Maroon">c<sub>75</sub></font></span>)</span> <a href="scmpds_2.html#K2">.</a> <span class="p1">(<span class="default"><a href="scmp_gcd.html#K1">intpos</a> <font color="Maroon">c<sub>86</sub></font></span>)</span>
<b>by </b><i><a class="txt" href="scpqsort.html#E42:46_4"><i><font color="Green">E83</font></i></a>, <a class="txt" href="scpqsort.html#E1:46_4_18"><i><font color="Green">E100</font></i></a>, <a class="txt" href="scpqsort.html#E4:46_4_18"><i><font color="Green">E103</font></i></a></i>
<br/>.= 
<span class="p1">(<span class="default"><a href="scmpds_4.html#K9">IExec</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a> ,<span class="p4">(<span class="default"><span class="p5">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 3</span>)</span> <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p4">(<span class="default"><span class="p5">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p3">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a> ,<span class="p4">(<span class="default"><span class="p5">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span> <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K2">GBP</a> ,4</span>)</span></span>)</span>,<font color="Maroon">c<sub>75</sub></font></span>)</span> <a href="scmpds_2.html#K2">.</a> <span class="p1">(<span class="default"><a href="scmp_gcd.html#K1">intpos</a> <font color="Maroon">c<sub>86</sub></font></span>)</span>
<b>by </b><i><a class="txt" href="scpqsort.html#E30:46_4"><i><font color="Green">E75</font></i></a>, <a class="txt" href="scpqsort.html#E1:46_4_18"><i><font color="Green">E100</font></i></a>, <a class="txt" href="scpqsort.html#E3:46_4_18"><i><font color="Green">E102</font></i></a></i>
<br/>.= 
<span class="p1">(<span class="default"><a href="ami_1.html#K4">Exec</a> <span class="p2">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a> ,<span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 3</span>)</span> <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span>,<span class="p2">(<span class="default"><a href="scmpds_5.html#K1">Initialized</a> <font color="Maroon">c<sub>75</sub></font></span>)</span></span>)</span> <a href="scmpds_2.html#K2">.</a> <span class="p1">(<span class="default"><a href="scmp_gcd.html#K1">intpos</a> <font color="Maroon">c<sub>86</sub></font></span>)</span>
<b>by </b><i><a class="txt" href="scpqsort.html#E19:46_4"><i><font color="Green">E67</font></i></a>, <a class="txt" href="scpqsort.html#E1:46_4_18"><i><font color="Green">E100</font></i></a>, <a class="txt" href="scpqsort.html#E4:46_4_18"><i><font color="Green">E103</font></i></a></i>
<br/>.= 
<font color="Maroon">c<sub>75</sub></font> <a href="scmpds_2.html#K2">.</a> <span class="p1">(<span class="default"><a href="scmp_gcd.html#K1">intpos</a> <font color="Maroon">c<sub>86</sub></font></span>)</span>
<b>by </b><i><a class="txt" href="scpqsort.html#E9:46_4"><i><font color="Green">E59</font></i></a>, <a class="txt" href="scpqsort.html#E1:46_4_18"><i><font color="Green">E100</font></i></a>, <a class="txt" href="scpqsort.html#E5:46_4_18"><i><font color="Green">E104</font></i></a></i>
;<br/></div>
<b>end;</b></div>


</div><b>end;</b></div>
<a NAME="E12:46"/><i><font color="Green">E52</font></i>: 
for <font color="Olive">b<sub>1</sub></font> being  <a href="ami_1.html#NM4">State</a> of <a href="scmpds_2.html#K1">SCMPDS</a> <br/>for <font color="Olive">b<sub>2</sub></font> being  <a href="nat_1.html#NM1">Nat</a> st <font color="Olive">b<sub>1</sub></font> <a href="scmpds_2.html#K2">.</a> <a href="scmp_gcd.html#K2">GBP</a>  <a href="hidden.html#R1">=</a> 0 &amp; <font color="Olive">b<sub>1</sub></font> <a href="scmpds_2.html#K2">.</a> <a href="scmp_gcd.html#K3">SBP</a>  <a href="hidden.html#R1">=</a> <font color="Olive">b<sub>2</sub></font> holds <br/>( <span class="p1">(<span class="default"><a href="scmpds_4.html#K9">IExec</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a> ,2 <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p4">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span></span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p3">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a> ,4 <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p4">(<span class="default"><span class="p5">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span>,<font color="Olive">b<sub>1</sub></font></span>)</span> <a href="scmpds_2.html#K2">.</a> <span class="p1">(<span class="default"><a href="scmp_gcd.html#K1">intpos</a> 2</span>)</span> <a href="hidden.html#R1">=</a> <font color="Olive">b<sub>1</sub></font> <a href="scmpds_2.html#K2">.</a> <span class="p1">(<span class="default"><a href="scmp_gcd.html#K1">intpos</a> <span class="p2">(<span class="default"><font color="Olive">b<sub>2</sub></font> <a href="nat_1.html#K1">+</a> <span class="p3">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span></span>)</span></span>)</span> &amp; <span class="p1">(<span class="default"><a href="scmpds_4.html#K9">IExec</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a> ,2 <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p4">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span></span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p3">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a> ,4 <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p4">(<span class="default"><span class="p5">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span>,<font color="Olive">b<sub>1</sub></font></span>)</span> <a href="scmpds_2.html#K2">.</a> <span class="p1">(<span class="default"><a href="scmp_gcd.html#K1">intpos</a> 4</span>)</span> <a href="hidden.html#R1">=</a> <font color="Olive">b<sub>1</sub></font> <a href="scmpds_2.html#K2">.</a> <span class="p1">(<span class="default"><a href="scmp_gcd.html#K1">intpos</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Olive">b<sub>2</sub></font> <a href="nat_1.html#K1">+</a> <span class="p4">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> &amp; ( for <font color="Olive">b<sub>3</sub></font> being  <a href="nat_1.html#NM1">Nat</a> st <font color="Olive">b<sub>3</sub></font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> 2 &amp; <font color="Olive">b<sub>3</sub></font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> 4 holds <br/><span class="p1">(<span class="default"><a href="scmpds_4.html#K9">IExec</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a> ,2 <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p4">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span></span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p3">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a> ,4 <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p4">(<span class="default"><span class="p5">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span>,<font color="Olive">b<sub>1</sub></font></span>)</span> <a href="scmpds_2.html#K2">.</a> <span class="p1">(<span class="default"><a href="scmp_gcd.html#K1">intpos</a> <font color="Olive">b<sub>3</sub></font></span>)</span> <a href="hidden.html#R1">=</a> <font color="Olive">b<sub>1</sub></font> <a href="scmpds_2.html#K2">.</a> <span class="p1">(<span class="default"><a href="scmp_gcd.html#K1">intpos</a> <font color="Olive">b<sub>3</sub></font></span>)</span> ) )
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="46_5"><b>proof </b></a><div class="add">

<b>let </b><font color="Maroon">c<sub>75</sub></font> be   <a href="ami_1.html#NM4">State</a> of <a href="scmpds_2.html#K1">SCMPDS</a> ;<br/><b>let </b><font color="Maroon">c<sub>76</sub></font> be   <a href="nat_1.html#NM1">Nat</a>;<br/>



<b>set </b><font color="Maroon">c<sub>77</sub></font> =  <a href="scmpds_5.html#K1">Initialized</a> <font color="Maroon">c<sub>75</sub></font>;<br/>
<b>set </b><font color="Maroon">c<sub>78</sub></font> =  <a href="scmpds_4.html#K9">IExec</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a> ,2 <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p3">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span></span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p2">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a> ,4 <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span>,<font color="Maroon">c<sub>75</sub></font>;<br/>
<b>set </b><font color="Maroon">c<sub>79</sub></font> =  <a href="ami_1.html#K4">Exec</a> <span class="p1">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a> ,2 <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p2">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span></span>)</span>,<span class="p1">(<span class="default"><a href="scmpds_5.html#K1">Initialized</a> <font color="Maroon">c<sub>75</sub></font></span>)</span>;<br/>
<b>set </b><font color="Maroon">c<sub>80</sub></font> = <font color="Maroon">c<sub>76</sub></font> <a href="nat_1.html#K1">+</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span>;<br/>
<b>assume </b><a NAME="E1:46_5"/><i><font color="Green">E53</font></i>: 
( <font color="Maroon">c<sub>75</sub></font> <a href="scmpds_2.html#K2">.</a> <a href="scmp_gcd.html#K2">GBP</a>  <a href="hidden.html#R1">=</a> 0 &amp; <font color="Maroon">c<sub>75</sub></font> <a href="scmpds_2.html#K2">.</a> <a href="scmp_gcd.html#K3">SBP</a>  <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>76</sub></font> )
 ;<br/>

<a NAME="E2:46_5"/>
<font color="Maroon">c<sub>76</sub></font> <a href="nat_1.html#K1">+</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="xxreal_0.html#NR2" target="_self">&gt;=</a> 0 <a href="nat_1.html#K1">+</a> 7
 
<b>by </b><i><a class="txt" href="scpqsort.html#E8:46"><i><font color="Green">E48</font></i></a>, <a class="ref" href="xreal_1.html#T9">XREAL_1:9</a></i>;<br/>
<a NAME="E3:46_5"/><b>then </b><i><font color="Green">E54</font></i>: 
<span class="p1">(<span class="default"><font color="Maroon">c<sub>76</sub></font> <a href="nat_1.html#K1">+</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span></span>)</span> <a href="nat_1.html#K1">+</a> 1 <a href="xxreal_0.html#NR2" target="_self">&gt;=</a> 7 <a href="nat_1.html#K1">+</a> 1
 
<b>by </b><i><a class="ref" href="xreal_1.html#T8">XREAL_1:8</a></i>;<br/>
<a NAME="E4:46_5"/><i><font color="Green">E55</font></i>: 
<span class="p1">(<span class="default"><a href="scmpds_5.html#K1">Initialized</a> <font color="Maroon">c<sub>75</sub></font></span>)</span> <a href="scmpds_2.html#K2">.</a> <a href="scmp_gcd.html#K2">GBP</a>  <a href="hidden.html#R1">=</a> 0
 
<b>by </b><i><a class="txt" href="scpqsort.html#E1:46_5"><i><font color="Green">E53</font></i></a>, <a class="ref" href="scmpds_5.html#T40">SCMPDS_5:40</a></i>;<br/>
<a NAME="E5:46_5"/><i><font color="Green">E56</font></i>: 
<span class="p1">(<span class="default"><a href="scmpds_5.html#K1">Initialized</a> <font color="Maroon">c<sub>75</sub></font></span>)</span> <a href="scmpds_2.html#K2">.</a> <a href="scmp_gcd.html#K3">SBP</a>  <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>76</sub></font>
 
<b>by </b><i><a class="txt" href="scpqsort.html#E1:46_5"><i><font color="Green">E53</font></i></a>, <a class="ref" href="scmpds_5.html#T40">SCMPDS_5:40</a></i>;<br/>
<a NAME="E6:46_5"/><i><font color="Green">E57</font></i>: 
 <a href="scmpds_2.html#K3">DataLoc</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="scmpds_5.html#K1">Initialized</a> <font color="Maroon">c<sub>75</sub></font></span>)</span> <a href="scmpds_2.html#K2">.</a> <a href="scmp_gcd.html#K2">GBP</a> </span>)</span>,2 <a href="hidden.html#R1">=</a>  <a href="scmp_gcd.html#K1">intpos</a> <span class="p1">(<span class="default">0 <a href="nat_1.html#K1">+</a> 2</span>)</span>
 
<b>by </b><i><a class="txt" href="scpqsort.html#E4:46_5"><i><font color="Green">E55</font></i></a>, <a class="ref" href="scmp_gcd.html#T5">SCMP_GCD:5</a></i>;<br/>
<a NAME="E7:46_5"/><b>then </b>
 <a href="scmp_gcd.html#K2">GBP</a>  <a href="hidden.html#NR2" target="_self">&lt;&gt;</a>  <a href="scmpds_2.html#K3">DataLoc</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="scmpds_5.html#K1">Initialized</a> <font color="Maroon">c<sub>75</sub></font></span>)</span> <a href="scmpds_2.html#K2">.</a> <a href="scmp_gcd.html#K2">GBP</a> </span>)</span>,2
 
<b>by </b><i><a class="ref" href="scmp_gcd.html#T4">SCMP_GCD:4</a>, <a class="ref" href="scmp_gcd.html#D2">SCMP_GCD:def 2</a></i>;<br/>
<a NAME="E8:46_5"/><b>then </b><i><font color="Green">E58</font></i>: 
<span class="p1">(<span class="default"><a href="ami_1.html#K4">Exec</a> <span class="p2">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a> ,2 <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p3">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span></span>)</span>,<span class="p2">(<span class="default"><a href="scmpds_5.html#K1">Initialized</a> <font color="Maroon">c<sub>75</sub></font></span>)</span></span>)</span> <a href="scmpds_2.html#K2">.</a> <a href="scmp_gcd.html#K2">GBP</a>  <a href="hidden.html#R1">=</a> 0
 
<b>by </b><i><a class="txt" href="scpqsort.html#E4:46_5"><i><font color="Green">E55</font></i></a>, <a class="ref" href="scmpds_2.html#T59">SCMPDS_2:59</a></i>;<br/>
<a NAME="E9:46_5"/>
 <a href="scmp_gcd.html#K3">SBP</a>  <a href="hidden.html#NR2" target="_self">&lt;&gt;</a>  <a href="scmpds_2.html#K3">DataLoc</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="scmpds_5.html#K1">Initialized</a> <font color="Maroon">c<sub>75</sub></font></span>)</span> <a href="scmpds_2.html#K2">.</a> <a href="scmp_gcd.html#K2">GBP</a> </span>)</span>,2
 
<b>by </b><i><a class="txt" href="scpqsort.html#E6:46_5"><i><font color="Green">E57</font></i></a>, <a class="ref" href="scmp_gcd.html#T4">SCMP_GCD:4</a>, <a class="ref" href="scmp_gcd.html#D3">SCMP_GCD:def 3</a></i>;<br/>
<a NAME="E10:46_5"/><b>then </b><i><font color="Green">E59</font></i>: 
<span class="p1">(<span class="default"><a href="ami_1.html#K4">Exec</a> <span class="p2">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a> ,2 <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p3">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span></span>)</span>,<span class="p2">(<span class="default"><a href="scmpds_5.html#K1">Initialized</a> <font color="Maroon">c<sub>75</sub></font></span>)</span></span>)</span> <a href="scmpds_2.html#K2">.</a> <a href="scmp_gcd.html#K3">SBP</a>  <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>76</sub></font>
 
<b>by </b><i><a class="txt" href="scpqsort.html#E5:46_5"><i><font color="Green">E56</font></i></a>, <a class="ref" href="scmpds_2.html#T59">SCMPDS_2:59</a></i>;<br/>
<i><font color="Green">E60</font></i>: <span class="p1">(<span class="default"><a href="ami_1.html#K4">Exec</a> <span class="p2">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a> ,2 <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p3">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span></span>)</span>,<span class="p2">(<span class="default"><a href="scmpds_5.html#K1">Initialized</a> <font color="Maroon">c<sub>75</sub></font></span>)</span></span>)</span> <a href="scmpds_2.html#K2">.</a> <span class="p1">(<span class="default"><a href="scmp_gcd.html#K1">intpos</a> 2</span>)</span> = 
<span class="p1">(<span class="default"><a href="scmpds_5.html#K1">Initialized</a> <font color="Maroon">c<sub>75</sub></font></span>)</span> <a href="scmpds_2.html#K2">.</a> <span class="p1">(<span class="default"><a href="scmpds_2.html#K3">DataLoc</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="scmpds_5.html#K1">Initialized</a> <font color="Maroon">c<sub>75</sub></font></span>)</span> <a href="scmpds_2.html#K2">.</a> <a href="scmp_gcd.html#K3">SBP</a> </span>)</span>,<span class="p2">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span></span>)</span>
<b>by </b><i><a class="txt" href="scpqsort.html#E6:46_5"><i><font color="Green">E57</font></i></a>, <a class="ref" href="scmpds_2.html#T59">SCMPDS_2:59</a></i>
<br/>.= 
<span class="p1">(<span class="default"><a href="scmpds_5.html#K1">Initialized</a> <font color="Maroon">c<sub>75</sub></font></span>)</span> <a href="scmpds_2.html#K2">.</a> <span class="p1">(<span class="default"><a href="scmp_gcd.html#K1">intpos</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>76</sub></font> <a href="nat_1.html#K1">+</a> <span class="p3">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span></span>)</span></span>)</span>
<b>by </b><i><a class="txt" href="scpqsort.html#E5:46_5"><i><font color="Green">E56</font></i></a>, <a class="ref" href="scmp_gcd.html#T5">SCMP_GCD:5</a></i>
<br/>.= 
<font color="Maroon">c<sub>75</sub></font> <a href="scmpds_2.html#K2">.</a> <span class="p1">(<span class="default"><a href="scmp_gcd.html#K1">intpos</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>76</sub></font> <a href="nat_1.html#K1">+</a> <span class="p3">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span></span>)</span></span>)</span>
<b>by </b><i><a class="ref" href="scmpds_5.html#T40">SCMPDS_5:40</a></i>
;<br/>
<a NAME="E12:46_5"/>
<span class="p1">(<span class="default"><font color="Maroon">c<sub>76</sub></font> <a href="nat_1.html#K1">+</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span></span>)</span> <a href="nat_1.html#K1">+</a> 1 <a href="xxreal_0.html#NR4" target="_self">&gt;</a> 2
 
<b>by </b><i><a class="txt" href="scpqsort.html#E3:46_5"><i><font color="Green">E54</font></i></a>, <a class="ref" href="xreal_1.html#T2">XREAL_1:2</a></i>;<br/>
<a NAME="E13:46_5"/><b>then </b>
 <a href="scmp_gcd.html#K1">intpos</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>76</sub></font> <a href="nat_1.html#K1">+</a> <span class="p3">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a>  <a href="scmpds_2.html#K3">DataLoc</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="scmpds_5.html#K1">Initialized</a> <font color="Maroon">c<sub>75</sub></font></span>)</span> <a href="scmpds_2.html#K2">.</a> <a href="scmp_gcd.html#K2">GBP</a> </span>)</span>,2
 
<b>by </b><i><a class="txt" href="scpqsort.html#E6:46_5"><i><font color="Green">E57</font></i></a>, <a class="ref" href="scmp_gcd.html#T4">SCMP_GCD:4</a></i>;<br/>
<b>then </b><i><font color="Green">E61</font></i>: <span class="p1">(<span class="default"><a href="ami_1.html#K4">Exec</a> <span class="p2">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a> ,2 <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p3">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span></span>)</span>,<span class="p2">(<span class="default"><a href="scmpds_5.html#K1">Initialized</a> <font color="Maroon">c<sub>75</sub></font></span>)</span></span>)</span> <a href="scmpds_2.html#K2">.</a> <span class="p1">(<span class="default"><a href="scmp_gcd.html#K1">intpos</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">c<sub>76</sub></font> <a href="nat_1.html#K1">+</a> <span class="p4">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> = 
<span class="p1">(<span class="default"><a href="scmpds_5.html#K1">Initialized</a> <font color="Maroon">c<sub>75</sub></font></span>)</span> <a href="scmpds_2.html#K2">.</a> <span class="p1">(<span class="default"><a href="scmp_gcd.html#K1">intpos</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">c<sub>76</sub></font> <a href="nat_1.html#K1">+</a> <span class="p4">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span>
<b>by </b><i><a class="ref" href="scmpds_2.html#T59">SCMPDS_2:59</a></i>
<br/>.= 
<font color="Maroon">c<sub>75</sub></font> <a href="scmpds_2.html#K2">.</a> <span class="p1">(<span class="default"><a href="scmp_gcd.html#K1">intpos</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">c<sub>76</sub></font> <a href="nat_1.html#K1">+</a> <span class="p4">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span>
<b>by </b><i><a class="ref" href="scmpds_5.html#T40">SCMPDS_5:40</a></i>
;<br/>
<a NAME="E15:46_5"/><i><font color="Green">E62</font></i>: 
 <a href="scmpds_2.html#K3">DataLoc</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K4">Exec</a> <span class="p3">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a> ,2 <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p4">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span></span>)</span>,<span class="p3">(<span class="default"><a href="scmpds_5.html#K1">Initialized</a> <font color="Maroon">c<sub>75</sub></font></span>)</span></span>)</span> <a href="scmpds_2.html#K2">.</a> <a href="scmp_gcd.html#K2">GBP</a> </span>)</span>,4 <a href="hidden.html#R1">=</a>  <a href="scmp_gcd.html#K1">intpos</a> <span class="p1">(<span class="default">0 <a href="nat_1.html#K1">+</a> 4</span>)</span>
 
<b>by </b><i><a class="txt" href="scpqsort.html#E8:46_5"><i><font color="Green">E58</font></i></a>, <a class="ref" href="scmp_gcd.html#T5">SCMP_GCD:5</a></i>;<br/>
<a NAME="E16:46_5"/><b>then </b><i><font color="Green">E63</font></i>: 
 <a href="scmp_gcd.html#K1">intpos</a> 2 <a href="hidden.html#NR2" target="_self">&lt;&gt;</a>  <a href="scmpds_2.html#K3">DataLoc</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K4">Exec</a> <span class="p3">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a> ,2 <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p4">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span></span>)</span>,<span class="p3">(<span class="default"><a href="scmpds_5.html#K1">Initialized</a> <font color="Maroon">c<sub>75</sub></font></span>)</span></span>)</span> <a href="scmpds_2.html#K2">.</a> <a href="scmp_gcd.html#K2">GBP</a> </span>)</span>,4
 
<b>by </b><i><a class="ref" href="scmp_gcd.html#T4">SCMP_GCD:4</a></i>;<br/>
<b>thus </b><span class="p1">(<span class="default"><a href="scmpds_4.html#K9">IExec</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a> ,2 <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p4">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span></span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p3">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a> ,4 <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p4">(<span class="default"><span class="p5">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span>,<font color="Maroon">c<sub>75</sub></font></span>)</span> <a href="scmpds_2.html#K2">.</a> <span class="p1">(<span class="default"><a href="scmp_gcd.html#K1">intpos</a> 2</span>)</span> = 
<span class="p1">(<span class="default"><a href="ami_1.html#K4">Exec</a> <span class="p2">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a> ,4 <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span>,<span class="p2">(<span class="default"><a href="ami_1.html#K4">Exec</a> <span class="p3">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a> ,2 <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p4">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span></span>)</span>,<span class="p3">(<span class="default"><a href="scmpds_5.html#K1">Initialized</a> <font color="Maroon">c<sub>75</sub></font></span>)</span></span>)</span></span>)</span> <a href="scmpds_2.html#K2">.</a> <span class="p1">(<span class="default"><a href="scmp_gcd.html#K1">intpos</a> 2</span>)</span>
<b>by </b><i><a class="ref" href="scmpds_5.html#T47">SCMPDS_5:47</a></i>
<br/>.= 
<font color="Maroon">c<sub>75</sub></font> <a href="scmpds_2.html#K2">.</a> <span class="p1">(<span class="default"><a href="scmp_gcd.html#K1">intpos</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>76</sub></font> <a href="nat_1.html#K1">+</a> <span class="p3">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span></span>)</span></span>)</span>
<b>by </b><i><a class="txt" href="scpqsort.html#E11:46_5"><i><font color="Green">E60</font></i></a>, <a class="txt" href="scpqsort.html#E16:46_5"><i><font color="Green">E63</font></i></a>, <a class="ref" href="scmpds_2.html#T59">SCMPDS_2:59</a></i>
;<br/>

<b>thus </b><span class="p1">(<span class="default"><a href="scmpds_4.html#K9">IExec</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a> ,2 <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p4">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span></span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p3">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a> ,4 <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p4">(<span class="default"><span class="p5">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span>,<font color="Maroon">c<sub>75</sub></font></span>)</span> <a href="scmpds_2.html#K2">.</a> <span class="p1">(<span class="default"><a href="scmp_gcd.html#K1">intpos</a> 4</span>)</span> = 
<span class="p1">(<span class="default"><a href="ami_1.html#K4">Exec</a> <span class="p2">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a> ,4 <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span>,<span class="p2">(<span class="default"><a href="ami_1.html#K4">Exec</a> <span class="p3">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a> ,2 <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p4">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span></span>)</span>,<span class="p3">(<span class="default"><a href="scmpds_5.html#K1">Initialized</a> <font color="Maroon">c<sub>75</sub></font></span>)</span></span>)</span></span>)</span> <a href="scmpds_2.html#K2">.</a> <span class="p1">(<span class="default"><a href="scmp_gcd.html#K1">intpos</a> 4</span>)</span>
<b>by </b><i><a class="ref" href="scmpds_5.html#T47">SCMPDS_5:47</a></i>
<br/>.= 
<span class="p1">(<span class="default"><a href="ami_1.html#K4">Exec</a> <span class="p2">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a> ,2 <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p3">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span></span>)</span>,<span class="p2">(<span class="default"><a href="scmpds_5.html#K1">Initialized</a> <font color="Maroon">c<sub>75</sub></font></span>)</span></span>)</span> <a href="scmpds_2.html#K2">.</a> <span class="p1">(<span class="default"><a href="scmpds_2.html#K3">DataLoc</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="ami_1.html#K4">Exec</a> <span class="p4">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a> ,2 <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p5">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span></span>)</span>,<span class="p4">(<span class="default"><a href="scmpds_5.html#K1">Initialized</a> <font color="Maroon">c<sub>75</sub></font></span>)</span></span>)</span> <a href="scmpds_2.html#K2">.</a> <a href="scmp_gcd.html#K3">SBP</a> </span>)</span>,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span>
<b>by </b><i><a class="txt" href="scpqsort.html#E15:46_5"><i><font color="Green">E62</font></i></a>, <a class="ref" href="scmpds_2.html#T59">SCMPDS_2:59</a></i>
<br/>.= 
<span class="p1">(<span class="default"><a href="ami_1.html#K4">Exec</a> <span class="p2">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a> ,2 <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p3">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span></span>)</span>,<span class="p2">(<span class="default"><a href="scmpds_5.html#K1">Initialized</a> <font color="Maroon">c<sub>75</sub></font></span>)</span></span>)</span> <a href="scmpds_2.html#K2">.</a> <span class="p1">(<span class="default"><a href="scmp_gcd.html#K1">intpos</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>76</sub></font> <a href="nat_1.html#K1">+</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span>
<b>by </b><i><a class="txt" href="scpqsort.html#E10:46_5"><i><font color="Green">E59</font></i></a>, <a class="ref" href="scmp_gcd.html#T5">SCMP_GCD:5</a></i>
<br/>.= 
<font color="Maroon">c<sub>75</sub></font> <a href="scmpds_2.html#K2">.</a> <span class="p1">(<span class="default"><a href="scmp_gcd.html#K1">intpos</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">c<sub>76</sub></font> <a href="nat_1.html#K1">+</a> <span class="p4">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span>
<b>by </b><i><a class="txt" href="scpqsort.html#E14:46_5"><i><font color="Green">E61</font></i></a></i>
;<br/>

<div><b>hereby </b>
<div class="add"><b>let </b><font color="Maroon">c<sub>81</sub></font> be   <a href="nat_1.html#NM1">Nat</a>;<br/><b>assume </b><a NAME="E1:46_5_5"/><i><font color="Green">E64</font></i>: 
( <font color="Maroon">c<sub>81</sub></font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> 2 &amp; <font color="Maroon">c<sub>81</sub></font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> 4 )
 ;<br/><a NAME="E2:46_5_5"/><b>then </b><i><font color="Green">E65</font></i>: 
 <a href="scmp_gcd.html#K1">intpos</a> <font color="Maroon">c<sub>81</sub></font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a>  <a href="scmpds_2.html#K3">DataLoc</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="scmpds_5.html#K1">Initialized</a> <font color="Maroon">c<sub>75</sub></font></span>)</span> <a href="scmpds_2.html#K2">.</a> <a href="scmp_gcd.html#K2">GBP</a> </span>)</span>,2
 <b>by </b><i><a class="txt" href="scpqsort.html#E6:46_5"><i><font color="Green">E57</font></i></a>, <a class="ref" href="scmp_gcd.html#T4">SCMP_GCD:4</a></i>;<br/><a NAME="E3:46_5_5"/><i><font color="Green">E66</font></i>: 
 <a href="scmp_gcd.html#K1">intpos</a> <font color="Maroon">c<sub>81</sub></font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a>  <a href="scmpds_2.html#K3">DataLoc</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K4">Exec</a> <span class="p3">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a> ,2 <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p4">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span></span>)</span>,<span class="p3">(<span class="default"><a href="scmpds_5.html#K1">Initialized</a> <font color="Maroon">c<sub>75</sub></font></span>)</span></span>)</span> <a href="scmpds_2.html#K2">.</a> <a href="scmp_gcd.html#K2">GBP</a> </span>)</span>,4
 <b>by </b><i><a class="txt" href="scpqsort.html#E15:46_5"><i><font color="Green">E62</font></i></a>, <a class="txt" href="scpqsort.html#E1:46_5_5"><i><font color="Green">E64</font></i></a>, <a class="ref" href="scmp_gcd.html#T4">SCMP_GCD:4</a></i>;<br/><b>thus </b><span class="p1">(<span class="default"><a href="scmpds_4.html#K9">IExec</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a> ,2 <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p4">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span></span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p3">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a> ,4 <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p4">(<span class="default"><span class="p5">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span>,<font color="Maroon">c<sub>75</sub></font></span>)</span> <a href="scmpds_2.html#K2">.</a> <span class="p1">(<span class="default"><a href="scmp_gcd.html#K1">intpos</a> <font color="Maroon">c<sub>81</sub></font></span>)</span> = 
<span class="p1">(<span class="default"><a href="ami_1.html#K4">Exec</a> <span class="p2">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a> ,4 <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span>,<span class="p2">(<span class="default"><a href="ami_1.html#K4">Exec</a> <span class="p3">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a> ,2 <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p4">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span></span>)</span>,<span class="p3">(<span class="default"><a href="scmpds_5.html#K1">Initialized</a> <font color="Maroon">c<sub>75</sub></font></span>)</span></span>)</span></span>)</span> <a href="scmpds_2.html#K2">.</a> <span class="p1">(<span class="default"><a href="scmp_gcd.html#K1">intpos</a> <font color="Maroon">c<sub>81</sub></font></span>)</span>
<b>by </b><i><a class="ref" href="scmpds_5.html#T47">SCMPDS_5:47</a></i>
<br/>.= 
<span class="p1">(<span class="default"><a href="ami_1.html#K4">Exec</a> <span class="p2">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a> ,2 <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p3">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span></span>)</span>,<span class="p2">(<span class="default"><a href="scmpds_5.html#K1">Initialized</a> <font color="Maroon">c<sub>75</sub></font></span>)</span></span>)</span> <a href="scmpds_2.html#K2">.</a> <span class="p1">(<span class="default"><a href="scmp_gcd.html#K1">intpos</a> <font color="Maroon">c<sub>81</sub></font></span>)</span>
<b>by </b><i><a class="txt" href="scpqsort.html#E3:46_5_5"><i><font color="Green">E66</font></i></a>, <a class="ref" href="scmpds_2.html#T59">SCMPDS_2:59</a></i>
<br/>.= 
<span class="p1">(<span class="default"><a href="scmpds_5.html#K1">Initialized</a> <font color="Maroon">c<sub>75</sub></font></span>)</span> <a href="scmpds_2.html#K2">.</a> <span class="p1">(<span class="default"><a href="scmp_gcd.html#K1">intpos</a> <font color="Maroon">c<sub>81</sub></font></span>)</span>
<b>by </b><i><a class="txt" href="scpqsort.html#E2:46_5_5"><i><font color="Green">E65</font></i></a>, <a class="ref" href="scmpds_2.html#T59">SCMPDS_2:59</a></i>
<br/>.= 
<font color="Maroon">c<sub>75</sub></font> <a href="scmpds_2.html#K2">.</a> <span class="p1">(<span class="default"><a href="scmp_gcd.html#K1">intpos</a> <font color="Maroon">c<sub>81</sub></font></span>)</span>
<b>by </b><i><a class="ref" href="scmpds_5.html#T40">SCMPDS_5:40</a></i>
;<br/></div>
<b>end;</b></div>


</div><b>end;</b></div>
<a NAME="E13:46"/><i><font color="Green">E53</font></i>: 
for <font color="Olive">b<sub>1</sub></font> being  <a href="ami_1.html#NM4">State</a> of <a href="scmpds_2.html#K1">SCMPDS</a> <br/>for <font color="Olive">b<sub>2</sub></font>, <font color="Olive">b<sub>3</sub></font> being  <a href="nat_1.html#NM1">Nat</a> st <font color="Olive">b<sub>1</sub></font> <a href="scmpds_2.html#K2">.</a> <a href="scmp_gcd.html#K2">GBP</a>  <a href="hidden.html#R1">=</a> 0 &amp; <font color="Olive">b<sub>1</sub></font> <a href="scmpds_2.html#K2">.</a> <a href="scmp_gcd.html#K3">SBP</a>  <a href="hidden.html#R1">=</a> <font color="Olive">b<sub>2</sub></font> &amp; <font color="Olive">b<sub>1</sub></font> <a href="scmpds_2.html#K2">.</a> <span class="p1">(<span class="default"><a href="scmp_gcd.html#K1">intpos</a> <span class="p2">(<span class="default"><font color="Olive">b<sub>2</sub></font> <a href="nat_1.html#K1">+</a> <span class="p3">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span></span>)</span></span>)</span> <a href="hidden.html#R1">=</a> <font color="Olive">b<sub>3</sub></font> &amp; <font color="Olive">b<sub>3</sub></font> <a href="xxreal_0.html#NR2" target="_self">&gt;=</a> <font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> 1 &amp; <span class="p1">(<span class="default"><font color="Olive">b<sub>1</sub></font> <a href="scmpds_2.html#K2">.</a> <span class="p2">(<span class="default"><a href="scmp_gcd.html#K1">intpos</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Olive">b<sub>2</sub></font> <a href="nat_1.html#K1">+</a> <span class="p5">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span> <a href="xcmplx_0.html#K6">-</a> <font color="Olive">b<sub>3</sub></font> <a href="xxreal_0.html#NR4" target="_self">&gt;</a> 0 holds <br/>( <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a> ,2 <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p4">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span></span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p3">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a> ,4 <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p4">(<span class="default"><span class="p5">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span> <a href="scmpds_4.html#K3">';'</a> <font color="Maroon">c<sub>50</sub></font></span>)</span> <a href="scmpds_4.html#K3">';'</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><span class="p0">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a> ,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 3</span>)</span> <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p0">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a> ,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span> <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K2">GBP</a> ,4</span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p5">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a> ,<span class="p0">(<span class="default"><span class="p1">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 2</span>)</span> <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K2">GBP</a> ,4</span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p4">(<span class="default"><a href="scmpds_2.html#K12">AddTo</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p5">(<span class="default"><span class="p0">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span>,<span class="p5">(<span class="default"><a href="xcmplx_0.html#K4">-</a> 1</span>)</span></span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p3">(<span class="default"><a href="scmpds_2.html#K12">AddTo</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p4">(<span class="default"><span class="p5">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 2</span>)</span>,1</span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p2">(<span class="default"><a href="scmpds_2.html#K12">AddTo</a> <a href="scmp_gcd.html#K2">GBP</a> ,1,2</span>)</span></span>)</span> <a href="scmpds_6.html#R1">is_closed_on</a> <font color="Olive">b<sub>1</sub></font> &amp; <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a> ,2 <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p4">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span></span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p3">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a> ,4 <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p4">(<span class="default"><span class="p5">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span> <a href="scmpds_4.html#K3">';'</a> <font color="Maroon">c<sub>50</sub></font></span>)</span> <a href="scmpds_4.html#K3">';'</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><span class="p0">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a> ,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 3</span>)</span> <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p0">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a> ,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span> <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K2">GBP</a> ,4</span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p5">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a> ,<span class="p0">(<span class="default"><span class="p1">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 2</span>)</span> <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K2">GBP</a> ,4</span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p4">(<span class="default"><a href="scmpds_2.html#K12">AddTo</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p5">(<span class="default"><span class="p0">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span>,<span class="p5">(<span class="default"><a href="xcmplx_0.html#K4">-</a> 1</span>)</span></span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p3">(<span class="default"><a href="scmpds_2.html#K12">AddTo</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p4">(<span class="default"><span class="p5">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 2</span>)</span>,1</span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p2">(<span class="default"><a href="scmpds_2.html#K12">AddTo</a> <a href="scmp_gcd.html#K2">GBP</a> ,1,2</span>)</span></span>)</span> <a href="scmpds_6.html#R2">is_halting_on</a> <font color="Olive">b<sub>1</sub></font> )
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="46_6"><b>proof </b></a><div class="add">

<b>let </b><font color="Maroon">c<sub>75</sub></font> be   <a href="ami_1.html#NM4">State</a> of <a href="scmpds_2.html#K1">SCMPDS</a> ;<br/><b>let </b><font color="Maroon">c<sub>76</sub></font>, <font color="Maroon">c<sub>77</sub></font> be   <a href="nat_1.html#NM1">Nat</a>;<br/>



<b>set </b><font color="Maroon">c<sub>78</sub></font> = <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a> ,2 <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p3">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span></span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p2">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a> ,4 <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span> <a href="scmpds_4.html#K3">';'</a> <font color="Maroon">c<sub>50</sub></font>;<br/>
<b>set </b><font color="Maroon">c<sub>79</sub></font> =  <a href="scmpds_4.html#K9">IExec</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a> ,2 <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p3">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span></span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p2">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a> ,4 <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span>,<font color="Maroon">c<sub>75</sub></font>;<br/>
<b>set </b><font color="Maroon">c<sub>80</sub></font> = <font color="Maroon">c<sub>76</sub></font> <a href="nat_1.html#K1">+</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span>;<br/>
<b>assume </b><a NAME="E1:46_6"/><i><font color="Green">E54</font></i>: 
( <font color="Maroon">c<sub>75</sub></font> <a href="scmpds_2.html#K2">.</a> <a href="scmp_gcd.html#K2">GBP</a>  <a href="hidden.html#R1">=</a> 0 &amp; <font color="Maroon">c<sub>75</sub></font> <a href="scmpds_2.html#K2">.</a> <a href="scmp_gcd.html#K3">SBP</a>  <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>76</sub></font> &amp; <font color="Maroon">c<sub>75</sub></font> <a href="scmpds_2.html#K2">.</a> <span class="p1">(<span class="default"><a href="scmp_gcd.html#K1">intpos</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>76</sub></font> <a href="nat_1.html#K1">+</a> <span class="p3">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span></span>)</span></span>)</span> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>77</sub></font> &amp; <font color="Maroon">c<sub>77</sub></font> <a href="xxreal_0.html#NR2" target="_self">&gt;=</a> <font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> 1 &amp; <span class="p1">(<span class="default"><font color="Maroon">c<sub>75</sub></font> <a href="scmpds_2.html#K2">.</a> <span class="p2">(<span class="default"><a href="scmp_gcd.html#K1">intpos</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">c<sub>76</sub></font> <a href="nat_1.html#K1">+</a> <span class="p5">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span> <a href="xcmplx_0.html#K6">-</a> <font color="Maroon">c<sub>77</sub></font> <a href="xxreal_0.html#NR4" target="_self">&gt;</a> 0 )
 ;<br/>

<a NAME="E2:46_6"/><b>then </b><i><font color="Green">E55</font></i>: 
( <span class="p1">(<span class="default"><a href="scmpds_4.html#K9">IExec</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a> ,2 <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p4">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span></span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p3">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a> ,4 <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p4">(<span class="default"><span class="p5">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span>,<font color="Maroon">c<sub>75</sub></font></span>)</span> <a href="scmpds_2.html#K2">.</a> <span class="p1">(<span class="default"><a href="scmp_gcd.html#K1">intpos</a> 2</span>)</span> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>75</sub></font> <a href="scmpds_2.html#K2">.</a> <span class="p1">(<span class="default"><a href="scmp_gcd.html#K1">intpos</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>76</sub></font> <a href="nat_1.html#K1">+</a> <span class="p3">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span></span>)</span></span>)</span> &amp; <span class="p1">(<span class="default"><a href="scmpds_4.html#K9">IExec</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a> ,2 <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p4">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span></span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p3">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a> ,4 <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p4">(<span class="default"><span class="p5">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span>,<font color="Maroon">c<sub>75</sub></font></span>)</span> <a href="scmpds_2.html#K2">.</a> <span class="p1">(<span class="default"><a href="scmp_gcd.html#K1">intpos</a> 4</span>)</span> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>75</sub></font> <a href="scmpds_2.html#K2">.</a> <span class="p1">(<span class="default"><a href="scmp_gcd.html#K1">intpos</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">c<sub>76</sub></font> <a href="nat_1.html#K1">+</a> <span class="p4">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> &amp; ( for <font color="Olive">b<sub>1</sub></font> being  <a href="nat_1.html#NM1">Nat</a> st <font color="Olive">b<sub>1</sub></font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> 2 &amp; <font color="Olive">b<sub>1</sub></font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> 4 holds <br/><span class="p1">(<span class="default"><a href="scmpds_4.html#K9">IExec</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a> ,2 <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p4">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span></span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p3">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a> ,4 <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p4">(<span class="default"><span class="p5">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span>,<font color="Maroon">c<sub>75</sub></font></span>)</span> <a href="scmpds_2.html#K2">.</a> <span class="p1">(<span class="default"><a href="scmp_gcd.html#K1">intpos</a> <font color="Olive">b<sub>1</sub></font></span>)</span> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>75</sub></font> <a href="scmpds_2.html#K2">.</a> <span class="p1">(<span class="default"><a href="scmp_gcd.html#K1">intpos</a> <font color="Olive">b<sub>1</sub></font></span>)</span> ) )
 
<b>by </b><i><a class="txt" href="scpqsort.html#E12:46"><i><font color="Green">E52</font></i></a></i>;<br/>
<a NAME="E3:46_6"/>
<span class="p1">(<span class="default"><a href="scmpds_4.html#K9">IExec</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a> ,2 <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p4">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span></span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p3">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a> ,4 <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p4">(<span class="default"><span class="p5">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span>,<font color="Maroon">c<sub>75</sub></font></span>)</span> <a href="scmpds_2.html#K2">.</a> <a href="scmp_gcd.html#K2">GBP</a>  <a href="hidden.html#R1">=</a> 0
 
<b>by </b><i><a class="txt" href="scpqsort.html#E12:46"><i><font color="Green">E52</font></i></a>, <a class="txt" href="scpqsort.html#E1:46_6"><i><font color="Green">E54</font></i></a>, <a class="ref" href="scmp_gcd.html#D2">SCMP_GCD:def 2</a></i>;<br/>
<a NAME="E4:46_6"/><b>then </b>
( <font color="Maroon">c<sub>50</sub></font> <a href="scmpds_6.html#R1">is_closed_on</a>  <a href="scmpds_4.html#K9">IExec</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a> ,2 <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p3">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span></span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p2">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a> ,4 <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span>,<font color="Maroon">c<sub>75</sub></font> &amp; <font color="Maroon">c<sub>50</sub></font> <a href="scmpds_6.html#R2">is_halting_on</a>  <a href="scmpds_4.html#K9">IExec</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a> ,2 <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p3">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span></span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p2">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a> ,4 <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span>,<font color="Maroon">c<sub>75</sub></font> )
 
<b>by </b><i><a class="txt" href="scpqsort.html#E5:46"><i><font color="Green">E46</font></i></a>, <a class="txt" href="scpqsort.html#E1:46_6"><i><font color="Green">E54</font></i></a>, <a class="txt" href="scpqsort.html#E2:46_6"><i><font color="Green">E55</font></i></a>, <a class="ref" href="scpqsort.html#T13" target="_self">Th13</a></i>;<br/>
<a NAME="E5:46_6"/><b>then </b>
( <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a> ,2 <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p3">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span></span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p2">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a> ,4 <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span> <a href="scmpds_4.html#K3">';'</a> <font color="Maroon">c<sub>50</sub></font> <a href="scmpds_6.html#R1">is_closed_on</a> <font color="Maroon">c<sub>75</sub></font> &amp; <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a> ,2 <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p3">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span></span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p2">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a> ,4 <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span> <a href="scmpds_4.html#K3">';'</a> <font color="Maroon">c<sub>50</sub></font> <a href="scmpds_6.html#R2">is_halting_on</a> <font color="Maroon">c<sub>75</sub></font> )
 
<b>by </b><i><a class="ref" href="scpisort.html#T10">SCPISORT:10</a></i>;<br/>
<b>hence </b><a NAME="E6:46_6"/>
( <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a> ,2 <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p4">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span></span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p3">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a> ,4 <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p4">(<span class="default"><span class="p5">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span> <a href="scmpds_4.html#K3">';'</a> <font color="Maroon">c<sub>50</sub></font></span>)</span> <a href="scmpds_4.html#K3">';'</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><span class="p0">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a> ,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 3</span>)</span> <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p0">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a> ,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span> <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K2">GBP</a> ,4</span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p5">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a> ,<span class="p0">(<span class="default"><span class="p1">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 2</span>)</span> <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K2">GBP</a> ,4</span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p4">(<span class="default"><a href="scmpds_2.html#K12">AddTo</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p5">(<span class="default"><span class="p0">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span>,<span class="p5">(<span class="default"><a href="xcmplx_0.html#K4">-</a> 1</span>)</span></span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p3">(<span class="default"><a href="scmpds_2.html#K12">AddTo</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p4">(<span class="default"><span class="p5">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 2</span>)</span>,1</span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p2">(<span class="default"><a href="scmpds_2.html#K12">AddTo</a> <a href="scmp_gcd.html#K2">GBP</a> ,1,2</span>)</span></span>)</span> <a href="scmpds_6.html#R1">is_closed_on</a> <font color="Maroon">c<sub>75</sub></font> &amp; <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a> ,2 <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p4">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span></span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p3">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a> ,4 <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p4">(<span class="default"><span class="p5">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span> <a href="scmpds_4.html#K3">';'</a> <font color="Maroon">c<sub>50</sub></font></span>)</span> <a href="scmpds_4.html#K3">';'</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><span class="p0">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a> ,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 3</span>)</span> <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p0">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a> ,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span> <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K2">GBP</a> ,4</span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p5">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a> ,<span class="p0">(<span class="default"><span class="p1">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 2</span>)</span> <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K2">GBP</a> ,4</span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p4">(<span class="default"><a href="scmpds_2.html#K12">AddTo</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p5">(<span class="default"><span class="p0">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span>,<span class="p5">(<span class="default"><a href="xcmplx_0.html#K4">-</a> 1</span>)</span></span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p3">(<span class="default"><a href="scmpds_2.html#K12">AddTo</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p4">(<span class="default"><span class="p5">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 2</span>)</span>,1</span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p2">(<span class="default"><a href="scmpds_2.html#K12">AddTo</a> <a href="scmp_gcd.html#K2">GBP</a> ,1,2</span>)</span></span>)</span> <a href="scmpds_6.html#R2">is_halting_on</a> <font color="Maroon">c<sub>75</sub></font> )
 <b>by </b><i><a class="ref" href="scpisort.html#T9">SCPISORT:9</a></i>;<br/>


</div><b>end;</b></div>
<a NAME="E14:46"/><i><font color="Green">E54</font></i>: 
for <font color="Olive">b<sub>1</sub></font> being  <a href="ami_1.html#NM4">State</a> of <a href="scmpds_2.html#K1">SCMPDS</a> <br/>for <font color="Olive">b<sub>2</sub></font>, <font color="Olive">b<sub>3</sub></font>, <font color="Olive">b<sub>4</sub></font> being  <a href="nat_1.html#NM1">Nat</a><br/>for <font color="Olive">b<sub>5</sub></font> being  <a href="int_1.html#NM1">Integer</a><br/>for <font color="Olive">b<sub>6</sub></font>, <font color="Olive">b<sub>7</sub></font> being   <a href="finseq_1.html#M2">FinSequence</a> of  <a href="numbers.html#K4">INT</a>  st <font color="Olive">b<sub>1</sub></font> <a href="scmpds_2.html#K2">.</a> <a href="scmp_gcd.html#K2">GBP</a>  <a href="hidden.html#R1">=</a> 0 &amp; <font color="Olive">b<sub>1</sub></font> <a href="scmpds_2.html#K2">.</a> <a href="scmp_gcd.html#K3">SBP</a>  <a href="hidden.html#R1">=</a> <font color="Olive">b<sub>3</sub></font> &amp; <font color="Olive">b<sub>3</sub></font> <a href="hidden.html#R1">=</a> <font color="Olive">b<sub>2</sub></font> <a href="nat_1.html#K1">+</a> 1 &amp; <font color="Olive">b<sub>1</sub></font> <a href="scmpds_2.html#K2">.</a> <span class="p1">(<span class="default"><a href="scmp_gcd.html#K1">intpos</a> <span class="p2">(<span class="default"><font color="Olive">b<sub>3</sub></font> <a href="nat_1.html#K1">+</a> <span class="p3">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span></span>)</span></span>)</span> <a href="hidden.html#R1">=</a> <font color="Olive">b<sub>4</sub></font> &amp; <font color="Olive">b<sub>4</sub></font> <a href="xxreal_0.html#NR2" target="_self">&gt;=</a> <font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> 1 &amp; <font color="Olive">b<sub>5</sub></font> <a href="hidden.html#R1">=</a> <font color="Olive">b<sub>1</sub></font> <a href="scmpds_2.html#K2">.</a> <span class="p1">(<span class="default"><a href="scmp_gcd.html#K1">intpos</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Olive">b<sub>3</sub></font> <a href="nat_1.html#K1">+</a> <span class="p4">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> &amp; <font color="Olive">b<sub>5</sub></font> <a href="xcmplx_0.html#K6">-</a> <font color="Olive">b<sub>4</sub></font> <a href="xxreal_0.html#NR4" target="_self">&gt;</a> 0 &amp; <font color="Olive">b<sub>5</sub></font> <a href="xxreal_0.html#R1">&lt;=</a> <font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font> &amp; <font color="Olive">b<sub>6</sub></font> <a href="scpisort.html#R1">is_FinSequence_on</a> <font color="Olive">b<sub>1</sub></font>,<font color="Maroon">c<sub>48</sub></font> &amp;  <a href="finseq_1.html#K3">len</a> <font color="Olive">b<sub>6</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>49</sub></font> &amp; <font color="Olive">b<sub>7</sub></font> <a href="scpisort.html#R1">is_FinSequence_on</a>  <a href="scmpds_4.html#K9">IExec</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a> ,2 <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p5">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span></span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p4">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a> ,4 <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p5">(<span class="default"><span class="p0">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span> <a href="scmpds_4.html#K3">';'</a> <font color="Maroon">c<sub>50</sub></font></span>)</span> <a href="scmpds_4.html#K3">';'</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><span class="p0">(<span class="default"><span class="p1">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a> ,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 3</span>)</span> <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p1">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a> ,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span> <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K2">GBP</a> ,4</span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p0">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a> ,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 2</span>)</span> <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K2">GBP</a> ,4</span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p5">(<span class="default"><a href="scmpds_2.html#K12">AddTo</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p0">(<span class="default"><span class="p1">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span>,<span class="p0">(<span class="default"><a href="xcmplx_0.html#K4">-</a> 1</span>)</span></span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p4">(<span class="default"><a href="scmpds_2.html#K12">AddTo</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p5">(<span class="default"><span class="p0">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 2</span>)</span>,1</span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p3">(<span class="default"><a href="scmpds_2.html#K12">AddTo</a> <a href="scmp_gcd.html#K2">GBP</a> ,1,2</span>)</span></span>)</span></span>)</span>,<font color="Olive">b<sub>1</sub></font>,<font color="Maroon">c<sub>48</sub></font> &amp;  <a href="finseq_1.html#K3">len</a> <font color="Olive">b<sub>7</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>49</sub></font> holds <br/>( <span class="p1">(<span class="default"><a href="scmpds_4.html#K9">IExec</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a> ,2 <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p0">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span></span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p5">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a> ,4 <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p0">(<span class="default"><span class="p1">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span> <a href="scmpds_4.html#K3">';'</a> <font color="Maroon">c<sub>50</sub></font></span>)</span> <a href="scmpds_4.html#K3">';'</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><span class="p0">(<span class="default"><span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a> ,<span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 3</span>)</span> <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p2">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a> ,<span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span> <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K2">GBP</a> ,4</span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p1">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a> ,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 2</span>)</span> <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K2">GBP</a> ,4</span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p0">(<span class="default"><a href="scmpds_2.html#K12">AddTo</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span>,<span class="p1">(<span class="default"><a href="xcmplx_0.html#K4">-</a> 1</span>)</span></span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p5">(<span class="default"><a href="scmpds_2.html#K12">AddTo</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p0">(<span class="default"><span class="p1">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 2</span>)</span>,1</span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p4">(<span class="default"><a href="scmpds_2.html#K12">AddTo</a> <a href="scmp_gcd.html#K2">GBP</a> ,1,2</span>)</span></span>)</span></span>)</span>,<font color="Olive">b<sub>1</sub></font></span>)</span> <a href="scmpds_2.html#K2">.</a> <a href="scmp_gcd.html#K2">GBP</a>  <a href="hidden.html#R1">=</a> 0 &amp; <span class="p1">(<span class="default"><a href="scmpds_4.html#K9">IExec</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a> ,2 <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p0">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span></span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p5">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a> ,4 <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p0">(<span class="default"><span class="p1">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span> <a href="scmpds_4.html#K3">';'</a> <font color="Maroon">c<sub>50</sub></font></span>)</span> <a href="scmpds_4.html#K3">';'</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><span class="p0">(<span class="default"><span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a> ,<span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 3</span>)</span> <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p2">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a> ,<span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span> <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K2">GBP</a> ,4</span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p1">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a> ,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 2</span>)</span> <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K2">GBP</a> ,4</span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p0">(<span class="default"><a href="scmpds_2.html#K12">AddTo</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span>,<span class="p1">(<span class="default"><a href="xcmplx_0.html#K4">-</a> 1</span>)</span></span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p5">(<span class="default"><a href="scmpds_2.html#K12">AddTo</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p0">(<span class="default"><span class="p1">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 2</span>)</span>,1</span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p4">(<span class="default"><a href="scmpds_2.html#K12">AddTo</a> <a href="scmp_gcd.html#K2">GBP</a> ,1,2</span>)</span></span>)</span></span>)</span>,<font color="Olive">b<sub>1</sub></font></span>)</span> <a href="scmpds_2.html#K2">.</a> <span class="p1">(<span class="default"><a href="scmp_gcd.html#K1">intpos</a> 1</span>)</span> <a href="hidden.html#R1">=</a> <font color="Olive">b<sub>3</sub></font> <a href="nat_1.html#K1">+</a> 2 &amp; <font color="Olive">b<sub>4</sub></font> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><a href="scmpds_4.html#K9">IExec</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a> ,2 <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p0">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span></span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p5">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a> ,4 <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p0">(<span class="default"><span class="p1">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span> <a href="scmpds_4.html#K3">';'</a> <font color="Maroon">c<sub>50</sub></font></span>)</span> <a href="scmpds_4.html#K3">';'</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><span class="p0">(<span class="default"><span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a> ,<span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 3</span>)</span> <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p2">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a> ,<span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span> <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K2">GBP</a> ,4</span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p1">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a> ,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 2</span>)</span> <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K2">GBP</a> ,4</span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p0">(<span class="default"><a href="scmpds_2.html#K12">AddTo</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span>,<span class="p1">(<span class="default"><a href="xcmplx_0.html#K4">-</a> 1</span>)</span></span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p5">(<span class="default"><a href="scmpds_2.html#K12">AddTo</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p0">(<span class="default"><span class="p1">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 2</span>)</span>,1</span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p4">(<span class="default"><a href="scmpds_2.html#K12">AddTo</a> <a href="scmp_gcd.html#K2">GBP</a> ,1,2</span>)</span></span>)</span></span>)</span>,<font color="Olive">b<sub>1</sub></font></span>)</span> <a href="scmpds_2.html#K2">.</a> <span class="p1">(<span class="default"><a href="scmp_gcd.html#K1">intpos</a> <span class="p2">(<span class="default"><font color="Olive">b<sub>3</sub></font> <a href="nat_1.html#K1">+</a> <span class="p3">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span></span>)</span></span>)</span> &amp; <font color="Olive">b<sub>5</sub></font> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><a href="scmpds_4.html#K9">IExec</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a> ,2 <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p0">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span></span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p5">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a> ,4 <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p0">(<span class="default"><span class="p1">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span> <a href="scmpds_4.html#K3">';'</a> <font color="Maroon">c<sub>50</sub></font></span>)</span> <a href="scmpds_4.html#K3">';'</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><span class="p0">(<span class="default"><span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a> ,<span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 3</span>)</span> <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p2">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a> ,<span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span> <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K2">GBP</a> ,4</span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p1">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a> ,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 2</span>)</span> <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K2">GBP</a> ,4</span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p0">(<span class="default"><a href="scmpds_2.html#K12">AddTo</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span>,<span class="p1">(<span class="default"><a href="xcmplx_0.html#K4">-</a> 1</span>)</span></span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p5">(<span class="default"><a href="scmpds_2.html#K12">AddTo</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p0">(<span class="default"><span class="p1">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 2</span>)</span>,1</span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p4">(<span class="default"><a href="scmpds_2.html#K12">AddTo</a> <a href="scmp_gcd.html#K2">GBP</a> ,1,2</span>)</span></span>)</span></span>)</span>,<font color="Olive">b<sub>1</sub></font></span>)</span> <a href="scmpds_2.html#K2">.</a> <span class="p1">(<span class="default"><a href="scmp_gcd.html#K1">intpos</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Olive">b<sub>3</sub></font> <a href="nat_1.html#K1">+</a> <span class="p4">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span></span>)</span> <a href="nat_1.html#K1">+</a> 3</span>)</span></span>)</span> &amp; ( for <font color="Olive">b<sub>8</sub></font> being  <a href="nat_1.html#NM1">Nat</a> st 1 <a href="xxreal_0.html#R1">&lt;=</a> <font color="Olive">b<sub>8</sub></font> &amp; <font color="Olive">b<sub>8</sub></font> <a href="xxreal_0.html#NR3" target="_self">&lt;</a> <font color="Olive">b<sub>3</sub></font> holds <br/><span class="p1">(<span class="default"><a href="scmpds_4.html#K9">IExec</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a> ,2 <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p0">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span></span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p5">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a> ,4 <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p0">(<span class="default"><span class="p1">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span> <a href="scmpds_4.html#K3">';'</a> <font color="Maroon">c<sub>50</sub></font></span>)</span> <a href="scmpds_4.html#K3">';'</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><span class="p0">(<span class="default"><span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a> ,<span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 3</span>)</span> <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p2">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a> ,<span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span> <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K2">GBP</a> ,4</span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p1">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a> ,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 2</span>)</span> <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K2">GBP</a> ,4</span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p0">(<span class="default"><a href="scmpds_2.html#K12">AddTo</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span>,<span class="p1">(<span class="default"><a href="xcmplx_0.html#K4">-</a> 1</span>)</span></span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p5">(<span class="default"><a href="scmpds_2.html#K12">AddTo</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p0">(<span class="default"><span class="p1">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 2</span>)</span>,1</span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p4">(<span class="default"><a href="scmpds_2.html#K12">AddTo</a> <a href="scmp_gcd.html#K2">GBP</a> ,1,2</span>)</span></span>)</span></span>)</span>,<font color="Olive">b<sub>1</sub></font></span>)</span> <a href="scmpds_2.html#K2">.</a> <span class="p1">(<span class="default"><a href="scmp_gcd.html#K1">intpos</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> <font color="Olive">b<sub>8</sub></font></span>)</span></span>)</span> <a href="hidden.html#R1">=</a> <font color="Olive">b<sub>1</sub></font> <a href="scmpds_2.html#K2">.</a> <span class="p1">(<span class="default"><a href="scmp_gcd.html#K1">intpos</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> <font color="Olive">b<sub>8</sub></font></span>)</span></span>)</span> ) &amp; <font color="Olive">b<sub>6</sub></font>,<font color="Olive">b<sub>7</sub></font> <a href="rfinseq.html#R1">are_fiberwise_equipotent</a>  &amp; ex <font color="Olive">b<sub>8</sub></font> being  <a href="nat_1.html#NM1">Nat</a> st <br/>( <font color="Olive">b<sub>4</sub></font> <a href="xxreal_0.html#R1">&lt;=</a> <font color="Olive">b<sub>8</sub></font> &amp; <font color="Olive">b<sub>8</sub></font> <a href="xxreal_0.html#R1">&lt;=</a> <font color="Olive">b<sub>5</sub></font> &amp; <font color="Olive">b<sub>8</sub></font> <a href="xcmplx_0.html#K6">-</a> 1 <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><a href="scmpds_4.html#K9">IExec</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a> ,2 <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p0">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span></span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p5">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a> ,4 <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p0">(<span class="default"><span class="p1">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span> <a href="scmpds_4.html#K3">';'</a> <font color="Maroon">c<sub>50</sub></font></span>)</span> <a href="scmpds_4.html#K3">';'</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><span class="p0">(<span class="default"><span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a> ,<span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 3</span>)</span> <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p2">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a> ,<span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span> <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K2">GBP</a> ,4</span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p1">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a> ,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 2</span>)</span> <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K2">GBP</a> ,4</span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p0">(<span class="default"><a href="scmpds_2.html#K12">AddTo</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span>,<span class="p1">(<span class="default"><a href="xcmplx_0.html#K4">-</a> 1</span>)</span></span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p5">(<span class="default"><a href="scmpds_2.html#K12">AddTo</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p0">(<span class="default"><span class="p1">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 2</span>)</span>,1</span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p4">(<span class="default"><a href="scmpds_2.html#K12">AddTo</a> <a href="scmp_gcd.html#K2">GBP</a> ,1,2</span>)</span></span>)</span></span>)</span>,<font color="Olive">b<sub>1</sub></font></span>)</span> <a href="scmpds_2.html#K2">.</a> <span class="p1">(<span class="default"><a href="scmp_gcd.html#K1">intpos</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Olive">b<sub>3</sub></font> <a href="nat_1.html#K1">+</a> <span class="p4">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> &amp; <font color="Olive">b<sub>8</sub></font> <a href="nat_1.html#K1">+</a> 1 <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><a href="scmpds_4.html#K9">IExec</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a> ,2 <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p0">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span></span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p5">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a> ,4 <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p0">(<span class="default"><span class="p1">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span> <a href="scmpds_4.html#K3">';'</a> <font color="Maroon">c<sub>50</sub></font></span>)</span> <a href="scmpds_4.html#K3">';'</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><span class="p0">(<span class="default"><span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a> ,<span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 3</span>)</span> <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p2">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a> ,<span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span> <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K2">GBP</a> ,4</span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p1">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a> ,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 2</span>)</span> <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K2">GBP</a> ,4</span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p0">(<span class="default"><a href="scmpds_2.html#K12">AddTo</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span>,<span class="p1">(<span class="default"><a href="xcmplx_0.html#K4">-</a> 1</span>)</span></span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p5">(<span class="default"><a href="scmpds_2.html#K12">AddTo</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p0">(<span class="default"><span class="p1">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 2</span>)</span>,1</span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p4">(<span class="default"><a href="scmpds_2.html#K12">AddTo</a> <a href="scmp_gcd.html#K2">GBP</a> ,1,2</span>)</span></span>)</span></span>)</span>,<font color="Olive">b<sub>1</sub></font></span>)</span> <a href="scmpds_2.html#K2">.</a> <span class="p1">(<span class="default"><a href="scmp_gcd.html#K1">intpos</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Olive">b<sub>3</sub></font> <a href="nat_1.html#K1">+</a> <span class="p4">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span></span>)</span> <a href="nat_1.html#K1">+</a> 2</span>)</span></span>)</span> &amp; ( for <font color="Olive">b<sub>9</sub></font> being  <a href="nat_1.html#NM1">Nat</a> st <font color="Olive">b<sub>4</sub></font> <a href="xxreal_0.html#R1">&lt;=</a> <font color="Olive">b<sub>9</sub></font> &amp; <font color="Olive">b<sub>9</sub></font> <a href="xxreal_0.html#NR3" target="_self">&lt;</a> <font color="Olive">b<sub>8</sub></font> holds <br/><span class="p1">(<span class="default"><a href="scmpds_4.html#K9">IExec</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a> ,2 <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p0">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span></span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p5">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a> ,4 <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p0">(<span class="default"><span class="p1">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span> <a href="scmpds_4.html#K3">';'</a> <font color="Maroon">c<sub>50</sub></font></span>)</span> <a href="scmpds_4.html#K3">';'</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><span class="p0">(<span class="default"><span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a> ,<span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 3</span>)</span> <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p2">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a> ,<span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span> <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K2">GBP</a> ,4</span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p1">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a> ,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 2</span>)</span> <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K2">GBP</a> ,4</span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p0">(<span class="default"><a href="scmpds_2.html#K12">AddTo</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span>,<span class="p1">(<span class="default"><a href="xcmplx_0.html#K4">-</a> 1</span>)</span></span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p5">(<span class="default"><a href="scmpds_2.html#K12">AddTo</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p0">(<span class="default"><span class="p1">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 2</span>)</span>,1</span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p4">(<span class="default"><a href="scmpds_2.html#K12">AddTo</a> <a href="scmp_gcd.html#K2">GBP</a> ,1,2</span>)</span></span>)</span></span>)</span>,<font color="Olive">b<sub>1</sub></font></span>)</span> <a href="scmpds_2.html#K2">.</a> <span class="p1">(<span class="default"><a href="scmp_gcd.html#K1">intpos</a> <font color="Olive">b<sub>8</sub></font></span>)</span> <a href="xxreal_0.html#NR2" target="_self">&gt;=</a> <span class="p1">(<span class="default"><a href="scmpds_4.html#K9">IExec</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a> ,2 <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p0">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span></span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p5">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a> ,4 <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p0">(<span class="default"><span class="p1">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span> <a href="scmpds_4.html#K3">';'</a> <font color="Maroon">c<sub>50</sub></font></span>)</span> <a href="scmpds_4.html#K3">';'</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><span class="p0">(<span class="default"><span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a> ,<span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 3</span>)</span> <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p2">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a> ,<span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span> <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K2">GBP</a> ,4</span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p1">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a> ,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 2</span>)</span> <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K2">GBP</a> ,4</span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p0">(<span class="default"><a href="scmpds_2.html#K12">AddTo</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span>,<span class="p1">(<span class="default"><a href="xcmplx_0.html#K4">-</a> 1</span>)</span></span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p5">(<span class="default"><a href="scmpds_2.html#K12">AddTo</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p0">(<span class="default"><span class="p1">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 2</span>)</span>,1</span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p4">(<span class="default"><a href="scmpds_2.html#K12">AddTo</a> <a href="scmp_gcd.html#K2">GBP</a> ,1,2</span>)</span></span>)</span></span>)</span>,<font color="Olive">b<sub>1</sub></font></span>)</span> <a href="scmpds_2.html#K2">.</a> <span class="p1">(<span class="default"><a href="scmp_gcd.html#K1">intpos</a> <font color="Olive">b<sub>9</sub></font></span>)</span> ) &amp; ( for <font color="Olive">b<sub>9</sub></font> being  <a href="nat_1.html#NM1">Nat</a> st <font color="Olive">b<sub>8</sub></font> <a href="xxreal_0.html#NR3" target="_self">&lt;</a> <font color="Olive">b<sub>9</sub></font> &amp; <font color="Olive">b<sub>9</sub></font> <a href="xxreal_0.html#R1">&lt;=</a> <font color="Olive">b<sub>5</sub></font> holds <br/><span class="p1">(<span class="default"><a href="scmpds_4.html#K9">IExec</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a> ,2 <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p0">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span></span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p5">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a> ,4 <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p0">(<span class="default"><span class="p1">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span> <a href="scmpds_4.html#K3">';'</a> <font color="Maroon">c<sub>50</sub></font></span>)</span> <a href="scmpds_4.html#K3">';'</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><span class="p0">(<span class="default"><span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a> ,<span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 3</span>)</span> <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p2">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a> ,<span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span> <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K2">GBP</a> ,4</span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p1">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a> ,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 2</span>)</span> <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K2">GBP</a> ,4</span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p0">(<span class="default"><a href="scmpds_2.html#K12">AddTo</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span>,<span class="p1">(<span class="default"><a href="xcmplx_0.html#K4">-</a> 1</span>)</span></span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p5">(<span class="default"><a href="scmpds_2.html#K12">AddTo</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p0">(<span class="default"><span class="p1">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 2</span>)</span>,1</span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p4">(<span class="default"><a href="scmpds_2.html#K12">AddTo</a> <a href="scmp_gcd.html#K2">GBP</a> ,1,2</span>)</span></span>)</span></span>)</span>,<font color="Olive">b<sub>1</sub></font></span>)</span> <a href="scmpds_2.html#K2">.</a> <span class="p1">(<span class="default"><a href="scmp_gcd.html#K1">intpos</a> <font color="Olive">b<sub>8</sub></font></span>)</span> <a href="xxreal_0.html#R1">&lt;=</a> <span class="p1">(<span class="default"><a href="scmpds_4.html#K9">IExec</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a> ,2 <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p0">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span></span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p5">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a> ,4 <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p0">(<span class="default"><span class="p1">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span> <a href="scmpds_4.html#K3">';'</a> <font color="Maroon">c<sub>50</sub></font></span>)</span> <a href="scmpds_4.html#K3">';'</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><span class="p0">(<span class="default"><span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a> ,<span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 3</span>)</span> <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p2">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a> ,<span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span> <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K2">GBP</a> ,4</span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p1">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a> ,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 2</span>)</span> <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K2">GBP</a> ,4</span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p0">(<span class="default"><a href="scmpds_2.html#K12">AddTo</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span>,<span class="p1">(<span class="default"><a href="xcmplx_0.html#K4">-</a> 1</span>)</span></span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p5">(<span class="default"><a href="scmpds_2.html#K12">AddTo</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p0">(<span class="default"><span class="p1">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 2</span>)</span>,1</span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p4">(<span class="default"><a href="scmpds_2.html#K12">AddTo</a> <a href="scmp_gcd.html#K2">GBP</a> ,1,2</span>)</span></span>)</span></span>)</span>,<font color="Olive">b<sub>1</sub></font></span>)</span> <a href="scmpds_2.html#K2">.</a> <span class="p1">(<span class="default"><a href="scmp_gcd.html#K1">intpos</a> <font color="Olive">b<sub>9</sub></font></span>)</span> ) &amp; ( for <font color="Olive">b<sub>9</sub></font> being  <a href="nat_1.html#NM1">Nat</a> st ( ( <font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> 1 <a href="xxreal_0.html#R1">&lt;=</a> <font color="Olive">b<sub>9</sub></font> &amp; <font color="Olive">b<sub>9</sub></font> <a href="xxreal_0.html#NR3" target="_self">&lt;</a> <font color="Olive">b<sub>4</sub></font> ) or ( <font color="Olive">b<sub>5</sub></font> <a href="xxreal_0.html#NR3" target="_self">&lt;</a> <font color="Olive">b<sub>9</sub></font> &amp; <font color="Olive">b<sub>9</sub></font> <a href="xxreal_0.html#R1">&lt;=</a> <font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font> ) ) holds <br/><span class="p1">(<span class="default"><a href="scmpds_4.html#K9">IExec</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a> ,2 <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p0">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span></span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p5">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a> ,4 <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p0">(<span class="default"><span class="p1">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span> <a href="scmpds_4.html#K3">';'</a> <font color="Maroon">c<sub>50</sub></font></span>)</span> <a href="scmpds_4.html#K3">';'</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><span class="p0">(<span class="default"><span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a> ,<span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 3</span>)</span> <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p2">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a> ,<span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span> <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K2">GBP</a> ,4</span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p1">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a> ,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 2</span>)</span> <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K2">GBP</a> ,4</span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p0">(<span class="default"><a href="scmpds_2.html#K12">AddTo</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span>,<span class="p1">(<span class="default"><a href="xcmplx_0.html#K4">-</a> 1</span>)</span></span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p5">(<span class="default"><a href="scmpds_2.html#K12">AddTo</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p0">(<span class="default"><span class="p1">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 2</span>)</span>,1</span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p4">(<span class="default"><a href="scmpds_2.html#K12">AddTo</a> <a href="scmp_gcd.html#K2">GBP</a> ,1,2</span>)</span></span>)</span></span>)</span>,<font color="Olive">b<sub>1</sub></font></span>)</span> <a href="scmpds_2.html#K2">.</a> <span class="p1">(<span class="default"><a href="scmp_gcd.html#K1">intpos</a> <font color="Olive">b<sub>9</sub></font></span>)</span> <a href="hidden.html#R1">=</a> <font color="Olive">b<sub>1</sub></font> <a href="scmpds_2.html#K2">.</a> <span class="p1">(<span class="default"><a href="scmp_gcd.html#K1">intpos</a> <font color="Olive">b<sub>9</sub></font></span>)</span> ) ) )
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="46_7"><b>proof </b></a><div class="add">

<b>let </b><font color="Maroon">c<sub>75</sub></font> be   <a href="ami_1.html#NM4">State</a> of <a href="scmpds_2.html#K1">SCMPDS</a> ;<br/><b>let </b><font color="Maroon">c<sub>76</sub></font>, <font color="Maroon">c<sub>77</sub></font>, <font color="Maroon">c<sub>78</sub></font> be   <a href="nat_1.html#NM1">Nat</a>;<br/><b>let </b><font color="Maroon">c<sub>79</sub></font> be   <a href="int_1.html#NM1">Integer</a>;<br/><b>let </b><font color="Maroon">c<sub>80</sub></font>, <font color="Maroon">c<sub>81</sub></font> be    <a href="finseq_1.html#M2">FinSequence</a> of  <a href="numbers.html#K4">INT</a> ;<br/>







<b>set </b><font color="Maroon">c<sub>82</sub></font> =  <a href="scmpds_4.html#K9">IExec</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a> ,2 <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p5">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span></span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p4">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a> ,4 <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p5">(<span class="default"><span class="p0">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span> <a href="scmpds_4.html#K3">';'</a> <font color="Maroon">c<sub>50</sub></font></span>)</span> <a href="scmpds_4.html#K3">';'</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><span class="p0">(<span class="default"><span class="p1">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a> ,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 3</span>)</span> <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p1">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a> ,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span> <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K2">GBP</a> ,4</span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p0">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a> ,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 2</span>)</span> <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K2">GBP</a> ,4</span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p5">(<span class="default"><a href="scmpds_2.html#K12">AddTo</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p0">(<span class="default"><span class="p1">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span>,<span class="p0">(<span class="default"><a href="xcmplx_0.html#K4">-</a> 1</span>)</span></span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p4">(<span class="default"><a href="scmpds_2.html#K12">AddTo</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p5">(<span class="default"><span class="p0">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 2</span>)</span>,1</span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p3">(<span class="default"><a href="scmpds_2.html#K12">AddTo</a> <a href="scmp_gcd.html#K2">GBP</a> ,1,2</span>)</span></span>)</span></span>)</span>,<font color="Maroon">c<sub>75</sub></font>;<br/>
<b>set </b><font color="Maroon">c<sub>83</sub></font> = <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a> ,2 <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p3">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span></span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p2">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a> ,4 <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span> <a href="scmpds_4.html#K3">';'</a> <font color="Maroon">c<sub>50</sub></font>;<br/>
<b>set </b><font color="Maroon">c<sub>84</sub></font> =  <a href="scmpds_4.html#K9">IExec</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a> ,2 <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p4">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span></span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p3">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a> ,4 <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p4">(<span class="default"><span class="p5">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span> <a href="scmpds_4.html#K3">';'</a> <font color="Maroon">c<sub>50</sub></font></span>)</span>,<font color="Maroon">c<sub>75</sub></font>;<br/>
<b>set </b><font color="Maroon">c<sub>85</sub></font> =  <a href="scmpds_4.html#K9">IExec</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a> ,2 <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p3">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span></span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p2">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a> ,4 <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span>,<font color="Maroon">c<sub>75</sub></font>;<br/>
<b>set </b><font color="Maroon">c<sub>86</sub></font> = <font color="Maroon">c<sub>77</sub></font> <a href="nat_1.html#K1">+</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span>;<br/>
<b>set </b><font color="Maroon">c<sub>87</sub></font> =  <a href="scmpds_4.html#K9">IExec</a> <font color="Maroon">c<sub>50</sub></font>,<span class="p1">(<span class="default"><a href="scmpds_4.html#K9">IExec</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a> ,2 <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p4">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span></span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p3">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a> ,4 <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p4">(<span class="default"><span class="p5">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span>,<font color="Maroon">c<sub>75</sub></font></span>)</span>;<br/>
<b>assume </b><a NAME="E1:46_7"/><i><font color="Green">E55</font></i>: 
( <font color="Maroon">c<sub>75</sub></font> <a href="scmpds_2.html#K2">.</a> <a href="scmp_gcd.html#K2">GBP</a>  <a href="hidden.html#R1">=</a> 0 &amp; <font color="Maroon">c<sub>75</sub></font> <a href="scmpds_2.html#K2">.</a> <a href="scmp_gcd.html#K3">SBP</a>  <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>77</sub></font> &amp; <font color="Maroon">c<sub>77</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>76</sub></font> <a href="nat_1.html#K1">+</a> 1 &amp; <font color="Maroon">c<sub>75</sub></font> <a href="scmpds_2.html#K2">.</a> <span class="p1">(<span class="default"><a href="scmp_gcd.html#K1">intpos</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>77</sub></font> <a href="nat_1.html#K1">+</a> <span class="p3">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span></span>)</span></span>)</span> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>78</sub></font> &amp; <font color="Maroon">c<sub>78</sub></font> <a href="xxreal_0.html#NR2" target="_self">&gt;=</a> <font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> 1 &amp; <font color="Maroon">c<sub>79</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>75</sub></font> <a href="scmpds_2.html#K2">.</a> <span class="p1">(<span class="default"><a href="scmp_gcd.html#K1">intpos</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">c<sub>77</sub></font> <a href="nat_1.html#K1">+</a> <span class="p4">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> &amp; <font color="Maroon">c<sub>79</sub></font> <a href="xcmplx_0.html#K6">-</a> <font color="Maroon">c<sub>78</sub></font> <a href="xxreal_0.html#NR4" target="_self">&gt;</a> 0 &amp; <font color="Maroon">c<sub>79</sub></font> <a href="xxreal_0.html#R1">&lt;=</a> <font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font> )
 ;<br/>

<b>assume </b><a NAME="E2:46_7"/><i><font color="Green">E56</font></i>: 
( <font color="Maroon">c<sub>80</sub></font> <a href="scpisort.html#R1">is_FinSequence_on</a> <font color="Maroon">c<sub>75</sub></font>,<font color="Maroon">c<sub>48</sub></font> &amp;  <a href="finseq_1.html#K3">len</a> <font color="Maroon">c<sub>80</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>49</sub></font> )
 ;<br/>

<b>assume </b><a NAME="E3:46_7"/><i><font color="Green">E57</font></i>: 
( <font color="Maroon">c<sub>81</sub></font> <a href="scpisort.html#R1">is_FinSequence_on</a>  <a href="scmpds_4.html#K9">IExec</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a> ,2 <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p5">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span></span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p4">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a> ,4 <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p5">(<span class="default"><span class="p0">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span> <a href="scmpds_4.html#K3">';'</a> <font color="Maroon">c<sub>50</sub></font></span>)</span> <a href="scmpds_4.html#K3">';'</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><span class="p0">(<span class="default"><span class="p1">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a> ,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 3</span>)</span> <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p1">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a> ,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span> <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K2">GBP</a> ,4</span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p0">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a> ,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 2</span>)</span> <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K2">GBP</a> ,4</span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p5">(<span class="default"><a href="scmpds_2.html#K12">AddTo</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p0">(<span class="default"><span class="p1">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span>,<span class="p0">(<span class="default"><a href="xcmplx_0.html#K4">-</a> 1</span>)</span></span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p4">(<span class="default"><a href="scmpds_2.html#K12">AddTo</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p5">(<span class="default"><span class="p0">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 2</span>)</span>,1</span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p3">(<span class="default"><a href="scmpds_2.html#K12">AddTo</a> <a href="scmp_gcd.html#K2">GBP</a> ,1,2</span>)</span></span>)</span></span>)</span>,<font color="Maroon">c<sub>75</sub></font>,<font color="Maroon">c<sub>48</sub></font> &amp;  <a href="finseq_1.html#K3">len</a> <font color="Maroon">c<sub>81</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>49</sub></font> )
 ;<br/>

<a NAME="E4:46_7"/><i><font color="Green">E58</font></i>: 
( <span class="p1">(<span class="default"><a href="scmpds_4.html#K9">IExec</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a> ,2 <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p4">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span></span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p3">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a> ,4 <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p4">(<span class="default"><span class="p5">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span>,<font color="Maroon">c<sub>75</sub></font></span>)</span> <a href="scmpds_2.html#K2">.</a> <span class="p1">(<span class="default"><a href="scmp_gcd.html#K1">intpos</a> 2</span>)</span> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>75</sub></font> <a href="scmpds_2.html#K2">.</a> <span class="p1">(<span class="default"><a href="scmp_gcd.html#K1">intpos</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>77</sub></font> <a href="nat_1.html#K1">+</a> <span class="p3">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span></span>)</span></span>)</span> &amp; <span class="p1">(<span class="default"><a href="scmpds_4.html#K9">IExec</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a> ,2 <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p4">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span></span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p3">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a> ,4 <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p4">(<span class="default"><span class="p5">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span>,<font color="Maroon">c<sub>75</sub></font></span>)</span> <a href="scmpds_2.html#K2">.</a> <span class="p1">(<span class="default"><a href="scmp_gcd.html#K1">intpos</a> 4</span>)</span> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>75</sub></font> <a href="scmpds_2.html#K2">.</a> <span class="p1">(<span class="default"><a href="scmp_gcd.html#K1">intpos</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">c<sub>77</sub></font> <a href="nat_1.html#K1">+</a> <span class="p4">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> &amp; ( for <font color="Olive">b<sub>1</sub></font> being  <a href="nat_1.html#NM1">Nat</a> st <font color="Olive">b<sub>1</sub></font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> 2 &amp; <font color="Olive">b<sub>1</sub></font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> 4 holds <br/><span class="p1">(<span class="default"><a href="scmpds_4.html#K9">IExec</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a> ,2 <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p4">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span></span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p3">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a> ,4 <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p4">(<span class="default"><span class="p5">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span>,<font color="Maroon">c<sub>75</sub></font></span>)</span> <a href="scmpds_2.html#K2">.</a> <span class="p1">(<span class="default"><a href="scmp_gcd.html#K1">intpos</a> <font color="Olive">b<sub>1</sub></font></span>)</span> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>75</sub></font> <a href="scmpds_2.html#K2">.</a> <span class="p1">(<span class="default"><a href="scmp_gcd.html#K1">intpos</a> <font color="Olive">b<sub>1</sub></font></span>)</span> ) )
 
<b>by </b><i><a class="txt" href="scpqsort.html#E12:46"><i><font color="Green">E52</font></i></a>, <a class="txt" href="scpqsort.html#E1:46_7"><i><font color="Green">E55</font></i></a></i>;<br/>
<a NAME="E5:46_7"/><i><font color="Green">E59</font></i>: 
<span class="p1">(<span class="default"><a href="scmpds_4.html#K9">IExec</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a> ,2 <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p4">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span></span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p3">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a> ,4 <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p4">(<span class="default"><span class="p5">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span>,<font color="Maroon">c<sub>75</sub></font></span>)</span> <a href="scmpds_2.html#K2">.</a> <a href="scmp_gcd.html#K2">GBP</a>  <a href="hidden.html#R1">=</a> 0
 
<b>by </b><i><a class="txt" href="scpqsort.html#E12:46"><i><font color="Green">E52</font></i></a>, <a class="txt" href="scpqsort.html#E1:46_7"><i><font color="Green">E55</font></i></a>, <a class="ref" href="scmp_gcd.html#D2">SCMP_GCD:def 2</a></i>;<br/>
<a NAME="E6:46_7"/><i><font color="Green">E60</font></i>: 
<span class="p1">(<span class="default"><a href="scmpds_4.html#K9">IExec</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a> ,2 <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p4">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span></span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p3">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a> ,4 <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p4">(<span class="default"><span class="p5">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span>,<font color="Maroon">c<sub>75</sub></font></span>)</span> <a href="scmpds_2.html#K2">.</a> <span class="p1">(<span class="default"><a href="scmp_gcd.html#K1">intpos</a> 4</span>)</span> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>79</sub></font>
 
<b>by </b><i><a class="txt" href="scpqsort.html#E12:46"><i><font color="Green">E52</font></i></a>, <a class="txt" href="scpqsort.html#E1:46_7"><i><font color="Green">E55</font></i></a></i>;<br/>
<a NAME="E7:46_7"/><i><font color="Green">E61</font></i>: 
<font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> 1 <a href="xxreal_0.html#NR2" target="_self">&gt;=</a> 7 <a href="nat_1.html#K1">+</a> 1
 
<b>by </b><i><a class="txt" href="scpqsort.html#E5:46"><i><font color="Green">E46</font></i></a>, <a class="ref" href="xreal_1.html#T8">XREAL_1:8</a></i>;<br/>
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="46_7_1"><b>now </b></a><div class="add"><b>let </b><font color="Maroon">c<sub>88</sub></font> be   <a href="nat_1.html#NM1">Nat</a>;<br/><b>assume </b><a NAME="E1:46_7_1"/><i><font color="Green">E62</font></i>: 
( 1 <a href="xxreal_0.html#R1">&lt;=</a> <font color="Maroon">c<sub>88</sub></font> &amp; <font color="Maroon">c<sub>88</sub></font> <a href="xxreal_0.html#R1">&lt;=</a>  <a href="finseq_1.html#K3">len</a> <font color="Maroon">c<sub>80</sub></font> )
 ;<br/><a NAME="E2:46_7_1"/><b>then </b>
<font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>88</sub></font> <a href="xxreal_0.html#NR2" target="_self">&gt;=</a> <font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> 1
 <b>by </b><i><a class="ref" href="xreal_1.html#T8">XREAL_1:8</a></i>;<br/><a NAME="E3:46_7_1"/><b>then </b>
<font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>88</sub></font> <a href="xxreal_0.html#NR2" target="_self">&gt;=</a> 8
 <b>by </b><i><a class="txt" href="scpqsort.html#E7:46_7"><i><font color="Green">E61</font></i></a>, <a class="ref" href="xreal_1.html#T2">XREAL_1:2</a></i>;<br/><a NAME="E4:46_7_1"/><b>then </b><i><font color="Green">E63</font></i>: 
( <font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>88</sub></font> <a href="xxreal_0.html#NR4" target="_self">&gt;</a> 2 &amp; <font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>88</sub></font> <a href="xxreal_0.html#NR4" target="_self">&gt;</a> 4 )
 <b>by </b><i><a class="ref" href="xreal_1.html#T2">XREAL_1:2</a></i>;<br/><b>thus </b><font color="Maroon">c<sub>80</sub></font> <a href="funct_1.html#K1">.</a> <font color="Maroon">c<sub>88</sub></font> = 
<font color="Maroon">c<sub>75</sub></font> <a href="scmpds_2.html#K2">.</a> <span class="p1">(<span class="default"><a href="scmp_gcd.html#K1">intpos</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>88</sub></font></span>)</span></span>)</span>
<b>by </b><i><a class="txt" href="scpqsort.html#E2:46_7"><i><font color="Green">E56</font></i></a>, <a class="txt" href="scpqsort.html#E1:46_7_1"><i><font color="Green">E62</font></i></a>, <a class="ref" href="scpisort.html#D1">SCPISORT:def 1</a></i>
<br/>.= 
<span class="p1">(<span class="default"><a href="scmpds_4.html#K9">IExec</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a> ,2 <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p4">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span></span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p3">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a> ,4 <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p4">(<span class="default"><span class="p5">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span>,<font color="Maroon">c<sub>75</sub></font></span>)</span> <a href="scmpds_2.html#K2">.</a> <span class="p1">(<span class="default"><a href="scmp_gcd.html#K1">intpos</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>88</sub></font></span>)</span></span>)</span>
<b>by </b><i><a class="txt" href="scpqsort.html#E12:46"><i><font color="Green">E52</font></i></a>, <a class="txt" href="scpqsort.html#E1:46_7"><i><font color="Green">E55</font></i></a>, <a class="txt" href="scpqsort.html#E4:46_7_1"><i><font color="Green">E63</font></i></a></i>
;<br/></div><b>end;</b></div>
<a NAME="E9:46_7"/><b>then </b><i><font color="Green">E62</font></i>: 
<font color="Maroon">c<sub>80</sub></font> <a href="scpisort.html#R1">is_FinSequence_on</a>  <a href="scmpds_4.html#K9">IExec</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a> ,2 <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p3">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span></span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p2">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a> ,4 <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span>,<font color="Maroon">c<sub>75</sub></font>,<font color="Maroon">c<sub>48</sub></font>
 
<b>by </b><i><a class="ref" href="scpisort.html#D1">SCPISORT:def 1</a></i>;<br/>
<b>consider </b><font color="Maroon">c<sub>88</sub></font> being    <a href="finseq_1.html#M2">FinSequence</a> of  <a href="numbers.html#K4">INT</a> <b> such that </b><br/><a NAME="E11:46_7"/><i><font color="Green">E63</font></i>: 
(  <a href="finseq_1.html#K3">len</a> <font color="Maroon">c<sub>88</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>49</sub></font> &amp; ( for <font color="Olive">b<sub>1</sub></font> being  <a href="nat_1.html#NM1">Nat</a> st 1 <a href="xxreal_0.html#R1">&lt;=</a> <font color="Olive">b<sub>1</sub></font> &amp; <font color="Olive">b<sub>1</sub></font> <a href="xxreal_0.html#R1">&lt;=</a>  <a href="finseq_1.html#K3">len</a> <font color="Maroon">c<sub>88</sub></font> holds <br/><font color="Maroon">c<sub>88</sub></font> <a href="funct_1.html#K1">.</a> <font color="Olive">b<sub>1</sub></font> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><a href="scmpds_4.html#K9">IExec</a> <font color="Maroon">c<sub>50</sub></font>,<span class="p2">(<span class="default"><a href="scmpds_4.html#K9">IExec</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a> ,2 <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p5">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span></span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p4">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a> ,4 <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p5">(<span class="default"><span class="p0">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span>,<font color="Maroon">c<sub>75</sub></font></span>)</span></span>)</span> <a href="scmpds_2.html#K2">.</a> <span class="p1">(<span class="default"><a href="scmp_gcd.html#K1">intpos</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Olive">b<sub>1</sub></font></span>)</span></span>)</span> ) )
 <b>by </b><i><a class="ref" href="scpisort.html#T2">SCPISORT:2</a></i>;<br/>
<a NAME="E12:46_7"/><i><font color="Green">E64</font></i>: 
<font color="Maroon">c<sub>88</sub></font> <a href="scpisort.html#R1">is_FinSequence_on</a>  <a href="scmpds_4.html#K9">IExec</a> <font color="Maroon">c<sub>50</sub></font>,<span class="p1">(<span class="default"><a href="scmpds_4.html#K9">IExec</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a> ,2 <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p4">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span></span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p3">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a> ,4 <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p4">(<span class="default"><span class="p5">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span>,<font color="Maroon">c<sub>75</sub></font></span>)</span>,<font color="Maroon">c<sub>48</sub></font>
 
<b>by </b><i><a class="txt" href="scpqsort.html#E11:46_7"><i><font color="Green">E63</font></i></a>, <a class="ref" href="scpisort.html#D1">SCPISORT:def 1</a></i>;<br/>
<a NAME="E13:46_7"/><b>then </b><i><font color="Green">E65</font></i>: 
( <span class="p1">(<span class="default"><a href="scmpds_4.html#K9">IExec</a> <font color="Maroon">c<sub>50</sub></font>,<span class="p2">(<span class="default"><a href="scmpds_4.html#K9">IExec</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a> ,2 <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p5">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span></span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p4">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a> ,4 <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p5">(<span class="default"><span class="p0">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span>,<font color="Maroon">c<sub>75</sub></font></span>)</span></span>)</span> <a href="scmpds_2.html#K2">.</a> <a href="scmp_gcd.html#K2">GBP</a>  <a href="hidden.html#R1">=</a> 0 &amp; <span class="p1">(<span class="default"><a href="scmpds_4.html#K9">IExec</a> <font color="Maroon">c<sub>50</sub></font>,<span class="p2">(<span class="default"><a href="scmpds_4.html#K9">IExec</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a> ,2 <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p5">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span></span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p4">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a> ,4 <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p5">(<span class="default"><span class="p0">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span>,<font color="Maroon">c<sub>75</sub></font></span>)</span></span>)</span> <a href="scmpds_2.html#K2">.</a> <span class="p1">(<span class="default"><a href="scmp_gcd.html#K1">intpos</a> 1</span>)</span> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><a href="scmpds_4.html#K9">IExec</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a> ,2 <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p4">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span></span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p3">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a> ,4 <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p4">(<span class="default"><span class="p5">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span>,<font color="Maroon">c<sub>75</sub></font></span>)</span> <a href="scmpds_2.html#K2">.</a> <span class="p1">(<span class="default"><a href="scmp_gcd.html#K1">intpos</a> 1</span>)</span> &amp; <font color="Maroon">c<sub>80</sub></font>,<font color="Maroon">c<sub>88</sub></font> <a href="rfinseq.html#R1">are_fiberwise_equipotent</a>  )
 
<b>by </b><i><a class="txt" href="scpqsort.html#E5:46"><i><font color="Green">E46</font></i></a>, <a class="txt" href="scpqsort.html#E1:46_7"><i><font color="Green">E55</font></i></a>, <a class="txt" href="scpqsort.html#E2:46_7"><i><font color="Green">E56</font></i></a>, <a class="txt" href="scpqsort.html#E4:46_7"><i><font color="Green">E58</font></i></a>, <a class="txt" href="scpqsort.html#E5:46_7"><i><font color="Green">E59</font></i></a>, <a class="txt" href="scpqsort.html#E9:46_7"><i><font color="Green">E62</font></i></a>, <a class="txt" href="scpqsort.html#E11:46_7"><i><font color="Green">E63</font></i></a>, <a class="ref" href="scpqsort.html#T14" target="_self">Th14</a></i>;<br/>
<b>consider </b><font color="Maroon">c<sub>89</sub></font> being   <a href="nat_1.html#NM1">Nat</a><b> such that </b><br/><a NAME="E15:46_7"/><i><font color="Green">E66</font></i>: 
( <font color="Maroon">c<sub>89</sub></font> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><a href="scmpds_4.html#K9">IExec</a> <font color="Maroon">c<sub>50</sub></font>,<span class="p2">(<span class="default"><a href="scmpds_4.html#K9">IExec</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a> ,2 <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p5">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span></span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p4">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a> ,4 <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p5">(<span class="default"><span class="p0">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span>,<font color="Maroon">c<sub>75</sub></font></span>)</span></span>)</span> <a href="scmpds_2.html#K2">.</a> <span class="p1">(<span class="default"><a href="scmp_gcd.html#K1">intpos</a> 4</span>)</span> &amp; <font color="Maroon">c<sub>78</sub></font> <a href="xxreal_0.html#R1">&lt;=</a> <font color="Maroon">c<sub>89</sub></font> &amp; <font color="Maroon">c<sub>89</sub></font> <a href="xxreal_0.html#R1">&lt;=</a> <span class="p1">(<span class="default"><a href="scmpds_4.html#K9">IExec</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a> ,2 <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p4">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span></span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p3">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a> ,4 <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p4">(<span class="default"><span class="p5">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span>,<font color="Maroon">c<sub>75</sub></font></span>)</span> <a href="scmpds_2.html#K2">.</a> <span class="p1">(<span class="default"><a href="scmp_gcd.html#K1">intpos</a> 4</span>)</span> &amp; ( for <font color="Olive">b<sub>1</sub></font> being  <a href="nat_1.html#NM1">Nat</a> st <font color="Maroon">c<sub>78</sub></font> <a href="xxreal_0.html#R1">&lt;=</a> <font color="Olive">b<sub>1</sub></font> &amp; <font color="Olive">b<sub>1</sub></font> <a href="xxreal_0.html#NR3" target="_self">&lt;</a> <font color="Maroon">c<sub>89</sub></font> holds <br/><span class="p1">(<span class="default"><a href="scmpds_4.html#K9">IExec</a> <font color="Maroon">c<sub>50</sub></font>,<span class="p2">(<span class="default"><a href="scmpds_4.html#K9">IExec</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a> ,2 <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p5">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span></span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p4">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a> ,4 <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p5">(<span class="default"><span class="p0">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span>,<font color="Maroon">c<sub>75</sub></font></span>)</span></span>)</span> <a href="scmpds_2.html#K2">.</a> <span class="p1">(<span class="default"><a href="scmp_gcd.html#K1">intpos</a> <font color="Maroon">c<sub>89</sub></font></span>)</span> <a href="xxreal_0.html#NR2" target="_self">&gt;=</a> <span class="p1">(<span class="default"><a href="scmpds_4.html#K9">IExec</a> <font color="Maroon">c<sub>50</sub></font>,<span class="p2">(<span class="default"><a href="scmpds_4.html#K9">IExec</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a> ,2 <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p5">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span></span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p4">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a> ,4 <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p5">(<span class="default"><span class="p0">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span>,<font color="Maroon">c<sub>75</sub></font></span>)</span></span>)</span> <a href="scmpds_2.html#K2">.</a> <span class="p1">(<span class="default"><a href="scmp_gcd.html#K1">intpos</a> <font color="Olive">b<sub>1</sub></font></span>)</span> ) &amp; ( for <font color="Olive">b<sub>1</sub></font> being  <a href="nat_1.html#NM1">Nat</a> st <font color="Maroon">c<sub>89</sub></font> <a href="xxreal_0.html#NR3" target="_self">&lt;</a> <font color="Olive">b<sub>1</sub></font> &amp; <font color="Olive">b<sub>1</sub></font> <a href="xxreal_0.html#R1">&lt;=</a> <span class="p1">(<span class="default"><a href="scmpds_4.html#K9">IExec</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a> ,2 <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p4">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span></span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p3">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a> ,4 <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p4">(<span class="default"><span class="p5">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span>,<font color="Maroon">c<sub>75</sub></font></span>)</span> <a href="scmpds_2.html#K2">.</a> <span class="p1">(<span class="default"><a href="scmp_gcd.html#K1">intpos</a> 4</span>)</span> holds <br/><span class="p1">(<span class="default"><a href="scmpds_4.html#K9">IExec</a> <font color="Maroon">c<sub>50</sub></font>,<span class="p2">(<span class="default"><a href="scmpds_4.html#K9">IExec</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a> ,2 <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p5">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span></span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p4">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a> ,4 <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p5">(<span class="default"><span class="p0">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span>,<font color="Maroon">c<sub>75</sub></font></span>)</span></span>)</span> <a href="scmpds_2.html#K2">.</a> <span class="p1">(<span class="default"><a href="scmp_gcd.html#K1">intpos</a> <font color="Maroon">c<sub>89</sub></font></span>)</span> <a href="xxreal_0.html#R1">&lt;=</a> <span class="p1">(<span class="default"><a href="scmpds_4.html#K9">IExec</a> <font color="Maroon">c<sub>50</sub></font>,<span class="p2">(<span class="default"><a href="scmpds_4.html#K9">IExec</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a> ,2 <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p5">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span></span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p4">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a> ,4 <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p5">(<span class="default"><span class="p0">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span>,<font color="Maroon">c<sub>75</sub></font></span>)</span></span>)</span> <a href="scmpds_2.html#K2">.</a> <span class="p1">(<span class="default"><a href="scmp_gcd.html#K1">intpos</a> <font color="Olive">b<sub>1</sub></font></span>)</span> ) &amp; ( for <font color="Olive">b<sub>1</sub></font> being  <a href="nat_1.html#NM1">Nat</a> st <font color="Olive">b<sub>1</sub></font> <a href="xxreal_0.html#NR2" target="_self">&gt;=</a> <font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> 1 &amp; ( <font color="Olive">b<sub>1</sub></font> <a href="xxreal_0.html#NR3" target="_self">&lt;</a> <span class="p1">(<span class="default"><a href="scmpds_4.html#K9">IExec</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a> ,2 <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p4">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span></span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p3">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a> ,4 <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p4">(<span class="default"><span class="p5">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span>,<font color="Maroon">c<sub>75</sub></font></span>)</span> <a href="scmpds_2.html#K2">.</a> <span class="p1">(<span class="default"><a href="scmp_gcd.html#K1">intpos</a> 2</span>)</span> or <font color="Olive">b<sub>1</sub></font> <a href="xxreal_0.html#NR4" target="_self">&gt;</a> <span class="p1">(<span class="default"><a href="scmpds_4.html#K9">IExec</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a> ,2 <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p4">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span></span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p3">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a> ,4 <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p4">(<span class="default"><span class="p5">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span>,<font color="Maroon">c<sub>75</sub></font></span>)</span> <a href="scmpds_2.html#K2">.</a> <span class="p1">(<span class="default"><a href="scmp_gcd.html#K1">intpos</a> 4</span>)</span> ) holds <br/><span class="p1">(<span class="default"><a href="scmpds_4.html#K9">IExec</a> <font color="Maroon">c<sub>50</sub></font>,<span class="p2">(<span class="default"><a href="scmpds_4.html#K9">IExec</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a> ,2 <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p5">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span></span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p4">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a> ,4 <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p5">(<span class="default"><span class="p0">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span>,<font color="Maroon">c<sub>75</sub></font></span>)</span></span>)</span> <a href="scmpds_2.html#K2">.</a> <span class="p1">(<span class="default"><a href="scmp_gcd.html#K1">intpos</a> <font color="Olive">b<sub>1</sub></font></span>)</span> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><a href="scmpds_4.html#K9">IExec</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a> ,2 <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p4">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span></span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p3">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a> ,4 <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p4">(<span class="default"><span class="p5">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span>,<font color="Maroon">c<sub>75</sub></font></span>)</span> <a href="scmpds_2.html#K2">.</a> <span class="p1">(<span class="default"><a href="scmp_gcd.html#K1">intpos</a> <font color="Olive">b<sub>1</sub></font></span>)</span> ) )
 <b>by </b><i><a class="txt" href="scpqsort.html#E5:46"><i><font color="Green">E46</font></i></a>, <a class="txt" href="scpqsort.html#E1:46_7"><i><font color="Green">E55</font></i></a>, <a class="txt" href="scpqsort.html#E2:46_7"><i><font color="Green">E56</font></i></a>, <a class="txt" href="scpqsort.html#E4:46_7"><i><font color="Green">E58</font></i></a>, <a class="txt" href="scpqsort.html#E5:46_7"><i><font color="Green">E59</font></i></a>, <a class="txt" href="scpqsort.html#E9:46_7"><i><font color="Green">E62</font></i></a>, <a class="txt" href="scpqsort.html#E11:46_7"><i><font color="Green">E63</font></i></a>, <a class="txt" href="scpqsort.html#E12:46_7"><i><font color="Green">E64</font></i></a>, <a class="ref" href="scpqsort.html#T14" target="_self">Th14</a></i>;<br/>
<a NAME="E16:46_7"/><i><font color="Green">E67</font></i>: 
( <font color="Maroon">c<sub>50</sub></font> <a href="scmpds_6.html#R1">is_closed_on</a>  <a href="scmpds_4.html#K9">IExec</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a> ,2 <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p3">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span></span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p2">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a> ,4 <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span>,<font color="Maroon">c<sub>75</sub></font> &amp; <font color="Maroon">c<sub>50</sub></font> <a href="scmpds_6.html#R2">is_halting_on</a>  <a href="scmpds_4.html#K9">IExec</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a> ,2 <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p3">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span></span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p2">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a> ,4 <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span>,<font color="Maroon">c<sub>75</sub></font> )
 
<b>by </b><i><a class="txt" href="scpqsort.html#E5:46"><i><font color="Green">E46</font></i></a>, <a class="txt" href="scpqsort.html#E1:46_7"><i><font color="Green">E55</font></i></a>, <a class="txt" href="scpqsort.html#E4:46_7"><i><font color="Green">E58</font></i></a>, <a class="txt" href="scpqsort.html#E5:46_7"><i><font color="Green">E59</font></i></a>, <a class="ref" href="scpqsort.html#T13" target="_self">Th13</a></i>;<br/>
<a NAME="E17:46_7"/><b>then </b><i><font color="Green">E68</font></i>: 
( <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a> ,2 <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p3">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span></span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p2">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a> ,4 <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span> <a href="scmpds_4.html#K3">';'</a> <font color="Maroon">c<sub>50</sub></font> <a href="scmpds_6.html#R1">is_closed_on</a> <font color="Maroon">c<sub>75</sub></font> &amp; <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a> ,2 <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p3">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span></span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p2">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a> ,4 <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span> <a href="scmpds_4.html#K3">';'</a> <font color="Maroon">c<sub>50</sub></font> <a href="scmpds_6.html#R2">is_halting_on</a> <font color="Maroon">c<sub>75</sub></font> )
 
<b>by </b><i><a class="ref" href="scpisort.html#T10">SCPISORT:10</a></i>;<br/>
<a NAME="E18:46_7"/><i><font color="Green">E69</font></i>: 
<span class="p1">(<span class="default"><a href="scmpds_4.html#K9">IExec</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a> ,2 <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p5">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span></span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p4">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a> ,4 <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p5">(<span class="default"><span class="p0">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span> <a href="scmpds_4.html#K3">';'</a> <font color="Maroon">c<sub>50</sub></font></span>)</span>,<font color="Maroon">c<sub>75</sub></font></span>)</span> <a href="scmpds_2.html#K2">.</a> <a href="scmp_gcd.html#K2">GBP</a>  <a href="hidden.html#R1">=</a> 0
 
<b>by </b><i><a class="txt" href="scpqsort.html#E13:46_7"><i><font color="Green">E65</font></i></a>, <a class="txt" href="scpqsort.html#E16:46_7"><i><font color="Green">E67</font></i></a>, <a class="ref" href="scpisort.html#T8">SCPISORT:8</a></i>;<br/>
<i><font color="Green">E70</font></i>: <span class="p1">(<span class="default"><a href="scmpds_4.html#K9">IExec</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a> ,2 <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p5">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span></span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p4">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a> ,4 <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p5">(<span class="default"><span class="p0">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span> <a href="scmpds_4.html#K3">';'</a> <font color="Maroon">c<sub>50</sub></font></span>)</span>,<font color="Maroon">c<sub>75</sub></font></span>)</span> <a href="scmpds_2.html#K2">.</a> <a href="scmp_gcd.html#K3">SBP</a>  = 
<span class="p1">(<span class="default"><a href="scmpds_4.html#K9">IExec</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a> ,2 <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p4">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span></span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p3">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a> ,4 <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p4">(<span class="default"><span class="p5">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span>,<font color="Maroon">c<sub>75</sub></font></span>)</span> <a href="scmpds_2.html#K2">.</a> <span class="p1">(<span class="default"><a href="scmp_gcd.html#K1">intpos</a> 1</span>)</span>
<b>by </b><i><a class="txt" href="scpqsort.html#E13:46_7"><i><font color="Green">E65</font></i></a>, <a class="txt" href="scpqsort.html#E16:46_7"><i><font color="Green">E67</font></i></a>, <a class="ref" href="scmp_gcd.html#D3">SCMP_GCD:def 3</a>, <a class="ref" href="scpisort.html#T8">SCPISORT:8</a></i>
<br/>.= 
<font color="Maroon">c<sub>77</sub></font>
<b>by </b><i><a class="txt" href="scpqsort.html#E12:46"><i><font color="Green">E52</font></i></a>, <a class="txt" href="scpqsort.html#E1:46_7"><i><font color="Green">E55</font></i></a>, <a class="ref" href="scmp_gcd.html#D3">SCMP_GCD:def 3</a></i>
;<br/>
<a NAME="E20:46_7"/><b>then </b><i><font color="Green">E71</font></i>: 
( <span class="p1">(<span class="default"><a href="scmpds_4.html#K9">IExec</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><span class="p0">(<span class="default"><span class="p1">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a> ,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 3</span>)</span> <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p1">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a> ,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span> <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K2">GBP</a> ,4</span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p0">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a> ,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 2</span>)</span> <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K2">GBP</a> ,4</span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p5">(<span class="default"><a href="scmpds_2.html#K12">AddTo</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p0">(<span class="default"><span class="p1">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span>,<span class="p0">(<span class="default"><a href="xcmplx_0.html#K4">-</a> 1</span>)</span></span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p4">(<span class="default"><a href="scmpds_2.html#K12">AddTo</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p5">(<span class="default"><span class="p0">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 2</span>)</span>,1</span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p3">(<span class="default"><a href="scmpds_2.html#K12">AddTo</a> <a href="scmp_gcd.html#K2">GBP</a> ,1,2</span>)</span></span>)</span>,<span class="p2">(<span class="default"><a href="scmpds_4.html#K9">IExec</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a> ,2 <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p0">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span></span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p5">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a> ,4 <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p0">(<span class="default"><span class="p1">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span> <a href="scmpds_4.html#K3">';'</a> <font color="Maroon">c<sub>50</sub></font></span>)</span>,<font color="Maroon">c<sub>75</sub></font></span>)</span></span>)</span> <a href="scmpds_2.html#K2">.</a> <a href="scmp_gcd.html#K2">GBP</a>  <a href="hidden.html#R1">=</a> 0 &amp; <span class="p1">(<span class="default"><a href="scmpds_4.html#K9">IExec</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><span class="p0">(<span class="default"><span class="p1">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a> ,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 3</span>)</span> <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p1">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a> ,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span> <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K2">GBP</a> ,4</span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p0">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a> ,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 2</span>)</span> <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K2">GBP</a> ,4</span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p5">(<span class="default"><a href="scmpds_2.html#K12">AddTo</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p0">(<span class="default"><span class="p1">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span>,<span class="p0">(<span class="default"><a href="xcmplx_0.html#K4">-</a> 1</span>)</span></span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p4">(<span class="default"><a href="scmpds_2.html#K12">AddTo</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p5">(<span class="default"><span class="p0">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 2</span>)</span>,1</span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p3">(<span class="default"><a href="scmpds_2.html#K12">AddTo</a> <a href="scmp_gcd.html#K2">GBP</a> ,1,2</span>)</span></span>)</span>,<span class="p2">(<span class="default"><a href="scmpds_4.html#K9">IExec</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a> ,2 <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p0">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span></span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p5">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a> ,4 <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p0">(<span class="default"><span class="p1">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span> <a href="scmpds_4.html#K3">';'</a> <font color="Maroon">c<sub>50</sub></font></span>)</span>,<font color="Maroon">c<sub>75</sub></font></span>)</span></span>)</span> <a href="scmpds_2.html#K2">.</a> <a href="scmp_gcd.html#K3">SBP</a>  <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>77</sub></font> <a href="nat_1.html#K1">+</a> 2 &amp; <span class="p1">(<span class="default"><a href="scmpds_4.html#K9">IExec</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><span class="p0">(<span class="default"><span class="p1">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a> ,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 3</span>)</span> <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p1">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a> ,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span> <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K2">GBP</a> ,4</span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p0">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a> ,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 2</span>)</span> <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K2">GBP</a> ,4</span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p5">(<span class="default"><a href="scmpds_2.html#K12">AddTo</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p0">(<span class="default"><span class="p1">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span>,<span class="p0">(<span class="default"><a href="xcmplx_0.html#K4">-</a> 1</span>)</span></span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p4">(<span class="default"><a href="scmpds_2.html#K12">AddTo</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p5">(<span class="default"><span class="p0">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 2</span>)</span>,1</span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p3">(<span class="default"><a href="scmpds_2.html#K12">AddTo</a> <a href="scmp_gcd.html#K2">GBP</a> ,1,2</span>)</span></span>)</span>,<span class="p2">(<span class="default"><a href="scmpds_4.html#K9">IExec</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a> ,2 <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p0">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span></span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p5">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a> ,4 <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p0">(<span class="default"><span class="p1">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span> <a href="scmpds_4.html#K3">';'</a> <font color="Maroon">c<sub>50</sub></font></span>)</span>,<font color="Maroon">c<sub>75</sub></font></span>)</span></span>)</span> <a href="scmpds_2.html#K2">.</a> <span class="p1">(<span class="default"><a href="scmp_gcd.html#K1">intpos</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>77</sub></font> <a href="nat_1.html#K1">+</a> <span class="p3">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span></span>)</span></span>)</span> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><a href="scmpds_4.html#K9">IExec</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a> ,2 <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p5">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span></span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p4">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a> ,4 <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p5">(<span class="default"><span class="p0">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span> <a href="scmpds_4.html#K3">';'</a> <font color="Maroon">c<sub>50</sub></font></span>)</span>,<font color="Maroon">c<sub>75</sub></font></span>)</span> <a href="scmpds_2.html#K2">.</a> <span class="p1">(<span class="default"><a href="scmp_gcd.html#K1">intpos</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>77</sub></font> <a href="nat_1.html#K1">+</a> <span class="p3">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span></span>)</span></span>)</span> &amp; <span class="p1">(<span class="default"><a href="scmpds_4.html#K9">IExec</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><span class="p0">(<span class="default"><span class="p1">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a> ,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 3</span>)</span> <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p1">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a> ,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span> <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K2">GBP</a> ,4</span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p0">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a> ,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 2</span>)</span> <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K2">GBP</a> ,4</span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p5">(<span class="default"><a href="scmpds_2.html#K12">AddTo</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p0">(<span class="default"><span class="p1">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span>,<span class="p0">(<span class="default"><a href="xcmplx_0.html#K4">-</a> 1</span>)</span></span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p4">(<span class="default"><a href="scmpds_2.html#K12">AddTo</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p5">(<span class="default"><span class="p0">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 2</span>)</span>,1</span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p3">(<span class="default"><a href="scmpds_2.html#K12">AddTo</a> <a href="scmp_gcd.html#K2">GBP</a> ,1,2</span>)</span></span>)</span>,<span class="p2">(<span class="default"><a href="scmpds_4.html#K9">IExec</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a> ,2 <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p0">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span></span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p5">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a> ,4 <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p0">(<span class="default"><span class="p1">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span> <a href="scmpds_4.html#K3">';'</a> <font color="Maroon">c<sub>50</sub></font></span>)</span>,<font color="Maroon">c<sub>75</sub></font></span>)</span></span>)</span> <a href="scmpds_2.html#K2">.</a> <span class="p1">(<span class="default"><a href="scmp_gcd.html#K1">intpos</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">c<sub>77</sub></font> <a href="nat_1.html#K1">+</a> <span class="p4">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="scmpds_4.html#K9">IExec</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a> ,2 <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p0">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span></span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p5">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a> ,4 <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p0">(<span class="default"><span class="p1">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span> <a href="scmpds_4.html#K3">';'</a> <font color="Maroon">c<sub>50</sub></font></span>)</span>,<font color="Maroon">c<sub>75</sub></font></span>)</span> <a href="scmpds_2.html#K2">.</a> <span class="p2">(<span class="default"><a href="scmp_gcd.html#K1">intpos</a> 4</span>)</span></span>)</span> <a href="xcmplx_0.html#K6">-</a> 1 &amp; <span class="p1">(<span class="default"><a href="scmpds_4.html#K9">IExec</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><span class="p0">(<span class="default"><span class="p1">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a> ,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 3</span>)</span> <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p1">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a> ,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span> <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K2">GBP</a> ,4</span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p0">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a> ,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 2</span>)</span> <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K2">GBP</a> ,4</span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p5">(<span class="default"><a href="scmpds_2.html#K12">AddTo</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p0">(<span class="default"><span class="p1">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span>,<span class="p0">(<span class="default"><a href="xcmplx_0.html#K4">-</a> 1</span>)</span></span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p4">(<span class="default"><a href="scmpds_2.html#K12">AddTo</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p5">(<span class="default"><span class="p0">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 2</span>)</span>,1</span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p3">(<span class="default"><a href="scmpds_2.html#K12">AddTo</a> <a href="scmp_gcd.html#K2">GBP</a> ,1,2</span>)</span></span>)</span>,<span class="p2">(<span class="default"><a href="scmpds_4.html#K9">IExec</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a> ,2 <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p0">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span></span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p5">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a> ,4 <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p0">(<span class="default"><span class="p1">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span> <a href="scmpds_4.html#K3">';'</a> <font color="Maroon">c<sub>50</sub></font></span>)</span>,<font color="Maroon">c<sub>75</sub></font></span>)</span></span>)</span> <a href="scmpds_2.html#K2">.</a> <span class="p1">(<span class="default"><a href="scmp_gcd.html#K1">intpos</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">c<sub>77</sub></font> <a href="nat_1.html#K1">+</a> <span class="p4">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span></span>)</span> <a href="nat_1.html#K1">+</a> 2</span>)</span></span>)</span> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="scmpds_4.html#K9">IExec</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a> ,2 <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p0">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span></span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p5">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a> ,4 <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p0">(<span class="default"><span class="p1">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span> <a href="scmpds_4.html#K3">';'</a> <font color="Maroon">c<sub>50</sub></font></span>)</span>,<font color="Maroon">c<sub>75</sub></font></span>)</span> <a href="scmpds_2.html#K2">.</a> <span class="p2">(<span class="default"><a href="scmp_gcd.html#K1">intpos</a> 4</span>)</span></span>)</span> <a href="xcmplx_0.html#K2">+</a> 1 &amp; <span class="p1">(<span class="default"><a href="scmpds_4.html#K9">IExec</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><span class="p0">(<span class="default"><span class="p1">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a> ,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 3</span>)</span> <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p1">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a> ,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span> <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K2">GBP</a> ,4</span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p0">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a> ,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 2</span>)</span> <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K2">GBP</a> ,4</span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p5">(<span class="default"><a href="scmpds_2.html#K12">AddTo</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p0">(<span class="default"><span class="p1">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span>,<span class="p0">(<span class="default"><a href="xcmplx_0.html#K4">-</a> 1</span>)</span></span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p4">(<span class="default"><a href="scmpds_2.html#K12">AddTo</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p5">(<span class="default"><span class="p0">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 2</span>)</span>,1</span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p3">(<span class="default"><a href="scmpds_2.html#K12">AddTo</a> <a href="scmp_gcd.html#K2">GBP</a> ,1,2</span>)</span></span>)</span>,<span class="p2">(<span class="default"><a href="scmpds_4.html#K9">IExec</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a> ,2 <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p0">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span></span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p5">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a> ,4 <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p0">(<span class="default"><span class="p1">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span> <a href="scmpds_4.html#K3">';'</a> <font color="Maroon">c<sub>50</sub></font></span>)</span>,<font color="Maroon">c<sub>75</sub></font></span>)</span></span>)</span> <a href="scmpds_2.html#K2">.</a> <span class="p1">(<span class="default"><a href="scmp_gcd.html#K1">intpos</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">c<sub>77</sub></font> <a href="nat_1.html#K1">+</a> <span class="p4">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span></span>)</span> <a href="nat_1.html#K1">+</a> 3</span>)</span></span>)</span> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><a href="scmpds_4.html#K9">IExec</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a> ,2 <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p5">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span></span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p4">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a> ,4 <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p5">(<span class="default"><span class="p0">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span> <a href="scmpds_4.html#K3">';'</a> <font color="Maroon">c<sub>50</sub></font></span>)</span>,<font color="Maroon">c<sub>75</sub></font></span>)</span> <a href="scmpds_2.html#K2">.</a> <span class="p1">(<span class="default"><a href="scmp_gcd.html#K1">intpos</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">c<sub>77</sub></font> <a href="nat_1.html#K1">+</a> <span class="p4">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> &amp; ( for <font color="Olive">b<sub>1</sub></font> being  <a href="nat_1.html#NM1">Nat</a> st <font color="Olive">b<sub>1</sub></font> <a href="xxreal_0.html#NR2" target="_self">&gt;=</a> 8 &amp; <font color="Olive">b<sub>1</sub></font> <a href="xxreal_0.html#NR3" target="_self">&lt;</a> <font color="Maroon">c<sub>77</sub></font> <a href="nat_1.html#K1">+</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> holds <br/><span class="p1">(<span class="default"><a href="scmpds_4.html#K9">IExec</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><span class="p0">(<span class="default"><span class="p1">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a> ,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 3</span>)</span> <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p1">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a> ,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span> <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K2">GBP</a> ,4</span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p0">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a> ,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 2</span>)</span> <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K2">GBP</a> ,4</span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p5">(<span class="default"><a href="scmpds_2.html#K12">AddTo</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p0">(<span class="default"><span class="p1">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span>,<span class="p0">(<span class="default"><a href="xcmplx_0.html#K4">-</a> 1</span>)</span></span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p4">(<span class="default"><a href="scmpds_2.html#K12">AddTo</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p5">(<span class="default"><span class="p0">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 2</span>)</span>,1</span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p3">(<span class="default"><a href="scmpds_2.html#K12">AddTo</a> <a href="scmp_gcd.html#K2">GBP</a> ,1,2</span>)</span></span>)</span>,<span class="p2">(<span class="default"><a href="scmpds_4.html#K9">IExec</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a> ,2 <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p0">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span></span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p5">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a> ,4 <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p0">(<span class="default"><span class="p1">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span> <a href="scmpds_4.html#K3">';'</a> <font color="Maroon">c<sub>50</sub></font></span>)</span>,<font color="Maroon">c<sub>75</sub></font></span>)</span></span>)</span> <a href="scmpds_2.html#K2">.</a> <span class="p1">(<span class="default"><a href="scmp_gcd.html#K1">intpos</a> <font color="Olive">b<sub>1</sub></font></span>)</span> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><a href="scmpds_4.html#K9">IExec</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a> ,2 <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p5">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span></span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p4">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a> ,4 <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p5">(<span class="default"><span class="p0">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span> <a href="scmpds_4.html#K3">';'</a> <font color="Maroon">c<sub>50</sub></font></span>)</span>,<font color="Maroon">c<sub>75</sub></font></span>)</span> <a href="scmpds_2.html#K2">.</a> <span class="p1">(<span class="default"><a href="scmp_gcd.html#K1">intpos</a> <font color="Olive">b<sub>1</sub></font></span>)</span> ) )
 
<b>by </b><i><a class="txt" href="scpqsort.html#E11:46"><i><font color="Green">E51</font></i></a>, <a class="txt" href="scpqsort.html#E1:46_7"><i><font color="Green">E55</font></i></a>, <a class="txt" href="scpqsort.html#E18:46_7"><i><font color="Green">E69</font></i></a></i>;<br/>
<a NAME="E21:46_7"/><i><font color="Green">E72</font></i>: 
<font color="Maroon">c<sub>77</sub></font> <a href="xxreal_0.html#NR2" target="_self">&gt;=</a> 1
 
<b>by </b><i><a class="txt" href="scpqsort.html#E1:46_7"><i><font color="Green">E55</font></i></a>, <a class="ref" href="nat_1.html#T29">NAT_1:29</a></i>;<br/>
<a NAME="E22:46_7"/><b>then </b><i><font color="Green">E73</font></i>: 
<font color="Maroon">c<sub>77</sub></font> <a href="nat_1.html#K1">+</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="xxreal_0.html#NR2" target="_self">&gt;=</a> 1 <a href="nat_1.html#K1">+</a> 7
 
<b>by </b><i><a class="txt" href="scpqsort.html#E8:46"><i><font color="Green">E48</font></i></a>, <a class="ref" href="xreal_1.html#T9">XREAL_1:9</a></i>;<br/>
<a NAME="E23:46_7"/><i><font color="Green">E74</font></i>: 
<font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font> <a href="xxreal_0.html#NR2" target="_self">&gt;=</a> <font color="Maroon">c<sub>48</sub></font>
 
<b>by </b><i><a class="ref" href="nat_1.html#T29">NAT_1:29</a></i>;<br/>
<a NAME="E24:46_7"/><b>then </b><i><font color="Green">E75</font></i>: 
<font color="Maroon">c<sub>77</sub></font> <a href="nat_1.html#K1">+</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="xxreal_0.html#NR2" target="_self">&gt;=</a> <font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> 1
 
<b>by </b><i><a class="txt" href="scpqsort.html#E21:46_7"><i><font color="Green">E72</font></i></a>, <a class="ref" href="xreal_1.html#T9">XREAL_1:9</a></i>;<br/>
<a NAME="E25:46_7"/><i><font color="Green">E76</font></i>: 
<font color="Maroon">c<sub>77</sub></font> <a href="nat_1.html#K1">+</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="xxreal_0.html#NR2" target="_self">&gt;=</a> 1 <a href="nat_1.html#K1">+</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span>
 
<b>by </b><i><a class="txt" href="scpqsort.html#E21:46_7"><i><font color="Green">E72</font></i></a>, <a class="ref" href="xreal_1.html#T8">XREAL_1:8</a></i>;<br/>
<a NAME="E26:46_7"/><i><font color="Green">E77</font></i>: 
1 <a href="nat_1.html#K1">+</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="xxreal_0.html#NR4" target="_self">&gt;</a> <font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font>
 
<b>by </b><i><a class="ref" href="xreal_1.html#T31">XREAL_1:31</a></i>;<br/>
<a NAME="E27:46_7"/><b>then </b><i><font color="Green">E78</font></i>: 
<font color="Maroon">c<sub>77</sub></font> <a href="nat_1.html#K1">+</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="xxreal_0.html#NR4" target="_self">&gt;</a> <font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font>
 
<b>by </b><i><a class="txt" href="scpqsort.html#E25:46_7"><i><font color="Green">E76</font></i></a>, <a class="ref" href="xreal_1.html#T2">XREAL_1:2</a></i>;<br/>
<a NAME="E28:46_7"/><b>then </b><i><font color="Green">E79</font></i>: 
<font color="Maroon">c<sub>77</sub></font> <a href="nat_1.html#K1">+</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="xxreal_0.html#NR4" target="_self">&gt;</a> <span class="p1">(<span class="default"><a href="scmpds_4.html#K9">IExec</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a> ,2 <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p4">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span></span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p3">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a> ,4 <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p4">(<span class="default"><span class="p5">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span>,<font color="Maroon">c<sub>75</sub></font></span>)</span> <a href="scmpds_2.html#K2">.</a> <span class="p1">(<span class="default"><a href="scmp_gcd.html#K1">intpos</a> 4</span>)</span>
 
<b>by </b><i><a class="txt" href="scpqsort.html#E1:46_7"><i><font color="Green">E55</font></i></a>, <a class="txt" href="scpqsort.html#E6:46_7"><i><font color="Green">E60</font></i></a>, <a class="ref" href="xreal_1.html#T2">XREAL_1:2</a></i>;<br/>
<b>thus </b><a NAME="E29:46_7"/>
<span class="p1">(<span class="default"><a href="scmpds_4.html#K9">IExec</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a> ,2 <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p0">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span></span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p5">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a> ,4 <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p0">(<span class="default"><span class="p1">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span> <a href="scmpds_4.html#K3">';'</a> <font color="Maroon">c<sub>50</sub></font></span>)</span> <a href="scmpds_4.html#K3">';'</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><span class="p0">(<span class="default"><span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a> ,<span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 3</span>)</span> <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p2">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a> ,<span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span> <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K2">GBP</a> ,4</span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p1">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a> ,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 2</span>)</span> <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K2">GBP</a> ,4</span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p0">(<span class="default"><a href="scmpds_2.html#K12">AddTo</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span>,<span class="p1">(<span class="default"><a href="xcmplx_0.html#K4">-</a> 1</span>)</span></span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p5">(<span class="default"><a href="scmpds_2.html#K12">AddTo</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p0">(<span class="default"><span class="p1">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 2</span>)</span>,1</span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p4">(<span class="default"><a href="scmpds_2.html#K12">AddTo</a> <a href="scmp_gcd.html#K2">GBP</a> ,1,2</span>)</span></span>)</span></span>)</span>,<font color="Maroon">c<sub>75</sub></font></span>)</span> <a href="scmpds_2.html#K2">.</a> <a href="scmp_gcd.html#K2">GBP</a>  <a href="hidden.html#R1">=</a> 0
 <b>by </b><i><a class="txt" href="scpqsort.html#E17:46_7"><i><font color="Green">E68</font></i></a>, <a class="txt" href="scpqsort.html#E20:46_7"><i><font color="Green">E71</font></i></a>, <a class="ref" href="scpisort.html#T7">SCPISORT:7</a></i>;<br/>

<b>thus </b><a NAME="E30:46_7"/>
<span class="p1">(<span class="default"><a href="scmpds_4.html#K9">IExec</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a> ,2 <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p0">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span></span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p5">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a> ,4 <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p0">(<span class="default"><span class="p1">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span> <a href="scmpds_4.html#K3">';'</a> <font color="Maroon">c<sub>50</sub></font></span>)</span> <a href="scmpds_4.html#K3">';'</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><span class="p0">(<span class="default"><span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a> ,<span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 3</span>)</span> <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p2">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a> ,<span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span> <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K2">GBP</a> ,4</span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p1">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a> ,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 2</span>)</span> <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K2">GBP</a> ,4</span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p0">(<span class="default"><a href="scmpds_2.html#K12">AddTo</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span>,<span class="p1">(<span class="default"><a href="xcmplx_0.html#K4">-</a> 1</span>)</span></span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p5">(<span class="default"><a href="scmpds_2.html#K12">AddTo</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p0">(<span class="default"><span class="p1">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 2</span>)</span>,1</span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p4">(<span class="default"><a href="scmpds_2.html#K12">AddTo</a> <a href="scmp_gcd.html#K2">GBP</a> ,1,2</span>)</span></span>)</span></span>)</span>,<font color="Maroon">c<sub>75</sub></font></span>)</span> <a href="scmpds_2.html#K2">.</a> <span class="p1">(<span class="default"><a href="scmp_gcd.html#K1">intpos</a> 1</span>)</span> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>77</sub></font> <a href="nat_1.html#K1">+</a> 2
 <b>by </b><i><a class="txt" href="scpqsort.html#E17:46_7"><i><font color="Green">E68</font></i></a>, <a class="txt" href="scpqsort.html#E20:46_7"><i><font color="Green">E71</font></i></a>, <a class="ref" href="scmp_gcd.html#D3">SCMP_GCD:def 3</a>, <a class="ref" href="scpisort.html#T7">SCPISORT:7</a></i>;<br/>

<a NAME="E31:46_7"/>
( <font color="Maroon">c<sub>77</sub></font> <a href="nat_1.html#K1">+</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="xxreal_0.html#NR4" target="_self">&gt;</a> 2 &amp; <font color="Maroon">c<sub>77</sub></font> <a href="nat_1.html#K1">+</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="xxreal_0.html#NR4" target="_self">&gt;</a> 4 )
 
<b>by </b><i><a class="txt" href="scpqsort.html#E22:46_7"><i><font color="Green">E73</font></i></a>, <a class="ref" href="xreal_1.html#T2">XREAL_1:2</a></i>;<br/>
<b>hence </b><font color="Maroon">c<sub>78</sub></font> = 
<span class="p1">(<span class="default"><a href="scmpds_4.html#K9">IExec</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a> ,2 <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p4">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span></span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p3">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a> ,4 <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p4">(<span class="default"><span class="p5">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span>,<font color="Maroon">c<sub>75</sub></font></span>)</span> <a href="scmpds_2.html#K2">.</a> <span class="p1">(<span class="default"><a href="scmp_gcd.html#K1">intpos</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>77</sub></font> <a href="nat_1.html#K1">+</a> <span class="p3">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span></span>)</span></span>)</span>
<b>by </b><i><a class="txt" href="scpqsort.html#E12:46"><i><font color="Green">E52</font></i></a>, <a class="txt" href="scpqsort.html#E1:46_7"><i><font color="Green">E55</font></i></a></i>
<br/>.= 
<span class="p1">(<span class="default"><a href="scmpds_4.html#K9">IExec</a> <font color="Maroon">c<sub>50</sub></font>,<span class="p2">(<span class="default"><a href="scmpds_4.html#K9">IExec</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a> ,2 <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p5">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span></span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p4">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a> ,4 <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p5">(<span class="default"><span class="p0">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span>,<font color="Maroon">c<sub>75</sub></font></span>)</span></span>)</span> <a href="scmpds_2.html#K2">.</a> <span class="p1">(<span class="default"><a href="scmp_gcd.html#K1">intpos</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>77</sub></font> <a href="nat_1.html#K1">+</a> <span class="p3">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span></span>)</span></span>)</span>
<b>by </b><i><a class="txt" href="scpqsort.html#E15:46_7"><i><font color="Green">E66</font></i></a>, <a class="txt" href="scpqsort.html#E24:46_7"><i><font color="Green">E75</font></i></a>, <a class="txt" href="scpqsort.html#E28:46_7"><i><font color="Green">E79</font></i></a></i>
<br/>.= 
<span class="p1">(<span class="default"><a href="scmpds_4.html#K9">IExec</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><span class="p0">(<span class="default"><span class="p1">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a> ,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 3</span>)</span> <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p1">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a> ,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span> <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K2">GBP</a> ,4</span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p0">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a> ,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 2</span>)</span> <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K2">GBP</a> ,4</span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p5">(<span class="default"><a href="scmpds_2.html#K12">AddTo</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p0">(<span class="default"><span class="p1">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span>,<span class="p0">(<span class="default"><a href="xcmplx_0.html#K4">-</a> 1</span>)</span></span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p4">(<span class="default"><a href="scmpds_2.html#K12">AddTo</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p5">(<span class="default"><span class="p0">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 2</span>)</span>,1</span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p3">(<span class="default"><a href="scmpds_2.html#K12">AddTo</a> <a href="scmp_gcd.html#K2">GBP</a> ,1,2</span>)</span></span>)</span>,<span class="p2">(<span class="default"><a href="scmpds_4.html#K9">IExec</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a> ,2 <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p0">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span></span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p5">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a> ,4 <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p0">(<span class="default"><span class="p1">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span> <a href="scmpds_4.html#K3">';'</a> <font color="Maroon">c<sub>50</sub></font></span>)</span>,<font color="Maroon">c<sub>75</sub></font></span>)</span></span>)</span> <a href="scmpds_2.html#K2">.</a> <span class="p1">(<span class="default"><a href="scmp_gcd.html#K1">intpos</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>77</sub></font> <a href="nat_1.html#K1">+</a> <span class="p3">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span></span>)</span></span>)</span>
<b>by </b><i><a class="txt" href="scpqsort.html#E16:46_7"><i><font color="Green">E67</font></i></a>, <a class="txt" href="scpqsort.html#E20:46_7"><i><font color="Green">E71</font></i></a>, <a class="ref" href="scpisort.html#T8">SCPISORT:8</a></i>
<br/>.= 
<span class="p1">(<span class="default"><a href="scmpds_4.html#K9">IExec</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a> ,2 <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p0">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span></span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p5">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a> ,4 <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p0">(<span class="default"><span class="p1">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span> <a href="scmpds_4.html#K3">';'</a> <font color="Maroon">c<sub>50</sub></font></span>)</span> <a href="scmpds_4.html#K3">';'</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><span class="p0">(<span class="default"><span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a> ,<span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 3</span>)</span> <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p2">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a> ,<span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span> <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K2">GBP</a> ,4</span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p1">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a> ,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 2</span>)</span> <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K2">GBP</a> ,4</span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p0">(<span class="default"><a href="scmpds_2.html#K12">AddTo</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span>,<span class="p1">(<span class="default"><a href="xcmplx_0.html#K4">-</a> 1</span>)</span></span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p5">(<span class="default"><a href="scmpds_2.html#K12">AddTo</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p0">(<span class="default"><span class="p1">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 2</span>)</span>,1</span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p4">(<span class="default"><a href="scmpds_2.html#K12">AddTo</a> <a href="scmp_gcd.html#K2">GBP</a> ,1,2</span>)</span></span>)</span></span>)</span>,<font color="Maroon">c<sub>75</sub></font></span>)</span> <a href="scmpds_2.html#K2">.</a> <span class="p1">(<span class="default"><a href="scmp_gcd.html#K1">intpos</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>77</sub></font> <a href="nat_1.html#K1">+</a> <span class="p3">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span></span>)</span></span>)</span>
<b>by </b><i><a class="txt" href="scpqsort.html#E17:46_7"><i><font color="Green">E68</font></i></a>, <a class="ref" href="scpisort.html#T7">SCPISORT:7</a></i>
;<br/><br/>

<a NAME="E33:46_7"/><i><font color="Green">E80</font></i>: 
<span class="p1">(<span class="default"><font color="Maroon">c<sub>77</sub></font> <a href="nat_1.html#K1">+</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span></span>)</span> <a href="nat_1.html#K1">+</a> 1 <a href="xxreal_0.html#NR2" target="_self">&gt;=</a> 8 <a href="nat_1.html#K1">+</a> 1
 
<b>by </b><i><a class="txt" href="scpqsort.html#E22:46_7"><i><font color="Green">E73</font></i></a>, <a class="ref" href="xreal_1.html#T8">XREAL_1:8</a></i>;<br/>
<a NAME="E34:46_7"/><i><font color="Green">E81</font></i>: 
<span class="p1">(<span class="default"><font color="Maroon">c<sub>77</sub></font> <a href="nat_1.html#K1">+</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span></span>)</span> <a href="nat_1.html#K1">+</a> 1 <a href="xxreal_0.html#NR4" target="_self">&gt;</a> <font color="Maroon">c<sub>77</sub></font> <a href="nat_1.html#K1">+</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span>
 
<b>by </b><i><a class="ref" href="xreal_1.html#T31">XREAL_1:31</a></i>;<br/>
<a NAME="E35:46_7"/><b>then </b><i><font color="Green">E82</font></i>: 
<span class="p1">(<span class="default"><font color="Maroon">c<sub>77</sub></font> <a href="nat_1.html#K1">+</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span></span>)</span> <a href="nat_1.html#K1">+</a> 1 <a href="xxreal_0.html#NR2" target="_self">&gt;=</a> <font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> 1
 
<b>by </b><i><a class="txt" href="scpqsort.html#E24:46_7"><i><font color="Green">E75</font></i></a>, <a class="ref" href="xreal_1.html#T2">XREAL_1:2</a></i>;<br/>
<a NAME="E36:46_7"/><i><font color="Green">E83</font></i>: 
<span class="p1">(<span class="default"><font color="Maroon">c<sub>77</sub></font> <a href="nat_1.html#K1">+</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span></span>)</span> <a href="nat_1.html#K1">+</a> 1 <a href="xxreal_0.html#NR4" target="_self">&gt;</a> <span class="p1">(<span class="default"><a href="scmpds_4.html#K9">IExec</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a> ,2 <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p4">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span></span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p3">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a> ,4 <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p4">(<span class="default"><span class="p5">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span>,<font color="Maroon">c<sub>75</sub></font></span>)</span> <a href="scmpds_2.html#K2">.</a> <span class="p1">(<span class="default"><a href="scmp_gcd.html#K1">intpos</a> 4</span>)</span>
 
<b>by </b><i><a class="txt" href="scpqsort.html#E28:46_7"><i><font color="Green">E79</font></i></a>, <a class="txt" href="scpqsort.html#E34:46_7"><i><font color="Green">E81</font></i></a>, <a class="ref" href="xreal_1.html#T2">XREAL_1:2</a></i>;<br/>
<a NAME="E37:46_7"/>
( <span class="p1">(<span class="default"><font color="Maroon">c<sub>77</sub></font> <a href="nat_1.html#K1">+</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span></span>)</span> <a href="nat_1.html#K1">+</a> 1 <a href="xxreal_0.html#NR4" target="_self">&gt;</a> 2 &amp; <span class="p1">(<span class="default"><font color="Maroon">c<sub>77</sub></font> <a href="nat_1.html#K1">+</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span></span>)</span> <a href="nat_1.html#K1">+</a> 1 <a href="xxreal_0.html#NR4" target="_self">&gt;</a> 4 )
 
<b>by </b><i><a class="txt" href="scpqsort.html#E33:46_7"><i><font color="Green">E80</font></i></a>, <a class="ref" href="xreal_1.html#T2">XREAL_1:2</a></i>;<br/>
<b>hence </b><font color="Maroon">c<sub>79</sub></font> = 
<span class="p1">(<span class="default"><a href="scmpds_4.html#K9">IExec</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a> ,2 <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p4">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span></span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p3">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a> ,4 <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p4">(<span class="default"><span class="p5">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span>,<font color="Maroon">c<sub>75</sub></font></span>)</span> <a href="scmpds_2.html#K2">.</a> <span class="p1">(<span class="default"><a href="scmp_gcd.html#K1">intpos</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">c<sub>77</sub></font> <a href="nat_1.html#K1">+</a> <span class="p4">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span>
<b>by </b><i><a class="txt" href="scpqsort.html#E12:46"><i><font color="Green">E52</font></i></a>, <a class="txt" href="scpqsort.html#E1:46_7"><i><font color="Green">E55</font></i></a></i>
<br/>.= 
<span class="p1">(<span class="default"><a href="scmpds_4.html#K9">IExec</a> <font color="Maroon">c<sub>50</sub></font>,<span class="p2">(<span class="default"><a href="scmpds_4.html#K9">IExec</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a> ,2 <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p5">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span></span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p4">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a> ,4 <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p5">(<span class="default"><span class="p0">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span>,<font color="Maroon">c<sub>75</sub></font></span>)</span></span>)</span> <a href="scmpds_2.html#K2">.</a> <span class="p1">(<span class="default"><a href="scmp_gcd.html#K1">intpos</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">c<sub>77</sub></font> <a href="nat_1.html#K1">+</a> <span class="p4">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span>
<b>by </b><i><a class="txt" href="scpqsort.html#E15:46_7"><i><font color="Green">E66</font></i></a>, <a class="txt" href="scpqsort.html#E35:46_7"><i><font color="Green">E82</font></i></a>, <a class="txt" href="scpqsort.html#E36:46_7"><i><font color="Green">E83</font></i></a></i>
<br/>.= 
<span class="p1">(<span class="default"><a href="scmpds_4.html#K9">IExec</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><span class="p0">(<span class="default"><span class="p1">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a> ,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 3</span>)</span> <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p1">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a> ,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span> <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K2">GBP</a> ,4</span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p0">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a> ,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 2</span>)</span> <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K2">GBP</a> ,4</span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p5">(<span class="default"><a href="scmpds_2.html#K12">AddTo</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p0">(<span class="default"><span class="p1">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span>,<span class="p0">(<span class="default"><a href="xcmplx_0.html#K4">-</a> 1</span>)</span></span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p4">(<span class="default"><a href="scmpds_2.html#K12">AddTo</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p5">(<span class="default"><span class="p0">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 2</span>)</span>,1</span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p3">(<span class="default"><a href="scmpds_2.html#K12">AddTo</a> <a href="scmp_gcd.html#K2">GBP</a> ,1,2</span>)</span></span>)</span>,<span class="p2">(<span class="default"><a href="scmpds_4.html#K9">IExec</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a> ,2 <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p0">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span></span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p5">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a> ,4 <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p0">(<span class="default"><span class="p1">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span> <a href="scmpds_4.html#K3">';'</a> <font color="Maroon">c<sub>50</sub></font></span>)</span>,<font color="Maroon">c<sub>75</sub></font></span>)</span></span>)</span> <a href="scmpds_2.html#K2">.</a> <span class="p1">(<span class="default"><a href="scmp_gcd.html#K1">intpos</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">c<sub>77</sub></font> <a href="nat_1.html#K1">+</a> <span class="p4">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span></span>)</span> <a href="nat_1.html#K1">+</a> 3</span>)</span></span>)</span>
<b>by </b><i><a class="txt" href="scpqsort.html#E16:46_7"><i><font color="Green">E67</font></i></a>, <a class="txt" href="scpqsort.html#E20:46_7"><i><font color="Green">E71</font></i></a>, <a class="ref" href="scpisort.html#T8">SCPISORT:8</a></i>
<br/>.= 
<span class="p1">(<span class="default"><a href="scmpds_4.html#K9">IExec</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a> ,2 <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p0">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span></span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p5">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a> ,4 <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p0">(<span class="default"><span class="p1">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span> <a href="scmpds_4.html#K3">';'</a> <font color="Maroon">c<sub>50</sub></font></span>)</span> <a href="scmpds_4.html#K3">';'</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><span class="p0">(<span class="default"><span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a> ,<span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 3</span>)</span> <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p2">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a> ,<span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span> <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K2">GBP</a> ,4</span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p1">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a> ,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 2</span>)</span> <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K2">GBP</a> ,4</span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p0">(<span class="default"><a href="scmpds_2.html#K12">AddTo</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span>,<span class="p1">(<span class="default"><a href="xcmplx_0.html#K4">-</a> 1</span>)</span></span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p5">(<span class="default"><a href="scmpds_2.html#K12">AddTo</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p0">(<span class="default"><span class="p1">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 2</span>)</span>,1</span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p4">(<span class="default"><a href="scmpds_2.html#K12">AddTo</a> <a href="scmp_gcd.html#K2">GBP</a> ,1,2</span>)</span></span>)</span></span>)</span>,<font color="Maroon">c<sub>75</sub></font></span>)</span> <a href="scmpds_2.html#K2">.</a> <span class="p1">(<span class="default"><a href="scmp_gcd.html#K1">intpos</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">c<sub>77</sub></font> <a href="nat_1.html#K1">+</a> <span class="p4">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span></span>)</span> <a href="nat_1.html#K1">+</a> 3</span>)</span></span>)</span>
<b>by </b><i><a class="txt" href="scpqsort.html#E17:46_7"><i><font color="Green">E68</font></i></a>, <a class="ref" href="scpisort.html#T7">SCPISORT:7</a></i>
;<br/><br/>

<div><b>hereby </b>
<div class="add"><b>let </b><font color="Maroon">c<sub>90</sub></font> be   <a href="nat_1.html#NM1">Nat</a>;<br/><b>assume </b><a NAME="E1:46_7_5"/><i><font color="Green">E84</font></i>: 
( 1 <a href="xxreal_0.html#R1">&lt;=</a> <font color="Maroon">c<sub>90</sub></font> &amp; <font color="Maroon">c<sub>90</sub></font> <a href="xxreal_0.html#NR3" target="_self">&lt;</a> <font color="Maroon">c<sub>77</sub></font> )
 ;<br/><a NAME="E2:46_7_5"/><b>then </b><i><font color="Green">E85</font></i>: 
<span class="p1">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>90</sub></font> <a href="xxreal_0.html#NR2" target="_self">&gt;=</a> 1 <a href="nat_1.html#K1">+</a> 7
 <b>by </b><i><a class="txt" href="scpqsort.html#E8:46"><i><font color="Green">E48</font></i></a>, <a class="ref" href="xreal_1.html#T9">XREAL_1:9</a></i>;<br/><a NAME="E3:46_7_5"/><i><font color="Green">E86</font></i>: 
<span class="p1">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>90</sub></font> <a href="xxreal_0.html#NR3" target="_self">&lt;</a> <font color="Maroon">c<sub>77</sub></font> <a href="nat_1.html#K1">+</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span>
 <b>by </b><i><a class="txt" href="scpqsort.html#E1:46_7_5"><i><font color="Green">E84</font></i></a>, <a class="ref" href="xreal_1.html#T8">XREAL_1:8</a></i>;<br/><a NAME="E4:46_7_5"/><i><font color="Green">E87</font></i>: 
<span class="p1">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>90</sub></font> <a href="xxreal_0.html#NR2" target="_self">&gt;=</a> <font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> 1
 <b>by </b><i><a class="txt" href="scpqsort.html#E23:46_7"><i><font color="Green">E74</font></i></a>, <a class="txt" href="scpqsort.html#E1:46_7_5"><i><font color="Green">E84</font></i></a>, <a class="ref" href="xreal_1.html#T9">XREAL_1:9</a></i>;<br/><a NAME="E5:46_7_5"/>
<span class="p1">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>90</sub></font> <a href="xxreal_0.html#NR2" target="_self">&gt;=</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 1
 <b>by </b><i><a class="txt" href="scpqsort.html#E1:46_7_5"><i><font color="Green">E84</font></i></a>, <a class="ref" href="xreal_1.html#T8">XREAL_1:8</a></i>;<br/><a NAME="E6:46_7_5"/><b>then </b>
<span class="p1">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>90</sub></font> <a href="xxreal_0.html#NR4" target="_self">&gt;</a> <font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font>
 <b>by </b><i><a class="txt" href="scpqsort.html#E26:46_7"><i><font color="Green">E77</font></i></a>, <a class="ref" href="xreal_1.html#T2">XREAL_1:2</a></i>;<br/><a NAME="E7:46_7_5"/><b>then </b><i><font color="Green">E88</font></i>: 
<span class="p1">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>90</sub></font> <a href="xxreal_0.html#NR4" target="_self">&gt;</a> <span class="p1">(<span class="default"><a href="scmpds_4.html#K9">IExec</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a> ,2 <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p4">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span></span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p3">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a> ,4 <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p4">(<span class="default"><span class="p5">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span>,<font color="Maroon">c<sub>75</sub></font></span>)</span> <a href="scmpds_2.html#K2">.</a> <span class="p1">(<span class="default"><a href="scmp_gcd.html#K1">intpos</a> 4</span>)</span>
 <b>by </b><i><a class="txt" href="scpqsort.html#E1:46_7"><i><font color="Green">E55</font></i></a>, <a class="txt" href="scpqsort.html#E6:46_7"><i><font color="Green">E60</font></i></a>, <a class="ref" href="xreal_1.html#T2">XREAL_1:2</a></i>;<br/><a NAME="E8:46_7_5"/><i><font color="Green">E89</font></i>: 
( <span class="p1">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>90</sub></font> <a href="xxreal_0.html#NR4" target="_self">&gt;</a> 2 &amp; <span class="p1">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>90</sub></font> <a href="xxreal_0.html#NR4" target="_self">&gt;</a> 4 )
 <b>by </b><i><a class="txt" href="scpqsort.html#E2:46_7_5"><i><font color="Green">E85</font></i></a>, <a class="ref" href="xreal_1.html#T2">XREAL_1:2</a></i>;<br/><b>thus </b><span class="p1">(<span class="default"><a href="scmpds_4.html#K9">IExec</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a> ,2 <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p0">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span></span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p5">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a> ,4 <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p0">(<span class="default"><span class="p1">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span> <a href="scmpds_4.html#K3">';'</a> <font color="Maroon">c<sub>50</sub></font></span>)</span> <a href="scmpds_4.html#K3">';'</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><span class="p0">(<span class="default"><span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a> ,<span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 3</span>)</span> <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p2">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a> ,<span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span> <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K2">GBP</a> ,4</span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p1">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a> ,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 2</span>)</span> <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K2">GBP</a> ,4</span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p0">(<span class="default"><a href="scmpds_2.html#K12">AddTo</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span>,<span class="p1">(<span class="default"><a href="xcmplx_0.html#K4">-</a> 1</span>)</span></span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p5">(<span class="default"><a href="scmpds_2.html#K12">AddTo</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p0">(<span class="default"><span class="p1">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 2</span>)</span>,1</span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p4">(<span class="default"><a href="scmpds_2.html#K12">AddTo</a> <a href="scmp_gcd.html#K2">GBP</a> ,1,2</span>)</span></span>)</span></span>)</span>,<font color="Maroon">c<sub>75</sub></font></span>)</span> <a href="scmpds_2.html#K2">.</a> <span class="p1">(<span class="default"><a href="scmp_gcd.html#K1">intpos</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>90</sub></font></span>)</span></span>)</span> = 
<span class="p1">(<span class="default"><a href="scmpds_4.html#K9">IExec</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><span class="p0">(<span class="default"><span class="p1">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a> ,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 3</span>)</span> <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p1">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a> ,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span> <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K2">GBP</a> ,4</span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p0">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a> ,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 2</span>)</span> <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K2">GBP</a> ,4</span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p5">(<span class="default"><a href="scmpds_2.html#K12">AddTo</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p0">(<span class="default"><span class="p1">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span>,<span class="p0">(<span class="default"><a href="xcmplx_0.html#K4">-</a> 1</span>)</span></span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p4">(<span class="default"><a href="scmpds_2.html#K12">AddTo</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p5">(<span class="default"><span class="p0">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 2</span>)</span>,1</span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p3">(<span class="default"><a href="scmpds_2.html#K12">AddTo</a> <a href="scmp_gcd.html#K2">GBP</a> ,1,2</span>)</span></span>)</span>,<span class="p2">(<span class="default"><a href="scmpds_4.html#K9">IExec</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a> ,2 <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p0">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span></span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p5">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a> ,4 <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p0">(<span class="default"><span class="p1">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span> <a href="scmpds_4.html#K3">';'</a> <font color="Maroon">c<sub>50</sub></font></span>)</span>,<font color="Maroon">c<sub>75</sub></font></span>)</span></span>)</span> <a href="scmpds_2.html#K2">.</a> <span class="p1">(<span class="default"><a href="scmp_gcd.html#K1">intpos</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>90</sub></font></span>)</span></span>)</span>
<b>by </b><i><a class="txt" href="scpqsort.html#E17:46_7"><i><font color="Green">E68</font></i></a>, <a class="ref" href="scpisort.html#T7">SCPISORT:7</a></i>
<br/>.= 
<span class="p1">(<span class="default"><a href="scmpds_4.html#K9">IExec</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a> ,2 <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p5">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span></span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p4">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a> ,4 <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p5">(<span class="default"><span class="p0">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span> <a href="scmpds_4.html#K3">';'</a> <font color="Maroon">c<sub>50</sub></font></span>)</span>,<font color="Maroon">c<sub>75</sub></font></span>)</span> <a href="scmpds_2.html#K2">.</a> <span class="p1">(<span class="default"><a href="scmp_gcd.html#K1">intpos</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>90</sub></font></span>)</span></span>)</span>
<b>by </b><i><a class="txt" href="scpqsort.html#E11:46"><i><font color="Green">E51</font></i></a>, <a class="txt" href="scpqsort.html#E1:46_7"><i><font color="Green">E55</font></i></a>, <a class="txt" href="scpqsort.html#E18:46_7"><i><font color="Green">E69</font></i></a>, <a class="txt" href="scpqsort.html#E19:46_7"><i><font color="Green">E70</font></i></a>, <a class="txt" href="scpqsort.html#E2:46_7_5"><i><font color="Green">E85</font></i></a>, <a class="txt" href="scpqsort.html#E3:46_7_5"><i><font color="Green">E86</font></i></a></i>
<br/>.= 
<span class="p1">(<span class="default"><a href="scmpds_4.html#K9">IExec</a> <font color="Maroon">c<sub>50</sub></font>,<span class="p2">(<span class="default"><a href="scmpds_4.html#K9">IExec</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a> ,2 <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p5">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span></span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p4">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a> ,4 <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p5">(<span class="default"><span class="p0">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span>,<font color="Maroon">c<sub>75</sub></font></span>)</span></span>)</span> <a href="scmpds_2.html#K2">.</a> <span class="p1">(<span class="default"><a href="scmp_gcd.html#K1">intpos</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>90</sub></font></span>)</span></span>)</span>
<b>by </b><i><a class="txt" href="scpqsort.html#E16:46_7"><i><font color="Green">E67</font></i></a>, <a class="ref" href="scpisort.html#T8">SCPISORT:8</a></i>
<br/>.= 
<span class="p1">(<span class="default"><a href="scmpds_4.html#K9">IExec</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a> ,2 <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p4">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span></span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p3">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a> ,4 <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p4">(<span class="default"><span class="p5">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span>,<font color="Maroon">c<sub>75</sub></font></span>)</span> <a href="scmpds_2.html#K2">.</a> <span class="p1">(<span class="default"><a href="scmp_gcd.html#K1">intpos</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>90</sub></font></span>)</span></span>)</span>
<b>by </b><i><a class="txt" href="scpqsort.html#E15:46_7"><i><font color="Green">E66</font></i></a>, <a class="txt" href="scpqsort.html#E4:46_7_5"><i><font color="Green">E87</font></i></a>, <a class="txt" href="scpqsort.html#E7:46_7_5"><i><font color="Green">E88</font></i></a></i>
<br/>.= 
<font color="Maroon">c<sub>75</sub></font> <a href="scmpds_2.html#K2">.</a> <span class="p1">(<span class="default"><a href="scmp_gcd.html#K1">intpos</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>90</sub></font></span>)</span></span>)</span>
<b>by </b><i><a class="txt" href="scpqsort.html#E12:46"><i><font color="Green">E52</font></i></a>, <a class="txt" href="scpqsort.html#E1:46_7"><i><font color="Green">E55</font></i></a>, <a class="txt" href="scpqsort.html#E8:46_7_5"><i><font color="Green">E89</font></i></a></i>
;<br/></div>
<b>end;</b></div>

<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="46_7_6"><b>now </b></a><div class="add"><b>let </b><font color="Maroon">c<sub>90</sub></font> be   <a href="nat_1.html#NM1">Nat</a>;<br/><b>assume </b><a NAME="E1:46_7_6"/>
<font color="Maroon">c<sub>90</sub></font> <a href="hidden.html#R2">in</a>  <a href="finseq_1.html#K2">Seg</a> <font color="Maroon">c<sub>49</sub></font>
 ;<br/><a NAME="E2:46_7_6"/><b>then </b><i><font color="Green">E84</font></i>: 
( 1 <a href="xxreal_0.html#R1">&lt;=</a> <font color="Maroon">c<sub>90</sub></font> &amp; <font color="Maroon">c<sub>90</sub></font> <a href="xxreal_0.html#R1">&lt;=</a> <font color="Maroon">c<sub>49</sub></font> )
 <b>by </b><i><a class="ref" href="finseq_1.html#T3">FINSEQ_1:3</a></i>;<br/><a NAME="E3:46_7_6"/><b>then </b>
<font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>90</sub></font> <a href="xxreal_0.html#NR2" target="_self">&gt;=</a> <font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> 1
 <b>by </b><i><a class="ref" href="xreal_1.html#T8">XREAL_1:8</a></i>;<br/><a NAME="E4:46_7_6"/><b>then </b><i><font color="Green">E85</font></i>: 
<font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>90</sub></font> <a href="xxreal_0.html#NR2" target="_self">&gt;=</a> 8
 <b>by </b><i><a class="txt" href="scpqsort.html#E7:46_7"><i><font color="Green">E61</font></i></a>, <a class="ref" href="xreal_1.html#T2">XREAL_1:2</a></i>;<br/><a NAME="E5:46_7_6"/>
<font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>90</sub></font> <a href="xxreal_0.html#R1">&lt;=</a> <font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font>
 <b>by </b><i><a class="txt" href="scpqsort.html#E2:46_7_6"><i><font color="Green">E84</font></i></a>, <a class="ref" href="xreal_1.html#T8">XREAL_1:8</a></i>;<br/><a NAME="E6:46_7_6"/><b>then </b><i><font color="Green">E86</font></i>: 
<font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>90</sub></font> <a href="xxreal_0.html#NR3" target="_self">&lt;</a> <font color="Maroon">c<sub>77</sub></font> <a href="nat_1.html#K1">+</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span>
 <b>by </b><i><a class="txt" href="scpqsort.html#E27:46_7"><i><font color="Green">E78</font></i></a>, <a class="ref" href="xreal_1.html#T2">XREAL_1:2</a></i>;<br/><b>thus </b><font color="Maroon">c<sub>81</sub></font> <a href="funct_1.html#K1">.</a> <font color="Maroon">c<sub>90</sub></font> = 
<span class="p1">(<span class="default"><a href="scmpds_4.html#K9">IExec</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a> ,2 <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p0">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span></span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p5">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a> ,4 <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p0">(<span class="default"><span class="p1">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span> <a href="scmpds_4.html#K3">';'</a> <font color="Maroon">c<sub>50</sub></font></span>)</span> <a href="scmpds_4.html#K3">';'</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><span class="p0">(<span class="default"><span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a> ,<span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 3</span>)</span> <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p2">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a> ,<span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span> <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K2">GBP</a> ,4</span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p1">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a> ,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 2</span>)</span> <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K2">GBP</a> ,4</span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p0">(<span class="default"><a href="scmpds_2.html#K12">AddTo</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span>,<span class="p1">(<span class="default"><a href="xcmplx_0.html#K4">-</a> 1</span>)</span></span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p5">(<span class="default"><a href="scmpds_2.html#K12">AddTo</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p0">(<span class="default"><span class="p1">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 2</span>)</span>,1</span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p4">(<span class="default"><a href="scmpds_2.html#K12">AddTo</a> <a href="scmp_gcd.html#K2">GBP</a> ,1,2</span>)</span></span>)</span></span>)</span>,<font color="Maroon">c<sub>75</sub></font></span>)</span> <a href="scmpds_2.html#K2">.</a> <span class="p1">(<span class="default"><a href="scmp_gcd.html#K1">intpos</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>90</sub></font></span>)</span></span>)</span>
<b>by </b><i><a class="txt" href="scpqsort.html#E3:46_7"><i><font color="Green">E57</font></i></a>, <a class="txt" href="scpqsort.html#E2:46_7_6"><i><font color="Green">E84</font></i></a>, <a class="ref" href="scpisort.html#D1">SCPISORT:def 1</a></i>
<br/>.= 
<span class="p1">(<span class="default"><a href="scmpds_4.html#K9">IExec</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><span class="p0">(<span class="default"><span class="p1">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a> ,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 3</span>)</span> <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p1">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a> ,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span> <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K2">GBP</a> ,4</span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p0">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a> ,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 2</span>)</span> <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K2">GBP</a> ,4</span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p5">(<span class="default"><a href="scmpds_2.html#K12">AddTo</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p0">(<span class="default"><span class="p1">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span>,<span class="p0">(<span class="default"><a href="xcmplx_0.html#K4">-</a> 1</span>)</span></span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p4">(<span class="default"><a href="scmpds_2.html#K12">AddTo</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p5">(<span class="default"><span class="p0">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 2</span>)</span>,1</span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p3">(<span class="default"><a href="scmpds_2.html#K12">AddTo</a> <a href="scmp_gcd.html#K2">GBP</a> ,1,2</span>)</span></span>)</span>,<span class="p2">(<span class="default"><a href="scmpds_4.html#K9">IExec</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a> ,2 <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p0">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span></span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p5">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a> ,4 <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p0">(<span class="default"><span class="p1">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span> <a href="scmpds_4.html#K3">';'</a> <font color="Maroon">c<sub>50</sub></font></span>)</span>,<font color="Maroon">c<sub>75</sub></font></span>)</span></span>)</span> <a href="scmpds_2.html#K2">.</a> <span class="p1">(<span class="default"><a href="scmp_gcd.html#K1">intpos</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>90</sub></font></span>)</span></span>)</span>
<b>by </b><i><a class="txt" href="scpqsort.html#E17:46_7"><i><font color="Green">E68</font></i></a>, <a class="ref" href="scpisort.html#T7">SCPISORT:7</a></i>
<br/>.= 
<span class="p1">(<span class="default"><a href="scmpds_4.html#K9">IExec</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a> ,2 <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p5">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span></span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p4">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a> ,4 <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p5">(<span class="default"><span class="p0">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span> <a href="scmpds_4.html#K3">';'</a> <font color="Maroon">c<sub>50</sub></font></span>)</span>,<font color="Maroon">c<sub>75</sub></font></span>)</span> <a href="scmpds_2.html#K2">.</a> <span class="p1">(<span class="default"><a href="scmp_gcd.html#K1">intpos</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>90</sub></font></span>)</span></span>)</span>
<b>by </b><i><a class="txt" href="scpqsort.html#E11:46"><i><font color="Green">E51</font></i></a>, <a class="txt" href="scpqsort.html#E1:46_7"><i><font color="Green">E55</font></i></a>, <a class="txt" href="scpqsort.html#E18:46_7"><i><font color="Green">E69</font></i></a>, <a class="txt" href="scpqsort.html#E19:46_7"><i><font color="Green">E70</font></i></a>, <a class="txt" href="scpqsort.html#E4:46_7_6"><i><font color="Green">E85</font></i></a>, <a class="txt" href="scpqsort.html#E6:46_7_6"><i><font color="Green">E86</font></i></a></i>
<br/>.= 
<span class="p1">(<span class="default"><a href="scmpds_4.html#K9">IExec</a> <font color="Maroon">c<sub>50</sub></font>,<span class="p2">(<span class="default"><a href="scmpds_4.html#K9">IExec</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a> ,2 <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p5">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span></span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p4">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a> ,4 <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p5">(<span class="default"><span class="p0">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span>,<font color="Maroon">c<sub>75</sub></font></span>)</span></span>)</span> <a href="scmpds_2.html#K2">.</a> <span class="p1">(<span class="default"><a href="scmp_gcd.html#K1">intpos</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>90</sub></font></span>)</span></span>)</span>
<b>by </b><i><a class="txt" href="scpqsort.html#E16:46_7"><i><font color="Green">E67</font></i></a>, <a class="ref" href="scpisort.html#T8">SCPISORT:8</a></i>
<br/>.= 
<font color="Maroon">c<sub>88</sub></font> <a href="funct_1.html#K1">.</a> <font color="Maroon">c<sub>90</sub></font>
<b>by </b><i><a class="txt" href="scpqsort.html#E11:46_7"><i><font color="Green">E63</font></i></a>, <a class="txt" href="scpqsort.html#E2:46_7_6"><i><font color="Green">E84</font></i></a></i>
;<br/></div><b>end;</b></div>
<b>hence </b><a NAME="E41:46_7"/>
<font color="Maroon">c<sub>80</sub></font>,<font color="Maroon">c<sub>81</sub></font> <a href="rfinseq.html#R1">are_fiberwise_equipotent</a> 
 <b>by </b><i><a class="txt" href="scpqsort.html#E3:46_7"><i><font color="Green">E57</font></i></a>, <a class="txt" href="scpqsort.html#E11:46_7"><i><font color="Green">E63</font></i></a>, <a class="txt" href="scpqsort.html#E13:46_7"><i><font color="Green">E65</font></i></a>, <a class="ref" href="finseq_2.html#T10">FINSEQ_2:10</a></i>;<br/>

<b>take </b>
<font color="Maroon">c<sub>89</sub></font>
;<br/>

<b>thus </b><a NAME="E42:46_7"/>
( <font color="Maroon">c<sub>78</sub></font> <a href="xxreal_0.html#R1">&lt;=</a> <font color="Maroon">c<sub>89</sub></font> &amp; <font color="Maroon">c<sub>89</sub></font> <a href="xxreal_0.html#R1">&lt;=</a> <font color="Maroon">c<sub>79</sub></font> )
 <b>by </b><i><a class="txt" href="scpqsort.html#E12:46"><i><font color="Green">E52</font></i></a>, <a class="txt" href="scpqsort.html#E1:46_7"><i><font color="Green">E55</font></i></a>, <a class="txt" href="scpqsort.html#E15:46_7"><i><font color="Green">E66</font></i></a></i>;<br/>

<a NAME="E43:46_7"/><i><font color="Green">E84</font></i>: 
<font color="Maroon">c<sub>78</sub></font> <a href="xxreal_0.html#NR2" target="_self">&gt;=</a> 8
 
<b>by </b><i><a class="txt" href="scpqsort.html#E1:46_7"><i><font color="Green">E55</font></i></a>, <a class="txt" href="scpqsort.html#E7:46_7"><i><font color="Green">E61</font></i></a>, <a class="ref" href="xreal_1.html#T2">XREAL_1:2</a></i>;<br/>
<a NAME="E44:46_7"/><i><font color="Green">E85</font></i>: 
<font color="Maroon">c<sub>89</sub></font> <a href="xxreal_0.html#NR3" target="_self">&lt;</a> <font color="Maroon">c<sub>77</sub></font> <a href="nat_1.html#K1">+</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span>
 
<b>by </b><i><a class="txt" href="scpqsort.html#E15:46_7"><i><font color="Green">E66</font></i></a>, <a class="txt" href="scpqsort.html#E28:46_7"><i><font color="Green">E79</font></i></a>, <a class="ref" href="xreal_1.html#T2">XREAL_1:2</a></i>;<br/>
<a NAME="E45:46_7"/><i><font color="Green">E86</font></i>: 
<font color="Maroon">c<sub>89</sub></font> <a href="xxreal_0.html#NR2" target="_self">&gt;=</a> 8
 
<b>by </b><i><a class="txt" href="scpqsort.html#E15:46_7"><i><font color="Green">E66</font></i></a>, <a class="txt" href="scpqsort.html#E43:46_7"><i><font color="Green">E84</font></i></a>, <a class="ref" href="xreal_1.html#T2">XREAL_1:2</a></i>;<br/>
<b>thus </b><font color="Maroon">c<sub>89</sub></font> <a href="xcmplx_0.html#K6">-</a> 1 = 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="scmpds_4.html#K9">IExec</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a> ,2 <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p0">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span></span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p5">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a> ,4 <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p0">(<span class="default"><span class="p1">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span> <a href="scmpds_4.html#K3">';'</a> <font color="Maroon">c<sub>50</sub></font></span>)</span>,<font color="Maroon">c<sub>75</sub></font></span>)</span> <a href="scmpds_2.html#K2">.</a> <span class="p2">(<span class="default"><a href="scmp_gcd.html#K1">intpos</a> 4</span>)</span></span>)</span> <a href="xcmplx_0.html#K6">-</a> 1
<b>by </b><i><a class="txt" href="scpqsort.html#E15:46_7"><i><font color="Green">E66</font></i></a>, <a class="txt" href="scpqsort.html#E16:46_7"><i><font color="Green">E67</font></i></a>, <a class="ref" href="scpisort.html#T8">SCPISORT:8</a></i>
<br/>.= 
<span class="p1">(<span class="default"><a href="scmpds_4.html#K9">IExec</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a> ,2 <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p0">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span></span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p5">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a> ,4 <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p0">(<span class="default"><span class="p1">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span> <a href="scmpds_4.html#K3">';'</a> <font color="Maroon">c<sub>50</sub></font></span>)</span> <a href="scmpds_4.html#K3">';'</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><span class="p0">(<span class="default"><span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a> ,<span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 3</span>)</span> <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p2">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a> ,<span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span> <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K2">GBP</a> ,4</span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p1">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a> ,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 2</span>)</span> <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K2">GBP</a> ,4</span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p0">(<span class="default"><a href="scmpds_2.html#K12">AddTo</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span>,<span class="p1">(<span class="default"><a href="xcmplx_0.html#K4">-</a> 1</span>)</span></span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p5">(<span class="default"><a href="scmpds_2.html#K12">AddTo</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p0">(<span class="default"><span class="p1">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 2</span>)</span>,1</span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p4">(<span class="default"><a href="scmpds_2.html#K12">AddTo</a> <a href="scmp_gcd.html#K2">GBP</a> ,1,2</span>)</span></span>)</span></span>)</span>,<font color="Maroon">c<sub>75</sub></font></span>)</span> <a href="scmpds_2.html#K2">.</a> <span class="p1">(<span class="default"><a href="scmp_gcd.html#K1">intpos</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">c<sub>77</sub></font> <a href="nat_1.html#K1">+</a> <span class="p4">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span>
<b>by </b><i><a class="txt" href="scpqsort.html#E17:46_7"><i><font color="Green">E68</font></i></a>, <a class="txt" href="scpqsort.html#E20:46_7"><i><font color="Green">E71</font></i></a>, <a class="ref" href="scpisort.html#T7">SCPISORT:7</a></i>
;<br/>

<b>thus </b><font color="Maroon">c<sub>89</sub></font> <a href="nat_1.html#K1">+</a> 1 = 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="scmpds_4.html#K9">IExec</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a> ,2 <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p0">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span></span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p5">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a> ,4 <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p0">(<span class="default"><span class="p1">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span> <a href="scmpds_4.html#K3">';'</a> <font color="Maroon">c<sub>50</sub></font></span>)</span>,<font color="Maroon">c<sub>75</sub></font></span>)</span> <a href="scmpds_2.html#K2">.</a> <span class="p2">(<span class="default"><a href="scmp_gcd.html#K1">intpos</a> 4</span>)</span></span>)</span> <a href="xcmplx_0.html#K2">+</a> 1
<b>by </b><i><a class="txt" href="scpqsort.html#E15:46_7"><i><font color="Green">E66</font></i></a>, <a class="txt" href="scpqsort.html#E16:46_7"><i><font color="Green">E67</font></i></a>, <a class="ref" href="scpisort.html#T8">SCPISORT:8</a></i>
<br/>.= 
<span class="p1">(<span class="default"><a href="scmpds_4.html#K9">IExec</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a> ,2 <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p0">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span></span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p5">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a> ,4 <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p0">(<span class="default"><span class="p1">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span> <a href="scmpds_4.html#K3">';'</a> <font color="Maroon">c<sub>50</sub></font></span>)</span> <a href="scmpds_4.html#K3">';'</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><span class="p0">(<span class="default"><span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a> ,<span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 3</span>)</span> <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p2">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a> ,<span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span> <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K2">GBP</a> ,4</span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p1">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a> ,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 2</span>)</span> <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K2">GBP</a> ,4</span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p0">(<span class="default"><a href="scmpds_2.html#K12">AddTo</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span>,<span class="p1">(<span class="default"><a href="xcmplx_0.html#K4">-</a> 1</span>)</span></span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p5">(<span class="default"><a href="scmpds_2.html#K12">AddTo</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p0">(<span class="default"><span class="p1">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 2</span>)</span>,1</span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p4">(<span class="default"><a href="scmpds_2.html#K12">AddTo</a> <a href="scmp_gcd.html#K2">GBP</a> ,1,2</span>)</span></span>)</span></span>)</span>,<font color="Maroon">c<sub>75</sub></font></span>)</span> <a href="scmpds_2.html#K2">.</a> <span class="p1">(<span class="default"><a href="scmp_gcd.html#K1">intpos</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">c<sub>77</sub></font> <a href="nat_1.html#K1">+</a> <span class="p4">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span></span>)</span> <a href="nat_1.html#K1">+</a> 2</span>)</span></span>)</span>
<b>by </b><i><a class="txt" href="scpqsort.html#E17:46_7"><i><font color="Green">E68</font></i></a>, <a class="txt" href="scpqsort.html#E20:46_7"><i><font color="Green">E71</font></i></a>, <a class="ref" href="scpisort.html#T7">SCPISORT:7</a></i>
;<br/>

<div><b>hereby </b>
<div class="add"><b>let </b><font color="Maroon">c<sub>90</sub></font> be   <a href="nat_1.html#NM1">Nat</a>;<br/><b>assume </b><a NAME="E1:46_7_9"/><i><font color="Green">E87</font></i>: 
( <font color="Maroon">c<sub>78</sub></font> <a href="xxreal_0.html#R1">&lt;=</a> <font color="Maroon">c<sub>90</sub></font> &amp; <font color="Maroon">c<sub>90</sub></font> <a href="xxreal_0.html#NR3" target="_self">&lt;</a> <font color="Maroon">c<sub>89</sub></font> )
 ;<br/><a NAME="E2:46_7_9"/><b>then </b><i><font color="Green">E88</font></i>: 
<font color="Maroon">c<sub>90</sub></font> <a href="xxreal_0.html#NR3" target="_self">&lt;</a> <font color="Maroon">c<sub>77</sub></font> <a href="nat_1.html#K1">+</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span>
 <b>by </b><i><a class="txt" href="scpqsort.html#E44:46_7"><i><font color="Green">E85</font></i></a>, <a class="ref" href="xreal_1.html#T2">XREAL_1:2</a></i>;<br/><a NAME="E3:46_7_9"/><i><font color="Green">E89</font></i>: 
<font color="Maroon">c<sub>90</sub></font> <a href="xxreal_0.html#NR2" target="_self">&gt;=</a> 8
 <b>by </b><i><a class="txt" href="scpqsort.html#E43:46_7"><i><font color="Green">E84</font></i></a>, <a class="txt" href="scpqsort.html#E1:46_7_9"><i><font color="Green">E87</font></i></a>, <a class="ref" href="xreal_1.html#T2">XREAL_1:2</a></i>;<br/><i><font color="Green">E90</font></i>: <span class="p1">(<span class="default"><a href="scmpds_4.html#K9">IExec</a> <font color="Maroon">c<sub>50</sub></font>,<span class="p2">(<span class="default"><a href="scmpds_4.html#K9">IExec</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a> ,2 <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p5">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span></span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p4">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a> ,4 <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p5">(<span class="default"><span class="p0">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span>,<font color="Maroon">c<sub>75</sub></font></span>)</span></span>)</span> <a href="scmpds_2.html#K2">.</a> <span class="p1">(<span class="default"><a href="scmp_gcd.html#K1">intpos</a> <font color="Maroon">c<sub>90</sub></font></span>)</span> = 
<span class="p1">(<span class="default"><a href="scmpds_4.html#K9">IExec</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a> ,2 <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p5">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span></span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p4">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a> ,4 <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p5">(<span class="default"><span class="p0">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span> <a href="scmpds_4.html#K3">';'</a> <font color="Maroon">c<sub>50</sub></font></span>)</span>,<font color="Maroon">c<sub>75</sub></font></span>)</span> <a href="scmpds_2.html#K2">.</a> <span class="p1">(<span class="default"><a href="scmp_gcd.html#K1">intpos</a> <font color="Maroon">c<sub>90</sub></font></span>)</span>
<b>by </b><i><a class="txt" href="scpqsort.html#E16:46_7"><i><font color="Green">E67</font></i></a>, <a class="ref" href="scpisort.html#T8">SCPISORT:8</a></i>
<br/>.= 
<span class="p1">(<span class="default"><a href="scmpds_4.html#K9">IExec</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><span class="p0">(<span class="default"><span class="p1">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a> ,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 3</span>)</span> <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p1">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a> ,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span> <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K2">GBP</a> ,4</span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p0">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a> ,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 2</span>)</span> <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K2">GBP</a> ,4</span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p5">(<span class="default"><a href="scmpds_2.html#K12">AddTo</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p0">(<span class="default"><span class="p1">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span>,<span class="p0">(<span class="default"><a href="xcmplx_0.html#K4">-</a> 1</span>)</span></span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p4">(<span class="default"><a href="scmpds_2.html#K12">AddTo</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p5">(<span class="default"><span class="p0">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 2</span>)</span>,1</span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p3">(<span class="default"><a href="scmpds_2.html#K12">AddTo</a> <a href="scmp_gcd.html#K2">GBP</a> ,1,2</span>)</span></span>)</span>,<span class="p2">(<span class="default"><a href="scmpds_4.html#K9">IExec</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a> ,2 <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p0">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span></span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p5">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a> ,4 <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p0">(<span class="default"><span class="p1">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span> <a href="scmpds_4.html#K3">';'</a> <font color="Maroon">c<sub>50</sub></font></span>)</span>,<font color="Maroon">c<sub>75</sub></font></span>)</span></span>)</span> <a href="scmpds_2.html#K2">.</a> <span class="p1">(<span class="default"><a href="scmp_gcd.html#K1">intpos</a> <font color="Maroon">c<sub>90</sub></font></span>)</span>
<b>by </b><i><a class="txt" href="scpqsort.html#E11:46"><i><font color="Green">E51</font></i></a>, <a class="txt" href="scpqsort.html#E1:46_7"><i><font color="Green">E55</font></i></a>, <a class="txt" href="scpqsort.html#E18:46_7"><i><font color="Green">E69</font></i></a>, <a class="txt" href="scpqsort.html#E19:46_7"><i><font color="Green">E70</font></i></a>, <a class="txt" href="scpqsort.html#E2:46_7_9"><i><font color="Green">E88</font></i></a>, <a class="txt" href="scpqsort.html#E3:46_7_9"><i><font color="Green">E89</font></i></a></i>
<br/>.= 
<span class="p1">(<span class="default"><a href="scmpds_4.html#K9">IExec</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a> ,2 <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p0">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span></span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p5">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a> ,4 <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p0">(<span class="default"><span class="p1">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span> <a href="scmpds_4.html#K3">';'</a> <font color="Maroon">c<sub>50</sub></font></span>)</span> <a href="scmpds_4.html#K3">';'</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><span class="p0">(<span class="default"><span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a> ,<span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 3</span>)</span> <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p2">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a> ,<span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span> <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K2">GBP</a> ,4</span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p1">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a> ,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 2</span>)</span> <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K2">GBP</a> ,4</span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p0">(<span class="default"><a href="scmpds_2.html#K12">AddTo</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span>,<span class="p1">(<span class="default"><a href="xcmplx_0.html#K4">-</a> 1</span>)</span></span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p5">(<span class="default"><a href="scmpds_2.html#K12">AddTo</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p0">(<span class="default"><span class="p1">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 2</span>)</span>,1</span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p4">(<span class="default"><a href="scmpds_2.html#K12">AddTo</a> <a href="scmp_gcd.html#K2">GBP</a> ,1,2</span>)</span></span>)</span></span>)</span>,<font color="Maroon">c<sub>75</sub></font></span>)</span> <a href="scmpds_2.html#K2">.</a> <span class="p1">(<span class="default"><a href="scmp_gcd.html#K1">intpos</a> <font color="Maroon">c<sub>90</sub></font></span>)</span>
<b>by </b><i><a class="txt" href="scpqsort.html#E17:46_7"><i><font color="Green">E68</font></i></a>, <a class="ref" href="scpisort.html#T7">SCPISORT:7</a></i>
;<br/><span class="p1">(<span class="default"><a href="scmpds_4.html#K9">IExec</a> <font color="Maroon">c<sub>50</sub></font>,<span class="p2">(<span class="default"><a href="scmpds_4.html#K9">IExec</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a> ,2 <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p5">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span></span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p4">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a> ,4 <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p5">(<span class="default"><span class="p0">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span>,<font color="Maroon">c<sub>75</sub></font></span>)</span></span>)</span> <a href="scmpds_2.html#K2">.</a> <span class="p1">(<span class="default"><a href="scmp_gcd.html#K1">intpos</a> <font color="Maroon">c<sub>89</sub></font></span>)</span> = 
<span class="p1">(<span class="default"><a href="scmpds_4.html#K9">IExec</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a> ,2 <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p5">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span></span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p4">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a> ,4 <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p5">(<span class="default"><span class="p0">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span> <a href="scmpds_4.html#K3">';'</a> <font color="Maroon">c<sub>50</sub></font></span>)</span>,<font color="Maroon">c<sub>75</sub></font></span>)</span> <a href="scmpds_2.html#K2">.</a> <span class="p1">(<span class="default"><a href="scmp_gcd.html#K1">intpos</a> <font color="Maroon">c<sub>89</sub></font></span>)</span>
<b>by </b><i><a class="txt" href="scpqsort.html#E16:46_7"><i><font color="Green">E67</font></i></a>, <a class="ref" href="scpisort.html#T8">SCPISORT:8</a></i>
<br/>.= 
<span class="p1">(<span class="default"><a href="scmpds_4.html#K9">IExec</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><span class="p0">(<span class="default"><span class="p1">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a> ,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 3</span>)</span> <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p1">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a> ,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span> <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K2">GBP</a> ,4</span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p0">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a> ,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 2</span>)</span> <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K2">GBP</a> ,4</span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p5">(<span class="default"><a href="scmpds_2.html#K12">AddTo</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p0">(<span class="default"><span class="p1">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span>,<span class="p0">(<span class="default"><a href="xcmplx_0.html#K4">-</a> 1</span>)</span></span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p4">(<span class="default"><a href="scmpds_2.html#K12">AddTo</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p5">(<span class="default"><span class="p0">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 2</span>)</span>,1</span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p3">(<span class="default"><a href="scmpds_2.html#K12">AddTo</a> <a href="scmp_gcd.html#K2">GBP</a> ,1,2</span>)</span></span>)</span>,<span class="p2">(<span class="default"><a href="scmpds_4.html#K9">IExec</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a> ,2 <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p0">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span></span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p5">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a> ,4 <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p0">(<span class="default"><span class="p1">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span> <a href="scmpds_4.html#K3">';'</a> <font color="Maroon">c<sub>50</sub></font></span>)</span>,<font color="Maroon">c<sub>75</sub></font></span>)</span></span>)</span> <a href="scmpds_2.html#K2">.</a> <span class="p1">(<span class="default"><a href="scmp_gcd.html#K1">intpos</a> <font color="Maroon">c<sub>89</sub></font></span>)</span>
<b>by </b><i><a class="txt" href="scpqsort.html#E11:46"><i><font color="Green">E51</font></i></a>, <a class="txt" href="scpqsort.html#E1:46_7"><i><font color="Green">E55</font></i></a>, <a class="txt" href="scpqsort.html#E18:46_7"><i><font color="Green">E69</font></i></a>, <a class="txt" href="scpqsort.html#E19:46_7"><i><font color="Green">E70</font></i></a>, <a class="txt" href="scpqsort.html#E44:46_7"><i><font color="Green">E85</font></i></a>, <a class="txt" href="scpqsort.html#E45:46_7"><i><font color="Green">E86</font></i></a></i>
<br/>.= 
<span class="p1">(<span class="default"><a href="scmpds_4.html#K9">IExec</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a> ,2 <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p0">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span></span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p5">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a> ,4 <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p0">(<span class="default"><span class="p1">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span> <a href="scmpds_4.html#K3">';'</a> <font color="Maroon">c<sub>50</sub></font></span>)</span> <a href="scmpds_4.html#K3">';'</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><span class="p0">(<span class="default"><span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a> ,<span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 3</span>)</span> <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p2">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a> ,<span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span> <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K2">GBP</a> ,4</span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p1">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a> ,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 2</span>)</span> <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K2">GBP</a> ,4</span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p0">(<span class="default"><a href="scmpds_2.html#K12">AddTo</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span>,<span class="p1">(<span class="default"><a href="xcmplx_0.html#K4">-</a> 1</span>)</span></span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p5">(<span class="default"><a href="scmpds_2.html#K12">AddTo</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p0">(<span class="default"><span class="p1">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 2</span>)</span>,1</span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p4">(<span class="default"><a href="scmpds_2.html#K12">AddTo</a> <a href="scmp_gcd.html#K2">GBP</a> ,1,2</span>)</span></span>)</span></span>)</span>,<font color="Maroon">c<sub>75</sub></font></span>)</span> <a href="scmpds_2.html#K2">.</a> <span class="p1">(<span class="default"><a href="scmp_gcd.html#K1">intpos</a> <font color="Maroon">c<sub>89</sub></font></span>)</span>
<b>by </b><i><a class="txt" href="scpqsort.html#E17:46_7"><i><font color="Green">E68</font></i></a>, <a class="ref" href="scpisort.html#T7">SCPISORT:7</a></i>
;<br/><b>hence </b><a NAME="E6:46_7_9"/>
<span class="p1">(<span class="default"><a href="scmpds_4.html#K9">IExec</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a> ,2 <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p0">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span></span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p5">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a> ,4 <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p0">(<span class="default"><span class="p1">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span> <a href="scmpds_4.html#K3">';'</a> <font color="Maroon">c<sub>50</sub></font></span>)</span> <a href="scmpds_4.html#K3">';'</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><span class="p0">(<span class="default"><span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a> ,<span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 3</span>)</span> <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p2">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a> ,<span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span> <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K2">GBP</a> ,4</span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p1">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a> ,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 2</span>)</span> <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K2">GBP</a> ,4</span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p0">(<span class="default"><a href="scmpds_2.html#K12">AddTo</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span>,<span class="p1">(<span class="default"><a href="xcmplx_0.html#K4">-</a> 1</span>)</span></span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p5">(<span class="default"><a href="scmpds_2.html#K12">AddTo</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p0">(<span class="default"><span class="p1">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 2</span>)</span>,1</span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p4">(<span class="default"><a href="scmpds_2.html#K12">AddTo</a> <a href="scmp_gcd.html#K2">GBP</a> ,1,2</span>)</span></span>)</span></span>)</span>,<font color="Maroon">c<sub>75</sub></font></span>)</span> <a href="scmpds_2.html#K2">.</a> <span class="p1">(<span class="default"><a href="scmp_gcd.html#K1">intpos</a> <font color="Maroon">c<sub>89</sub></font></span>)</span> <a href="xxreal_0.html#NR2" target="_self">&gt;=</a> <span class="p1">(<span class="default"><a href="scmpds_4.html#K9">IExec</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a> ,2 <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p0">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span></span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p5">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a> ,4 <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p0">(<span class="default"><span class="p1">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span> <a href="scmpds_4.html#K3">';'</a> <font color="Maroon">c<sub>50</sub></font></span>)</span> <a href="scmpds_4.html#K3">';'</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><span class="p0">(<span class="default"><span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a> ,<span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 3</span>)</span> <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p2">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a> ,<span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span> <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K2">GBP</a> ,4</span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p1">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a> ,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 2</span>)</span> <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K2">GBP</a> ,4</span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p0">(<span class="default"><a href="scmpds_2.html#K12">AddTo</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span>,<span class="p1">(<span class="default"><a href="xcmplx_0.html#K4">-</a> 1</span>)</span></span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p5">(<span class="default"><a href="scmpds_2.html#K12">AddTo</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p0">(<span class="default"><span class="p1">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 2</span>)</span>,1</span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p4">(<span class="default"><a href="scmpds_2.html#K12">AddTo</a> <a href="scmp_gcd.html#K2">GBP</a> ,1,2</span>)</span></span>)</span></span>)</span>,<font color="Maroon">c<sub>75</sub></font></span>)</span> <a href="scmpds_2.html#K2">.</a> <span class="p1">(<span class="default"><a href="scmp_gcd.html#K1">intpos</a> <font color="Maroon">c<sub>90</sub></font></span>)</span>
 <b>by </b><i><a class="txt" href="scpqsort.html#E15:46_7"><i><font color="Green">E66</font></i></a>, <a class="txt" href="scpqsort.html#E1:46_7_9"><i><font color="Green">E87</font></i></a>, <a class="txt" href="scpqsort.html#E4:46_7_9"><i><font color="Green">E90</font></i></a></i>;<br/></div>
<b>end;</b></div>

<div><b>hereby </b>
<div class="add"><b>let </b><font color="Maroon">c<sub>90</sub></font> be   <a href="nat_1.html#NM1">Nat</a>;<br/><b>assume </b><a NAME="E1:46_7_10"/><i><font color="Green">E87</font></i>: 
( <font color="Maroon">c<sub>89</sub></font> <a href="xxreal_0.html#NR3" target="_self">&lt;</a> <font color="Maroon">c<sub>90</sub></font> &amp; <font color="Maroon">c<sub>90</sub></font> <a href="xxreal_0.html#R1">&lt;=</a> <font color="Maroon">c<sub>79</sub></font> )
 ;<br/><a NAME="E2:46_7_10"/><b>then </b><i><font color="Green">E88</font></i>: 
<font color="Maroon">c<sub>90</sub></font> <a href="xxreal_0.html#NR3" target="_self">&lt;</a> <font color="Maroon">c<sub>77</sub></font> <a href="nat_1.html#K1">+</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span>
 <b>by </b><i><a class="txt" href="scpqsort.html#E1:46_7"><i><font color="Green">E55</font></i></a>, <a class="txt" href="scpqsort.html#E4:46_7"><i><font color="Green">E58</font></i></a>, <a class="txt" href="scpqsort.html#E28:46_7"><i><font color="Green">E79</font></i></a>, <a class="ref" href="xreal_1.html#T2">XREAL_1:2</a></i>;<br/><a NAME="E3:46_7_10"/>
<font color="Maroon">c<sub>90</sub></font> <a href="xxreal_0.html#NR2" target="_self">&gt;=</a> <font color="Maroon">c<sub>78</sub></font>
 <b>by </b><i><a class="txt" href="scpqsort.html#E15:46_7"><i><font color="Green">E66</font></i></a>, <a class="txt" href="scpqsort.html#E1:46_7_10"><i><font color="Green">E87</font></i></a>, <a class="ref" href="xreal_1.html#T2">XREAL_1:2</a></i>;<br/><a NAME="E4:46_7_10"/><b>then </b><i><font color="Green">E89</font></i>: 
<font color="Maroon">c<sub>90</sub></font> <a href="xxreal_0.html#NR2" target="_self">&gt;=</a> 8
 <b>by </b><i><a class="txt" href="scpqsort.html#E43:46_7"><i><font color="Green">E84</font></i></a>, <a class="ref" href="xreal_1.html#T2">XREAL_1:2</a></i>;<br/><i><font color="Green">E90</font></i>: <span class="p1">(<span class="default"><a href="scmpds_4.html#K9">IExec</a> <font color="Maroon">c<sub>50</sub></font>,<span class="p2">(<span class="default"><a href="scmpds_4.html#K9">IExec</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a> ,2 <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p5">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span></span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p4">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a> ,4 <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p5">(<span class="default"><span class="p0">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span>,<font color="Maroon">c<sub>75</sub></font></span>)</span></span>)</span> <a href="scmpds_2.html#K2">.</a> <span class="p1">(<span class="default"><a href="scmp_gcd.html#K1">intpos</a> <font color="Maroon">c<sub>90</sub></font></span>)</span> = 
<span class="p1">(<span class="default"><a href="scmpds_4.html#K9">IExec</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a> ,2 <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p5">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span></span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p4">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a> ,4 <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p5">(<span class="default"><span class="p0">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span> <a href="scmpds_4.html#K3">';'</a> <font color="Maroon">c<sub>50</sub></font></span>)</span>,<font color="Maroon">c<sub>75</sub></font></span>)</span> <a href="scmpds_2.html#K2">.</a> <span class="p1">(<span class="default"><a href="scmp_gcd.html#K1">intpos</a> <font color="Maroon">c<sub>90</sub></font></span>)</span>
<b>by </b><i><a class="txt" href="scpqsort.html#E16:46_7"><i><font color="Green">E67</font></i></a>, <a class="ref" href="scpisort.html#T8">SCPISORT:8</a></i>
<br/>.= 
<span class="p1">(<span class="default"><a href="scmpds_4.html#K9">IExec</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><span class="p0">(<span class="default"><span class="p1">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a> ,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 3</span>)</span> <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p1">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a> ,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span> <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K2">GBP</a> ,4</span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p0">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a> ,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 2</span>)</span> <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K2">GBP</a> ,4</span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p5">(<span class="default"><a href="scmpds_2.html#K12">AddTo</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p0">(<span class="default"><span class="p1">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span>,<span class="p0">(<span class="default"><a href="xcmplx_0.html#K4">-</a> 1</span>)</span></span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p4">(<span class="default"><a href="scmpds_2.html#K12">AddTo</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p5">(<span class="default"><span class="p0">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 2</span>)</span>,1</span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p3">(<span class="default"><a href="scmpds_2.html#K12">AddTo</a> <a href="scmp_gcd.html#K2">GBP</a> ,1,2</span>)</span></span>)</span>,<span class="p2">(<span class="default"><a href="scmpds_4.html#K9">IExec</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a> ,2 <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p0">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span></span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p5">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a> ,4 <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p0">(<span class="default"><span class="p1">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span> <a href="scmpds_4.html#K3">';'</a> <font color="Maroon">c<sub>50</sub></font></span>)</span>,<font color="Maroon">c<sub>75</sub></font></span>)</span></span>)</span> <a href="scmpds_2.html#K2">.</a> <span class="p1">(<span class="default"><a href="scmp_gcd.html#K1">intpos</a> <font color="Maroon">c<sub>90</sub></font></span>)</span>
<b>by </b><i><a class="txt" href="scpqsort.html#E11:46"><i><font color="Green">E51</font></i></a>, <a class="txt" href="scpqsort.html#E1:46_7"><i><font color="Green">E55</font></i></a>, <a class="txt" href="scpqsort.html#E18:46_7"><i><font color="Green">E69</font></i></a>, <a class="txt" href="scpqsort.html#E19:46_7"><i><font color="Green">E70</font></i></a>, <a class="txt" href="scpqsort.html#E2:46_7_10"><i><font color="Green">E88</font></i></a>, <a class="txt" href="scpqsort.html#E4:46_7_10"><i><font color="Green">E89</font></i></a></i>
<br/>.= 
<span class="p1">(<span class="default"><a href="scmpds_4.html#K9">IExec</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a> ,2 <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p0">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span></span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p5">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a> ,4 <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p0">(<span class="default"><span class="p1">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span> <a href="scmpds_4.html#K3">';'</a> <font color="Maroon">c<sub>50</sub></font></span>)</span> <a href="scmpds_4.html#K3">';'</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><span class="p0">(<span class="default"><span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a> ,<span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 3</span>)</span> <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p2">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a> ,<span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span> <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K2">GBP</a> ,4</span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p1">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a> ,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 2</span>)</span> <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K2">GBP</a> ,4</span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p0">(<span class="default"><a href="scmpds_2.html#K12">AddTo</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span>,<span class="p1">(<span class="default"><a href="xcmplx_0.html#K4">-</a> 1</span>)</span></span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p5">(<span class="default"><a href="scmpds_2.html#K12">AddTo</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p0">(<span class="default"><span class="p1">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 2</span>)</span>,1</span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p4">(<span class="default"><a href="scmpds_2.html#K12">AddTo</a> <a href="scmp_gcd.html#K2">GBP</a> ,1,2</span>)</span></span>)</span></span>)</span>,<font color="Maroon">c<sub>75</sub></font></span>)</span> <a href="scmpds_2.html#K2">.</a> <span class="p1">(<span class="default"><a href="scmp_gcd.html#K1">intpos</a> <font color="Maroon">c<sub>90</sub></font></span>)</span>
<b>by </b><i><a class="txt" href="scpqsort.html#E17:46_7"><i><font color="Green">E68</font></i></a>, <a class="ref" href="scpisort.html#T7">SCPISORT:7</a></i>
;<br/><span class="p1">(<span class="default"><a href="scmpds_4.html#K9">IExec</a> <font color="Maroon">c<sub>50</sub></font>,<span class="p2">(<span class="default"><a href="scmpds_4.html#K9">IExec</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a> ,2 <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p5">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span></span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p4">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a> ,4 <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p5">(<span class="default"><span class="p0">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span>,<font color="Maroon">c<sub>75</sub></font></span>)</span></span>)</span> <a href="scmpds_2.html#K2">.</a> <span class="p1">(<span class="default"><a href="scmp_gcd.html#K1">intpos</a> <font color="Maroon">c<sub>89</sub></font></span>)</span> = 
<span class="p1">(<span class="default"><a href="scmpds_4.html#K9">IExec</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a> ,2 <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p5">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span></span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p4">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a> ,4 <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p5">(<span class="default"><span class="p0">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span> <a href="scmpds_4.html#K3">';'</a> <font color="Maroon">c<sub>50</sub></font></span>)</span>,<font color="Maroon">c<sub>75</sub></font></span>)</span> <a href="scmpds_2.html#K2">.</a> <span class="p1">(<span class="default"><a href="scmp_gcd.html#K1">intpos</a> <font color="Maroon">c<sub>89</sub></font></span>)</span>
<b>by </b><i><a class="txt" href="scpqsort.html#E16:46_7"><i><font color="Green">E67</font></i></a>, <a class="ref" href="scpisort.html#T8">SCPISORT:8</a></i>
<br/>.= 
<span class="p1">(<span class="default"><a href="scmpds_4.html#K9">IExec</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><span class="p0">(<span class="default"><span class="p1">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a> ,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 3</span>)</span> <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p1">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a> ,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span> <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K2">GBP</a> ,4</span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p0">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a> ,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 2</span>)</span> <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K2">GBP</a> ,4</span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p5">(<span class="default"><a href="scmpds_2.html#K12">AddTo</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p0">(<span class="default"><span class="p1">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span>,<span class="p0">(<span class="default"><a href="xcmplx_0.html#K4">-</a> 1</span>)</span></span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p4">(<span class="default"><a href="scmpds_2.html#K12">AddTo</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p5">(<span class="default"><span class="p0">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 2</span>)</span>,1</span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p3">(<span class="default"><a href="scmpds_2.html#K12">AddTo</a> <a href="scmp_gcd.html#K2">GBP</a> ,1,2</span>)</span></span>)</span>,<span class="p2">(<span class="default"><a href="scmpds_4.html#K9">IExec</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a> ,2 <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p0">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span></span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p5">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a> ,4 <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p0">(<span class="default"><span class="p1">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span> <a href="scmpds_4.html#K3">';'</a> <font color="Maroon">c<sub>50</sub></font></span>)</span>,<font color="Maroon">c<sub>75</sub></font></span>)</span></span>)</span> <a href="scmpds_2.html#K2">.</a> <span class="p1">(<span class="default"><a href="scmp_gcd.html#K1">intpos</a> <font color="Maroon">c<sub>89</sub></font></span>)</span>
<b>by </b><i><a class="txt" href="scpqsort.html#E11:46"><i><font color="Green">E51</font></i></a>, <a class="txt" href="scpqsort.html#E1:46_7"><i><font color="Green">E55</font></i></a>, <a class="txt" href="scpqsort.html#E18:46_7"><i><font color="Green">E69</font></i></a>, <a class="txt" href="scpqsort.html#E19:46_7"><i><font color="Green">E70</font></i></a>, <a class="txt" href="scpqsort.html#E44:46_7"><i><font color="Green">E85</font></i></a>, <a class="txt" href="scpqsort.html#E45:46_7"><i><font color="Green">E86</font></i></a></i>
<br/>.= 
<span class="p1">(<span class="default"><a href="scmpds_4.html#K9">IExec</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a> ,2 <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p0">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span></span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p5">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a> ,4 <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p0">(<span class="default"><span class="p1">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span> <a href="scmpds_4.html#K3">';'</a> <font color="Maroon">c<sub>50</sub></font></span>)</span> <a href="scmpds_4.html#K3">';'</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><span class="p0">(<span class="default"><span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a> ,<span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 3</span>)</span> <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p2">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a> ,<span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span> <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K2">GBP</a> ,4</span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p1">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a> ,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 2</span>)</span> <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K2">GBP</a> ,4</span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p0">(<span class="default"><a href="scmpds_2.html#K12">AddTo</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span>,<span class="p1">(<span class="default"><a href="xcmplx_0.html#K4">-</a> 1</span>)</span></span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p5">(<span class="default"><a href="scmpds_2.html#K12">AddTo</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p0">(<span class="default"><span class="p1">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 2</span>)</span>,1</span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p4">(<span class="default"><a href="scmpds_2.html#K12">AddTo</a> <a href="scmp_gcd.html#K2">GBP</a> ,1,2</span>)</span></span>)</span></span>)</span>,<font color="Maroon">c<sub>75</sub></font></span>)</span> <a href="scmpds_2.html#K2">.</a> <span class="p1">(<span class="default"><a href="scmp_gcd.html#K1">intpos</a> <font color="Maroon">c<sub>89</sub></font></span>)</span>
<b>by </b><i><a class="txt" href="scpqsort.html#E17:46_7"><i><font color="Green">E68</font></i></a>, <a class="ref" href="scpisort.html#T7">SCPISORT:7</a></i>
;<br/><b>hence </b><a NAME="E7:46_7_10"/>
<span class="p1">(<span class="default"><a href="scmpds_4.html#K9">IExec</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a> ,2 <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p0">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span></span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p5">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a> ,4 <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p0">(<span class="default"><span class="p1">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span> <a href="scmpds_4.html#K3">';'</a> <font color="Maroon">c<sub>50</sub></font></span>)</span> <a href="scmpds_4.html#K3">';'</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><span class="p0">(<span class="default"><span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a> ,<span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 3</span>)</span> <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p2">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a> ,<span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span> <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K2">GBP</a> ,4</span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p1">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a> ,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 2</span>)</span> <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K2">GBP</a> ,4</span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p0">(<span class="default"><a href="scmpds_2.html#K12">AddTo</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span>,<span class="p1">(<span class="default"><a href="xcmplx_0.html#K4">-</a> 1</span>)</span></span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p5">(<span class="default"><a href="scmpds_2.html#K12">AddTo</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p0">(<span class="default"><span class="p1">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 2</span>)</span>,1</span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p4">(<span class="default"><a href="scmpds_2.html#K12">AddTo</a> <a href="scmp_gcd.html#K2">GBP</a> ,1,2</span>)</span></span>)</span></span>)</span>,<font color="Maroon">c<sub>75</sub></font></span>)</span> <a href="scmpds_2.html#K2">.</a> <span class="p1">(<span class="default"><a href="scmp_gcd.html#K1">intpos</a> <font color="Maroon">c<sub>89</sub></font></span>)</span> <a href="xxreal_0.html#R1">&lt;=</a> <span class="p1">(<span class="default"><a href="scmpds_4.html#K9">IExec</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a> ,2 <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p0">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span></span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p5">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a> ,4 <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p0">(<span class="default"><span class="p1">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span> <a href="scmpds_4.html#K3">';'</a> <font color="Maroon">c<sub>50</sub></font></span>)</span> <a href="scmpds_4.html#K3">';'</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><span class="p0">(<span class="default"><span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a> ,<span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 3</span>)</span> <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p2">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a> ,<span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span> <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K2">GBP</a> ,4</span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p1">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a> ,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 2</span>)</span> <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K2">GBP</a> ,4</span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p0">(<span class="default"><a href="scmpds_2.html#K12">AddTo</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span>,<span class="p1">(<span class="default"><a href="xcmplx_0.html#K4">-</a> 1</span>)</span></span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p5">(<span class="default"><a href="scmpds_2.html#K12">AddTo</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p0">(<span class="default"><span class="p1">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 2</span>)</span>,1</span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p4">(<span class="default"><a href="scmpds_2.html#K12">AddTo</a> <a href="scmp_gcd.html#K2">GBP</a> ,1,2</span>)</span></span>)</span></span>)</span>,<font color="Maroon">c<sub>75</sub></font></span>)</span> <a href="scmpds_2.html#K2">.</a> <span class="p1">(<span class="default"><a href="scmp_gcd.html#K1">intpos</a> <font color="Maroon">c<sub>90</sub></font></span>)</span>
 <b>by </b><i><a class="txt" href="scpqsort.html#E6:46_7"><i><font color="Green">E60</font></i></a>, <a class="txt" href="scpqsort.html#E15:46_7"><i><font color="Green">E66</font></i></a>, <a class="txt" href="scpqsort.html#E1:46_7_10"><i><font color="Green">E87</font></i></a>, <a class="txt" href="scpqsort.html#E5:46_7_10"><i><font color="Green">E90</font></i></a></i>;<br/></div>
<b>end;</b></div>

<div><b>hereby </b>
<div class="add"><b>let </b><font color="Maroon">c<sub>90</sub></font> be   <a href="nat_1.html#NM1">Nat</a>;<br/><b>assume </b><a NAME="E1:46_7_11"/><i><font color="Green">E87</font></i>: 
( ( <font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> 1 <a href="xxreal_0.html#R1">&lt;=</a> <font color="Maroon">c<sub>90</sub></font> &amp; <font color="Maroon">c<sub>90</sub></font> <a href="xxreal_0.html#NR3" target="_self">&lt;</a> <font color="Maroon">c<sub>78</sub></font> ) or ( <font color="Maroon">c<sub>79</sub></font> <a href="xxreal_0.html#NR3" target="_self">&lt;</a> <font color="Maroon">c<sub>90</sub></font> &amp; <font color="Maroon">c<sub>90</sub></font> <a href="xxreal_0.html#R1">&lt;=</a> <font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font> ) )
 ;<br/><div><i><font color="Green">E88</font></i>: <a class="txt" onclick="hs2(this)" href="javascript:()" title="46_7_11_1"><b>now </b></a><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="46_7_11_1_1"><b>per </b></a><a class="txt" onclick="hs(this)" href="javascript:()"><b>cases </b></a><span class="hide"><a NAME="E1:46_7_11_1_1"/>
( ( <font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> 1 <a href="xxreal_0.html#R1">&lt;=</a> <font color="Maroon">c<sub>90</sub></font> &amp; <font color="Maroon">c<sub>90</sub></font> <a href="xxreal_0.html#NR3" target="_self">&lt;</a> <font color="Maroon">c<sub>78</sub></font> ) or ( <font color="Maroon">c<sub>79</sub></font> <a href="xxreal_0.html#NR3" target="_self">&lt;</a> <font color="Maroon">c<sub>90</sub></font> &amp; <font color="Maroon">c<sub>90</sub></font> <a href="xxreal_0.html#R1">&lt;=</a> <font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font> ) )
 </span><b>by </b><i><a class="txt" href="scpqsort.html#E1:46_7_11"><i><font color="Green">E87</font></i></a></i>;<br/><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="46_7_11_1_1_1"><b>suppose </b></a><a NAME="E1:46_7_11_1_1_1"/><i><font color="Green">E89</font></i>: 
( <font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> 1 <a href="xxreal_0.html#R1">&lt;=</a> <font color="Maroon">c<sub>90</sub></font> &amp; <font color="Maroon">c<sub>90</sub></font> <a href="xxreal_0.html#NR3" target="_self">&lt;</a> <font color="Maroon">c<sub>78</sub></font> )
 ;<br/><div class="add"><b>hence </b><a NAME="E2:46_7_11_1_1_1"/>
( <font color="Maroon">c<sub>90</sub></font> <a href="xxreal_0.html#NR2" target="_self">&gt;=</a> <font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> 1 &amp; ( <font color="Maroon">c<sub>90</sub></font> <a href="xxreal_0.html#NR3" target="_self">&lt;</a> <span class="p1">(<span class="default"><a href="scmpds_4.html#K9">IExec</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a> ,2 <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p4">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span></span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p3">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a> ,4 <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p4">(<span class="default"><span class="p5">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span>,<font color="Maroon">c<sub>75</sub></font></span>)</span> <a href="scmpds_2.html#K2">.</a> <span class="p1">(<span class="default"><a href="scmp_gcd.html#K1">intpos</a> 2</span>)</span> or <font color="Maroon">c<sub>90</sub></font> <a href="xxreal_0.html#NR4" target="_self">&gt;</a> <span class="p1">(<span class="default"><a href="scmpds_4.html#K9">IExec</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a> ,2 <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p4">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span></span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p3">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a> ,4 <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p4">(<span class="default"><span class="p5">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span>,<font color="Maroon">c<sub>75</sub></font></span>)</span> <a href="scmpds_2.html#K2">.</a> <span class="p1">(<span class="default"><a href="scmp_gcd.html#K1">intpos</a> 4</span>)</span> ) )
 <b>by </b><i><a class="txt" href="scpqsort.html#E12:46"><i><font color="Green">E52</font></i></a>, <a class="txt" href="scpqsort.html#E1:46_7"><i><font color="Green">E55</font></i></a></i>;<br/><a NAME="E3:46_7_11_1_1_1"/>
<font color="Maroon">c<sub>78</sub></font> <a href="xxreal_0.html#NR3" target="_self">&lt;</a> <font color="Maroon">c<sub>77</sub></font> <a href="nat_1.html#K1">+</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span>
 <b>by </b><i><a class="txt" href="scpqsort.html#E15:46_7"><i><font color="Green">E66</font></i></a>, <a class="txt" href="scpqsort.html#E44:46_7"><i><font color="Green">E85</font></i></a>, <a class="ref" href="xreal_1.html#T2">XREAL_1:2</a></i>;<br/><b>hence </b><a NAME="E4:46_7_11_1_1_1"/>
<font color="Maroon">c<sub>90</sub></font> <a href="xxreal_0.html#NR3" target="_self">&lt;</a> <font color="Maroon">c<sub>77</sub></font> <a href="nat_1.html#K1">+</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span>
 <b>by </b><i><a class="txt" href="scpqsort.html#E1:46_7_11_1_1_1"><i><font color="Green">E89</font></i></a>, <a class="ref" href="xreal_1.html#T2">XREAL_1:2</a></i>;<br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="46_7_11_1_1_2"><b>suppose </b></a><a NAME="E1:46_7_11_1_1_2"/><i><font color="Green">E89</font></i>: 
( <font color="Maroon">c<sub>79</sub></font> <a href="xxreal_0.html#NR3" target="_self">&lt;</a> <font color="Maroon">c<sub>90</sub></font> &amp; <font color="Maroon">c<sub>90</sub></font> <a href="xxreal_0.html#R1">&lt;=</a> <font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font> )
 ;<br/><div class="add"><a NAME="E2:46_7_11_1_1_2"/>
<font color="Maroon">c<sub>79</sub></font> <a href="xxreal_0.html#NR2" target="_self">&gt;=</a> <font color="Maroon">c<sub>78</sub></font>
 <b>by </b><i><a class="txt" href="scpqsort.html#E6:46_7"><i><font color="Green">E60</font></i></a>, <a class="txt" href="scpqsort.html#E15:46_7"><i><font color="Green">E66</font></i></a>, <a class="ref" href="xreal_1.html#T2">XREAL_1:2</a></i>;<br/><a NAME="E3:46_7_11_1_1_2"/><b>then </b>
<font color="Maroon">c<sub>90</sub></font> <a href="xxreal_0.html#NR2" target="_self">&gt;=</a> <font color="Maroon">c<sub>78</sub></font>
 <b>by </b><i><a class="txt" href="scpqsort.html#E1:46_7_11_1_1_2"><i><font color="Green">E89</font></i></a>, <a class="ref" href="xreal_1.html#T2">XREAL_1:2</a></i>;<br/><b>hence </b><a NAME="E4:46_7_11_1_1_2"/>
<font color="Maroon">c<sub>90</sub></font> <a href="xxreal_0.html#NR2" target="_self">&gt;=</a> <font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> 1
 <b>by </b><i><a class="txt" href="scpqsort.html#E1:46_7"><i><font color="Green">E55</font></i></a>, <a class="ref" href="xreal_1.html#T2">XREAL_1:2</a></i>;<br/><b>thus </b><a NAME="E5:46_7_11_1_1_2"/>
( <font color="Maroon">c<sub>90</sub></font> <a href="xxreal_0.html#NR3" target="_self">&lt;</a> <span class="p1">(<span class="default"><a href="scmpds_4.html#K9">IExec</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a> ,2 <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p4">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span></span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p3">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a> ,4 <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p4">(<span class="default"><span class="p5">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span>,<font color="Maroon">c<sub>75</sub></font></span>)</span> <a href="scmpds_2.html#K2">.</a> <span class="p1">(<span class="default"><a href="scmp_gcd.html#K1">intpos</a> 2</span>)</span> or <font color="Maroon">c<sub>90</sub></font> <a href="xxreal_0.html#NR4" target="_self">&gt;</a> <span class="p1">(<span class="default"><a href="scmpds_4.html#K9">IExec</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a> ,2 <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p4">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span></span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p3">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a> ,4 <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p4">(<span class="default"><span class="p5">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span>,<font color="Maroon">c<sub>75</sub></font></span>)</span> <a href="scmpds_2.html#K2">.</a> <span class="p1">(<span class="default"><a href="scmp_gcd.html#K1">intpos</a> 4</span>)</span> )
 <b>by </b><i><a class="txt" href="scpqsort.html#E12:46"><i><font color="Green">E52</font></i></a>, <a class="txt" href="scpqsort.html#E1:46_7"><i><font color="Green">E55</font></i></a>, <a class="txt" href="scpqsort.html#E1:46_7_11_1_1_2"><i><font color="Green">E89</font></i></a></i>;<br/><b>thus </b><a NAME="E6:46_7_11_1_1_2"/>
<font color="Maroon">c<sub>90</sub></font> <a href="xxreal_0.html#NR3" target="_self">&lt;</a> <font color="Maroon">c<sub>77</sub></font> <a href="nat_1.html#K1">+</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span>
 <b>by </b><i><a class="txt" href="scpqsort.html#E27:46_7"><i><font color="Green">E78</font></i></a>, <a class="txt" href="scpqsort.html#E1:46_7_11_1_1_2"><i><font color="Green">E89</font></i></a>, <a class="ref" href="xreal_1.html#T2">XREAL_1:2</a></i>;<br/></div><b>end;</b></div></div><b>end;</b></div></div><b>end;</b></div><a NAME="E3:46_7_11"/><b>then </b><i><font color="Green">E89</font></i>: 
<font color="Maroon">c<sub>90</sub></font> <a href="xxreal_0.html#NR2" target="_self">&gt;=</a> 8
 <b>by </b><i><a class="txt" href="scpqsort.html#E7:46_7"><i><font color="Green">E61</font></i></a>, <a class="ref" href="xreal_1.html#T2">XREAL_1:2</a></i>;<br/><a NAME="E4:46_7_11"/><b>then </b><i><font color="Green">E90</font></i>: 
( <font color="Maroon">c<sub>90</sub></font> <a href="xxreal_0.html#NR4" target="_self">&gt;</a> 2 &amp; <font color="Maroon">c<sub>90</sub></font> <a href="xxreal_0.html#NR4" target="_self">&gt;</a> 4 )
 <b>by </b><i><a class="ref" href="xreal_1.html#T2">XREAL_1:2</a></i>;<br/><b>thus </b><span class="p1">(<span class="default"><a href="scmpds_4.html#K9">IExec</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a> ,2 <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p0">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span></span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p5">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a> ,4 <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p0">(<span class="default"><span class="p1">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span> <a href="scmpds_4.html#K3">';'</a> <font color="Maroon">c<sub>50</sub></font></span>)</span> <a href="scmpds_4.html#K3">';'</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><span class="p0">(<span class="default"><span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a> ,<span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 3</span>)</span> <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p2">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a> ,<span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span> <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K2">GBP</a> ,4</span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p1">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a> ,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 2</span>)</span> <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K2">GBP</a> ,4</span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p0">(<span class="default"><a href="scmpds_2.html#K12">AddTo</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span>,<span class="p1">(<span class="default"><a href="xcmplx_0.html#K4">-</a> 1</span>)</span></span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p5">(<span class="default"><a href="scmpds_2.html#K12">AddTo</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p0">(<span class="default"><span class="p1">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 2</span>)</span>,1</span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p4">(<span class="default"><a href="scmpds_2.html#K12">AddTo</a> <a href="scmp_gcd.html#K2">GBP</a> ,1,2</span>)</span></span>)</span></span>)</span>,<font color="Maroon">c<sub>75</sub></font></span>)</span> <a href="scmpds_2.html#K2">.</a> <span class="p1">(<span class="default"><a href="scmp_gcd.html#K1">intpos</a> <font color="Maroon">c<sub>90</sub></font></span>)</span> = 
<span class="p1">(<span class="default"><a href="scmpds_4.html#K9">IExec</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><span class="p0">(<span class="default"><span class="p1">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a> ,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 3</span>)</span> <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p1">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a> ,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span> <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K2">GBP</a> ,4</span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p0">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a> ,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 2</span>)</span> <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K2">GBP</a> ,4</span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p5">(<span class="default"><a href="scmpds_2.html#K12">AddTo</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p0">(<span class="default"><span class="p1">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span>,<span class="p0">(<span class="default"><a href="xcmplx_0.html#K4">-</a> 1</span>)</span></span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p4">(<span class="default"><a href="scmpds_2.html#K12">AddTo</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p5">(<span class="default"><span class="p0">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 2</span>)</span>,1</span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p3">(<span class="default"><a href="scmpds_2.html#K12">AddTo</a> <a href="scmp_gcd.html#K2">GBP</a> ,1,2</span>)</span></span>)</span>,<span class="p2">(<span class="default"><a href="scmpds_4.html#K9">IExec</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a> ,2 <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p0">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span></span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p5">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a> ,4 <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p0">(<span class="default"><span class="p1">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span> <a href="scmpds_4.html#K3">';'</a> <font color="Maroon">c<sub>50</sub></font></span>)</span>,<font color="Maroon">c<sub>75</sub></font></span>)</span></span>)</span> <a href="scmpds_2.html#K2">.</a> <span class="p1">(<span class="default"><a href="scmp_gcd.html#K1">intpos</a> <font color="Maroon">c<sub>90</sub></font></span>)</span>
<b>by </b><i><a class="txt" href="scpqsort.html#E17:46_7"><i><font color="Green">E68</font></i></a>, <a class="ref" href="scpisort.html#T7">SCPISORT:7</a></i>
<br/>.= 
<span class="p1">(<span class="default"><a href="scmpds_4.html#K9">IExec</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a> ,2 <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p5">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span></span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p4">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a> ,4 <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p5">(<span class="default"><span class="p0">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span> <a href="scmpds_4.html#K3">';'</a> <font color="Maroon">c<sub>50</sub></font></span>)</span>,<font color="Maroon">c<sub>75</sub></font></span>)</span> <a href="scmpds_2.html#K2">.</a> <span class="p1">(<span class="default"><a href="scmp_gcd.html#K1">intpos</a> <font color="Maroon">c<sub>90</sub></font></span>)</span>
<b>by </b><i><a class="txt" href="scpqsort.html#E11:46"><i><font color="Green">E51</font></i></a>, <a class="txt" href="scpqsort.html#E1:46_7"><i><font color="Green">E55</font></i></a>, <a class="txt" href="scpqsort.html#E18:46_7"><i><font color="Green">E69</font></i></a>, <a class="txt" href="scpqsort.html#E19:46_7"><i><font color="Green">E70</font></i></a>, <a class="txt" href="scpqsort.html#E2:46_7_11"><i><font color="Green">E88</font></i></a>, <a class="txt" href="scpqsort.html#E3:46_7_11"><i><font color="Green">E89</font></i></a></i>
<br/>.= 
<span class="p1">(<span class="default"><a href="scmpds_4.html#K9">IExec</a> <font color="Maroon">c<sub>50</sub></font>,<span class="p2">(<span class="default"><a href="scmpds_4.html#K9">IExec</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a> ,2 <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p5">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span></span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p4">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a> ,4 <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p5">(<span class="default"><span class="p0">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span>,<font color="Maroon">c<sub>75</sub></font></span>)</span></span>)</span> <a href="scmpds_2.html#K2">.</a> <span class="p1">(<span class="default"><a href="scmp_gcd.html#K1">intpos</a> <font color="Maroon">c<sub>90</sub></font></span>)</span>
<b>by </b><i><a class="txt" href="scpqsort.html#E16:46_7"><i><font color="Green">E67</font></i></a>, <a class="ref" href="scpisort.html#T8">SCPISORT:8</a></i>
<br/>.= 
<span class="p1">(<span class="default"><a href="scmpds_4.html#K9">IExec</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a> ,2 <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p4">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span></span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p3">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a> ,4 <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p4">(<span class="default"><span class="p5">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span>,<font color="Maroon">c<sub>75</sub></font></span>)</span> <a href="scmpds_2.html#K2">.</a> <span class="p1">(<span class="default"><a href="scmp_gcd.html#K1">intpos</a> <font color="Maroon">c<sub>90</sub></font></span>)</span>
<b>by </b><i><a class="txt" href="scpqsort.html#E15:46_7"><i><font color="Green">E66</font></i></a>, <a class="txt" href="scpqsort.html#E2:46_7_11"><i><font color="Green">E88</font></i></a></i>
<br/>.= 
<font color="Maroon">c<sub>75</sub></font> <a href="scmpds_2.html#K2">.</a> <span class="p1">(<span class="default"><a href="scmp_gcd.html#K1">intpos</a> <font color="Maroon">c<sub>90</sub></font></span>)</span>
<b>by </b><i><a class="txt" href="scpqsort.html#E12:46"><i><font color="Green">E52</font></i></a>, <a class="txt" href="scpqsort.html#E1:46_7"><i><font color="Green">E55</font></i></a>, <a class="txt" href="scpqsort.html#E4:46_7_11"><i><font color="Green">E90</font></i></a></i>
;<br/></div>
<b>end;</b></div>


</div><b>end;</b></div>
<a NAME="E15:46"/><i><font color="Green">E55</font></i>: 
for <font color="Olive">b<sub>1</sub></font> being  <a href="ami_1.html#NM4">State</a> of <a href="scmpds_2.html#K1">SCMPDS</a> <br/>for <font color="Olive">b<sub>2</sub></font> being  <a href="nat_1.html#NM1">Nat</a> st <font color="Olive">b<sub>1</sub></font> <a href="scmpds_2.html#K2">.</a> <a href="scmp_gcd.html#K2">GBP</a>  <a href="hidden.html#R1">=</a> 0 &amp; <font color="Olive">b<sub>1</sub></font> <a href="scmpds_2.html#K2">.</a> <a href="scmp_gcd.html#K3">SBP</a>  <a href="hidden.html#R1">=</a> <font color="Olive">b<sub>2</sub></font> holds <br/>( <span class="p1">(<span class="default"><a href="scmpds_4.html#K9">IExec</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a> ,2 <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p4">(<span class="default"><span class="p5">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p3">(<span class="default"><a href="scmpds_2.html#K14">SubFrom</a> <a href="scmp_gcd.html#K2">GBP</a> ,2,<a href="scmp_gcd.html#K3">SBP</a> ,<span class="p4">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span></span>)</span></span>)</span>,<font color="Olive">b<sub>1</sub></font></span>)</span> <a href="scmpds_2.html#K2">.</a> <span class="p1">(<span class="default"><a href="scmp_gcd.html#K1">intpos</a> 2</span>)</span> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><font color="Olive">b<sub>1</sub></font> <a href="scmpds_2.html#K2">.</a> <span class="p2">(<span class="default"><a href="scmp_gcd.html#K1">intpos</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Olive">b<sub>2</sub></font> <a href="nat_1.html#K1">+</a> <span class="p5">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span> <a href="xcmplx_0.html#K6">-</a> <span class="p1">(<span class="default"><font color="Olive">b<sub>1</sub></font> <a href="scmpds_2.html#K2">.</a> <span class="p2">(<span class="default"><a href="scmp_gcd.html#K1">intpos</a> <span class="p3">(<span class="default"><font color="Olive">b<sub>2</sub></font> <a href="nat_1.html#K1">+</a> <span class="p4">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span></span>)</span></span>)</span></span>)</span> &amp; ( for <font color="Olive">b<sub>3</sub></font> being  <a href="nat_1.html#NM1">Nat</a> st <font color="Olive">b<sub>3</sub></font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> 2 holds <br/><span class="p1">(<span class="default"><a href="scmpds_4.html#K9">IExec</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a> ,2 <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p4">(<span class="default"><span class="p5">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p3">(<span class="default"><a href="scmpds_2.html#K14">SubFrom</a> <a href="scmp_gcd.html#K2">GBP</a> ,2,<a href="scmp_gcd.html#K3">SBP</a> ,<span class="p4">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span></span>)</span></span>)</span>,<font color="Olive">b<sub>1</sub></font></span>)</span> <a href="scmpds_2.html#K2">.</a> <span class="p1">(<span class="default"><a href="scmp_gcd.html#K1">intpos</a> <font color="Olive">b<sub>3</sub></font></span>)</span> <a href="hidden.html#R1">=</a> <font color="Olive">b<sub>1</sub></font> <a href="scmpds_2.html#K2">.</a> <span class="p1">(<span class="default"><a href="scmp_gcd.html#K1">intpos</a> <font color="Olive">b<sub>3</sub></font></span>)</span> ) )
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="46_8"><b>proof </b></a><div class="add">

<b>let </b><font color="Maroon">c<sub>75</sub></font> be   <a href="ami_1.html#NM4">State</a> of <a href="scmpds_2.html#K1">SCMPDS</a> ;<br/><b>let </b><font color="Maroon">c<sub>76</sub></font> be   <a href="nat_1.html#NM1">Nat</a>;<br/>



<b>assume </b><a NAME="E1:46_8"/><i><font color="Green">E56</font></i>: 
( <font color="Maroon">c<sub>75</sub></font> <a href="scmpds_2.html#K2">.</a> <a href="scmp_gcd.html#K2">GBP</a>  <a href="hidden.html#R1">=</a> 0 &amp; <font color="Maroon">c<sub>75</sub></font> <a href="scmpds_2.html#K2">.</a> <a href="scmp_gcd.html#K3">SBP</a>  <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>76</sub></font> )
 ;<br/>

<b>set </b><font color="Maroon">c<sub>77</sub></font> =  <a href="scmpds_5.html#K1">Initialized</a> <font color="Maroon">c<sub>75</sub></font>;<br/>
<b>set </b><font color="Maroon">c<sub>78</sub></font> =  <a href="scmpds_4.html#K9">IExec</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a> ,2 <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p2">(<span class="default"><a href="scmpds_2.html#K14">SubFrom</a> <a href="scmp_gcd.html#K2">GBP</a> ,2,<a href="scmp_gcd.html#K3">SBP</a> ,<span class="p3">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span></span>)</span></span>)</span>,<font color="Maroon">c<sub>75</sub></font>;<br/>
<b>set </b><font color="Maroon">c<sub>79</sub></font> =  <a href="ami_1.html#K4">Exec</a> <span class="p1">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a> ,2 <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span>,<span class="p1">(<span class="default"><a href="scmpds_5.html#K1">Initialized</a> <font color="Maroon">c<sub>75</sub></font></span>)</span>;<br/>
<b>set </b><font color="Maroon">c<sub>80</sub></font> = <font color="Maroon">c<sub>76</sub></font> <a href="nat_1.html#K1">+</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span>;<br/>
<a NAME="E2:46_8"/><i><font color="Green">E57</font></i>: 
<font color="Maroon">c<sub>76</sub></font> <a href="nat_1.html#K1">+</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="xxreal_0.html#NR2" target="_self">&gt;=</a> 0 <a href="nat_1.html#K1">+</a> 7
 
<b>by </b><i><a class="txt" href="scpqsort.html#E8:46"><i><font color="Green">E48</font></i></a>, <a class="ref" href="xreal_1.html#T9">XREAL_1:9</a></i>;<br/>
<a NAME="E3:46_8"/><i><font color="Green">E58</font></i>: 
<span class="p1">(<span class="default"><a href="scmpds_5.html#K1">Initialized</a> <font color="Maroon">c<sub>75</sub></font></span>)</span> <a href="scmpds_2.html#K2">.</a> <a href="scmp_gcd.html#K2">GBP</a>  <a href="hidden.html#R1">=</a> 0
 
<b>by </b><i><a class="txt" href="scpqsort.html#E1:46_8"><i><font color="Green">E56</font></i></a>, <a class="ref" href="scmpds_5.html#T40">SCMPDS_5:40</a></i>;<br/>
<a NAME="E4:46_8"/><i><font color="Green">E59</font></i>: 
<span class="p1">(<span class="default"><a href="scmpds_5.html#K1">Initialized</a> <font color="Maroon">c<sub>75</sub></font></span>)</span> <a href="scmpds_2.html#K2">.</a> <a href="scmp_gcd.html#K3">SBP</a>  <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>76</sub></font>
 
<b>by </b><i><a class="txt" href="scpqsort.html#E1:46_8"><i><font color="Green">E56</font></i></a>, <a class="ref" href="scmpds_5.html#T40">SCMPDS_5:40</a></i>;<br/>
<a NAME="E5:46_8"/><i><font color="Green">E60</font></i>: 
 <a href="scmpds_2.html#K3">DataLoc</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="scmpds_5.html#K1">Initialized</a> <font color="Maroon">c<sub>75</sub></font></span>)</span> <a href="scmpds_2.html#K2">.</a> <a href="scmp_gcd.html#K2">GBP</a> </span>)</span>,2 <a href="hidden.html#R1">=</a>  <a href="scmp_gcd.html#K1">intpos</a> <span class="p1">(<span class="default">0 <a href="nat_1.html#K1">+</a> 2</span>)</span>
 
<b>by </b><i><a class="txt" href="scpqsort.html#E3:46_8"><i><font color="Green">E58</font></i></a>, <a class="ref" href="scmp_gcd.html#T5">SCMP_GCD:5</a></i>;<br/>
<a NAME="E6:46_8"/><b>then </b>
 <a href="scmp_gcd.html#K2">GBP</a>  <a href="hidden.html#NR2" target="_self">&lt;&gt;</a>  <a href="scmpds_2.html#K3">DataLoc</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="scmpds_5.html#K1">Initialized</a> <font color="Maroon">c<sub>75</sub></font></span>)</span> <a href="scmpds_2.html#K2">.</a> <a href="scmp_gcd.html#K2">GBP</a> </span>)</span>,2
 
<b>by </b><i><a class="ref" href="scmp_gcd.html#T4">SCMP_GCD:4</a>, <a class="ref" href="scmp_gcd.html#D2">SCMP_GCD:def 2</a></i>;<br/>
<a NAME="E7:46_8"/><b>then </b><i><font color="Green">E61</font></i>: 
<span class="p1">(<span class="default"><a href="ami_1.html#K4">Exec</a> <span class="p2">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a> ,2 <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span>,<span class="p2">(<span class="default"><a href="scmpds_5.html#K1">Initialized</a> <font color="Maroon">c<sub>75</sub></font></span>)</span></span>)</span> <a href="scmpds_2.html#K2">.</a> <a href="scmp_gcd.html#K2">GBP</a>  <a href="hidden.html#R1">=</a> 0
 
<b>by </b><i><a class="txt" href="scpqsort.html#E3:46_8"><i><font color="Green">E58</font></i></a>, <a class="ref" href="scmpds_2.html#T59">SCMPDS_2:59</a></i>;<br/>
<a NAME="E8:46_8"/>
 <a href="scmp_gcd.html#K3">SBP</a>  <a href="hidden.html#NR2" target="_self">&lt;&gt;</a>  <a href="scmpds_2.html#K3">DataLoc</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="scmpds_5.html#K1">Initialized</a> <font color="Maroon">c<sub>75</sub></font></span>)</span> <a href="scmpds_2.html#K2">.</a> <a href="scmp_gcd.html#K2">GBP</a> </span>)</span>,2
 
<b>by </b><i><a class="txt" href="scpqsort.html#E5:46_8"><i><font color="Green">E60</font></i></a>, <a class="ref" href="scmp_gcd.html#T4">SCMP_GCD:4</a>, <a class="ref" href="scmp_gcd.html#D3">SCMP_GCD:def 3</a></i>;<br/>
<a NAME="E9:46_8"/><b>then </b><i><font color="Green">E62</font></i>: 
<span class="p1">(<span class="default"><a href="ami_1.html#K4">Exec</a> <span class="p2">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a> ,2 <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span>,<span class="p2">(<span class="default"><a href="scmpds_5.html#K1">Initialized</a> <font color="Maroon">c<sub>75</sub></font></span>)</span></span>)</span> <a href="scmpds_2.html#K2">.</a> <a href="scmp_gcd.html#K3">SBP</a>  <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>76</sub></font>
 
<b>by </b><i><a class="txt" href="scpqsort.html#E4:46_8"><i><font color="Green">E59</font></i></a>, <a class="ref" href="scmpds_2.html#T59">SCMPDS_2:59</a></i>;<br/>
<i><font color="Green">E63</font></i>: <span class="p1">(<span class="default"><a href="ami_1.html#K4">Exec</a> <span class="p2">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a> ,2 <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span>,<span class="p2">(<span class="default"><a href="scmpds_5.html#K1">Initialized</a> <font color="Maroon">c<sub>75</sub></font></span>)</span></span>)</span> <a href="scmpds_2.html#K2">.</a> <span class="p1">(<span class="default"><a href="scmp_gcd.html#K1">intpos</a> 2</span>)</span> = 
<span class="p1">(<span class="default"><a href="scmpds_5.html#K1">Initialized</a> <font color="Maroon">c<sub>75</sub></font></span>)</span> <a href="scmpds_2.html#K2">.</a> <span class="p1">(<span class="default"><a href="scmpds_2.html#K3">DataLoc</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="scmpds_5.html#K1">Initialized</a> <font color="Maroon">c<sub>75</sub></font></span>)</span> <a href="scmpds_2.html#K2">.</a> <a href="scmp_gcd.html#K3">SBP</a> </span>)</span>,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span>
<b>by </b><i><a class="txt" href="scpqsort.html#E5:46_8"><i><font color="Green">E60</font></i></a>, <a class="ref" href="scmpds_2.html#T59">SCMPDS_2:59</a></i>
<br/>.= 
<span class="p1">(<span class="default"><a href="scmpds_5.html#K1">Initialized</a> <font color="Maroon">c<sub>75</sub></font></span>)</span> <a href="scmpds_2.html#K2">.</a> <span class="p1">(<span class="default"><a href="scmp_gcd.html#K1">intpos</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>76</sub></font> <a href="nat_1.html#K1">+</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span>
<b>by </b><i><a class="txt" href="scpqsort.html#E4:46_8"><i><font color="Green">E59</font></i></a>, <a class="ref" href="scmp_gcd.html#T5">SCMP_GCD:5</a></i>
<br/>.= 
<font color="Maroon">c<sub>75</sub></font> <a href="scmpds_2.html#K2">.</a> <span class="p1">(<span class="default"><a href="scmp_gcd.html#K1">intpos</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">c<sub>76</sub></font> <a href="nat_1.html#K1">+</a> <span class="p4">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span>
<b>by </b><i><a class="ref" href="scmpds_5.html#T40">SCMPDS_5:40</a></i>
;<br/>
<a NAME="E11:46_8"/>
<font color="Maroon">c<sub>76</sub></font> <a href="nat_1.html#K1">+</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="xxreal_0.html#NR4" target="_self">&gt;</a> 2
 
<b>by </b><i><a class="txt" href="scpqsort.html#E2:46_8"><i><font color="Green">E57</font></i></a>, <a class="ref" href="xreal_1.html#T2">XREAL_1:2</a></i>;<br/>
<a NAME="E12:46_8"/><b>then </b>
 <a href="scmp_gcd.html#K1">intpos</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>76</sub></font> <a href="nat_1.html#K1">+</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span></span>)</span> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a>  <a href="scmpds_2.html#K3">DataLoc</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="scmpds_5.html#K1">Initialized</a> <font color="Maroon">c<sub>75</sub></font></span>)</span> <a href="scmpds_2.html#K2">.</a> <a href="scmp_gcd.html#K2">GBP</a> </span>)</span>,2
 
<b>by </b><i><a class="txt" href="scpqsort.html#E5:46_8"><i><font color="Green">E60</font></i></a>, <a class="ref" href="scmp_gcd.html#T4">SCMP_GCD:4</a></i>;<br/>
<b>then </b><i><font color="Green">E64</font></i>: <span class="p1">(<span class="default"><a href="ami_1.html#K4">Exec</a> <span class="p2">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a> ,2 <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span>,<span class="p2">(<span class="default"><a href="scmpds_5.html#K1">Initialized</a> <font color="Maroon">c<sub>75</sub></font></span>)</span></span>)</span> <a href="scmpds_2.html#K2">.</a> <span class="p1">(<span class="default"><a href="scmp_gcd.html#K1">intpos</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>76</sub></font> <a href="nat_1.html#K1">+</a> <span class="p3">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span></span>)</span></span>)</span> = 
<span class="p1">(<span class="default"><a href="scmpds_5.html#K1">Initialized</a> <font color="Maroon">c<sub>75</sub></font></span>)</span> <a href="scmpds_2.html#K2">.</a> <span class="p1">(<span class="default"><a href="scmp_gcd.html#K1">intpos</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>76</sub></font> <a href="nat_1.html#K1">+</a> <span class="p3">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span></span>)</span></span>)</span>
<b>by </b><i><a class="ref" href="scmpds_2.html#T59">SCMPDS_2:59</a></i>
<br/>.= 
<font color="Maroon">c<sub>75</sub></font> <a href="scmpds_2.html#K2">.</a> <span class="p1">(<span class="default"><a href="scmp_gcd.html#K1">intpos</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>76</sub></font> <a href="nat_1.html#K1">+</a> <span class="p3">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span></span>)</span></span>)</span>
<b>by </b><i><a class="ref" href="scmpds_5.html#T40">SCMPDS_5:40</a></i>
;<br/>
<a NAME="E14:46_8"/><i><font color="Green">E65</font></i>: 
 <a href="scmpds_2.html#K3">DataLoc</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K4">Exec</a> <span class="p3">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a> ,2 <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p4">(<span class="default"><span class="p5">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span>,<span class="p3">(<span class="default"><a href="scmpds_5.html#K1">Initialized</a> <font color="Maroon">c<sub>75</sub></font></span>)</span></span>)</span> <a href="scmpds_2.html#K2">.</a> <a href="scmp_gcd.html#K2">GBP</a> </span>)</span>,2 <a href="hidden.html#R1">=</a>  <a href="scmp_gcd.html#K1">intpos</a> <span class="p1">(<span class="default">0 <a href="nat_1.html#K1">+</a> 2</span>)</span>
 
<b>by </b><i><a class="txt" href="scpqsort.html#E7:46_8"><i><font color="Green">E61</font></i></a>, <a class="ref" href="scmp_gcd.html#T5">SCMP_GCD:5</a></i>;<br/>
<b>thus </b><span class="p1">(<span class="default"><a href="scmpds_4.html#K9">IExec</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a> ,2 <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p4">(<span class="default"><span class="p5">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p3">(<span class="default"><a href="scmpds_2.html#K14">SubFrom</a> <a href="scmp_gcd.html#K2">GBP</a> ,2,<a href="scmp_gcd.html#K3">SBP</a> ,<span class="p4">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span></span>)</span></span>)</span>,<font color="Maroon">c<sub>75</sub></font></span>)</span> <a href="scmpds_2.html#K2">.</a> <span class="p1">(<span class="default"><a href="scmp_gcd.html#K1">intpos</a> 2</span>)</span> = 
<span class="p1">(<span class="default"><a href="ami_1.html#K4">Exec</a> <span class="p2">(<span class="default"><a href="scmpds_2.html#K14">SubFrom</a> <a href="scmp_gcd.html#K2">GBP</a> ,2,<a href="scmp_gcd.html#K3">SBP</a> ,<span class="p3">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span></span>)</span>,<span class="p2">(<span class="default"><a href="ami_1.html#K4">Exec</a> <span class="p3">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a> ,2 <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p4">(<span class="default"><span class="p5">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span>,<span class="p3">(<span class="default"><a href="scmpds_5.html#K1">Initialized</a> <font color="Maroon">c<sub>75</sub></font></span>)</span></span>)</span></span>)</span> <a href="scmpds_2.html#K2">.</a> <span class="p1">(<span class="default"><a href="scmp_gcd.html#K1">intpos</a> 2</span>)</span>
<b>by </b><i><a class="ref" href="scmpds_5.html#T47">SCMPDS_5:47</a></i>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K4">Exec</a> <span class="p3">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a> ,2 <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p4">(<span class="default"><span class="p5">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span>,<span class="p3">(<span class="default"><a href="scmpds_5.html#K1">Initialized</a> <font color="Maroon">c<sub>75</sub></font></span>)</span></span>)</span> <a href="scmpds_2.html#K2">.</a> <span class="p2">(<span class="default"><a href="scmp_gcd.html#K1">intpos</a> 2</span>)</span></span>)</span> <a href="xcmplx_0.html#K6">-</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K4">Exec</a> <span class="p3">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a> ,2 <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p4">(<span class="default"><span class="p5">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span>,<span class="p3">(<span class="default"><a href="scmpds_5.html#K1">Initialized</a> <font color="Maroon">c<sub>75</sub></font></span>)</span></span>)</span> <a href="scmpds_2.html#K2">.</a> <span class="p2">(<span class="default"><a href="scmpds_2.html#K3">DataLoc</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="ami_1.html#K4">Exec</a> <span class="p5">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a> ,2 <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p0">(<span class="default"><span class="p1">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span>,<span class="p5">(<span class="default"><a href="scmpds_5.html#K1">Initialized</a> <font color="Maroon">c<sub>75</sub></font></span>)</span></span>)</span> <a href="scmpds_2.html#K2">.</a> <a href="scmp_gcd.html#K3">SBP</a> </span>)</span>,<span class="p3">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span></span>)</span></span>)</span>
<b>by </b><i><a class="txt" href="scpqsort.html#E14:46_8"><i><font color="Green">E65</font></i></a>, <a class="ref" href="scmpds_2.html#T62">SCMPDS_2:62</a></i>
<br/>.= 
<span class="p1">(<span class="default"><font color="Maroon">c<sub>75</sub></font> <a href="scmpds_2.html#K2">.</a> <span class="p2">(<span class="default"><a href="scmp_gcd.html#K1">intpos</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">c<sub>76</sub></font> <a href="nat_1.html#K1">+</a> <span class="p5">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span> <a href="xcmplx_0.html#K6">-</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>75</sub></font> <a href="scmpds_2.html#K2">.</a> <span class="p2">(<span class="default"><a href="scmp_gcd.html#K1">intpos</a> <span class="p3">(<span class="default"><font color="Maroon">c<sub>76</sub></font> <a href="nat_1.html#K1">+</a> <span class="p4">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span></span>)</span></span>)</span></span>)</span>
<b>by </b><i><a class="txt" href="scpqsort.html#E9:46_8"><i><font color="Green">E62</font></i></a>, <a class="txt" href="scpqsort.html#E10:46_8"><i><font color="Green">E63</font></i></a>, <a class="txt" href="scpqsort.html#E13:46_8"><i><font color="Green">E64</font></i></a>, <a class="ref" href="scmp_gcd.html#T5">SCMP_GCD:5</a></i>
;<br/>

<div><b>hereby </b>
<div class="add"><b>let </b><font color="Maroon">c<sub>81</sub></font> be   <a href="nat_1.html#NM1">Nat</a>;<br/><b>assume </b><a NAME="E1:46_8_4"/><i><font color="Green">E66</font></i>: 
<font color="Maroon">c<sub>81</sub></font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> 2
 ;<br/><a NAME="E2:46_8_4"/><b>then </b><i><font color="Green">E67</font></i>: 
 <a href="scmp_gcd.html#K1">intpos</a> <font color="Maroon">c<sub>81</sub></font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a>  <a href="scmpds_2.html#K3">DataLoc</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="scmpds_5.html#K1">Initialized</a> <font color="Maroon">c<sub>75</sub></font></span>)</span> <a href="scmpds_2.html#K2">.</a> <a href="scmp_gcd.html#K2">GBP</a> </span>)</span>,2
 <b>by </b><i><a class="txt" href="scpqsort.html#E5:46_8"><i><font color="Green">E60</font></i></a>, <a class="ref" href="scmp_gcd.html#T4">SCMP_GCD:4</a></i>;<br/><a NAME="E3:46_8_4"/><i><font color="Green">E68</font></i>: 
 <a href="scmp_gcd.html#K1">intpos</a> <font color="Maroon">c<sub>81</sub></font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a>  <a href="scmpds_2.html#K3">DataLoc</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K4">Exec</a> <span class="p3">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a> ,2 <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p4">(<span class="default"><span class="p5">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span>,<span class="p3">(<span class="default"><a href="scmpds_5.html#K1">Initialized</a> <font color="Maroon">c<sub>75</sub></font></span>)</span></span>)</span> <a href="scmpds_2.html#K2">.</a> <a href="scmp_gcd.html#K2">GBP</a> </span>)</span>,2
 <b>by </b><i><a class="txt" href="scpqsort.html#E14:46_8"><i><font color="Green">E65</font></i></a>, <a class="txt" href="scpqsort.html#E1:46_8_4"><i><font color="Green">E66</font></i></a>, <a class="ref" href="scmp_gcd.html#T4">SCMP_GCD:4</a></i>;<br/><b>thus </b><span class="p1">(<span class="default"><a href="scmpds_4.html#K9">IExec</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a> ,2 <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p4">(<span class="default"><span class="p5">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p3">(<span class="default"><a href="scmpds_2.html#K14">SubFrom</a> <a href="scmp_gcd.html#K2">GBP</a> ,2,<a href="scmp_gcd.html#K3">SBP</a> ,<span class="p4">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span></span>)</span></span>)</span>,<font color="Maroon">c<sub>75</sub></font></span>)</span> <a href="scmpds_2.html#K2">.</a> <span class="p1">(<span class="default"><a href="scmp_gcd.html#K1">intpos</a> <font color="Maroon">c<sub>81</sub></font></span>)</span> = 
<span class="p1">(<span class="default"><a href="ami_1.html#K4">Exec</a> <span class="p2">(<span class="default"><a href="scmpds_2.html#K14">SubFrom</a> <a href="scmp_gcd.html#K2">GBP</a> ,2,<a href="scmp_gcd.html#K3">SBP</a> ,<span class="p3">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span></span>)</span>,<span class="p2">(<span class="default"><a href="ami_1.html#K4">Exec</a> <span class="p3">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a> ,2 <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p4">(<span class="default"><span class="p5">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span>,<span class="p3">(<span class="default"><a href="scmpds_5.html#K1">Initialized</a> <font color="Maroon">c<sub>75</sub></font></span>)</span></span>)</span></span>)</span> <a href="scmpds_2.html#K2">.</a> <span class="p1">(<span class="default"><a href="scmp_gcd.html#K1">intpos</a> <font color="Maroon">c<sub>81</sub></font></span>)</span>
<b>by </b><i><a class="ref" href="scmpds_5.html#T47">SCMPDS_5:47</a></i>
<br/>.= 
<span class="p1">(<span class="default"><a href="ami_1.html#K4">Exec</a> <span class="p2">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a> ,2 <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span>,<span class="p2">(<span class="default"><a href="scmpds_5.html#K1">Initialized</a> <font color="Maroon">c<sub>75</sub></font></span>)</span></span>)</span> <a href="scmpds_2.html#K2">.</a> <span class="p1">(<span class="default"><a href="scmp_gcd.html#K1">intpos</a> <font color="Maroon">c<sub>81</sub></font></span>)</span>
<b>by </b><i><a class="txt" href="scpqsort.html#E3:46_8_4"><i><font color="Green">E68</font></i></a>, <a class="ref" href="scmpds_2.html#T62">SCMPDS_2:62</a></i>
<br/>.= 
<span class="p1">(<span class="default"><a href="scmpds_5.html#K1">Initialized</a> <font color="Maroon">c<sub>75</sub></font></span>)</span> <a href="scmpds_2.html#K2">.</a> <span class="p1">(<span class="default"><a href="scmp_gcd.html#K1">intpos</a> <font color="Maroon">c<sub>81</sub></font></span>)</span>
<b>by </b><i><a class="txt" href="scpqsort.html#E2:46_8_4"><i><font color="Green">E67</font></i></a>, <a class="ref" href="scmpds_2.html#T59">SCMPDS_2:59</a></i>
<br/>.= 
<font color="Maroon">c<sub>75</sub></font> <a href="scmpds_2.html#K2">.</a> <span class="p1">(<span class="default"><a href="scmp_gcd.html#K1">intpos</a> <font color="Maroon">c<sub>81</sub></font></span>)</span>
<b>by </b><i><a class="ref" href="scmpds_5.html#T40">SCMPDS_5:40</a></i>
;<br/></div>
<b>end;</b></div>


</div><b>end;</b></div>
<a NAME="E16:46"/><i><font color="Green">E56</font></i>: 
for <font color="Olive">b<sub>1</sub></font> being  <a href="ami_1.html#NM4">State</a> of <a href="scmpds_2.html#K1">SCMPDS</a> <br/>for <font color="Olive">b<sub>2</sub></font>, <font color="Olive">b<sub>3</sub></font> being  <a href="nat_1.html#NM1">Nat</a> st <font color="Olive">b<sub>1</sub></font> <a href="scmpds_2.html#K2">.</a> <a href="scmp_gcd.html#K2">GBP</a>  <a href="hidden.html#R1">=</a> 0 &amp; <font color="Olive">b<sub>1</sub></font> <a href="scmpds_2.html#K2">.</a> <a href="scmp_gcd.html#K3">SBP</a>  <a href="hidden.html#R1">=</a> <font color="Olive">b<sub>2</sub></font> &amp; <font color="Olive">b<sub>1</sub></font> <a href="scmpds_2.html#K2">.</a> <span class="p1">(<span class="default"><a href="scmp_gcd.html#K1">intpos</a> <span class="p2">(<span class="default"><font color="Olive">b<sub>2</sub></font> <a href="nat_1.html#K1">+</a> <span class="p3">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span></span>)</span></span>)</span> <a href="hidden.html#R1">=</a> <font color="Olive">b<sub>3</sub></font> &amp; ( <font color="Olive">b<sub>3</sub></font> <a href="xxreal_0.html#NR2" target="_self">&gt;=</a> <font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> 1 or <span class="p1">(<span class="default"><font color="Olive">b<sub>1</sub></font> <a href="scmpds_2.html#K2">.</a> <span class="p2">(<span class="default"><a href="scmp_gcd.html#K1">intpos</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Olive">b<sub>2</sub></font> <a href="nat_1.html#K1">+</a> <span class="p5">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span> <a href="xcmplx_0.html#K6">-</a> <font color="Olive">b<sub>3</sub></font> <a href="xxreal_0.html#R1">&lt;=</a> 0 ) holds <br/>( <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a> ,2 <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p2">(<span class="default"><a href="scmpds_2.html#K14">SubFrom</a> <a href="scmp_gcd.html#K2">GBP</a> ,2,<a href="scmp_gcd.html#K3">SBP</a> ,<span class="p3">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span></span>)</span></span>)</span> <a href="scmpds_4.html#K3">';'</a> <span class="p1">(<span class="default"><a href="scmpds_6.html#K3">if&gt;0</a> <a href="scmp_gcd.html#K2">GBP</a> ,2,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a> ,2 <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p0">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span></span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p5">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a> ,4 <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p0">(<span class="default"><span class="p1">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span> <a href="scmpds_4.html#K3">';'</a> <font color="Maroon">c<sub>50</sub></font></span>)</span> <a href="scmpds_4.html#K3">';'</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><span class="p0">(<span class="default"><span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a> ,<span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 3</span>)</span> <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p2">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a> ,<span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span> <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K2">GBP</a> ,4</span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p1">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a> ,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 2</span>)</span> <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K2">GBP</a> ,4</span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p0">(<span class="default"><a href="scmpds_2.html#K12">AddTo</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span>,<span class="p1">(<span class="default"><a href="xcmplx_0.html#K4">-</a> 1</span>)</span></span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p5">(<span class="default"><a href="scmpds_2.html#K12">AddTo</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p0">(<span class="default"><span class="p1">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 2</span>)</span>,1</span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p4">(<span class="default"><a href="scmpds_2.html#K12">AddTo</a> <a href="scmp_gcd.html#K2">GBP</a> ,1,2</span>)</span></span>)</span></span>)</span>,<span class="p2">(<span class="default"><a href="scmpds_4.html#K1">Load</a> <span class="p3">(<span class="default"><a href="scmpds_2.html#K12">AddTo</a> <a href="scmp_gcd.html#K2">GBP</a> ,1,<span class="p4">(<span class="default"><a href="xcmplx_0.html#K4">-</a> 2</span>)</span></span>)</span></span>)</span></span>)</span> <a href="scmpds_6.html#R1">is_closed_on</a> <font color="Olive">b<sub>1</sub></font> &amp; <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a> ,2 <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p2">(<span class="default"><a href="scmpds_2.html#K14">SubFrom</a> <a href="scmp_gcd.html#K2">GBP</a> ,2,<a href="scmp_gcd.html#K3">SBP</a> ,<span class="p3">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span></span>)</span></span>)</span> <a href="scmpds_4.html#K3">';'</a> <span class="p1">(<span class="default"><a href="scmpds_6.html#K3">if&gt;0</a> <a href="scmp_gcd.html#K2">GBP</a> ,2,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a> ,2 <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p0">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span></span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p5">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a> ,4 <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p0">(<span class="default"><span class="p1">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span> <a href="scmpds_4.html#K3">';'</a> <font color="Maroon">c<sub>50</sub></font></span>)</span> <a href="scmpds_4.html#K3">';'</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><span class="p0">(<span class="default"><span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a> ,<span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 3</span>)</span> <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p2">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a> ,<span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span> <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K2">GBP</a> ,4</span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p1">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a> ,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 2</span>)</span> <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K2">GBP</a> ,4</span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p0">(<span class="default"><a href="scmpds_2.html#K12">AddTo</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span>,<span class="p1">(<span class="default"><a href="xcmplx_0.html#K4">-</a> 1</span>)</span></span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p5">(<span class="default"><a href="scmpds_2.html#K12">AddTo</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p0">(<span class="default"><span class="p1">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 2</span>)</span>,1</span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p4">(<span class="default"><a href="scmpds_2.html#K12">AddTo</a> <a href="scmp_gcd.html#K2">GBP</a> ,1,2</span>)</span></span>)</span></span>)</span>,<span class="p2">(<span class="default"><a href="scmpds_4.html#K1">Load</a> <span class="p3">(<span class="default"><a href="scmpds_2.html#K12">AddTo</a> <a href="scmp_gcd.html#K2">GBP</a> ,1,<span class="p4">(<span class="default"><a href="xcmplx_0.html#K4">-</a> 2</span>)</span></span>)</span></span>)</span></span>)</span> <a href="scmpds_6.html#R2">is_halting_on</a> <font color="Olive">b<sub>1</sub></font> )
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="46_9"><b>proof </b></a><div class="add">

<b>let </b><font color="Maroon">c<sub>75</sub></font> be   <a href="ami_1.html#NM4">State</a> of <a href="scmpds_2.html#K1">SCMPDS</a> ;<br/><b>let </b><font color="Maroon">c<sub>76</sub></font>, <font color="Maroon">c<sub>77</sub></font> be   <a href="nat_1.html#NM1">Nat</a>;<br/>



<b>set </b><font color="Maroon">c<sub>78</sub></font> = <font color="Maroon">c<sub>76</sub></font> <a href="nat_1.html#K1">+</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span>;<br/>
<b>set </b><font color="Maroon">c<sub>79</sub></font> =  <a href="scmpds_4.html#K9">IExec</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a> ,2 <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p2">(<span class="default"><a href="scmpds_2.html#K14">SubFrom</a> <a href="scmp_gcd.html#K2">GBP</a> ,2,<a href="scmp_gcd.html#K3">SBP</a> ,<span class="p3">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span></span>)</span></span>)</span>,<font color="Maroon">c<sub>75</sub></font>;<br/>
<b>assume </b><a NAME="E1:46_9"/><i><font color="Green">E57</font></i>: 
( <font color="Maroon">c<sub>75</sub></font> <a href="scmpds_2.html#K2">.</a> <a href="scmp_gcd.html#K2">GBP</a>  <a href="hidden.html#R1">=</a> 0 &amp; <font color="Maroon">c<sub>75</sub></font> <a href="scmpds_2.html#K2">.</a> <a href="scmp_gcd.html#K3">SBP</a>  <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>76</sub></font> &amp; <font color="Maroon">c<sub>75</sub></font> <a href="scmpds_2.html#K2">.</a> <span class="p1">(<span class="default"><a href="scmp_gcd.html#K1">intpos</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>76</sub></font> <a href="nat_1.html#K1">+</a> <span class="p3">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span></span>)</span></span>)</span> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>77</sub></font> &amp; ( <font color="Maroon">c<sub>77</sub></font> <a href="xxreal_0.html#NR2" target="_self">&gt;=</a> <font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> 1 or <span class="p1">(<span class="default"><font color="Maroon">c<sub>75</sub></font> <a href="scmpds_2.html#K2">.</a> <span class="p2">(<span class="default"><a href="scmp_gcd.html#K1">intpos</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">c<sub>76</sub></font> <a href="nat_1.html#K1">+</a> <span class="p5">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span> <a href="xcmplx_0.html#K6">-</a> <font color="Maroon">c<sub>77</sub></font> <a href="xxreal_0.html#R1">&lt;=</a> 0 ) )
 ;<br/>

<a NAME="E2:46_9"/><b>then </b><i><font color="Green">E58</font></i>: 
( <span class="p1">(<span class="default"><a href="scmpds_4.html#K9">IExec</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a> ,2 <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p4">(<span class="default"><span class="p5">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p3">(<span class="default"><a href="scmpds_2.html#K14">SubFrom</a> <a href="scmp_gcd.html#K2">GBP</a> ,2,<a href="scmp_gcd.html#K3">SBP</a> ,<span class="p4">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span></span>)</span></span>)</span>,<font color="Maroon">c<sub>75</sub></font></span>)</span> <a href="scmpds_2.html#K2">.</a> <span class="p1">(<span class="default"><a href="scmp_gcd.html#K1">intpos</a> 2</span>)</span> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>75</sub></font> <a href="scmpds_2.html#K2">.</a> <span class="p2">(<span class="default"><a href="scmp_gcd.html#K1">intpos</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">c<sub>76</sub></font> <a href="nat_1.html#K1">+</a> <span class="p5">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span> <a href="xcmplx_0.html#K6">-</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>75</sub></font> <a href="scmpds_2.html#K2">.</a> <span class="p2">(<span class="default"><a href="scmp_gcd.html#K1">intpos</a> <span class="p3">(<span class="default"><font color="Maroon">c<sub>76</sub></font> <a href="nat_1.html#K1">+</a> <span class="p4">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span></span>)</span></span>)</span></span>)</span> &amp; ( for <font color="Olive">b<sub>1</sub></font> being  <a href="nat_1.html#NM1">Nat</a> st <font color="Olive">b<sub>1</sub></font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> 2 holds <br/><span class="p1">(<span class="default"><a href="scmpds_4.html#K9">IExec</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a> ,2 <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p4">(<span class="default"><span class="p5">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p3">(<span class="default"><a href="scmpds_2.html#K14">SubFrom</a> <a href="scmp_gcd.html#K2">GBP</a> ,2,<a href="scmp_gcd.html#K3">SBP</a> ,<span class="p4">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span></span>)</span></span>)</span>,<font color="Maroon">c<sub>75</sub></font></span>)</span> <a href="scmpds_2.html#K2">.</a> <span class="p1">(<span class="default"><a href="scmp_gcd.html#K1">intpos</a> <font color="Olive">b<sub>1</sub></font></span>)</span> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>75</sub></font> <a href="scmpds_2.html#K2">.</a> <span class="p1">(<span class="default"><a href="scmp_gcd.html#K1">intpos</a> <font color="Olive">b<sub>1</sub></font></span>)</span> ) )
 
<b>by </b><i><a class="txt" href="scpqsort.html#E15:46"><i><font color="Green">E55</font></i></a></i>;<br/>
<a NAME="E3:46_9"/><i><font color="Green">E59</font></i>: 
<span class="p1">(<span class="default"><a href="scmpds_4.html#K9">IExec</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a> ,2 <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p4">(<span class="default"><span class="p5">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p3">(<span class="default"><a href="scmpds_2.html#K14">SubFrom</a> <a href="scmp_gcd.html#K2">GBP</a> ,2,<a href="scmp_gcd.html#K3">SBP</a> ,<span class="p4">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span></span>)</span></span>)</span>,<font color="Maroon">c<sub>75</sub></font></span>)</span> <a href="scmpds_2.html#K2">.</a> <a href="scmp_gcd.html#K2">GBP</a>  <a href="hidden.html#R1">=</a> 0
 
<b>by </b><i><a class="txt" href="scpqsort.html#E15:46"><i><font color="Green">E55</font></i></a>, <a class="txt" href="scpqsort.html#E1:46_9"><i><font color="Green">E57</font></i></a>, <a class="ref" href="scmp_gcd.html#D2">SCMP_GCD:def 2</a></i>;<br/>
<a NAME="E4:46_9"/><b>then </b><i><font color="Green">E60</font></i>: 
 <a href="scmpds_2.html#K3">DataLoc</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="scmpds_4.html#K9">IExec</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a> ,2 <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p5">(<span class="default"><span class="p0">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p4">(<span class="default"><a href="scmpds_2.html#K14">SubFrom</a> <a href="scmp_gcd.html#K2">GBP</a> ,2,<a href="scmp_gcd.html#K3">SBP</a> ,<span class="p5">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span></span>)</span></span>)</span>,<font color="Maroon">c<sub>75</sub></font></span>)</span> <a href="scmpds_2.html#K2">.</a> <a href="scmp_gcd.html#K2">GBP</a> </span>)</span>,2 <a href="hidden.html#R1">=</a>  <a href="scmp_gcd.html#K1">intpos</a> <span class="p1">(<span class="default">0 <a href="nat_1.html#K1">+</a> 2</span>)</span>
 
<b>by </b><i><a class="ref" href="scmp_gcd.html#T5">SCMP_GCD:5</a></i>;<br/>
<div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="46_9_1"><b>per </b></a><a class="txt" onclick="hs(this)" href="javascript:()"><b>cases </b></a><span class="hide"><a NAME="E1:46_9_1"/>
( <span class="p1">(<span class="default"><a href="scmpds_4.html#K9">IExec</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a> ,2 <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p4">(<span class="default"><span class="p5">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p3">(<span class="default"><a href="scmpds_2.html#K14">SubFrom</a> <a href="scmp_gcd.html#K2">GBP</a> ,2,<a href="scmp_gcd.html#K3">SBP</a> ,<span class="p4">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span></span>)</span></span>)</span>,<font color="Maroon">c<sub>75</sub></font></span>)</span> <a href="scmpds_2.html#K2">.</a> <span class="p1">(<span class="default"><a href="scmpds_2.html#K3">DataLoc</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="scmpds_4.html#K9">IExec</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a> ,2 <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p0">(<span class="default"><span class="p1">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p5">(<span class="default"><a href="scmpds_2.html#K14">SubFrom</a> <a href="scmp_gcd.html#K2">GBP</a> ,2,<a href="scmp_gcd.html#K3">SBP</a> ,<span class="p0">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span></span>)</span></span>)</span>,<font color="Maroon">c<sub>75</sub></font></span>)</span> <a href="scmpds_2.html#K2">.</a> <a href="scmp_gcd.html#K2">GBP</a> </span>)</span>,2</span>)</span> <a href="xxreal_0.html#NR4" target="_self">&gt;</a> 0 or <span class="p1">(<span class="default"><a href="scmpds_4.html#K9">IExec</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a> ,2 <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p4">(<span class="default"><span class="p5">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p3">(<span class="default"><a href="scmpds_2.html#K14">SubFrom</a> <a href="scmp_gcd.html#K2">GBP</a> ,2,<a href="scmp_gcd.html#K3">SBP</a> ,<span class="p4">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span></span>)</span></span>)</span>,<font color="Maroon">c<sub>75</sub></font></span>)</span> <a href="scmpds_2.html#K2">.</a> <span class="p1">(<span class="default"><a href="scmpds_2.html#K3">DataLoc</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="scmpds_4.html#K9">IExec</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a> ,2 <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p0">(<span class="default"><span class="p1">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p5">(<span class="default"><a href="scmpds_2.html#K14">SubFrom</a> <a href="scmp_gcd.html#K2">GBP</a> ,2,<a href="scmp_gcd.html#K3">SBP</a> ,<span class="p0">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span></span>)</span></span>)</span>,<font color="Maroon">c<sub>75</sub></font></span>)</span> <a href="scmpds_2.html#K2">.</a> <a href="scmp_gcd.html#K2">GBP</a> </span>)</span>,2</span>)</span> <a href="xxreal_0.html#R1">&lt;=</a> 0 )
 </span>;<br/><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="46_9_1_1"><b>suppose </b></a><a NAME="E1:46_9_1_1"/><i><font color="Green">E61</font></i>: 
<span class="p1">(<span class="default"><a href="scmpds_4.html#K9">IExec</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a> ,2 <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p4">(<span class="default"><span class="p5">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p3">(<span class="default"><a href="scmpds_2.html#K14">SubFrom</a> <a href="scmp_gcd.html#K2">GBP</a> ,2,<a href="scmp_gcd.html#K3">SBP</a> ,<span class="p4">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span></span>)</span></span>)</span>,<font color="Maroon">c<sub>75</sub></font></span>)</span> <a href="scmpds_2.html#K2">.</a> <span class="p1">(<span class="default"><a href="scmpds_2.html#K3">DataLoc</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="scmpds_4.html#K9">IExec</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a> ,2 <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p0">(<span class="default"><span class="p1">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p5">(<span class="default"><a href="scmpds_2.html#K14">SubFrom</a> <a href="scmp_gcd.html#K2">GBP</a> ,2,<a href="scmp_gcd.html#K3">SBP</a> ,<span class="p0">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span></span>)</span></span>)</span>,<font color="Maroon">c<sub>75</sub></font></span>)</span> <a href="scmpds_2.html#K2">.</a> <a href="scmp_gcd.html#K2">GBP</a> </span>)</span>,2</span>)</span> <a href="xxreal_0.html#NR4" target="_self">&gt;</a> 0
 ;<br/><div class="add"><a NAME="E2:46_9_1_1"/><i><font color="Green">E62</font></i>: 
<span class="p1">(<span class="default"><a href="scmpds_4.html#K9">IExec</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a> ,2 <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p4">(<span class="default"><span class="p5">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p3">(<span class="default"><a href="scmpds_2.html#K14">SubFrom</a> <a href="scmp_gcd.html#K2">GBP</a> ,2,<a href="scmp_gcd.html#K3">SBP</a> ,<span class="p4">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span></span>)</span></span>)</span>,<font color="Maroon">c<sub>75</sub></font></span>)</span> <a href="scmpds_2.html#K2">.</a> <a href="scmp_gcd.html#K3">SBP</a>  <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>76</sub></font>
 <b>by </b><i><a class="txt" href="scpqsort.html#E15:46"><i><font color="Green">E55</font></i></a>, <a class="txt" href="scpqsort.html#E1:46_9"><i><font color="Green">E57</font></i></a>, <a class="ref" href="scmp_gcd.html#D3">SCMP_GCD:def 3</a></i>;<br/><a NAME="E3:46_9_1_1"/><i><font color="Green">E63</font></i>: 
<font color="Maroon">c<sub>76</sub></font> <a href="nat_1.html#K1">+</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="xxreal_0.html#NR2" target="_self">&gt;=</a> 0 <a href="nat_1.html#K1">+</a> 7
 <b>by </b><i><a class="txt" href="scpqsort.html#E8:46"><i><font color="Green">E48</font></i></a>, <a class="ref" href="xreal_1.html#T9">XREAL_1:9</a></i>;<br/><a NAME="E4:46_9_1_1"/><b>then </b>
<font color="Maroon">c<sub>76</sub></font> <a href="nat_1.html#K1">+</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="xxreal_0.html#NR4" target="_self">&gt;</a> 2
 <b>by </b><i><a class="ref" href="xreal_1.html#T2">XREAL_1:2</a></i>;<br/><a NAME="E5:46_9_1_1"/><b>then </b><i><font color="Green">E64</font></i>: 
<span class="p1">(<span class="default"><a href="scmpds_4.html#K9">IExec</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a> ,2 <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p4">(<span class="default"><span class="p5">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p3">(<span class="default"><a href="scmpds_2.html#K14">SubFrom</a> <a href="scmp_gcd.html#K2">GBP</a> ,2,<a href="scmp_gcd.html#K3">SBP</a> ,<span class="p4">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span></span>)</span></span>)</span>,<font color="Maroon">c<sub>75</sub></font></span>)</span> <a href="scmpds_2.html#K2">.</a> <span class="p1">(<span class="default"><a href="scmp_gcd.html#K1">intpos</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>76</sub></font> <a href="nat_1.html#K1">+</a> <span class="p3">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span></span>)</span></span>)</span> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>77</sub></font>
 <b>by </b><i><a class="txt" href="scpqsort.html#E15:46"><i><font color="Green">E55</font></i></a>, <a class="txt" href="scpqsort.html#E1:46_9"><i><font color="Green">E57</font></i></a></i>;<br/><a NAME="E6:46_9_1_1"/>
<span class="p1">(<span class="default"><font color="Maroon">c<sub>76</sub></font> <a href="nat_1.html#K1">+</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span></span>)</span> <a href="nat_1.html#K1">+</a> 1 <a href="xxreal_0.html#NR2" target="_self">&gt;=</a> 7 <a href="nat_1.html#K1">+</a> 1
 <b>by </b><i><a class="txt" href="scpqsort.html#E3:46_9_1_1"><i><font color="Green">E63</font></i></a>, <a class="ref" href="xreal_1.html#T8">XREAL_1:8</a></i>;<br/><a NAME="E7:46_9_1_1"/><b>then </b>
<span class="p1">(<span class="default"><font color="Maroon">c<sub>76</sub></font> <a href="nat_1.html#K1">+</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span></span>)</span> <a href="nat_1.html#K1">+</a> 1 <a href="xxreal_0.html#NR4" target="_self">&gt;</a> 2
 <b>by </b><i><a class="ref" href="xreal_1.html#T2">XREAL_1:2</a></i>;<br/><a NAME="E8:46_9_1_1"/><b>then </b>
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="scmpds_4.html#K9">IExec</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a> ,2 <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p5">(<span class="default"><span class="p0">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p4">(<span class="default"><a href="scmpds_2.html#K14">SubFrom</a> <a href="scmp_gcd.html#K2">GBP</a> ,2,<a href="scmp_gcd.html#K3">SBP</a> ,<span class="p5">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span></span>)</span></span>)</span>,<font color="Maroon">c<sub>75</sub></font></span>)</span> <a href="scmpds_2.html#K2">.</a> <span class="p2">(<span class="default"><a href="scmp_gcd.html#K1">intpos</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">c<sub>76</sub></font> <a href="nat_1.html#K1">+</a> <span class="p5">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span> <a href="xcmplx_0.html#K6">-</a> <font color="Maroon">c<sub>77</sub></font> <a href="xxreal_0.html#NR4" target="_self">&gt;</a> 0
 <b>by </b><i><a class="txt" href="scpqsort.html#E1:46_9"><i><font color="Green">E57</font></i></a>, <a class="txt" href="scpqsort.html#E2:46_9"><i><font color="Green">E58</font></i></a>, <a class="txt" href="scpqsort.html#E4:46_9"><i><font color="Green">E60</font></i></a>, <a class="txt" href="scpqsort.html#E1:46_9_1_1"><i><font color="Green">E61</font></i></a></i>;<br/><a NAME="E9:46_9_1_1"/><b>then </b>
( <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a> ,2 <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p4">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span></span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p3">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a> ,4 <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p4">(<span class="default"><span class="p5">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span> <a href="scmpds_4.html#K3">';'</a> <font color="Maroon">c<sub>50</sub></font></span>)</span> <a href="scmpds_4.html#K3">';'</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><span class="p0">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a> ,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 3</span>)</span> <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p0">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a> ,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span> <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K2">GBP</a> ,4</span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p5">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a> ,<span class="p0">(<span class="default"><span class="p1">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 2</span>)</span> <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K2">GBP</a> ,4</span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p4">(<span class="default"><a href="scmpds_2.html#K12">AddTo</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p5">(<span class="default"><span class="p0">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span>,<span class="p5">(<span class="default"><a href="xcmplx_0.html#K4">-</a> 1</span>)</span></span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p3">(<span class="default"><a href="scmpds_2.html#K12">AddTo</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p4">(<span class="default"><span class="p5">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 2</span>)</span>,1</span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p2">(<span class="default"><a href="scmpds_2.html#K12">AddTo</a> <a href="scmp_gcd.html#K2">GBP</a> ,1,2</span>)</span></span>)</span> <a href="scmpds_6.html#R1">is_closed_on</a>  <a href="scmpds_4.html#K9">IExec</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a> ,2 <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p2">(<span class="default"><a href="scmpds_2.html#K14">SubFrom</a> <a href="scmp_gcd.html#K2">GBP</a> ,2,<a href="scmp_gcd.html#K3">SBP</a> ,<span class="p3">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span></span>)</span></span>)</span>,<font color="Maroon">c<sub>75</sub></font> &amp; <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a> ,2 <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p4">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span></span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p3">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a> ,4 <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p4">(<span class="default"><span class="p5">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span> <a href="scmpds_4.html#K3">';'</a> <font color="Maroon">c<sub>50</sub></font></span>)</span> <a href="scmpds_4.html#K3">';'</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><span class="p0">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a> ,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 3</span>)</span> <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p0">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a> ,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span> <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K2">GBP</a> ,4</span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p5">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a> ,<span class="p0">(<span class="default"><span class="p1">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 2</span>)</span> <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K2">GBP</a> ,4</span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p4">(<span class="default"><a href="scmpds_2.html#K12">AddTo</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p5">(<span class="default"><span class="p0">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span>,<span class="p5">(<span class="default"><a href="xcmplx_0.html#K4">-</a> 1</span>)</span></span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p3">(<span class="default"><a href="scmpds_2.html#K12">AddTo</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p4">(<span class="default"><span class="p5">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 2</span>)</span>,1</span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p2">(<span class="default"><a href="scmpds_2.html#K12">AddTo</a> <a href="scmp_gcd.html#K2">GBP</a> ,1,2</span>)</span></span>)</span> <a href="scmpds_6.html#R2">is_halting_on</a>  <a href="scmpds_4.html#K9">IExec</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a> ,2 <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p2">(<span class="default"><a href="scmpds_2.html#K14">SubFrom</a> <a href="scmp_gcd.html#K2">GBP</a> ,2,<a href="scmp_gcd.html#K3">SBP</a> ,<span class="p3">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span></span>)</span></span>)</span>,<font color="Maroon">c<sub>75</sub></font> )
 <b>by </b><i><a class="txt" href="scpqsort.html#E13:46"><i><font color="Green">E53</font></i></a>, <a class="txt" href="scpqsort.html#E15:46"><i><font color="Green">E55</font></i></a>, <a class="txt" href="scpqsort.html#E1:46_9"><i><font color="Green">E57</font></i></a>, <a class="txt" href="scpqsort.html#E3:46_9"><i><font color="Green">E59</font></i></a>, <a class="txt" href="scpqsort.html#E4:46_9"><i><font color="Green">E60</font></i></a>, <a class="txt" href="scpqsort.html#E1:46_9_1_1"><i><font color="Green">E61</font></i></a>, <a class="txt" href="scpqsort.html#E2:46_9_1_1"><i><font color="Green">E62</font></i></a>, <a class="txt" href="scpqsort.html#E5:46_9_1_1"><i><font color="Green">E64</font></i></a></i>;<br/><a NAME="E10:46_9_1_1"/><b>then </b>
(  <a href="scmpds_6.html#K3">if&gt;0</a> <a href="scmp_gcd.html#K2">GBP</a> ,2,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a> ,2 <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p5">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span></span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p4">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a> ,4 <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p5">(<span class="default"><span class="p0">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span> <a href="scmpds_4.html#K3">';'</a> <font color="Maroon">c<sub>50</sub></font></span>)</span> <a href="scmpds_4.html#K3">';'</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><span class="p0">(<span class="default"><span class="p1">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a> ,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 3</span>)</span> <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p1">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a> ,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span> <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K2">GBP</a> ,4</span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p0">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a> ,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 2</span>)</span> <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K2">GBP</a> ,4</span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p5">(<span class="default"><a href="scmpds_2.html#K12">AddTo</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p0">(<span class="default"><span class="p1">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span>,<span class="p0">(<span class="default"><a href="xcmplx_0.html#K4">-</a> 1</span>)</span></span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p4">(<span class="default"><a href="scmpds_2.html#K12">AddTo</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p5">(<span class="default"><span class="p0">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 2</span>)</span>,1</span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p3">(<span class="default"><a href="scmpds_2.html#K12">AddTo</a> <a href="scmp_gcd.html#K2">GBP</a> ,1,2</span>)</span></span>)</span></span>)</span>,<span class="p1">(<span class="default"><a href="scmpds_4.html#K1">Load</a> <span class="p2">(<span class="default"><a href="scmpds_2.html#K12">AddTo</a> <a href="scmp_gcd.html#K2">GBP</a> ,1,<span class="p3">(<span class="default"><a href="xcmplx_0.html#K4">-</a> 2</span>)</span></span>)</span></span>)</span> <a href="scmpds_6.html#R1">is_closed_on</a>  <a href="scmpds_4.html#K9">IExec</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a> ,2 <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p2">(<span class="default"><a href="scmpds_2.html#K14">SubFrom</a> <a href="scmp_gcd.html#K2">GBP</a> ,2,<a href="scmp_gcd.html#K3">SBP</a> ,<span class="p3">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span></span>)</span></span>)</span>,<font color="Maroon">c<sub>75</sub></font> &amp;  <a href="scmpds_6.html#K3">if&gt;0</a> <a href="scmp_gcd.html#K2">GBP</a> ,2,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a> ,2 <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p5">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span></span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p4">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a> ,4 <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p5">(<span class="default"><span class="p0">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span> <a href="scmpds_4.html#K3">';'</a> <font color="Maroon">c<sub>50</sub></font></span>)</span> <a href="scmpds_4.html#K3">';'</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><span class="p0">(<span class="default"><span class="p1">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a> ,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 3</span>)</span> <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p1">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a> ,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span> <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K2">GBP</a> ,4</span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p0">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a> ,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 2</span>)</span> <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K2">GBP</a> ,4</span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p5">(<span class="default"><a href="scmpds_2.html#K12">AddTo</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p0">(<span class="default"><span class="p1">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span>,<span class="p0">(<span class="default"><a href="xcmplx_0.html#K4">-</a> 1</span>)</span></span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p4">(<span class="default"><a href="scmpds_2.html#K12">AddTo</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p5">(<span class="default"><span class="p0">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 2</span>)</span>,1</span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p3">(<span class="default"><a href="scmpds_2.html#K12">AddTo</a> <a href="scmp_gcd.html#K2">GBP</a> ,1,2</span>)</span></span>)</span></span>)</span>,<span class="p1">(<span class="default"><a href="scmpds_4.html#K1">Load</a> <span class="p2">(<span class="default"><a href="scmpds_2.html#K12">AddTo</a> <a href="scmp_gcd.html#K2">GBP</a> ,1,<span class="p3">(<span class="default"><a href="xcmplx_0.html#K4">-</a> 2</span>)</span></span>)</span></span>)</span> <a href="scmpds_6.html#R2">is_halting_on</a>  <a href="scmpds_4.html#K9">IExec</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a> ,2 <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p2">(<span class="default"><a href="scmpds_2.html#K14">SubFrom</a> <a href="scmp_gcd.html#K2">GBP</a> ,2,<a href="scmp_gcd.html#K3">SBP</a> ,<span class="p3">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span></span>)</span></span>)</span>,<font color="Maroon">c<sub>75</sub></font> )
 <b>by </b><i><a class="txt" href="scpqsort.html#E1:46_9_1_1"><i><font color="Green">E61</font></i></a>, <a class="ref" href="scmpds_6.html#T82">SCMPDS_6:82</a></i>;<br/><b>hence </b><a NAME="E11:46_9_1_1"/>
( <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a> ,2 <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p2">(<span class="default"><a href="scmpds_2.html#K14">SubFrom</a> <a href="scmp_gcd.html#K2">GBP</a> ,2,<a href="scmp_gcd.html#K3">SBP</a> ,<span class="p3">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span></span>)</span></span>)</span> <a href="scmpds_4.html#K3">';'</a> <span class="p1">(<span class="default"><a href="scmpds_6.html#K3">if&gt;0</a> <a href="scmp_gcd.html#K2">GBP</a> ,2,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a> ,2 <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p0">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span></span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p5">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a> ,4 <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p0">(<span class="default"><span class="p1">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span> <a href="scmpds_4.html#K3">';'</a> <font color="Maroon">c<sub>50</sub></font></span>)</span> <a href="scmpds_4.html#K3">';'</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><span class="p0">(<span class="default"><span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a> ,<span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 3</span>)</span> <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p2">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a> ,<span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span> <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K2">GBP</a> ,4</span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p1">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a> ,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 2</span>)</span> <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K2">GBP</a> ,4</span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p0">(<span class="default"><a href="scmpds_2.html#K12">AddTo</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span>,<span class="p1">(<span class="default"><a href="xcmplx_0.html#K4">-</a> 1</span>)</span></span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p5">(<span class="default"><a href="scmpds_2.html#K12">AddTo</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p0">(<span class="default"><span class="p1">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 2</span>)</span>,1</span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p4">(<span class="default"><a href="scmpds_2.html#K12">AddTo</a> <a href="scmp_gcd.html#K2">GBP</a> ,1,2</span>)</span></span>)</span></span>)</span>,<span class="p2">(<span class="default"><a href="scmpds_4.html#K1">Load</a> <span class="p3">(<span class="default"><a href="scmpds_2.html#K12">AddTo</a> <a href="scmp_gcd.html#K2">GBP</a> ,1,<span class="p4">(<span class="default"><a href="xcmplx_0.html#K4">-</a> 2</span>)</span></span>)</span></span>)</span></span>)</span> <a href="scmpds_6.html#R1">is_closed_on</a> <font color="Maroon">c<sub>75</sub></font> &amp; <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a> ,2 <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p2">(<span class="default"><a href="scmpds_2.html#K14">SubFrom</a> <a href="scmp_gcd.html#K2">GBP</a> ,2,<a href="scmp_gcd.html#K3">SBP</a> ,<span class="p3">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span></span>)</span></span>)</span> <a href="scmpds_4.html#K3">';'</a> <span class="p1">(<span class="default"><a href="scmpds_6.html#K3">if&gt;0</a> <a href="scmp_gcd.html#K2">GBP</a> ,2,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a> ,2 <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p0">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span></span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p5">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a> ,4 <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p0">(<span class="default"><span class="p1">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span> <a href="scmpds_4.html#K3">';'</a> <font color="Maroon">c<sub>50</sub></font></span>)</span> <a href="scmpds_4.html#K3">';'</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><span class="p0">(<span class="default"><span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a> ,<span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 3</span>)</span> <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p2">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a> ,<span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span> <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K2">GBP</a> ,4</span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p1">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a> ,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 2</span>)</span> <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K2">GBP</a> ,4</span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p0">(<span class="default"><a href="scmpds_2.html#K12">AddTo</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span>,<span class="p1">(<span class="default"><a href="xcmplx_0.html#K4">-</a> 1</span>)</span></span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p5">(<span class="default"><a href="scmpds_2.html#K12">AddTo</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p0">(<span class="default"><span class="p1">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 2</span>)</span>,1</span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p4">(<span class="default"><a href="scmpds_2.html#K12">AddTo</a> <a href="scmp_gcd.html#K2">GBP</a> ,1,2</span>)</span></span>)</span></span>)</span>,<span class="p2">(<span class="default"><a href="scmpds_4.html#K1">Load</a> <span class="p3">(<span class="default"><a href="scmpds_2.html#K12">AddTo</a> <a href="scmp_gcd.html#K2">GBP</a> ,1,<span class="p4">(<span class="default"><a href="xcmplx_0.html#K4">-</a> 2</span>)</span></span>)</span></span>)</span></span>)</span> <a href="scmpds_6.html#R2">is_halting_on</a> <font color="Maroon">c<sub>75</sub></font> )
 <b>by </b><i><a class="ref" href="scpisort.html#T10">SCPISORT:10</a></i>;<br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="46_9_1_2"><b>suppose </b></a><a NAME="E1:46_9_1_2"/><i><font color="Green">E61</font></i>: 
<span class="p1">(<span class="default"><a href="scmpds_4.html#K9">IExec</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a> ,2 <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p4">(<span class="default"><span class="p5">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p3">(<span class="default"><a href="scmpds_2.html#K14">SubFrom</a> <a href="scmp_gcd.html#K2">GBP</a> ,2,<a href="scmp_gcd.html#K3">SBP</a> ,<span class="p4">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span></span>)</span></span>)</span>,<font color="Maroon">c<sub>75</sub></font></span>)</span> <a href="scmpds_2.html#K2">.</a> <span class="p1">(<span class="default"><a href="scmpds_2.html#K3">DataLoc</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="scmpds_4.html#K9">IExec</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a> ,2 <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p0">(<span class="default"><span class="p1">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p5">(<span class="default"><a href="scmpds_2.html#K14">SubFrom</a> <a href="scmp_gcd.html#K2">GBP</a> ,2,<a href="scmp_gcd.html#K3">SBP</a> ,<span class="p0">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span></span>)</span></span>)</span>,<font color="Maroon">c<sub>75</sub></font></span>)</span> <a href="scmpds_2.html#K2">.</a> <a href="scmp_gcd.html#K2">GBP</a> </span>)</span>,2</span>)</span> <a href="xxreal_0.html#R1">&lt;=</a> 0
 ;<br/><div class="add"><a NAME="E2:46_9_1_2"/>
(  <a href="scmpds_4.html#K1">Load</a> <span class="p1">(<span class="default"><a href="scmpds_2.html#K12">AddTo</a> <a href="scmp_gcd.html#K2">GBP</a> ,1,<span class="p2">(<span class="default"><a href="xcmplx_0.html#K4">-</a> 2</span>)</span></span>)</span> <a href="scmpds_6.html#R1">is_closed_on</a>  <a href="scmpds_4.html#K9">IExec</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a> ,2 <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p2">(<span class="default"><a href="scmpds_2.html#K14">SubFrom</a> <a href="scmp_gcd.html#K2">GBP</a> ,2,<a href="scmp_gcd.html#K3">SBP</a> ,<span class="p3">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span></span>)</span></span>)</span>,<font color="Maroon">c<sub>75</sub></font> &amp;  <a href="scmpds_4.html#K1">Load</a> <span class="p1">(<span class="default"><a href="scmpds_2.html#K12">AddTo</a> <a href="scmp_gcd.html#K2">GBP</a> ,1,<span class="p2">(<span class="default"><a href="xcmplx_0.html#K4">-</a> 2</span>)</span></span>)</span> <a href="scmpds_6.html#R2">is_halting_on</a>  <a href="scmpds_4.html#K9">IExec</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a> ,2 <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p2">(<span class="default"><a href="scmpds_2.html#K14">SubFrom</a> <a href="scmp_gcd.html#K2">GBP</a> ,2,<a href="scmp_gcd.html#K3">SBP</a> ,<span class="p3">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span></span>)</span></span>)</span>,<font color="Maroon">c<sub>75</sub></font> )
 <b>by </b><i><a class="ref" href="scmpds_6.html#T34">SCMPDS_6:34</a>, <a class="ref" href="scmpds_6.html#T35">SCMPDS_6:35</a></i>;<br/><a NAME="E3:46_9_1_2"/><b>then </b>
(  <a href="scmpds_6.html#K3">if&gt;0</a> <a href="scmp_gcd.html#K2">GBP</a> ,2,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a> ,2 <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p5">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span></span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p4">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a> ,4 <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p5">(<span class="default"><span class="p0">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span> <a href="scmpds_4.html#K3">';'</a> <font color="Maroon">c<sub>50</sub></font></span>)</span> <a href="scmpds_4.html#K3">';'</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><span class="p0">(<span class="default"><span class="p1">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a> ,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 3</span>)</span> <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p1">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a> ,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span> <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K2">GBP</a> ,4</span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p0">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a> ,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 2</span>)</span> <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K2">GBP</a> ,4</span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p5">(<span class="default"><a href="scmpds_2.html#K12">AddTo</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p0">(<span class="default"><span class="p1">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span>,<span class="p0">(<span class="default"><a href="xcmplx_0.html#K4">-</a> 1</span>)</span></span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p4">(<span class="default"><a href="scmpds_2.html#K12">AddTo</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p5">(<span class="default"><span class="p0">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 2</span>)</span>,1</span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p3">(<span class="default"><a href="scmpds_2.html#K12">AddTo</a> <a href="scmp_gcd.html#K2">GBP</a> ,1,2</span>)</span></span>)</span></span>)</span>,<span class="p1">(<span class="default"><a href="scmpds_4.html#K1">Load</a> <span class="p2">(<span class="default"><a href="scmpds_2.html#K12">AddTo</a> <a href="scmp_gcd.html#K2">GBP</a> ,1,<span class="p3">(<span class="default"><a href="xcmplx_0.html#K4">-</a> 2</span>)</span></span>)</span></span>)</span> <a href="scmpds_6.html#R1">is_closed_on</a>  <a href="scmpds_4.html#K9">IExec</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a> ,2 <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p2">(<span class="default"><a href="scmpds_2.html#K14">SubFrom</a> <a href="scmp_gcd.html#K2">GBP</a> ,2,<a href="scmp_gcd.html#K3">SBP</a> ,<span class="p3">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span></span>)</span></span>)</span>,<font color="Maroon">c<sub>75</sub></font> &amp;  <a href="scmpds_6.html#K3">if&gt;0</a> <a href="scmp_gcd.html#K2">GBP</a> ,2,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a> ,2 <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p5">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span></span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p4">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a> ,4 <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p5">(<span class="default"><span class="p0">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span> <a href="scmpds_4.html#K3">';'</a> <font color="Maroon">c<sub>50</sub></font></span>)</span> <a href="scmpds_4.html#K3">';'</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><span class="p0">(<span class="default"><span class="p1">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a> ,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 3</span>)</span> <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p1">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a> ,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span> <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K2">GBP</a> ,4</span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p0">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a> ,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 2</span>)</span> <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K2">GBP</a> ,4</span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p5">(<span class="default"><a href="scmpds_2.html#K12">AddTo</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p0">(<span class="default"><span class="p1">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span>,<span class="p0">(<span class="default"><a href="xcmplx_0.html#K4">-</a> 1</span>)</span></span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p4">(<span class="default"><a href="scmpds_2.html#K12">AddTo</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p5">(<span class="default"><span class="p0">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 2</span>)</span>,1</span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p3">(<span class="default"><a href="scmpds_2.html#K12">AddTo</a> <a href="scmp_gcd.html#K2">GBP</a> ,1,2</span>)</span></span>)</span></span>)</span>,<span class="p1">(<span class="default"><a href="scmpds_4.html#K1">Load</a> <span class="p2">(<span class="default"><a href="scmpds_2.html#K12">AddTo</a> <a href="scmp_gcd.html#K2">GBP</a> ,1,<span class="p3">(<span class="default"><a href="xcmplx_0.html#K4">-</a> 2</span>)</span></span>)</span></span>)</span> <a href="scmpds_6.html#R2">is_halting_on</a>  <a href="scmpds_4.html#K9">IExec</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a> ,2 <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p2">(<span class="default"><a href="scmpds_2.html#K14">SubFrom</a> <a href="scmp_gcd.html#K2">GBP</a> ,2,<a href="scmp_gcd.html#K3">SBP</a> ,<span class="p3">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span></span>)</span></span>)</span>,<font color="Maroon">c<sub>75</sub></font> )
 <b>by </b><i><a class="txt" href="scpqsort.html#E1:46_9_1_2"><i><font color="Green">E61</font></i></a>, <a class="ref" href="scmpds_6.html#T83">SCMPDS_6:83</a></i>;<br/><b>hence </b><a NAME="E4:46_9_1_2"/>
( <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a> ,2 <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p2">(<span class="default"><a href="scmpds_2.html#K14">SubFrom</a> <a href="scmp_gcd.html#K2">GBP</a> ,2,<a href="scmp_gcd.html#K3">SBP</a> ,<span class="p3">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span></span>)</span></span>)</span> <a href="scmpds_4.html#K3">';'</a> <span class="p1">(<span class="default"><a href="scmpds_6.html#K3">if&gt;0</a> <a href="scmp_gcd.html#K2">GBP</a> ,2,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a> ,2 <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p0">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span></span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p5">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a> ,4 <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p0">(<span class="default"><span class="p1">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span> <a href="scmpds_4.html#K3">';'</a> <font color="Maroon">c<sub>50</sub></font></span>)</span> <a href="scmpds_4.html#K3">';'</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><span class="p0">(<span class="default"><span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a> ,<span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 3</span>)</span> <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p2">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a> ,<span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span> <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K2">GBP</a> ,4</span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p1">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a> ,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 2</span>)</span> <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K2">GBP</a> ,4</span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p0">(<span class="default"><a href="scmpds_2.html#K12">AddTo</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span>,<span class="p1">(<span class="default"><a href="xcmplx_0.html#K4">-</a> 1</span>)</span></span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p5">(<span class="default"><a href="scmpds_2.html#K12">AddTo</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p0">(<span class="default"><span class="p1">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 2</span>)</span>,1</span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p4">(<span class="default"><a href="scmpds_2.html#K12">AddTo</a> <a href="scmp_gcd.html#K2">GBP</a> ,1,2</span>)</span></span>)</span></span>)</span>,<span class="p2">(<span class="default"><a href="scmpds_4.html#K1">Load</a> <span class="p3">(<span class="default"><a href="scmpds_2.html#K12">AddTo</a> <a href="scmp_gcd.html#K2">GBP</a> ,1,<span class="p4">(<span class="default"><a href="xcmplx_0.html#K4">-</a> 2</span>)</span></span>)</span></span>)</span></span>)</span> <a href="scmpds_6.html#R1">is_closed_on</a> <font color="Maroon">c<sub>75</sub></font> &amp; <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a> ,2 <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p2">(<span class="default"><a href="scmpds_2.html#K14">SubFrom</a> <a href="scmp_gcd.html#K2">GBP</a> ,2,<a href="scmp_gcd.html#K3">SBP</a> ,<span class="p3">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span></span>)</span></span>)</span> <a href="scmpds_4.html#K3">';'</a> <span class="p1">(<span class="default"><a href="scmpds_6.html#K3">if&gt;0</a> <a href="scmp_gcd.html#K2">GBP</a> ,2,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a> ,2 <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p0">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span></span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p5">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a> ,4 <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p0">(<span class="default"><span class="p1">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span> <a href="scmpds_4.html#K3">';'</a> <font color="Maroon">c<sub>50</sub></font></span>)</span> <a href="scmpds_4.html#K3">';'</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><span class="p0">(<span class="default"><span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a> ,<span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 3</span>)</span> <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p2">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a> ,<span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span> <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K2">GBP</a> ,4</span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p1">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a> ,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 2</span>)</span> <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K2">GBP</a> ,4</span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p0">(<span class="default"><a href="scmpds_2.html#K12">AddTo</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span>,<span class="p1">(<span class="default"><a href="xcmplx_0.html#K4">-</a> 1</span>)</span></span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p5">(<span class="default"><a href="scmpds_2.html#K12">AddTo</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p0">(<span class="default"><span class="p1">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 2</span>)</span>,1</span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p4">(<span class="default"><a href="scmpds_2.html#K12">AddTo</a> <a href="scmp_gcd.html#K2">GBP</a> ,1,2</span>)</span></span>)</span></span>)</span>,<span class="p2">(<span class="default"><a href="scmpds_4.html#K1">Load</a> <span class="p3">(<span class="default"><a href="scmpds_2.html#K12">AddTo</a> <a href="scmp_gcd.html#K2">GBP</a> ,1,<span class="p4">(<span class="default"><a href="xcmplx_0.html#K4">-</a> 2</span>)</span></span>)</span></span>)</span></span>)</span> <a href="scmpds_6.html#R2">is_halting_on</a> <font color="Maroon">c<sub>75</sub></font> )
 <b>by </b><i><a class="ref" href="scpisort.html#T10">SCPISORT:10</a></i>;<br/></div><b>end;</b></div></div><b>end;</b></div>

</div><b>end;</b></div>
<a NAME="E17:46"/><i><font color="Green">E57</font></i>: 
for <font color="Olive">b<sub>1</sub></font> being  <a href="ami_1.html#NM4">State</a> of <a href="scmpds_2.html#K1">SCMPDS</a> <br/>for <font color="Olive">b<sub>2</sub></font>, <font color="Olive">b<sub>3</sub></font>, <font color="Olive">b<sub>4</sub></font> being  <a href="nat_1.html#NM1">Nat</a><br/>for <font color="Olive">b<sub>5</sub></font> being  <a href="int_1.html#NM1">Integer</a><br/>for <font color="Olive">b<sub>6</sub></font>, <font color="Olive">b<sub>7</sub></font> being   <a href="finseq_1.html#M2">FinSequence</a> of  <a href="numbers.html#K4">INT</a>  st <font color="Olive">b<sub>1</sub></font> <a href="scmpds_2.html#K2">.</a> <a href="scmp_gcd.html#K2">GBP</a>  <a href="hidden.html#R1">=</a> 0 &amp; <font color="Olive">b<sub>1</sub></font> <a href="scmpds_2.html#K2">.</a> <a href="scmp_gcd.html#K3">SBP</a>  <a href="hidden.html#R1">=</a> <font color="Olive">b<sub>3</sub></font> &amp; <font color="Olive">b<sub>3</sub></font> <a href="hidden.html#R1">=</a> <font color="Olive">b<sub>2</sub></font> <a href="nat_1.html#K1">+</a> 1 &amp; <font color="Olive">b<sub>1</sub></font> <a href="scmpds_2.html#K2">.</a> <span class="p1">(<span class="default"><a href="scmp_gcd.html#K1">intpos</a> <span class="p2">(<span class="default"><font color="Olive">b<sub>3</sub></font> <a href="nat_1.html#K1">+</a> <span class="p3">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span></span>)</span></span>)</span> <a href="hidden.html#R1">=</a> <font color="Olive">b<sub>4</sub></font> &amp; <font color="Olive">b<sub>4</sub></font> <a href="xxreal_0.html#NR2" target="_self">&gt;=</a> <font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> 1 &amp; <font color="Olive">b<sub>5</sub></font> <a href="hidden.html#R1">=</a> <font color="Olive">b<sub>1</sub></font> <a href="scmpds_2.html#K2">.</a> <span class="p1">(<span class="default"><a href="scmp_gcd.html#K1">intpos</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Olive">b<sub>3</sub></font> <a href="nat_1.html#K1">+</a> <span class="p4">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> &amp; <font color="Olive">b<sub>5</sub></font> <a href="xcmplx_0.html#K6">-</a> <font color="Olive">b<sub>4</sub></font> <a href="xxreal_0.html#NR4" target="_self">&gt;</a> 0 &amp; <font color="Olive">b<sub>5</sub></font> <a href="xxreal_0.html#R1">&lt;=</a> <font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font> &amp; <font color="Olive">b<sub>6</sub></font> <a href="scpisort.html#R1">is_FinSequence_on</a> <font color="Olive">b<sub>1</sub></font>,<font color="Maroon">c<sub>48</sub></font> &amp;  <a href="finseq_1.html#K3">len</a> <font color="Olive">b<sub>6</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>49</sub></font> &amp; <font color="Olive">b<sub>7</sub></font> <a href="scpisort.html#R1">is_FinSequence_on</a>  <a href="scmpds_4.html#K9">IExec</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a> ,2 <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p4">(<span class="default"><span class="p5">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p3">(<span class="default"><a href="scmpds_2.html#K14">SubFrom</a> <a href="scmp_gcd.html#K2">GBP</a> ,2,<a href="scmp_gcd.html#K3">SBP</a> ,<span class="p4">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span></span>)</span></span>)</span> <a href="scmpds_4.html#K3">';'</a> <span class="p2">(<span class="default"><a href="scmpds_6.html#K3">if&gt;0</a> <a href="scmp_gcd.html#K2">GBP</a> ,2,<span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><span class="p0">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a> ,2 <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p1">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span></span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p0">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a> ,4 <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span> <a href="scmpds_4.html#K3">';'</a> <font color="Maroon">c<sub>50</sub></font></span>)</span> <a href="scmpds_4.html#K3">';'</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><span class="p0">(<span class="default"><span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a> ,<span class="p4">(<span class="default"><span class="p5">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 3</span>)</span> <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p4">(<span class="default"><span class="p5">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p3">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a> ,<span class="p4">(<span class="default"><span class="p5">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span> <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K2">GBP</a> ,4</span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p2">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a> ,<span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 2</span>)</span> <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K2">GBP</a> ,4</span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p1">(<span class="default"><a href="scmpds_2.html#K12">AddTo</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span>,<span class="p2">(<span class="default"><a href="xcmplx_0.html#K4">-</a> 1</span>)</span></span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p0">(<span class="default"><a href="scmpds_2.html#K12">AddTo</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 2</span>)</span>,1</span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p5">(<span class="default"><a href="scmpds_2.html#K12">AddTo</a> <a href="scmp_gcd.html#K2">GBP</a> ,1,2</span>)</span></span>)</span></span>)</span>,<span class="p3">(<span class="default"><a href="scmpds_4.html#K1">Load</a> <span class="p4">(<span class="default"><a href="scmpds_2.html#K12">AddTo</a> <a href="scmp_gcd.html#K2">GBP</a> ,1,<span class="p5">(<span class="default"><a href="xcmplx_0.html#K4">-</a> 2</span>)</span></span>)</span></span>)</span></span>)</span></span>)</span>,<font color="Olive">b<sub>1</sub></font>,<font color="Maroon">c<sub>48</sub></font> &amp;  <a href="finseq_1.html#K3">len</a> <font color="Olive">b<sub>7</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>49</sub></font> holds <br/>( <span class="p1">(<span class="default"><a href="scmpds_4.html#K9">IExec</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a> ,2 <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p5">(<span class="default"><span class="p0">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p4">(<span class="default"><a href="scmpds_2.html#K14">SubFrom</a> <a href="scmp_gcd.html#K2">GBP</a> ,2,<a href="scmp_gcd.html#K3">SBP</a> ,<span class="p5">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span></span>)</span></span>)</span> <a href="scmpds_4.html#K3">';'</a> <span class="p3">(<span class="default"><a href="scmpds_6.html#K3">if&gt;0</a> <a href="scmp_gcd.html#K2">GBP</a> ,2,<span class="p4">(<span class="default"><span class="p5">(<span class="default"><span class="p0">(<span class="default"><span class="p1">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a> ,2 <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p2">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span></span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p1">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a> ,4 <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span> <a href="scmpds_4.html#K3">';'</a> <font color="Maroon">c<sub>50</sub></font></span>)</span> <a href="scmpds_4.html#K3">';'</a> <span class="p5">(<span class="default"><span class="p0">(<span class="default"><span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a> ,<span class="p5">(<span class="default"><span class="p0">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 3</span>)</span> <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p5">(<span class="default"><span class="p0">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p4">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a> ,<span class="p5">(<span class="default"><span class="p0">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span> <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K2">GBP</a> ,4</span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p3">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a> ,<span class="p4">(<span class="default"><span class="p5">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 2</span>)</span> <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K2">GBP</a> ,4</span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p2">(<span class="default"><a href="scmpds_2.html#K12">AddTo</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span>,<span class="p3">(<span class="default"><a href="xcmplx_0.html#K4">-</a> 1</span>)</span></span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p1">(<span class="default"><a href="scmpds_2.html#K12">AddTo</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 2</span>)</span>,1</span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p0">(<span class="default"><a href="scmpds_2.html#K12">AddTo</a> <a href="scmp_gcd.html#K2">GBP</a> ,1,2</span>)</span></span>)</span></span>)</span>,<span class="p4">(<span class="default"><a href="scmpds_4.html#K1">Load</a> <span class="p5">(<span class="default"><a href="scmpds_2.html#K12">AddTo</a> <a href="scmp_gcd.html#K2">GBP</a> ,1,<span class="p0">(<span class="default"><a href="xcmplx_0.html#K4">-</a> 2</span>)</span></span>)</span></span>)</span></span>)</span></span>)</span>,<font color="Olive">b<sub>1</sub></font></span>)</span> <a href="scmpds_2.html#K2">.</a> <a href="scmp_gcd.html#K2">GBP</a>  <a href="hidden.html#R1">=</a> 0 &amp; <span class="p1">(<span class="default"><a href="scmpds_4.html#K9">IExec</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a> ,2 <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p5">(<span class="default"><span class="p0">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p4">(<span class="default"><a href="scmpds_2.html#K14">SubFrom</a> <a href="scmp_gcd.html#K2">GBP</a> ,2,<a href="scmp_gcd.html#K3">SBP</a> ,<span class="p5">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span></span>)</span></span>)</span> <a href="scmpds_4.html#K3">';'</a> <span class="p3">(<span class="default"><a href="scmpds_6.html#K3">if&gt;0</a> <a href="scmp_gcd.html#K2">GBP</a> ,2,<span class="p4">(<span class="default"><span class="p5">(<span class="default"><span class="p0">(<span class="default"><span class="p1">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a> ,2 <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p2">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span></span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p1">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a> ,4 <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span> <a href="scmpds_4.html#K3">';'</a> <font color="Maroon">c<sub>50</sub></font></span>)</span> <a href="scmpds_4.html#K3">';'</a> <span class="p5">(<span class="default"><span class="p0">(<span class="default"><span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a> ,<span class="p5">(<span class="default"><span class="p0">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 3</span>)</span> <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p5">(<span class="default"><span class="p0">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p4">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a> ,<span class="p5">(<span class="default"><span class="p0">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span> <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K2">GBP</a> ,4</span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p3">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a> ,<span class="p4">(<span class="default"><span class="p5">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 2</span>)</span> <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K2">GBP</a> ,4</span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p2">(<span class="default"><a href="scmpds_2.html#K12">AddTo</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span>,<span class="p3">(<span class="default"><a href="xcmplx_0.html#K4">-</a> 1</span>)</span></span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p1">(<span class="default"><a href="scmpds_2.html#K12">AddTo</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 2</span>)</span>,1</span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p0">(<span class="default"><a href="scmpds_2.html#K12">AddTo</a> <a href="scmp_gcd.html#K2">GBP</a> ,1,2</span>)</span></span>)</span></span>)</span>,<span class="p4">(<span class="default"><a href="scmpds_4.html#K1">Load</a> <span class="p5">(<span class="default"><a href="scmpds_2.html#K12">AddTo</a> <a href="scmp_gcd.html#K2">GBP</a> ,1,<span class="p0">(<span class="default"><a href="xcmplx_0.html#K4">-</a> 2</span>)</span></span>)</span></span>)</span></span>)</span></span>)</span>,<font color="Olive">b<sub>1</sub></font></span>)</span> <a href="scmpds_2.html#K2">.</a> <span class="p1">(<span class="default"><a href="scmp_gcd.html#K1">intpos</a> 1</span>)</span> <a href="hidden.html#R1">=</a> <font color="Olive">b<sub>3</sub></font> <a href="nat_1.html#K1">+</a> 2 &amp; <font color="Olive">b<sub>4</sub></font> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><a href="scmpds_4.html#K9">IExec</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a> ,2 <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p5">(<span class="default"><span class="p0">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p4">(<span class="default"><a href="scmpds_2.html#K14">SubFrom</a> <a href="scmp_gcd.html#K2">GBP</a> ,2,<a href="scmp_gcd.html#K3">SBP</a> ,<span class="p5">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span></span>)</span></span>)</span> <a href="scmpds_4.html#K3">';'</a> <span class="p3">(<span class="default"><a href="scmpds_6.html#K3">if&gt;0</a> <a href="scmp_gcd.html#K2">GBP</a> ,2,<span class="p4">(<span class="default"><span class="p5">(<span class="default"><span class="p0">(<span class="default"><span class="p1">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a> ,2 <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p2">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span></span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p1">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a> ,4 <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span> <a href="scmpds_4.html#K3">';'</a> <font color="Maroon">c<sub>50</sub></font></span>)</span> <a href="scmpds_4.html#K3">';'</a> <span class="p5">(<span class="default"><span class="p0">(<span class="default"><span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a> ,<span class="p5">(<span class="default"><span class="p0">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 3</span>)</span> <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p5">(<span class="default"><span class="p0">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p4">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a> ,<span class="p5">(<span class="default"><span class="p0">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span> <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K2">GBP</a> ,4</span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p3">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a> ,<span class="p4">(<span class="default"><span class="p5">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 2</span>)</span> <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K2">GBP</a> ,4</span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p2">(<span class="default"><a href="scmpds_2.html#K12">AddTo</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span>,<span class="p3">(<span class="default"><a href="xcmplx_0.html#K4">-</a> 1</span>)</span></span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p1">(<span class="default"><a href="scmpds_2.html#K12">AddTo</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 2</span>)</span>,1</span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p0">(<span class="default"><a href="scmpds_2.html#K12">AddTo</a> <a href="scmp_gcd.html#K2">GBP</a> ,1,2</span>)</span></span>)</span></span>)</span>,<span class="p4">(<span class="default"><a href="scmpds_4.html#K1">Load</a> <span class="p5">(<span class="default"><a href="scmpds_2.html#K12">AddTo</a> <a href="scmp_gcd.html#K2">GBP</a> ,1,<span class="p0">(<span class="default"><a href="xcmplx_0.html#K4">-</a> 2</span>)</span></span>)</span></span>)</span></span>)</span></span>)</span>,<font color="Olive">b<sub>1</sub></font></span>)</span> <a href="scmpds_2.html#K2">.</a> <span class="p1">(<span class="default"><a href="scmp_gcd.html#K1">intpos</a> <span class="p2">(<span class="default"><font color="Olive">b<sub>3</sub></font> <a href="nat_1.html#K1">+</a> <span class="p3">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span></span>)</span></span>)</span> &amp; <font color="Olive">b<sub>5</sub></font> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><a href="scmpds_4.html#K9">IExec</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a> ,2 <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p5">(<span class="default"><span class="p0">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p4">(<span class="default"><a href="scmpds_2.html#K14">SubFrom</a> <a href="scmp_gcd.html#K2">GBP</a> ,2,<a href="scmp_gcd.html#K3">SBP</a> ,<span class="p5">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span></span>)</span></span>)</span> <a href="scmpds_4.html#K3">';'</a> <span class="p3">(<span class="default"><a href="scmpds_6.html#K3">if&gt;0</a> <a href="scmp_gcd.html#K2">GBP</a> ,2,<span class="p4">(<span class="default"><span class="p5">(<span class="default"><span class="p0">(<span class="default"><span class="p1">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a> ,2 <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p2">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span></span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p1">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a> ,4 <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span> <a href="scmpds_4.html#K3">';'</a> <font color="Maroon">c<sub>50</sub></font></span>)</span> <a href="scmpds_4.html#K3">';'</a> <span class="p5">(<span class="default"><span class="p0">(<span class="default"><span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a> ,<span class="p5">(<span class="default"><span class="p0">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 3</span>)</span> <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p5">(<span class="default"><span class="p0">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p4">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a> ,<span class="p5">(<span class="default"><span class="p0">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span> <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K2">GBP</a> ,4</span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p3">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a> ,<span class="p4">(<span class="default"><span class="p5">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 2</span>)</span> <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K2">GBP</a> ,4</span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p2">(<span class="default"><a href="scmpds_2.html#K12">AddTo</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span>,<span class="p3">(<span class="default"><a href="xcmplx_0.html#K4">-</a> 1</span>)</span></span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p1">(<span class="default"><a href="scmpds_2.html#K12">AddTo</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 2</span>)</span>,1</span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p0">(<span class="default"><a href="scmpds_2.html#K12">AddTo</a> <a href="scmp_gcd.html#K2">GBP</a> ,1,2</span>)</span></span>)</span></span>)</span>,<span class="p4">(<span class="default"><a href="scmpds_4.html#K1">Load</a> <span class="p5">(<span class="default"><a href="scmpds_2.html#K12">AddTo</a> <a href="scmp_gcd.html#K2">GBP</a> ,1,<span class="p0">(<span class="default"><a href="xcmplx_0.html#K4">-</a> 2</span>)</span></span>)</span></span>)</span></span>)</span></span>)</span>,<font color="Olive">b<sub>1</sub></font></span>)</span> <a href="scmpds_2.html#K2">.</a> <span class="p1">(<span class="default"><a href="scmp_gcd.html#K1">intpos</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Olive">b<sub>3</sub></font> <a href="nat_1.html#K1">+</a> <span class="p4">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span></span>)</span> <a href="nat_1.html#K1">+</a> 3</span>)</span></span>)</span> &amp; ( for <font color="Olive">b<sub>8</sub></font> being  <a href="nat_1.html#NM1">Nat</a> st 1 <a href="xxreal_0.html#R1">&lt;=</a> <font color="Olive">b<sub>8</sub></font> &amp; <font color="Olive">b<sub>8</sub></font> <a href="xxreal_0.html#NR3" target="_self">&lt;</a> <font color="Olive">b<sub>3</sub></font> holds <br/><span class="p1">(<span class="default"><a href="scmpds_4.html#K9">IExec</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a> ,2 <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p5">(<span class="default"><span class="p0">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p4">(<span class="default"><a href="scmpds_2.html#K14">SubFrom</a> <a href="scmp_gcd.html#K2">GBP</a> ,2,<a href="scmp_gcd.html#K3">SBP</a> ,<span class="p5">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span></span>)</span></span>)</span> <a href="scmpds_4.html#K3">';'</a> <span class="p3">(<span class="default"><a href="scmpds_6.html#K3">if&gt;0</a> <a href="scmp_gcd.html#K2">GBP</a> ,2,<span class="p4">(<span class="default"><span class="p5">(<span class="default"><span class="p0">(<span class="default"><span class="p1">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a> ,2 <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p2">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span></span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p1">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a> ,4 <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span> <a href="scmpds_4.html#K3">';'</a> <font color="Maroon">c<sub>50</sub></font></span>)</span> <a href="scmpds_4.html#K3">';'</a> <span class="p5">(<span class="default"><span class="p0">(<span class="default"><span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a> ,<span class="p5">(<span class="default"><span class="p0">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 3</span>)</span> <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p5">(<span class="default"><span class="p0">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p4">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a> ,<span class="p5">(<span class="default"><span class="p0">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span> <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K2">GBP</a> ,4</span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p3">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a> ,<span class="p4">(<span class="default"><span class="p5">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 2</span>)</span> <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K2">GBP</a> ,4</span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p2">(<span class="default"><a href="scmpds_2.html#K12">AddTo</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span>,<span class="p3">(<span class="default"><a href="xcmplx_0.html#K4">-</a> 1</span>)</span></span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p1">(<span class="default"><a href="scmpds_2.html#K12">AddTo</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 2</span>)</span>,1</span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p0">(<span class="default"><a href="scmpds_2.html#K12">AddTo</a> <a href="scmp_gcd.html#K2">GBP</a> ,1,2</span>)</span></span>)</span></span>)</span>,<span class="p4">(<span class="default"><a href="scmpds_4.html#K1">Load</a> <span class="p5">(<span class="default"><a href="scmpds_2.html#K12">AddTo</a> <a href="scmp_gcd.html#K2">GBP</a> ,1,<span class="p0">(<span class="default"><a href="xcmplx_0.html#K4">-</a> 2</span>)</span></span>)</span></span>)</span></span>)</span></span>)</span>,<font color="Olive">b<sub>1</sub></font></span>)</span> <a href="scmpds_2.html#K2">.</a> <span class="p1">(<span class="default"><a href="scmp_gcd.html#K1">intpos</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> <font color="Olive">b<sub>8</sub></font></span>)</span></span>)</span> <a href="hidden.html#R1">=</a> <font color="Olive">b<sub>1</sub></font> <a href="scmpds_2.html#K2">.</a> <span class="p1">(<span class="default"><a href="scmp_gcd.html#K1">intpos</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> <font color="Olive">b<sub>8</sub></font></span>)</span></span>)</span> ) &amp; <font color="Olive">b<sub>6</sub></font>,<font color="Olive">b<sub>7</sub></font> <a href="rfinseq.html#R1">are_fiberwise_equipotent</a>  &amp; ex <font color="Olive">b<sub>8</sub></font> being  <a href="nat_1.html#NM1">Nat</a> st <br/>( <font color="Olive">b<sub>4</sub></font> <a href="xxreal_0.html#R1">&lt;=</a> <font color="Olive">b<sub>8</sub></font> &amp; <font color="Olive">b<sub>8</sub></font> <a href="xxreal_0.html#R1">&lt;=</a> <font color="Olive">b<sub>5</sub></font> &amp; <font color="Olive">b<sub>8</sub></font> <a href="xcmplx_0.html#K6">-</a> 1 <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><a href="scmpds_4.html#K9">IExec</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a> ,2 <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p5">(<span class="default"><span class="p0">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p4">(<span class="default"><a href="scmpds_2.html#K14">SubFrom</a> <a href="scmp_gcd.html#K2">GBP</a> ,2,<a href="scmp_gcd.html#K3">SBP</a> ,<span class="p5">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span></span>)</span></span>)</span> <a href="scmpds_4.html#K3">';'</a> <span class="p3">(<span class="default"><a href="scmpds_6.html#K3">if&gt;0</a> <a href="scmp_gcd.html#K2">GBP</a> ,2,<span class="p4">(<span class="default"><span class="p5">(<span class="default"><span class="p0">(<span class="default"><span class="p1">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a> ,2 <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p2">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span></span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p1">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a> ,4 <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span> <a href="scmpds_4.html#K3">';'</a> <font color="Maroon">c<sub>50</sub></font></span>)</span> <a href="scmpds_4.html#K3">';'</a> <span class="p5">(<span class="default"><span class="p0">(<span class="default"><span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a> ,<span class="p5">(<span class="default"><span class="p0">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 3</span>)</span> <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p5">(<span class="default"><span class="p0">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p4">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a> ,<span class="p5">(<span class="default"><span class="p0">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span> <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K2">GBP</a> ,4</span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p3">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a> ,<span class="p4">(<span class="default"><span class="p5">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 2</span>)</span> <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K2">GBP</a> ,4</span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p2">(<span class="default"><a href="scmpds_2.html#K12">AddTo</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span>,<span class="p3">(<span class="default"><a href="xcmplx_0.html#K4">-</a> 1</span>)</span></span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p1">(<span class="default"><a href="scmpds_2.html#K12">AddTo</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 2</span>)</span>,1</span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p0">(<span class="default"><a href="scmpds_2.html#K12">AddTo</a> <a href="scmp_gcd.html#K2">GBP</a> ,1,2</span>)</span></span>)</span></span>)</span>,<span class="p4">(<span class="default"><a href="scmpds_4.html#K1">Load</a> <span class="p5">(<span class="default"><a href="scmpds_2.html#K12">AddTo</a> <a href="scmp_gcd.html#K2">GBP</a> ,1,<span class="p0">(<span class="default"><a href="xcmplx_0.html#K4">-</a> 2</span>)</span></span>)</span></span>)</span></span>)</span></span>)</span>,<font color="Olive">b<sub>1</sub></font></span>)</span> <a href="scmpds_2.html#K2">.</a> <span class="p1">(<span class="default"><a href="scmp_gcd.html#K1">intpos</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Olive">b<sub>3</sub></font> <a href="nat_1.html#K1">+</a> <span class="p4">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> &amp; <font color="Olive">b<sub>8</sub></font> <a href="nat_1.html#K1">+</a> 1 <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><a href="scmpds_4.html#K9">IExec</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a> ,2 <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p5">(<span class="default"><span class="p0">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p4">(<span class="default"><a href="scmpds_2.html#K14">SubFrom</a> <a href="scmp_gcd.html#K2">GBP</a> ,2,<a href="scmp_gcd.html#K3">SBP</a> ,<span class="p5">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span></span>)</span></span>)</span> <a href="scmpds_4.html#K3">';'</a> <span class="p3">(<span class="default"><a href="scmpds_6.html#K3">if&gt;0</a> <a href="scmp_gcd.html#K2">GBP</a> ,2,<span class="p4">(<span class="default"><span class="p5">(<span class="default"><span class="p0">(<span class="default"><span class="p1">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a> ,2 <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p2">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span></span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p1">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a> ,4 <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span> <a href="scmpds_4.html#K3">';'</a> <font color="Maroon">c<sub>50</sub></font></span>)</span> <a href="scmpds_4.html#K3">';'</a> <span class="p5">(<span class="default"><span class="p0">(<span class="default"><span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a> ,<span class="p5">(<span class="default"><span class="p0">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 3</span>)</span> <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p5">(<span class="default"><span class="p0">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p4">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a> ,<span class="p5">(<span class="default"><span class="p0">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span> <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K2">GBP</a> ,4</span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p3">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a> ,<span class="p4">(<span class="default"><span class="p5">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 2</span>)</span> <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K2">GBP</a> ,4</span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p2">(<span class="default"><a href="scmpds_2.html#K12">AddTo</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span>,<span class="p3">(<span class="default"><a href="xcmplx_0.html#K4">-</a> 1</span>)</span></span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p1">(<span class="default"><a href="scmpds_2.html#K12">AddTo</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 2</span>)</span>,1</span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p0">(<span class="default"><a href="scmpds_2.html#K12">AddTo</a> <a href="scmp_gcd.html#K2">GBP</a> ,1,2</span>)</span></span>)</span></span>)</span>,<span class="p4">(<span class="default"><a href="scmpds_4.html#K1">Load</a> <span class="p5">(<span class="default"><a href="scmpds_2.html#K12">AddTo</a> <a href="scmp_gcd.html#K2">GBP</a> ,1,<span class="p0">(<span class="default"><a href="xcmplx_0.html#K4">-</a> 2</span>)</span></span>)</span></span>)</span></span>)</span></span>)</span>,<font color="Olive">b<sub>1</sub></font></span>)</span> <a href="scmpds_2.html#K2">.</a> <span class="p1">(<span class="default"><a href="scmp_gcd.html#K1">intpos</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Olive">b<sub>3</sub></font> <a href="nat_1.html#K1">+</a> <span class="p4">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span></span>)</span> <a href="nat_1.html#K1">+</a> 2</span>)</span></span>)</span> &amp; ( for <font color="Olive">b<sub>9</sub></font> being  <a href="nat_1.html#NM1">Nat</a> st <font color="Olive">b<sub>4</sub></font> <a href="xxreal_0.html#R1">&lt;=</a> <font color="Olive">b<sub>9</sub></font> &amp; <font color="Olive">b<sub>9</sub></font> <a href="xxreal_0.html#NR3" target="_self">&lt;</a> <font color="Olive">b<sub>8</sub></font> holds <br/><span class="p1">(<span class="default"><a href="scmpds_4.html#K9">IExec</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a> ,2 <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p5">(<span class="default"><span class="p0">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p4">(<span class="default"><a href="scmpds_2.html#K14">SubFrom</a> <a href="scmp_gcd.html#K2">GBP</a> ,2,<a href="scmp_gcd.html#K3">SBP</a> ,<span class="p5">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span></span>)</span></span>)</span> <a href="scmpds_4.html#K3">';'</a> <span class="p3">(<span class="default"><a href="scmpds_6.html#K3">if&gt;0</a> <a href="scmp_gcd.html#K2">GBP</a> ,2,<span class="p4">(<span class="default"><span class="p5">(<span class="default"><span class="p0">(<span class="default"><span class="p1">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a> ,2 <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p2">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span></span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p1">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a> ,4 <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span> <a href="scmpds_4.html#K3">';'</a> <font color="Maroon">c<sub>50</sub></font></span>)</span> <a href="scmpds_4.html#K3">';'</a> <span class="p5">(<span class="default"><span class="p0">(<span class="default"><span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a> ,<span class="p5">(<span class="default"><span class="p0">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 3</span>)</span> <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p5">(<span class="default"><span class="p0">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p4">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a> ,<span class="p5">(<span class="default"><span class="p0">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span> <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K2">GBP</a> ,4</span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p3">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a> ,<span class="p4">(<span class="default"><span class="p5">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 2</span>)</span> <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K2">GBP</a> ,4</span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p2">(<span class="default"><a href="scmpds_2.html#K12">AddTo</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span>,<span class="p3">(<span class="default"><a href="xcmplx_0.html#K4">-</a> 1</span>)</span></span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p1">(<span class="default"><a href="scmpds_2.html#K12">AddTo</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 2</span>)</span>,1</span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p0">(<span class="default"><a href="scmpds_2.html#K12">AddTo</a> <a href="scmp_gcd.html#K2">GBP</a> ,1,2</span>)</span></span>)</span></span>)</span>,<span class="p4">(<span class="default"><a href="scmpds_4.html#K1">Load</a> <span class="p5">(<span class="default"><a href="scmpds_2.html#K12">AddTo</a> <a href="scmp_gcd.html#K2">GBP</a> ,1,<span class="p0">(<span class="default"><a href="xcmplx_0.html#K4">-</a> 2</span>)</span></span>)</span></span>)</span></span>)</span></span>)</span>,<font color="Olive">b<sub>1</sub></font></span>)</span> <a href="scmpds_2.html#K2">.</a> <span class="p1">(<span class="default"><a href="scmp_gcd.html#K1">intpos</a> <font color="Olive">b<sub>8</sub></font></span>)</span> <a href="xxreal_0.html#NR2" target="_self">&gt;=</a> <span class="p1">(<span class="default"><a href="scmpds_4.html#K9">IExec</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a> ,2 <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p5">(<span class="default"><span class="p0">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p4">(<span class="default"><a href="scmpds_2.html#K14">SubFrom</a> <a href="scmp_gcd.html#K2">GBP</a> ,2,<a href="scmp_gcd.html#K3">SBP</a> ,<span class="p5">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span></span>)</span></span>)</span> <a href="scmpds_4.html#K3">';'</a> <span class="p3">(<span class="default"><a href="scmpds_6.html#K3">if&gt;0</a> <a href="scmp_gcd.html#K2">GBP</a> ,2,<span class="p4">(<span class="default"><span class="p5">(<span class="default"><span class="p0">(<span class="default"><span class="p1">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a> ,2 <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p2">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span></span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p1">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a> ,4 <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span> <a href="scmpds_4.html#K3">';'</a> <font color="Maroon">c<sub>50</sub></font></span>)</span> <a href="scmpds_4.html#K3">';'</a> <span class="p5">(<span class="default"><span class="p0">(<span class="default"><span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a> ,<span class="p5">(<span class="default"><span class="p0">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 3</span>)</span> <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p5">(<span class="default"><span class="p0">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p4">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a> ,<span class="p5">(<span class="default"><span class="p0">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span> <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K2">GBP</a> ,4</span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p3">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a> ,<span class="p4">(<span class="default"><span class="p5">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 2</span>)</span> <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K2">GBP</a> ,4</span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p2">(<span class="default"><a href="scmpds_2.html#K12">AddTo</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span>,<span class="p3">(<span class="default"><a href="xcmplx_0.html#K4">-</a> 1</span>)</span></span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p1">(<span class="default"><a href="scmpds_2.html#K12">AddTo</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 2</span>)</span>,1</span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p0">(<span class="default"><a href="scmpds_2.html#K12">AddTo</a> <a href="scmp_gcd.html#K2">GBP</a> ,1,2</span>)</span></span>)</span></span>)</span>,<span class="p4">(<span class="default"><a href="scmpds_4.html#K1">Load</a> <span class="p5">(<span class="default"><a href="scmpds_2.html#K12">AddTo</a> <a href="scmp_gcd.html#K2">GBP</a> ,1,<span class="p0">(<span class="default"><a href="xcmplx_0.html#K4">-</a> 2</span>)</span></span>)</span></span>)</span></span>)</span></span>)</span>,<font color="Olive">b<sub>1</sub></font></span>)</span> <a href="scmpds_2.html#K2">.</a> <span class="p1">(<span class="default"><a href="scmp_gcd.html#K1">intpos</a> <font color="Olive">b<sub>9</sub></font></span>)</span> ) &amp; ( for <font color="Olive">b<sub>9</sub></font> being  <a href="nat_1.html#NM1">Nat</a> st <font color="Olive">b<sub>8</sub></font> <a href="xxreal_0.html#NR3" target="_self">&lt;</a> <font color="Olive">b<sub>9</sub></font> &amp; <font color="Olive">b<sub>9</sub></font> <a href="xxreal_0.html#R1">&lt;=</a> <font color="Olive">b<sub>5</sub></font> holds <br/><span class="p1">(<span class="default"><a href="scmpds_4.html#K9">IExec</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a> ,2 <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p5">(<span class="default"><span class="p0">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p4">(<span class="default"><a href="scmpds_2.html#K14">SubFrom</a> <a href="scmp_gcd.html#K2">GBP</a> ,2,<a href="scmp_gcd.html#K3">SBP</a> ,<span class="p5">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span></span>)</span></span>)</span> <a href="scmpds_4.html#K3">';'</a> <span class="p3">(<span class="default"><a href="scmpds_6.html#K3">if&gt;0</a> <a href="scmp_gcd.html#K2">GBP</a> ,2,<span class="p4">(<span class="default"><span class="p5">(<span class="default"><span class="p0">(<span class="default"><span class="p1">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a> ,2 <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p2">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span></span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p1">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a> ,4 <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span> <a href="scmpds_4.html#K3">';'</a> <font color="Maroon">c<sub>50</sub></font></span>)</span> <a href="scmpds_4.html#K3">';'</a> <span class="p5">(<span class="default"><span class="p0">(<span class="default"><span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a> ,<span class="p5">(<span class="default"><span class="p0">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 3</span>)</span> <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p5">(<span class="default"><span class="p0">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p4">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a> ,<span class="p5">(<span class="default"><span class="p0">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span> <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K2">GBP</a> ,4</span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p3">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a> ,<span class="p4">(<span class="default"><span class="p5">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 2</span>)</span> <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K2">GBP</a> ,4</span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p2">(<span class="default"><a href="scmpds_2.html#K12">AddTo</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span>,<span class="p3">(<span class="default"><a href="xcmplx_0.html#K4">-</a> 1</span>)</span></span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p1">(<span class="default"><a href="scmpds_2.html#K12">AddTo</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 2</span>)</span>,1</span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p0">(<span class="default"><a href="scmpds_2.html#K12">AddTo</a> <a href="scmp_gcd.html#K2">GBP</a> ,1,2</span>)</span></span>)</span></span>)</span>,<span class="p4">(<span class="default"><a href="scmpds_4.html#K1">Load</a> <span class="p5">(<span class="default"><a href="scmpds_2.html#K12">AddTo</a> <a href="scmp_gcd.html#K2">GBP</a> ,1,<span class="p0">(<span class="default"><a href="xcmplx_0.html#K4">-</a> 2</span>)</span></span>)</span></span>)</span></span>)</span></span>)</span>,<font color="Olive">b<sub>1</sub></font></span>)</span> <a href="scmpds_2.html#K2">.</a> <span class="p1">(<span class="default"><a href="scmp_gcd.html#K1">intpos</a> <font color="Olive">b<sub>8</sub></font></span>)</span> <a href="xxreal_0.html#R1">&lt;=</a> <span class="p1">(<span class="default"><a href="scmpds_4.html#K9">IExec</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a> ,2 <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p5">(<span class="default"><span class="p0">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p4">(<span class="default"><a href="scmpds_2.html#K14">SubFrom</a> <a href="scmp_gcd.html#K2">GBP</a> ,2,<a href="scmp_gcd.html#K3">SBP</a> ,<span class="p5">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span></span>)</span></span>)</span> <a href="scmpds_4.html#K3">';'</a> <span class="p3">(<span class="default"><a href="scmpds_6.html#K3">if&gt;0</a> <a href="scmp_gcd.html#K2">GBP</a> ,2,<span class="p4">(<span class="default"><span class="p5">(<span class="default"><span class="p0">(<span class="default"><span class="p1">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a> ,2 <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p2">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span></span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p1">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a> ,4 <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span> <a href="scmpds_4.html#K3">';'</a> <font color="Maroon">c<sub>50</sub></font></span>)</span> <a href="scmpds_4.html#K3">';'</a> <span class="p5">(<span class="default"><span class="p0">(<span class="default"><span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a> ,<span class="p5">(<span class="default"><span class="p0">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 3</span>)</span> <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p5">(<span class="default"><span class="p0">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p4">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a> ,<span class="p5">(<span class="default"><span class="p0">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span> <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K2">GBP</a> ,4</span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p3">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a> ,<span class="p4">(<span class="default"><span class="p5">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 2</span>)</span> <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K2">GBP</a> ,4</span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p2">(<span class="default"><a href="scmpds_2.html#K12">AddTo</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span>,<span class="p3">(<span class="default"><a href="xcmplx_0.html#K4">-</a> 1</span>)</span></span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p1">(<span class="default"><a href="scmpds_2.html#K12">AddTo</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 2</span>)</span>,1</span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p0">(<span class="default"><a href="scmpds_2.html#K12">AddTo</a> <a href="scmp_gcd.html#K2">GBP</a> ,1,2</span>)</span></span>)</span></span>)</span>,<span class="p4">(<span class="default"><a href="scmpds_4.html#K1">Load</a> <span class="p5">(<span class="default"><a href="scmpds_2.html#K12">AddTo</a> <a href="scmp_gcd.html#K2">GBP</a> ,1,<span class="p0">(<span class="default"><a href="xcmplx_0.html#K4">-</a> 2</span>)</span></span>)</span></span>)</span></span>)</span></span>)</span>,<font color="Olive">b<sub>1</sub></font></span>)</span> <a href="scmpds_2.html#K2">.</a> <span class="p1">(<span class="default"><a href="scmp_gcd.html#K1">intpos</a> <font color="Olive">b<sub>9</sub></font></span>)</span> ) &amp; ( for <font color="Olive">b<sub>9</sub></font> being  <a href="nat_1.html#NM1">Nat</a> st ( ( <font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> 1 <a href="xxreal_0.html#R1">&lt;=</a> <font color="Olive">b<sub>9</sub></font> &amp; <font color="Olive">b<sub>9</sub></font> <a href="xxreal_0.html#NR3" target="_self">&lt;</a> <font color="Olive">b<sub>4</sub></font> ) or ( <font color="Olive">b<sub>5</sub></font> <a href="xxreal_0.html#NR3" target="_self">&lt;</a> <font color="Olive">b<sub>9</sub></font> &amp; <font color="Olive">b<sub>9</sub></font> <a href="xxreal_0.html#R1">&lt;=</a> <font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font> ) ) holds <br/><span class="p1">(<span class="default"><a href="scmpds_4.html#K9">IExec</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a> ,2 <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p5">(<span class="default"><span class="p0">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p4">(<span class="default"><a href="scmpds_2.html#K14">SubFrom</a> <a href="scmp_gcd.html#K2">GBP</a> ,2,<a href="scmp_gcd.html#K3">SBP</a> ,<span class="p5">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span></span>)</span></span>)</span> <a href="scmpds_4.html#K3">';'</a> <span class="p3">(<span class="default"><a href="scmpds_6.html#K3">if&gt;0</a> <a href="scmp_gcd.html#K2">GBP</a> ,2,<span class="p4">(<span class="default"><span class="p5">(<span class="default"><span class="p0">(<span class="default"><span class="p1">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a> ,2 <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p2">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span></span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p1">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a> ,4 <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span> <a href="scmpds_4.html#K3">';'</a> <font color="Maroon">c<sub>50</sub></font></span>)</span> <a href="scmpds_4.html#K3">';'</a> <span class="p5">(<span class="default"><span class="p0">(<span class="default"><span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a> ,<span class="p5">(<span class="default"><span class="p0">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 3</span>)</span> <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p5">(<span class="default"><span class="p0">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p4">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a> ,<span class="p5">(<span class="default"><span class="p0">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span> <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K2">GBP</a> ,4</span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p3">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a> ,<span class="p4">(<span class="default"><span class="p5">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 2</span>)</span> <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K2">GBP</a> ,4</span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p2">(<span class="default"><a href="scmpds_2.html#K12">AddTo</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span>,<span class="p3">(<span class="default"><a href="xcmplx_0.html#K4">-</a> 1</span>)</span></span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p1">(<span class="default"><a href="scmpds_2.html#K12">AddTo</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 2</span>)</span>,1</span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p0">(<span class="default"><a href="scmpds_2.html#K12">AddTo</a> <a href="scmp_gcd.html#K2">GBP</a> ,1,2</span>)</span></span>)</span></span>)</span>,<span class="p4">(<span class="default"><a href="scmpds_4.html#K1">Load</a> <span class="p5">(<span class="default"><a href="scmpds_2.html#K12">AddTo</a> <a href="scmp_gcd.html#K2">GBP</a> ,1,<span class="p0">(<span class="default"><a href="xcmplx_0.html#K4">-</a> 2</span>)</span></span>)</span></span>)</span></span>)</span></span>)</span>,<font color="Olive">b<sub>1</sub></font></span>)</span> <a href="scmpds_2.html#K2">.</a> <span class="p1">(<span class="default"><a href="scmp_gcd.html#K1">intpos</a> <font color="Olive">b<sub>9</sub></font></span>)</span> <a href="hidden.html#R1">=</a> <font color="Olive">b<sub>1</sub></font> <a href="scmpds_2.html#K2">.</a> <span class="p1">(<span class="default"><a href="scmp_gcd.html#K1">intpos</a> <font color="Olive">b<sub>9</sub></font></span>)</span> ) ) )
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="46_10"><b>proof </b></a><div class="add">

<b>let </b><font color="Maroon">c<sub>75</sub></font> be   <a href="ami_1.html#NM4">State</a> of <a href="scmpds_2.html#K1">SCMPDS</a> ;<br/><b>let </b><font color="Maroon">c<sub>76</sub></font>, <font color="Maroon">c<sub>77</sub></font>, <font color="Maroon">c<sub>78</sub></font> be   <a href="nat_1.html#NM1">Nat</a>;<br/><b>let </b><font color="Maroon">c<sub>79</sub></font> be   <a href="int_1.html#NM1">Integer</a>;<br/><b>let </b><font color="Maroon">c<sub>80</sub></font>, <font color="Maroon">c<sub>81</sub></font> be    <a href="finseq_1.html#M2">FinSequence</a> of  <a href="numbers.html#K4">INT</a> ;<br/>







<b>set </b><font color="Maroon">c<sub>82</sub></font> = <font color="Maroon">c<sub>77</sub></font> <a href="nat_1.html#K1">+</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span>;<br/>
<b>set </b><font color="Maroon">c<sub>83</sub></font> =  <a href="scmpds_4.html#K9">IExec</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a> ,2 <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p2">(<span class="default"><a href="scmpds_2.html#K14">SubFrom</a> <a href="scmp_gcd.html#K2">GBP</a> ,2,<a href="scmp_gcd.html#K3">SBP</a> ,<span class="p3">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span></span>)</span></span>)</span>,<font color="Maroon">c<sub>75</sub></font>;<br/>
<b>assume </b><a NAME="E1:46_10"/><i><font color="Green">E58</font></i>: 
( <font color="Maroon">c<sub>75</sub></font> <a href="scmpds_2.html#K2">.</a> <a href="scmp_gcd.html#K2">GBP</a>  <a href="hidden.html#R1">=</a> 0 &amp; <font color="Maroon">c<sub>75</sub></font> <a href="scmpds_2.html#K2">.</a> <a href="scmp_gcd.html#K3">SBP</a>  <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>77</sub></font> &amp; <font color="Maroon">c<sub>77</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>76</sub></font> <a href="nat_1.html#K1">+</a> 1 &amp; <font color="Maroon">c<sub>75</sub></font> <a href="scmpds_2.html#K2">.</a> <span class="p1">(<span class="default"><a href="scmp_gcd.html#K1">intpos</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>77</sub></font> <a href="nat_1.html#K1">+</a> <span class="p3">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span></span>)</span></span>)</span> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>78</sub></font> &amp; <font color="Maroon">c<sub>78</sub></font> <a href="xxreal_0.html#NR2" target="_self">&gt;=</a> <font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> 1 &amp; <font color="Maroon">c<sub>79</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>75</sub></font> <a href="scmpds_2.html#K2">.</a> <span class="p1">(<span class="default"><a href="scmp_gcd.html#K1">intpos</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">c<sub>77</sub></font> <a href="nat_1.html#K1">+</a> <span class="p4">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> &amp; <font color="Maroon">c<sub>79</sub></font> <a href="xcmplx_0.html#K6">-</a> <font color="Maroon">c<sub>78</sub></font> <a href="xxreal_0.html#NR4" target="_self">&gt;</a> 0 &amp; <font color="Maroon">c<sub>79</sub></font> <a href="xxreal_0.html#R1">&lt;=</a> <font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font> )
 ;<br/>

<b>assume </b><a NAME="E2:46_10"/><i><font color="Green">E59</font></i>: 
( <font color="Maroon">c<sub>80</sub></font> <a href="scpisort.html#R1">is_FinSequence_on</a> <font color="Maroon">c<sub>75</sub></font>,<font color="Maroon">c<sub>48</sub></font> &amp;  <a href="finseq_1.html#K3">len</a> <font color="Maroon">c<sub>80</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>49</sub></font> )
 ;<br/>

<b>assume </b><a NAME="E3:46_10"/><i><font color="Green">E60</font></i>: 
( <font color="Maroon">c<sub>81</sub></font> <a href="scpisort.html#R1">is_FinSequence_on</a>  <a href="scmpds_4.html#K9">IExec</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a> ,2 <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p4">(<span class="default"><span class="p5">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p3">(<span class="default"><a href="scmpds_2.html#K14">SubFrom</a> <a href="scmp_gcd.html#K2">GBP</a> ,2,<a href="scmp_gcd.html#K3">SBP</a> ,<span class="p4">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span></span>)</span></span>)</span> <a href="scmpds_4.html#K3">';'</a> <span class="p2">(<span class="default"><a href="scmpds_6.html#K3">if&gt;0</a> <a href="scmp_gcd.html#K2">GBP</a> ,2,<span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><span class="p0">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a> ,2 <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p1">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span></span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p0">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a> ,4 <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span> <a href="scmpds_4.html#K3">';'</a> <font color="Maroon">c<sub>50</sub></font></span>)</span> <a href="scmpds_4.html#K3">';'</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><span class="p0">(<span class="default"><span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a> ,<span class="p4">(<span class="default"><span class="p5">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 3</span>)</span> <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p4">(<span class="default"><span class="p5">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p3">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a> ,<span class="p4">(<span class="default"><span class="p5">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span> <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K2">GBP</a> ,4</span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p2">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a> ,<span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 2</span>)</span> <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K2">GBP</a> ,4</span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p1">(<span class="default"><a href="scmpds_2.html#K12">AddTo</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span>,<span class="p2">(<span class="default"><a href="xcmplx_0.html#K4">-</a> 1</span>)</span></span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p0">(<span class="default"><a href="scmpds_2.html#K12">AddTo</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 2</span>)</span>,1</span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p5">(<span class="default"><a href="scmpds_2.html#K12">AddTo</a> <a href="scmp_gcd.html#K2">GBP</a> ,1,2</span>)</span></span>)</span></span>)</span>,<span class="p3">(<span class="default"><a href="scmpds_4.html#K1">Load</a> <span class="p4">(<span class="default"><a href="scmpds_2.html#K12">AddTo</a> <a href="scmp_gcd.html#K2">GBP</a> ,1,<span class="p5">(<span class="default"><a href="xcmplx_0.html#K4">-</a> 2</span>)</span></span>)</span></span>)</span></span>)</span></span>)</span>,<font color="Maroon">c<sub>75</sub></font>,<font color="Maroon">c<sub>48</sub></font> &amp;  <a href="finseq_1.html#K3">len</a> <font color="Maroon">c<sub>81</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>49</sub></font> )
 ;<br/>

<a NAME="E4:46_10"/><i><font color="Green">E61</font></i>: 
<span class="p1">(<span class="default"><a href="scmpds_4.html#K9">IExec</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a> ,2 <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p4">(<span class="default"><span class="p5">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p3">(<span class="default"><a href="scmpds_2.html#K14">SubFrom</a> <a href="scmp_gcd.html#K2">GBP</a> ,2,<a href="scmp_gcd.html#K3">SBP</a> ,<span class="p4">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span></span>)</span></span>)</span>,<font color="Maroon">c<sub>75</sub></font></span>)</span> <a href="scmpds_2.html#K2">.</a> <a href="scmp_gcd.html#K3">SBP</a>  <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>77</sub></font>
 
<b>by </b><i><a class="txt" href="scpqsort.html#E15:46"><i><font color="Green">E55</font></i></a>, <a class="txt" href="scpqsort.html#E1:46_10"><i><font color="Green">E58</font></i></a>, <a class="ref" href="scmp_gcd.html#D3">SCMP_GCD:def 3</a></i>;<br/>
<a NAME="E5:46_10"/><i><font color="Green">E62</font></i>: 
<font color="Maroon">c<sub>77</sub></font> <a href="nat_1.html#K1">+</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="xxreal_0.html#NR2" target="_self">&gt;=</a> 0 <a href="nat_1.html#K1">+</a> 7
 
<b>by </b><i><a class="txt" href="scpqsort.html#E8:46"><i><font color="Green">E48</font></i></a>, <a class="ref" href="xreal_1.html#T9">XREAL_1:9</a></i>;<br/>
<a NAME="E6:46_10"/><b>then </b>
<font color="Maroon">c<sub>77</sub></font> <a href="nat_1.html#K1">+</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="xxreal_0.html#NR4" target="_self">&gt;</a> 2
 
<b>by </b><i><a class="ref" href="xreal_1.html#T2">XREAL_1:2</a></i>;<br/>
<a NAME="E7:46_10"/><b>then </b><i><font color="Green">E63</font></i>: 
<span class="p1">(<span class="default"><a href="scmpds_4.html#K9">IExec</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a> ,2 <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p4">(<span class="default"><span class="p5">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p3">(<span class="default"><a href="scmpds_2.html#K14">SubFrom</a> <a href="scmp_gcd.html#K2">GBP</a> ,2,<a href="scmp_gcd.html#K3">SBP</a> ,<span class="p4">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span></span>)</span></span>)</span>,<font color="Maroon">c<sub>75</sub></font></span>)</span> <a href="scmpds_2.html#K2">.</a> <span class="p1">(<span class="default"><a href="scmp_gcd.html#K1">intpos</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>77</sub></font> <a href="nat_1.html#K1">+</a> <span class="p3">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span></span>)</span></span>)</span> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>78</sub></font>
 
<b>by </b><i><a class="txt" href="scpqsort.html#E15:46"><i><font color="Green">E55</font></i></a>, <a class="txt" href="scpqsort.html#E1:46_10"><i><font color="Green">E58</font></i></a></i>;<br/>
<a NAME="E8:46_10"/>
<span class="p1">(<span class="default"><font color="Maroon">c<sub>77</sub></font> <a href="nat_1.html#K1">+</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span></span>)</span> <a href="nat_1.html#K1">+</a> 1 <a href="xxreal_0.html#NR2" target="_self">&gt;=</a> 7 <a href="nat_1.html#K1">+</a> 1
 
<b>by </b><i><a class="txt" href="scpqsort.html#E5:46_10"><i><font color="Green">E62</font></i></a>, <a class="ref" href="xreal_1.html#T8">XREAL_1:8</a></i>;<br/>
<a NAME="E9:46_10"/><b>then </b>
<span class="p1">(<span class="default"><font color="Maroon">c<sub>77</sub></font> <a href="nat_1.html#K1">+</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span></span>)</span> <a href="nat_1.html#K1">+</a> 1 <a href="xxreal_0.html#NR4" target="_self">&gt;</a> 2
 
<b>by </b><i><a class="ref" href="xreal_1.html#T2">XREAL_1:2</a></i>;<br/>
<a NAME="E10:46_10"/><b>then </b><i><font color="Green">E64</font></i>: 
<font color="Maroon">c<sub>79</sub></font> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><a href="scmpds_4.html#K9">IExec</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a> ,2 <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p4">(<span class="default"><span class="p5">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p3">(<span class="default"><a href="scmpds_2.html#K14">SubFrom</a> <a href="scmp_gcd.html#K2">GBP</a> ,2,<a href="scmp_gcd.html#K3">SBP</a> ,<span class="p4">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span></span>)</span></span>)</span>,<font color="Maroon">c<sub>75</sub></font></span>)</span> <a href="scmpds_2.html#K2">.</a> <span class="p1">(<span class="default"><a href="scmp_gcd.html#K1">intpos</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">c<sub>77</sub></font> <a href="nat_1.html#K1">+</a> <span class="p4">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span>
 
<b>by </b><i><a class="txt" href="scpqsort.html#E15:46"><i><font color="Green">E55</font></i></a>, <a class="txt" href="scpqsort.html#E1:46_10"><i><font color="Green">E58</font></i></a></i>;<br/>
<a NAME="E11:46_10"/><i><font color="Green">E65</font></i>: 
<span class="p1">(<span class="default"><a href="scmpds_4.html#K9">IExec</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a> ,2 <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p4">(<span class="default"><span class="p5">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p3">(<span class="default"><a href="scmpds_2.html#K14">SubFrom</a> <a href="scmp_gcd.html#K2">GBP</a> ,2,<a href="scmp_gcd.html#K3">SBP</a> ,<span class="p4">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span></span>)</span></span>)</span>,<font color="Maroon">c<sub>75</sub></font></span>)</span> <a href="scmpds_2.html#K2">.</a> <a href="scmp_gcd.html#K2">GBP</a>  <a href="hidden.html#R1">=</a> 0
 
<b>by </b><i><a class="txt" href="scpqsort.html#E15:46"><i><font color="Green">E55</font></i></a>, <a class="txt" href="scpqsort.html#E1:46_10"><i><font color="Green">E58</font></i></a>, <a class="ref" href="scmp_gcd.html#D2">SCMP_GCD:def 2</a></i>;<br/>
<a NAME="E12:46_10"/><b>then </b><i><font color="Green">E66</font></i>: 
 <a href="scmpds_2.html#K3">DataLoc</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="scmpds_4.html#K9">IExec</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a> ,2 <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p5">(<span class="default"><span class="p0">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p4">(<span class="default"><a href="scmpds_2.html#K14">SubFrom</a> <a href="scmp_gcd.html#K2">GBP</a> ,2,<a href="scmp_gcd.html#K3">SBP</a> ,<span class="p5">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span></span>)</span></span>)</span>,<font color="Maroon">c<sub>75</sub></font></span>)</span> <a href="scmpds_2.html#K2">.</a> <a href="scmp_gcd.html#K2">GBP</a> </span>)</span>,2 <a href="hidden.html#R1">=</a>  <a href="scmp_gcd.html#K1">intpos</a> <span class="p1">(<span class="default">0 <a href="nat_1.html#K1">+</a> 2</span>)</span>
 
<b>by </b><i><a class="ref" href="scmp_gcd.html#T5">SCMP_GCD:5</a></i>;<br/>
<a NAME="E13:46_10"/><i><font color="Green">E67</font></i>: 
<span class="p1">(<span class="default"><a href="scmpds_4.html#K9">IExec</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a> ,2 <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p4">(<span class="default"><span class="p5">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p3">(<span class="default"><a href="scmpds_2.html#K14">SubFrom</a> <a href="scmp_gcd.html#K2">GBP</a> ,2,<a href="scmp_gcd.html#K3">SBP</a> ,<span class="p4">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span></span>)</span></span>)</span>,<font color="Maroon">c<sub>75</sub></font></span>)</span> <a href="scmpds_2.html#K2">.</a> <span class="p1">(<span class="default"><a href="scmp_gcd.html#K1">intpos</a> 2</span>)</span> <a href="xxreal_0.html#NR4" target="_self">&gt;</a> 0
 
<b>by </b><i><a class="txt" href="scpqsort.html#E15:46"><i><font color="Green">E55</font></i></a>, <a class="txt" href="scpqsort.html#E1:46_10"><i><font color="Green">E58</font></i></a></i>;<br/>
<a NAME="E14:46_10"/><i><font color="Green">E68</font></i>: 
( <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a> ,2 <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p4">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span></span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p3">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a> ,4 <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p4">(<span class="default"><span class="p5">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span> <a href="scmpds_4.html#K3">';'</a> <font color="Maroon">c<sub>50</sub></font></span>)</span> <a href="scmpds_4.html#K3">';'</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><span class="p0">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a> ,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 3</span>)</span> <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p0">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a> ,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span> <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K2">GBP</a> ,4</span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p5">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a> ,<span class="p0">(<span class="default"><span class="p1">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 2</span>)</span> <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K2">GBP</a> ,4</span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p4">(<span class="default"><a href="scmpds_2.html#K12">AddTo</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p5">(<span class="default"><span class="p0">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span>,<span class="p5">(<span class="default"><a href="xcmplx_0.html#K4">-</a> 1</span>)</span></span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p3">(<span class="default"><a href="scmpds_2.html#K12">AddTo</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p4">(<span class="default"><span class="p5">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 2</span>)</span>,1</span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p2">(<span class="default"><a href="scmpds_2.html#K12">AddTo</a> <a href="scmp_gcd.html#K2">GBP</a> ,1,2</span>)</span></span>)</span> <a href="scmpds_6.html#R1">is_closed_on</a>  <a href="scmpds_4.html#K9">IExec</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a> ,2 <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p2">(<span class="default"><a href="scmpds_2.html#K14">SubFrom</a> <a href="scmp_gcd.html#K2">GBP</a> ,2,<a href="scmp_gcd.html#K3">SBP</a> ,<span class="p3">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span></span>)</span></span>)</span>,<font color="Maroon">c<sub>75</sub></font> &amp; <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a> ,2 <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p4">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span></span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p3">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a> ,4 <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p4">(<span class="default"><span class="p5">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span> <a href="scmpds_4.html#K3">';'</a> <font color="Maroon">c<sub>50</sub></font></span>)</span> <a href="scmpds_4.html#K3">';'</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><span class="p0">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a> ,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 3</span>)</span> <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p0">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a> ,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span> <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K2">GBP</a> ,4</span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p5">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a> ,<span class="p0">(<span class="default"><span class="p1">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 2</span>)</span> <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K2">GBP</a> ,4</span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p4">(<span class="default"><a href="scmpds_2.html#K12">AddTo</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p5">(<span class="default"><span class="p0">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span>,<span class="p5">(<span class="default"><a href="xcmplx_0.html#K4">-</a> 1</span>)</span></span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p3">(<span class="default"><a href="scmpds_2.html#K12">AddTo</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p4">(<span class="default"><span class="p5">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 2</span>)</span>,1</span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p2">(<span class="default"><a href="scmpds_2.html#K12">AddTo</a> <a href="scmp_gcd.html#K2">GBP</a> ,1,2</span>)</span></span>)</span> <a href="scmpds_6.html#R2">is_halting_on</a>  <a href="scmpds_4.html#K9">IExec</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a> ,2 <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p2">(<span class="default"><a href="scmpds_2.html#K14">SubFrom</a> <a href="scmp_gcd.html#K2">GBP</a> ,2,<a href="scmp_gcd.html#K3">SBP</a> ,<span class="p3">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span></span>)</span></span>)</span>,<font color="Maroon">c<sub>75</sub></font> )
 
<b>by </b><i><a class="txt" href="scpqsort.html#E13:46"><i><font color="Green">E53</font></i></a>, <a class="txt" href="scpqsort.html#E1:46_10"><i><font color="Green">E58</font></i></a>, <a class="txt" href="scpqsort.html#E4:46_10"><i><font color="Green">E61</font></i></a>, <a class="txt" href="scpqsort.html#E7:46_10"><i><font color="Green">E63</font></i></a>, <a class="txt" href="scpqsort.html#E10:46_10"><i><font color="Green">E64</font></i></a>, <a class="txt" href="scpqsort.html#E11:46_10"><i><font color="Green">E65</font></i></a></i>;<br/>
<a NAME="E15:46_10"/><b>then </b><i><font color="Green">E69</font></i>: 
(  <a href="scmpds_6.html#K3">if&gt;0</a> <a href="scmp_gcd.html#K2">GBP</a> ,2,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a> ,2 <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p5">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span></span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p4">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a> ,4 <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p5">(<span class="default"><span class="p0">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span> <a href="scmpds_4.html#K3">';'</a> <font color="Maroon">c<sub>50</sub></font></span>)</span> <a href="scmpds_4.html#K3">';'</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><span class="p0">(<span class="default"><span class="p1">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a> ,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 3</span>)</span> <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p1">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a> ,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span> <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K2">GBP</a> ,4</span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p0">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a> ,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 2</span>)</span> <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K2">GBP</a> ,4</span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p5">(<span class="default"><a href="scmpds_2.html#K12">AddTo</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p0">(<span class="default"><span class="p1">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span>,<span class="p0">(<span class="default"><a href="xcmplx_0.html#K4">-</a> 1</span>)</span></span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p4">(<span class="default"><a href="scmpds_2.html#K12">AddTo</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p5">(<span class="default"><span class="p0">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 2</span>)</span>,1</span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p3">(<span class="default"><a href="scmpds_2.html#K12">AddTo</a> <a href="scmp_gcd.html#K2">GBP</a> ,1,2</span>)</span></span>)</span></span>)</span>,<span class="p1">(<span class="default"><a href="scmpds_4.html#K1">Load</a> <span class="p2">(<span class="default"><a href="scmpds_2.html#K12">AddTo</a> <a href="scmp_gcd.html#K2">GBP</a> ,1,<span class="p3">(<span class="default"><a href="xcmplx_0.html#K4">-</a> 2</span>)</span></span>)</span></span>)</span> <a href="scmpds_6.html#R1">is_closed_on</a>  <a href="scmpds_4.html#K9">IExec</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a> ,2 <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p2">(<span class="default"><a href="scmpds_2.html#K14">SubFrom</a> <a href="scmp_gcd.html#K2">GBP</a> ,2,<a href="scmp_gcd.html#K3">SBP</a> ,<span class="p3">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span></span>)</span></span>)</span>,<font color="Maroon">c<sub>75</sub></font> &amp;  <a href="scmpds_6.html#K3">if&gt;0</a> <a href="scmp_gcd.html#K2">GBP</a> ,2,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a> ,2 <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p5">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span></span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p4">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a> ,4 <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p5">(<span class="default"><span class="p0">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span> <a href="scmpds_4.html#K3">';'</a> <font color="Maroon">c<sub>50</sub></font></span>)</span> <a href="scmpds_4.html#K3">';'</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><span class="p0">(<span class="default"><span class="p1">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a> ,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 3</span>)</span> <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p1">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a> ,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span> <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K2">GBP</a> ,4</span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p0">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a> ,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 2</span>)</span> <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K2">GBP</a> ,4</span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p5">(<span class="default"><a href="scmpds_2.html#K12">AddTo</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p0">(<span class="default"><span class="p1">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span>,<span class="p0">(<span class="default"><a href="xcmplx_0.html#K4">-</a> 1</span>)</span></span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p4">(<span class="default"><a href="scmpds_2.html#K12">AddTo</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p5">(<span class="default"><span class="p0">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 2</span>)</span>,1</span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p3">(<span class="default"><a href="scmpds_2.html#K12">AddTo</a> <a href="scmp_gcd.html#K2">GBP</a> ,1,2</span>)</span></span>)</span></span>)</span>,<span class="p1">(<span class="default"><a href="scmpds_4.html#K1">Load</a> <span class="p2">(<span class="default"><a href="scmpds_2.html#K12">AddTo</a> <a href="scmp_gcd.html#K2">GBP</a> ,1,<span class="p3">(<span class="default"><a href="xcmplx_0.html#K4">-</a> 2</span>)</span></span>)</span></span>)</span> <a href="scmpds_6.html#R2">is_halting_on</a>  <a href="scmpds_4.html#K9">IExec</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a> ,2 <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p2">(<span class="default"><a href="scmpds_2.html#K14">SubFrom</a> <a href="scmp_gcd.html#K2">GBP</a> ,2,<a href="scmp_gcd.html#K3">SBP</a> ,<span class="p3">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span></span>)</span></span>)</span>,<font color="Maroon">c<sub>75</sub></font> )
 
<b>by </b><i><a class="txt" href="scpqsort.html#E12:46_10"><i><font color="Green">E66</font></i></a>, <a class="txt" href="scpqsort.html#E13:46_10"><i><font color="Green">E67</font></i></a>, <a class="ref" href="scmpds_6.html#T82">SCMPDS_6:82</a></i>;<br/>
<div><i><font color="Green">E70</font></i>: <a class="txt" onclick="hs2(this)" href="javascript:()" title="46_10_1"><b>now </b></a><div class="add"><b>let </b><font color="Maroon">c<sub>84</sub></font> be    <a href="scmpds_2.html#M1">Int_position</a> ;<br/><b>thus </b><span class="p1">(<span class="default"><a href="scmpds_4.html#K9">IExec</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a> ,2 <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p5">(<span class="default"><span class="p0">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p4">(<span class="default"><a href="scmpds_2.html#K14">SubFrom</a> <a href="scmp_gcd.html#K2">GBP</a> ,2,<a href="scmp_gcd.html#K3">SBP</a> ,<span class="p5">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span></span>)</span></span>)</span> <a href="scmpds_4.html#K3">';'</a> <span class="p3">(<span class="default"><a href="scmpds_6.html#K3">if&gt;0</a> <a href="scmp_gcd.html#K2">GBP</a> ,2,<span class="p4">(<span class="default"><span class="p5">(<span class="default"><span class="p0">(<span class="default"><span class="p1">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a> ,2 <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p2">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span></span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p1">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a> ,4 <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span> <a href="scmpds_4.html#K3">';'</a> <font color="Maroon">c<sub>50</sub></font></span>)</span> <a href="scmpds_4.html#K3">';'</a> <span class="p5">(<span class="default"><span class="p0">(<span class="default"><span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a> ,<span class="p5">(<span class="default"><span class="p0">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 3</span>)</span> <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p5">(<span class="default"><span class="p0">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p4">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a> ,<span class="p5">(<span class="default"><span class="p0">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span> <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K2">GBP</a> ,4</span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p3">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a> ,<span class="p4">(<span class="default"><span class="p5">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 2</span>)</span> <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K2">GBP</a> ,4</span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p2">(<span class="default"><a href="scmpds_2.html#K12">AddTo</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span>,<span class="p3">(<span class="default"><a href="xcmplx_0.html#K4">-</a> 1</span>)</span></span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p1">(<span class="default"><a href="scmpds_2.html#K12">AddTo</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 2</span>)</span>,1</span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p0">(<span class="default"><a href="scmpds_2.html#K12">AddTo</a> <a href="scmp_gcd.html#K2">GBP</a> ,1,2</span>)</span></span>)</span></span>)</span>,<span class="p4">(<span class="default"><a href="scmpds_4.html#K1">Load</a> <span class="p5">(<span class="default"><a href="scmpds_2.html#K12">AddTo</a> <a href="scmp_gcd.html#K2">GBP</a> ,1,<span class="p0">(<span class="default"><a href="xcmplx_0.html#K4">-</a> 2</span>)</span></span>)</span></span>)</span></span>)</span></span>)</span>,<font color="Maroon">c<sub>75</sub></font></span>)</span> <a href="scmpds_2.html#K2">.</a> <font color="Maroon">c<sub>84</sub></font> = 
<span class="p1">(<span class="default"><a href="scmpds_4.html#K9">IExec</a> <span class="p2">(<span class="default"><a href="scmpds_6.html#K3">if&gt;0</a> <a href="scmp_gcd.html#K2">GBP</a> ,2,<span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><span class="p0">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a> ,2 <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p1">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span></span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p0">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a> ,4 <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span> <a href="scmpds_4.html#K3">';'</a> <font color="Maroon">c<sub>50</sub></font></span>)</span> <a href="scmpds_4.html#K3">';'</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><span class="p0">(<span class="default"><span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a> ,<span class="p4">(<span class="default"><span class="p5">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 3</span>)</span> <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p4">(<span class="default"><span class="p5">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p3">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a> ,<span class="p4">(<span class="default"><span class="p5">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span> <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K2">GBP</a> ,4</span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p2">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a> ,<span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 2</span>)</span> <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K2">GBP</a> ,4</span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p1">(<span class="default"><a href="scmpds_2.html#K12">AddTo</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span>,<span class="p2">(<span class="default"><a href="xcmplx_0.html#K4">-</a> 1</span>)</span></span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p0">(<span class="default"><a href="scmpds_2.html#K12">AddTo</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 2</span>)</span>,1</span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p5">(<span class="default"><a href="scmpds_2.html#K12">AddTo</a> <a href="scmp_gcd.html#K2">GBP</a> ,1,2</span>)</span></span>)</span></span>)</span>,<span class="p3">(<span class="default"><a href="scmpds_4.html#K1">Load</a> <span class="p4">(<span class="default"><a href="scmpds_2.html#K12">AddTo</a> <a href="scmp_gcd.html#K2">GBP</a> ,1,<span class="p5">(<span class="default"><a href="xcmplx_0.html#K4">-</a> 2</span>)</span></span>)</span></span>)</span></span>)</span>,<span class="p2">(<span class="default"><a href="scmpds_4.html#K9">IExec</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a> ,2 <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p5">(<span class="default"><span class="p0">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p4">(<span class="default"><a href="scmpds_2.html#K14">SubFrom</a> <a href="scmp_gcd.html#K2">GBP</a> ,2,<a href="scmp_gcd.html#K3">SBP</a> ,<span class="p5">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span></span>)</span></span>)</span>,<font color="Maroon">c<sub>75</sub></font></span>)</span></span>)</span> <a href="scmpds_2.html#K2">.</a> <font color="Maroon">c<sub>84</sub></font>
<b>by </b><i><a class="txt" href="scpqsort.html#E15:46_10"><i><font color="Green">E69</font></i></a>, <a class="ref" href="scpisort.html#T8">SCPISORT:8</a></i>
<br/>.= 
<span class="p1">(<span class="default"><a href="scmpds_4.html#K9">IExec</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a> ,2 <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p0">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span></span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p5">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a> ,4 <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p0">(<span class="default"><span class="p1">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span> <a href="scmpds_4.html#K3">';'</a> <font color="Maroon">c<sub>50</sub></font></span>)</span> <a href="scmpds_4.html#K3">';'</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><span class="p0">(<span class="default"><span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a> ,<span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 3</span>)</span> <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p2">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a> ,<span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span> <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K2">GBP</a> ,4</span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p1">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a> ,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 2</span>)</span> <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K2">GBP</a> ,4</span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p0">(<span class="default"><a href="scmpds_2.html#K12">AddTo</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span>,<span class="p1">(<span class="default"><a href="xcmplx_0.html#K4">-</a> 1</span>)</span></span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p5">(<span class="default"><a href="scmpds_2.html#K12">AddTo</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p0">(<span class="default"><span class="p1">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 2</span>)</span>,1</span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p4">(<span class="default"><a href="scmpds_2.html#K12">AddTo</a> <a href="scmp_gcd.html#K2">GBP</a> ,1,2</span>)</span></span>)</span></span>)</span>,<span class="p2">(<span class="default"><a href="scmpds_4.html#K9">IExec</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a> ,2 <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p5">(<span class="default"><span class="p0">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p4">(<span class="default"><a href="scmpds_2.html#K14">SubFrom</a> <a href="scmp_gcd.html#K2">GBP</a> ,2,<a href="scmp_gcd.html#K3">SBP</a> ,<span class="p5">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span></span>)</span></span>)</span>,<font color="Maroon">c<sub>75</sub></font></span>)</span></span>)</span> <a href="scmpds_2.html#K2">.</a> <font color="Maroon">c<sub>84</sub></font>
<b>by </b><i><a class="txt" href="scpqsort.html#E12:46_10"><i><font color="Green">E66</font></i></a>, <a class="txt" href="scpqsort.html#E13:46_10"><i><font color="Green">E67</font></i></a>, <a class="txt" href="scpqsort.html#E14:46_10"><i><font color="Green">E68</font></i></a>, <a class="ref" href="scpqsort.html#T1" target="_self">Th1</a></i>
;<br/></div><b>end;</b></div>
<a NAME="E17:46_10"/><i><font color="Green">E71</font></i>: 
<font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> 1 <a href="xxreal_0.html#NR2" target="_self">&gt;=</a> 7 <a href="nat_1.html#K1">+</a> 1
 
<b>by </b><i><a class="txt" href="scpqsort.html#E5:46"><i><font color="Green">E46</font></i></a>, <a class="ref" href="xreal_1.html#T8">XREAL_1:8</a></i>;<br/>
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="46_10_2"><b>now </b></a><div class="add"><b>let </b><font color="Maroon">c<sub>84</sub></font> be   <a href="nat_1.html#NM1">Nat</a>;<br/><b>assume </b><a NAME="E1:46_10_2"/><i><font color="Green">E72</font></i>: 
( 1 <a href="xxreal_0.html#R1">&lt;=</a> <font color="Maroon">c<sub>84</sub></font> &amp; <font color="Maroon">c<sub>84</sub></font> <a href="xxreal_0.html#R1">&lt;=</a>  <a href="finseq_1.html#K3">len</a> <font color="Maroon">c<sub>80</sub></font> )
 ;<br/><a NAME="E2:46_10_2"/><b>then </b>
<font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>84</sub></font> <a href="xxreal_0.html#NR2" target="_self">&gt;=</a> <font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> 1
 <b>by </b><i><a class="ref" href="xreal_1.html#T8">XREAL_1:8</a></i>;<br/><a NAME="E3:46_10_2"/><b>then </b>
<font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>84</sub></font> <a href="xxreal_0.html#NR2" target="_self">&gt;=</a> 8
 <b>by </b><i><a class="txt" href="scpqsort.html#E17:46_10"><i><font color="Green">E71</font></i></a>, <a class="ref" href="xreal_1.html#T2">XREAL_1:2</a></i>;<br/><a NAME="E4:46_10_2"/><b>then </b><i><font color="Green">E73</font></i>: 
<font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>84</sub></font> <a href="xxreal_0.html#NR4" target="_self">&gt;</a> 2
 <b>by </b><i><a class="ref" href="xreal_1.html#T2">XREAL_1:2</a></i>;<br/><b>thus </b><font color="Maroon">c<sub>80</sub></font> <a href="funct_1.html#K1">.</a> <font color="Maroon">c<sub>84</sub></font> = 
<font color="Maroon">c<sub>75</sub></font> <a href="scmpds_2.html#K2">.</a> <span class="p1">(<span class="default"><a href="scmp_gcd.html#K1">intpos</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>84</sub></font></span>)</span></span>)</span>
<b>by </b><i><a class="txt" href="scpqsort.html#E2:46_10"><i><font color="Green">E59</font></i></a>, <a class="txt" href="scpqsort.html#E1:46_10_2"><i><font color="Green">E72</font></i></a>, <a class="ref" href="scpisort.html#D1">SCPISORT:def 1</a></i>
<br/>.= 
<span class="p1">(<span class="default"><a href="scmpds_4.html#K9">IExec</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a> ,2 <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p4">(<span class="default"><span class="p5">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p3">(<span class="default"><a href="scmpds_2.html#K14">SubFrom</a> <a href="scmp_gcd.html#K2">GBP</a> ,2,<a href="scmp_gcd.html#K3">SBP</a> ,<span class="p4">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span></span>)</span></span>)</span>,<font color="Maroon">c<sub>75</sub></font></span>)</span> <a href="scmpds_2.html#K2">.</a> <span class="p1">(<span class="default"><a href="scmp_gcd.html#K1">intpos</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>84</sub></font></span>)</span></span>)</span>
<b>by </b><i><a class="txt" href="scpqsort.html#E15:46"><i><font color="Green">E55</font></i></a>, <a class="txt" href="scpqsort.html#E1:46_10"><i><font color="Green">E58</font></i></a>, <a class="txt" href="scpqsort.html#E4:46_10_2"><i><font color="Green">E73</font></i></a></i>
;<br/></div><b>end;</b></div>
<a NAME="E19:46_10"/><b>then </b><i><font color="Green">E72</font></i>: 
<font color="Maroon">c<sub>80</sub></font> <a href="scpisort.html#R1">is_FinSequence_on</a>  <a href="scmpds_4.html#K9">IExec</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a> ,2 <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p2">(<span class="default"><a href="scmpds_2.html#K14">SubFrom</a> <a href="scmp_gcd.html#K2">GBP</a> ,2,<a href="scmp_gcd.html#K3">SBP</a> ,<span class="p3">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span></span>)</span></span>)</span>,<font color="Maroon">c<sub>75</sub></font>,<font color="Maroon">c<sub>48</sub></font>
 
<b>by </b><i><a class="ref" href="scpisort.html#D1">SCPISORT:def 1</a></i>;<br/>
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="46_10_3"><b>now </b></a><div class="add"><b>let </b><font color="Maroon">c<sub>84</sub></font> be   <a href="nat_1.html#NM1">Nat</a>;<br/><b>assume </b><a NAME="E1:46_10_3"/>
( 1 <a href="xxreal_0.html#R1">&lt;=</a> <font color="Maroon">c<sub>84</sub></font> &amp; <font color="Maroon">c<sub>84</sub></font> <a href="xxreal_0.html#R1">&lt;=</a>  <a href="finseq_1.html#K3">len</a> <font color="Maroon">c<sub>81</sub></font> )
 ;<br/><b>hence </b><font color="Maroon">c<sub>81</sub></font> <a href="funct_1.html#K1">.</a> <font color="Maroon">c<sub>84</sub></font> = 
<span class="p1">(<span class="default"><a href="scmpds_4.html#K9">IExec</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a> ,2 <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p5">(<span class="default"><span class="p0">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p4">(<span class="default"><a href="scmpds_2.html#K14">SubFrom</a> <a href="scmp_gcd.html#K2">GBP</a> ,2,<a href="scmp_gcd.html#K3">SBP</a> ,<span class="p5">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span></span>)</span></span>)</span> <a href="scmpds_4.html#K3">';'</a> <span class="p3">(<span class="default"><a href="scmpds_6.html#K3">if&gt;0</a> <a href="scmp_gcd.html#K2">GBP</a> ,2,<span class="p4">(<span class="default"><span class="p5">(<span class="default"><span class="p0">(<span class="default"><span class="p1">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a> ,2 <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p2">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span></span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p1">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a> ,4 <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span> <a href="scmpds_4.html#K3">';'</a> <font color="Maroon">c<sub>50</sub></font></span>)</span> <a href="scmpds_4.html#K3">';'</a> <span class="p5">(<span class="default"><span class="p0">(<span class="default"><span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a> ,<span class="p5">(<span class="default"><span class="p0">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 3</span>)</span> <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p5">(<span class="default"><span class="p0">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p4">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a> ,<span class="p5">(<span class="default"><span class="p0">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span> <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K2">GBP</a> ,4</span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p3">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a> ,<span class="p4">(<span class="default"><span class="p5">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 2</span>)</span> <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K2">GBP</a> ,4</span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p2">(<span class="default"><a href="scmpds_2.html#K12">AddTo</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span>,<span class="p3">(<span class="default"><a href="xcmplx_0.html#K4">-</a> 1</span>)</span></span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p1">(<span class="default"><a href="scmpds_2.html#K12">AddTo</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 2</span>)</span>,1</span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p0">(<span class="default"><a href="scmpds_2.html#K12">AddTo</a> <a href="scmp_gcd.html#K2">GBP</a> ,1,2</span>)</span></span>)</span></span>)</span>,<span class="p4">(<span class="default"><a href="scmpds_4.html#K1">Load</a> <span class="p5">(<span class="default"><a href="scmpds_2.html#K12">AddTo</a> <a href="scmp_gcd.html#K2">GBP</a> ,1,<span class="p0">(<span class="default"><a href="xcmplx_0.html#K4">-</a> 2</span>)</span></span>)</span></span>)</span></span>)</span></span>)</span>,<font color="Maroon">c<sub>75</sub></font></span>)</span> <a href="scmpds_2.html#K2">.</a> <span class="p1">(<span class="default"><a href="scmp_gcd.html#K1">intpos</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>84</sub></font></span>)</span></span>)</span>
<b>by </b><i><a class="txt" href="scpqsort.html#E3:46_10"><i><font color="Green">E60</font></i></a>, <a class="ref" href="scpisort.html#D1">SCPISORT:def 1</a></i>
<br/>.= 
<span class="p1">(<span class="default"><a href="scmpds_4.html#K9">IExec</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a> ,2 <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p0">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span></span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p5">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a> ,4 <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p0">(<span class="default"><span class="p1">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span> <a href="scmpds_4.html#K3">';'</a> <font color="Maroon">c<sub>50</sub></font></span>)</span> <a href="scmpds_4.html#K3">';'</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><span class="p0">(<span class="default"><span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a> ,<span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 3</span>)</span> <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p2">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a> ,<span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span> <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K2">GBP</a> ,4</span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p1">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a> ,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 2</span>)</span> <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K2">GBP</a> ,4</span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p0">(<span class="default"><a href="scmpds_2.html#K12">AddTo</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span>,<span class="p1">(<span class="default"><a href="xcmplx_0.html#K4">-</a> 1</span>)</span></span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p5">(<span class="default"><a href="scmpds_2.html#K12">AddTo</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p0">(<span class="default"><span class="p1">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 2</span>)</span>,1</span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p4">(<span class="default"><a href="scmpds_2.html#K12">AddTo</a> <a href="scmp_gcd.html#K2">GBP</a> ,1,2</span>)</span></span>)</span></span>)</span>,<span class="p2">(<span class="default"><a href="scmpds_4.html#K9">IExec</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a> ,2 <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p5">(<span class="default"><span class="p0">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p4">(<span class="default"><a href="scmpds_2.html#K14">SubFrom</a> <a href="scmp_gcd.html#K2">GBP</a> ,2,<a href="scmp_gcd.html#K3">SBP</a> ,<span class="p5">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span></span>)</span></span>)</span>,<font color="Maroon">c<sub>75</sub></font></span>)</span></span>)</span> <a href="scmpds_2.html#K2">.</a> <span class="p1">(<span class="default"><a href="scmp_gcd.html#K1">intpos</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>84</sub></font></span>)</span></span>)</span>
<b>by </b><i><a class="txt" href="scpqsort.html#E16:46_10"><i><font color="Green">E70</font></i></a></i>
;<br/><br/></div><b>end;</b></div>
<a NAME="E21:46_10"/><b>then </b><i><font color="Green">E73</font></i>: 
<font color="Maroon">c<sub>81</sub></font> <a href="scpisort.html#R1">is_FinSequence_on</a>  <a href="scmpds_4.html#K9">IExec</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a> ,2 <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p5">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span></span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p4">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a> ,4 <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p5">(<span class="default"><span class="p0">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span> <a href="scmpds_4.html#K3">';'</a> <font color="Maroon">c<sub>50</sub></font></span>)</span> <a href="scmpds_4.html#K3">';'</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><span class="p0">(<span class="default"><span class="p1">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a> ,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 3</span>)</span> <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p1">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a> ,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span> <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K2">GBP</a> ,4</span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p0">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a> ,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 2</span>)</span> <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K2">GBP</a> ,4</span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p5">(<span class="default"><a href="scmpds_2.html#K12">AddTo</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p0">(<span class="default"><span class="p1">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span>,<span class="p0">(<span class="default"><a href="xcmplx_0.html#K4">-</a> 1</span>)</span></span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p4">(<span class="default"><a href="scmpds_2.html#K12">AddTo</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p5">(<span class="default"><span class="p0">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 2</span>)</span>,1</span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p3">(<span class="default"><a href="scmpds_2.html#K12">AddTo</a> <a href="scmp_gcd.html#K2">GBP</a> ,1,2</span>)</span></span>)</span></span>)</span>,<span class="p1">(<span class="default"><a href="scmpds_4.html#K9">IExec</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a> ,2 <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p4">(<span class="default"><span class="p5">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p3">(<span class="default"><a href="scmpds_2.html#K14">SubFrom</a> <a href="scmp_gcd.html#K2">GBP</a> ,2,<a href="scmp_gcd.html#K3">SBP</a> ,<span class="p4">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span></span>)</span></span>)</span>,<font color="Maroon">c<sub>75</sub></font></span>)</span>,<font color="Maroon">c<sub>48</sub></font>
 
<b>by </b><i><a class="ref" href="scpisort.html#D1">SCPISORT:def 1</a></i>;<br/>
<a NAME="E22:46_10"/><b>then </b><i><font color="Green">E74</font></i>: 
( <span class="p1">(<span class="default"><a href="scmpds_4.html#K9">IExec</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a> ,2 <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p0">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span></span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p5">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a> ,4 <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p0">(<span class="default"><span class="p1">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span> <a href="scmpds_4.html#K3">';'</a> <font color="Maroon">c<sub>50</sub></font></span>)</span> <a href="scmpds_4.html#K3">';'</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><span class="p0">(<span class="default"><span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a> ,<span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 3</span>)</span> <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p2">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a> ,<span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span> <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K2">GBP</a> ,4</span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p1">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a> ,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 2</span>)</span> <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K2">GBP</a> ,4</span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p0">(<span class="default"><a href="scmpds_2.html#K12">AddTo</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span>,<span class="p1">(<span class="default"><a href="xcmplx_0.html#K4">-</a> 1</span>)</span></span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p5">(<span class="default"><a href="scmpds_2.html#K12">AddTo</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p0">(<span class="default"><span class="p1">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 2</span>)</span>,1</span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p4">(<span class="default"><a href="scmpds_2.html#K12">AddTo</a> <a href="scmp_gcd.html#K2">GBP</a> ,1,2</span>)</span></span>)</span></span>)</span>,<span class="p2">(<span class="default"><a href="scmpds_4.html#K9">IExec</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a> ,2 <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p5">(<span class="default"><span class="p0">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p4">(<span class="default"><a href="scmpds_2.html#K14">SubFrom</a> <a href="scmp_gcd.html#K2">GBP</a> ,2,<a href="scmp_gcd.html#K3">SBP</a> ,<span class="p5">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span></span>)</span></span>)</span>,<font color="Maroon">c<sub>75</sub></font></span>)</span></span>)</span> <a href="scmpds_2.html#K2">.</a> <a href="scmp_gcd.html#K2">GBP</a>  <a href="hidden.html#R1">=</a> 0 &amp; <span class="p1">(<span class="default"><a href="scmpds_4.html#K9">IExec</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a> ,2 <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p0">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span></span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p5">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a> ,4 <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p0">(<span class="default"><span class="p1">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span> <a href="scmpds_4.html#K3">';'</a> <font color="Maroon">c<sub>50</sub></font></span>)</span> <a href="scmpds_4.html#K3">';'</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><span class="p0">(<span class="default"><span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a> ,<span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 3</span>)</span> <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p2">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a> ,<span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span> <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K2">GBP</a> ,4</span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p1">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a> ,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 2</span>)</span> <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K2">GBP</a> ,4</span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p0">(<span class="default"><a href="scmpds_2.html#K12">AddTo</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span>,<span class="p1">(<span class="default"><a href="xcmplx_0.html#K4">-</a> 1</span>)</span></span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p5">(<span class="default"><a href="scmpds_2.html#K12">AddTo</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p0">(<span class="default"><span class="p1">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 2</span>)</span>,1</span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p4">(<span class="default"><a href="scmpds_2.html#K12">AddTo</a> <a href="scmp_gcd.html#K2">GBP</a> ,1,2</span>)</span></span>)</span></span>)</span>,<span class="p2">(<span class="default"><a href="scmpds_4.html#K9">IExec</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a> ,2 <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p5">(<span class="default"><span class="p0">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p4">(<span class="default"><a href="scmpds_2.html#K14">SubFrom</a> <a href="scmp_gcd.html#K2">GBP</a> ,2,<a href="scmp_gcd.html#K3">SBP</a> ,<span class="p5">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span></span>)</span></span>)</span>,<font color="Maroon">c<sub>75</sub></font></span>)</span></span>)</span> <a href="scmpds_2.html#K2">.</a> <span class="p1">(<span class="default"><a href="scmp_gcd.html#K1">intpos</a> 1</span>)</span> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>77</sub></font> <a href="nat_1.html#K1">+</a> 2 &amp; <font color="Maroon">c<sub>78</sub></font> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><a href="scmpds_4.html#K9">IExec</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a> ,2 <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p0">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span></span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p5">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a> ,4 <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p0">(<span class="default"><span class="p1">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span> <a href="scmpds_4.html#K3">';'</a> <font color="Maroon">c<sub>50</sub></font></span>)</span> <a href="scmpds_4.html#K3">';'</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><span class="p0">(<span class="default"><span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a> ,<span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 3</span>)</span> <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p2">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a> ,<span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span> <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K2">GBP</a> ,4</span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p1">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a> ,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 2</span>)</span> <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K2">GBP</a> ,4</span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p0">(<span class="default"><a href="scmpds_2.html#K12">AddTo</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span>,<span class="p1">(<span class="default"><a href="xcmplx_0.html#K4">-</a> 1</span>)</span></span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p5">(<span class="default"><a href="scmpds_2.html#K12">AddTo</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p0">(<span class="default"><span class="p1">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 2</span>)</span>,1</span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p4">(<span class="default"><a href="scmpds_2.html#K12">AddTo</a> <a href="scmp_gcd.html#K2">GBP</a> ,1,2</span>)</span></span>)</span></span>)</span>,<span class="p2">(<span class="default"><a href="scmpds_4.html#K9">IExec</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a> ,2 <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p5">(<span class="default"><span class="p0">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p4">(<span class="default"><a href="scmpds_2.html#K14">SubFrom</a> <a href="scmp_gcd.html#K2">GBP</a> ,2,<a href="scmp_gcd.html#K3">SBP</a> ,<span class="p5">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span></span>)</span></span>)</span>,<font color="Maroon">c<sub>75</sub></font></span>)</span></span>)</span> <a href="scmpds_2.html#K2">.</a> <span class="p1">(<span class="default"><a href="scmp_gcd.html#K1">intpos</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>77</sub></font> <a href="nat_1.html#K1">+</a> <span class="p3">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span></span>)</span></span>)</span> &amp; <font color="Maroon">c<sub>79</sub></font> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><a href="scmpds_4.html#K9">IExec</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a> ,2 <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p0">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span></span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p5">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a> ,4 <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p0">(<span class="default"><span class="p1">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span> <a href="scmpds_4.html#K3">';'</a> <font color="Maroon">c<sub>50</sub></font></span>)</span> <a href="scmpds_4.html#K3">';'</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><span class="p0">(<span class="default"><span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a> ,<span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 3</span>)</span> <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p2">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a> ,<span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span> <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K2">GBP</a> ,4</span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p1">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a> ,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 2</span>)</span> <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K2">GBP</a> ,4</span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p0">(<span class="default"><a href="scmpds_2.html#K12">AddTo</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span>,<span class="p1">(<span class="default"><a href="xcmplx_0.html#K4">-</a> 1</span>)</span></span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p5">(<span class="default"><a href="scmpds_2.html#K12">AddTo</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p0">(<span class="default"><span class="p1">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 2</span>)</span>,1</span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p4">(<span class="default"><a href="scmpds_2.html#K12">AddTo</a> <a href="scmp_gcd.html#K2">GBP</a> ,1,2</span>)</span></span>)</span></span>)</span>,<span class="p2">(<span class="default"><a href="scmpds_4.html#K9">IExec</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a> ,2 <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p5">(<span class="default"><span class="p0">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p4">(<span class="default"><a href="scmpds_2.html#K14">SubFrom</a> <a href="scmp_gcd.html#K2">GBP</a> ,2,<a href="scmp_gcd.html#K3">SBP</a> ,<span class="p5">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span></span>)</span></span>)</span>,<font color="Maroon">c<sub>75</sub></font></span>)</span></span>)</span> <a href="scmpds_2.html#K2">.</a> <span class="p1">(<span class="default"><a href="scmp_gcd.html#K1">intpos</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">c<sub>77</sub></font> <a href="nat_1.html#K1">+</a> <span class="p4">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span></span>)</span> <a href="nat_1.html#K1">+</a> 3</span>)</span></span>)</span> &amp; ( for <font color="Olive">b<sub>1</sub></font> being  <a href="nat_1.html#NM1">Nat</a> st 1 <a href="xxreal_0.html#R1">&lt;=</a> <font color="Olive">b<sub>1</sub></font> &amp; <font color="Olive">b<sub>1</sub></font> <a href="xxreal_0.html#NR3" target="_self">&lt;</a> <font color="Maroon">c<sub>77</sub></font> holds <br/><span class="p1">(<span class="default"><a href="scmpds_4.html#K9">IExec</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a> ,2 <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p0">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span></span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p5">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a> ,4 <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p0">(<span class="default"><span class="p1">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span> <a href="scmpds_4.html#K3">';'</a> <font color="Maroon">c<sub>50</sub></font></span>)</span> <a href="scmpds_4.html#K3">';'</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><span class="p0">(<span class="default"><span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a> ,<span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 3</span>)</span> <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p2">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a> ,<span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span> <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K2">GBP</a> ,4</span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p1">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a> ,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 2</span>)</span> <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K2">GBP</a> ,4</span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p0">(<span class="default"><a href="scmpds_2.html#K12">AddTo</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span>,<span class="p1">(<span class="default"><a href="xcmplx_0.html#K4">-</a> 1</span>)</span></span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p5">(<span class="default"><a href="scmpds_2.html#K12">AddTo</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p0">(<span class="default"><span class="p1">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 2</span>)</span>,1</span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p4">(<span class="default"><a href="scmpds_2.html#K12">AddTo</a> <a href="scmp_gcd.html#K2">GBP</a> ,1,2</span>)</span></span>)</span></span>)</span>,<span class="p2">(<span class="default"><a href="scmpds_4.html#K9">IExec</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a> ,2 <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p5">(<span class="default"><span class="p0">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p4">(<span class="default"><a href="scmpds_2.html#K14">SubFrom</a> <a href="scmp_gcd.html#K2">GBP</a> ,2,<a href="scmp_gcd.html#K3">SBP</a> ,<span class="p5">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span></span>)</span></span>)</span>,<font color="Maroon">c<sub>75</sub></font></span>)</span></span>)</span> <a href="scmpds_2.html#K2">.</a> <span class="p1">(<span class="default"><a href="scmp_gcd.html#K1">intpos</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> <font color="Olive">b<sub>1</sub></font></span>)</span></span>)</span> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><a href="scmpds_4.html#K9">IExec</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a> ,2 <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p4">(<span class="default"><span class="p5">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p3">(<span class="default"><a href="scmpds_2.html#K14">SubFrom</a> <a href="scmp_gcd.html#K2">GBP</a> ,2,<a href="scmp_gcd.html#K3">SBP</a> ,<span class="p4">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span></span>)</span></span>)</span>,<font color="Maroon">c<sub>75</sub></font></span>)</span> <a href="scmpds_2.html#K2">.</a> <span class="p1">(<span class="default"><a href="scmp_gcd.html#K1">intpos</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> <font color="Olive">b<sub>1</sub></font></span>)</span></span>)</span> ) )
 
<b>by </b><i><a class="txt" href="scpqsort.html#E14:46"><i><font color="Green">E54</font></i></a>, <a class="txt" href="scpqsort.html#E1:46_10"><i><font color="Green">E58</font></i></a>, <a class="txt" href="scpqsort.html#E2:46_10"><i><font color="Green">E59</font></i></a>, <a class="txt" href="scpqsort.html#E3:46_10"><i><font color="Green">E60</font></i></a>, <a class="txt" href="scpqsort.html#E4:46_10"><i><font color="Green">E61</font></i></a>, <a class="txt" href="scpqsort.html#E7:46_10"><i><font color="Green">E63</font></i></a>, <a class="txt" href="scpqsort.html#E10:46_10"><i><font color="Green">E64</font></i></a>, <a class="txt" href="scpqsort.html#E11:46_10"><i><font color="Green">E65</font></i></a>, <a class="txt" href="scpqsort.html#E19:46_10"><i><font color="Green">E72</font></i></a></i>;<br/>
<b>hence </b><a NAME="E23:46_10"/>
<span class="p1">(<span class="default"><a href="scmpds_4.html#K9">IExec</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a> ,2 <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p5">(<span class="default"><span class="p0">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p4">(<span class="default"><a href="scmpds_2.html#K14">SubFrom</a> <a href="scmp_gcd.html#K2">GBP</a> ,2,<a href="scmp_gcd.html#K3">SBP</a> ,<span class="p5">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span></span>)</span></span>)</span> <a href="scmpds_4.html#K3">';'</a> <span class="p3">(<span class="default"><a href="scmpds_6.html#K3">if&gt;0</a> <a href="scmp_gcd.html#K2">GBP</a> ,2,<span class="p4">(<span class="default"><span class="p5">(<span class="default"><span class="p0">(<span class="default"><span class="p1">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a> ,2 <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p2">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span></span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p1">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a> ,4 <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span> <a href="scmpds_4.html#K3">';'</a> <font color="Maroon">c<sub>50</sub></font></span>)</span> <a href="scmpds_4.html#K3">';'</a> <span class="p5">(<span class="default"><span class="p0">(<span class="default"><span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a> ,<span class="p5">(<span class="default"><span class="p0">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 3</span>)</span> <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p5">(<span class="default"><span class="p0">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p4">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a> ,<span class="p5">(<span class="default"><span class="p0">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span> <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K2">GBP</a> ,4</span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p3">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a> ,<span class="p4">(<span class="default"><span class="p5">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 2</span>)</span> <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K2">GBP</a> ,4</span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p2">(<span class="default"><a href="scmpds_2.html#K12">AddTo</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span>,<span class="p3">(<span class="default"><a href="xcmplx_0.html#K4">-</a> 1</span>)</span></span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p1">(<span class="default"><a href="scmpds_2.html#K12">AddTo</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 2</span>)</span>,1</span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p0">(<span class="default"><a href="scmpds_2.html#K12">AddTo</a> <a href="scmp_gcd.html#K2">GBP</a> ,1,2</span>)</span></span>)</span></span>)</span>,<span class="p4">(<span class="default"><a href="scmpds_4.html#K1">Load</a> <span class="p5">(<span class="default"><a href="scmpds_2.html#K12">AddTo</a> <a href="scmp_gcd.html#K2">GBP</a> ,1,<span class="p0">(<span class="default"><a href="xcmplx_0.html#K4">-</a> 2</span>)</span></span>)</span></span>)</span></span>)</span></span>)</span>,<font color="Maroon">c<sub>75</sub></font></span>)</span> <a href="scmpds_2.html#K2">.</a> <a href="scmp_gcd.html#K2">GBP</a>  <a href="hidden.html#R1">=</a> 0
 <b>by </b><i><a class="txt" href="scpqsort.html#E16:46_10"><i><font color="Green">E70</font></i></a></i>;<br/>

<b>thus </b><a NAME="E24:46_10"/>
<span class="p1">(<span class="default"><a href="scmpds_4.html#K9">IExec</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a> ,2 <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p5">(<span class="default"><span class="p0">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p4">(<span class="default"><a href="scmpds_2.html#K14">SubFrom</a> <a href="scmp_gcd.html#K2">GBP</a> ,2,<a href="scmp_gcd.html#K3">SBP</a> ,<span class="p5">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span></span>)</span></span>)</span> <a href="scmpds_4.html#K3">';'</a> <span class="p3">(<span class="default"><a href="scmpds_6.html#K3">if&gt;0</a> <a href="scmp_gcd.html#K2">GBP</a> ,2,<span class="p4">(<span class="default"><span class="p5">(<span class="default"><span class="p0">(<span class="default"><span class="p1">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a> ,2 <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p2">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span></span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p1">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a> ,4 <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span> <a href="scmpds_4.html#K3">';'</a> <font color="Maroon">c<sub>50</sub></font></span>)</span> <a href="scmpds_4.html#K3">';'</a> <span class="p5">(<span class="default"><span class="p0">(<span class="default"><span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a> ,<span class="p5">(<span class="default"><span class="p0">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 3</span>)</span> <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p5">(<span class="default"><span class="p0">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p4">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a> ,<span class="p5">(<span class="default"><span class="p0">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span> <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K2">GBP</a> ,4</span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p3">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a> ,<span class="p4">(<span class="default"><span class="p5">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 2</span>)</span> <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K2">GBP</a> ,4</span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p2">(<span class="default"><a href="scmpds_2.html#K12">AddTo</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span>,<span class="p3">(<span class="default"><a href="xcmplx_0.html#K4">-</a> 1</span>)</span></span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p1">(<span class="default"><a href="scmpds_2.html#K12">AddTo</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 2</span>)</span>,1</span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p0">(<span class="default"><a href="scmpds_2.html#K12">AddTo</a> <a href="scmp_gcd.html#K2">GBP</a> ,1,2</span>)</span></span>)</span></span>)</span>,<span class="p4">(<span class="default"><a href="scmpds_4.html#K1">Load</a> <span class="p5">(<span class="default"><a href="scmpds_2.html#K12">AddTo</a> <a href="scmp_gcd.html#K2">GBP</a> ,1,<span class="p0">(<span class="default"><a href="xcmplx_0.html#K4">-</a> 2</span>)</span></span>)</span></span>)</span></span>)</span></span>)</span>,<font color="Maroon">c<sub>75</sub></font></span>)</span> <a href="scmpds_2.html#K2">.</a> <span class="p1">(<span class="default"><a href="scmp_gcd.html#K1">intpos</a> 1</span>)</span> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>77</sub></font> <a href="nat_1.html#K1">+</a> 2
 <b>by </b><i><a class="txt" href="scpqsort.html#E16:46_10"><i><font color="Green">E70</font></i></a>, <a class="txt" href="scpqsort.html#E22:46_10"><i><font color="Green">E74</font></i></a></i>;<br/>

<b>thus </b><a NAME="E25:46_10"/>
<font color="Maroon">c<sub>78</sub></font> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><a href="scmpds_4.html#K9">IExec</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a> ,2 <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p5">(<span class="default"><span class="p0">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p4">(<span class="default"><a href="scmpds_2.html#K14">SubFrom</a> <a href="scmp_gcd.html#K2">GBP</a> ,2,<a href="scmp_gcd.html#K3">SBP</a> ,<span class="p5">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span></span>)</span></span>)</span> <a href="scmpds_4.html#K3">';'</a> <span class="p3">(<span class="default"><a href="scmpds_6.html#K3">if&gt;0</a> <a href="scmp_gcd.html#K2">GBP</a> ,2,<span class="p4">(<span class="default"><span class="p5">(<span class="default"><span class="p0">(<span class="default"><span class="p1">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a> ,2 <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p2">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span></span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p1">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a> ,4 <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span> <a href="scmpds_4.html#K3">';'</a> <font color="Maroon">c<sub>50</sub></font></span>)</span> <a href="scmpds_4.html#K3">';'</a> <span class="p5">(<span class="default"><span class="p0">(<span class="default"><span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a> ,<span class="p5">(<span class="default"><span class="p0">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 3</span>)</span> <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p5">(<span class="default"><span class="p0">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p4">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a> ,<span class="p5">(<span class="default"><span class="p0">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span> <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K2">GBP</a> ,4</span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p3">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a> ,<span class="p4">(<span class="default"><span class="p5">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 2</span>)</span> <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K2">GBP</a> ,4</span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p2">(<span class="default"><a href="scmpds_2.html#K12">AddTo</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span>,<span class="p3">(<span class="default"><a href="xcmplx_0.html#K4">-</a> 1</span>)</span></span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p1">(<span class="default"><a href="scmpds_2.html#K12">AddTo</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 2</span>)</span>,1</span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p0">(<span class="default"><a href="scmpds_2.html#K12">AddTo</a> <a href="scmp_gcd.html#K2">GBP</a> ,1,2</span>)</span></span>)</span></span>)</span>,<span class="p4">(<span class="default"><a href="scmpds_4.html#K1">Load</a> <span class="p5">(<span class="default"><a href="scmpds_2.html#K12">AddTo</a> <a href="scmp_gcd.html#K2">GBP</a> ,1,<span class="p0">(<span class="default"><a href="xcmplx_0.html#K4">-</a> 2</span>)</span></span>)</span></span>)</span></span>)</span></span>)</span>,<font color="Maroon">c<sub>75</sub></font></span>)</span> <a href="scmpds_2.html#K2">.</a> <span class="p1">(<span class="default"><a href="scmp_gcd.html#K1">intpos</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>77</sub></font> <a href="nat_1.html#K1">+</a> <span class="p3">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span></span>)</span></span>)</span>
 <b>by </b><i><a class="txt" href="scpqsort.html#E16:46_10"><i><font color="Green">E70</font></i></a>, <a class="txt" href="scpqsort.html#E22:46_10"><i><font color="Green">E74</font></i></a></i>;<br/>

<b>thus </b><a NAME="E26:46_10"/>
<font color="Maroon">c<sub>79</sub></font> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><a href="scmpds_4.html#K9">IExec</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a> ,2 <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p5">(<span class="default"><span class="p0">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p4">(<span class="default"><a href="scmpds_2.html#K14">SubFrom</a> <a href="scmp_gcd.html#K2">GBP</a> ,2,<a href="scmp_gcd.html#K3">SBP</a> ,<span class="p5">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span></span>)</span></span>)</span> <a href="scmpds_4.html#K3">';'</a> <span class="p3">(<span class="default"><a href="scmpds_6.html#K3">if&gt;0</a> <a href="scmp_gcd.html#K2">GBP</a> ,2,<span class="p4">(<span class="default"><span class="p5">(<span class="default"><span class="p0">(<span class="default"><span class="p1">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a> ,2 <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p2">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span></span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p1">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a> ,4 <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span> <a href="scmpds_4.html#K3">';'</a> <font color="Maroon">c<sub>50</sub></font></span>)</span> <a href="scmpds_4.html#K3">';'</a> <span class="p5">(<span class="default"><span class="p0">(<span class="default"><span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a> ,<span class="p5">(<span class="default"><span class="p0">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 3</span>)</span> <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p5">(<span class="default"><span class="p0">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p4">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a> ,<span class="p5">(<span class="default"><span class="p0">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span> <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K2">GBP</a> ,4</span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p3">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a> ,<span class="p4">(<span class="default"><span class="p5">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 2</span>)</span> <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K2">GBP</a> ,4</span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p2">(<span class="default"><a href="scmpds_2.html#K12">AddTo</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span>,<span class="p3">(<span class="default"><a href="xcmplx_0.html#K4">-</a> 1</span>)</span></span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p1">(<span class="default"><a href="scmpds_2.html#K12">AddTo</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 2</span>)</span>,1</span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p0">(<span class="default"><a href="scmpds_2.html#K12">AddTo</a> <a href="scmp_gcd.html#K2">GBP</a> ,1,2</span>)</span></span>)</span></span>)</span>,<span class="p4">(<span class="default"><a href="scmpds_4.html#K1">Load</a> <span class="p5">(<span class="default"><a href="scmpds_2.html#K12">AddTo</a> <a href="scmp_gcd.html#K2">GBP</a> ,1,<span class="p0">(<span class="default"><a href="xcmplx_0.html#K4">-</a> 2</span>)</span></span>)</span></span>)</span></span>)</span></span>)</span>,<font color="Maroon">c<sub>75</sub></font></span>)</span> <a href="scmpds_2.html#K2">.</a> <span class="p1">(<span class="default"><a href="scmp_gcd.html#K1">intpos</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">c<sub>77</sub></font> <a href="nat_1.html#K1">+</a> <span class="p4">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span></span>)</span> <a href="nat_1.html#K1">+</a> 3</span>)</span></span>)</span>
 <b>by </b><i><a class="txt" href="scpqsort.html#E16:46_10"><i><font color="Green">E70</font></i></a>, <a class="txt" href="scpqsort.html#E22:46_10"><i><font color="Green">E74</font></i></a></i>;<br/>

<div><b>hereby </b>
<div class="add"><b>let </b><font color="Maroon">c<sub>84</sub></font> be   <a href="nat_1.html#NM1">Nat</a>;<br/><b>assume </b><a NAME="E1:46_10_4"/><i><font color="Green">E75</font></i>: 
( 1 <a href="xxreal_0.html#R1">&lt;=</a> <font color="Maroon">c<sub>84</sub></font> &amp; <font color="Maroon">c<sub>84</sub></font> <a href="xxreal_0.html#NR3" target="_self">&lt;</a> <font color="Maroon">c<sub>77</sub></font> )
 ;<br/><a NAME="E2:46_10_4"/><b>then </b>
<span class="p1">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>84</sub></font> <a href="xxreal_0.html#NR2" target="_self">&gt;=</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 1
 <b>by </b><i><a class="ref" href="xreal_1.html#T8">XREAL_1:8</a></i>;<br/><a NAME="E3:46_10_4"/><b>then </b>
<span class="p1">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>84</sub></font> <a href="xxreal_0.html#NR2" target="_self">&gt;=</a> 8
 <b>by </b><i><a class="txt" href="scpqsort.html#E9:46"><i><font color="Green">E49</font></i></a>, <a class="ref" href="xreal_1.html#T2">XREAL_1:2</a></i>;<br/><a NAME="E4:46_10_4"/><b>then </b><i><font color="Green">E76</font></i>: 
<span class="p1">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>84</sub></font> <a href="xxreal_0.html#NR4" target="_self">&gt;</a> 2
 <b>by </b><i><a class="ref" href="xreal_1.html#T2">XREAL_1:2</a></i>;<br/><b>thus </b><span class="p1">(<span class="default"><a href="scmpds_4.html#K9">IExec</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a> ,2 <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p5">(<span class="default"><span class="p0">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p4">(<span class="default"><a href="scmpds_2.html#K14">SubFrom</a> <a href="scmp_gcd.html#K2">GBP</a> ,2,<a href="scmp_gcd.html#K3">SBP</a> ,<span class="p5">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span></span>)</span></span>)</span> <a href="scmpds_4.html#K3">';'</a> <span class="p3">(<span class="default"><a href="scmpds_6.html#K3">if&gt;0</a> <a href="scmp_gcd.html#K2">GBP</a> ,2,<span class="p4">(<span class="default"><span class="p5">(<span class="default"><span class="p0">(<span class="default"><span class="p1">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a> ,2 <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p2">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span></span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p1">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a> ,4 <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span> <a href="scmpds_4.html#K3">';'</a> <font color="Maroon">c<sub>50</sub></font></span>)</span> <a href="scmpds_4.html#K3">';'</a> <span class="p5">(<span class="default"><span class="p0">(<span class="default"><span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a> ,<span class="p5">(<span class="default"><span class="p0">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 3</span>)</span> <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p5">(<span class="default"><span class="p0">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p4">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a> ,<span class="p5">(<span class="default"><span class="p0">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span> <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K2">GBP</a> ,4</span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p3">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a> ,<span class="p4">(<span class="default"><span class="p5">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 2</span>)</span> <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K2">GBP</a> ,4</span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p2">(<span class="default"><a href="scmpds_2.html#K12">AddTo</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span>,<span class="p3">(<span class="default"><a href="xcmplx_0.html#K4">-</a> 1</span>)</span></span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p1">(<span class="default"><a href="scmpds_2.html#K12">AddTo</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 2</span>)</span>,1</span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p0">(<span class="default"><a href="scmpds_2.html#K12">AddTo</a> <a href="scmp_gcd.html#K2">GBP</a> ,1,2</span>)</span></span>)</span></span>)</span>,<span class="p4">(<span class="default"><a href="scmpds_4.html#K1">Load</a> <span class="p5">(<span class="default"><a href="scmpds_2.html#K12">AddTo</a> <a href="scmp_gcd.html#K2">GBP</a> ,1,<span class="p0">(<span class="default"><a href="xcmplx_0.html#K4">-</a> 2</span>)</span></span>)</span></span>)</span></span>)</span></span>)</span>,<font color="Maroon">c<sub>75</sub></font></span>)</span> <a href="scmpds_2.html#K2">.</a> <span class="p1">(<span class="default"><a href="scmp_gcd.html#K1">intpos</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>84</sub></font></span>)</span></span>)</span> = 
<span class="p1">(<span class="default"><a href="scmpds_4.html#K9">IExec</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a> ,2 <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p0">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span></span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p5">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a> ,4 <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p0">(<span class="default"><span class="p1">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span> <a href="scmpds_4.html#K3">';'</a> <font color="Maroon">c<sub>50</sub></font></span>)</span> <a href="scmpds_4.html#K3">';'</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><span class="p0">(<span class="default"><span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a> ,<span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 3</span>)</span> <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p2">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a> ,<span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span> <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K2">GBP</a> ,4</span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p1">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a> ,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 2</span>)</span> <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K2">GBP</a> ,4</span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p0">(<span class="default"><a href="scmpds_2.html#K12">AddTo</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span>,<span class="p1">(<span class="default"><a href="xcmplx_0.html#K4">-</a> 1</span>)</span></span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p5">(<span class="default"><a href="scmpds_2.html#K12">AddTo</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p0">(<span class="default"><span class="p1">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 2</span>)</span>,1</span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p4">(<span class="default"><a href="scmpds_2.html#K12">AddTo</a> <a href="scmp_gcd.html#K2">GBP</a> ,1,2</span>)</span></span>)</span></span>)</span>,<span class="p2">(<span class="default"><a href="scmpds_4.html#K9">IExec</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a> ,2 <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p5">(<span class="default"><span class="p0">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p4">(<span class="default"><a href="scmpds_2.html#K14">SubFrom</a> <a href="scmp_gcd.html#K2">GBP</a> ,2,<a href="scmp_gcd.html#K3">SBP</a> ,<span class="p5">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span></span>)</span></span>)</span>,<font color="Maroon">c<sub>75</sub></font></span>)</span></span>)</span> <a href="scmpds_2.html#K2">.</a> <span class="p1">(<span class="default"><a href="scmp_gcd.html#K1">intpos</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>84</sub></font></span>)</span></span>)</span>
<b>by </b><i><a class="txt" href="scpqsort.html#E16:46_10"><i><font color="Green">E70</font></i></a></i>
<br/>.= 
<span class="p1">(<span class="default"><a href="scmpds_4.html#K9">IExec</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a> ,2 <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p4">(<span class="default"><span class="p5">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p3">(<span class="default"><a href="scmpds_2.html#K14">SubFrom</a> <a href="scmp_gcd.html#K2">GBP</a> ,2,<a href="scmp_gcd.html#K3">SBP</a> ,<span class="p4">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span></span>)</span></span>)</span>,<font color="Maroon">c<sub>75</sub></font></span>)</span> <a href="scmpds_2.html#K2">.</a> <span class="p1">(<span class="default"><a href="scmp_gcd.html#K1">intpos</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>84</sub></font></span>)</span></span>)</span>
<b>by </b><i><a class="txt" href="scpqsort.html#E14:46"><i><font color="Green">E54</font></i></a>, <a class="txt" href="scpqsort.html#E1:46_10"><i><font color="Green">E58</font></i></a>, <a class="txt" href="scpqsort.html#E2:46_10"><i><font color="Green">E59</font></i></a>, <a class="txt" href="scpqsort.html#E3:46_10"><i><font color="Green">E60</font></i></a>, <a class="txt" href="scpqsort.html#E4:46_10"><i><font color="Green">E61</font></i></a>, <a class="txt" href="scpqsort.html#E7:46_10"><i><font color="Green">E63</font></i></a>, <a class="txt" href="scpqsort.html#E10:46_10"><i><font color="Green">E64</font></i></a>, <a class="txt" href="scpqsort.html#E11:46_10"><i><font color="Green">E65</font></i></a>, <a class="txt" href="scpqsort.html#E19:46_10"><i><font color="Green">E72</font></i></a>, <a class="txt" href="scpqsort.html#E21:46_10"><i><font color="Green">E73</font></i></a>, <a class="txt" href="scpqsort.html#E1:46_10_4"><i><font color="Green">E75</font></i></a></i>
<br/>.= 
<font color="Maroon">c<sub>75</sub></font> <a href="scmpds_2.html#K2">.</a> <span class="p1">(<span class="default"><a href="scmp_gcd.html#K1">intpos</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>84</sub></font></span>)</span></span>)</span>
<b>by </b><i><a class="txt" href="scpqsort.html#E15:46"><i><font color="Green">E55</font></i></a>, <a class="txt" href="scpqsort.html#E1:46_10"><i><font color="Green">E58</font></i></a>, <a class="txt" href="scpqsort.html#E4:46_10_4"><i><font color="Green">E76</font></i></a></i>
;<br/></div>
<b>end;</b></div>

<b>thus </b><a NAME="E28:46_10"/>
<font color="Maroon">c<sub>80</sub></font>,<font color="Maroon">c<sub>81</sub></font> <a href="rfinseq.html#R1">are_fiberwise_equipotent</a> 
 <b>by </b><i><a class="txt" href="scpqsort.html#E14:46"><i><font color="Green">E54</font></i></a>, <a class="txt" href="scpqsort.html#E1:46_10"><i><font color="Green">E58</font></i></a>, <a class="txt" href="scpqsort.html#E2:46_10"><i><font color="Green">E59</font></i></a>, <a class="txt" href="scpqsort.html#E3:46_10"><i><font color="Green">E60</font></i></a>, <a class="txt" href="scpqsort.html#E4:46_10"><i><font color="Green">E61</font></i></a>, <a class="txt" href="scpqsort.html#E7:46_10"><i><font color="Green">E63</font></i></a>, <a class="txt" href="scpqsort.html#E10:46_10"><i><font color="Green">E64</font></i></a>, <a class="txt" href="scpqsort.html#E11:46_10"><i><font color="Green">E65</font></i></a>, <a class="txt" href="scpqsort.html#E19:46_10"><i><font color="Green">E72</font></i></a>, <a class="txt" href="scpqsort.html#E21:46_10"><i><font color="Green">E73</font></i></a></i>;<br/>

<b>consider </b><font color="Maroon">c<sub>84</sub></font> being   <a href="nat_1.html#NM1">Nat</a><b> such that </b><br/><a NAME="E30:46_10"/><i><font color="Green">E75</font></i>: 
( <font color="Maroon">c<sub>78</sub></font> <a href="xxreal_0.html#R1">&lt;=</a> <font color="Maroon">c<sub>84</sub></font> &amp; <font color="Maroon">c<sub>84</sub></font> <a href="xxreal_0.html#R1">&lt;=</a> <font color="Maroon">c<sub>79</sub></font> &amp; <font color="Maroon">c<sub>84</sub></font> <a href="xcmplx_0.html#K6">-</a> 1 <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><a href="scmpds_4.html#K9">IExec</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a> ,2 <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p0">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span></span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p5">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a> ,4 <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p0">(<span class="default"><span class="p1">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span> <a href="scmpds_4.html#K3">';'</a> <font color="Maroon">c<sub>50</sub></font></span>)</span> <a href="scmpds_4.html#K3">';'</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><span class="p0">(<span class="default"><span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a> ,<span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 3</span>)</span> <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p2">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a> ,<span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span> <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K2">GBP</a> ,4</span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p1">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a> ,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 2</span>)</span> <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K2">GBP</a> ,4</span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p0">(<span class="default"><a href="scmpds_2.html#K12">AddTo</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span>,<span class="p1">(<span class="default"><a href="xcmplx_0.html#K4">-</a> 1</span>)</span></span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p5">(<span class="default"><a href="scmpds_2.html#K12">AddTo</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p0">(<span class="default"><span class="p1">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 2</span>)</span>,1</span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p4">(<span class="default"><a href="scmpds_2.html#K12">AddTo</a> <a href="scmp_gcd.html#K2">GBP</a> ,1,2</span>)</span></span>)</span></span>)</span>,<span class="p2">(<span class="default"><a href="scmpds_4.html#K9">IExec</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a> ,2 <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p5">(<span class="default"><span class="p0">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p4">(<span class="default"><a href="scmpds_2.html#K14">SubFrom</a> <a href="scmp_gcd.html#K2">GBP</a> ,2,<a href="scmp_gcd.html#K3">SBP</a> ,<span class="p5">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span></span>)</span></span>)</span>,<font color="Maroon">c<sub>75</sub></font></span>)</span></span>)</span> <a href="scmpds_2.html#K2">.</a> <span class="p1">(<span class="default"><a href="scmp_gcd.html#K1">intpos</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">c<sub>77</sub></font> <a href="nat_1.html#K1">+</a> <span class="p4">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> &amp; <font color="Maroon">c<sub>84</sub></font> <a href="nat_1.html#K1">+</a> 1 <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><a href="scmpds_4.html#K9">IExec</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a> ,2 <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p0">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span></span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p5">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a> ,4 <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p0">(<span class="default"><span class="p1">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span> <a href="scmpds_4.html#K3">';'</a> <font color="Maroon">c<sub>50</sub></font></span>)</span> <a href="scmpds_4.html#K3">';'</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><span class="p0">(<span class="default"><span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a> ,<span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 3</span>)</span> <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p2">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a> ,<span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span> <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K2">GBP</a> ,4</span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p1">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a> ,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 2</span>)</span> <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K2">GBP</a> ,4</span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p0">(<span class="default"><a href="scmpds_2.html#K12">AddTo</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span>,<span class="p1">(<span class="default"><a href="xcmplx_0.html#K4">-</a> 1</span>)</span></span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p5">(<span class="default"><a href="scmpds_2.html#K12">AddTo</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p0">(<span class="default"><span class="p1">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 2</span>)</span>,1</span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p4">(<span class="default"><a href="scmpds_2.html#K12">AddTo</a> <a href="scmp_gcd.html#K2">GBP</a> ,1,2</span>)</span></span>)</span></span>)</span>,<span class="p2">(<span class="default"><a href="scmpds_4.html#K9">IExec</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a> ,2 <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p5">(<span class="default"><span class="p0">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p4">(<span class="default"><a href="scmpds_2.html#K14">SubFrom</a> <a href="scmp_gcd.html#K2">GBP</a> ,2,<a href="scmp_gcd.html#K3">SBP</a> ,<span class="p5">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span></span>)</span></span>)</span>,<font color="Maroon">c<sub>75</sub></font></span>)</span></span>)</span> <a href="scmpds_2.html#K2">.</a> <span class="p1">(<span class="default"><a href="scmp_gcd.html#K1">intpos</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">c<sub>77</sub></font> <a href="nat_1.html#K1">+</a> <span class="p4">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span></span>)</span> <a href="nat_1.html#K1">+</a> 2</span>)</span></span>)</span> &amp; ( for <font color="Olive">b<sub>1</sub></font> being  <a href="nat_1.html#NM1">Nat</a> st <font color="Maroon">c<sub>78</sub></font> <a href="xxreal_0.html#R1">&lt;=</a> <font color="Olive">b<sub>1</sub></font> &amp; <font color="Olive">b<sub>1</sub></font> <a href="xxreal_0.html#NR3" target="_self">&lt;</a> <font color="Maroon">c<sub>84</sub></font> holds <br/><span class="p1">(<span class="default"><a href="scmpds_4.html#K9">IExec</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a> ,2 <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p0">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span></span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p5">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a> ,4 <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p0">(<span class="default"><span class="p1">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span> <a href="scmpds_4.html#K3">';'</a> <font color="Maroon">c<sub>50</sub></font></span>)</span> <a href="scmpds_4.html#K3">';'</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><span class="p0">(<span class="default"><span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a> ,<span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 3</span>)</span> <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p2">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a> ,<span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span> <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K2">GBP</a> ,4</span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p1">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a> ,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 2</span>)</span> <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K2">GBP</a> ,4</span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p0">(<span class="default"><a href="scmpds_2.html#K12">AddTo</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span>,<span class="p1">(<span class="default"><a href="xcmplx_0.html#K4">-</a> 1</span>)</span></span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p5">(<span class="default"><a href="scmpds_2.html#K12">AddTo</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p0">(<span class="default"><span class="p1">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 2</span>)</span>,1</span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p4">(<span class="default"><a href="scmpds_2.html#K12">AddTo</a> <a href="scmp_gcd.html#K2">GBP</a> ,1,2</span>)</span></span>)</span></span>)</span>,<span class="p2">(<span class="default"><a href="scmpds_4.html#K9">IExec</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a> ,2 <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p5">(<span class="default"><span class="p0">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p4">(<span class="default"><a href="scmpds_2.html#K14">SubFrom</a> <a href="scmp_gcd.html#K2">GBP</a> ,2,<a href="scmp_gcd.html#K3">SBP</a> ,<span class="p5">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span></span>)</span></span>)</span>,<font color="Maroon">c<sub>75</sub></font></span>)</span></span>)</span> <a href="scmpds_2.html#K2">.</a> <span class="p1">(<span class="default"><a href="scmp_gcd.html#K1">intpos</a> <font color="Maroon">c<sub>84</sub></font></span>)</span> <a href="xxreal_0.html#NR2" target="_self">&gt;=</a> <span class="p1">(<span class="default"><a href="scmpds_4.html#K9">IExec</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a> ,2 <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p0">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span></span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p5">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a> ,4 <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p0">(<span class="default"><span class="p1">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span> <a href="scmpds_4.html#K3">';'</a> <font color="Maroon">c<sub>50</sub></font></span>)</span> <a href="scmpds_4.html#K3">';'</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><span class="p0">(<span class="default"><span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a> ,<span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 3</span>)</span> <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p2">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a> ,<span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span> <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K2">GBP</a> ,4</span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p1">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a> ,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 2</span>)</span> <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K2">GBP</a> ,4</span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p0">(<span class="default"><a href="scmpds_2.html#K12">AddTo</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span>,<span class="p1">(<span class="default"><a href="xcmplx_0.html#K4">-</a> 1</span>)</span></span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p5">(<span class="default"><a href="scmpds_2.html#K12">AddTo</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p0">(<span class="default"><span class="p1">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 2</span>)</span>,1</span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p4">(<span class="default"><a href="scmpds_2.html#K12">AddTo</a> <a href="scmp_gcd.html#K2">GBP</a> ,1,2</span>)</span></span>)</span></span>)</span>,<span class="p2">(<span class="default"><a href="scmpds_4.html#K9">IExec</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a> ,2 <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p5">(<span class="default"><span class="p0">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p4">(<span class="default"><a href="scmpds_2.html#K14">SubFrom</a> <a href="scmp_gcd.html#K2">GBP</a> ,2,<a href="scmp_gcd.html#K3">SBP</a> ,<span class="p5">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span></span>)</span></span>)</span>,<font color="Maroon">c<sub>75</sub></font></span>)</span></span>)</span> <a href="scmpds_2.html#K2">.</a> <span class="p1">(<span class="default"><a href="scmp_gcd.html#K1">intpos</a> <font color="Olive">b<sub>1</sub></font></span>)</span> ) &amp; ( for <font color="Olive">b<sub>1</sub></font> being  <a href="nat_1.html#NM1">Nat</a> st <font color="Maroon">c<sub>84</sub></font> <a href="xxreal_0.html#NR3" target="_self">&lt;</a> <font color="Olive">b<sub>1</sub></font> &amp; <font color="Olive">b<sub>1</sub></font> <a href="xxreal_0.html#R1">&lt;=</a> <font color="Maroon">c<sub>79</sub></font> holds <br/><span class="p1">(<span class="default"><a href="scmpds_4.html#K9">IExec</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a> ,2 <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p0">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span></span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p5">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a> ,4 <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p0">(<span class="default"><span class="p1">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span> <a href="scmpds_4.html#K3">';'</a> <font color="Maroon">c<sub>50</sub></font></span>)</span> <a href="scmpds_4.html#K3">';'</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><span class="p0">(<span class="default"><span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a> ,<span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 3</span>)</span> <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p2">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a> ,<span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span> <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K2">GBP</a> ,4</span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p1">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a> ,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 2</span>)</span> <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K2">GBP</a> ,4</span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p0">(<span class="default"><a href="scmpds_2.html#K12">AddTo</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span>,<span class="p1">(<span class="default"><a href="xcmplx_0.html#K4">-</a> 1</span>)</span></span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p5">(<span class="default"><a href="scmpds_2.html#K12">AddTo</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p0">(<span class="default"><span class="p1">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 2</span>)</span>,1</span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p4">(<span class="default"><a href="scmpds_2.html#K12">AddTo</a> <a href="scmp_gcd.html#K2">GBP</a> ,1,2</span>)</span></span>)</span></span>)</span>,<span class="p2">(<span class="default"><a href="scmpds_4.html#K9">IExec</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a> ,2 <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p5">(<span class="default"><span class="p0">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p4">(<span class="default"><a href="scmpds_2.html#K14">SubFrom</a> <a href="scmp_gcd.html#K2">GBP</a> ,2,<a href="scmp_gcd.html#K3">SBP</a> ,<span class="p5">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span></span>)</span></span>)</span>,<font color="Maroon">c<sub>75</sub></font></span>)</span></span>)</span> <a href="scmpds_2.html#K2">.</a> <span class="p1">(<span class="default"><a href="scmp_gcd.html#K1">intpos</a> <font color="Maroon">c<sub>84</sub></font></span>)</span> <a href="xxreal_0.html#R1">&lt;=</a> <span class="p1">(<span class="default"><a href="scmpds_4.html#K9">IExec</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a> ,2 <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p0">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span></span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p5">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a> ,4 <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p0">(<span class="default"><span class="p1">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span> <a href="scmpds_4.html#K3">';'</a> <font color="Maroon">c<sub>50</sub></font></span>)</span> <a href="scmpds_4.html#K3">';'</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><span class="p0">(<span class="default"><span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a> ,<span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 3</span>)</span> <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p2">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a> ,<span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span> <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K2">GBP</a> ,4</span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p1">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a> ,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 2</span>)</span> <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K2">GBP</a> ,4</span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p0">(<span class="default"><a href="scmpds_2.html#K12">AddTo</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span>,<span class="p1">(<span class="default"><a href="xcmplx_0.html#K4">-</a> 1</span>)</span></span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p5">(<span class="default"><a href="scmpds_2.html#K12">AddTo</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p0">(<span class="default"><span class="p1">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 2</span>)</span>,1</span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p4">(<span class="default"><a href="scmpds_2.html#K12">AddTo</a> <a href="scmp_gcd.html#K2">GBP</a> ,1,2</span>)</span></span>)</span></span>)</span>,<span class="p2">(<span class="default"><a href="scmpds_4.html#K9">IExec</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a> ,2 <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p5">(<span class="default"><span class="p0">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p4">(<span class="default"><a href="scmpds_2.html#K14">SubFrom</a> <a href="scmp_gcd.html#K2">GBP</a> ,2,<a href="scmp_gcd.html#K3">SBP</a> ,<span class="p5">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span></span>)</span></span>)</span>,<font color="Maroon">c<sub>75</sub></font></span>)</span></span>)</span> <a href="scmpds_2.html#K2">.</a> <span class="p1">(<span class="default"><a href="scmp_gcd.html#K1">intpos</a> <font color="Olive">b<sub>1</sub></font></span>)</span> ) &amp; ( for <font color="Olive">b<sub>1</sub></font> being  <a href="nat_1.html#NM1">Nat</a> st ( ( <font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> 1 <a href="xxreal_0.html#R1">&lt;=</a> <font color="Olive">b<sub>1</sub></font> &amp; <font color="Olive">b<sub>1</sub></font> <a href="xxreal_0.html#NR3" target="_self">&lt;</a> <font color="Maroon">c<sub>78</sub></font> ) or ( <font color="Maroon">c<sub>79</sub></font> <a href="xxreal_0.html#NR3" target="_self">&lt;</a> <font color="Olive">b<sub>1</sub></font> &amp; <font color="Olive">b<sub>1</sub></font> <a href="xxreal_0.html#R1">&lt;=</a> <font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font> ) ) holds <br/><span class="p1">(<span class="default"><a href="scmpds_4.html#K9">IExec</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a> ,2 <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p0">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span></span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p5">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a> ,4 <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p0">(<span class="default"><span class="p1">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span> <a href="scmpds_4.html#K3">';'</a> <font color="Maroon">c<sub>50</sub></font></span>)</span> <a href="scmpds_4.html#K3">';'</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><span class="p0">(<span class="default"><span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a> ,<span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 3</span>)</span> <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p2">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a> ,<span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span> <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K2">GBP</a> ,4</span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p1">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a> ,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 2</span>)</span> <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K2">GBP</a> ,4</span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p0">(<span class="default"><a href="scmpds_2.html#K12">AddTo</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span>,<span class="p1">(<span class="default"><a href="xcmplx_0.html#K4">-</a> 1</span>)</span></span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p5">(<span class="default"><a href="scmpds_2.html#K12">AddTo</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p0">(<span class="default"><span class="p1">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 2</span>)</span>,1</span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p4">(<span class="default"><a href="scmpds_2.html#K12">AddTo</a> <a href="scmp_gcd.html#K2">GBP</a> ,1,2</span>)</span></span>)</span></span>)</span>,<span class="p2">(<span class="default"><a href="scmpds_4.html#K9">IExec</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a> ,2 <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p5">(<span class="default"><span class="p0">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p4">(<span class="default"><a href="scmpds_2.html#K14">SubFrom</a> <a href="scmp_gcd.html#K2">GBP</a> ,2,<a href="scmp_gcd.html#K3">SBP</a> ,<span class="p5">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span></span>)</span></span>)</span>,<font color="Maroon">c<sub>75</sub></font></span>)</span></span>)</span> <a href="scmpds_2.html#K2">.</a> <span class="p1">(<span class="default"><a href="scmp_gcd.html#K1">intpos</a> <font color="Olive">b<sub>1</sub></font></span>)</span> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><a href="scmpds_4.html#K9">IExec</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a> ,2 <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p4">(<span class="default"><span class="p5">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p3">(<span class="default"><a href="scmpds_2.html#K14">SubFrom</a> <a href="scmp_gcd.html#K2">GBP</a> ,2,<a href="scmp_gcd.html#K3">SBP</a> ,<span class="p4">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span></span>)</span></span>)</span>,<font color="Maroon">c<sub>75</sub></font></span>)</span> <a href="scmpds_2.html#K2">.</a> <span class="p1">(<span class="default"><a href="scmp_gcd.html#K1">intpos</a> <font color="Olive">b<sub>1</sub></font></span>)</span> ) )
 <b>by </b><i><a class="txt" href="scpqsort.html#E14:46"><i><font color="Green">E54</font></i></a>, <a class="txt" href="scpqsort.html#E1:46_10"><i><font color="Green">E58</font></i></a>, <a class="txt" href="scpqsort.html#E2:46_10"><i><font color="Green">E59</font></i></a>, <a class="txt" href="scpqsort.html#E3:46_10"><i><font color="Green">E60</font></i></a>, <a class="txt" href="scpqsort.html#E4:46_10"><i><font color="Green">E61</font></i></a>, <a class="txt" href="scpqsort.html#E7:46_10"><i><font color="Green">E63</font></i></a>, <a class="txt" href="scpqsort.html#E10:46_10"><i><font color="Green">E64</font></i></a>, <a class="txt" href="scpqsort.html#E11:46_10"><i><font color="Green">E65</font></i></a>, <a class="txt" href="scpqsort.html#E19:46_10"><i><font color="Green">E72</font></i></a>, <a class="txt" href="scpqsort.html#E21:46_10"><i><font color="Green">E73</font></i></a></i>;<br/>
<b>take </b>
<font color="Maroon">c<sub>84</sub></font>
;<br/>

<b>thus </b><a NAME="E31:46_10"/>
( <font color="Maroon">c<sub>78</sub></font> <a href="xxreal_0.html#R1">&lt;=</a> <font color="Maroon">c<sub>84</sub></font> &amp; <font color="Maroon">c<sub>84</sub></font> <a href="xxreal_0.html#R1">&lt;=</a> <font color="Maroon">c<sub>79</sub></font> )
 <b>by </b><i><a class="txt" href="scpqsort.html#E30:46_10"><i><font color="Green">E75</font></i></a></i>;<br/>

<b>thus </b><a NAME="E32:46_10"/>
<font color="Maroon">c<sub>84</sub></font> <a href="xcmplx_0.html#K6">-</a> 1 <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><a href="scmpds_4.html#K9">IExec</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a> ,2 <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p5">(<span class="default"><span class="p0">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p4">(<span class="default"><a href="scmpds_2.html#K14">SubFrom</a> <a href="scmp_gcd.html#K2">GBP</a> ,2,<a href="scmp_gcd.html#K3">SBP</a> ,<span class="p5">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span></span>)</span></span>)</span> <a href="scmpds_4.html#K3">';'</a> <span class="p3">(<span class="default"><a href="scmpds_6.html#K3">if&gt;0</a> <a href="scmp_gcd.html#K2">GBP</a> ,2,<span class="p4">(<span class="default"><span class="p5">(<span class="default"><span class="p0">(<span class="default"><span class="p1">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a> ,2 <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p2">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span></span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p1">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a> ,4 <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span> <a href="scmpds_4.html#K3">';'</a> <font color="Maroon">c<sub>50</sub></font></span>)</span> <a href="scmpds_4.html#K3">';'</a> <span class="p5">(<span class="default"><span class="p0">(<span class="default"><span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a> ,<span class="p5">(<span class="default"><span class="p0">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 3</span>)</span> <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p5">(<span class="default"><span class="p0">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p4">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a> ,<span class="p5">(<span class="default"><span class="p0">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span> <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K2">GBP</a> ,4</span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p3">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a> ,<span class="p4">(<span class="default"><span class="p5">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 2</span>)</span> <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K2">GBP</a> ,4</span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p2">(<span class="default"><a href="scmpds_2.html#K12">AddTo</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span>,<span class="p3">(<span class="default"><a href="xcmplx_0.html#K4">-</a> 1</span>)</span></span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p1">(<span class="default"><a href="scmpds_2.html#K12">AddTo</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 2</span>)</span>,1</span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p0">(<span class="default"><a href="scmpds_2.html#K12">AddTo</a> <a href="scmp_gcd.html#K2">GBP</a> ,1,2</span>)</span></span>)</span></span>)</span>,<span class="p4">(<span class="default"><a href="scmpds_4.html#K1">Load</a> <span class="p5">(<span class="default"><a href="scmpds_2.html#K12">AddTo</a> <a href="scmp_gcd.html#K2">GBP</a> ,1,<span class="p0">(<span class="default"><a href="xcmplx_0.html#K4">-</a> 2</span>)</span></span>)</span></span>)</span></span>)</span></span>)</span>,<font color="Maroon">c<sub>75</sub></font></span>)</span> <a href="scmpds_2.html#K2">.</a> <span class="p1">(<span class="default"><a href="scmp_gcd.html#K1">intpos</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">c<sub>77</sub></font> <a href="nat_1.html#K1">+</a> <span class="p4">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span>
 <b>by </b><i><a class="txt" href="scpqsort.html#E16:46_10"><i><font color="Green">E70</font></i></a>, <a class="txt" href="scpqsort.html#E30:46_10"><i><font color="Green">E75</font></i></a></i>;<br/>

<b>thus </b><a NAME="E33:46_10"/>
<font color="Maroon">c<sub>84</sub></font> <a href="nat_1.html#K1">+</a> 1 <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><a href="scmpds_4.html#K9">IExec</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a> ,2 <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p5">(<span class="default"><span class="p0">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p4">(<span class="default"><a href="scmpds_2.html#K14">SubFrom</a> <a href="scmp_gcd.html#K2">GBP</a> ,2,<a href="scmp_gcd.html#K3">SBP</a> ,<span class="p5">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span></span>)</span></span>)</span> <a href="scmpds_4.html#K3">';'</a> <span class="p3">(<span class="default"><a href="scmpds_6.html#K3">if&gt;0</a> <a href="scmp_gcd.html#K2">GBP</a> ,2,<span class="p4">(<span class="default"><span class="p5">(<span class="default"><span class="p0">(<span class="default"><span class="p1">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a> ,2 <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p2">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span></span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p1">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a> ,4 <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span> <a href="scmpds_4.html#K3">';'</a> <font color="Maroon">c<sub>50</sub></font></span>)</span> <a href="scmpds_4.html#K3">';'</a> <span class="p5">(<span class="default"><span class="p0">(<span class="default"><span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a> ,<span class="p5">(<span class="default"><span class="p0">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 3</span>)</span> <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p5">(<span class="default"><span class="p0">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p4">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a> ,<span class="p5">(<span class="default"><span class="p0">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span> <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K2">GBP</a> ,4</span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p3">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a> ,<span class="p4">(<span class="default"><span class="p5">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 2</span>)</span> <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K2">GBP</a> ,4</span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p2">(<span class="default"><a href="scmpds_2.html#K12">AddTo</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span>,<span class="p3">(<span class="default"><a href="xcmplx_0.html#K4">-</a> 1</span>)</span></span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p1">(<span class="default"><a href="scmpds_2.html#K12">AddTo</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 2</span>)</span>,1</span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p0">(<span class="default"><a href="scmpds_2.html#K12">AddTo</a> <a href="scmp_gcd.html#K2">GBP</a> ,1,2</span>)</span></span>)</span></span>)</span>,<span class="p4">(<span class="default"><a href="scmpds_4.html#K1">Load</a> <span class="p5">(<span class="default"><a href="scmpds_2.html#K12">AddTo</a> <a href="scmp_gcd.html#K2">GBP</a> ,1,<span class="p0">(<span class="default"><a href="xcmplx_0.html#K4">-</a> 2</span>)</span></span>)</span></span>)</span></span>)</span></span>)</span>,<font color="Maroon">c<sub>75</sub></font></span>)</span> <a href="scmpds_2.html#K2">.</a> <span class="p1">(<span class="default"><a href="scmp_gcd.html#K1">intpos</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">c<sub>77</sub></font> <a href="nat_1.html#K1">+</a> <span class="p4">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span></span>)</span> <a href="nat_1.html#K1">+</a> 2</span>)</span></span>)</span>
 <b>by </b><i><a class="txt" href="scpqsort.html#E16:46_10"><i><font color="Green">E70</font></i></a>, <a class="txt" href="scpqsort.html#E30:46_10"><i><font color="Green">E75</font></i></a></i>;<br/>

<div><b>hereby </b>
<div class="add"><b>let </b><font color="Maroon">c<sub>85</sub></font> be   <a href="nat_1.html#NM1">Nat</a>;<br/><b>assume </b><a NAME="E1:46_10_5"/>
( <font color="Maroon">c<sub>78</sub></font> <a href="xxreal_0.html#R1">&lt;=</a> <font color="Maroon">c<sub>85</sub></font> &amp; <font color="Maroon">c<sub>85</sub></font> <a href="xxreal_0.html#NR3" target="_self">&lt;</a> <font color="Maroon">c<sub>84</sub></font> )
 ;<br/><a NAME="E2:46_10_5"/><b>then </b>
<span class="p1">(<span class="default"><a href="scmpds_4.html#K9">IExec</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a> ,2 <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p0">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span></span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p5">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a> ,4 <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p0">(<span class="default"><span class="p1">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span> <a href="scmpds_4.html#K3">';'</a> <font color="Maroon">c<sub>50</sub></font></span>)</span> <a href="scmpds_4.html#K3">';'</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><span class="p0">(<span class="default"><span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a> ,<span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 3</span>)</span> <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p2">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a> ,<span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span> <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K2">GBP</a> ,4</span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p1">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a> ,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 2</span>)</span> <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K2">GBP</a> ,4</span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p0">(<span class="default"><a href="scmpds_2.html#K12">AddTo</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span>,<span class="p1">(<span class="default"><a href="xcmplx_0.html#K4">-</a> 1</span>)</span></span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p5">(<span class="default"><a href="scmpds_2.html#K12">AddTo</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p0">(<span class="default"><span class="p1">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 2</span>)</span>,1</span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p4">(<span class="default"><a href="scmpds_2.html#K12">AddTo</a> <a href="scmp_gcd.html#K2">GBP</a> ,1,2</span>)</span></span>)</span></span>)</span>,<span class="p2">(<span class="default"><a href="scmpds_4.html#K9">IExec</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a> ,2 <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p5">(<span class="default"><span class="p0">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p4">(<span class="default"><a href="scmpds_2.html#K14">SubFrom</a> <a href="scmp_gcd.html#K2">GBP</a> ,2,<a href="scmp_gcd.html#K3">SBP</a> ,<span class="p5">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span></span>)</span></span>)</span>,<font color="Maroon">c<sub>75</sub></font></span>)</span></span>)</span> <a href="scmpds_2.html#K2">.</a> <span class="p1">(<span class="default"><a href="scmp_gcd.html#K1">intpos</a> <font color="Maroon">c<sub>84</sub></font></span>)</span> <a href="xxreal_0.html#NR2" target="_self">&gt;=</a> <span class="p1">(<span class="default"><a href="scmpds_4.html#K9">IExec</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a> ,2 <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p0">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span></span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p5">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a> ,4 <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p0">(<span class="default"><span class="p1">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span> <a href="scmpds_4.html#K3">';'</a> <font color="Maroon">c<sub>50</sub></font></span>)</span> <a href="scmpds_4.html#K3">';'</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><span class="p0">(<span class="default"><span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a> ,<span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 3</span>)</span> <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p2">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a> ,<span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span> <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K2">GBP</a> ,4</span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p1">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a> ,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 2</span>)</span> <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K2">GBP</a> ,4</span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p0">(<span class="default"><a href="scmpds_2.html#K12">AddTo</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span>,<span class="p1">(<span class="default"><a href="xcmplx_0.html#K4">-</a> 1</span>)</span></span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p5">(<span class="default"><a href="scmpds_2.html#K12">AddTo</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p0">(<span class="default"><span class="p1">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 2</span>)</span>,1</span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p4">(<span class="default"><a href="scmpds_2.html#K12">AddTo</a> <a href="scmp_gcd.html#K2">GBP</a> ,1,2</span>)</span></span>)</span></span>)</span>,<span class="p2">(<span class="default"><a href="scmpds_4.html#K9">IExec</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a> ,2 <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p5">(<span class="default"><span class="p0">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p4">(<span class="default"><a href="scmpds_2.html#K14">SubFrom</a> <a href="scmp_gcd.html#K2">GBP</a> ,2,<a href="scmp_gcd.html#K3">SBP</a> ,<span class="p5">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span></span>)</span></span>)</span>,<font color="Maroon">c<sub>75</sub></font></span>)</span></span>)</span> <a href="scmpds_2.html#K2">.</a> <span class="p1">(<span class="default"><a href="scmp_gcd.html#K1">intpos</a> <font color="Maroon">c<sub>85</sub></font></span>)</span>
 <b>by </b><i><a class="txt" href="scpqsort.html#E30:46_10"><i><font color="Green">E75</font></i></a></i>;<br/><a NAME="E3:46_10_5"/><b>then </b>
<span class="p1">(<span class="default"><a href="scmpds_4.html#K9">IExec</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a> ,2 <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p5">(<span class="default"><span class="p0">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p4">(<span class="default"><a href="scmpds_2.html#K14">SubFrom</a> <a href="scmp_gcd.html#K2">GBP</a> ,2,<a href="scmp_gcd.html#K3">SBP</a> ,<span class="p5">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span></span>)</span></span>)</span> <a href="scmpds_4.html#K3">';'</a> <span class="p3">(<span class="default"><a href="scmpds_6.html#K3">if&gt;0</a> <a href="scmp_gcd.html#K2">GBP</a> ,2,<span class="p4">(<span class="default"><span class="p5">(<span class="default"><span class="p0">(<span class="default"><span class="p1">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a> ,2 <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p2">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span></span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p1">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a> ,4 <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span> <a href="scmpds_4.html#K3">';'</a> <font color="Maroon">c<sub>50</sub></font></span>)</span> <a href="scmpds_4.html#K3">';'</a> <span class="p5">(<span class="default"><span class="p0">(<span class="default"><span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a> ,<span class="p5">(<span class="default"><span class="p0">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 3</span>)</span> <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p5">(<span class="default"><span class="p0">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p4">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a> ,<span class="p5">(<span class="default"><span class="p0">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span> <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K2">GBP</a> ,4</span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p3">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a> ,<span class="p4">(<span class="default"><span class="p5">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 2</span>)</span> <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K2">GBP</a> ,4</span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p2">(<span class="default"><a href="scmpds_2.html#K12">AddTo</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span>,<span class="p3">(<span class="default"><a href="xcmplx_0.html#K4">-</a> 1</span>)</span></span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p1">(<span class="default"><a href="scmpds_2.html#K12">AddTo</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 2</span>)</span>,1</span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p0">(<span class="default"><a href="scmpds_2.html#K12">AddTo</a> <a href="scmp_gcd.html#K2">GBP</a> ,1,2</span>)</span></span>)</span></span>)</span>,<span class="p4">(<span class="default"><a href="scmpds_4.html#K1">Load</a> <span class="p5">(<span class="default"><a href="scmpds_2.html#K12">AddTo</a> <a href="scmp_gcd.html#K2">GBP</a> ,1,<span class="p0">(<span class="default"><a href="xcmplx_0.html#K4">-</a> 2</span>)</span></span>)</span></span>)</span></span>)</span></span>)</span>,<font color="Maroon">c<sub>75</sub></font></span>)</span> <a href="scmpds_2.html#K2">.</a> <span class="p1">(<span class="default"><a href="scmp_gcd.html#K1">intpos</a> <font color="Maroon">c<sub>84</sub></font></span>)</span> <a href="xxreal_0.html#NR2" target="_self">&gt;=</a> <span class="p1">(<span class="default"><a href="scmpds_4.html#K9">IExec</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a> ,2 <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p0">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span></span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p5">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a> ,4 <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p0">(<span class="default"><span class="p1">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span> <a href="scmpds_4.html#K3">';'</a> <font color="Maroon">c<sub>50</sub></font></span>)</span> <a href="scmpds_4.html#K3">';'</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><span class="p0">(<span class="default"><span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a> ,<span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 3</span>)</span> <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p2">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a> ,<span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span> <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K2">GBP</a> ,4</span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p1">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a> ,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 2</span>)</span> <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K2">GBP</a> ,4</span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p0">(<span class="default"><a href="scmpds_2.html#K12">AddTo</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span>,<span class="p1">(<span class="default"><a href="xcmplx_0.html#K4">-</a> 1</span>)</span></span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p5">(<span class="default"><a href="scmpds_2.html#K12">AddTo</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p0">(<span class="default"><span class="p1">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 2</span>)</span>,1</span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p4">(<span class="default"><a href="scmpds_2.html#K12">AddTo</a> <a href="scmp_gcd.html#K2">GBP</a> ,1,2</span>)</span></span>)</span></span>)</span>,<span class="p2">(<span class="default"><a href="scmpds_4.html#K9">IExec</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a> ,2 <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p5">(<span class="default"><span class="p0">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p4">(<span class="default"><a href="scmpds_2.html#K14">SubFrom</a> <a href="scmp_gcd.html#K2">GBP</a> ,2,<a href="scmp_gcd.html#K3">SBP</a> ,<span class="p5">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span></span>)</span></span>)</span>,<font color="Maroon">c<sub>75</sub></font></span>)</span></span>)</span> <a href="scmpds_2.html#K2">.</a> <span class="p1">(<span class="default"><a href="scmp_gcd.html#K1">intpos</a> <font color="Maroon">c<sub>85</sub></font></span>)</span>
 <b>by </b><i><a class="txt" href="scpqsort.html#E16:46_10"><i><font color="Green">E70</font></i></a></i>;<br/><b>hence </b><a NAME="E4:46_10_5"/>
<span class="p1">(<span class="default"><a href="scmpds_4.html#K9">IExec</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a> ,2 <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p5">(<span class="default"><span class="p0">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p4">(<span class="default"><a href="scmpds_2.html#K14">SubFrom</a> <a href="scmp_gcd.html#K2">GBP</a> ,2,<a href="scmp_gcd.html#K3">SBP</a> ,<span class="p5">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span></span>)</span></span>)</span> <a href="scmpds_4.html#K3">';'</a> <span class="p3">(<span class="default"><a href="scmpds_6.html#K3">if&gt;0</a> <a href="scmp_gcd.html#K2">GBP</a> ,2,<span class="p4">(<span class="default"><span class="p5">(<span class="default"><span class="p0">(<span class="default"><span class="p1">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a> ,2 <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p2">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span></span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p1">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a> ,4 <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span> <a href="scmpds_4.html#K3">';'</a> <font color="Maroon">c<sub>50</sub></font></span>)</span> <a href="scmpds_4.html#K3">';'</a> <span class="p5">(<span class="default"><span class="p0">(<span class="default"><span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a> ,<span class="p5">(<span class="default"><span class="p0">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 3</span>)</span> <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p5">(<span class="default"><span class="p0">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p4">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a> ,<span class="p5">(<span class="default"><span class="p0">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span> <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K2">GBP</a> ,4</span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p3">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a> ,<span class="p4">(<span class="default"><span class="p5">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 2</span>)</span> <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K2">GBP</a> ,4</span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p2">(<span class="default"><a href="scmpds_2.html#K12">AddTo</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span>,<span class="p3">(<span class="default"><a href="xcmplx_0.html#K4">-</a> 1</span>)</span></span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p1">(<span class="default"><a href="scmpds_2.html#K12">AddTo</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 2</span>)</span>,1</span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p0">(<span class="default"><a href="scmpds_2.html#K12">AddTo</a> <a href="scmp_gcd.html#K2">GBP</a> ,1,2</span>)</span></span>)</span></span>)</span>,<span class="p4">(<span class="default"><a href="scmpds_4.html#K1">Load</a> <span class="p5">(<span class="default"><a href="scmpds_2.html#K12">AddTo</a> <a href="scmp_gcd.html#K2">GBP</a> ,1,<span class="p0">(<span class="default"><a href="xcmplx_0.html#K4">-</a> 2</span>)</span></span>)</span></span>)</span></span>)</span></span>)</span>,<font color="Maroon">c<sub>75</sub></font></span>)</span> <a href="scmpds_2.html#K2">.</a> <span class="p1">(<span class="default"><a href="scmp_gcd.html#K1">intpos</a> <font color="Maroon">c<sub>84</sub></font></span>)</span> <a href="xxreal_0.html#NR2" target="_self">&gt;=</a> <span class="p1">(<span class="default"><a href="scmpds_4.html#K9">IExec</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a> ,2 <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p5">(<span class="default"><span class="p0">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p4">(<span class="default"><a href="scmpds_2.html#K14">SubFrom</a> <a href="scmp_gcd.html#K2">GBP</a> ,2,<a href="scmp_gcd.html#K3">SBP</a> ,<span class="p5">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span></span>)</span></span>)</span> <a href="scmpds_4.html#K3">';'</a> <span class="p3">(<span class="default"><a href="scmpds_6.html#K3">if&gt;0</a> <a href="scmp_gcd.html#K2">GBP</a> ,2,<span class="p4">(<span class="default"><span class="p5">(<span class="default"><span class="p0">(<span class="default"><span class="p1">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a> ,2 <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p2">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span></span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p1">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a> ,4 <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span> <a href="scmpds_4.html#K3">';'</a> <font color="Maroon">c<sub>50</sub></font></span>)</span> <a href="scmpds_4.html#K3">';'</a> <span class="p5">(<span class="default"><span class="p0">(<span class="default"><span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a> ,<span class="p5">(<span class="default"><span class="p0">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 3</span>)</span> <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p5">(<span class="default"><span class="p0">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p4">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a> ,<span class="p5">(<span class="default"><span class="p0">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span> <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K2">GBP</a> ,4</span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p3">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a> ,<span class="p4">(<span class="default"><span class="p5">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 2</span>)</span> <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K2">GBP</a> ,4</span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p2">(<span class="default"><a href="scmpds_2.html#K12">AddTo</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span>,<span class="p3">(<span class="default"><a href="xcmplx_0.html#K4">-</a> 1</span>)</span></span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p1">(<span class="default"><a href="scmpds_2.html#K12">AddTo</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 2</span>)</span>,1</span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p0">(<span class="default"><a href="scmpds_2.html#K12">AddTo</a> <a href="scmp_gcd.html#K2">GBP</a> ,1,2</span>)</span></span>)</span></span>)</span>,<span class="p4">(<span class="default"><a href="scmpds_4.html#K1">Load</a> <span class="p5">(<span class="default"><a href="scmpds_2.html#K12">AddTo</a> <a href="scmp_gcd.html#K2">GBP</a> ,1,<span class="p0">(<span class="default"><a href="xcmplx_0.html#K4">-</a> 2</span>)</span></span>)</span></span>)</span></span>)</span></span>)</span>,<font color="Maroon">c<sub>75</sub></font></span>)</span> <a href="scmpds_2.html#K2">.</a> <span class="p1">(<span class="default"><a href="scmp_gcd.html#K1">intpos</a> <font color="Maroon">c<sub>85</sub></font></span>)</span>
 <b>by </b><i><a class="txt" href="scpqsort.html#E16:46_10"><i><font color="Green">E70</font></i></a></i>;<br/></div>
<b>end;</b></div>

<div><b>hereby </b>
<div class="add"><b>let </b><font color="Maroon">c<sub>85</sub></font> be   <a href="nat_1.html#NM1">Nat</a>;<br/><b>assume </b><a NAME="E1:46_10_6"/>
( <font color="Maroon">c<sub>84</sub></font> <a href="xxreal_0.html#NR3" target="_self">&lt;</a> <font color="Maroon">c<sub>85</sub></font> &amp; <font color="Maroon">c<sub>85</sub></font> <a href="xxreal_0.html#R1">&lt;=</a> <font color="Maroon">c<sub>79</sub></font> )
 ;<br/><a NAME="E2:46_10_6"/><b>then </b>
<span class="p1">(<span class="default"><a href="scmpds_4.html#K9">IExec</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a> ,2 <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p0">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span></span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p5">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a> ,4 <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p0">(<span class="default"><span class="p1">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span> <a href="scmpds_4.html#K3">';'</a> <font color="Maroon">c<sub>50</sub></font></span>)</span> <a href="scmpds_4.html#K3">';'</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><span class="p0">(<span class="default"><span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a> ,<span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 3</span>)</span> <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p2">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a> ,<span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span> <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K2">GBP</a> ,4</span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p1">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a> ,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 2</span>)</span> <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K2">GBP</a> ,4</span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p0">(<span class="default"><a href="scmpds_2.html#K12">AddTo</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span>,<span class="p1">(<span class="default"><a href="xcmplx_0.html#K4">-</a> 1</span>)</span></span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p5">(<span class="default"><a href="scmpds_2.html#K12">AddTo</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p0">(<span class="default"><span class="p1">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 2</span>)</span>,1</span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p4">(<span class="default"><a href="scmpds_2.html#K12">AddTo</a> <a href="scmp_gcd.html#K2">GBP</a> ,1,2</span>)</span></span>)</span></span>)</span>,<span class="p2">(<span class="default"><a href="scmpds_4.html#K9">IExec</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a> ,2 <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p5">(<span class="default"><span class="p0">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p4">(<span class="default"><a href="scmpds_2.html#K14">SubFrom</a> <a href="scmp_gcd.html#K2">GBP</a> ,2,<a href="scmp_gcd.html#K3">SBP</a> ,<span class="p5">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span></span>)</span></span>)</span>,<font color="Maroon">c<sub>75</sub></font></span>)</span></span>)</span> <a href="scmpds_2.html#K2">.</a> <span class="p1">(<span class="default"><a href="scmp_gcd.html#K1">intpos</a> <font color="Maroon">c<sub>84</sub></font></span>)</span> <a href="xxreal_0.html#R1">&lt;=</a> <span class="p1">(<span class="default"><a href="scmpds_4.html#K9">IExec</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a> ,2 <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p0">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span></span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p5">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a> ,4 <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p0">(<span class="default"><span class="p1">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span> <a href="scmpds_4.html#K3">';'</a> <font color="Maroon">c<sub>50</sub></font></span>)</span> <a href="scmpds_4.html#K3">';'</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><span class="p0">(<span class="default"><span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a> ,<span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 3</span>)</span> <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p2">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a> ,<span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span> <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K2">GBP</a> ,4</span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p1">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a> ,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 2</span>)</span> <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K2">GBP</a> ,4</span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p0">(<span class="default"><a href="scmpds_2.html#K12">AddTo</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span>,<span class="p1">(<span class="default"><a href="xcmplx_0.html#K4">-</a> 1</span>)</span></span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p5">(<span class="default"><a href="scmpds_2.html#K12">AddTo</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p0">(<span class="default"><span class="p1">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 2</span>)</span>,1</span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p4">(<span class="default"><a href="scmpds_2.html#K12">AddTo</a> <a href="scmp_gcd.html#K2">GBP</a> ,1,2</span>)</span></span>)</span></span>)</span>,<span class="p2">(<span class="default"><a href="scmpds_4.html#K9">IExec</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a> ,2 <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p5">(<span class="default"><span class="p0">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p4">(<span class="default"><a href="scmpds_2.html#K14">SubFrom</a> <a href="scmp_gcd.html#K2">GBP</a> ,2,<a href="scmp_gcd.html#K3">SBP</a> ,<span class="p5">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span></span>)</span></span>)</span>,<font color="Maroon">c<sub>75</sub></font></span>)</span></span>)</span> <a href="scmpds_2.html#K2">.</a> <span class="p1">(<span class="default"><a href="scmp_gcd.html#K1">intpos</a> <font color="Maroon">c<sub>85</sub></font></span>)</span>
 <b>by </b><i><a class="txt" href="scpqsort.html#E30:46_10"><i><font color="Green">E75</font></i></a></i>;<br/><a NAME="E3:46_10_6"/><b>then </b>
<span class="p1">(<span class="default"><a href="scmpds_4.html#K9">IExec</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a> ,2 <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p5">(<span class="default"><span class="p0">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p4">(<span class="default"><a href="scmpds_2.html#K14">SubFrom</a> <a href="scmp_gcd.html#K2">GBP</a> ,2,<a href="scmp_gcd.html#K3">SBP</a> ,<span class="p5">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span></span>)</span></span>)</span> <a href="scmpds_4.html#K3">';'</a> <span class="p3">(<span class="default"><a href="scmpds_6.html#K3">if&gt;0</a> <a href="scmp_gcd.html#K2">GBP</a> ,2,<span class="p4">(<span class="default"><span class="p5">(<span class="default"><span class="p0">(<span class="default"><span class="p1">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a> ,2 <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p2">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span></span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p1">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a> ,4 <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span> <a href="scmpds_4.html#K3">';'</a> <font color="Maroon">c<sub>50</sub></font></span>)</span> <a href="scmpds_4.html#K3">';'</a> <span class="p5">(<span class="default"><span class="p0">(<span class="default"><span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a> ,<span class="p5">(<span class="default"><span class="p0">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 3</span>)</span> <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p5">(<span class="default"><span class="p0">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p4">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a> ,<span class="p5">(<span class="default"><span class="p0">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span> <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K2">GBP</a> ,4</span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p3">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a> ,<span class="p4">(<span class="default"><span class="p5">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 2</span>)</span> <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K2">GBP</a> ,4</span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p2">(<span class="default"><a href="scmpds_2.html#K12">AddTo</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span>,<span class="p3">(<span class="default"><a href="xcmplx_0.html#K4">-</a> 1</span>)</span></span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p1">(<span class="default"><a href="scmpds_2.html#K12">AddTo</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 2</span>)</span>,1</span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p0">(<span class="default"><a href="scmpds_2.html#K12">AddTo</a> <a href="scmp_gcd.html#K2">GBP</a> ,1,2</span>)</span></span>)</span></span>)</span>,<span class="p4">(<span class="default"><a href="scmpds_4.html#K1">Load</a> <span class="p5">(<span class="default"><a href="scmpds_2.html#K12">AddTo</a> <a href="scmp_gcd.html#K2">GBP</a> ,1,<span class="p0">(<span class="default"><a href="xcmplx_0.html#K4">-</a> 2</span>)</span></span>)</span></span>)</span></span>)</span></span>)</span>,<font color="Maroon">c<sub>75</sub></font></span>)</span> <a href="scmpds_2.html#K2">.</a> <span class="p1">(<span class="default"><a href="scmp_gcd.html#K1">intpos</a> <font color="Maroon">c<sub>84</sub></font></span>)</span> <a href="xxreal_0.html#R1">&lt;=</a> <span class="p1">(<span class="default"><a href="scmpds_4.html#K9">IExec</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a> ,2 <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p0">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span></span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p5">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a> ,4 <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p0">(<span class="default"><span class="p1">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span> <a href="scmpds_4.html#K3">';'</a> <font color="Maroon">c<sub>50</sub></font></span>)</span> <a href="scmpds_4.html#K3">';'</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><span class="p0">(<span class="default"><span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a> ,<span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 3</span>)</span> <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p2">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a> ,<span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span> <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K2">GBP</a> ,4</span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p1">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a> ,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 2</span>)</span> <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K2">GBP</a> ,4</span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p0">(<span class="default"><a href="scmpds_2.html#K12">AddTo</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span>,<span class="p1">(<span class="default"><a href="xcmplx_0.html#K4">-</a> 1</span>)</span></span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p5">(<span class="default"><a href="scmpds_2.html#K12">AddTo</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p0">(<span class="default"><span class="p1">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 2</span>)</span>,1</span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p4">(<span class="default"><a href="scmpds_2.html#K12">AddTo</a> <a href="scmp_gcd.html#K2">GBP</a> ,1,2</span>)</span></span>)</span></span>)</span>,<span class="p2">(<span class="default"><a href="scmpds_4.html#K9">IExec</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a> ,2 <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p5">(<span class="default"><span class="p0">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p4">(<span class="default"><a href="scmpds_2.html#K14">SubFrom</a> <a href="scmp_gcd.html#K2">GBP</a> ,2,<a href="scmp_gcd.html#K3">SBP</a> ,<span class="p5">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span></span>)</span></span>)</span>,<font color="Maroon">c<sub>75</sub></font></span>)</span></span>)</span> <a href="scmpds_2.html#K2">.</a> <span class="p1">(<span class="default"><a href="scmp_gcd.html#K1">intpos</a> <font color="Maroon">c<sub>85</sub></font></span>)</span>
 <b>by </b><i><a class="txt" href="scpqsort.html#E16:46_10"><i><font color="Green">E70</font></i></a></i>;<br/><b>hence </b><a NAME="E4:46_10_6"/>
<span class="p1">(<span class="default"><a href="scmpds_4.html#K9">IExec</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a> ,2 <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p5">(<span class="default"><span class="p0">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p4">(<span class="default"><a href="scmpds_2.html#K14">SubFrom</a> <a href="scmp_gcd.html#K2">GBP</a> ,2,<a href="scmp_gcd.html#K3">SBP</a> ,<span class="p5">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span></span>)</span></span>)</span> <a href="scmpds_4.html#K3">';'</a> <span class="p3">(<span class="default"><a href="scmpds_6.html#K3">if&gt;0</a> <a href="scmp_gcd.html#K2">GBP</a> ,2,<span class="p4">(<span class="default"><span class="p5">(<span class="default"><span class="p0">(<span class="default"><span class="p1">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a> ,2 <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p2">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span></span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p1">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a> ,4 <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span> <a href="scmpds_4.html#K3">';'</a> <font color="Maroon">c<sub>50</sub></font></span>)</span> <a href="scmpds_4.html#K3">';'</a> <span class="p5">(<span class="default"><span class="p0">(<span class="default"><span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a> ,<span class="p5">(<span class="default"><span class="p0">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 3</span>)</span> <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p5">(<span class="default"><span class="p0">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p4">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a> ,<span class="p5">(<span class="default"><span class="p0">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span> <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K2">GBP</a> ,4</span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p3">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a> ,<span class="p4">(<span class="default"><span class="p5">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 2</span>)</span> <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K2">GBP</a> ,4</span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p2">(<span class="default"><a href="scmpds_2.html#K12">AddTo</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span>,<span class="p3">(<span class="default"><a href="xcmplx_0.html#K4">-</a> 1</span>)</span></span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p1">(<span class="default"><a href="scmpds_2.html#K12">AddTo</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 2</span>)</span>,1</span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p0">(<span class="default"><a href="scmpds_2.html#K12">AddTo</a> <a href="scmp_gcd.html#K2">GBP</a> ,1,2</span>)</span></span>)</span></span>)</span>,<span class="p4">(<span class="default"><a href="scmpds_4.html#K1">Load</a> <span class="p5">(<span class="default"><a href="scmpds_2.html#K12">AddTo</a> <a href="scmp_gcd.html#K2">GBP</a> ,1,<span class="p0">(<span class="default"><a href="xcmplx_0.html#K4">-</a> 2</span>)</span></span>)</span></span>)</span></span>)</span></span>)</span>,<font color="Maroon">c<sub>75</sub></font></span>)</span> <a href="scmpds_2.html#K2">.</a> <span class="p1">(<span class="default"><a href="scmp_gcd.html#K1">intpos</a> <font color="Maroon">c<sub>84</sub></font></span>)</span> <a href="xxreal_0.html#R1">&lt;=</a> <span class="p1">(<span class="default"><a href="scmpds_4.html#K9">IExec</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a> ,2 <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p5">(<span class="default"><span class="p0">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p4">(<span class="default"><a href="scmpds_2.html#K14">SubFrom</a> <a href="scmp_gcd.html#K2">GBP</a> ,2,<a href="scmp_gcd.html#K3">SBP</a> ,<span class="p5">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span></span>)</span></span>)</span> <a href="scmpds_4.html#K3">';'</a> <span class="p3">(<span class="default"><a href="scmpds_6.html#K3">if&gt;0</a> <a href="scmp_gcd.html#K2">GBP</a> ,2,<span class="p4">(<span class="default"><span class="p5">(<span class="default"><span class="p0">(<span class="default"><span class="p1">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a> ,2 <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p2">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span></span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p1">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a> ,4 <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span> <a href="scmpds_4.html#K3">';'</a> <font color="Maroon">c<sub>50</sub></font></span>)</span> <a href="scmpds_4.html#K3">';'</a> <span class="p5">(<span class="default"><span class="p0">(<span class="default"><span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a> ,<span class="p5">(<span class="default"><span class="p0">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 3</span>)</span> <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p5">(<span class="default"><span class="p0">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p4">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a> ,<span class="p5">(<span class="default"><span class="p0">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span> <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K2">GBP</a> ,4</span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p3">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a> ,<span class="p4">(<span class="default"><span class="p5">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 2</span>)</span> <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K2">GBP</a> ,4</span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p2">(<span class="default"><a href="scmpds_2.html#K12">AddTo</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span>,<span class="p3">(<span class="default"><a href="xcmplx_0.html#K4">-</a> 1</span>)</span></span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p1">(<span class="default"><a href="scmpds_2.html#K12">AddTo</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 2</span>)</span>,1</span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p0">(<span class="default"><a href="scmpds_2.html#K12">AddTo</a> <a href="scmp_gcd.html#K2">GBP</a> ,1,2</span>)</span></span>)</span></span>)</span>,<span class="p4">(<span class="default"><a href="scmpds_4.html#K1">Load</a> <span class="p5">(<span class="default"><a href="scmpds_2.html#K12">AddTo</a> <a href="scmp_gcd.html#K2">GBP</a> ,1,<span class="p0">(<span class="default"><a href="xcmplx_0.html#K4">-</a> 2</span>)</span></span>)</span></span>)</span></span>)</span></span>)</span>,<font color="Maroon">c<sub>75</sub></font></span>)</span> <a href="scmpds_2.html#K2">.</a> <span class="p1">(<span class="default"><a href="scmp_gcd.html#K1">intpos</a> <font color="Maroon">c<sub>85</sub></font></span>)</span>
 <b>by </b><i><a class="txt" href="scpqsort.html#E16:46_10"><i><font color="Green">E70</font></i></a></i>;<br/></div>
<b>end;</b></div>

<div><b>hereby </b>
<div class="add"><b>let </b><font color="Maroon">c<sub>85</sub></font> be   <a href="nat_1.html#NM1">Nat</a>;<br/><b>assume </b><a NAME="E1:46_10_7"/><i><font color="Green">E76</font></i>: 
( ( <font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> 1 <a href="xxreal_0.html#R1">&lt;=</a> <font color="Maroon">c<sub>85</sub></font> &amp; <font color="Maroon">c<sub>85</sub></font> <a href="xxreal_0.html#NR3" target="_self">&lt;</a> <font color="Maroon">c<sub>78</sub></font> ) or ( <font color="Maroon">c<sub>79</sub></font> <a href="xxreal_0.html#NR3" target="_self">&lt;</a> <font color="Maroon">c<sub>85</sub></font> &amp; <font color="Maroon">c<sub>85</sub></font> <a href="xxreal_0.html#R1">&lt;=</a> <font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font> ) )
 ;<br/><div><a class="txt" onclick="hs2(this)" href="javascript:()" title="46_10_7_1"><b>now </b></a><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="46_10_7_1_1"><b>per </b></a><a class="txt" onclick="hs(this)" href="javascript:()"><b>cases </b></a><span class="hide"><a NAME="E1:46_10_7_1_1"/>
( ( <font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> 1 <a href="xxreal_0.html#R1">&lt;=</a> <font color="Maroon">c<sub>85</sub></font> &amp; <font color="Maroon">c<sub>85</sub></font> <a href="xxreal_0.html#NR3" target="_self">&lt;</a> <font color="Maroon">c<sub>78</sub></font> ) or ( <font color="Maroon">c<sub>79</sub></font> <a href="xxreal_0.html#NR3" target="_self">&lt;</a> <font color="Maroon">c<sub>85</sub></font> &amp; <font color="Maroon">c<sub>85</sub></font> <a href="xxreal_0.html#R1">&lt;=</a> <font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font> ) )
 </span><b>by </b><i><a class="txt" href="scpqsort.html#E1:46_10_7"><i><font color="Green">E76</font></i></a></i>;<br/><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="46_10_7_1_1_1"><b>suppose </b></a><a NAME="E1:46_10_7_1_1_1"/>
( <font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> 1 <a href="xxreal_0.html#R1">&lt;=</a> <font color="Maroon">c<sub>85</sub></font> &amp; <font color="Maroon">c<sub>85</sub></font> <a href="xxreal_0.html#NR3" target="_self">&lt;</a> <font color="Maroon">c<sub>78</sub></font> )
 ;<br/><div class="add"><b>hence </b><a NAME="E2:46_10_7_1_1_1"/>
<font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> 1 <a href="xxreal_0.html#R1">&lt;=</a> <font color="Maroon">c<sub>85</sub></font>
 ;<br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="46_10_7_1_1_2"><b>suppose </b></a><a NAME="E1:46_10_7_1_1_2"/>
( <font color="Maroon">c<sub>79</sub></font> <a href="xxreal_0.html#NR3" target="_self">&lt;</a> <font color="Maroon">c<sub>85</sub></font> &amp; <font color="Maroon">c<sub>85</sub></font> <a href="xxreal_0.html#R1">&lt;=</a> <font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font> )
 ;<br/><div class="add"><a NAME="E2:46_10_7_1_1_2"/><b>then </b>
<font color="Maroon">c<sub>85</sub></font> <a href="xxreal_0.html#NR2" target="_self">&gt;=</a> <font color="Maroon">c<sub>84</sub></font>
 <b>by </b><i><a class="txt" href="scpqsort.html#E30:46_10"><i><font color="Green">E75</font></i></a>, <a class="ref" href="xreal_1.html#T2">XREAL_1:2</a></i>;<br/><a NAME="E3:46_10_7_1_1_2"/><b>then </b>
<font color="Maroon">c<sub>85</sub></font> <a href="xxreal_0.html#NR2" target="_self">&gt;=</a> <font color="Maroon">c<sub>78</sub></font>
 <b>by </b><i><a class="txt" href="scpqsort.html#E30:46_10"><i><font color="Green">E75</font></i></a>, <a class="ref" href="xreal_1.html#T2">XREAL_1:2</a></i>;<br/><b>hence </b><a NAME="E4:46_10_7_1_1_2"/>
<font color="Maroon">c<sub>85</sub></font> <a href="xxreal_0.html#NR2" target="_self">&gt;=</a> <font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> 1
 <b>by </b><i><a class="txt" href="scpqsort.html#E1:46_10"><i><font color="Green">E58</font></i></a>, <a class="ref" href="xreal_1.html#T2">XREAL_1:2</a></i>;<br/></div><b>end;</b></div></div><b>end;</b></div></div><b>end;</b></div><a NAME="E3:46_10_7"/><b>then </b>
<font color="Maroon">c<sub>85</sub></font> <a href="xxreal_0.html#NR2" target="_self">&gt;=</a> 8
 <b>by </b><i><a class="txt" href="scpqsort.html#E17:46_10"><i><font color="Green">E71</font></i></a>, <a class="ref" href="xreal_1.html#T2">XREAL_1:2</a></i>;<br/><a NAME="E4:46_10_7"/><b>then </b><i><font color="Green">E77</font></i>: 
<font color="Maroon">c<sub>85</sub></font> <a href="xxreal_0.html#NR4" target="_self">&gt;</a> 2
 <b>by </b><i><a class="ref" href="xreal_1.html#T2">XREAL_1:2</a></i>;<br/><b>thus </b><span class="p1">(<span class="default"><a href="scmpds_4.html#K9">IExec</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a> ,2 <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p5">(<span class="default"><span class="p0">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p4">(<span class="default"><a href="scmpds_2.html#K14">SubFrom</a> <a href="scmp_gcd.html#K2">GBP</a> ,2,<a href="scmp_gcd.html#K3">SBP</a> ,<span class="p5">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span></span>)</span></span>)</span> <a href="scmpds_4.html#K3">';'</a> <span class="p3">(<span class="default"><a href="scmpds_6.html#K3">if&gt;0</a> <a href="scmp_gcd.html#K2">GBP</a> ,2,<span class="p4">(<span class="default"><span class="p5">(<span class="default"><span class="p0">(<span class="default"><span class="p1">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a> ,2 <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p2">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span></span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p1">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a> ,4 <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span> <a href="scmpds_4.html#K3">';'</a> <font color="Maroon">c<sub>50</sub></font></span>)</span> <a href="scmpds_4.html#K3">';'</a> <span class="p5">(<span class="default"><span class="p0">(<span class="default"><span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a> ,<span class="p5">(<span class="default"><span class="p0">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 3</span>)</span> <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p5">(<span class="default"><span class="p0">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p4">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a> ,<span class="p5">(<span class="default"><span class="p0">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span> <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K2">GBP</a> ,4</span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p3">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a> ,<span class="p4">(<span class="default"><span class="p5">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 2</span>)</span> <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K2">GBP</a> ,4</span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p2">(<span class="default"><a href="scmpds_2.html#K12">AddTo</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span>,<span class="p3">(<span class="default"><a href="xcmplx_0.html#K4">-</a> 1</span>)</span></span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p1">(<span class="default"><a href="scmpds_2.html#K12">AddTo</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 2</span>)</span>,1</span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p0">(<span class="default"><a href="scmpds_2.html#K12">AddTo</a> <a href="scmp_gcd.html#K2">GBP</a> ,1,2</span>)</span></span>)</span></span>)</span>,<span class="p4">(<span class="default"><a href="scmpds_4.html#K1">Load</a> <span class="p5">(<span class="default"><a href="scmpds_2.html#K12">AddTo</a> <a href="scmp_gcd.html#K2">GBP</a> ,1,<span class="p0">(<span class="default"><a href="xcmplx_0.html#K4">-</a> 2</span>)</span></span>)</span></span>)</span></span>)</span></span>)</span>,<font color="Maroon">c<sub>75</sub></font></span>)</span> <a href="scmpds_2.html#K2">.</a> <span class="p1">(<span class="default"><a href="scmp_gcd.html#K1">intpos</a> <font color="Maroon">c<sub>85</sub></font></span>)</span> = 
<span class="p1">(<span class="default"><a href="scmpds_4.html#K9">IExec</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a> ,2 <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p0">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span></span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p5">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a> ,4 <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p0">(<span class="default"><span class="p1">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span> <a href="scmpds_4.html#K3">';'</a> <font color="Maroon">c<sub>50</sub></font></span>)</span> <a href="scmpds_4.html#K3">';'</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><span class="p0">(<span class="default"><span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a> ,<span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 3</span>)</span> <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p2">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a> ,<span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span> <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K2">GBP</a> ,4</span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p1">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a> ,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 2</span>)</span> <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K2">GBP</a> ,4</span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p0">(<span class="default"><a href="scmpds_2.html#K12">AddTo</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span>,<span class="p1">(<span class="default"><a href="xcmplx_0.html#K4">-</a> 1</span>)</span></span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p5">(<span class="default"><a href="scmpds_2.html#K12">AddTo</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p0">(<span class="default"><span class="p1">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 2</span>)</span>,1</span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p4">(<span class="default"><a href="scmpds_2.html#K12">AddTo</a> <a href="scmp_gcd.html#K2">GBP</a> ,1,2</span>)</span></span>)</span></span>)</span>,<span class="p2">(<span class="default"><a href="scmpds_4.html#K9">IExec</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a> ,2 <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p5">(<span class="default"><span class="p0">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p4">(<span class="default"><a href="scmpds_2.html#K14">SubFrom</a> <a href="scmp_gcd.html#K2">GBP</a> ,2,<a href="scmp_gcd.html#K3">SBP</a> ,<span class="p5">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span></span>)</span></span>)</span>,<font color="Maroon">c<sub>75</sub></font></span>)</span></span>)</span> <a href="scmpds_2.html#K2">.</a> <span class="p1">(<span class="default"><a href="scmp_gcd.html#K1">intpos</a> <font color="Maroon">c<sub>85</sub></font></span>)</span>
<b>by </b><i><a class="txt" href="scpqsort.html#E16:46_10"><i><font color="Green">E70</font></i></a></i>
<br/>.= 
<span class="p1">(<span class="default"><a href="scmpds_4.html#K9">IExec</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a> ,2 <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p4">(<span class="default"><span class="p5">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p3">(<span class="default"><a href="scmpds_2.html#K14">SubFrom</a> <a href="scmp_gcd.html#K2">GBP</a> ,2,<a href="scmp_gcd.html#K3">SBP</a> ,<span class="p4">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span></span>)</span></span>)</span>,<font color="Maroon">c<sub>75</sub></font></span>)</span> <a href="scmpds_2.html#K2">.</a> <span class="p1">(<span class="default"><a href="scmp_gcd.html#K1">intpos</a> <font color="Maroon">c<sub>85</sub></font></span>)</span>
<b>by </b><i><a class="txt" href="scpqsort.html#E30:46_10"><i><font color="Green">E75</font></i></a>, <a class="txt" href="scpqsort.html#E1:46_10_7"><i><font color="Green">E76</font></i></a></i>
<br/>.= 
<font color="Maroon">c<sub>75</sub></font> <a href="scmpds_2.html#K2">.</a> <span class="p1">(<span class="default"><a href="scmp_gcd.html#K1">intpos</a> <font color="Maroon">c<sub>85</sub></font></span>)</span>
<b>by </b><i><a class="txt" href="scpqsort.html#E15:46"><i><font color="Green">E55</font></i></a>, <a class="txt" href="scpqsort.html#E1:46_10"><i><font color="Green">E58</font></i></a>, <a class="txt" href="scpqsort.html#E4:46_10_7"><i><font color="Green">E77</font></i></a></i>
;<br/></div>
<b>end;</b></div>


</div><b>end;</b></div>
<a NAME="E18:46"/><i><font color="Green">E58</font></i>: 
for <font color="Olive">b<sub>1</sub></font> being  <a href="ami_1.html#NM4">State</a> of <a href="scmpds_2.html#K1">SCMPDS</a> <br/>for <font color="Olive">b<sub>2</sub></font> being  <a href="nat_1.html#NM1">Nat</a> st <font color="Olive">b<sub>1</sub></font> <a href="scmpds_2.html#K2">.</a> <a href="scmp_gcd.html#K2">GBP</a>  <a href="hidden.html#R1">=</a> 0 &amp; <font color="Olive">b<sub>1</sub></font> <a href="scmpds_2.html#K2">.</a> <a href="scmp_gcd.html#K3">SBP</a>  <a href="hidden.html#R1">=</a> <font color="Olive">b<sub>2</sub></font> &amp; <font color="Olive">b<sub>1</sub></font> <a href="scmpds_2.html#K2">.</a> <span class="p1">(<span class="default"><a href="scmp_gcd.html#K1">intpos</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Olive">b<sub>2</sub></font> <a href="nat_1.html#K1">+</a> <span class="p4">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> <a href="xxreal_0.html#R1">&lt;=</a> <font color="Olive">b<sub>1</sub></font> <a href="scmpds_2.html#K2">.</a> <span class="p1">(<span class="default"><a href="scmp_gcd.html#K1">intpos</a> <span class="p2">(<span class="default"><font color="Olive">b<sub>2</sub></font> <a href="nat_1.html#K1">+</a> <span class="p3">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span></span>)</span></span>)</span> holds <br/>( <span class="p1">(<span class="default"><a href="scmpds_4.html#K9">IExec</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a> ,2 <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p5">(<span class="default"><span class="p0">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p4">(<span class="default"><a href="scmpds_2.html#K14">SubFrom</a> <a href="scmp_gcd.html#K2">GBP</a> ,2,<a href="scmp_gcd.html#K3">SBP</a> ,<span class="p5">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span></span>)</span></span>)</span> <a href="scmpds_4.html#K3">';'</a> <span class="p3">(<span class="default"><a href="scmpds_6.html#K3">if&gt;0</a> <a href="scmp_gcd.html#K2">GBP</a> ,2,<span class="p4">(<span class="default"><span class="p5">(<span class="default"><span class="p0">(<span class="default"><span class="p1">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a> ,2 <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p2">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span></span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p1">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a> ,4 <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span> <a href="scmpds_4.html#K3">';'</a> <font color="Maroon">c<sub>50</sub></font></span>)</span> <a href="scmpds_4.html#K3">';'</a> <span class="p5">(<span class="default"><span class="p0">(<span class="default"><span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a> ,<span class="p5">(<span class="default"><span class="p0">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 3</span>)</span> <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p5">(<span class="default"><span class="p0">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p4">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a> ,<span class="p5">(<span class="default"><span class="p0">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span> <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K2">GBP</a> ,4</span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p3">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a> ,<span class="p4">(<span class="default"><span class="p5">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 2</span>)</span> <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K2">GBP</a> ,4</span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p2">(<span class="default"><a href="scmpds_2.html#K12">AddTo</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span>,<span class="p3">(<span class="default"><a href="xcmplx_0.html#K4">-</a> 1</span>)</span></span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p1">(<span class="default"><a href="scmpds_2.html#K12">AddTo</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 2</span>)</span>,1</span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p0">(<span class="default"><a href="scmpds_2.html#K12">AddTo</a> <a href="scmp_gcd.html#K2">GBP</a> ,1,2</span>)</span></span>)</span></span>)</span>,<span class="p4">(<span class="default"><a href="scmpds_4.html#K1">Load</a> <span class="p5">(<span class="default"><a href="scmpds_2.html#K12">AddTo</a> <a href="scmp_gcd.html#K2">GBP</a> ,1,<span class="p0">(<span class="default"><a href="xcmplx_0.html#K4">-</a> 2</span>)</span></span>)</span></span>)</span></span>)</span></span>)</span>,<font color="Olive">b<sub>1</sub></font></span>)</span> <a href="scmpds_2.html#K2">.</a> <a href="scmp_gcd.html#K2">GBP</a>  <a href="hidden.html#R1">=</a> 0 &amp; <span class="p1">(<span class="default"><a href="scmpds_4.html#K9">IExec</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a> ,2 <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p5">(<span class="default"><span class="p0">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p4">(<span class="default"><a href="scmpds_2.html#K14">SubFrom</a> <a href="scmp_gcd.html#K2">GBP</a> ,2,<a href="scmp_gcd.html#K3">SBP</a> ,<span class="p5">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span></span>)</span></span>)</span> <a href="scmpds_4.html#K3">';'</a> <span class="p3">(<span class="default"><a href="scmpds_6.html#K3">if&gt;0</a> <a href="scmp_gcd.html#K2">GBP</a> ,2,<span class="p4">(<span class="default"><span class="p5">(<span class="default"><span class="p0">(<span class="default"><span class="p1">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a> ,2 <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p2">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span></span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p1">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a> ,4 <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span> <a href="scmpds_4.html#K3">';'</a> <font color="Maroon">c<sub>50</sub></font></span>)</span> <a href="scmpds_4.html#K3">';'</a> <span class="p5">(<span class="default"><span class="p0">(<span class="default"><span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a> ,<span class="p5">(<span class="default"><span class="p0">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 3</span>)</span> <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p5">(<span class="default"><span class="p0">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p4">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a> ,<span class="p5">(<span class="default"><span class="p0">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span> <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K2">GBP</a> ,4</span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p3">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a> ,<span class="p4">(<span class="default"><span class="p5">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 2</span>)</span> <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K2">GBP</a> ,4</span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p2">(<span class="default"><a href="scmpds_2.html#K12">AddTo</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span>,<span class="p3">(<span class="default"><a href="xcmplx_0.html#K4">-</a> 1</span>)</span></span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p1">(<span class="default"><a href="scmpds_2.html#K12">AddTo</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 2</span>)</span>,1</span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p0">(<span class="default"><a href="scmpds_2.html#K12">AddTo</a> <a href="scmp_gcd.html#K2">GBP</a> ,1,2</span>)</span></span>)</span></span>)</span>,<span class="p4">(<span class="default"><a href="scmpds_4.html#K1">Load</a> <span class="p5">(<span class="default"><a href="scmpds_2.html#K12">AddTo</a> <a href="scmp_gcd.html#K2">GBP</a> ,1,<span class="p0">(<span class="default"><a href="xcmplx_0.html#K4">-</a> 2</span>)</span></span>)</span></span>)</span></span>)</span></span>)</span>,<font color="Olive">b<sub>1</sub></font></span>)</span> <a href="scmpds_2.html#K2">.</a> <span class="p1">(<span class="default"><a href="scmp_gcd.html#K1">intpos</a> 1</span>)</span> <a href="hidden.html#R1">=</a> <font color="Olive">b<sub>2</sub></font> <a href="xcmplx_0.html#K6">-</a> 2 &amp; ( for <font color="Olive">b<sub>3</sub></font> being  <a href="nat_1.html#NM1">Nat</a> st 1 <a href="xxreal_0.html#R1">&lt;=</a> <font color="Olive">b<sub>3</sub></font> &amp; <font color="Olive">b<sub>3</sub></font> <a href="xxreal_0.html#NR3" target="_self">&lt;</a> <font color="Olive">b<sub>2</sub></font> holds <br/><span class="p1">(<span class="default"><a href="scmpds_4.html#K9">IExec</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a> ,2 <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p5">(<span class="default"><span class="p0">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p4">(<span class="default"><a href="scmpds_2.html#K14">SubFrom</a> <a href="scmp_gcd.html#K2">GBP</a> ,2,<a href="scmp_gcd.html#K3">SBP</a> ,<span class="p5">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span></span>)</span></span>)</span> <a href="scmpds_4.html#K3">';'</a> <span class="p3">(<span class="default"><a href="scmpds_6.html#K3">if&gt;0</a> <a href="scmp_gcd.html#K2">GBP</a> ,2,<span class="p4">(<span class="default"><span class="p5">(<span class="default"><span class="p0">(<span class="default"><span class="p1">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a> ,2 <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p2">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span></span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p1">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a> ,4 <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span> <a href="scmpds_4.html#K3">';'</a> <font color="Maroon">c<sub>50</sub></font></span>)</span> <a href="scmpds_4.html#K3">';'</a> <span class="p5">(<span class="default"><span class="p0">(<span class="default"><span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a> ,<span class="p5">(<span class="default"><span class="p0">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 3</span>)</span> <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p5">(<span class="default"><span class="p0">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p4">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a> ,<span class="p5">(<span class="default"><span class="p0">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span> <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K2">GBP</a> ,4</span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p3">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a> ,<span class="p4">(<span class="default"><span class="p5">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 2</span>)</span> <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K2">GBP</a> ,4</span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p2">(<span class="default"><a href="scmpds_2.html#K12">AddTo</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span>,<span class="p3">(<span class="default"><a href="xcmplx_0.html#K4">-</a> 1</span>)</span></span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p1">(<span class="default"><a href="scmpds_2.html#K12">AddTo</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 2</span>)</span>,1</span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p0">(<span class="default"><a href="scmpds_2.html#K12">AddTo</a> <a href="scmp_gcd.html#K2">GBP</a> ,1,2</span>)</span></span>)</span></span>)</span>,<span class="p4">(<span class="default"><a href="scmpds_4.html#K1">Load</a> <span class="p5">(<span class="default"><a href="scmpds_2.html#K12">AddTo</a> <a href="scmp_gcd.html#K2">GBP</a> ,1,<span class="p0">(<span class="default"><a href="xcmplx_0.html#K4">-</a> 2</span>)</span></span>)</span></span>)</span></span>)</span></span>)</span>,<font color="Olive">b<sub>1</sub></font></span>)</span> <a href="scmpds_2.html#K2">.</a> <span class="p1">(<span class="default"><a href="scmp_gcd.html#K1">intpos</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> <font color="Olive">b<sub>3</sub></font></span>)</span></span>)</span> <a href="hidden.html#R1">=</a> <font color="Olive">b<sub>1</sub></font> <a href="scmpds_2.html#K2">.</a> <span class="p1">(<span class="default"><a href="scmp_gcd.html#K1">intpos</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> <font color="Olive">b<sub>3</sub></font></span>)</span></span>)</span> ) &amp; ( for <font color="Olive">b<sub>3</sub></font> being  <a href="nat_1.html#NM1">Nat</a> st 1 <a href="xxreal_0.html#R1">&lt;=</a> <font color="Olive">b<sub>3</sub></font> &amp; <font color="Olive">b<sub>3</sub></font> <a href="xxreal_0.html#R1">&lt;=</a> <font color="Maroon">c<sub>49</sub></font> holds <br/><span class="p1">(<span class="default"><a href="scmpds_4.html#K9">IExec</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a> ,2 <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p5">(<span class="default"><span class="p0">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p4">(<span class="default"><a href="scmpds_2.html#K14">SubFrom</a> <a href="scmp_gcd.html#K2">GBP</a> ,2,<a href="scmp_gcd.html#K3">SBP</a> ,<span class="p5">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span></span>)</span></span>)</span> <a href="scmpds_4.html#K3">';'</a> <span class="p3">(<span class="default"><a href="scmpds_6.html#K3">if&gt;0</a> <a href="scmp_gcd.html#K2">GBP</a> ,2,<span class="p4">(<span class="default"><span class="p5">(<span class="default"><span class="p0">(<span class="default"><span class="p1">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a> ,2 <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p2">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span></span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p1">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a> ,4 <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span> <a href="scmpds_4.html#K3">';'</a> <font color="Maroon">c<sub>50</sub></font></span>)</span> <a href="scmpds_4.html#K3">';'</a> <span class="p5">(<span class="default"><span class="p0">(<span class="default"><span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a> ,<span class="p5">(<span class="default"><span class="p0">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 3</span>)</span> <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p5">(<span class="default"><span class="p0">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p4">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a> ,<span class="p5">(<span class="default"><span class="p0">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span> <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K2">GBP</a> ,4</span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p3">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a> ,<span class="p4">(<span class="default"><span class="p5">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 2</span>)</span> <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K2">GBP</a> ,4</span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p2">(<span class="default"><a href="scmpds_2.html#K12">AddTo</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span>,<span class="p3">(<span class="default"><a href="xcmplx_0.html#K4">-</a> 1</span>)</span></span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p1">(<span class="default"><a href="scmpds_2.html#K12">AddTo</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 2</span>)</span>,1</span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p0">(<span class="default"><a href="scmpds_2.html#K12">AddTo</a> <a href="scmp_gcd.html#K2">GBP</a> ,1,2</span>)</span></span>)</span></span>)</span>,<span class="p4">(<span class="default"><a href="scmpds_4.html#K1">Load</a> <span class="p5">(<span class="default"><a href="scmpds_2.html#K12">AddTo</a> <a href="scmp_gcd.html#K2">GBP</a> ,1,<span class="p0">(<span class="default"><a href="xcmplx_0.html#K4">-</a> 2</span>)</span></span>)</span></span>)</span></span>)</span></span>)</span>,<font color="Olive">b<sub>1</sub></font></span>)</span> <a href="scmpds_2.html#K2">.</a> <span class="p1">(<span class="default"><a href="scmp_gcd.html#K1">intpos</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Olive">b<sub>3</sub></font></span>)</span></span>)</span> <a href="hidden.html#R1">=</a> <font color="Olive">b<sub>1</sub></font> <a href="scmpds_2.html#K2">.</a> <span class="p1">(<span class="default"><a href="scmp_gcd.html#K1">intpos</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Olive">b<sub>3</sub></font></span>)</span></span>)</span> ) )
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="46_11"><b>proof </b></a><div class="add">

<b>let </b><font color="Maroon">c<sub>75</sub></font> be   <a href="ami_1.html#NM4">State</a> of <a href="scmpds_2.html#K1">SCMPDS</a> ;<br/><b>let </b><font color="Maroon">c<sub>76</sub></font> be   <a href="nat_1.html#NM1">Nat</a>;<br/>



<b>set </b><font color="Maroon">c<sub>77</sub></font> = <font color="Maroon">c<sub>76</sub></font> <a href="nat_1.html#K1">+</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span>;<br/>
<b>set </b><font color="Maroon">c<sub>78</sub></font> =  <a href="scmpds_4.html#K9">IExec</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a> ,2 <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p2">(<span class="default"><a href="scmpds_2.html#K14">SubFrom</a> <a href="scmp_gcd.html#K2">GBP</a> ,2,<a href="scmp_gcd.html#K3">SBP</a> ,<span class="p3">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span></span>)</span></span>)</span>,<font color="Maroon">c<sub>75</sub></font>;<br/>
<b>assume </b><a NAME="E1:46_11"/><i><font color="Green">E59</font></i>: 
( <font color="Maroon">c<sub>75</sub></font> <a href="scmpds_2.html#K2">.</a> <a href="scmp_gcd.html#K2">GBP</a>  <a href="hidden.html#R1">=</a> 0 &amp; <font color="Maroon">c<sub>75</sub></font> <a href="scmpds_2.html#K2">.</a> <a href="scmp_gcd.html#K3">SBP</a>  <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>76</sub></font> &amp; <font color="Maroon">c<sub>75</sub></font> <a href="scmpds_2.html#K2">.</a> <span class="p1">(<span class="default"><a href="scmp_gcd.html#K1">intpos</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">c<sub>76</sub></font> <a href="nat_1.html#K1">+</a> <span class="p4">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> <a href="xxreal_0.html#R1">&lt;=</a> <font color="Maroon">c<sub>75</sub></font> <a href="scmpds_2.html#K2">.</a> <span class="p1">(<span class="default"><a href="scmp_gcd.html#K1">intpos</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>76</sub></font> <a href="nat_1.html#K1">+</a> <span class="p3">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span></span>)</span></span>)</span> )
 ;<br/>

<a NAME="E2:46_11"/><b>then </b><i><font color="Green">E60</font></i>: 
( <span class="p1">(<span class="default"><a href="scmpds_4.html#K9">IExec</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a> ,2 <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p4">(<span class="default"><span class="p5">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p3">(<span class="default"><a href="scmpds_2.html#K14">SubFrom</a> <a href="scmp_gcd.html#K2">GBP</a> ,2,<a href="scmp_gcd.html#K3">SBP</a> ,<span class="p4">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span></span>)</span></span>)</span>,<font color="Maroon">c<sub>75</sub></font></span>)</span> <a href="scmpds_2.html#K2">.</a> <span class="p1">(<span class="default"><a href="scmp_gcd.html#K1">intpos</a> 2</span>)</span> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>75</sub></font> <a href="scmpds_2.html#K2">.</a> <span class="p2">(<span class="default"><a href="scmp_gcd.html#K1">intpos</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">c<sub>76</sub></font> <a href="nat_1.html#K1">+</a> <span class="p5">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span> <a href="xcmplx_0.html#K6">-</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>75</sub></font> <a href="scmpds_2.html#K2">.</a> <span class="p2">(<span class="default"><a href="scmp_gcd.html#K1">intpos</a> <span class="p3">(<span class="default"><font color="Maroon">c<sub>76</sub></font> <a href="nat_1.html#K1">+</a> <span class="p4">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span></span>)</span></span>)</span></span>)</span> &amp; ( for <font color="Olive">b<sub>1</sub></font> being  <a href="nat_1.html#NM1">Nat</a> st <font color="Olive">b<sub>1</sub></font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> 2 holds <br/><span class="p1">(<span class="default"><a href="scmpds_4.html#K9">IExec</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a> ,2 <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p4">(<span class="default"><span class="p5">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p3">(<span class="default"><a href="scmpds_2.html#K14">SubFrom</a> <a href="scmp_gcd.html#K2">GBP</a> ,2,<a href="scmp_gcd.html#K3">SBP</a> ,<span class="p4">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span></span>)</span></span>)</span>,<font color="Maroon">c<sub>75</sub></font></span>)</span> <a href="scmpds_2.html#K2">.</a> <span class="p1">(<span class="default"><a href="scmp_gcd.html#K1">intpos</a> <font color="Olive">b<sub>1</sub></font></span>)</span> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>75</sub></font> <a href="scmpds_2.html#K2">.</a> <span class="p1">(<span class="default"><a href="scmp_gcd.html#K1">intpos</a> <font color="Olive">b<sub>1</sub></font></span>)</span> ) )
 
<b>by </b><i><a class="txt" href="scpqsort.html#E15:46"><i><font color="Green">E55</font></i></a></i>;<br/>
<a NAME="E3:46_11"/><i><font color="Green">E61</font></i>: 
<span class="p1">(<span class="default"><a href="scmpds_4.html#K9">IExec</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a> ,2 <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p4">(<span class="default"><span class="p5">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p3">(<span class="default"><a href="scmpds_2.html#K14">SubFrom</a> <a href="scmp_gcd.html#K2">GBP</a> ,2,<a href="scmp_gcd.html#K3">SBP</a> ,<span class="p4">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span></span>)</span></span>)</span>,<font color="Maroon">c<sub>75</sub></font></span>)</span> <a href="scmpds_2.html#K2">.</a> <a href="scmp_gcd.html#K2">GBP</a>  <a href="hidden.html#R1">=</a> 0
 
<b>by </b><i><a class="txt" href="scpqsort.html#E15:46"><i><font color="Green">E55</font></i></a>, <a class="txt" href="scpqsort.html#E1:46_11"><i><font color="Green">E59</font></i></a>, <a class="ref" href="scmp_gcd.html#D2">SCMP_GCD:def 2</a></i>;<br/>
<a NAME="E4:46_11"/><b>then </b><i><font color="Green">E62</font></i>: 
 <a href="scmpds_2.html#K3">DataLoc</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="scmpds_4.html#K9">IExec</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a> ,2 <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p5">(<span class="default"><span class="p0">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p4">(<span class="default"><a href="scmpds_2.html#K14">SubFrom</a> <a href="scmp_gcd.html#K2">GBP</a> ,2,<a href="scmp_gcd.html#K3">SBP</a> ,<span class="p5">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span></span>)</span></span>)</span>,<font color="Maroon">c<sub>75</sub></font></span>)</span> <a href="scmpds_2.html#K2">.</a> <a href="scmp_gcd.html#K2">GBP</a> </span>)</span>,2 <a href="hidden.html#R1">=</a>  <a href="scmp_gcd.html#K1">intpos</a> <span class="p1">(<span class="default">0 <a href="nat_1.html#K1">+</a> 2</span>)</span>
 
<b>by </b><i><a class="ref" href="scmp_gcd.html#T5">SCMP_GCD:5</a></i>;<br/>
<a NAME="E5:46_11"/><i><font color="Green">E63</font></i>: 
<span class="p1">(<span class="default"><a href="scmpds_4.html#K9">IExec</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a> ,2 <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p4">(<span class="default"><span class="p5">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p3">(<span class="default"><a href="scmpds_2.html#K14">SubFrom</a> <a href="scmp_gcd.html#K2">GBP</a> ,2,<a href="scmp_gcd.html#K3">SBP</a> ,<span class="p4">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span></span>)</span></span>)</span>,<font color="Maroon">c<sub>75</sub></font></span>)</span> <a href="scmpds_2.html#K2">.</a> <span class="p1">(<span class="default"><a href="scmp_gcd.html#K1">intpos</a> 2</span>)</span> <a href="xxreal_0.html#R1">&lt;=</a> 0
 
<b>by </b><i><a class="txt" href="scpqsort.html#E1:46_11"><i><font color="Green">E59</font></i></a>, <a class="txt" href="scpqsort.html#E2:46_11"><i><font color="Green">E60</font></i></a>, <a class="ref" href="real_2.html#T106">REAL_2:106</a></i>;<br/>
<a NAME="E6:46_11"/>
(  <a href="scmpds_4.html#K1">Load</a> <span class="p1">(<span class="default"><a href="scmpds_2.html#K12">AddTo</a> <a href="scmp_gcd.html#K2">GBP</a> ,1,<span class="p2">(<span class="default"><a href="xcmplx_0.html#K4">-</a> 2</span>)</span></span>)</span> <a href="scmpds_6.html#R1">is_closed_on</a>  <a href="scmpds_4.html#K9">IExec</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a> ,2 <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p2">(<span class="default"><a href="scmpds_2.html#K14">SubFrom</a> <a href="scmp_gcd.html#K2">GBP</a> ,2,<a href="scmp_gcd.html#K3">SBP</a> ,<span class="p3">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span></span>)</span></span>)</span>,<font color="Maroon">c<sub>75</sub></font> &amp;  <a href="scmpds_4.html#K1">Load</a> <span class="p1">(<span class="default"><a href="scmpds_2.html#K12">AddTo</a> <a href="scmp_gcd.html#K2">GBP</a> ,1,<span class="p2">(<span class="default"><a href="xcmplx_0.html#K4">-</a> 2</span>)</span></span>)</span> <a href="scmpds_6.html#R2">is_halting_on</a>  <a href="scmpds_4.html#K9">IExec</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a> ,2 <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p2">(<span class="default"><a href="scmpds_2.html#K14">SubFrom</a> <a href="scmp_gcd.html#K2">GBP</a> ,2,<a href="scmp_gcd.html#K3">SBP</a> ,<span class="p3">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span></span>)</span></span>)</span>,<font color="Maroon">c<sub>75</sub></font> )
 
<b>by </b><i><a class="ref" href="scmpds_6.html#T34">SCMPDS_6:34</a>, <a class="ref" href="scmpds_6.html#T35">SCMPDS_6:35</a></i>;<br/>
<a NAME="E7:46_11"/><b>then </b><i><font color="Green">E64</font></i>: 
(  <a href="scmpds_6.html#K3">if&gt;0</a> <a href="scmp_gcd.html#K2">GBP</a> ,2,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a> ,2 <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p5">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span></span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p4">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a> ,4 <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p5">(<span class="default"><span class="p0">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span> <a href="scmpds_4.html#K3">';'</a> <font color="Maroon">c<sub>50</sub></font></span>)</span> <a href="scmpds_4.html#K3">';'</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><span class="p0">(<span class="default"><span class="p1">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a> ,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 3</span>)</span> <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p1">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a> ,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span> <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K2">GBP</a> ,4</span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p0">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a> ,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 2</span>)</span> <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K2">GBP</a> ,4</span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p5">(<span class="default"><a href="scmpds_2.html#K12">AddTo</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p0">(<span class="default"><span class="p1">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span>,<span class="p0">(<span class="default"><a href="xcmplx_0.html#K4">-</a> 1</span>)</span></span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p4">(<span class="default"><a href="scmpds_2.html#K12">AddTo</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p5">(<span class="default"><span class="p0">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 2</span>)</span>,1</span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p3">(<span class="default"><a href="scmpds_2.html#K12">AddTo</a> <a href="scmp_gcd.html#K2">GBP</a> ,1,2</span>)</span></span>)</span></span>)</span>,<span class="p1">(<span class="default"><a href="scmpds_4.html#K1">Load</a> <span class="p2">(<span class="default"><a href="scmpds_2.html#K12">AddTo</a> <a href="scmp_gcd.html#K2">GBP</a> ,1,<span class="p3">(<span class="default"><a href="xcmplx_0.html#K4">-</a> 2</span>)</span></span>)</span></span>)</span> <a href="scmpds_6.html#R1">is_closed_on</a>  <a href="scmpds_4.html#K9">IExec</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a> ,2 <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p2">(<span class="default"><a href="scmpds_2.html#K14">SubFrom</a> <a href="scmp_gcd.html#K2">GBP</a> ,2,<a href="scmp_gcd.html#K3">SBP</a> ,<span class="p3">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span></span>)</span></span>)</span>,<font color="Maroon">c<sub>75</sub></font> &amp;  <a href="scmpds_6.html#K3">if&gt;0</a> <a href="scmp_gcd.html#K2">GBP</a> ,2,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a> ,2 <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p5">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span></span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p4">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a> ,4 <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p5">(<span class="default"><span class="p0">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span> <a href="scmpds_4.html#K3">';'</a> <font color="Maroon">c<sub>50</sub></font></span>)</span> <a href="scmpds_4.html#K3">';'</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><span class="p0">(<span class="default"><span class="p1">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a> ,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 3</span>)</span> <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p1">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a> ,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span> <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K2">GBP</a> ,4</span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p0">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a> ,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 2</span>)</span> <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K2">GBP</a> ,4</span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p5">(<span class="default"><a href="scmpds_2.html#K12">AddTo</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p0">(<span class="default"><span class="p1">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span>,<span class="p0">(<span class="default"><a href="xcmplx_0.html#K4">-</a> 1</span>)</span></span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p4">(<span class="default"><a href="scmpds_2.html#K12">AddTo</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p5">(<span class="default"><span class="p0">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 2</span>)</span>,1</span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p3">(<span class="default"><a href="scmpds_2.html#K12">AddTo</a> <a href="scmp_gcd.html#K2">GBP</a> ,1,2</span>)</span></span>)</span></span>)</span>,<span class="p1">(<span class="default"><a href="scmpds_4.html#K1">Load</a> <span class="p2">(<span class="default"><a href="scmpds_2.html#K12">AddTo</a> <a href="scmp_gcd.html#K2">GBP</a> ,1,<span class="p3">(<span class="default"><a href="xcmplx_0.html#K4">-</a> 2</span>)</span></span>)</span></span>)</span> <a href="scmpds_6.html#R2">is_halting_on</a>  <a href="scmpds_4.html#K9">IExec</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a> ,2 <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p2">(<span class="default"><a href="scmpds_2.html#K14">SubFrom</a> <a href="scmp_gcd.html#K2">GBP</a> ,2,<a href="scmp_gcd.html#K3">SBP</a> ,<span class="p3">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span></span>)</span></span>)</span>,<font color="Maroon">c<sub>75</sub></font> )
 
<b>by </b><i><a class="txt" href="scpqsort.html#E4:46_11"><i><font color="Green">E62</font></i></a>, <a class="txt" href="scpqsort.html#E5:46_11"><i><font color="Green">E63</font></i></a>, <a class="ref" href="scmpds_6.html#T83">SCMPDS_6:83</a></i>;<br/>
<b>set </b><font color="Maroon">c<sub>79</sub></font> =  <a href="scmpds_2.html#K12">AddTo</a> <a href="scmp_gcd.html#K2">GBP</a> ,1,<span class="p1">(<span class="default"><a href="xcmplx_0.html#K4">-</a> 2</span>)</span>;<br/>
<b>set </b><font color="Maroon">c<sub>80</sub></font> =  <a href="scmpds_5.html#K1">Initialized</a> <span class="p1">(<span class="default"><a href="scmpds_4.html#K9">IExec</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a> ,2 <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p4">(<span class="default"><span class="p5">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p3">(<span class="default"><a href="scmpds_2.html#K14">SubFrom</a> <a href="scmp_gcd.html#K2">GBP</a> ,2,<a href="scmp_gcd.html#K3">SBP</a> ,<span class="p4">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span></span>)</span></span>)</span>,<font color="Maroon">c<sub>75</sub></font></span>)</span>;<br/>
<div><i><font color="Green">E65</font></i>: <a class="txt" onclick="hs2(this)" href="javascript:()" title="46_11_1"><b>now </b></a><div class="add"><b>let </b><font color="Maroon">c<sub>81</sub></font> be    <a href="scmpds_2.html#M1">Int_position</a> ;<br/><b>thus </b><span class="p1">(<span class="default"><a href="scmpds_4.html#K9">IExec</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a> ,2 <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p5">(<span class="default"><span class="p0">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p4">(<span class="default"><a href="scmpds_2.html#K14">SubFrom</a> <a href="scmp_gcd.html#K2">GBP</a> ,2,<a href="scmp_gcd.html#K3">SBP</a> ,<span class="p5">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span></span>)</span></span>)</span> <a href="scmpds_4.html#K3">';'</a> <span class="p3">(<span class="default"><a href="scmpds_6.html#K3">if&gt;0</a> <a href="scmp_gcd.html#K2">GBP</a> ,2,<span class="p4">(<span class="default"><span class="p5">(<span class="default"><span class="p0">(<span class="default"><span class="p1">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a> ,2 <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p2">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span></span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p1">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a> ,4 <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span> <a href="scmpds_4.html#K3">';'</a> <font color="Maroon">c<sub>50</sub></font></span>)</span> <a href="scmpds_4.html#K3">';'</a> <span class="p5">(<span class="default"><span class="p0">(<span class="default"><span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a> ,<span class="p5">(<span class="default"><span class="p0">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 3</span>)</span> <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p5">(<span class="default"><span class="p0">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p4">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a> ,<span class="p5">(<span class="default"><span class="p0">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span> <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K2">GBP</a> ,4</span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p3">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a> ,<span class="p4">(<span class="default"><span class="p5">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 2</span>)</span> <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K2">GBP</a> ,4</span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p2">(<span class="default"><a href="scmpds_2.html#K12">AddTo</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span>,<span class="p3">(<span class="default"><a href="xcmplx_0.html#K4">-</a> 1</span>)</span></span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p1">(<span class="default"><a href="scmpds_2.html#K12">AddTo</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 2</span>)</span>,1</span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p0">(<span class="default"><a href="scmpds_2.html#K12">AddTo</a> <a href="scmp_gcd.html#K2">GBP</a> ,1,2</span>)</span></span>)</span></span>)</span>,<span class="p4">(<span class="default"><a href="scmpds_4.html#K1">Load</a> <span class="p5">(<span class="default"><a href="scmpds_2.html#K12">AddTo</a> <a href="scmp_gcd.html#K2">GBP</a> ,1,<span class="p0">(<span class="default"><a href="xcmplx_0.html#K4">-</a> 2</span>)</span></span>)</span></span>)</span></span>)</span></span>)</span>,<font color="Maroon">c<sub>75</sub></font></span>)</span> <a href="scmpds_2.html#K2">.</a> <font color="Maroon">c<sub>81</sub></font> = 
<span class="p1">(<span class="default"><a href="scmpds_4.html#K9">IExec</a> <span class="p2">(<span class="default"><a href="scmpds_6.html#K3">if&gt;0</a> <a href="scmp_gcd.html#K2">GBP</a> ,2,<span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><span class="p0">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a> ,2 <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p1">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span></span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p0">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a> ,4 <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span> <a href="scmpds_4.html#K3">';'</a> <font color="Maroon">c<sub>50</sub></font></span>)</span> <a href="scmpds_4.html#K3">';'</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><span class="p0">(<span class="default"><span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a> ,<span class="p4">(<span class="default"><span class="p5">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 3</span>)</span> <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p4">(<span class="default"><span class="p5">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p3">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a> ,<span class="p4">(<span class="default"><span class="p5">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span> <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K2">GBP</a> ,4</span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p2">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a> ,<span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 2</span>)</span> <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K2">GBP</a> ,4</span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p1">(<span class="default"><a href="scmpds_2.html#K12">AddTo</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span>,<span class="p2">(<span class="default"><a href="xcmplx_0.html#K4">-</a> 1</span>)</span></span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p0">(<span class="default"><a href="scmpds_2.html#K12">AddTo</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 2</span>)</span>,1</span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p5">(<span class="default"><a href="scmpds_2.html#K12">AddTo</a> <a href="scmp_gcd.html#K2">GBP</a> ,1,2</span>)</span></span>)</span></span>)</span>,<span class="p3">(<span class="default"><a href="scmpds_4.html#K1">Load</a> <span class="p4">(<span class="default"><a href="scmpds_2.html#K12">AddTo</a> <a href="scmp_gcd.html#K2">GBP</a> ,1,<span class="p5">(<span class="default"><a href="xcmplx_0.html#K4">-</a> 2</span>)</span></span>)</span></span>)</span></span>)</span>,<span class="p2">(<span class="default"><a href="scmpds_4.html#K9">IExec</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a> ,2 <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p5">(<span class="default"><span class="p0">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p4">(<span class="default"><a href="scmpds_2.html#K14">SubFrom</a> <a href="scmp_gcd.html#K2">GBP</a> ,2,<a href="scmp_gcd.html#K3">SBP</a> ,<span class="p5">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span></span>)</span></span>)</span>,<font color="Maroon">c<sub>75</sub></font></span>)</span></span>)</span> <a href="scmpds_2.html#K2">.</a> <font color="Maroon">c<sub>81</sub></font>
<b>by </b><i><a class="txt" href="scpqsort.html#E7:46_11"><i><font color="Green">E64</font></i></a>, <a class="ref" href="scpisort.html#T8">SCPISORT:8</a></i>
<br/>.= 
<span class="p1">(<span class="default"><a href="scmpds_4.html#K9">IExec</a> <span class="p2">(<span class="default"><a href="scmpds_4.html#K1">Load</a> <span class="p3">(<span class="default"><a href="scmpds_2.html#K12">AddTo</a> <a href="scmp_gcd.html#K2">GBP</a> ,1,<span class="p4">(<span class="default"><a href="xcmplx_0.html#K4">-</a> 2</span>)</span></span>)</span></span>)</span>,<span class="p2">(<span class="default"><a href="scmpds_4.html#K9">IExec</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a> ,2 <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p5">(<span class="default"><span class="p0">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p4">(<span class="default"><a href="scmpds_2.html#K14">SubFrom</a> <a href="scmp_gcd.html#K2">GBP</a> ,2,<a href="scmp_gcd.html#K3">SBP</a> ,<span class="p5">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span></span>)</span></span>)</span>,<font color="Maroon">c<sub>75</sub></font></span>)</span></span>)</span> <a href="scmpds_2.html#K2">.</a> <font color="Maroon">c<sub>81</sub></font>
<b>by </b><i><a class="txt" href="scpqsort.html#E4:46_11"><i><font color="Green">E62</font></i></a>, <a class="txt" href="scpqsort.html#E5:46_11"><i><font color="Green">E63</font></i></a>, <a class="ref" href="scmpds_6.html#T88">SCMPDS_6:88</a></i>
<br/>.= 
<span class="p1">(<span class="default"><a href="ami_1.html#K4">Exec</a> <span class="p2">(<span class="default"><a href="scmpds_2.html#K12">AddTo</a> <a href="scmp_gcd.html#K2">GBP</a> ,1,<span class="p3">(<span class="default"><a href="xcmplx_0.html#K4">-</a> 2</span>)</span></span>)</span>,<span class="p2">(<span class="default"><a href="scmpds_5.html#K1">Initialized</a> <span class="p3">(<span class="default"><a href="scmpds_4.html#K9">IExec</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a> ,2 <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p0">(<span class="default"><span class="p1">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p5">(<span class="default"><a href="scmpds_2.html#K14">SubFrom</a> <a href="scmp_gcd.html#K2">GBP</a> ,2,<a href="scmp_gcd.html#K3">SBP</a> ,<span class="p0">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span></span>)</span></span>)</span>,<font color="Maroon">c<sub>75</sub></font></span>)</span></span>)</span></span>)</span> <a href="scmpds_2.html#K2">.</a> <font color="Maroon">c<sub>81</sub></font>
<b>by </b><i><a class="ref" href="scmpds_5.html#T45">SCMPDS_5:45</a></i>
;<br/></div><b>end;</b></div>
<a NAME="E9:46_11"/><i><font color="Green">E66</font></i>: 
<span class="p1">(<span class="default"><a href="scmpds_4.html#K9">IExec</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a> ,2 <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p4">(<span class="default"><span class="p5">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p3">(<span class="default"><a href="scmpds_2.html#K14">SubFrom</a> <a href="scmp_gcd.html#K2">GBP</a> ,2,<a href="scmp_gcd.html#K3">SBP</a> ,<span class="p4">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span></span>)</span></span>)</span>,<font color="Maroon">c<sub>75</sub></font></span>)</span> <a href="scmpds_2.html#K2">.</a> <span class="p1">(<span class="default"><a href="scmp_gcd.html#K1">intpos</a> 1</span>)</span> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>76</sub></font>
 
<b>by </b><i><a class="txt" href="scpqsort.html#E15:46"><i><font color="Green">E55</font></i></a>, <a class="txt" href="scpqsort.html#E1:46_11"><i><font color="Green">E59</font></i></a>, <a class="ref" href="scmp_gcd.html#D3">SCMP_GCD:def 3</a></i>;<br/>
<a NAME="E10:46_11"/>
<span class="p1">(<span class="default"><a href="scmpds_5.html#K1">Initialized</a> <span class="p2">(<span class="default"><a href="scmpds_4.html#K9">IExec</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a> ,2 <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p5">(<span class="default"><span class="p0">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p4">(<span class="default"><a href="scmpds_2.html#K14">SubFrom</a> <a href="scmp_gcd.html#K2">GBP</a> ,2,<a href="scmp_gcd.html#K3">SBP</a> ,<span class="p5">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span></span>)</span></span>)</span>,<font color="Maroon">c<sub>75</sub></font></span>)</span></span>)</span> <a href="scmpds_2.html#K2">.</a> <a href="scmp_gcd.html#K2">GBP</a>  <a href="hidden.html#R1">=</a> 0
 
<b>by </b><i><a class="txt" href="scpqsort.html#E3:46_11"><i><font color="Green">E61</font></i></a>, <a class="ref" href="scmpds_5.html#T40">SCMPDS_5:40</a></i>;<br/>
<a NAME="E11:46_11"/><b>then </b><i><font color="Green">E67</font></i>: 
 <a href="scmpds_2.html#K3">DataLoc</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="scmpds_5.html#K1">Initialized</a> <span class="p3">(<span class="default"><a href="scmpds_4.html#K9">IExec</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a> ,2 <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p0">(<span class="default"><span class="p1">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p5">(<span class="default"><a href="scmpds_2.html#K14">SubFrom</a> <a href="scmp_gcd.html#K2">GBP</a> ,2,<a href="scmp_gcd.html#K3">SBP</a> ,<span class="p0">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span></span>)</span></span>)</span>,<font color="Maroon">c<sub>75</sub></font></span>)</span></span>)</span> <a href="scmpds_2.html#K2">.</a> <a href="scmp_gcd.html#K2">GBP</a> </span>)</span>,1 <a href="hidden.html#R1">=</a>  <a href="scmp_gcd.html#K1">intpos</a> <span class="p1">(<span class="default">0 <a href="nat_1.html#K1">+</a> 1</span>)</span>
 
<b>by </b><i><a class="ref" href="scmp_gcd.html#T5">SCMP_GCD:5</a></i>;<br/>
<div><i><font color="Green">E68</font></i>: <a class="txt" onclick="hs2(this)" href="javascript:()" title="46_11_2"><b>now </b></a><div class="add"><b>let </b><font color="Maroon">c<sub>81</sub></font> be   <a href="nat_1.html#NM1">Nat</a>;<br/><b>assume </b><a NAME="E1:46_11_2"/>
<font color="Maroon">c<sub>81</sub></font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> 1
 ;<br/><a NAME="E2:46_11_2"/><b>then </b><i><font color="Green">E69</font></i>: 
 <a href="scmp_gcd.html#K1">intpos</a> <font color="Maroon">c<sub>81</sub></font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a>  <a href="scmpds_2.html#K3">DataLoc</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="scmpds_5.html#K1">Initialized</a> <span class="p3">(<span class="default"><a href="scmpds_4.html#K9">IExec</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a> ,2 <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p0">(<span class="default"><span class="p1">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p5">(<span class="default"><a href="scmpds_2.html#K14">SubFrom</a> <a href="scmp_gcd.html#K2">GBP</a> ,2,<a href="scmp_gcd.html#K3">SBP</a> ,<span class="p0">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span></span>)</span></span>)</span>,<font color="Maroon">c<sub>75</sub></font></span>)</span></span>)</span> <a href="scmpds_2.html#K2">.</a> <a href="scmp_gcd.html#K2">GBP</a> </span>)</span>,1
 <b>by </b><i><a class="txt" href="scpqsort.html#E11:46_11"><i><font color="Green">E67</font></i></a>, <a class="ref" href="scmp_gcd.html#T4">SCMP_GCD:4</a></i>;<br/><b>thus </b><span class="p1">(<span class="default"><a href="scmpds_4.html#K9">IExec</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a> ,2 <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p5">(<span class="default"><span class="p0">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p4">(<span class="default"><a href="scmpds_2.html#K14">SubFrom</a> <a href="scmp_gcd.html#K2">GBP</a> ,2,<a href="scmp_gcd.html#K3">SBP</a> ,<span class="p5">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span></span>)</span></span>)</span> <a href="scmpds_4.html#K3">';'</a> <span class="p3">(<span class="default"><a href="scmpds_6.html#K3">if&gt;0</a> <a href="scmp_gcd.html#K2">GBP</a> ,2,<span class="p4">(<span class="default"><span class="p5">(<span class="default"><span class="p0">(<span class="default"><span class="p1">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a> ,2 <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p2">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span></span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p1">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a> ,4 <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span> <a href="scmpds_4.html#K3">';'</a> <font color="Maroon">c<sub>50</sub></font></span>)</span> <a href="scmpds_4.html#K3">';'</a> <span class="p5">(<span class="default"><span class="p0">(<span class="default"><span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a> ,<span class="p5">(<span class="default"><span class="p0">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 3</span>)</span> <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p5">(<span class="default"><span class="p0">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p4">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a> ,<span class="p5">(<span class="default"><span class="p0">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span> <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K2">GBP</a> ,4</span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p3">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a> ,<span class="p4">(<span class="default"><span class="p5">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 2</span>)</span> <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K2">GBP</a> ,4</span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p2">(<span class="default"><a href="scmpds_2.html#K12">AddTo</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span>,<span class="p3">(<span class="default"><a href="xcmplx_0.html#K4">-</a> 1</span>)</span></span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p1">(<span class="default"><a href="scmpds_2.html#K12">AddTo</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 2</span>)</span>,1</span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p0">(<span class="default"><a href="scmpds_2.html#K12">AddTo</a> <a href="scmp_gcd.html#K2">GBP</a> ,1,2</span>)</span></span>)</span></span>)</span>,<span class="p4">(<span class="default"><a href="scmpds_4.html#K1">Load</a> <span class="p5">(<span class="default"><a href="scmpds_2.html#K12">AddTo</a> <a href="scmp_gcd.html#K2">GBP</a> ,1,<span class="p0">(<span class="default"><a href="xcmplx_0.html#K4">-</a> 2</span>)</span></span>)</span></span>)</span></span>)</span></span>)</span>,<font color="Maroon">c<sub>75</sub></font></span>)</span> <a href="scmpds_2.html#K2">.</a> <span class="p1">(<span class="default"><a href="scmp_gcd.html#K1">intpos</a> <font color="Maroon">c<sub>81</sub></font></span>)</span> = 
<span class="p1">(<span class="default"><a href="ami_1.html#K4">Exec</a> <span class="p2">(<span class="default"><a href="scmpds_2.html#K12">AddTo</a> <a href="scmp_gcd.html#K2">GBP</a> ,1,<span class="p3">(<span class="default"><a href="xcmplx_0.html#K4">-</a> 2</span>)</span></span>)</span>,<span class="p2">(<span class="default"><a href="scmpds_5.html#K1">Initialized</a> <span class="p3">(<span class="default"><a href="scmpds_4.html#K9">IExec</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a> ,2 <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p0">(<span class="default"><span class="p1">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p5">(<span class="default"><a href="scmpds_2.html#K14">SubFrom</a> <a href="scmp_gcd.html#K2">GBP</a> ,2,<a href="scmp_gcd.html#K3">SBP</a> ,<span class="p0">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span></span>)</span></span>)</span>,<font color="Maroon">c<sub>75</sub></font></span>)</span></span>)</span></span>)</span> <a href="scmpds_2.html#K2">.</a> <span class="p1">(<span class="default"><a href="scmp_gcd.html#K1">intpos</a> <font color="Maroon">c<sub>81</sub></font></span>)</span>
<b>by </b><i><a class="txt" href="scpqsort.html#E8:46_11"><i><font color="Green">E65</font></i></a></i>
<br/>.= 
<span class="p1">(<span class="default"><a href="scmpds_5.html#K1">Initialized</a> <span class="p2">(<span class="default"><a href="scmpds_4.html#K9">IExec</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a> ,2 <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p5">(<span class="default"><span class="p0">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p4">(<span class="default"><a href="scmpds_2.html#K14">SubFrom</a> <a href="scmp_gcd.html#K2">GBP</a> ,2,<a href="scmp_gcd.html#K3">SBP</a> ,<span class="p5">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span></span>)</span></span>)</span>,<font color="Maroon">c<sub>75</sub></font></span>)</span></span>)</span> <a href="scmpds_2.html#K2">.</a> <span class="p1">(<span class="default"><a href="scmp_gcd.html#K1">intpos</a> <font color="Maroon">c<sub>81</sub></font></span>)</span>
<b>by </b><i><a class="txt" href="scpqsort.html#E2:46_11_2"><i><font color="Green">E69</font></i></a>, <a class="ref" href="scmpds_2.html#T60">SCMPDS_2:60</a></i>
<br/>.= 
<span class="p1">(<span class="default"><a href="scmpds_4.html#K9">IExec</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a> ,2 <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p4">(<span class="default"><span class="p5">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p3">(<span class="default"><a href="scmpds_2.html#K14">SubFrom</a> <a href="scmp_gcd.html#K2">GBP</a> ,2,<a href="scmp_gcd.html#K3">SBP</a> ,<span class="p4">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span></span>)</span></span>)</span>,<font color="Maroon">c<sub>75</sub></font></span>)</span> <a href="scmpds_2.html#K2">.</a> <span class="p1">(<span class="default"><a href="scmp_gcd.html#K1">intpos</a> <font color="Maroon">c<sub>81</sub></font></span>)</span>
<b>by </b><i><a class="ref" href="scmpds_5.html#T40">SCMPDS_5:40</a></i>
;<br/></div><b>end;</b></div>
<b>hence </b><a NAME="E13:46_11"/>
<span class="p1">(<span class="default"><a href="scmpds_4.html#K9">IExec</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a> ,2 <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p5">(<span class="default"><span class="p0">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p4">(<span class="default"><a href="scmpds_2.html#K14">SubFrom</a> <a href="scmp_gcd.html#K2">GBP</a> ,2,<a href="scmp_gcd.html#K3">SBP</a> ,<span class="p5">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span></span>)</span></span>)</span> <a href="scmpds_4.html#K3">';'</a> <span class="p3">(<span class="default"><a href="scmpds_6.html#K3">if&gt;0</a> <a href="scmp_gcd.html#K2">GBP</a> ,2,<span class="p4">(<span class="default"><span class="p5">(<span class="default"><span class="p0">(<span class="default"><span class="p1">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a> ,2 <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p2">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span></span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p1">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a> ,4 <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span> <a href="scmpds_4.html#K3">';'</a> <font color="Maroon">c<sub>50</sub></font></span>)</span> <a href="scmpds_4.html#K3">';'</a> <span class="p5">(<span class="default"><span class="p0">(<span class="default"><span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a> ,<span class="p5">(<span class="default"><span class="p0">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 3</span>)</span> <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p5">(<span class="default"><span class="p0">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p4">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a> ,<span class="p5">(<span class="default"><span class="p0">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span> <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K2">GBP</a> ,4</span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p3">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a> ,<span class="p4">(<span class="default"><span class="p5">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 2</span>)</span> <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K2">GBP</a> ,4</span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p2">(<span class="default"><a href="scmpds_2.html#K12">AddTo</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span>,<span class="p3">(<span class="default"><a href="xcmplx_0.html#K4">-</a> 1</span>)</span></span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p1">(<span class="default"><a href="scmpds_2.html#K12">AddTo</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 2</span>)</span>,1</span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p0">(<span class="default"><a href="scmpds_2.html#K12">AddTo</a> <a href="scmp_gcd.html#K2">GBP</a> ,1,2</span>)</span></span>)</span></span>)</span>,<span class="p4">(<span class="default"><a href="scmpds_4.html#K1">Load</a> <span class="p5">(<span class="default"><a href="scmpds_2.html#K12">AddTo</a> <a href="scmp_gcd.html#K2">GBP</a> ,1,<span class="p0">(<span class="default"><a href="xcmplx_0.html#K4">-</a> 2</span>)</span></span>)</span></span>)</span></span>)</span></span>)</span>,<font color="Maroon">c<sub>75</sub></font></span>)</span> <a href="scmpds_2.html#K2">.</a> <a href="scmp_gcd.html#K2">GBP</a>  <a href="hidden.html#R1">=</a> 0
 <b>by </b><i><a class="txt" href="scpqsort.html#E3:46_11"><i><font color="Green">E61</font></i></a>, <a class="ref" href="scmp_gcd.html#D2">SCMP_GCD:def 2</a></i>;<br/>

<b>thus </b><span class="p1">(<span class="default"><a href="scmpds_4.html#K9">IExec</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a> ,2 <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p5">(<span class="default"><span class="p0">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p4">(<span class="default"><a href="scmpds_2.html#K14">SubFrom</a> <a href="scmp_gcd.html#K2">GBP</a> ,2,<a href="scmp_gcd.html#K3">SBP</a> ,<span class="p5">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span></span>)</span></span>)</span> <a href="scmpds_4.html#K3">';'</a> <span class="p3">(<span class="default"><a href="scmpds_6.html#K3">if&gt;0</a> <a href="scmp_gcd.html#K2">GBP</a> ,2,<span class="p4">(<span class="default"><span class="p5">(<span class="default"><span class="p0">(<span class="default"><span class="p1">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a> ,2 <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p2">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span></span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p1">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a> ,4 <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span> <a href="scmpds_4.html#K3">';'</a> <font color="Maroon">c<sub>50</sub></font></span>)</span> <a href="scmpds_4.html#K3">';'</a> <span class="p5">(<span class="default"><span class="p0">(<span class="default"><span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a> ,<span class="p5">(<span class="default"><span class="p0">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 3</span>)</span> <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p5">(<span class="default"><span class="p0">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p4">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a> ,<span class="p5">(<span class="default"><span class="p0">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span> <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K2">GBP</a> ,4</span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p3">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a> ,<span class="p4">(<span class="default"><span class="p5">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 2</span>)</span> <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K2">GBP</a> ,4</span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p2">(<span class="default"><a href="scmpds_2.html#K12">AddTo</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span>,<span class="p3">(<span class="default"><a href="xcmplx_0.html#K4">-</a> 1</span>)</span></span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p1">(<span class="default"><a href="scmpds_2.html#K12">AddTo</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 2</span>)</span>,1</span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p0">(<span class="default"><a href="scmpds_2.html#K12">AddTo</a> <a href="scmp_gcd.html#K2">GBP</a> ,1,2</span>)</span></span>)</span></span>)</span>,<span class="p4">(<span class="default"><a href="scmpds_4.html#K1">Load</a> <span class="p5">(<span class="default"><a href="scmpds_2.html#K12">AddTo</a> <a href="scmp_gcd.html#K2">GBP</a> ,1,<span class="p0">(<span class="default"><a href="xcmplx_0.html#K4">-</a> 2</span>)</span></span>)</span></span>)</span></span>)</span></span>)</span>,<font color="Maroon">c<sub>75</sub></font></span>)</span> <a href="scmpds_2.html#K2">.</a> <span class="p1">(<span class="default"><a href="scmp_gcd.html#K1">intpos</a> 1</span>)</span> = 
<span class="p1">(<span class="default"><a href="ami_1.html#K4">Exec</a> <span class="p2">(<span class="default"><a href="scmpds_2.html#K12">AddTo</a> <a href="scmp_gcd.html#K2">GBP</a> ,1,<span class="p3">(<span class="default"><a href="xcmplx_0.html#K4">-</a> 2</span>)</span></span>)</span>,<span class="p2">(<span class="default"><a href="scmpds_5.html#K1">Initialized</a> <span class="p3">(<span class="default"><a href="scmpds_4.html#K9">IExec</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a> ,2 <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p0">(<span class="default"><span class="p1">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p5">(<span class="default"><a href="scmpds_2.html#K14">SubFrom</a> <a href="scmp_gcd.html#K2">GBP</a> ,2,<a href="scmp_gcd.html#K3">SBP</a> ,<span class="p0">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span></span>)</span></span>)</span>,<font color="Maroon">c<sub>75</sub></font></span>)</span></span>)</span></span>)</span> <a href="scmpds_2.html#K2">.</a> <span class="p1">(<span class="default"><a href="scmp_gcd.html#K1">intpos</a> 1</span>)</span>
<b>by </b><i><a class="txt" href="scpqsort.html#E8:46_11"><i><font color="Green">E65</font></i></a></i>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="scmpds_5.html#K1">Initialized</a> <span class="p3">(<span class="default"><a href="scmpds_4.html#K9">IExec</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a> ,2 <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p0">(<span class="default"><span class="p1">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p5">(<span class="default"><a href="scmpds_2.html#K14">SubFrom</a> <a href="scmp_gcd.html#K2">GBP</a> ,2,<a href="scmp_gcd.html#K3">SBP</a> ,<span class="p0">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span></span>)</span></span>)</span>,<font color="Maroon">c<sub>75</sub></font></span>)</span></span>)</span> <a href="scmpds_2.html#K2">.</a> <span class="p2">(<span class="default"><a href="scmp_gcd.html#K1">intpos</a> 1</span>)</span></span>)</span> <a href="xcmplx_0.html#K2">+</a> <span class="p1">(<span class="default"><a href="xcmplx_0.html#K4">-</a> 2</span>)</span>
<b>by </b><i><a class="txt" href="scpqsort.html#E11:46_11"><i><font color="Green">E67</font></i></a>, <a class="ref" href="scmpds_2.html#T60">SCMPDS_2:60</a></i>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="scmpds_5.html#K1">Initialized</a> <span class="p3">(<span class="default"><a href="scmpds_4.html#K9">IExec</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a> ,2 <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p0">(<span class="default"><span class="p1">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p5">(<span class="default"><a href="scmpds_2.html#K14">SubFrom</a> <a href="scmp_gcd.html#K2">GBP</a> ,2,<a href="scmp_gcd.html#K3">SBP</a> ,<span class="p0">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span></span>)</span></span>)</span>,<font color="Maroon">c<sub>75</sub></font></span>)</span></span>)</span> <a href="scmpds_2.html#K2">.</a> <span class="p2">(<span class="default"><a href="scmp_gcd.html#K1">intpos</a> 1</span>)</span></span>)</span> <a href="xcmplx_0.html#K6">-</a> 2

<br/>.= 
<font color="Maroon">c<sub>76</sub></font> <a href="xcmplx_0.html#K6">-</a> 2
<b>by </b><i><a class="txt" href="scpqsort.html#E9:46_11"><i><font color="Green">E66</font></i></a>, <a class="ref" href="scmpds_5.html#T40">SCMPDS_5:40</a></i>
;<br/>

<div><b>hereby </b>
<div class="add"><b>let </b><font color="Maroon">c<sub>81</sub></font> be   <a href="nat_1.html#NM1">Nat</a>;<br/><b>assume </b><a NAME="E1:46_11_4"/>
( 1 <a href="xxreal_0.html#R1">&lt;=</a> <font color="Maroon">c<sub>81</sub></font> &amp; <font color="Maroon">c<sub>81</sub></font> <a href="xxreal_0.html#NR3" target="_self">&lt;</a> <font color="Maroon">c<sub>76</sub></font> )
 ;<br/><a NAME="E2:46_11_4"/><b>then </b>
<span class="p1">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>81</sub></font> <a href="xxreal_0.html#NR2" target="_self">&gt;=</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 1
 <b>by </b><i><a class="ref" href="xreal_1.html#T8">XREAL_1:8</a></i>;<br/><a NAME="E3:46_11_4"/><b>then </b><i><font color="Green">E69</font></i>: 
<span class="p1">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>81</sub></font> <a href="xxreal_0.html#NR2" target="_self">&gt;=</a> 8
 <b>by </b><i><a class="txt" href="scpqsort.html#E9:46"><i><font color="Green">E49</font></i></a>, <a class="ref" href="xreal_1.html#T2">XREAL_1:2</a></i>;<br/><a NAME="E4:46_11_4"/><b>then </b><i><font color="Green">E70</font></i>: 
<span class="p1">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>81</sub></font> <a href="xxreal_0.html#NR4" target="_self">&gt;</a> 2
 <b>by </b><i><a class="ref" href="xreal_1.html#T2">XREAL_1:2</a></i>;<br/><a NAME="E5:46_11_4"/>
<span class="p1">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>81</sub></font> <a href="xxreal_0.html#NR4" target="_self">&gt;</a> 1
 <b>by </b><i><a class="txt" href="scpqsort.html#E3:46_11_4"><i><font color="Green">E69</font></i></a>, <a class="ref" href="xreal_1.html#T2">XREAL_1:2</a></i>;<br/><b>hence </b><span class="p1">(<span class="default"><a href="scmpds_4.html#K9">IExec</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a> ,2 <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p5">(<span class="default"><span class="p0">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p4">(<span class="default"><a href="scmpds_2.html#K14">SubFrom</a> <a href="scmp_gcd.html#K2">GBP</a> ,2,<a href="scmp_gcd.html#K3">SBP</a> ,<span class="p5">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span></span>)</span></span>)</span> <a href="scmpds_4.html#K3">';'</a> <span class="p3">(<span class="default"><a href="scmpds_6.html#K3">if&gt;0</a> <a href="scmp_gcd.html#K2">GBP</a> ,2,<span class="p4">(<span class="default"><span class="p5">(<span class="default"><span class="p0">(<span class="default"><span class="p1">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a> ,2 <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p2">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span></span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p1">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a> ,4 <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span> <a href="scmpds_4.html#K3">';'</a> <font color="Maroon">c<sub>50</sub></font></span>)</span> <a href="scmpds_4.html#K3">';'</a> <span class="p5">(<span class="default"><span class="p0">(<span class="default"><span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a> ,<span class="p5">(<span class="default"><span class="p0">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 3</span>)</span> <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p5">(<span class="default"><span class="p0">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p4">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a> ,<span class="p5">(<span class="default"><span class="p0">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span> <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K2">GBP</a> ,4</span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p3">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a> ,<span class="p4">(<span class="default"><span class="p5">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 2</span>)</span> <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K2">GBP</a> ,4</span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p2">(<span class="default"><a href="scmpds_2.html#K12">AddTo</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span>,<span class="p3">(<span class="default"><a href="xcmplx_0.html#K4">-</a> 1</span>)</span></span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p1">(<span class="default"><a href="scmpds_2.html#K12">AddTo</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 2</span>)</span>,1</span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p0">(<span class="default"><a href="scmpds_2.html#K12">AddTo</a> <a href="scmp_gcd.html#K2">GBP</a> ,1,2</span>)</span></span>)</span></span>)</span>,<span class="p4">(<span class="default"><a href="scmpds_4.html#K1">Load</a> <span class="p5">(<span class="default"><a href="scmpds_2.html#K12">AddTo</a> <a href="scmp_gcd.html#K2">GBP</a> ,1,<span class="p0">(<span class="default"><a href="xcmplx_0.html#K4">-</a> 2</span>)</span></span>)</span></span>)</span></span>)</span></span>)</span>,<font color="Maroon">c<sub>75</sub></font></span>)</span> <a href="scmpds_2.html#K2">.</a> <span class="p1">(<span class="default"><a href="scmp_gcd.html#K1">intpos</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>81</sub></font></span>)</span></span>)</span> = 
<span class="p1">(<span class="default"><a href="scmpds_4.html#K9">IExec</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a> ,2 <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p4">(<span class="default"><span class="p5">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p3">(<span class="default"><a href="scmpds_2.html#K14">SubFrom</a> <a href="scmp_gcd.html#K2">GBP</a> ,2,<a href="scmp_gcd.html#K3">SBP</a> ,<span class="p4">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span></span>)</span></span>)</span>,<font color="Maroon">c<sub>75</sub></font></span>)</span> <a href="scmpds_2.html#K2">.</a> <span class="p1">(<span class="default"><a href="scmp_gcd.html#K1">intpos</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>81</sub></font></span>)</span></span>)</span>
<b>by </b><i><a class="txt" href="scpqsort.html#E12:46_11"><i><font color="Green">E68</font></i></a></i>
<br/>.= 
<font color="Maroon">c<sub>75</sub></font> <a href="scmpds_2.html#K2">.</a> <span class="p1">(<span class="default"><a href="scmp_gcd.html#K1">intpos</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>81</sub></font></span>)</span></span>)</span>
<b>by </b><i><a class="txt" href="scpqsort.html#E15:46"><i><font color="Green">E55</font></i></a>, <a class="txt" href="scpqsort.html#E1:46_11"><i><font color="Green">E59</font></i></a>, <a class="txt" href="scpqsort.html#E4:46_11_4"><i><font color="Green">E70</font></i></a></i>
;<br/><br/></div>
<b>end;</b></div>

<div><b>hereby </b>
<div class="add"><b>let </b><font color="Maroon">c<sub>81</sub></font> be   <a href="nat_1.html#NM1">Nat</a>;<br/><b>assume </b><a NAME="E1:46_11_5"/>
( 1 <a href="xxreal_0.html#R1">&lt;=</a> <font color="Maroon">c<sub>81</sub></font> &amp; <font color="Maroon">c<sub>81</sub></font> <a href="xxreal_0.html#R1">&lt;=</a> <font color="Maroon">c<sub>49</sub></font> )
 ;<br/><a NAME="E2:46_11_5"/><b>then </b><i><font color="Green">E69</font></i>: 
<font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>81</sub></font> <a href="xxreal_0.html#NR2" target="_self">&gt;=</a> <font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> 1
 <b>by </b><i><a class="ref" href="xreal_1.html#T8">XREAL_1:8</a></i>;<br/><a NAME="E3:46_11_5"/>
<font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> 1 <a href="xxreal_0.html#NR2" target="_self">&gt;=</a> 7 <a href="nat_1.html#K1">+</a> 1
 <b>by </b><i><a class="txt" href="scpqsort.html#E5:46"><i><font color="Green">E46</font></i></a>, <a class="ref" href="xreal_1.html#T8">XREAL_1:8</a></i>;<br/><a NAME="E4:46_11_5"/><b>then </b><i><font color="Green">E70</font></i>: 
<font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>81</sub></font> <a href="xxreal_0.html#NR2" target="_self">&gt;=</a> 8
 <b>by </b><i><a class="txt" href="scpqsort.html#E2:46_11_5"><i><font color="Green">E69</font></i></a>, <a class="ref" href="xreal_1.html#T2">XREAL_1:2</a></i>;<br/><a NAME="E5:46_11_5"/><b>then </b><i><font color="Green">E71</font></i>: 
<font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>81</sub></font> <a href="xxreal_0.html#NR4" target="_self">&gt;</a> 2
 <b>by </b><i><a class="ref" href="xreal_1.html#T2">XREAL_1:2</a></i>;<br/><a NAME="E6:46_11_5"/>
<font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>81</sub></font> <a href="xxreal_0.html#NR4" target="_self">&gt;</a> 1
 <b>by </b><i><a class="txt" href="scpqsort.html#E4:46_11_5"><i><font color="Green">E70</font></i></a>, <a class="ref" href="xreal_1.html#T2">XREAL_1:2</a></i>;<br/><b>hence </b><span class="p1">(<span class="default"><a href="scmpds_4.html#K9">IExec</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a> ,2 <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p5">(<span class="default"><span class="p0">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p4">(<span class="default"><a href="scmpds_2.html#K14">SubFrom</a> <a href="scmp_gcd.html#K2">GBP</a> ,2,<a href="scmp_gcd.html#K3">SBP</a> ,<span class="p5">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span></span>)</span></span>)</span> <a href="scmpds_4.html#K3">';'</a> <span class="p3">(<span class="default"><a href="scmpds_6.html#K3">if&gt;0</a> <a href="scmp_gcd.html#K2">GBP</a> ,2,<span class="p4">(<span class="default"><span class="p5">(<span class="default"><span class="p0">(<span class="default"><span class="p1">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a> ,2 <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p2">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span></span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p1">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a> ,4 <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span> <a href="scmpds_4.html#K3">';'</a> <font color="Maroon">c<sub>50</sub></font></span>)</span> <a href="scmpds_4.html#K3">';'</a> <span class="p5">(<span class="default"><span class="p0">(<span class="default"><span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a> ,<span class="p5">(<span class="default"><span class="p0">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 3</span>)</span> <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p5">(<span class="default"><span class="p0">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p4">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a> ,<span class="p5">(<span class="default"><span class="p0">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span> <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K2">GBP</a> ,4</span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p3">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a> ,<span class="p4">(<span class="default"><span class="p5">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 2</span>)</span> <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K2">GBP</a> ,4</span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p2">(<span class="default"><a href="scmpds_2.html#K12">AddTo</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span>,<span class="p3">(<span class="default"><a href="xcmplx_0.html#K4">-</a> 1</span>)</span></span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p1">(<span class="default"><a href="scmpds_2.html#K12">AddTo</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 2</span>)</span>,1</span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p0">(<span class="default"><a href="scmpds_2.html#K12">AddTo</a> <a href="scmp_gcd.html#K2">GBP</a> ,1,2</span>)</span></span>)</span></span>)</span>,<span class="p4">(<span class="default"><a href="scmpds_4.html#K1">Load</a> <span class="p5">(<span class="default"><a href="scmpds_2.html#K12">AddTo</a> <a href="scmp_gcd.html#K2">GBP</a> ,1,<span class="p0">(<span class="default"><a href="xcmplx_0.html#K4">-</a> 2</span>)</span></span>)</span></span>)</span></span>)</span></span>)</span>,<font color="Maroon">c<sub>75</sub></font></span>)</span> <a href="scmpds_2.html#K2">.</a> <span class="p1">(<span class="default"><a href="scmp_gcd.html#K1">intpos</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>81</sub></font></span>)</span></span>)</span> = 
<span class="p1">(<span class="default"><a href="scmpds_4.html#K9">IExec</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a> ,2 <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p4">(<span class="default"><span class="p5">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p3">(<span class="default"><a href="scmpds_2.html#K14">SubFrom</a> <a href="scmp_gcd.html#K2">GBP</a> ,2,<a href="scmp_gcd.html#K3">SBP</a> ,<span class="p4">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span></span>)</span></span>)</span>,<font color="Maroon">c<sub>75</sub></font></span>)</span> <a href="scmpds_2.html#K2">.</a> <span class="p1">(<span class="default"><a href="scmp_gcd.html#K1">intpos</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>81</sub></font></span>)</span></span>)</span>
<b>by </b><i><a class="txt" href="scpqsort.html#E12:46_11"><i><font color="Green">E68</font></i></a></i>
<br/>.= 
<font color="Maroon">c<sub>75</sub></font> <a href="scmpds_2.html#K2">.</a> <span class="p1">(<span class="default"><a href="scmp_gcd.html#K1">intpos</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>81</sub></font></span>)</span></span>)</span>
<b>by </b><i><a class="txt" href="scpqsort.html#E15:46"><i><font color="Green">E55</font></i></a>, <a class="txt" href="scpqsort.html#E1:46_11"><i><font color="Green">E59</font></i></a>, <a class="txt" href="scpqsort.html#E5:46_11_5"><i><font color="Green">E71</font></i></a></i>
;<br/><br/></div>
<b>end;</b></div>


</div><b>end;</b></div>
<b>set </b><font color="Maroon">c<sub>75</sub></font> =  <a href="scmpds_2.html#K3">DataLoc</a> 0,1;<br/>
<a NAME="E19:46"/><i><font color="Green">E59</font></i>: 
 <a href="scmpds_2.html#K3">DataLoc</a> 0,1 <a href="hidden.html#R1">=</a>  <a href="scmp_gcd.html#K1">intpos</a> <span class="p1">(<span class="default">0 <a href="nat_1.html#K1">+</a> 1</span>)</span>
 
<b>by </b><i><a class="ref" href="scmp_gcd.html#T5">SCMP_GCD:5</a></i>;<br/>
<div><i><font color="Green">E60</font></i>: <a class="txt" onclick="hs2(this)" href="javascript:()" title="46_12"><b>now </b></a><div class="add"><b>let </b><font color="Maroon">c<sub>76</sub></font> be   <a href="ami_1.html#NM4">State</a> of <a href="scmpds_2.html#K1">SCMPDS</a> ;<br/><b>let </b><font color="Maroon">c<sub>77</sub></font>, <font color="Maroon">c<sub>78</sub></font> be    <a href="finseq_1.html#M2">FinSequence</a> of  <a href="numbers.html#K4">INT</a> ;<br/><b>let </b><font color="Maroon">c<sub>79</sub></font>, <font color="Maroon">c<sub>80</sub></font>, <font color="Maroon">c<sub>81</sub></font>, <font color="Maroon">c<sub>82</sub></font> be   <a href="nat_1.html#NM1">Nat</a>;<br/><b>set </b><font color="Maroon">c<sub>83</sub></font> = <span class="p1">(<span class="default">2 <a href="nat_1.html#K2">*</a> <font color="Maroon">c<sub>79</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 1;<br/><b>set </b><font color="Maroon">c<sub>84</sub></font> = <font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>81</sub></font>;<br/><b>set </b><font color="Maroon">c<sub>85</sub></font> = <font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>82</sub></font>;<br/><b>assume </b><a NAME="E1:46_12"/><i><font color="Green">E61</font></i>: 
( <font color="Maroon">c<sub>76</sub></font> <a href="scmpds_2.html#K2">.</a> <a href="scmp_gcd.html#K2">GBP</a>  <a href="hidden.html#R1">=</a> 0 &amp; <span class="p1">(<span class="default">2 <a href="nat_1.html#K2">*</a> <font color="Maroon">c<sub>79</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 1 <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>76</sub></font> <a href="scmpds_2.html#K2">.</a> <span class="p1">(<span class="default"><a href="scmpds_2.html#K3">DataLoc</a> 0,1</span>)</span> &amp; <font color="Maroon">c<sub>80</sub></font> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> <span class="p2">(<span class="default">2 <a href="nat_1.html#K2">*</a> <font color="Maroon">c<sub>79</sub></font></span>)</span></span>)</span> <a href="nat_1.html#K1">+</a> 1 &amp; <font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>81</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>76</sub></font> <a href="scmpds_2.html#K2">.</a> <span class="p1">(<span class="default"><a href="scmp_gcd.html#K1">intpos</a> <font color="Maroon">c<sub>80</sub></font></span>)</span> &amp; <font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>82</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>76</sub></font> <a href="scmpds_2.html#K2">.</a> <span class="p1">(<span class="default"><a href="scmp_gcd.html#K1">intpos</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>80</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> &amp; ( ( 1 <a href="xxreal_0.html#R1">&lt;=</a> <font color="Maroon">c<sub>81</sub></font> &amp; <font color="Maroon">c<sub>82</sub></font> <a href="xxreal_0.html#R1">&lt;=</a> <font color="Maroon">c<sub>49</sub></font> ) or <font color="Maroon">c<sub>81</sub></font> <a href="xxreal_0.html#NR2" target="_self">&gt;=</a> <font color="Maroon">c<sub>82</sub></font> ) )
 ;<br/><b>set </b><font color="Maroon">c<sub>86</sub></font> = <span class="p1">(<span class="default"><span class="p2">(<span class="default">2 <a href="nat_1.html#K2">*</a> <font color="Maroon">c<sub>79</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span> <a href="nat_1.html#K1">+</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span>;<br/><a NAME="E2:46_12"/><i><font color="Green">E62</font></i>: 
<font color="Maroon">c<sub>80</sub></font> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default">2 <a href="nat_1.html#K2">*</a> <font color="Maroon">c<sub>79</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span> <a href="nat_1.html#K1">+</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span>
 <b>by </b><i><a class="txt" href="scpqsort.html#E1:46_12"><i><font color="Green">E61</font></i></a></i>;<br/><a NAME="E3:46_12"/><i><font color="Green">E63</font></i>: 
<font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>81</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>76</sub></font> <a href="scmpds_2.html#K2">.</a> <span class="p1">(<span class="default"><a href="scmp_gcd.html#K1">intpos</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default">2 <a href="nat_1.html#K2">*</a> <font color="Maroon">c<sub>79</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span> <a href="nat_1.html#K1">+</a> <span class="p3">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span></span>)</span></span>)</span>
 <b>by </b><i><a class="txt" href="scpqsort.html#E1:46_12"><i><font color="Green">E61</font></i></a></i>;<br/><a NAME="E4:46_12"/><i><font color="Green">E64</font></i>: 
<font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>82</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>76</sub></font> <a href="scmpds_2.html#K2">.</a> <span class="p1">(<span class="default"><a href="scmp_gcd.html#K1">intpos</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default">2 <a href="nat_1.html#K2">*</a> <font color="Maroon">c<sub>79</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span> <a href="nat_1.html#K1">+</a> <span class="p4">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span>
 <b>by </b><i><a class="txt" href="scpqsort.html#E1:46_12"><i><font color="Green">E61</font></i></a></i>;<br/><div><a class="txt" onclick="hs2(this)" href="javascript:()" title="46_12_1"><b>now </b></a><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="46_12_1_1"><b>per </b></a><a class="txt" onclick="hs(this)" href="javascript:()"><b>cases </b></a><span class="hide"><a NAME="E1:46_12_1_1"/>
( ( 1 <a href="xxreal_0.html#R1">&lt;=</a> <font color="Maroon">c<sub>81</sub></font> &amp; <font color="Maroon">c<sub>82</sub></font> <a href="xxreal_0.html#R1">&lt;=</a> <font color="Maroon">c<sub>49</sub></font> ) or <font color="Maroon">c<sub>81</sub></font> <a href="xxreal_0.html#NR2" target="_self">&gt;=</a> <font color="Maroon">c<sub>82</sub></font> )
 </span><b>by </b><i><a class="txt" href="scpqsort.html#E1:46_12"><i><font color="Green">E61</font></i></a></i>;<br/><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="46_12_1_1_1"><b>case </b></a><a NAME="E1:46_12_1_1_1"/>
( 1 <a href="xxreal_0.html#R1">&lt;=</a> <font color="Maroon">c<sub>81</sub></font> &amp; <font color="Maroon">c<sub>82</sub></font> <a href="xxreal_0.html#R1">&lt;=</a> <font color="Maroon">c<sub>49</sub></font> )
 ;<br/><div class="add"><b>hence </b><a NAME="E2:46_12_1_1_1"/>
<font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> 1 <a href="xxreal_0.html#R1">&lt;=</a> <font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>81</sub></font>
 <b>by </b><i><a class="ref" href="xreal_1.html#T8">XREAL_1:8</a></i>;<br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="46_12_1_1_2"><b>case </b></a><a NAME="E1:46_12_1_1_2"/>
<font color="Maroon">c<sub>81</sub></font> <a href="xxreal_0.html#NR2" target="_self">&gt;=</a> <font color="Maroon">c<sub>82</sub></font>
 ;<br/><div class="add"><a NAME="E2:46_12_1_1_2"/><b>then </b>
<font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>81</sub></font> <a href="xxreal_0.html#NR2" target="_self">&gt;=</a> <font color="Maroon">c<sub>76</sub></font> <a href="scmpds_2.html#K2">.</a> <span class="p1">(<span class="default"><a href="scmp_gcd.html#K1">intpos</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default">2 <a href="nat_1.html#K2">*</a> <font color="Maroon">c<sub>79</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span> <a href="nat_1.html#K1">+</a> <span class="p4">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span>
 <b>by </b><i><a class="txt" href="scpqsort.html#E1:46_12"><i><font color="Green">E61</font></i></a>, <a class="ref" href="xreal_1.html#T8">XREAL_1:8</a></i>;<br/><b>hence </b><a NAME="E3:46_12_1_1_2"/>
<span class="p1">(<span class="default"><font color="Maroon">c<sub>76</sub></font> <a href="scmpds_2.html#K2">.</a> <span class="p2">(<span class="default"><a href="scmp_gcd.html#K1">intpos</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><span class="p0">(<span class="default">2 <a href="nat_1.html#K2">*</a> <font color="Maroon">c<sub>79</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span> <a href="nat_1.html#K1">+</a> <span class="p5">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span> <a href="xcmplx_0.html#K6">-</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>81</sub></font></span>)</span> <a href="xxreal_0.html#R1">&lt;=</a> 0
 <b>by </b><i><a class="ref" href="real_2.html#T106">REAL_2:106</a></i>;<br/></div><b>end;</b></div></div><b>end;</b></div></div><b>end;</b></div><b>hence </b><a NAME="E6:46_12"/>
( <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a> ,2 <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p2">(<span class="default"><a href="scmpds_2.html#K14">SubFrom</a> <a href="scmp_gcd.html#K2">GBP</a> ,2,<a href="scmp_gcd.html#K3">SBP</a> ,<span class="p3">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span></span>)</span></span>)</span> <a href="scmpds_4.html#K3">';'</a> <span class="p1">(<span class="default"><a href="scmpds_6.html#K3">if&gt;0</a> <a href="scmp_gcd.html#K2">GBP</a> ,2,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a> ,2 <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p0">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span></span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p5">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a> ,4 <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p0">(<span class="default"><span class="p1">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span> <a href="scmpds_4.html#K3">';'</a> <font color="Maroon">c<sub>50</sub></font></span>)</span> <a href="scmpds_4.html#K3">';'</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><span class="p0">(<span class="default"><span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a> ,<span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 3</span>)</span> <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p2">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a> ,<span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span> <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K2">GBP</a> ,4</span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p1">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a> ,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 2</span>)</span> <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K2">GBP</a> ,4</span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p0">(<span class="default"><a href="scmpds_2.html#K12">AddTo</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span>,<span class="p1">(<span class="default"><a href="xcmplx_0.html#K4">-</a> 1</span>)</span></span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p5">(<span class="default"><a href="scmpds_2.html#K12">AddTo</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p0">(<span class="default"><span class="p1">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 2</span>)</span>,1</span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p4">(<span class="default"><a href="scmpds_2.html#K12">AddTo</a> <a href="scmp_gcd.html#K2">GBP</a> ,1,2</span>)</span></span>)</span></span>)</span>,<span class="p2">(<span class="default"><a href="scmpds_4.html#K1">Load</a> <span class="p3">(<span class="default"><a href="scmpds_2.html#K12">AddTo</a> <a href="scmp_gcd.html#K2">GBP</a> ,1,<span class="p4">(<span class="default"><a href="xcmplx_0.html#K4">-</a> 2</span>)</span></span>)</span></span>)</span></span>)</span> <a href="scmpds_6.html#R1">is_closed_on</a> <font color="Maroon">c<sub>76</sub></font> &amp; <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a> ,2 <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p2">(<span class="default"><a href="scmpds_2.html#K14">SubFrom</a> <a href="scmp_gcd.html#K2">GBP</a> ,2,<a href="scmp_gcd.html#K3">SBP</a> ,<span class="p3">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span></span>)</span></span>)</span> <a href="scmpds_4.html#K3">';'</a> <span class="p1">(<span class="default"><a href="scmpds_6.html#K3">if&gt;0</a> <a href="scmp_gcd.html#K2">GBP</a> ,2,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a> ,2 <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p0">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span></span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p5">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a> ,4 <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p0">(<span class="default"><span class="p1">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span> <a href="scmpds_4.html#K3">';'</a> <font color="Maroon">c<sub>50</sub></font></span>)</span> <a href="scmpds_4.html#K3">';'</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><span class="p0">(<span class="default"><span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a> ,<span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 3</span>)</span> <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p2">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a> ,<span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span> <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K2">GBP</a> ,4</span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p1">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a> ,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 2</span>)</span> <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K2">GBP</a> ,4</span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p0">(<span class="default"><a href="scmpds_2.html#K12">AddTo</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span>,<span class="p1">(<span class="default"><a href="xcmplx_0.html#K4">-</a> 1</span>)</span></span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p5">(<span class="default"><a href="scmpds_2.html#K12">AddTo</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p0">(<span class="default"><span class="p1">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 2</span>)</span>,1</span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p4">(<span class="default"><a href="scmpds_2.html#K12">AddTo</a> <a href="scmp_gcd.html#K2">GBP</a> ,1,2</span>)</span></span>)</span></span>)</span>,<span class="p2">(<span class="default"><a href="scmpds_4.html#K1">Load</a> <span class="p3">(<span class="default"><a href="scmpds_2.html#K12">AddTo</a> <a href="scmp_gcd.html#K2">GBP</a> ,1,<span class="p4">(<span class="default"><a href="xcmplx_0.html#K4">-</a> 2</span>)</span></span>)</span></span>)</span></span>)</span> <a href="scmpds_6.html#R2">is_halting_on</a> <font color="Maroon">c<sub>76</sub></font> )
 <b>by </b><i><a class="txt" href="scpqsort.html#E16:46"><i><font color="Green">E56</font></i></a>, <a class="txt" href="scpqsort.html#E19:46"><i><font color="Green">E59</font></i></a>, <a class="txt" href="scpqsort.html#E1:46_12"><i><font color="Green">E61</font></i></a>, <a class="txt" href="scpqsort.html#E3:46_12"><i><font color="Green">E63</font></i></a>, <a class="ref" href="scmp_gcd.html#D3">SCMP_GCD:def 3</a></i>;<br/><b>consider </b><font color="Maroon">c<sub>87</sub></font> being    <a href="finseq_1.html#M2">FinSequence</a> of  <a href="numbers.html#K4">INT</a> <b> such that </b><br/><a NAME="E8:46_12"/><i><font color="Green">E65</font></i>: 
(  <a href="finseq_1.html#K3">len</a> <font color="Maroon">c<sub>87</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>49</sub></font> &amp; ( for <font color="Olive">b<sub>1</sub></font> being  <a href="nat_1.html#NM1">Nat</a> st 1 <a href="xxreal_0.html#R1">&lt;=</a> <font color="Olive">b<sub>1</sub></font> &amp; <font color="Olive">b<sub>1</sub></font> <a href="xxreal_0.html#R1">&lt;=</a>  <a href="finseq_1.html#K3">len</a> <font color="Maroon">c<sub>87</sub></font> holds <br/><font color="Maroon">c<sub>87</sub></font> <a href="funct_1.html#K1">.</a> <font color="Olive">b<sub>1</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>76</sub></font> <a href="scmpds_2.html#K2">.</a> <span class="p1">(<span class="default"><a href="scmp_gcd.html#K1">intpos</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Olive">b<sub>1</sub></font></span>)</span></span>)</span> ) )
 <b>by </b><i><a class="ref" href="scpisort.html#T2">SCPISORT:2</a></i>;<br/><a NAME="E9:46_12"/><i><font color="Green">E66</font></i>: 
<font color="Maroon">c<sub>87</sub></font> <a href="scpisort.html#R1">is_FinSequence_on</a> <font color="Maroon">c<sub>76</sub></font>,<font color="Maroon">c<sub>48</sub></font>
 <b>by </b><i><a class="txt" href="scpqsort.html#E8:46_12"><i><font color="Green">E65</font></i></a>, <a class="ref" href="scpisort.html#D1">SCPISORT:def 1</a></i>;<br/><b>consider </b><font color="Maroon">c<sub>88</sub></font> being    <a href="finseq_1.html#M2">FinSequence</a> of  <a href="numbers.html#K4">INT</a> <b> such that </b><br/><a NAME="E11:46_12"/><i><font color="Green">E67</font></i>: 
(  <a href="finseq_1.html#K3">len</a> <font color="Maroon">c<sub>88</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>49</sub></font> &amp; ( for <font color="Olive">b<sub>1</sub></font> being  <a href="nat_1.html#NM1">Nat</a> st 1 <a href="xxreal_0.html#R1">&lt;=</a> <font color="Olive">b<sub>1</sub></font> &amp; <font color="Olive">b<sub>1</sub></font> <a href="xxreal_0.html#R1">&lt;=</a>  <a href="finseq_1.html#K3">len</a> <font color="Maroon">c<sub>88</sub></font> holds <br/><font color="Maroon">c<sub>88</sub></font> <a href="funct_1.html#K1">.</a> <font color="Olive">b<sub>1</sub></font> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><a href="scmpds_4.html#K9">IExec</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a> ,2 <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p5">(<span class="default"><span class="p0">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p4">(<span class="default"><a href="scmpds_2.html#K14">SubFrom</a> <a href="scmp_gcd.html#K2">GBP</a> ,2,<a href="scmp_gcd.html#K3">SBP</a> ,<span class="p5">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span></span>)</span></span>)</span> <a href="scmpds_4.html#K3">';'</a> <span class="p3">(<span class="default"><a href="scmpds_6.html#K3">if&gt;0</a> <a href="scmp_gcd.html#K2">GBP</a> ,2,<span class="p4">(<span class="default"><span class="p5">(<span class="default"><span class="p0">(<span class="default"><span class="p1">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a> ,2 <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p2">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span></span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p1">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a> ,4 <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span> <a href="scmpds_4.html#K3">';'</a> <font color="Maroon">c<sub>50</sub></font></span>)</span> <a href="scmpds_4.html#K3">';'</a> <span class="p5">(<span class="default"><span class="p0">(<span class="default"><span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a> ,<span class="p5">(<span class="default"><span class="p0">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 3</span>)</span> <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p5">(<span class="default"><span class="p0">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p4">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a> ,<span class="p5">(<span class="default"><span class="p0">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span> <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K2">GBP</a> ,4</span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p3">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a> ,<span class="p4">(<span class="default"><span class="p5">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 2</span>)</span> <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K2">GBP</a> ,4</span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p2">(<span class="default"><a href="scmpds_2.html#K12">AddTo</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span>,<span class="p3">(<span class="default"><a href="xcmplx_0.html#K4">-</a> 1</span>)</span></span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p1">(<span class="default"><a href="scmpds_2.html#K12">AddTo</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 2</span>)</span>,1</span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p0">(<span class="default"><a href="scmpds_2.html#K12">AddTo</a> <a href="scmp_gcd.html#K2">GBP</a> ,1,2</span>)</span></span>)</span></span>)</span>,<span class="p4">(<span class="default"><a href="scmpds_4.html#K1">Load</a> <span class="p5">(<span class="default"><a href="scmpds_2.html#K12">AddTo</a> <a href="scmp_gcd.html#K2">GBP</a> ,1,<span class="p0">(<span class="default"><a href="xcmplx_0.html#K4">-</a> 2</span>)</span></span>)</span></span>)</span></span>)</span></span>)</span>,<font color="Maroon">c<sub>76</sub></font></span>)</span> <a href="scmpds_2.html#K2">.</a> <span class="p1">(<span class="default"><a href="scmp_gcd.html#K1">intpos</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Olive">b<sub>1</sub></font></span>)</span></span>)</span> ) )
 <b>by </b><i><a class="ref" href="scpisort.html#T2">SCPISORT:2</a></i>;<br/><a NAME="E12:46_12"/><i><font color="Green">E68</font></i>: 
<font color="Maroon">c<sub>88</sub></font> <a href="scpisort.html#R1">is_FinSequence_on</a>  <a href="scmpds_4.html#K9">IExec</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a> ,2 <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p4">(<span class="default"><span class="p5">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p3">(<span class="default"><a href="scmpds_2.html#K14">SubFrom</a> <a href="scmp_gcd.html#K2">GBP</a> ,2,<a href="scmp_gcd.html#K3">SBP</a> ,<span class="p4">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span></span>)</span></span>)</span> <a href="scmpds_4.html#K3">';'</a> <span class="p2">(<span class="default"><a href="scmpds_6.html#K3">if&gt;0</a> <a href="scmp_gcd.html#K2">GBP</a> ,2,<span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><span class="p0">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a> ,2 <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p1">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span></span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p0">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a> ,4 <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span> <a href="scmpds_4.html#K3">';'</a> <font color="Maroon">c<sub>50</sub></font></span>)</span> <a href="scmpds_4.html#K3">';'</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><span class="p0">(<span class="default"><span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a> ,<span class="p4">(<span class="default"><span class="p5">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 3</span>)</span> <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p4">(<span class="default"><span class="p5">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p3">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a> ,<span class="p4">(<span class="default"><span class="p5">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span> <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K2">GBP</a> ,4</span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p2">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a> ,<span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 2</span>)</span> <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K2">GBP</a> ,4</span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p1">(<span class="default"><a href="scmpds_2.html#K12">AddTo</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span>,<span class="p2">(<span class="default"><a href="xcmplx_0.html#K4">-</a> 1</span>)</span></span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p0">(<span class="default"><a href="scmpds_2.html#K12">AddTo</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 2</span>)</span>,1</span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p5">(<span class="default"><a href="scmpds_2.html#K12">AddTo</a> <a href="scmp_gcd.html#K2">GBP</a> ,1,2</span>)</span></span>)</span></span>)</span>,<span class="p3">(<span class="default"><a href="scmpds_4.html#K1">Load</a> <span class="p4">(<span class="default"><a href="scmpds_2.html#K12">AddTo</a> <a href="scmp_gcd.html#K2">GBP</a> ,1,<span class="p5">(<span class="default"><a href="xcmplx_0.html#K4">-</a> 2</span>)</span></span>)</span></span>)</span></span>)</span></span>)</span>,<font color="Maroon">c<sub>76</sub></font>,<font color="Maroon">c<sub>48</sub></font>
 <b>by </b><i><a class="txt" href="scpqsort.html#E11:46_12"><i><font color="Green">E67</font></i></a>, <a class="ref" href="scpisort.html#D1">SCPISORT:def 1</a></i>;<br/><div><b>hereby </b>
<div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="46_12_2_1"><b>per </b></a><a class="txt" onclick="hs(this)" href="javascript:()"><b>cases </b></a><span class="hide"><a NAME="E1:46_12_2_1"/>
( <font color="Maroon">c<sub>76</sub></font> <a href="scmpds_2.html#K2">.</a> <span class="p1">(<span class="default"><a href="scmp_gcd.html#K1">intpos</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default">2 <a href="nat_1.html#K2">*</a> <font color="Maroon">c<sub>79</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span> <a href="nat_1.html#K1">+</a> <span class="p4">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> <a href="xxreal_0.html#R1">&lt;=</a> <font color="Maroon">c<sub>76</sub></font> <a href="scmpds_2.html#K2">.</a> <span class="p1">(<span class="default"><a href="scmp_gcd.html#K1">intpos</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default">2 <a href="nat_1.html#K2">*</a> <font color="Maroon">c<sub>79</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span> <a href="nat_1.html#K1">+</a> <span class="p3">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span></span>)</span></span>)</span> or <font color="Maroon">c<sub>76</sub></font> <a href="scmpds_2.html#K2">.</a> <span class="p1">(<span class="default"><a href="scmp_gcd.html#K1">intpos</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default">2 <a href="nat_1.html#K2">*</a> <font color="Maroon">c<sub>79</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span> <a href="nat_1.html#K1">+</a> <span class="p4">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> <a href="xxreal_0.html#NR4" target="_self">&gt;</a> <font color="Maroon">c<sub>76</sub></font> <a href="scmpds_2.html#K2">.</a> <span class="p1">(<span class="default"><a href="scmp_gcd.html#K1">intpos</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default">2 <a href="nat_1.html#K2">*</a> <font color="Maroon">c<sub>79</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span> <a href="nat_1.html#K1">+</a> <span class="p3">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span></span>)</span></span>)</span> )
 </span>;<br/><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="46_12_2_1_1"><b>suppose </b></a><a NAME="E1:46_12_2_1_1"/>
<font color="Maroon">c<sub>76</sub></font> <a href="scmpds_2.html#K2">.</a> <span class="p1">(<span class="default"><a href="scmp_gcd.html#K1">intpos</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default">2 <a href="nat_1.html#K2">*</a> <font color="Maroon">c<sub>79</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span> <a href="nat_1.html#K1">+</a> <span class="p4">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> <a href="xxreal_0.html#R1">&lt;=</a> <font color="Maroon">c<sub>76</sub></font> <a href="scmpds_2.html#K2">.</a> <span class="p1">(<span class="default"><a href="scmp_gcd.html#K1">intpos</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default">2 <a href="nat_1.html#K2">*</a> <font color="Maroon">c<sub>79</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span> <a href="nat_1.html#K1">+</a> <span class="p3">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span></span>)</span></span>)</span>
 ;<br/><div class="add"><b>hence </b><a NAME="E2:46_12_2_1_1"/>
( <span class="p1">(<span class="default"><a href="scmpds_4.html#K9">IExec</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a> ,2 <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p5">(<span class="default"><span class="p0">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p4">(<span class="default"><a href="scmpds_2.html#K14">SubFrom</a> <a href="scmp_gcd.html#K2">GBP</a> ,2,<a href="scmp_gcd.html#K3">SBP</a> ,<span class="p5">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span></span>)</span></span>)</span> <a href="scmpds_4.html#K3">';'</a> <span class="p3">(<span class="default"><a href="scmpds_6.html#K3">if&gt;0</a> <a href="scmp_gcd.html#K2">GBP</a> ,2,<span class="p4">(<span class="default"><span class="p5">(<span class="default"><span class="p0">(<span class="default"><span class="p1">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a> ,2 <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p2">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span></span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p1">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a> ,4 <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span> <a href="scmpds_4.html#K3">';'</a> <font color="Maroon">c<sub>50</sub></font></span>)</span> <a href="scmpds_4.html#K3">';'</a> <span class="p5">(<span class="default"><span class="p0">(<span class="default"><span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a> ,<span class="p5">(<span class="default"><span class="p0">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 3</span>)</span> <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p5">(<span class="default"><span class="p0">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p4">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a> ,<span class="p5">(<span class="default"><span class="p0">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span> <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K2">GBP</a> ,4</span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p3">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a> ,<span class="p4">(<span class="default"><span class="p5">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 2</span>)</span> <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K2">GBP</a> ,4</span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p2">(<span class="default"><a href="scmpds_2.html#K12">AddTo</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span>,<span class="p3">(<span class="default"><a href="xcmplx_0.html#K4">-</a> 1</span>)</span></span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p1">(<span class="default"><a href="scmpds_2.html#K12">AddTo</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 2</span>)</span>,1</span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p0">(<span class="default"><a href="scmpds_2.html#K12">AddTo</a> <a href="scmp_gcd.html#K2">GBP</a> ,1,2</span>)</span></span>)</span></span>)</span>,<span class="p4">(<span class="default"><a href="scmpds_4.html#K1">Load</a> <span class="p5">(<span class="default"><a href="scmpds_2.html#K12">AddTo</a> <a href="scmp_gcd.html#K2">GBP</a> ,1,<span class="p0">(<span class="default"><a href="xcmplx_0.html#K4">-</a> 2</span>)</span></span>)</span></span>)</span></span>)</span></span>)</span>,<font color="Maroon">c<sub>76</sub></font></span>)</span> <a href="scmpds_2.html#K2">.</a> <a href="scmp_gcd.html#K2">GBP</a>  <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>76</sub></font> <a href="scmpds_2.html#K2">.</a> <a href="scmp_gcd.html#K2">GBP</a>  &amp; ( for <font color="Olive">b<sub>1</sub></font> being  <a href="nat_1.html#NM1">Nat</a> st 1 <a href="xxreal_0.html#R1">&lt;=</a> <font color="Olive">b<sub>1</sub></font> &amp; <font color="Olive">b<sub>1</sub></font> <a href="xxreal_0.html#NR3" target="_self">&lt;</a> <span class="p1">(<span class="default">2 <a href="nat_1.html#K2">*</a> <font color="Maroon">c<sub>79</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 1 holds <br/><span class="p1">(<span class="default"><a href="scmpds_4.html#K9">IExec</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a> ,2 <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p5">(<span class="default"><span class="p0">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p4">(<span class="default"><a href="scmpds_2.html#K14">SubFrom</a> <a href="scmp_gcd.html#K2">GBP</a> ,2,<a href="scmp_gcd.html#K3">SBP</a> ,<span class="p5">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span></span>)</span></span>)</span> <a href="scmpds_4.html#K3">';'</a> <span class="p3">(<span class="default"><a href="scmpds_6.html#K3">if&gt;0</a> <a href="scmp_gcd.html#K2">GBP</a> ,2,<span class="p4">(<span class="default"><span class="p5">(<span class="default"><span class="p0">(<span class="default"><span class="p1">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a> ,2 <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p2">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span></span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p1">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a> ,4 <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span> <a href="scmpds_4.html#K3">';'</a> <font color="Maroon">c<sub>50</sub></font></span>)</span> <a href="scmpds_4.html#K3">';'</a> <span class="p5">(<span class="default"><span class="p0">(<span class="default"><span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a> ,<span class="p5">(<span class="default"><span class="p0">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 3</span>)</span> <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p5">(<span class="default"><span class="p0">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p4">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a> ,<span class="p5">(<span class="default"><span class="p0">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span> <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K2">GBP</a> ,4</span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p3">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a> ,<span class="p4">(<span class="default"><span class="p5">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 2</span>)</span> <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K2">GBP</a> ,4</span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p2">(<span class="default"><a href="scmpds_2.html#K12">AddTo</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span>,<span class="p3">(<span class="default"><a href="xcmplx_0.html#K4">-</a> 1</span>)</span></span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p1">(<span class="default"><a href="scmpds_2.html#K12">AddTo</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 2</span>)</span>,1</span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p0">(<span class="default"><a href="scmpds_2.html#K12">AddTo</a> <a href="scmp_gcd.html#K2">GBP</a> ,1,2</span>)</span></span>)</span></span>)</span>,<span class="p4">(<span class="default"><a href="scmpds_4.html#K1">Load</a> <span class="p5">(<span class="default"><a href="scmpds_2.html#K12">AddTo</a> <a href="scmp_gcd.html#K2">GBP</a> ,1,<span class="p0">(<span class="default"><a href="xcmplx_0.html#K4">-</a> 2</span>)</span></span>)</span></span>)</span></span>)</span></span>)</span>,<font color="Maroon">c<sub>76</sub></font></span>)</span> <a href="scmpds_2.html#K2">.</a> <span class="p1">(<span class="default"><a href="scmp_gcd.html#K1">intpos</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> <font color="Olive">b<sub>1</sub></font></span>)</span></span>)</span> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>76</sub></font> <a href="scmpds_2.html#K2">.</a> <span class="p1">(<span class="default"><a href="scmp_gcd.html#K1">intpos</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> <font color="Olive">b<sub>1</sub></font></span>)</span></span>)</span> ) )
 <b>by </b><i><a class="txt" href="scpqsort.html#E18:46"><i><font color="Green">E58</font></i></a>, <a class="txt" href="scpqsort.html#E19:46"><i><font color="Green">E59</font></i></a>, <a class="txt" href="scpqsort.html#E1:46_12"><i><font color="Green">E61</font></i></a>, <a class="ref" href="scmp_gcd.html#D3">SCMP_GCD:def 3</a></i>;<br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="46_12_2_1_2"><b>suppose </b></a><a NAME="E1:46_12_2_1_2"/><i><font color="Green">E69</font></i>: 
<font color="Maroon">c<sub>76</sub></font> <a href="scmpds_2.html#K2">.</a> <span class="p1">(<span class="default"><a href="scmp_gcd.html#K1">intpos</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default">2 <a href="nat_1.html#K2">*</a> <font color="Maroon">c<sub>79</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span> <a href="nat_1.html#K1">+</a> <span class="p4">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> <a href="xxreal_0.html#NR4" target="_self">&gt;</a> <font color="Maroon">c<sub>76</sub></font> <a href="scmpds_2.html#K2">.</a> <span class="p1">(<span class="default"><a href="scmp_gcd.html#K1">intpos</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default">2 <a href="nat_1.html#K2">*</a> <font color="Maroon">c<sub>79</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span> <a href="nat_1.html#K1">+</a> <span class="p3">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span></span>)</span></span>)</span>
 ;<br/><div class="add"><a NAME="E2:46_12_2_1_2"/><b>then </b><i><font color="Green">E70</font></i>: 
<span class="p1">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>82</sub></font></span>)</span> <a href="xcmplx_0.html#K6">-</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>81</sub></font></span>)</span> <a href="xxreal_0.html#NR4" target="_self">&gt;</a> 0
 <b>by </b><i><a class="txt" href="scpqsort.html#E3:46_12"><i><font color="Green">E63</font></i></a>, <a class="txt" href="scpqsort.html#E4:46_12"><i><font color="Green">E64</font></i></a>, <a class="ref" href="xreal_1.html#T52">XREAL_1:52</a></i>;<br/><a NAME="E3:46_12_2_1_2"/>
( <font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> 1 <a href="xxreal_0.html#R1">&lt;=</a> <font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>81</sub></font> &amp; <font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>82</sub></font> <a href="xxreal_0.html#R1">&lt;=</a> <font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font> )
 <b>by </b><i><a class="txt" href="scpqsort.html#E1:46_12"><i><font color="Green">E61</font></i></a>, <a class="txt" href="scpqsort.html#E1:46_12_2_1_2"><i><font color="Green">E69</font></i></a>, <a class="ref" href="xreal_1.html#T8">XREAL_1:8</a></i>;<br/><b>hence </b><a NAME="E4:46_12_2_1_2"/>
( <span class="p1">(<span class="default"><a href="scmpds_4.html#K9">IExec</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a> ,2 <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p5">(<span class="default"><span class="p0">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p4">(<span class="default"><a href="scmpds_2.html#K14">SubFrom</a> <a href="scmp_gcd.html#K2">GBP</a> ,2,<a href="scmp_gcd.html#K3">SBP</a> ,<span class="p5">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span></span>)</span></span>)</span> <a href="scmpds_4.html#K3">';'</a> <span class="p3">(<span class="default"><a href="scmpds_6.html#K3">if&gt;0</a> <a href="scmp_gcd.html#K2">GBP</a> ,2,<span class="p4">(<span class="default"><span class="p5">(<span class="default"><span class="p0">(<span class="default"><span class="p1">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a> ,2 <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p2">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span></span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p1">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a> ,4 <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span> <a href="scmpds_4.html#K3">';'</a> <font color="Maroon">c<sub>50</sub></font></span>)</span> <a href="scmpds_4.html#K3">';'</a> <span class="p5">(<span class="default"><span class="p0">(<span class="default"><span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a> ,<span class="p5">(<span class="default"><span class="p0">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 3</span>)</span> <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p5">(<span class="default"><span class="p0">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p4">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a> ,<span class="p5">(<span class="default"><span class="p0">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span> <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K2">GBP</a> ,4</span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p3">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a> ,<span class="p4">(<span class="default"><span class="p5">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 2</span>)</span> <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K2">GBP</a> ,4</span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p2">(<span class="default"><a href="scmpds_2.html#K12">AddTo</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span>,<span class="p3">(<span class="default"><a href="xcmplx_0.html#K4">-</a> 1</span>)</span></span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p1">(<span class="default"><a href="scmpds_2.html#K12">AddTo</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 2</span>)</span>,1</span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p0">(<span class="default"><a href="scmpds_2.html#K12">AddTo</a> <a href="scmp_gcd.html#K2">GBP</a> ,1,2</span>)</span></span>)</span></span>)</span>,<span class="p4">(<span class="default"><a href="scmpds_4.html#K1">Load</a> <span class="p5">(<span class="default"><a href="scmpds_2.html#K12">AddTo</a> <a href="scmp_gcd.html#K2">GBP</a> ,1,<span class="p0">(<span class="default"><a href="xcmplx_0.html#K4">-</a> 2</span>)</span></span>)</span></span>)</span></span>)</span></span>)</span>,<font color="Maroon">c<sub>76</sub></font></span>)</span> <a href="scmpds_2.html#K2">.</a> <a href="scmp_gcd.html#K2">GBP</a>  <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>76</sub></font> <a href="scmpds_2.html#K2">.</a> <a href="scmp_gcd.html#K2">GBP</a>  &amp; ( for <font color="Olive">b<sub>1</sub></font> being  <a href="nat_1.html#NM1">Nat</a> st 1 <a href="xxreal_0.html#R1">&lt;=</a> <font color="Olive">b<sub>1</sub></font> &amp; <font color="Olive">b<sub>1</sub></font> <a href="xxreal_0.html#NR3" target="_self">&lt;</a> <span class="p1">(<span class="default">2 <a href="nat_1.html#K2">*</a> <font color="Maroon">c<sub>79</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 1 holds <br/><span class="p1">(<span class="default"><a href="scmpds_4.html#K9">IExec</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a> ,2 <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p5">(<span class="default"><span class="p0">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p4">(<span class="default"><a href="scmpds_2.html#K14">SubFrom</a> <a href="scmp_gcd.html#K2">GBP</a> ,2,<a href="scmp_gcd.html#K3">SBP</a> ,<span class="p5">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span></span>)</span></span>)</span> <a href="scmpds_4.html#K3">';'</a> <span class="p3">(<span class="default"><a href="scmpds_6.html#K3">if&gt;0</a> <a href="scmp_gcd.html#K2">GBP</a> ,2,<span class="p4">(<span class="default"><span class="p5">(<span class="default"><span class="p0">(<span class="default"><span class="p1">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a> ,2 <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p2">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span></span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p1">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a> ,4 <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span> <a href="scmpds_4.html#K3">';'</a> <font color="Maroon">c<sub>50</sub></font></span>)</span> <a href="scmpds_4.html#K3">';'</a> <span class="p5">(<span class="default"><span class="p0">(<span class="default"><span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a> ,<span class="p5">(<span class="default"><span class="p0">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 3</span>)</span> <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p5">(<span class="default"><span class="p0">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p4">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a> ,<span class="p5">(<span class="default"><span class="p0">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span> <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K2">GBP</a> ,4</span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p3">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a> ,<span class="p4">(<span class="default"><span class="p5">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 2</span>)</span> <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K2">GBP</a> ,4</span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p2">(<span class="default"><a href="scmpds_2.html#K12">AddTo</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span>,<span class="p3">(<span class="default"><a href="xcmplx_0.html#K4">-</a> 1</span>)</span></span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p1">(<span class="default"><a href="scmpds_2.html#K12">AddTo</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 2</span>)</span>,1</span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p0">(<span class="default"><a href="scmpds_2.html#K12">AddTo</a> <a href="scmp_gcd.html#K2">GBP</a> ,1,2</span>)</span></span>)</span></span>)</span>,<span class="p4">(<span class="default"><a href="scmpds_4.html#K1">Load</a> <span class="p5">(<span class="default"><a href="scmpds_2.html#K12">AddTo</a> <a href="scmp_gcd.html#K2">GBP</a> ,1,<span class="p0">(<span class="default"><a href="xcmplx_0.html#K4">-</a> 2</span>)</span></span>)</span></span>)</span></span>)</span></span>)</span>,<font color="Maroon">c<sub>76</sub></font></span>)</span> <a href="scmpds_2.html#K2">.</a> <span class="p1">(<span class="default"><a href="scmp_gcd.html#K1">intpos</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> <font color="Olive">b<sub>1</sub></font></span>)</span></span>)</span> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>76</sub></font> <a href="scmpds_2.html#K2">.</a> <span class="p1">(<span class="default"><a href="scmp_gcd.html#K1">intpos</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> <font color="Olive">b<sub>1</sub></font></span>)</span></span>)</span> ) )
 <b>by </b><i><a class="txt" href="scpqsort.html#E17:46"><i><font color="Green">E57</font></i></a>, <a class="txt" href="scpqsort.html#E19:46"><i><font color="Green">E59</font></i></a>, <a class="txt" href="scpqsort.html#E1:46_12"><i><font color="Green">E61</font></i></a>, <a class="txt" href="scpqsort.html#E3:46_12"><i><font color="Green">E63</font></i></a>, <a class="txt" href="scpqsort.html#E8:46_12"><i><font color="Green">E65</font></i></a>, <a class="txt" href="scpqsort.html#E9:46_12"><i><font color="Green">E66</font></i></a>, <a class="txt" href="scpqsort.html#E11:46_12"><i><font color="Green">E67</font></i></a>, <a class="txt" href="scpqsort.html#E12:46_12"><i><font color="Green">E68</font></i></a>, <a class="txt" href="scpqsort.html#E2:46_12_2_1_2"><i><font color="Green">E70</font></i></a>, <a class="ref" href="scmp_gcd.html#D3">SCMP_GCD:def 3</a></i>;<br/></div><b>end;</b></div></div><b>end;</b></div></div>
<b>end;</b></div><div><b>hereby </b>
<div class="add"><b>assume </b><a NAME="E1:46_12_3"/>
<font color="Maroon">c<sub>81</sub></font> <a href="xxreal_0.html#NR2" target="_self">&gt;=</a> <font color="Maroon">c<sub>82</sub></font>
 ;<br/><a NAME="E2:46_12_3"/><b>then </b><i><font color="Green">E69</font></i>: 
<font color="Maroon">c<sub>76</sub></font> <a href="scmpds_2.html#K2">.</a> <span class="p1">(<span class="default"><a href="scmp_gcd.html#K1">intpos</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default">2 <a href="nat_1.html#K2">*</a> <font color="Maroon">c<sub>79</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span> <a href="nat_1.html#K1">+</a> <span class="p4">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> <a href="xxreal_0.html#R1">&lt;=</a> <font color="Maroon">c<sub>76</sub></font> <a href="scmpds_2.html#K2">.</a> <span class="p1">(<span class="default"><a href="scmp_gcd.html#K1">intpos</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default">2 <a href="nat_1.html#K2">*</a> <font color="Maroon">c<sub>79</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span> <a href="nat_1.html#K1">+</a> <span class="p3">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span></span>)</span></span>)</span>
 <b>by </b><i><a class="txt" href="scpqsort.html#E3:46_12"><i><font color="Green">E63</font></i></a>, <a class="txt" href="scpqsort.html#E4:46_12"><i><font color="Green">E64</font></i></a>, <a class="ref" href="xreal_1.html#T8">XREAL_1:8</a></i>;<br/><b>hence </b><span class="p1">(<span class="default"><a href="scmpds_4.html#K9">IExec</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a> ,2 <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p5">(<span class="default"><span class="p0">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p4">(<span class="default"><a href="scmpds_2.html#K14">SubFrom</a> <a href="scmp_gcd.html#K2">GBP</a> ,2,<a href="scmp_gcd.html#K3">SBP</a> ,<span class="p5">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span></span>)</span></span>)</span> <a href="scmpds_4.html#K3">';'</a> <span class="p3">(<span class="default"><a href="scmpds_6.html#K3">if&gt;0</a> <a href="scmp_gcd.html#K2">GBP</a> ,2,<span class="p4">(<span class="default"><span class="p5">(<span class="default"><span class="p0">(<span class="default"><span class="p1">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a> ,2 <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p2">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span></span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p1">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a> ,4 <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span> <a href="scmpds_4.html#K3">';'</a> <font color="Maroon">c<sub>50</sub></font></span>)</span> <a href="scmpds_4.html#K3">';'</a> <span class="p5">(<span class="default"><span class="p0">(<span class="default"><span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a> ,<span class="p5">(<span class="default"><span class="p0">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 3</span>)</span> <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p5">(<span class="default"><span class="p0">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p4">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a> ,<span class="p5">(<span class="default"><span class="p0">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span> <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K2">GBP</a> ,4</span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p3">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a> ,<span class="p4">(<span class="default"><span class="p5">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 2</span>)</span> <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K2">GBP</a> ,4</span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p2">(<span class="default"><a href="scmpds_2.html#K12">AddTo</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span>,<span class="p3">(<span class="default"><a href="xcmplx_0.html#K4">-</a> 1</span>)</span></span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p1">(<span class="default"><a href="scmpds_2.html#K12">AddTo</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 2</span>)</span>,1</span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p0">(<span class="default"><a href="scmpds_2.html#K12">AddTo</a> <a href="scmp_gcd.html#K2">GBP</a> ,1,2</span>)</span></span>)</span></span>)</span>,<span class="p4">(<span class="default"><a href="scmpds_4.html#K1">Load</a> <span class="p5">(<span class="default"><a href="scmpds_2.html#K12">AddTo</a> <a href="scmp_gcd.html#K2">GBP</a> ,1,<span class="p0">(<span class="default"><a href="xcmplx_0.html#K4">-</a> 2</span>)</span></span>)</span></span>)</span></span>)</span></span>)</span>,<font color="Maroon">c<sub>76</sub></font></span>)</span> <a href="scmpds_2.html#K2">.</a> <span class="p1">(<span class="default"><a href="scmpds_2.html#K3">DataLoc</a> 0,1</span>)</span> = 
<span class="p1">(<span class="default"><span class="p2">(<span class="default">2 <a href="nat_1.html#K2">*</a> <font color="Maroon">c<sub>79</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span> <a href="xcmplx_0.html#K6">-</a> 2
<b>by </b><i><a class="txt" href="scpqsort.html#E18:46"><i><font color="Green">E58</font></i></a>, <a class="txt" href="scpqsort.html#E19:46"><i><font color="Green">E59</font></i></a>, <a class="txt" href="scpqsort.html#E1:46_12"><i><font color="Green">E61</font></i></a>, <a class="ref" href="scmp_gcd.html#D3">SCMP_GCD:def 3</a></i>
<br/>.= 
<span class="p1">(<span class="default">2 <a href="nat_1.html#K2">*</a> <font color="Maroon">c<sub>79</sub></font></span>)</span> <a href="xcmplx_0.html#K6">-</a> 1

;<br/><br/><b>thus </b><a NAME="E4:46_12_3"/>
for <font color="Olive">b<sub>1</sub></font> being  <a href="nat_1.html#NM1">Nat</a> st 1 <a href="xxreal_0.html#R1">&lt;=</a> <font color="Olive">b<sub>1</sub></font> &amp; <font color="Olive">b<sub>1</sub></font> <a href="xxreal_0.html#R1">&lt;=</a> <font color="Maroon">c<sub>49</sub></font> holds <br/><span class="p1">(<span class="default"><a href="scmpds_4.html#K9">IExec</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a> ,2 <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p5">(<span class="default"><span class="p0">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p4">(<span class="default"><a href="scmpds_2.html#K14">SubFrom</a> <a href="scmp_gcd.html#K2">GBP</a> ,2,<a href="scmp_gcd.html#K3">SBP</a> ,<span class="p5">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span></span>)</span></span>)</span> <a href="scmpds_4.html#K3">';'</a> <span class="p3">(<span class="default"><a href="scmpds_6.html#K3">if&gt;0</a> <a href="scmp_gcd.html#K2">GBP</a> ,2,<span class="p4">(<span class="default"><span class="p5">(<span class="default"><span class="p0">(<span class="default"><span class="p1">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a> ,2 <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p2">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span></span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p1">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a> ,4 <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span> <a href="scmpds_4.html#K3">';'</a> <font color="Maroon">c<sub>50</sub></font></span>)</span> <a href="scmpds_4.html#K3">';'</a> <span class="p5">(<span class="default"><span class="p0">(<span class="default"><span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a> ,<span class="p5">(<span class="default"><span class="p0">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 3</span>)</span> <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p5">(<span class="default"><span class="p0">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p4">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a> ,<span class="p5">(<span class="default"><span class="p0">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span> <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K2">GBP</a> ,4</span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p3">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a> ,<span class="p4">(<span class="default"><span class="p5">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 2</span>)</span> <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K2">GBP</a> ,4</span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p2">(<span class="default"><a href="scmpds_2.html#K12">AddTo</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span>,<span class="p3">(<span class="default"><a href="xcmplx_0.html#K4">-</a> 1</span>)</span></span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p1">(<span class="default"><a href="scmpds_2.html#K12">AddTo</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 2</span>)</span>,1</span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p0">(<span class="default"><a href="scmpds_2.html#K12">AddTo</a> <a href="scmp_gcd.html#K2">GBP</a> ,1,2</span>)</span></span>)</span></span>)</span>,<span class="p4">(<span class="default"><a href="scmpds_4.html#K1">Load</a> <span class="p5">(<span class="default"><a href="scmpds_2.html#K12">AddTo</a> <a href="scmp_gcd.html#K2">GBP</a> ,1,<span class="p0">(<span class="default"><a href="xcmplx_0.html#K4">-</a> 2</span>)</span></span>)</span></span>)</span></span>)</span></span>)</span>,<font color="Maroon">c<sub>76</sub></font></span>)</span> <a href="scmpds_2.html#K2">.</a> <span class="p1">(<span class="default"><a href="scmp_gcd.html#K1">intpos</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Olive">b<sub>1</sub></font></span>)</span></span>)</span> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>76</sub></font> <a href="scmpds_2.html#K2">.</a> <span class="p1">(<span class="default"><a href="scmp_gcd.html#K1">intpos</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Olive">b<sub>1</sub></font></span>)</span></span>)</span>
 <b>by </b><i><a class="txt" href="scpqsort.html#E18:46"><i><font color="Green">E58</font></i></a>, <a class="txt" href="scpqsort.html#E19:46"><i><font color="Green">E59</font></i></a>, <a class="txt" href="scpqsort.html#E1:46_12"><i><font color="Green">E61</font></i></a>, <a class="txt" href="scpqsort.html#E2:46_12_3"><i><font color="Green">E69</font></i></a>, <a class="ref" href="scmp_gcd.html#D3">SCMP_GCD:def 3</a></i>;<br/></div>
<b>end;</b></div><div><b>hereby </b>
<div class="add"><b>assume </b><a NAME="E1:46_12_4"/><i><font color="Green">E69</font></i>: 
<font color="Maroon">c<sub>81</sub></font> <a href="xxreal_0.html#NR3" target="_self">&lt;</a> <font color="Maroon">c<sub>82</sub></font>
 ;<br/><a NAME="E2:46_12_4"/><b>then </b>
<font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>82</sub></font> <a href="xxreal_0.html#NR4" target="_self">&gt;</a> <font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>81</sub></font>
 <b>by </b><i><a class="ref" href="xreal_1.html#T8">XREAL_1:8</a></i>;<br/><a NAME="E3:46_12_4"/><b>then </b><i><font color="Green">E70</font></i>: 
<span class="p1">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>82</sub></font></span>)</span> <a href="xcmplx_0.html#K6">-</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>81</sub></font></span>)</span> <a href="xxreal_0.html#NR4" target="_self">&gt;</a> 0
 <b>by </b><i><a class="ref" href="xreal_1.html#T52">XREAL_1:52</a></i>;<br/><a NAME="E4:46_12_4"/><i><font color="Green">E71</font></i>: 
( <font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> 1 <a href="xxreal_0.html#R1">&lt;=</a> <font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>81</sub></font> &amp; <font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>82</sub></font> <a href="xxreal_0.html#R1">&lt;=</a> <font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font> )
 <b>by </b><i><a class="txt" href="scpqsort.html#E1:46_12"><i><font color="Green">E61</font></i></a>, <a class="txt" href="scpqsort.html#E1:46_12_4"><i><font color="Green">E69</font></i></a>, <a class="ref" href="xreal_1.html#T8">XREAL_1:8</a></i>;<br/><b>hence </b><span class="p1">(<span class="default"><a href="scmpds_4.html#K9">IExec</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a> ,2 <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p5">(<span class="default"><span class="p0">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p4">(<span class="default"><a href="scmpds_2.html#K14">SubFrom</a> <a href="scmp_gcd.html#K2">GBP</a> ,2,<a href="scmp_gcd.html#K3">SBP</a> ,<span class="p5">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span></span>)</span></span>)</span> <a href="scmpds_4.html#K3">';'</a> <span class="p3">(<span class="default"><a href="scmpds_6.html#K3">if&gt;0</a> <a href="scmp_gcd.html#K2">GBP</a> ,2,<span class="p4">(<span class="default"><span class="p5">(<span class="default"><span class="p0">(<span class="default"><span class="p1">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a> ,2 <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p2">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span></span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p1">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a> ,4 <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span> <a href="scmpds_4.html#K3">';'</a> <font color="Maroon">c<sub>50</sub></font></span>)</span> <a href="scmpds_4.html#K3">';'</a> <span class="p5">(<span class="default"><span class="p0">(<span class="default"><span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a> ,<span class="p5">(<span class="default"><span class="p0">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 3</span>)</span> <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p5">(<span class="default"><span class="p0">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p4">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a> ,<span class="p5">(<span class="default"><span class="p0">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span> <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K2">GBP</a> ,4</span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p3">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a> ,<span class="p4">(<span class="default"><span class="p5">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 2</span>)</span> <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K2">GBP</a> ,4</span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p2">(<span class="default"><a href="scmpds_2.html#K12">AddTo</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span>,<span class="p3">(<span class="default"><a href="xcmplx_0.html#K4">-</a> 1</span>)</span></span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p1">(<span class="default"><a href="scmpds_2.html#K12">AddTo</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 2</span>)</span>,1</span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p0">(<span class="default"><a href="scmpds_2.html#K12">AddTo</a> <a href="scmp_gcd.html#K2">GBP</a> ,1,2</span>)</span></span>)</span></span>)</span>,<span class="p4">(<span class="default"><a href="scmpds_4.html#K1">Load</a> <span class="p5">(<span class="default"><a href="scmpds_2.html#K12">AddTo</a> <a href="scmp_gcd.html#K2">GBP</a> ,1,<span class="p0">(<span class="default"><a href="xcmplx_0.html#K4">-</a> 2</span>)</span></span>)</span></span>)</span></span>)</span></span>)</span>,<font color="Maroon">c<sub>76</sub></font></span>)</span> <a href="scmpds_2.html#K2">.</a> <span class="p1">(<span class="default"><a href="scmpds_2.html#K3">DataLoc</a> 0,1</span>)</span> = 
<span class="p1">(<span class="default"><span class="p2">(<span class="default">2 <a href="nat_1.html#K2">*</a> <font color="Maroon">c<sub>79</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span> <a href="nat_1.html#K1">+</a> 2
<b>by </b><i><a class="txt" href="scpqsort.html#E17:46"><i><font color="Green">E57</font></i></a>, <a class="txt" href="scpqsort.html#E19:46"><i><font color="Green">E59</font></i></a>, <a class="txt" href="scpqsort.html#E1:46_12"><i><font color="Green">E61</font></i></a>, <a class="txt" href="scpqsort.html#E3:46_12"><i><font color="Green">E63</font></i></a>, <a class="txt" href="scpqsort.html#E8:46_12"><i><font color="Green">E65</font></i></a>, <a class="txt" href="scpqsort.html#E9:46_12"><i><font color="Green">E66</font></i></a>, <a class="txt" href="scpqsort.html#E11:46_12"><i><font color="Green">E67</font></i></a>, <a class="txt" href="scpqsort.html#E12:46_12"><i><font color="Green">E68</font></i></a>, <a class="txt" href="scpqsort.html#E3:46_12_4"><i><font color="Green">E70</font></i></a>, <a class="ref" href="scmp_gcd.html#D3">SCMP_GCD:def 3</a></i>
<br/>.= 
<span class="p1">(<span class="default">2 <a href="nat_1.html#K2">*</a> <font color="Maroon">c<sub>79</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 3

;<br/><br/><b>consider </b><font color="Maroon">c<sub>89</sub></font> being   <a href="nat_1.html#NM1">Nat</a><b> such that </b><br/><a NAME="E7:46_12_4"/><i><font color="Green">E72</font></i>: 
( <font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>81</sub></font> <a href="xxreal_0.html#R1">&lt;=</a> <font color="Maroon">c<sub>89</sub></font> &amp; <font color="Maroon">c<sub>89</sub></font> <a href="xxreal_0.html#R1">&lt;=</a> <font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>82</sub></font> &amp; <font color="Maroon">c<sub>89</sub></font> <a href="xcmplx_0.html#K6">-</a> 1 <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><a href="scmpds_4.html#K9">IExec</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a> ,2 <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p5">(<span class="default"><span class="p0">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p4">(<span class="default"><a href="scmpds_2.html#K14">SubFrom</a> <a href="scmp_gcd.html#K2">GBP</a> ,2,<a href="scmp_gcd.html#K3">SBP</a> ,<span class="p5">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span></span>)</span></span>)</span> <a href="scmpds_4.html#K3">';'</a> <span class="p3">(<span class="default"><a href="scmpds_6.html#K3">if&gt;0</a> <a href="scmp_gcd.html#K2">GBP</a> ,2,<span class="p4">(<span class="default"><span class="p5">(<span class="default"><span class="p0">(<span class="default"><span class="p1">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a> ,2 <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p2">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span></span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p1">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a> ,4 <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span> <a href="scmpds_4.html#K3">';'</a> <font color="Maroon">c<sub>50</sub></font></span>)</span> <a href="scmpds_4.html#K3">';'</a> <span class="p5">(<span class="default"><span class="p0">(<span class="default"><span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a> ,<span class="p5">(<span class="default"><span class="p0">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 3</span>)</span> <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p5">(<span class="default"><span class="p0">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p4">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a> ,<span class="p5">(<span class="default"><span class="p0">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span> <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K2">GBP</a> ,4</span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p3">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a> ,<span class="p4">(<span class="default"><span class="p5">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 2</span>)</span> <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K2">GBP</a> ,4</span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p2">(<span class="default"><a href="scmpds_2.html#K12">AddTo</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span>,<span class="p3">(<span class="default"><a href="xcmplx_0.html#K4">-</a> 1</span>)</span></span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p1">(<span class="default"><a href="scmpds_2.html#K12">AddTo</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 2</span>)</span>,1</span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p0">(<span class="default"><a href="scmpds_2.html#K12">AddTo</a> <a href="scmp_gcd.html#K2">GBP</a> ,1,2</span>)</span></span>)</span></span>)</span>,<span class="p4">(<span class="default"><a href="scmpds_4.html#K1">Load</a> <span class="p5">(<span class="default"><a href="scmpds_2.html#K12">AddTo</a> <a href="scmp_gcd.html#K2">GBP</a> ,1,<span class="p0">(<span class="default"><a href="xcmplx_0.html#K4">-</a> 2</span>)</span></span>)</span></span>)</span></span>)</span></span>)</span>,<font color="Maroon">c<sub>76</sub></font></span>)</span> <a href="scmpds_2.html#K2">.</a> <span class="p1">(<span class="default"><a href="scmp_gcd.html#K1">intpos</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default">2 <a href="nat_1.html#K2">*</a> <font color="Maroon">c<sub>79</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span> <a href="nat_1.html#K1">+</a> <span class="p4">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> &amp; <font color="Maroon">c<sub>89</sub></font> <a href="nat_1.html#K1">+</a> 1 <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><a href="scmpds_4.html#K9">IExec</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a> ,2 <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p5">(<span class="default"><span class="p0">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p4">(<span class="default"><a href="scmpds_2.html#K14">SubFrom</a> <a href="scmp_gcd.html#K2">GBP</a> ,2,<a href="scmp_gcd.html#K3">SBP</a> ,<span class="p5">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span></span>)</span></span>)</span> <a href="scmpds_4.html#K3">';'</a> <span class="p3">(<span class="default"><a href="scmpds_6.html#K3">if&gt;0</a> <a href="scmp_gcd.html#K2">GBP</a> ,2,<span class="p4">(<span class="default"><span class="p5">(<span class="default"><span class="p0">(<span class="default"><span class="p1">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a> ,2 <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p2">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span></span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p1">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a> ,4 <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span> <a href="scmpds_4.html#K3">';'</a> <font color="Maroon">c<sub>50</sub></font></span>)</span> <a href="scmpds_4.html#K3">';'</a> <span class="p5">(<span class="default"><span class="p0">(<span class="default"><span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a> ,<span class="p5">(<span class="default"><span class="p0">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 3</span>)</span> <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p5">(<span class="default"><span class="p0">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p4">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a> ,<span class="p5">(<span class="default"><span class="p0">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span> <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K2">GBP</a> ,4</span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p3">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a> ,<span class="p4">(<span class="default"><span class="p5">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 2</span>)</span> <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K2">GBP</a> ,4</span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p2">(<span class="default"><a href="scmpds_2.html#K12">AddTo</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span>,<span class="p3">(<span class="default"><a href="xcmplx_0.html#K4">-</a> 1</span>)</span></span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p1">(<span class="default"><a href="scmpds_2.html#K12">AddTo</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 2</span>)</span>,1</span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p0">(<span class="default"><a href="scmpds_2.html#K12">AddTo</a> <a href="scmp_gcd.html#K2">GBP</a> ,1,2</span>)</span></span>)</span></span>)</span>,<span class="p4">(<span class="default"><a href="scmpds_4.html#K1">Load</a> <span class="p5">(<span class="default"><a href="scmpds_2.html#K12">AddTo</a> <a href="scmp_gcd.html#K2">GBP</a> ,1,<span class="p0">(<span class="default"><a href="xcmplx_0.html#K4">-</a> 2</span>)</span></span>)</span></span>)</span></span>)</span></span>)</span>,<font color="Maroon">c<sub>76</sub></font></span>)</span> <a href="scmpds_2.html#K2">.</a> <span class="p1">(<span class="default"><a href="scmp_gcd.html#K1">intpos</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default">2 <a href="nat_1.html#K2">*</a> <font color="Maroon">c<sub>79</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span> <a href="nat_1.html#K1">+</a> <span class="p4">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span></span>)</span> <a href="nat_1.html#K1">+</a> 2</span>)</span></span>)</span> &amp; ( for <font color="Olive">b<sub>1</sub></font> being  <a href="nat_1.html#NM1">Nat</a> st <font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>81</sub></font> <a href="xxreal_0.html#R1">&lt;=</a> <font color="Olive">b<sub>1</sub></font> &amp; <font color="Olive">b<sub>1</sub></font> <a href="xxreal_0.html#NR3" target="_self">&lt;</a> <font color="Maroon">c<sub>89</sub></font> holds <br/><span class="p1">(<span class="default"><a href="scmpds_4.html#K9">IExec</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a> ,2 <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p5">(<span class="default"><span class="p0">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p4">(<span class="default"><a href="scmpds_2.html#K14">SubFrom</a> <a href="scmp_gcd.html#K2">GBP</a> ,2,<a href="scmp_gcd.html#K3">SBP</a> ,<span class="p5">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span></span>)</span></span>)</span> <a href="scmpds_4.html#K3">';'</a> <span class="p3">(<span class="default"><a href="scmpds_6.html#K3">if&gt;0</a> <a href="scmp_gcd.html#K2">GBP</a> ,2,<span class="p4">(<span class="default"><span class="p5">(<span class="default"><span class="p0">(<span class="default"><span class="p1">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a> ,2 <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p2">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span></span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p1">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a> ,4 <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span> <a href="scmpds_4.html#K3">';'</a> <font color="Maroon">c<sub>50</sub></font></span>)</span> <a href="scmpds_4.html#K3">';'</a> <span class="p5">(<span class="default"><span class="p0">(<span class="default"><span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a> ,<span class="p5">(<span class="default"><span class="p0">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 3</span>)</span> <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p5">(<span class="default"><span class="p0">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p4">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a> ,<span class="p5">(<span class="default"><span class="p0">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span> <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K2">GBP</a> ,4</span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p3">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a> ,<span class="p4">(<span class="default"><span class="p5">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 2</span>)</span> <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K2">GBP</a> ,4</span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p2">(<span class="default"><a href="scmpds_2.html#K12">AddTo</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span>,<span class="p3">(<span class="default"><a href="xcmplx_0.html#K4">-</a> 1</span>)</span></span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p1">(<span class="default"><a href="scmpds_2.html#K12">AddTo</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 2</span>)</span>,1</span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p0">(<span class="default"><a href="scmpds_2.html#K12">AddTo</a> <a href="scmp_gcd.html#K2">GBP</a> ,1,2</span>)</span></span>)</span></span>)</span>,<span class="p4">(<span class="default"><a href="scmpds_4.html#K1">Load</a> <span class="p5">(<span class="default"><a href="scmpds_2.html#K12">AddTo</a> <a href="scmp_gcd.html#K2">GBP</a> ,1,<span class="p0">(<span class="default"><a href="xcmplx_0.html#K4">-</a> 2</span>)</span></span>)</span></span>)</span></span>)</span></span>)</span>,<font color="Maroon">c<sub>76</sub></font></span>)</span> <a href="scmpds_2.html#K2">.</a> <span class="p1">(<span class="default"><a href="scmp_gcd.html#K1">intpos</a> <font color="Maroon">c<sub>89</sub></font></span>)</span> <a href="xxreal_0.html#NR2" target="_self">&gt;=</a> <span class="p1">(<span class="default"><a href="scmpds_4.html#K9">IExec</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a> ,2 <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p5">(<span class="default"><span class="p0">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p4">(<span class="default"><a href="scmpds_2.html#K14">SubFrom</a> <a href="scmp_gcd.html#K2">GBP</a> ,2,<a href="scmp_gcd.html#K3">SBP</a> ,<span class="p5">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span></span>)</span></span>)</span> <a href="scmpds_4.html#K3">';'</a> <span class="p3">(<span class="default"><a href="scmpds_6.html#K3">if&gt;0</a> <a href="scmp_gcd.html#K2">GBP</a> ,2,<span class="p4">(<span class="default"><span class="p5">(<span class="default"><span class="p0">(<span class="default"><span class="p1">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a> ,2 <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p2">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span></span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p1">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a> ,4 <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span> <a href="scmpds_4.html#K3">';'</a> <font color="Maroon">c<sub>50</sub></font></span>)</span> <a href="scmpds_4.html#K3">';'</a> <span class="p5">(<span class="default"><span class="p0">(<span class="default"><span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a> ,<span class="p5">(<span class="default"><span class="p0">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 3</span>)</span> <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p5">(<span class="default"><span class="p0">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p4">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a> ,<span class="p5">(<span class="default"><span class="p0">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span> <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K2">GBP</a> ,4</span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p3">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a> ,<span class="p4">(<span class="default"><span class="p5">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 2</span>)</span> <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K2">GBP</a> ,4</span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p2">(<span class="default"><a href="scmpds_2.html#K12">AddTo</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span>,<span class="p3">(<span class="default"><a href="xcmplx_0.html#K4">-</a> 1</span>)</span></span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p1">(<span class="default"><a href="scmpds_2.html#K12">AddTo</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 2</span>)</span>,1</span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p0">(<span class="default"><a href="scmpds_2.html#K12">AddTo</a> <a href="scmp_gcd.html#K2">GBP</a> ,1,2</span>)</span></span>)</span></span>)</span>,<span class="p4">(<span class="default"><a href="scmpds_4.html#K1">Load</a> <span class="p5">(<span class="default"><a href="scmpds_2.html#K12">AddTo</a> <a href="scmp_gcd.html#K2">GBP</a> ,1,<span class="p0">(<span class="default"><a href="xcmplx_0.html#K4">-</a> 2</span>)</span></span>)</span></span>)</span></span>)</span></span>)</span>,<font color="Maroon">c<sub>76</sub></font></span>)</span> <a href="scmpds_2.html#K2">.</a> <span class="p1">(<span class="default"><a href="scmp_gcd.html#K1">intpos</a> <font color="Olive">b<sub>1</sub></font></span>)</span> ) &amp; ( for <font color="Olive">b<sub>1</sub></font> being  <a href="nat_1.html#NM1">Nat</a> st <font color="Maroon">c<sub>89</sub></font> <a href="xxreal_0.html#NR3" target="_self">&lt;</a> <font color="Olive">b<sub>1</sub></font> &amp; <font color="Olive">b<sub>1</sub></font> <a href="xxreal_0.html#R1">&lt;=</a> <font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>82</sub></font> holds <br/><span class="p1">(<span class="default"><a href="scmpds_4.html#K9">IExec</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a> ,2 <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p5">(<span class="default"><span class="p0">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p4">(<span class="default"><a href="scmpds_2.html#K14">SubFrom</a> <a href="scmp_gcd.html#K2">GBP</a> ,2,<a href="scmp_gcd.html#K3">SBP</a> ,<span class="p5">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span></span>)</span></span>)</span> <a href="scmpds_4.html#K3">';'</a> <span class="p3">(<span class="default"><a href="scmpds_6.html#K3">if&gt;0</a> <a href="scmp_gcd.html#K2">GBP</a> ,2,<span class="p4">(<span class="default"><span class="p5">(<span class="default"><span class="p0">(<span class="default"><span class="p1">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a> ,2 <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p2">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span></span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p1">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a> ,4 <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span> <a href="scmpds_4.html#K3">';'</a> <font color="Maroon">c<sub>50</sub></font></span>)</span> <a href="scmpds_4.html#K3">';'</a> <span class="p5">(<span class="default"><span class="p0">(<span class="default"><span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a> ,<span class="p5">(<span class="default"><span class="p0">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 3</span>)</span> <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p5">(<span class="default"><span class="p0">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p4">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a> ,<span class="p5">(<span class="default"><span class="p0">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span> <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K2">GBP</a> ,4</span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p3">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a> ,<span class="p4">(<span class="default"><span class="p5">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 2</span>)</span> <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K2">GBP</a> ,4</span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p2">(<span class="default"><a href="scmpds_2.html#K12">AddTo</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span>,<span class="p3">(<span class="default"><a href="xcmplx_0.html#K4">-</a> 1</span>)</span></span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p1">(<span class="default"><a href="scmpds_2.html#K12">AddTo</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 2</span>)</span>,1</span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p0">(<span class="default"><a href="scmpds_2.html#K12">AddTo</a> <a href="scmp_gcd.html#K2">GBP</a> ,1,2</span>)</span></span>)</span></span>)</span>,<span class="p4">(<span class="default"><a href="scmpds_4.html#K1">Load</a> <span class="p5">(<span class="default"><a href="scmpds_2.html#K12">AddTo</a> <a href="scmp_gcd.html#K2">GBP</a> ,1,<span class="p0">(<span class="default"><a href="xcmplx_0.html#K4">-</a> 2</span>)</span></span>)</span></span>)</span></span>)</span></span>)</span>,<font color="Maroon">c<sub>76</sub></font></span>)</span> <a href="scmpds_2.html#K2">.</a> <span class="p1">(<span class="default"><a href="scmp_gcd.html#K1">intpos</a> <font color="Maroon">c<sub>89</sub></font></span>)</span> <a href="xxreal_0.html#R1">&lt;=</a> <span class="p1">(<span class="default"><a href="scmpds_4.html#K9">IExec</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a> ,2 <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p5">(<span class="default"><span class="p0">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p4">(<span class="default"><a href="scmpds_2.html#K14">SubFrom</a> <a href="scmp_gcd.html#K2">GBP</a> ,2,<a href="scmp_gcd.html#K3">SBP</a> ,<span class="p5">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span></span>)</span></span>)</span> <a href="scmpds_4.html#K3">';'</a> <span class="p3">(<span class="default"><a href="scmpds_6.html#K3">if&gt;0</a> <a href="scmp_gcd.html#K2">GBP</a> ,2,<span class="p4">(<span class="default"><span class="p5">(<span class="default"><span class="p0">(<span class="default"><span class="p1">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a> ,2 <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p2">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span></span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p1">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a> ,4 <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span> <a href="scmpds_4.html#K3">';'</a> <font color="Maroon">c<sub>50</sub></font></span>)</span> <a href="scmpds_4.html#K3">';'</a> <span class="p5">(<span class="default"><span class="p0">(<span class="default"><span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a> ,<span class="p5">(<span class="default"><span class="p0">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 3</span>)</span> <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p5">(<span class="default"><span class="p0">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p4">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a> ,<span class="p5">(<span class="default"><span class="p0">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span> <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K2">GBP</a> ,4</span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p3">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a> ,<span class="p4">(<span class="default"><span class="p5">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 2</span>)</span> <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K2">GBP</a> ,4</span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p2">(<span class="default"><a href="scmpds_2.html#K12">AddTo</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span>,<span class="p3">(<span class="default"><a href="xcmplx_0.html#K4">-</a> 1</span>)</span></span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p1">(<span class="default"><a href="scmpds_2.html#K12">AddTo</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 2</span>)</span>,1</span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p0">(<span class="default"><a href="scmpds_2.html#K12">AddTo</a> <a href="scmp_gcd.html#K2">GBP</a> ,1,2</span>)</span></span>)</span></span>)</span>,<span class="p4">(<span class="default"><a href="scmpds_4.html#K1">Load</a> <span class="p5">(<span class="default"><a href="scmpds_2.html#K12">AddTo</a> <a href="scmp_gcd.html#K2">GBP</a> ,1,<span class="p0">(<span class="default"><a href="xcmplx_0.html#K4">-</a> 2</span>)</span></span>)</span></span>)</span></span>)</span></span>)</span>,<font color="Maroon">c<sub>76</sub></font></span>)</span> <a href="scmpds_2.html#K2">.</a> <span class="p1">(<span class="default"><a href="scmp_gcd.html#K1">intpos</a> <font color="Olive">b<sub>1</sub></font></span>)</span> ) &amp; ( for <font color="Olive">b<sub>1</sub></font> being  <a href="nat_1.html#NM1">Nat</a> st ( ( <font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> 1 <a href="xxreal_0.html#R1">&lt;=</a> <font color="Olive">b<sub>1</sub></font> &amp; <font color="Olive">b<sub>1</sub></font> <a href="xxreal_0.html#NR3" target="_self">&lt;</a> <font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>81</sub></font> ) or ( <font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>82</sub></font> <a href="xxreal_0.html#NR3" target="_self">&lt;</a> <font color="Olive">b<sub>1</sub></font> &amp; <font color="Olive">b<sub>1</sub></font> <a href="xxreal_0.html#R1">&lt;=</a> <font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font> ) ) holds <br/><span class="p1">(<span class="default"><a href="scmpds_4.html#K9">IExec</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a> ,2 <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p5">(<span class="default"><span class="p0">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p4">(<span class="default"><a href="scmpds_2.html#K14">SubFrom</a> <a href="scmp_gcd.html#K2">GBP</a> ,2,<a href="scmp_gcd.html#K3">SBP</a> ,<span class="p5">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span></span>)</span></span>)</span> <a href="scmpds_4.html#K3">';'</a> <span class="p3">(<span class="default"><a href="scmpds_6.html#K3">if&gt;0</a> <a href="scmp_gcd.html#K2">GBP</a> ,2,<span class="p4">(<span class="default"><span class="p5">(<span class="default"><span class="p0">(<span class="default"><span class="p1">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a> ,2 <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p2">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span></span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p1">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a> ,4 <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span> <a href="scmpds_4.html#K3">';'</a> <font color="Maroon">c<sub>50</sub></font></span>)</span> <a href="scmpds_4.html#K3">';'</a> <span class="p5">(<span class="default"><span class="p0">(<span class="default"><span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a> ,<span class="p5">(<span class="default"><span class="p0">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 3</span>)</span> <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p5">(<span class="default"><span class="p0">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p4">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a> ,<span class="p5">(<span class="default"><span class="p0">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span> <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K2">GBP</a> ,4</span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p3">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a> ,<span class="p4">(<span class="default"><span class="p5">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 2</span>)</span> <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K2">GBP</a> ,4</span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p2">(<span class="default"><a href="scmpds_2.html#K12">AddTo</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span>,<span class="p3">(<span class="default"><a href="xcmplx_0.html#K4">-</a> 1</span>)</span></span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p1">(<span class="default"><a href="scmpds_2.html#K12">AddTo</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 2</span>)</span>,1</span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p0">(<span class="default"><a href="scmpds_2.html#K12">AddTo</a> <a href="scmp_gcd.html#K2">GBP</a> ,1,2</span>)</span></span>)</span></span>)</span>,<span class="p4">(<span class="default"><a href="scmpds_4.html#K1">Load</a> <span class="p5">(<span class="default"><a href="scmpds_2.html#K12">AddTo</a> <a href="scmp_gcd.html#K2">GBP</a> ,1,<span class="p0">(<span class="default"><a href="xcmplx_0.html#K4">-</a> 2</span>)</span></span>)</span></span>)</span></span>)</span></span>)</span>,<font color="Maroon">c<sub>76</sub></font></span>)</span> <a href="scmpds_2.html#K2">.</a> <span class="p1">(<span class="default"><a href="scmp_gcd.html#K1">intpos</a> <font color="Olive">b<sub>1</sub></font></span>)</span> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>76</sub></font> <a href="scmpds_2.html#K2">.</a> <span class="p1">(<span class="default"><a href="scmp_gcd.html#K1">intpos</a> <font color="Olive">b<sub>1</sub></font></span>)</span> ) )
 <b>by </b><i><a class="txt" href="scpqsort.html#E17:46"><i><font color="Green">E57</font></i></a>, <a class="txt" href="scpqsort.html#E19:46"><i><font color="Green">E59</font></i></a>, <a class="txt" href="scpqsort.html#E1:46_12"><i><font color="Green">E61</font></i></a>, <a class="txt" href="scpqsort.html#E8:46_12"><i><font color="Green">E65</font></i></a>, <a class="txt" href="scpqsort.html#E9:46_12"><i><font color="Green">E66</font></i></a>, <a class="txt" href="scpqsort.html#E11:46_12"><i><font color="Green">E67</font></i></a>, <a class="txt" href="scpqsort.html#E12:46_12"><i><font color="Green">E68</font></i></a>, <a class="txt" href="scpqsort.html#E3:46_12_4"><i><font color="Green">E70</font></i></a>, <a class="txt" href="scpqsort.html#E4:46_12_4"><i><font color="Green">E71</font></i></a>, <a class="ref" href="scmp_gcd.html#D3">SCMP_GCD:def 3</a></i>;<br/><div><b>hereby </b>
<div class="add"><b>let </b><font color="Maroon">c<sub>90</sub></font> be   <a href="nat_1.html#NM1">Nat</a>;<br/><b>assume </b><a NAME="E1:46_12_4_2"/>
( ( 1 <a href="xxreal_0.html#R1">&lt;=</a> <font color="Maroon">c<sub>90</sub></font> &amp; <font color="Maroon">c<sub>90</sub></font> <a href="xxreal_0.html#NR3" target="_self">&lt;</a> <font color="Maroon">c<sub>81</sub></font> ) or ( <font color="Maroon">c<sub>82</sub></font> <a href="xxreal_0.html#NR3" target="_self">&lt;</a> <font color="Maroon">c<sub>90</sub></font> &amp; <font color="Maroon">c<sub>90</sub></font> <a href="xxreal_0.html#R1">&lt;=</a> <font color="Maroon">c<sub>49</sub></font> ) )
 ;<br/><a NAME="E2:46_12_4_2"/><b>then </b>
( ( <font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> 1 <a href="xxreal_0.html#R1">&lt;=</a> <font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>90</sub></font> &amp; <font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>90</sub></font> <a href="xxreal_0.html#NR3" target="_self">&lt;</a> <font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>81</sub></font> ) or ( <font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>82</sub></font> <a href="xxreal_0.html#NR3" target="_self">&lt;</a> <font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>90</sub></font> &amp; <font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>90</sub></font> <a href="xxreal_0.html#R1">&lt;=</a> <font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font> ) )
 <b>by </b><i><a class="ref" href="xreal_1.html#T8">XREAL_1:8</a></i>;<br/><b>hence </b><a NAME="E3:46_12_4_2"/>
<span class="p1">(<span class="default"><a href="scmpds_4.html#K9">IExec</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a> ,2 <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p5">(<span class="default"><span class="p0">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p4">(<span class="default"><a href="scmpds_2.html#K14">SubFrom</a> <a href="scmp_gcd.html#K2">GBP</a> ,2,<a href="scmp_gcd.html#K3">SBP</a> ,<span class="p5">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span></span>)</span></span>)</span> <a href="scmpds_4.html#K3">';'</a> <span class="p3">(<span class="default"><a href="scmpds_6.html#K3">if&gt;0</a> <a href="scmp_gcd.html#K2">GBP</a> ,2,<span class="p4">(<span class="default"><span class="p5">(<span class="default"><span class="p0">(<span class="default"><span class="p1">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a> ,2 <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p2">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span></span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p1">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a> ,4 <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span> <a href="scmpds_4.html#K3">';'</a> <font color="Maroon">c<sub>50</sub></font></span>)</span> <a href="scmpds_4.html#K3">';'</a> <span class="p5">(<span class="default"><span class="p0">(<span class="default"><span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a> ,<span class="p5">(<span class="default"><span class="p0">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 3</span>)</span> <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p5">(<span class="default"><span class="p0">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p4">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a> ,<span class="p5">(<span class="default"><span class="p0">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span> <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K2">GBP</a> ,4</span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p3">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a> ,<span class="p4">(<span class="default"><span class="p5">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 2</span>)</span> <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K2">GBP</a> ,4</span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p2">(<span class="default"><a href="scmpds_2.html#K12">AddTo</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span>,<span class="p3">(<span class="default"><a href="xcmplx_0.html#K4">-</a> 1</span>)</span></span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p1">(<span class="default"><a href="scmpds_2.html#K12">AddTo</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 2</span>)</span>,1</span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p0">(<span class="default"><a href="scmpds_2.html#K12">AddTo</a> <a href="scmp_gcd.html#K2">GBP</a> ,1,2</span>)</span></span>)</span></span>)</span>,<span class="p4">(<span class="default"><a href="scmpds_4.html#K1">Load</a> <span class="p5">(<span class="default"><a href="scmpds_2.html#K12">AddTo</a> <a href="scmp_gcd.html#K2">GBP</a> ,1,<span class="p0">(<span class="default"><a href="xcmplx_0.html#K4">-</a> 2</span>)</span></span>)</span></span>)</span></span>)</span></span>)</span>,<font color="Maroon">c<sub>76</sub></font></span>)</span> <a href="scmpds_2.html#K2">.</a> <span class="p1">(<span class="default"><a href="scmp_gcd.html#K1">intpos</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>90</sub></font></span>)</span></span>)</span> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>76</sub></font> <a href="scmpds_2.html#K2">.</a> <span class="p1">(<span class="default"><a href="scmp_gcd.html#K1">intpos</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>90</sub></font></span>)</span></span>)</span>
 <b>by </b><i><a class="txt" href="scpqsort.html#E7:46_12_4"><i><font color="Green">E72</font></i></a></i>;<br/></div>
<b>end;</b></div><a NAME="E9:46_12_4"/><i><font color="Green">E73</font></i>: 
<font color="Maroon">c<sub>89</sub></font> <a href="xcmplx_0.html#K6">-</a> <font color="Maroon">c<sub>48</sub></font> <a href="xxreal_0.html#NR2" target="_self">&gt;=</a> <font color="Maroon">c<sub>81</sub></font>
 <b>by </b><i><a class="txt" href="scpqsort.html#E7:46_12_4"><i><font color="Green">E72</font></i></a>, <a class="ref" href="xreal_1.html#T21">XREAL_1:21</a></i>;<br/><b>reconsider </b><font color="Maroon">c<sub>90</sub></font> = <font color="Maroon">c<sub>89</sub></font> <a href="xcmplx_0.html#K6">-</a> <font color="Maroon">c<sub>48</sub></font> as   <a href="nat_1.html#NM1">Nat</a> <b>by </b><i><a class="txt" href="scpqsort.html#E9:46_12_4"><i><font color="Green">E73</font></i></a>, <a class="ref" href="int_1.html#T16">INT_1:16</a></i>;<br/><a NAME="E11:46_12_4"/><i><font color="Green">E74</font></i>: 
<font color="Maroon">c<sub>89</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>90</sub></font>
 ;<br/><b>take </b><font color="Maroon">c<sub>91</sub></font> = <font color="Maroon">c<sub>90</sub></font>;<br/><b>thus </b><a NAME="E12:46_12_4"/>
( <font color="Maroon">c<sub>81</sub></font> <a href="xxreal_0.html#R1">&lt;=</a> <font color="Maroon">c<sub>91</sub></font> &amp; <font color="Maroon">c<sub>91</sub></font> <a href="xxreal_0.html#R1">&lt;=</a> <font color="Maroon">c<sub>82</sub></font> )
 <b>by </b><i><a class="txt" href="scpqsort.html#E7:46_12_4"><i><font color="Green">E72</font></i></a>, <a class="txt" href="scpqsort.html#E11:46_12_4"><i><font color="Green">E74</font></i></a>, <a class="ref" href="xreal_1.html#T8">XREAL_1:8</a></i>;<br/><b>thus </b><a NAME="E13:46_12_4"/>
<font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>81</sub></font> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><a href="scmpds_4.html#K9">IExec</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a> ,2 <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p5">(<span class="default"><span class="p0">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p4">(<span class="default"><a href="scmpds_2.html#K14">SubFrom</a> <a href="scmp_gcd.html#K2">GBP</a> ,2,<a href="scmp_gcd.html#K3">SBP</a> ,<span class="p5">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span></span>)</span></span>)</span> <a href="scmpds_4.html#K3">';'</a> <span class="p3">(<span class="default"><a href="scmpds_6.html#K3">if&gt;0</a> <a href="scmp_gcd.html#K2">GBP</a> ,2,<span class="p4">(<span class="default"><span class="p5">(<span class="default"><span class="p0">(<span class="default"><span class="p1">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a> ,2 <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p2">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span></span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p1">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a> ,4 <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span> <a href="scmpds_4.html#K3">';'</a> <font color="Maroon">c<sub>50</sub></font></span>)</span> <a href="scmpds_4.html#K3">';'</a> <span class="p5">(<span class="default"><span class="p0">(<span class="default"><span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a> ,<span class="p5">(<span class="default"><span class="p0">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 3</span>)</span> <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p5">(<span class="default"><span class="p0">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p4">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a> ,<span class="p5">(<span class="default"><span class="p0">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span> <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K2">GBP</a> ,4</span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p3">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a> ,<span class="p4">(<span class="default"><span class="p5">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 2</span>)</span> <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K2">GBP</a> ,4</span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p2">(<span class="default"><a href="scmpds_2.html#K12">AddTo</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span>,<span class="p3">(<span class="default"><a href="xcmplx_0.html#K4">-</a> 1</span>)</span></span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p1">(<span class="default"><a href="scmpds_2.html#K12">AddTo</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 2</span>)</span>,1</span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p0">(<span class="default"><a href="scmpds_2.html#K12">AddTo</a> <a href="scmp_gcd.html#K2">GBP</a> ,1,2</span>)</span></span>)</span></span>)</span>,<span class="p4">(<span class="default"><a href="scmpds_4.html#K1">Load</a> <span class="p5">(<span class="default"><a href="scmpds_2.html#K12">AddTo</a> <a href="scmp_gcd.html#K2">GBP</a> ,1,<span class="p0">(<span class="default"><a href="xcmplx_0.html#K4">-</a> 2</span>)</span></span>)</span></span>)</span></span>)</span></span>)</span>,<font color="Maroon">c<sub>76</sub></font></span>)</span> <a href="scmpds_2.html#K2">.</a> <span class="p1">(<span class="default"><a href="scmp_gcd.html#K1">intpos</a> <font color="Maroon">c<sub>80</sub></font></span>)</span>
 <b>by </b><i><a class="txt" href="scpqsort.html#E17:46"><i><font color="Green">E57</font></i></a>, <a class="txt" href="scpqsort.html#E19:46"><i><font color="Green">E59</font></i></a>, <a class="txt" href="scpqsort.html#E1:46_12"><i><font color="Green">E61</font></i></a>, <a class="txt" href="scpqsort.html#E2:46_12"><i><font color="Green">E62</font></i></a>, <a class="txt" href="scpqsort.html#E8:46_12"><i><font color="Green">E65</font></i></a>, <a class="txt" href="scpqsort.html#E9:46_12"><i><font color="Green">E66</font></i></a>, <a class="txt" href="scpqsort.html#E11:46_12"><i><font color="Green">E67</font></i></a>, <a class="txt" href="scpqsort.html#E12:46_12"><i><font color="Green">E68</font></i></a>, <a class="txt" href="scpqsort.html#E3:46_12_4"><i><font color="Green">E70</font></i></a>, <a class="txt" href="scpqsort.html#E4:46_12_4"><i><font color="Green">E71</font></i></a>, <a class="ref" href="scmp_gcd.html#D3">SCMP_GCD:def 3</a></i>;<br/><b>thus </b><a NAME="E14:46_12_4"/>
<span class="p1">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>91</sub></font></span>)</span> <a href="xcmplx_0.html#K6">-</a> 1 <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><a href="scmpds_4.html#K9">IExec</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a> ,2 <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p5">(<span class="default"><span class="p0">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p4">(<span class="default"><a href="scmpds_2.html#K14">SubFrom</a> <a href="scmp_gcd.html#K2">GBP</a> ,2,<a href="scmp_gcd.html#K3">SBP</a> ,<span class="p5">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span></span>)</span></span>)</span> <a href="scmpds_4.html#K3">';'</a> <span class="p3">(<span class="default"><a href="scmpds_6.html#K3">if&gt;0</a> <a href="scmp_gcd.html#K2">GBP</a> ,2,<span class="p4">(<span class="default"><span class="p5">(<span class="default"><span class="p0">(<span class="default"><span class="p1">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a> ,2 <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p2">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span></span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p1">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a> ,4 <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span> <a href="scmpds_4.html#K3">';'</a> <font color="Maroon">c<sub>50</sub></font></span>)</span> <a href="scmpds_4.html#K3">';'</a> <span class="p5">(<span class="default"><span class="p0">(<span class="default"><span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a> ,<span class="p5">(<span class="default"><span class="p0">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 3</span>)</span> <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p5">(<span class="default"><span class="p0">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p4">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a> ,<span class="p5">(<span class="default"><span class="p0">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span> <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K2">GBP</a> ,4</span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p3">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a> ,<span class="p4">(<span class="default"><span class="p5">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 2</span>)</span> <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K2">GBP</a> ,4</span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p2">(<span class="default"><a href="scmpds_2.html#K12">AddTo</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span>,<span class="p3">(<span class="default"><a href="xcmplx_0.html#K4">-</a> 1</span>)</span></span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p1">(<span class="default"><a href="scmpds_2.html#K12">AddTo</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 2</span>)</span>,1</span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p0">(<span class="default"><a href="scmpds_2.html#K12">AddTo</a> <a href="scmp_gcd.html#K2">GBP</a> ,1,2</span>)</span></span>)</span></span>)</span>,<span class="p4">(<span class="default"><a href="scmpds_4.html#K1">Load</a> <span class="p5">(<span class="default"><a href="scmpds_2.html#K12">AddTo</a> <a href="scmp_gcd.html#K2">GBP</a> ,1,<span class="p0">(<span class="default"><a href="xcmplx_0.html#K4">-</a> 2</span>)</span></span>)</span></span>)</span></span>)</span></span>)</span>,<font color="Maroon">c<sub>76</sub></font></span>)</span> <a href="scmpds_2.html#K2">.</a> <span class="p1">(<span class="default"><a href="scmp_gcd.html#K1">intpos</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>80</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span>
 <b>by </b><i><a class="txt" href="scpqsort.html#E1:46_12"><i><font color="Green">E61</font></i></a>, <a class="txt" href="scpqsort.html#E7:46_12_4"><i><font color="Green">E72</font></i></a></i>;<br/><b>thus </b><a NAME="E15:46_12_4"/>
<span class="p1">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>91</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 1 <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><a href="scmpds_4.html#K9">IExec</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a> ,2 <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p5">(<span class="default"><span class="p0">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p4">(<span class="default"><a href="scmpds_2.html#K14">SubFrom</a> <a href="scmp_gcd.html#K2">GBP</a> ,2,<a href="scmp_gcd.html#K3">SBP</a> ,<span class="p5">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span></span>)</span></span>)</span> <a href="scmpds_4.html#K3">';'</a> <span class="p3">(<span class="default"><a href="scmpds_6.html#K3">if&gt;0</a> <a href="scmp_gcd.html#K2">GBP</a> ,2,<span class="p4">(<span class="default"><span class="p5">(<span class="default"><span class="p0">(<span class="default"><span class="p1">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a> ,2 <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p2">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span></span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p1">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a> ,4 <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span> <a href="scmpds_4.html#K3">';'</a> <font color="Maroon">c<sub>50</sub></font></span>)</span> <a href="scmpds_4.html#K3">';'</a> <span class="p5">(<span class="default"><span class="p0">(<span class="default"><span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a> ,<span class="p5">(<span class="default"><span class="p0">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 3</span>)</span> <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p5">(<span class="default"><span class="p0">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p4">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a> ,<span class="p5">(<span class="default"><span class="p0">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span> <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K2">GBP</a> ,4</span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p3">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a> ,<span class="p4">(<span class="default"><span class="p5">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 2</span>)</span> <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K2">GBP</a> ,4</span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p2">(<span class="default"><a href="scmpds_2.html#K12">AddTo</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span>,<span class="p3">(<span class="default"><a href="xcmplx_0.html#K4">-</a> 1</span>)</span></span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p1">(<span class="default"><a href="scmpds_2.html#K12">AddTo</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 2</span>)</span>,1</span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p0">(<span class="default"><a href="scmpds_2.html#K12">AddTo</a> <a href="scmp_gcd.html#K2">GBP</a> ,1,2</span>)</span></span>)</span></span>)</span>,<span class="p4">(<span class="default"><a href="scmpds_4.html#K1">Load</a> <span class="p5">(<span class="default"><a href="scmpds_2.html#K12">AddTo</a> <a href="scmp_gcd.html#K2">GBP</a> ,1,<span class="p0">(<span class="default"><a href="xcmplx_0.html#K4">-</a> 2</span>)</span></span>)</span></span>)</span></span>)</span></span>)</span>,<font color="Maroon">c<sub>76</sub></font></span>)</span> <a href="scmpds_2.html#K2">.</a> <span class="p1">(<span class="default"><a href="scmp_gcd.html#K1">intpos</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>80</sub></font> <a href="nat_1.html#K1">+</a> 2</span>)</span></span>)</span>
 <b>by </b><i><a class="txt" href="scpqsort.html#E1:46_12"><i><font color="Green">E61</font></i></a>, <a class="txt" href="scpqsort.html#E7:46_12_4"><i><font color="Green">E72</font></i></a></i>;<br/><b>thus </b><a NAME="E16:46_12_4"/>
<font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>82</sub></font> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><a href="scmpds_4.html#K9">IExec</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a> ,2 <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p5">(<span class="default"><span class="p0">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p4">(<span class="default"><a href="scmpds_2.html#K14">SubFrom</a> <a href="scmp_gcd.html#K2">GBP</a> ,2,<a href="scmp_gcd.html#K3">SBP</a> ,<span class="p5">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span></span>)</span></span>)</span> <a href="scmpds_4.html#K3">';'</a> <span class="p3">(<span class="default"><a href="scmpds_6.html#K3">if&gt;0</a> <a href="scmp_gcd.html#K2">GBP</a> ,2,<span class="p4">(<span class="default"><span class="p5">(<span class="default"><span class="p0">(<span class="default"><span class="p1">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a> ,2 <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p2">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span></span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p1">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a> ,4 <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span> <a href="scmpds_4.html#K3">';'</a> <font color="Maroon">c<sub>50</sub></font></span>)</span> <a href="scmpds_4.html#K3">';'</a> <span class="p5">(<span class="default"><span class="p0">(<span class="default"><span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a> ,<span class="p5">(<span class="default"><span class="p0">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 3</span>)</span> <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p5">(<span class="default"><span class="p0">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p4">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a> ,<span class="p5">(<span class="default"><span class="p0">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span> <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K2">GBP</a> ,4</span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p3">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a> ,<span class="p4">(<span class="default"><span class="p5">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 2</span>)</span> <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K2">GBP</a> ,4</span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p2">(<span class="default"><a href="scmpds_2.html#K12">AddTo</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span>,<span class="p3">(<span class="default"><a href="xcmplx_0.html#K4">-</a> 1</span>)</span></span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p1">(<span class="default"><a href="scmpds_2.html#K12">AddTo</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 2</span>)</span>,1</span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p0">(<span class="default"><a href="scmpds_2.html#K12">AddTo</a> <a href="scmp_gcd.html#K2">GBP</a> ,1,2</span>)</span></span>)</span></span>)</span>,<span class="p4">(<span class="default"><a href="scmpds_4.html#K1">Load</a> <span class="p5">(<span class="default"><a href="scmpds_2.html#K12">AddTo</a> <a href="scmp_gcd.html#K2">GBP</a> ,1,<span class="p0">(<span class="default"><a href="xcmplx_0.html#K4">-</a> 2</span>)</span></span>)</span></span>)</span></span>)</span></span>)</span>,<font color="Maroon">c<sub>76</sub></font></span>)</span> <a href="scmpds_2.html#K2">.</a> <span class="p1">(<span class="default"><a href="scmp_gcd.html#K1">intpos</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>80</sub></font> <a href="nat_1.html#K1">+</a> 3</span>)</span></span>)</span>
 <b>by </b><i><a class="txt" href="scpqsort.html#E17:46"><i><font color="Green">E57</font></i></a>, <a class="txt" href="scpqsort.html#E19:46"><i><font color="Green">E59</font></i></a>, <a class="txt" href="scpqsort.html#E1:46_12"><i><font color="Green">E61</font></i></a>, <a class="txt" href="scpqsort.html#E2:46_12"><i><font color="Green">E62</font></i></a>, <a class="txt" href="scpqsort.html#E8:46_12"><i><font color="Green">E65</font></i></a>, <a class="txt" href="scpqsort.html#E9:46_12"><i><font color="Green">E66</font></i></a>, <a class="txt" href="scpqsort.html#E11:46_12"><i><font color="Green">E67</font></i></a>, <a class="txt" href="scpqsort.html#E12:46_12"><i><font color="Green">E68</font></i></a>, <a class="txt" href="scpqsort.html#E3:46_12_4"><i><font color="Green">E70</font></i></a>, <a class="txt" href="scpqsort.html#E4:46_12_4"><i><font color="Green">E71</font></i></a>, <a class="ref" href="scmp_gcd.html#D3">SCMP_GCD:def 3</a></i>;<br/><div><b>hereby </b>
<div class="add"><b>let </b><font color="Maroon">c<sub>92</sub></font> be   <a href="nat_1.html#NM1">Nat</a>;<br/><b>assume </b><a NAME="E1:46_12_4_3"/>
( <font color="Maroon">c<sub>81</sub></font> <a href="xxreal_0.html#R1">&lt;=</a> <font color="Maroon">c<sub>92</sub></font> &amp; <font color="Maroon">c<sub>92</sub></font> <a href="xxreal_0.html#NR3" target="_self">&lt;</a> <font color="Maroon">c<sub>91</sub></font> )
 ;<br/><a NAME="E2:46_12_4_3"/><b>then </b>
( <font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>81</sub></font> <a href="xxreal_0.html#R1">&lt;=</a> <font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>92</sub></font> &amp; <font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>92</sub></font> <a href="xxreal_0.html#NR3" target="_self">&lt;</a> <font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>91</sub></font> )
 <b>by </b><i><a class="ref" href="xreal_1.html#T8">XREAL_1:8</a></i>;<br/><b>hence </b><a NAME="E3:46_12_4_3"/>
<span class="p1">(<span class="default"><a href="scmpds_4.html#K9">IExec</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a> ,2 <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p5">(<span class="default"><span class="p0">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p4">(<span class="default"><a href="scmpds_2.html#K14">SubFrom</a> <a href="scmp_gcd.html#K2">GBP</a> ,2,<a href="scmp_gcd.html#K3">SBP</a> ,<span class="p5">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span></span>)</span></span>)</span> <a href="scmpds_4.html#K3">';'</a> <span class="p3">(<span class="default"><a href="scmpds_6.html#K3">if&gt;0</a> <a href="scmp_gcd.html#K2">GBP</a> ,2,<span class="p4">(<span class="default"><span class="p5">(<span class="default"><span class="p0">(<span class="default"><span class="p1">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a> ,2 <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p2">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span></span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p1">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a> ,4 <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span> <a href="scmpds_4.html#K3">';'</a> <font color="Maroon">c<sub>50</sub></font></span>)</span> <a href="scmpds_4.html#K3">';'</a> <span class="p5">(<span class="default"><span class="p0">(<span class="default"><span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a> ,<span class="p5">(<span class="default"><span class="p0">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 3</span>)</span> <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p5">(<span class="default"><span class="p0">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p4">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a> ,<span class="p5">(<span class="default"><span class="p0">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span> <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K2">GBP</a> ,4</span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p3">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a> ,<span class="p4">(<span class="default"><span class="p5">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 2</span>)</span> <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K2">GBP</a> ,4</span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p2">(<span class="default"><a href="scmpds_2.html#K12">AddTo</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span>,<span class="p3">(<span class="default"><a href="xcmplx_0.html#K4">-</a> 1</span>)</span></span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p1">(<span class="default"><a href="scmpds_2.html#K12">AddTo</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 2</span>)</span>,1</span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p0">(<span class="default"><a href="scmpds_2.html#K12">AddTo</a> <a href="scmp_gcd.html#K2">GBP</a> ,1,2</span>)</span></span>)</span></span>)</span>,<span class="p4">(<span class="default"><a href="scmpds_4.html#K1">Load</a> <span class="p5">(<span class="default"><a href="scmpds_2.html#K12">AddTo</a> <a href="scmp_gcd.html#K2">GBP</a> ,1,<span class="p0">(<span class="default"><a href="xcmplx_0.html#K4">-</a> 2</span>)</span></span>)</span></span>)</span></span>)</span></span>)</span>,<font color="Maroon">c<sub>76</sub></font></span>)</span> <a href="scmpds_2.html#K2">.</a> <span class="p1">(<span class="default"><a href="scmp_gcd.html#K1">intpos</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>92</sub></font></span>)</span></span>)</span> <a href="xxreal_0.html#R1">&lt;=</a> <span class="p1">(<span class="default"><a href="scmpds_4.html#K9">IExec</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a> ,2 <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p5">(<span class="default"><span class="p0">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p4">(<span class="default"><a href="scmpds_2.html#K14">SubFrom</a> <a href="scmp_gcd.html#K2">GBP</a> ,2,<a href="scmp_gcd.html#K3">SBP</a> ,<span class="p5">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span></span>)</span></span>)</span> <a href="scmpds_4.html#K3">';'</a> <span class="p3">(<span class="default"><a href="scmpds_6.html#K3">if&gt;0</a> <a href="scmp_gcd.html#K2">GBP</a> ,2,<span class="p4">(<span class="default"><span class="p5">(<span class="default"><span class="p0">(<span class="default"><span class="p1">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a> ,2 <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p2">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span></span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p1">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a> ,4 <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span> <a href="scmpds_4.html#K3">';'</a> <font color="Maroon">c<sub>50</sub></font></span>)</span> <a href="scmpds_4.html#K3">';'</a> <span class="p5">(<span class="default"><span class="p0">(<span class="default"><span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a> ,<span class="p5">(<span class="default"><span class="p0">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 3</span>)</span> <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p5">(<span class="default"><span class="p0">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p4">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a> ,<span class="p5">(<span class="default"><span class="p0">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span> <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K2">GBP</a> ,4</span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p3">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a> ,<span class="p4">(<span class="default"><span class="p5">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 2</span>)</span> <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K2">GBP</a> ,4</span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p2">(<span class="default"><a href="scmpds_2.html#K12">AddTo</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span>,<span class="p3">(<span class="default"><a href="xcmplx_0.html#K4">-</a> 1</span>)</span></span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p1">(<span class="default"><a href="scmpds_2.html#K12">AddTo</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 2</span>)</span>,1</span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p0">(<span class="default"><a href="scmpds_2.html#K12">AddTo</a> <a href="scmp_gcd.html#K2">GBP</a> ,1,2</span>)</span></span>)</span></span>)</span>,<span class="p4">(<span class="default"><a href="scmpds_4.html#K1">Load</a> <span class="p5">(<span class="default"><a href="scmpds_2.html#K12">AddTo</a> <a href="scmp_gcd.html#K2">GBP</a> ,1,<span class="p0">(<span class="default"><a href="xcmplx_0.html#K4">-</a> 2</span>)</span></span>)</span></span>)</span></span>)</span></span>)</span>,<font color="Maroon">c<sub>76</sub></font></span>)</span> <a href="scmpds_2.html#K2">.</a> <span class="p1">(<span class="default"><a href="scmp_gcd.html#K1">intpos</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>91</sub></font></span>)</span></span>)</span>
 <b>by </b><i><a class="txt" href="scpqsort.html#E7:46_12_4"><i><font color="Green">E72</font></i></a></i>;<br/></div>
<b>end;</b></div><div><b>hereby </b>
<div class="add"><b>let </b><font color="Maroon">c<sub>92</sub></font> be   <a href="nat_1.html#NM1">Nat</a>;<br/><b>assume </b><a NAME="E1:46_12_4_4"/>
( <font color="Maroon">c<sub>91</sub></font> <a href="xxreal_0.html#NR3" target="_self">&lt;</a> <font color="Maroon">c<sub>92</sub></font> &amp; <font color="Maroon">c<sub>92</sub></font> <a href="xxreal_0.html#R1">&lt;=</a> <font color="Maroon">c<sub>82</sub></font> )
 ;<br/><a NAME="E2:46_12_4_4"/><b>then </b>
( <font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>91</sub></font> <a href="xxreal_0.html#NR3" target="_self">&lt;</a> <font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>92</sub></font> &amp; <font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>92</sub></font> <a href="xxreal_0.html#R1">&lt;=</a> <font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>82</sub></font> )
 <b>by </b><i><a class="ref" href="xreal_1.html#T8">XREAL_1:8</a></i>;<br/><b>hence </b><a NAME="E3:46_12_4_4"/>
<span class="p1">(<span class="default"><a href="scmpds_4.html#K9">IExec</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a> ,2 <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p5">(<span class="default"><span class="p0">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p4">(<span class="default"><a href="scmpds_2.html#K14">SubFrom</a> <a href="scmp_gcd.html#K2">GBP</a> ,2,<a href="scmp_gcd.html#K3">SBP</a> ,<span class="p5">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span></span>)</span></span>)</span> <a href="scmpds_4.html#K3">';'</a> <span class="p3">(<span class="default"><a href="scmpds_6.html#K3">if&gt;0</a> <a href="scmp_gcd.html#K2">GBP</a> ,2,<span class="p4">(<span class="default"><span class="p5">(<span class="default"><span class="p0">(<span class="default"><span class="p1">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a> ,2 <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p2">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span></span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p1">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a> ,4 <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span> <a href="scmpds_4.html#K3">';'</a> <font color="Maroon">c<sub>50</sub></font></span>)</span> <a href="scmpds_4.html#K3">';'</a> <span class="p5">(<span class="default"><span class="p0">(<span class="default"><span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a> ,<span class="p5">(<span class="default"><span class="p0">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 3</span>)</span> <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p5">(<span class="default"><span class="p0">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p4">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a> ,<span class="p5">(<span class="default"><span class="p0">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span> <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K2">GBP</a> ,4</span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p3">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a> ,<span class="p4">(<span class="default"><span class="p5">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 2</span>)</span> <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K2">GBP</a> ,4</span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p2">(<span class="default"><a href="scmpds_2.html#K12">AddTo</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span>,<span class="p3">(<span class="default"><a href="xcmplx_0.html#K4">-</a> 1</span>)</span></span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p1">(<span class="default"><a href="scmpds_2.html#K12">AddTo</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 2</span>)</span>,1</span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p0">(<span class="default"><a href="scmpds_2.html#K12">AddTo</a> <a href="scmp_gcd.html#K2">GBP</a> ,1,2</span>)</span></span>)</span></span>)</span>,<span class="p4">(<span class="default"><a href="scmpds_4.html#K1">Load</a> <span class="p5">(<span class="default"><a href="scmpds_2.html#K12">AddTo</a> <a href="scmp_gcd.html#K2">GBP</a> ,1,<span class="p0">(<span class="default"><a href="xcmplx_0.html#K4">-</a> 2</span>)</span></span>)</span></span>)</span></span>)</span></span>)</span>,<font color="Maroon">c<sub>76</sub></font></span>)</span> <a href="scmpds_2.html#K2">.</a> <span class="p1">(<span class="default"><a href="scmp_gcd.html#K1">intpos</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>92</sub></font></span>)</span></span>)</span> <a href="xxreal_0.html#NR2" target="_self">&gt;=</a> <span class="p1">(<span class="default"><a href="scmpds_4.html#K9">IExec</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a> ,2 <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p5">(<span class="default"><span class="p0">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p4">(<span class="default"><a href="scmpds_2.html#K14">SubFrom</a> <a href="scmp_gcd.html#K2">GBP</a> ,2,<a href="scmp_gcd.html#K3">SBP</a> ,<span class="p5">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span></span>)</span></span>)</span> <a href="scmpds_4.html#K3">';'</a> <span class="p3">(<span class="default"><a href="scmpds_6.html#K3">if&gt;0</a> <a href="scmp_gcd.html#K2">GBP</a> ,2,<span class="p4">(<span class="default"><span class="p5">(<span class="default"><span class="p0">(<span class="default"><span class="p1">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a> ,2 <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p2">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span></span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p1">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a> ,4 <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span> <a href="scmpds_4.html#K3">';'</a> <font color="Maroon">c<sub>50</sub></font></span>)</span> <a href="scmpds_4.html#K3">';'</a> <span class="p5">(<span class="default"><span class="p0">(<span class="default"><span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a> ,<span class="p5">(<span class="default"><span class="p0">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 3</span>)</span> <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p5">(<span class="default"><span class="p0">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p4">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a> ,<span class="p5">(<span class="default"><span class="p0">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span> <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K2">GBP</a> ,4</span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p3">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a> ,<span class="p4">(<span class="default"><span class="p5">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 2</span>)</span> <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K2">GBP</a> ,4</span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p2">(<span class="default"><a href="scmpds_2.html#K12">AddTo</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span>,<span class="p3">(<span class="default"><a href="xcmplx_0.html#K4">-</a> 1</span>)</span></span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p1">(<span class="default"><a href="scmpds_2.html#K12">AddTo</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 2</span>)</span>,1</span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p0">(<span class="default"><a href="scmpds_2.html#K12">AddTo</a> <a href="scmp_gcd.html#K2">GBP</a> ,1,2</span>)</span></span>)</span></span>)</span>,<span class="p4">(<span class="default"><a href="scmpds_4.html#K1">Load</a> <span class="p5">(<span class="default"><a href="scmpds_2.html#K12">AddTo</a> <a href="scmp_gcd.html#K2">GBP</a> ,1,<span class="p0">(<span class="default"><a href="xcmplx_0.html#K4">-</a> 2</span>)</span></span>)</span></span>)</span></span>)</span></span>)</span>,<font color="Maroon">c<sub>76</sub></font></span>)</span> <a href="scmpds_2.html#K2">.</a> <span class="p1">(<span class="default"><a href="scmp_gcd.html#K1">intpos</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>91</sub></font></span>)</span></span>)</span>
 <b>by </b><i><a class="txt" href="scpqsort.html#E7:46_12_4"><i><font color="Green">E72</font></i></a></i>;<br/></div>
<b>end;</b></div></div>
<b>end;</b></div><div><b>hereby </b>
<div class="add"><b>assume </b><a NAME="E1:46_12_5"/><i><font color="Green">E69</font></i>: 
( <font color="Maroon">c<sub>77</sub></font> <a href="scpisort.html#R1">is_FinSequence_on</a> <font color="Maroon">c<sub>76</sub></font>,<font color="Maroon">c<sub>48</sub></font> &amp; <font color="Maroon">c<sub>78</sub></font> <a href="scpisort.html#R1">is_FinSequence_on</a>  <a href="scmpds_4.html#K9">IExec</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a> ,2 <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p4">(<span class="default"><span class="p5">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p3">(<span class="default"><a href="scmpds_2.html#K14">SubFrom</a> <a href="scmp_gcd.html#K2">GBP</a> ,2,<a href="scmp_gcd.html#K3">SBP</a> ,<span class="p4">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span></span>)</span></span>)</span> <a href="scmpds_4.html#K3">';'</a> <span class="p2">(<span class="default"><a href="scmpds_6.html#K3">if&gt;0</a> <a href="scmp_gcd.html#K2">GBP</a> ,2,<span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><span class="p0">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a> ,2 <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p1">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span></span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p0">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a> ,4 <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span> <a href="scmpds_4.html#K3">';'</a> <font color="Maroon">c<sub>50</sub></font></span>)</span> <a href="scmpds_4.html#K3">';'</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><span class="p0">(<span class="default"><span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a> ,<span class="p4">(<span class="default"><span class="p5">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 3</span>)</span> <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p4">(<span class="default"><span class="p5">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p3">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a> ,<span class="p4">(<span class="default"><span class="p5">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span> <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K2">GBP</a> ,4</span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p2">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a> ,<span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 2</span>)</span> <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K2">GBP</a> ,4</span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p1">(<span class="default"><a href="scmpds_2.html#K12">AddTo</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span>,<span class="p2">(<span class="default"><a href="xcmplx_0.html#K4">-</a> 1</span>)</span></span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p0">(<span class="default"><a href="scmpds_2.html#K12">AddTo</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 2</span>)</span>,1</span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p5">(<span class="default"><a href="scmpds_2.html#K12">AddTo</a> <a href="scmp_gcd.html#K2">GBP</a> ,1,2</span>)</span></span>)</span></span>)</span>,<span class="p3">(<span class="default"><a href="scmpds_4.html#K1">Load</a> <span class="p4">(<span class="default"><a href="scmpds_2.html#K12">AddTo</a> <a href="scmp_gcd.html#K2">GBP</a> ,1,<span class="p5">(<span class="default"><a href="xcmplx_0.html#K4">-</a> 2</span>)</span></span>)</span></span>)</span></span>)</span></span>)</span>,<font color="Maroon">c<sub>76</sub></font>,<font color="Maroon">c<sub>48</sub></font> &amp;  <a href="finseq_1.html#K3">len</a> <font color="Maroon">c<sub>77</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>49</sub></font> &amp;  <a href="finseq_1.html#K3">len</a> <font color="Maroon">c<sub>78</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>49</sub></font> )
 ;<br/><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="46_12_5_1"><b>per </b></a><a class="txt" onclick="hs(this)" href="javascript:()"><b>cases </b></a><span class="hide"><a NAME="E1:46_12_5_1"/>
( <font color="Maroon">c<sub>76</sub></font> <a href="scmpds_2.html#K2">.</a> <span class="p1">(<span class="default"><a href="scmp_gcd.html#K1">intpos</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default">2 <a href="nat_1.html#K2">*</a> <font color="Maroon">c<sub>79</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span> <a href="nat_1.html#K1">+</a> <span class="p4">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> <a href="xxreal_0.html#R1">&lt;=</a> <font color="Maroon">c<sub>76</sub></font> <a href="scmpds_2.html#K2">.</a> <span class="p1">(<span class="default"><a href="scmp_gcd.html#K1">intpos</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default">2 <a href="nat_1.html#K2">*</a> <font color="Maroon">c<sub>79</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span> <a href="nat_1.html#K1">+</a> <span class="p3">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span></span>)</span></span>)</span> or <font color="Maroon">c<sub>76</sub></font> <a href="scmpds_2.html#K2">.</a> <span class="p1">(<span class="default"><a href="scmp_gcd.html#K1">intpos</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default">2 <a href="nat_1.html#K2">*</a> <font color="Maroon">c<sub>79</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span> <a href="nat_1.html#K1">+</a> <span class="p4">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> <a href="xxreal_0.html#NR4" target="_self">&gt;</a> <font color="Maroon">c<sub>76</sub></font> <a href="scmpds_2.html#K2">.</a> <span class="p1">(<span class="default"><a href="scmp_gcd.html#K1">intpos</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default">2 <a href="nat_1.html#K2">*</a> <font color="Maroon">c<sub>79</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span> <a href="nat_1.html#K1">+</a> <span class="p3">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span></span>)</span></span>)</span> )
 </span>;<br/><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="46_12_5_1_1"><b>suppose </b></a><a NAME="E1:46_12_5_1_1"/><i><font color="Green">E70</font></i>: 
<font color="Maroon">c<sub>76</sub></font> <a href="scmpds_2.html#K2">.</a> <span class="p1">(<span class="default"><a href="scmp_gcd.html#K1">intpos</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default">2 <a href="nat_1.html#K2">*</a> <font color="Maroon">c<sub>79</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span> <a href="nat_1.html#K1">+</a> <span class="p4">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> <a href="xxreal_0.html#R1">&lt;=</a> <font color="Maroon">c<sub>76</sub></font> <a href="scmpds_2.html#K2">.</a> <span class="p1">(<span class="default"><a href="scmp_gcd.html#K1">intpos</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default">2 <a href="nat_1.html#K2">*</a> <font color="Maroon">c<sub>79</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span> <a href="nat_1.html#K1">+</a> <span class="p3">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span></span>)</span></span>)</span>
 ;<br/><div class="add"><div><a class="txt" onclick="hs2(this)" href="javascript:()" title="46_12_5_1_1_1"><b>now </b></a><div class="add"><b>let </b><font color="Maroon">c<sub>89</sub></font> be   <a href="nat_1.html#NM1">Nat</a>;<br/><b>assume </b><a NAME="E1:46_12_5_1_1_1"/>
<font color="Maroon">c<sub>89</sub></font> <a href="hidden.html#R2">in</a>  <a href="finseq_1.html#K2">Seg</a> <font color="Maroon">c<sub>49</sub></font>
 ;<br/><a NAME="E2:46_12_5_1_1_1"/><b>then </b><i><font color="Green">E71</font></i>: 
( 1 <a href="xxreal_0.html#R1">&lt;=</a> <font color="Maroon">c<sub>89</sub></font> &amp; <font color="Maroon">c<sub>89</sub></font> <a href="xxreal_0.html#R1">&lt;=</a> <font color="Maroon">c<sub>49</sub></font> )
 <b>by </b><i><a class="ref" href="finseq_1.html#T3">FINSEQ_1:3</a></i>;<br/><b>hence </b><font color="Maroon">c<sub>77</sub></font> <a href="funct_1.html#K1">.</a> <font color="Maroon">c<sub>89</sub></font> = 
<font color="Maroon">c<sub>76</sub></font> <a href="scmpds_2.html#K2">.</a> <span class="p1">(<span class="default"><a href="scmp_gcd.html#K1">intpos</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>89</sub></font></span>)</span></span>)</span>
<b>by </b><i><a class="txt" href="scpqsort.html#E1:46_12_5"><i><font color="Green">E69</font></i></a>, <a class="ref" href="scpisort.html#D1">SCPISORT:def 1</a></i>
<br/>.= 
<span class="p1">(<span class="default"><a href="scmpds_4.html#K9">IExec</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a> ,2 <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p5">(<span class="default"><span class="p0">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p4">(<span class="default"><a href="scmpds_2.html#K14">SubFrom</a> <a href="scmp_gcd.html#K2">GBP</a> ,2,<a href="scmp_gcd.html#K3">SBP</a> ,<span class="p5">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span></span>)</span></span>)</span> <a href="scmpds_4.html#K3">';'</a> <span class="p3">(<span class="default"><a href="scmpds_6.html#K3">if&gt;0</a> <a href="scmp_gcd.html#K2">GBP</a> ,2,<span class="p4">(<span class="default"><span class="p5">(<span class="default"><span class="p0">(<span class="default"><span class="p1">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a> ,2 <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p2">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span></span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p1">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a> ,4 <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span> <a href="scmpds_4.html#K3">';'</a> <font color="Maroon">c<sub>50</sub></font></span>)</span> <a href="scmpds_4.html#K3">';'</a> <span class="p5">(<span class="default"><span class="p0">(<span class="default"><span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a> ,<span class="p5">(<span class="default"><span class="p0">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 3</span>)</span> <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p5">(<span class="default"><span class="p0">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p4">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a> ,<span class="p5">(<span class="default"><span class="p0">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span> <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K2">GBP</a> ,4</span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p3">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a> ,<span class="p4">(<span class="default"><span class="p5">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 2</span>)</span> <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K2">GBP</a> ,4</span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p2">(<span class="default"><a href="scmpds_2.html#K12">AddTo</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span>,<span class="p3">(<span class="default"><a href="xcmplx_0.html#K4">-</a> 1</span>)</span></span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p1">(<span class="default"><a href="scmpds_2.html#K12">AddTo</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 2</span>)</span>,1</span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p0">(<span class="default"><a href="scmpds_2.html#K12">AddTo</a> <a href="scmp_gcd.html#K2">GBP</a> ,1,2</span>)</span></span>)</span></span>)</span>,<span class="p4">(<span class="default"><a href="scmpds_4.html#K1">Load</a> <span class="p5">(<span class="default"><a href="scmpds_2.html#K12">AddTo</a> <a href="scmp_gcd.html#K2">GBP</a> ,1,<span class="p0">(<span class="default"><a href="xcmplx_0.html#K4">-</a> 2</span>)</span></span>)</span></span>)</span></span>)</span></span>)</span>,<font color="Maroon">c<sub>76</sub></font></span>)</span> <a href="scmpds_2.html#K2">.</a> <span class="p1">(<span class="default"><a href="scmp_gcd.html#K1">intpos</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>89</sub></font></span>)</span></span>)</span>
<b>by </b><i><a class="txt" href="scpqsort.html#E18:46"><i><font color="Green">E58</font></i></a>, <a class="txt" href="scpqsort.html#E19:46"><i><font color="Green">E59</font></i></a>, <a class="txt" href="scpqsort.html#E1:46_12"><i><font color="Green">E61</font></i></a>, <a class="txt" href="scpqsort.html#E1:46_12_5_1_1"><i><font color="Green">E70</font></i></a>, <a class="txt" href="scpqsort.html#E2:46_12_5_1_1_1"><i><font color="Green">E71</font></i></a>, <a class="ref" href="scmp_gcd.html#D3">SCMP_GCD:def 3</a></i>
<br/>.= 
<font color="Maroon">c<sub>78</sub></font> <a href="funct_1.html#K1">.</a> <font color="Maroon">c<sub>89</sub></font>
<b>by </b><i><a class="txt" href="scpqsort.html#E1:46_12_5"><i><font color="Green">E69</font></i></a>, <a class="txt" href="scpqsort.html#E2:46_12_5_1_1_1"><i><font color="Green">E71</font></i></a>, <a class="ref" href="scpisort.html#D1">SCPISORT:def 1</a></i>
;<br/><br/></div><b>end;</b></div><b>hence </b><a NAME="E3:46_12_5_1_1"/>
<font color="Maroon">c<sub>77</sub></font>,<font color="Maroon">c<sub>78</sub></font> <a href="rfinseq.html#R1">are_fiberwise_equipotent</a> 
 <b>by </b><i><a class="txt" href="scpqsort.html#E1:46_12_5"><i><font color="Green">E69</font></i></a>, <a class="ref" href="finseq_2.html#T10">FINSEQ_2:10</a></i>;<br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="46_12_5_1_2"><b>suppose </b></a><a NAME="E1:46_12_5_1_2"/><i><font color="Green">E70</font></i>: 
<font color="Maroon">c<sub>76</sub></font> <a href="scmpds_2.html#K2">.</a> <span class="p1">(<span class="default"><a href="scmp_gcd.html#K1">intpos</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default">2 <a href="nat_1.html#K2">*</a> <font color="Maroon">c<sub>79</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span> <a href="nat_1.html#K1">+</a> <span class="p4">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> <a href="xxreal_0.html#NR4" target="_self">&gt;</a> <font color="Maroon">c<sub>76</sub></font> <a href="scmpds_2.html#K2">.</a> <span class="p1">(<span class="default"><a href="scmp_gcd.html#K1">intpos</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default">2 <a href="nat_1.html#K2">*</a> <font color="Maroon">c<sub>79</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span> <a href="nat_1.html#K1">+</a> <span class="p3">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span></span>)</span></span>)</span>
 ;<br/><div class="add"><a NAME="E2:46_12_5_1_2"/><b>then </b><i><font color="Green">E71</font></i>: 
<span class="p1">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>82</sub></font></span>)</span> <a href="xcmplx_0.html#K6">-</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>81</sub></font></span>)</span> <a href="xxreal_0.html#NR4" target="_self">&gt;</a> 0
 <b>by </b><i><a class="txt" href="scpqsort.html#E3:46_12"><i><font color="Green">E63</font></i></a>, <a class="txt" href="scpqsort.html#E4:46_12"><i><font color="Green">E64</font></i></a>, <a class="ref" href="xreal_1.html#T52">XREAL_1:52</a></i>;<br/><a NAME="E3:46_12_5_1_2"/>
( <font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> 1 <a href="xxreal_0.html#R1">&lt;=</a> <font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>81</sub></font> &amp; <font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>82</sub></font> <a href="xxreal_0.html#R1">&lt;=</a> <font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font> )
 <b>by </b><i><a class="txt" href="scpqsort.html#E1:46_12"><i><font color="Green">E61</font></i></a>, <a class="txt" href="scpqsort.html#E1:46_12_5_1_2"><i><font color="Green">E70</font></i></a>, <a class="ref" href="xreal_1.html#T8">XREAL_1:8</a></i>;<br/><b>hence </b><a NAME="E4:46_12_5_1_2"/>
<font color="Maroon">c<sub>77</sub></font>,<font color="Maroon">c<sub>78</sub></font> <a href="rfinseq.html#R1">are_fiberwise_equipotent</a> 
 <b>by </b><i><a class="txt" href="scpqsort.html#E17:46"><i><font color="Green">E57</font></i></a>, <a class="txt" href="scpqsort.html#E19:46"><i><font color="Green">E59</font></i></a>, <a class="txt" href="scpqsort.html#E1:46_12"><i><font color="Green">E61</font></i></a>, <a class="txt" href="scpqsort.html#E3:46_12"><i><font color="Green">E63</font></i></a>, <a class="txt" href="scpqsort.html#E1:46_12_5"><i><font color="Green">E69</font></i></a>, <a class="txt" href="scpqsort.html#E2:46_12_5_1_2"><i><font color="Green">E71</font></i></a>, <a class="ref" href="scmp_gcd.html#D3">SCMP_GCD:def 3</a></i>;<br/></div><b>end;</b></div></div><b>end;</b></div></div>
<b>end;</b></div></div><b>end;</b></div>
<a NAME="E21:46"/><i><font color="Green">E61</font></i>: 
( <span class="p1">(<span class="default"><a href="scmpds_4.html#K9">IExec</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a>  <a href="scmpds_2.html#K6">:=</a> 0</span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p5">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a>  <a href="scmpds_2.html#K6">:=</a> 1</span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p4">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a> ,<span class="p5">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="scmpds_2.html#K11">:=</a> <span class="p5">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p3">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a> ,<span class="p4">(<span class="default"><span class="p5">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span> <a href="scmpds_2.html#K11">:=</a> <span class="p4">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span></span>)</span></span>)</span>,<font color="Maroon">c<sub>47</sub></font></span>)</span> <a href="scmpds_2.html#K2">.</a> <a href="scmp_gcd.html#K2">GBP</a>  <a href="hidden.html#R1">=</a> 0 &amp; <span class="p1">(<span class="default"><a href="scmpds_4.html#K9">IExec</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a>  <a href="scmpds_2.html#K6">:=</a> 0</span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p5">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a>  <a href="scmpds_2.html#K6">:=</a> 1</span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p4">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a> ,<span class="p5">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="scmpds_2.html#K11">:=</a> <span class="p5">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p3">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a> ,<span class="p4">(<span class="default"><span class="p5">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span> <a href="scmpds_2.html#K11">:=</a> <span class="p4">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span></span>)</span></span>)</span>,<font color="Maroon">c<sub>47</sub></font></span>)</span> <a href="scmpds_2.html#K2">.</a> <span class="p1">(<span class="default"><a href="scmp_gcd.html#K1">intpos</a> 1</span>)</span> <a href="hidden.html#R1">=</a> 1 &amp; <span class="p1">(<span class="default"><a href="scmpds_4.html#K9">IExec</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a>  <a href="scmpds_2.html#K6">:=</a> 0</span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p5">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a>  <a href="scmpds_2.html#K6">:=</a> 1</span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p4">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a> ,<span class="p5">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="scmpds_2.html#K11">:=</a> <span class="p5">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p3">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a> ,<span class="p4">(<span class="default"><span class="p5">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span> <a href="scmpds_2.html#K11">:=</a> <span class="p4">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span></span>)</span></span>)</span>,<font color="Maroon">c<sub>47</sub></font></span>)</span> <a href="scmpds_2.html#K2">.</a> <span class="p1">(<span class="default"><a href="scmp_gcd.html#K1">intpos</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> 1 &amp; <span class="p1">(<span class="default"><a href="scmpds_4.html#K9">IExec</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a>  <a href="scmpds_2.html#K6">:=</a> 0</span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p5">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a>  <a href="scmpds_2.html#K6">:=</a> 1</span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p4">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a> ,<span class="p5">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="scmpds_2.html#K11">:=</a> <span class="p5">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p3">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a> ,<span class="p4">(<span class="default"><span class="p5">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span> <a href="scmpds_2.html#K11">:=</a> <span class="p4">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span></span>)</span></span>)</span>,<font color="Maroon">c<sub>47</sub></font></span>)</span> <a href="scmpds_2.html#K2">.</a> <span class="p1">(<span class="default"><a href="scmp_gcd.html#K1">intpos</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 2</span>)</span></span>)</span> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font> &amp; ( for <font color="Olive">b<sub>1</sub></font> being  <a href="nat_1.html#NM1">Nat</a> st <font color="Olive">b<sub>1</sub></font> <a href="xxreal_0.html#NR2" target="_self">&gt;=</a> 8 &amp; <font color="Olive">b<sub>1</sub></font> <a href="xxreal_0.html#R1">&lt;=</a> <font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font> holds <br/><span class="p1">(<span class="default"><a href="scmpds_4.html#K9">IExec</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a>  <a href="scmpds_2.html#K6">:=</a> 0</span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p5">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a>  <a href="scmpds_2.html#K6">:=</a> 1</span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p4">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a> ,<span class="p5">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="scmpds_2.html#K11">:=</a> <span class="p5">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p3">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a> ,<span class="p4">(<span class="default"><span class="p5">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span> <a href="scmpds_2.html#K11">:=</a> <span class="p4">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span></span>)</span></span>)</span>,<font color="Maroon">c<sub>47</sub></font></span>)</span> <a href="scmpds_2.html#K2">.</a> <span class="p1">(<span class="default"><a href="scmp_gcd.html#K1">intpos</a> <font color="Olive">b<sub>1</sub></font></span>)</span> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>47</sub></font> <a href="scmpds_2.html#K2">.</a> <span class="p1">(<span class="default"><a href="scmp_gcd.html#K1">intpos</a> <font color="Olive">b<sub>1</sub></font></span>)</span> ) )
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="46_13"><b>proof </b></a><div class="add">

<b>set </b><font color="Maroon">c<sub>76</sub></font> =  <a href="scmpds_5.html#K1">Initialized</a> <font color="Maroon">c<sub>47</sub></font>;<br/>
<b>set </b><font color="Maroon">c<sub>77</sub></font> =  <a href="scmpds_4.html#K9">IExec</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a>  <a href="scmpds_2.html#K6">:=</a> 0</span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p3">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a>  <a href="scmpds_2.html#K6">:=</a> 1</span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p2">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a> ,<span class="p3">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="scmpds_2.html#K11">:=</a> <span class="p3">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span>,<font color="Maroon">c<sub>47</sub></font>;<br/>
<b>set </b><font color="Maroon">c<sub>78</sub></font> =  <a href="scmpds_4.html#K9">IExec</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a>  <a href="scmpds_2.html#K6">:=</a> 0</span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p2">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a>  <a href="scmpds_2.html#K6">:=</a> 1</span>)</span></span>)</span>,<font color="Maroon">c<sub>47</sub></font>;<br/>
<b>set </b><font color="Maroon">c<sub>79</sub></font> =  <a href="ami_1.html#K4">Exec</a> <span class="p1">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a>  <a href="scmpds_2.html#K6">:=</a> 0</span>)</span>,<span class="p1">(<span class="default"><a href="scmpds_5.html#K1">Initialized</a> <font color="Maroon">c<sub>47</sub></font></span>)</span>;<br/>
<a NAME="E1:46_13"/><i><font color="Green">E62</font></i>: 
<span class="p1">(<span class="default"><a href="ami_1.html#K4">Exec</a> <span class="p2">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a>  <a href="scmpds_2.html#K6">:=</a> 0</span>)</span>,<span class="p2">(<span class="default"><a href="scmpds_5.html#K1">Initialized</a> <font color="Maroon">c<sub>47</sub></font></span>)</span></span>)</span> <a href="scmpds_2.html#K2">.</a> <a href="scmp_gcd.html#K2">GBP</a>  <a href="hidden.html#R1">=</a> 0
 
<b>by </b><i><a class="ref" href="scmpds_2.html#T57">SCMPDS_2:57</a></i>;<br/>
<div><i><font color="Green">E63</font></i>: <a class="txt" onclick="hs2(this)" href="javascript:()" title="46_13_1"><b>now </b></a><div class="add"><b>let </b><font color="Maroon">c<sub>80</sub></font> be   <a href="nat_1.html#NM1">Nat</a>;<br/><b>assume </b><a NAME="E1:46_13_1"/>
<font color="Maroon">c<sub>80</sub></font> <a href="xxreal_0.html#NR2" target="_self">&gt;=</a> 8
 ;<br/><a NAME="E2:46_13_1"/><b>then </b>
<font color="Maroon">c<sub>80</sub></font> <a href="xxreal_0.html#NR4" target="_self">&gt;</a> 0
 ;<br/><a NAME="E3:46_13_1"/><b>then </b>
 <a href="scmp_gcd.html#K2">GBP</a>  <a href="hidden.html#NR2" target="_self">&lt;&gt;</a>  <a href="scmp_gcd.html#K1">intpos</a> <font color="Maroon">c<sub>80</sub></font>
 <b>by </b><i><a class="ref" href="scmp_gcd.html#T4">SCMP_GCD:4</a>, <a class="ref" href="scmp_gcd.html#D2">SCMP_GCD:def 2</a></i>;<br/><b>hence </b><span class="p1">(<span class="default"><a href="ami_1.html#K4">Exec</a> <span class="p2">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a>  <a href="scmpds_2.html#K6">:=</a> 0</span>)</span>,<span class="p2">(<span class="default"><a href="scmpds_5.html#K1">Initialized</a> <font color="Maroon">c<sub>47</sub></font></span>)</span></span>)</span> <a href="scmpds_2.html#K2">.</a> <span class="p1">(<span class="default"><a href="scmp_gcd.html#K1">intpos</a> <font color="Maroon">c<sub>80</sub></font></span>)</span> = 
<span class="p1">(<span class="default"><a href="scmpds_5.html#K1">Initialized</a> <font color="Maroon">c<sub>47</sub></font></span>)</span> <a href="scmpds_2.html#K2">.</a> <span class="p1">(<span class="default"><a href="scmp_gcd.html#K1">intpos</a> <font color="Maroon">c<sub>80</sub></font></span>)</span>
<b>by </b><i><a class="ref" href="scmpds_2.html#T57">SCMPDS_2:57</a></i>
<br/>.= 
<font color="Maroon">c<sub>47</sub></font> <a href="scmpds_2.html#K2">.</a> <span class="p1">(<span class="default"><a href="scmp_gcd.html#K1">intpos</a> <font color="Maroon">c<sub>80</sub></font></span>)</span>
<b>by </b><i><a class="ref" href="scmpds_5.html#T40">SCMPDS_5:40</a></i>
;<br/><br/></div><b>end;</b></div>
<i><font color="Green">E64</font></i>: <span class="p1">(<span class="default"><a href="scmpds_4.html#K9">IExec</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a>  <a href="scmpds_2.html#K6">:=</a> 0</span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p3">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a>  <a href="scmpds_2.html#K6">:=</a> 1</span>)</span></span>)</span>,<font color="Maroon">c<sub>47</sub></font></span>)</span> <a href="scmpds_2.html#K2">.</a> <a href="scmp_gcd.html#K2">GBP</a>  = 
<span class="p1">(<span class="default"><a href="ami_1.html#K4">Exec</a> <span class="p2">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a>  <a href="scmpds_2.html#K6">:=</a> 1</span>)</span>,<span class="p2">(<span class="default"><a href="ami_1.html#K4">Exec</a> <span class="p3">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a>  <a href="scmpds_2.html#K6">:=</a> 0</span>)</span>,<span class="p3">(<span class="default"><a href="scmpds_5.html#K1">Initialized</a> <font color="Maroon">c<sub>47</sub></font></span>)</span></span>)</span></span>)</span> <a href="scmpds_2.html#K2">.</a> <a href="scmp_gcd.html#K2">GBP</a> 
<b>by </b><i><a class="ref" href="scmpds_5.html#T47">SCMPDS_5:47</a></i>
<br/>.= 
0
<b>by </b><i><a class="txt" href="scpqsort.html#E1:46_13"><i><font color="Green">E62</font></i></a>, <a class="ref" href="scmpds_2.html#T57">SCMPDS_2:57</a>, <a class="ref" href="scmp_gcd.html#T7">SCMP_GCD:7</a></i>
;<br/>
<i><font color="Green">E65</font></i>: <span class="p1">(<span class="default"><a href="scmpds_4.html#K9">IExec</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a>  <a href="scmpds_2.html#K6">:=</a> 0</span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p3">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a>  <a href="scmpds_2.html#K6">:=</a> 1</span>)</span></span>)</span>,<font color="Maroon">c<sub>47</sub></font></span>)</span> <a href="scmpds_2.html#K2">.</a> <a href="scmp_gcd.html#K3">SBP</a>  = 
<span class="p1">(<span class="default"><a href="ami_1.html#K4">Exec</a> <span class="p2">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a>  <a href="scmpds_2.html#K6">:=</a> 1</span>)</span>,<span class="p2">(<span class="default"><a href="ami_1.html#K4">Exec</a> <span class="p3">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a>  <a href="scmpds_2.html#K6">:=</a> 0</span>)</span>,<span class="p3">(<span class="default"><a href="scmpds_5.html#K1">Initialized</a> <font color="Maroon">c<sub>47</sub></font></span>)</span></span>)</span></span>)</span> <a href="scmpds_2.html#K2">.</a> <a href="scmp_gcd.html#K3">SBP</a> 
<b>by </b><i><a class="ref" href="scmpds_5.html#T47">SCMPDS_5:47</a></i>
<br/>.= 
1
<b>by </b><i><a class="ref" href="scmpds_2.html#T57">SCMPDS_2:57</a></i>
;<br/>
<div><i><font color="Green">E66</font></i>: <a class="txt" onclick="hs2(this)" href="javascript:()" title="46_13_4"><b>now </b></a><div class="add"><b>let </b><font color="Maroon">c<sub>80</sub></font> be   <a href="nat_1.html#NM1">Nat</a>;<br/><b>assume </b><a NAME="E1:46_13_4"/><i><font color="Green">E67</font></i>: 
<font color="Maroon">c<sub>80</sub></font> <a href="xxreal_0.html#NR2" target="_self">&gt;=</a> 8
 ;<br/><a NAME="E2:46_13_4"/><b>then </b>
<font color="Maroon">c<sub>80</sub></font> <a href="xxreal_0.html#NR4" target="_self">&gt;</a> 1
 <b>by </b><i><a class="ref" href="xreal_1.html#T2">XREAL_1:2</a></i>;<br/><a NAME="E3:46_13_4"/><b>then </b><i><font color="Green">E68</font></i>: 
 <a href="scmp_gcd.html#K3">SBP</a>  <a href="hidden.html#NR2" target="_self">&lt;&gt;</a>  <a href="scmp_gcd.html#K1">intpos</a> <font color="Maroon">c<sub>80</sub></font>
 <b>by </b><i><a class="ref" href="scmp_gcd.html#T4">SCMP_GCD:4</a>, <a class="ref" href="scmp_gcd.html#D3">SCMP_GCD:def 3</a></i>;<br/><b>thus </b><span class="p1">(<span class="default"><a href="scmpds_4.html#K9">IExec</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a>  <a href="scmpds_2.html#K6">:=</a> 0</span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p3">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a>  <a href="scmpds_2.html#K6">:=</a> 1</span>)</span></span>)</span>,<font color="Maroon">c<sub>47</sub></font></span>)</span> <a href="scmpds_2.html#K2">.</a> <span class="p1">(<span class="default"><a href="scmp_gcd.html#K1">intpos</a> <font color="Maroon">c<sub>80</sub></font></span>)</span> = 
<span class="p1">(<span class="default"><a href="ami_1.html#K4">Exec</a> <span class="p2">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a>  <a href="scmpds_2.html#K6">:=</a> 1</span>)</span>,<span class="p2">(<span class="default"><a href="ami_1.html#K4">Exec</a> <span class="p3">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a>  <a href="scmpds_2.html#K6">:=</a> 0</span>)</span>,<span class="p3">(<span class="default"><a href="scmpds_5.html#K1">Initialized</a> <font color="Maroon">c<sub>47</sub></font></span>)</span></span>)</span></span>)</span> <a href="scmpds_2.html#K2">.</a> <span class="p1">(<span class="default"><a href="scmp_gcd.html#K1">intpos</a> <font color="Maroon">c<sub>80</sub></font></span>)</span>
<b>by </b><i><a class="ref" href="scmpds_5.html#T47">SCMPDS_5:47</a></i>
<br/>.= 
<span class="p1">(<span class="default"><a href="ami_1.html#K4">Exec</a> <span class="p2">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a>  <a href="scmpds_2.html#K6">:=</a> 0</span>)</span>,<span class="p2">(<span class="default"><a href="scmpds_5.html#K1">Initialized</a> <font color="Maroon">c<sub>47</sub></font></span>)</span></span>)</span> <a href="scmpds_2.html#K2">.</a> <span class="p1">(<span class="default"><a href="scmp_gcd.html#K1">intpos</a> <font color="Maroon">c<sub>80</sub></font></span>)</span>
<b>by </b><i><a class="txt" href="scpqsort.html#E3:46_13_4"><i><font color="Green">E68</font></i></a>, <a class="ref" href="scmpds_2.html#T57">SCMPDS_2:57</a></i>
<br/>.= 
<font color="Maroon">c<sub>47</sub></font> <a href="scmpds_2.html#K2">.</a> <span class="p1">(<span class="default"><a href="scmp_gcd.html#K1">intpos</a> <font color="Maroon">c<sub>80</sub></font></span>)</span>
<b>by </b><i><a class="txt" href="scpqsort.html#E2:46_13"><i><font color="Green">E63</font></i></a>, <a class="txt" href="scpqsort.html#E1:46_13_4"><i><font color="Green">E67</font></i></a></i>
;<br/></div><b>end;</b></div>
<a NAME="E6:46_13"/><i><font color="Green">E67</font></i>: 
 <a href="scmpds_2.html#K3">DataLoc</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="scmpds_4.html#K9">IExec</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a>  <a href="scmpds_2.html#K6">:=</a> 0</span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p4">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a>  <a href="scmpds_2.html#K6">:=</a> 1</span>)</span></span>)</span>,<font color="Maroon">c<sub>47</sub></font></span>)</span> <a href="scmpds_2.html#K2">.</a> <a href="scmp_gcd.html#K3">SBP</a> </span>)</span>,<span class="p1">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="hidden.html#R1">=</a>  <a href="scmp_gcd.html#K1">intpos</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span>
 
<b>by </b><i><a class="txt" href="scpqsort.html#E4:46_13"><i><font color="Green">E65</font></i></a>, <a class="ref" href="scmp_gcd.html#T5">SCMP_GCD:5</a></i>;<br/>
<a NAME="E7:46_13"/><b>then </b><i><font color="Green">E68</font></i>: 
 <a href="scmp_gcd.html#K2">GBP</a>  <a href="hidden.html#NR2" target="_self">&lt;&gt;</a>  <a href="scmpds_2.html#K3">DataLoc</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="scmpds_4.html#K9">IExec</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a>  <a href="scmpds_2.html#K6">:=</a> 0</span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p4">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a>  <a href="scmpds_2.html#K6">:=</a> 1</span>)</span></span>)</span>,<font color="Maroon">c<sub>47</sub></font></span>)</span> <a href="scmpds_2.html#K2">.</a> <a href="scmp_gcd.html#K3">SBP</a> </span>)</span>,<span class="p1">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span>
 
<b>by </b><i><a class="ref" href="scmp_gcd.html#T4">SCMP_GCD:4</a>, <a class="ref" href="scmp_gcd.html#D2">SCMP_GCD:def 2</a></i>;<br/>
<i><font color="Green">E69</font></i>: <span class="p1">(<span class="default"><a href="scmpds_4.html#K9">IExec</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a>  <a href="scmpds_2.html#K6">:=</a> 0</span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p4">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a>  <a href="scmpds_2.html#K6">:=</a> 1</span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p3">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a> ,<span class="p4">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="scmpds_2.html#K11">:=</a> <span class="p4">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span>,<font color="Maroon">c<sub>47</sub></font></span>)</span> <a href="scmpds_2.html#K2">.</a> <a href="scmp_gcd.html#K2">GBP</a>  = 
<span class="p1">(<span class="default"><a href="ami_1.html#K4">Exec</a> <span class="p2">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a> ,<span class="p3">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="scmpds_2.html#K11">:=</a> <span class="p3">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span>,<span class="p2">(<span class="default"><a href="scmpds_4.html#K9">IExec</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a>  <a href="scmpds_2.html#K6">:=</a> 0</span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p4">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a>  <a href="scmpds_2.html#K6">:=</a> 1</span>)</span></span>)</span>,<font color="Maroon">c<sub>47</sub></font></span>)</span></span>)</span> <a href="scmpds_2.html#K2">.</a> <a href="scmp_gcd.html#K2">GBP</a> 
<b>by </b><i><a class="ref" href="scmpds_5.html#T46">SCMPDS_5:46</a></i>
<br/>.= 
0
<b>by </b><i><a class="txt" href="scpqsort.html#E3:46_13"><i><font color="Green">E64</font></i></a>, <a class="txt" href="scpqsort.html#E7:46_13"><i><font color="Green">E68</font></i></a>, <a class="ref" href="scmpds_2.html#T58">SCMPDS_2:58</a></i>
;<br/>
<a NAME="E9:46_13"/>
<span class="p1">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 1 <a href="xxreal_0.html#NR4" target="_self">&gt;</a> 1
 
<b>by </b><i><a class="txt" href="scpqsort.html#E9:46"><i><font color="Green">E49</font></i></a>, <a class="ref" href="xreal_1.html#T2">XREAL_1:2</a></i>;<br/>
<a NAME="E10:46_13"/><b>then </b><i><font color="Green">E70</font></i>: 
 <a href="scmp_gcd.html#K3">SBP</a>  <a href="hidden.html#NR2" target="_self">&lt;&gt;</a>  <a href="scmpds_2.html#K3">DataLoc</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="scmpds_4.html#K9">IExec</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a>  <a href="scmpds_2.html#K6">:=</a> 0</span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p4">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a>  <a href="scmpds_2.html#K6">:=</a> 1</span>)</span></span>)</span>,<font color="Maroon">c<sub>47</sub></font></span>)</span> <a href="scmpds_2.html#K2">.</a> <a href="scmp_gcd.html#K3">SBP</a> </span>)</span>,<span class="p1">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span>
 
<b>by </b><i><a class="txt" href="scpqsort.html#E6:46_13"><i><font color="Green">E67</font></i></a>, <a class="ref" href="scmp_gcd.html#T4">SCMP_GCD:4</a>, <a class="ref" href="scmp_gcd.html#D3">SCMP_GCD:def 3</a></i>;<br/>
<i><font color="Green">E71</font></i>: <span class="p1">(<span class="default"><a href="scmpds_4.html#K9">IExec</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a>  <a href="scmpds_2.html#K6">:=</a> 0</span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p4">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a>  <a href="scmpds_2.html#K6">:=</a> 1</span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p3">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a> ,<span class="p4">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="scmpds_2.html#K11">:=</a> <span class="p4">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span>,<font color="Maroon">c<sub>47</sub></font></span>)</span> <a href="scmpds_2.html#K2">.</a> <a href="scmp_gcd.html#K3">SBP</a>  = 
<span class="p1">(<span class="default"><a href="ami_1.html#K4">Exec</a> <span class="p2">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a> ,<span class="p3">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="scmpds_2.html#K11">:=</a> <span class="p3">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span>,<span class="p2">(<span class="default"><a href="scmpds_4.html#K9">IExec</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a>  <a href="scmpds_2.html#K6">:=</a> 0</span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p4">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a>  <a href="scmpds_2.html#K6">:=</a> 1</span>)</span></span>)</span>,<font color="Maroon">c<sub>47</sub></font></span>)</span></span>)</span> <a href="scmpds_2.html#K2">.</a> <a href="scmp_gcd.html#K3">SBP</a> 
<b>by </b><i><a class="ref" href="scmpds_5.html#T46">SCMPDS_5:46</a></i>
<br/>.= 
1
<b>by </b><i><a class="txt" href="scpqsort.html#E4:46_13"><i><font color="Green">E65</font></i></a>, <a class="txt" href="scpqsort.html#E10:46_13"><i><font color="Green">E70</font></i></a>, <a class="ref" href="scmpds_2.html#T58">SCMPDS_2:58</a></i>
;<br/>
<i><font color="Green">E72</font></i>: <span class="p1">(<span class="default"><a href="scmpds_4.html#K9">IExec</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a>  <a href="scmpds_2.html#K6">:=</a> 0</span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p4">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a>  <a href="scmpds_2.html#K6">:=</a> 1</span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p3">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a> ,<span class="p4">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="scmpds_2.html#K11">:=</a> <span class="p4">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span>,<font color="Maroon">c<sub>47</sub></font></span>)</span> <a href="scmpds_2.html#K2">.</a> <span class="p1">(<span class="default"><a href="scmp_gcd.html#K1">intpos</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> = 
<span class="p1">(<span class="default"><a href="ami_1.html#K4">Exec</a> <span class="p2">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a> ,<span class="p3">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="scmpds_2.html#K11">:=</a> <span class="p3">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span>,<span class="p2">(<span class="default"><a href="scmpds_4.html#K9">IExec</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a>  <a href="scmpds_2.html#K6">:=</a> 0</span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p4">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a>  <a href="scmpds_2.html#K6">:=</a> 1</span>)</span></span>)</span>,<font color="Maroon">c<sub>47</sub></font></span>)</span></span>)</span> <a href="scmpds_2.html#K2">.</a> <span class="p1">(<span class="default"><a href="scmp_gcd.html#K1">intpos</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span>
<b>by </b><i><a class="ref" href="scmpds_5.html#T46">SCMPDS_5:46</a></i>
<br/>.= 
<font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> 1
<b>by </b><i><a class="txt" href="scpqsort.html#E6:46_13"><i><font color="Green">E67</font></i></a>, <a class="ref" href="scmpds_2.html#T58">SCMPDS_2:58</a></i>
;<br/>
<div><i><font color="Green">E73</font></i>: <a class="txt" onclick="hs2(this)" href="javascript:()" title="46_13_8"><b>now </b></a><div class="add"><b>let </b><font color="Maroon">c<sub>80</sub></font> be   <a href="nat_1.html#NM1">Nat</a>;<br/><b>assume </b><a NAME="E1:46_13_8"/><i><font color="Green">E74</font></i>: 
( <font color="Maroon">c<sub>80</sub></font> <a href="xxreal_0.html#NR2" target="_self">&gt;=</a> 8 &amp; <font color="Maroon">c<sub>80</sub></font> <a href="xxreal_0.html#R1">&lt;=</a> <font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font> )
 ;<br/><a NAME="E2:46_13_8"/>
<span class="p1">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 1 <a href="xxreal_0.html#NR4" target="_self">&gt;</a> <font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font>
 <b>by </b><i><a class="ref" href="xreal_1.html#T31">XREAL_1:31</a></i>;<br/><a NAME="E3:46_13_8"/><b>then </b><i><font color="Green">E75</font></i>: 
 <a href="scmpds_2.html#K3">DataLoc</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="scmpds_4.html#K9">IExec</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a>  <a href="scmpds_2.html#K6">:=</a> 0</span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p4">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a>  <a href="scmpds_2.html#K6">:=</a> 1</span>)</span></span>)</span>,<font color="Maroon">c<sub>47</sub></font></span>)</span> <a href="scmpds_2.html#K2">.</a> <a href="scmp_gcd.html#K3">SBP</a> </span>)</span>,<span class="p1">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a>  <a href="scmp_gcd.html#K1">intpos</a> <font color="Maroon">c<sub>80</sub></font>
 <b>by </b><i><a class="txt" href="scpqsort.html#E6:46_13"><i><font color="Green">E67</font></i></a>, <a class="txt" href="scpqsort.html#E1:46_13_8"><i><font color="Green">E74</font></i></a>, <a class="ref" href="scmp_gcd.html#T4">SCMP_GCD:4</a></i>;<br/><b>thus </b><span class="p1">(<span class="default"><a href="scmpds_4.html#K9">IExec</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a>  <a href="scmpds_2.html#K6">:=</a> 0</span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p4">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a>  <a href="scmpds_2.html#K6">:=</a> 1</span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p3">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a> ,<span class="p4">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="scmpds_2.html#K11">:=</a> <span class="p4">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span>,<font color="Maroon">c<sub>47</sub></font></span>)</span> <a href="scmpds_2.html#K2">.</a> <span class="p1">(<span class="default"><a href="scmp_gcd.html#K1">intpos</a> <font color="Maroon">c<sub>80</sub></font></span>)</span> = 
<span class="p1">(<span class="default"><a href="ami_1.html#K4">Exec</a> <span class="p2">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a> ,<span class="p3">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="scmpds_2.html#K11">:=</a> <span class="p3">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span>,<span class="p2">(<span class="default"><a href="scmpds_4.html#K9">IExec</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a>  <a href="scmpds_2.html#K6">:=</a> 0</span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p4">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a>  <a href="scmpds_2.html#K6">:=</a> 1</span>)</span></span>)</span>,<font color="Maroon">c<sub>47</sub></font></span>)</span></span>)</span> <a href="scmpds_2.html#K2">.</a> <span class="p1">(<span class="default"><a href="scmp_gcd.html#K1">intpos</a> <font color="Maroon">c<sub>80</sub></font></span>)</span>
<b>by </b><i><a class="ref" href="scmpds_5.html#T46">SCMPDS_5:46</a></i>
<br/>.= 
<span class="p1">(<span class="default"><a href="scmpds_4.html#K9">IExec</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a>  <a href="scmpds_2.html#K6">:=</a> 0</span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p3">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a>  <a href="scmpds_2.html#K6">:=</a> 1</span>)</span></span>)</span>,<font color="Maroon">c<sub>47</sub></font></span>)</span> <a href="scmpds_2.html#K2">.</a> <span class="p1">(<span class="default"><a href="scmp_gcd.html#K1">intpos</a> <font color="Maroon">c<sub>80</sub></font></span>)</span>
<b>by </b><i><a class="txt" href="scpqsort.html#E3:46_13_8"><i><font color="Green">E75</font></i></a>, <a class="ref" href="scmpds_2.html#T58">SCMPDS_2:58</a></i>
<br/>.= 
<font color="Maroon">c<sub>47</sub></font> <a href="scmpds_2.html#K2">.</a> <span class="p1">(<span class="default"><a href="scmp_gcd.html#K1">intpos</a> <font color="Maroon">c<sub>80</sub></font></span>)</span>
<b>by </b><i><a class="txt" href="scpqsort.html#E5:46_13"><i><font color="Green">E66</font></i></a>, <a class="txt" href="scpqsort.html#E1:46_13_8"><i><font color="Green">E74</font></i></a></i>
;<br/></div><b>end;</b></div>
<i><font color="Green">E74</font></i>:  <a href="scmpds_2.html#K3">DataLoc</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="scmpds_4.html#K9">IExec</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a>  <a href="scmpds_2.html#K6">:=</a> 0</span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p5">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a>  <a href="scmpds_2.html#K6">:=</a> 1</span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p4">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a> ,<span class="p5">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="scmpds_2.html#K11">:=</a> <span class="p5">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span>,<font color="Maroon">c<sub>47</sub></font></span>)</span> <a href="scmpds_2.html#K2">.</a> <a href="scmp_gcd.html#K3">SBP</a> </span>)</span>,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span> = 
 <a href="scmp_gcd.html#K1">intpos</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span>
<b>by </b><i><a class="txt" href="scpqsort.html#E11:46_13"><i><font color="Green">E71</font></i></a>, <a class="ref" href="scmp_gcd.html#T5">SCMP_GCD:5</a></i>
<br/>.= 
 <a href="scmp_gcd.html#K1">intpos</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> <span class="p2">(<span class="default">1 <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span>

;<br/>
<a NAME="E15:46_13"/><b>then </b><i><font color="Green">E75</font></i>: 
 <a href="scmp_gcd.html#K2">GBP</a>  <a href="hidden.html#NR2" target="_self">&lt;&gt;</a>  <a href="scmpds_2.html#K3">DataLoc</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="scmpds_4.html#K9">IExec</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a>  <a href="scmpds_2.html#K6">:=</a> 0</span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p5">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a>  <a href="scmpds_2.html#K6">:=</a> 1</span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p4">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a> ,<span class="p5">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="scmpds_2.html#K11">:=</a> <span class="p5">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span>,<font color="Maroon">c<sub>47</sub></font></span>)</span> <a href="scmpds_2.html#K2">.</a> <a href="scmp_gcd.html#K3">SBP</a> </span>)</span>,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span>
 
<b>by </b><i><a class="ref" href="scmp_gcd.html#T4">SCMP_GCD:4</a>, <a class="ref" href="scmp_gcd.html#D2">SCMP_GCD:def 2</a></i>;<br/>
<b>thus </b><span class="p1">(<span class="default"><a href="scmpds_4.html#K9">IExec</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a>  <a href="scmpds_2.html#K6">:=</a> 0</span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p5">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a>  <a href="scmpds_2.html#K6">:=</a> 1</span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p4">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a> ,<span class="p5">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="scmpds_2.html#K11">:=</a> <span class="p5">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p3">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a> ,<span class="p4">(<span class="default"><span class="p5">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span> <a href="scmpds_2.html#K11">:=</a> <span class="p4">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span></span>)</span></span>)</span>,<font color="Maroon">c<sub>47</sub></font></span>)</span> <a href="scmpds_2.html#K2">.</a> <a href="scmp_gcd.html#K2">GBP</a>  = 
<span class="p1">(<span class="default"><a href="ami_1.html#K4">Exec</a> <span class="p2">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a> ,<span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span> <a href="scmpds_2.html#K11">:=</a> <span class="p3">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span></span>)</span>,<span class="p2">(<span class="default"><a href="scmpds_4.html#K9">IExec</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a>  <a href="scmpds_2.html#K6">:=</a> 0</span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p5">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a>  <a href="scmpds_2.html#K6">:=</a> 1</span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p4">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a> ,<span class="p5">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="scmpds_2.html#K11">:=</a> <span class="p5">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span>,<font color="Maroon">c<sub>47</sub></font></span>)</span></span>)</span> <a href="scmpds_2.html#K2">.</a> <a href="scmp_gcd.html#K2">GBP</a> 
<b>by </b><i><a class="ref" href="scmpds_5.html#T46">SCMPDS_5:46</a></i>
<br/>.= 
0
<b>by </b><i><a class="txt" href="scpqsort.html#E8:46_13"><i><font color="Green">E69</font></i></a>, <a class="txt" href="scpqsort.html#E15:46_13"><i><font color="Green">E75</font></i></a>, <a class="ref" href="scmpds_2.html#T58">SCMPDS_2:58</a></i>
;<br/>

<a NAME="E17:46_13"/>
<span class="p1">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 2 <a href="xxreal_0.html#NR4" target="_self">&gt;</a> 1
 
<b>by </b><i><a class="txt" href="scpqsort.html#E10:46"><i><font color="Green">E50</font></i></a>, <a class="ref" href="xreal_1.html#T2">XREAL_1:2</a></i>;<br/>
<a NAME="E18:46_13"/><b>then </b><i><font color="Green">E76</font></i>: 
 <a href="scmp_gcd.html#K3">SBP</a>  <a href="hidden.html#NR2" target="_self">&lt;&gt;</a>  <a href="scmpds_2.html#K3">DataLoc</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="scmpds_4.html#K9">IExec</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a>  <a href="scmpds_2.html#K6">:=</a> 0</span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p5">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a>  <a href="scmpds_2.html#K6">:=</a> 1</span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p4">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a> ,<span class="p5">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="scmpds_2.html#K11">:=</a> <span class="p5">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span>,<font color="Maroon">c<sub>47</sub></font></span>)</span> <a href="scmpds_2.html#K2">.</a> <a href="scmp_gcd.html#K3">SBP</a> </span>)</span>,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span>
 
<b>by </b><i><a class="txt" href="scpqsort.html#E14:46_13"><i><font color="Green">E74</font></i></a>, <a class="ref" href="scmp_gcd.html#T4">SCMP_GCD:4</a>, <a class="ref" href="scmp_gcd.html#D3">SCMP_GCD:def 3</a></i>;<br/>
<b>thus </b><span class="p1">(<span class="default"><a href="scmpds_4.html#K9">IExec</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a>  <a href="scmpds_2.html#K6">:=</a> 0</span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p5">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a>  <a href="scmpds_2.html#K6">:=</a> 1</span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p4">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a> ,<span class="p5">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="scmpds_2.html#K11">:=</a> <span class="p5">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p3">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a> ,<span class="p4">(<span class="default"><span class="p5">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span> <a href="scmpds_2.html#K11">:=</a> <span class="p4">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span></span>)</span></span>)</span>,<font color="Maroon">c<sub>47</sub></font></span>)</span> <a href="scmpds_2.html#K2">.</a> <span class="p1">(<span class="default"><a href="scmp_gcd.html#K1">intpos</a> 1</span>)</span> = 
<span class="p1">(<span class="default"><a href="ami_1.html#K4">Exec</a> <span class="p2">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a> ,<span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span> <a href="scmpds_2.html#K11">:=</a> <span class="p3">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span></span>)</span>,<span class="p2">(<span class="default"><a href="scmpds_4.html#K9">IExec</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a>  <a href="scmpds_2.html#K6">:=</a> 0</span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p5">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a>  <a href="scmpds_2.html#K6">:=</a> 1</span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p4">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a> ,<span class="p5">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="scmpds_2.html#K11">:=</a> <span class="p5">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span>,<font color="Maroon">c<sub>47</sub></font></span>)</span></span>)</span> <a href="scmpds_2.html#K2">.</a> <a href="scmp_gcd.html#K3">SBP</a> 
<b>by </b><i><a class="ref" href="scmpds_5.html#T46">SCMPDS_5:46</a>, <a class="ref" href="scmp_gcd.html#D3">SCMP_GCD:def 3</a></i>
<br/>.= 
1
<b>by </b><i><a class="txt" href="scpqsort.html#E11:46_13"><i><font color="Green">E71</font></i></a>, <a class="txt" href="scpqsort.html#E18:46_13"><i><font color="Green">E76</font></i></a>, <a class="ref" href="scmpds_2.html#T58">SCMPDS_2:58</a></i>
;<br/>

<a NAME="E20:46_13"/>
<span class="p1">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 2 <a href="xxreal_0.html#NR4" target="_self">&gt;</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 1
 
<b>by </b><i><a class="ref" href="xreal_1.html#T8">XREAL_1:8</a></i>;<br/>
<a NAME="E21:46_13"/><b>then </b><i><font color="Green">E77</font></i>: 
 <a href="scmp_gcd.html#K1">intpos</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a>  <a href="scmpds_2.html#K3">DataLoc</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="scmpds_4.html#K9">IExec</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a>  <a href="scmpds_2.html#K6">:=</a> 0</span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p5">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a>  <a href="scmpds_2.html#K6">:=</a> 1</span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p4">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a> ,<span class="p5">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="scmpds_2.html#K11">:=</a> <span class="p5">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span>,<font color="Maroon">c<sub>47</sub></font></span>)</span> <a href="scmpds_2.html#K2">.</a> <a href="scmp_gcd.html#K3">SBP</a> </span>)</span>,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span>
 
<b>by </b><i><a class="txt" href="scpqsort.html#E14:46_13"><i><font color="Green">E74</font></i></a>, <a class="ref" href="scmp_gcd.html#T4">SCMP_GCD:4</a></i>;<br/>
<b>thus </b><span class="p1">(<span class="default"><a href="scmpds_4.html#K9">IExec</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a>  <a href="scmpds_2.html#K6">:=</a> 0</span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p5">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a>  <a href="scmpds_2.html#K6">:=</a> 1</span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p4">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a> ,<span class="p5">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="scmpds_2.html#K11">:=</a> <span class="p5">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p3">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a> ,<span class="p4">(<span class="default"><span class="p5">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span> <a href="scmpds_2.html#K11">:=</a> <span class="p4">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span></span>)</span></span>)</span>,<font color="Maroon">c<sub>47</sub></font></span>)</span> <a href="scmpds_2.html#K2">.</a> <span class="p1">(<span class="default"><a href="scmp_gcd.html#K1">intpos</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> = 
<span class="p1">(<span class="default"><a href="ami_1.html#K4">Exec</a> <span class="p2">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a> ,<span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span> <a href="scmpds_2.html#K11">:=</a> <span class="p3">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span></span>)</span>,<span class="p2">(<span class="default"><a href="scmpds_4.html#K9">IExec</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a>  <a href="scmpds_2.html#K6">:=</a> 0</span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p5">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a>  <a href="scmpds_2.html#K6">:=</a> 1</span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p4">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a> ,<span class="p5">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="scmpds_2.html#K11">:=</a> <span class="p5">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span>,<font color="Maroon">c<sub>47</sub></font></span>)</span></span>)</span> <a href="scmpds_2.html#K2">.</a> <span class="p1">(<span class="default"><a href="scmp_gcd.html#K1">intpos</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span>
<b>by </b><i><a class="ref" href="scmpds_5.html#T46">SCMPDS_5:46</a></i>
<br/>.= 
<font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> 1
<b>by </b><i><a class="txt" href="scpqsort.html#E12:46_13"><i><font color="Green">E72</font></i></a>, <a class="txt" href="scpqsort.html#E21:46_13"><i><font color="Green">E77</font></i></a>, <a class="ref" href="scmpds_2.html#T58">SCMPDS_2:58</a></i>
;<br/>

<b>thus </b><span class="p1">(<span class="default"><a href="scmpds_4.html#K9">IExec</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a>  <a href="scmpds_2.html#K6">:=</a> 0</span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p5">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a>  <a href="scmpds_2.html#K6">:=</a> 1</span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p4">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a> ,<span class="p5">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="scmpds_2.html#K11">:=</a> <span class="p5">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p3">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a> ,<span class="p4">(<span class="default"><span class="p5">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span> <a href="scmpds_2.html#K11">:=</a> <span class="p4">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span></span>)</span></span>)</span>,<font color="Maroon">c<sub>47</sub></font></span>)</span> <a href="scmpds_2.html#K2">.</a> <span class="p1">(<span class="default"><a href="scmp_gcd.html#K1">intpos</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 2</span>)</span></span>)</span> = 
<span class="p1">(<span class="default"><a href="ami_1.html#K4">Exec</a> <span class="p2">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a> ,<span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span> <a href="scmpds_2.html#K11">:=</a> <span class="p3">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span></span>)</span>,<span class="p2">(<span class="default"><a href="scmpds_4.html#K9">IExec</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a>  <a href="scmpds_2.html#K6">:=</a> 0</span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p5">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a>  <a href="scmpds_2.html#K6">:=</a> 1</span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p4">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a> ,<span class="p5">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="scmpds_2.html#K11">:=</a> <span class="p5">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span>,<font color="Maroon">c<sub>47</sub></font></span>)</span></span>)</span> <a href="scmpds_2.html#K2">.</a> <span class="p1">(<span class="default"><a href="scmp_gcd.html#K1">intpos</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 2</span>)</span></span>)</span>
<b>by </b><i><a class="ref" href="scmpds_5.html#T46">SCMPDS_5:46</a></i>
<br/>.= 
<font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font>
<b>by </b><i><a class="txt" href="scpqsort.html#E14:46_13"><i><font color="Green">E74</font></i></a>, <a class="ref" href="scmpds_2.html#T58">SCMPDS_2:58</a></i>
;<br/>

<div><b>hereby </b>
<div class="add"><b>let </b><font color="Maroon">c<sub>80</sub></font> be   <a href="nat_1.html#NM1">Nat</a>;<br/><b>assume </b><a NAME="E1:46_13_14"/><i><font color="Green">E78</font></i>: 
( <font color="Maroon">c<sub>80</sub></font> <a href="xxreal_0.html#NR2" target="_self">&gt;=</a> 8 &amp; <font color="Maroon">c<sub>80</sub></font> <a href="xxreal_0.html#R1">&lt;=</a> <font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font> )
 ;<br/><a NAME="E2:46_13_14"/>
<span class="p1">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 2 <a href="xxreal_0.html#NR4" target="_self">&gt;</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 0
 <b>by </b><i><a class="ref" href="xreal_1.html#T8">XREAL_1:8</a></i>;<br/><a NAME="E3:46_13_14"/><b>then </b><i><font color="Green">E79</font></i>: 
 <a href="scmpds_2.html#K3">DataLoc</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="scmpds_4.html#K9">IExec</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a>  <a href="scmpds_2.html#K6">:=</a> 0</span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p5">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a>  <a href="scmpds_2.html#K6">:=</a> 1</span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p4">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a> ,<span class="p5">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="scmpds_2.html#K11">:=</a> <span class="p5">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span>,<font color="Maroon">c<sub>47</sub></font></span>)</span> <a href="scmpds_2.html#K2">.</a> <a href="scmp_gcd.html#K3">SBP</a> </span>)</span>,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a>  <a href="scmp_gcd.html#K1">intpos</a> <font color="Maroon">c<sub>80</sub></font>
 <b>by </b><i><a class="txt" href="scpqsort.html#E14:46_13"><i><font color="Green">E74</font></i></a>, <a class="txt" href="scpqsort.html#E1:46_13_14"><i><font color="Green">E78</font></i></a>, <a class="ref" href="scmp_gcd.html#T4">SCMP_GCD:4</a></i>;<br/><b>thus </b><span class="p1">(<span class="default"><a href="scmpds_4.html#K9">IExec</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a>  <a href="scmpds_2.html#K6">:=</a> 0</span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p5">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a>  <a href="scmpds_2.html#K6">:=</a> 1</span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p4">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a> ,<span class="p5">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="scmpds_2.html#K11">:=</a> <span class="p5">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p3">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a> ,<span class="p4">(<span class="default"><span class="p5">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span> <a href="scmpds_2.html#K11">:=</a> <span class="p4">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span></span>)</span></span>)</span>,<font color="Maroon">c<sub>47</sub></font></span>)</span> <a href="scmpds_2.html#K2">.</a> <span class="p1">(<span class="default"><a href="scmp_gcd.html#K1">intpos</a> <font color="Maroon">c<sub>80</sub></font></span>)</span> = 
<span class="p1">(<span class="default"><a href="ami_1.html#K4">Exec</a> <span class="p2">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a> ,<span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span> <a href="scmpds_2.html#K11">:=</a> <span class="p3">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span></span>)</span>,<span class="p2">(<span class="default"><a href="scmpds_4.html#K9">IExec</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a>  <a href="scmpds_2.html#K6">:=</a> 0</span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p5">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a>  <a href="scmpds_2.html#K6">:=</a> 1</span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p4">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a> ,<span class="p5">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="scmpds_2.html#K11">:=</a> <span class="p5">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span>,<font color="Maroon">c<sub>47</sub></font></span>)</span></span>)</span> <a href="scmpds_2.html#K2">.</a> <span class="p1">(<span class="default"><a href="scmp_gcd.html#K1">intpos</a> <font color="Maroon">c<sub>80</sub></font></span>)</span>
<b>by </b><i><a class="ref" href="scmpds_5.html#T46">SCMPDS_5:46</a></i>
<br/>.= 
<span class="p1">(<span class="default"><a href="scmpds_4.html#K9">IExec</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a>  <a href="scmpds_2.html#K6">:=</a> 0</span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p4">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a>  <a href="scmpds_2.html#K6">:=</a> 1</span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p3">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a> ,<span class="p4">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="scmpds_2.html#K11">:=</a> <span class="p4">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span>,<font color="Maroon">c<sub>47</sub></font></span>)</span> <a href="scmpds_2.html#K2">.</a> <span class="p1">(<span class="default"><a href="scmp_gcd.html#K1">intpos</a> <font color="Maroon">c<sub>80</sub></font></span>)</span>
<b>by </b><i><a class="txt" href="scpqsort.html#E3:46_13_14"><i><font color="Green">E79</font></i></a>, <a class="ref" href="scmpds_2.html#T58">SCMPDS_2:58</a></i>
<br/>.= 
<font color="Maroon">c<sub>47</sub></font> <a href="scmpds_2.html#K2">.</a> <span class="p1">(<span class="default"><a href="scmp_gcd.html#K1">intpos</a> <font color="Maroon">c<sub>80</sub></font></span>)</span>
<b>by </b><i><a class="txt" href="scpqsort.html#E13:46_13"><i><font color="Green">E73</font></i></a>, <a class="txt" href="scpqsort.html#E1:46_13_14"><i><font color="Green">E78</font></i></a></i>
;<br/></div>
<b>end;</b></div>


</div><b>end;</b></div>
<i><font color="Green">E62</font></i>: <span class="p1">(<span class="default"><a href="scmpds_4.html#K9">IExec</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a>  <a href="scmpds_2.html#K6">:=</a> 0</span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p5">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a>  <a href="scmpds_2.html#K6">:=</a> 1</span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p4">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a> ,<span class="p5">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="scmpds_2.html#K11">:=</a> <span class="p5">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p3">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a> ,<span class="p4">(<span class="default"><span class="p5">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span> <a href="scmpds_2.html#K11">:=</a> <span class="p4">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span></span>)</span></span>)</span>,<font color="Maroon">c<sub>47</sub></font></span>)</span> <a href="scmpds_2.html#K2">.</a> <span class="p1">(<span class="default"><a href="scmp_gcd.html#K1">intpos</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> = 
<span class="p1">(<span class="default"><a href="scmpds_4.html#K9">IExec</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a>  <a href="scmpds_2.html#K6">:=</a> 0</span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p5">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a>  <a href="scmpds_2.html#K6">:=</a> 1</span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p4">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a> ,<span class="p5">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="scmpds_2.html#K11">:=</a> <span class="p5">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p3">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a> ,<span class="p4">(<span class="default"><span class="p5">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span> <a href="scmpds_2.html#K11">:=</a> <span class="p4">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span></span>)</span></span>)</span>,<font color="Maroon">c<sub>47</sub></font></span>)</span> <a href="scmpds_2.html#K2">.</a> <span class="p1">(<span class="default"><a href="scmp_gcd.html#K1">intpos</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> <span class="p3">(<span class="default">1 <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span>

<br/>.= 
<font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font>
<b>by </b><i><a class="txt" href="scpqsort.html#E21:46"><i><font color="Green">E61</font></i></a></i>
;<br/>
<a NAME="E23:46"/><b>then </b><i><font color="Green">E63</font></i>: 
(  <a href="scmpds_8.html#K3">while&gt;0</a> <a href="scmp_gcd.html#K2">GBP</a> ,1,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a> ,2 <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p4">(<span class="default"><span class="p5">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p3">(<span class="default"><a href="scmpds_2.html#K14">SubFrom</a> <a href="scmp_gcd.html#K2">GBP</a> ,2,<a href="scmp_gcd.html#K3">SBP</a> ,<span class="p4">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span></span>)</span></span>)</span> <a href="scmpds_4.html#K3">';'</a> <span class="p2">(<span class="default"><a href="scmpds_6.html#K3">if&gt;0</a> <a href="scmp_gcd.html#K2">GBP</a> ,2,<span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><span class="p0">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a> ,2 <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p1">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span></span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p0">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a> ,4 <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span> <a href="scmpds_4.html#K3">';'</a> <font color="Maroon">c<sub>50</sub></font></span>)</span> <a href="scmpds_4.html#K3">';'</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><span class="p0">(<span class="default"><span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a> ,<span class="p4">(<span class="default"><span class="p5">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 3</span>)</span> <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p4">(<span class="default"><span class="p5">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p3">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a> ,<span class="p4">(<span class="default"><span class="p5">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span> <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K2">GBP</a> ,4</span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p2">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a> ,<span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 2</span>)</span> <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K2">GBP</a> ,4</span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p1">(<span class="default"><a href="scmpds_2.html#K12">AddTo</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span>,<span class="p2">(<span class="default"><a href="xcmplx_0.html#K4">-</a> 1</span>)</span></span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p0">(<span class="default"><a href="scmpds_2.html#K12">AddTo</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 2</span>)</span>,1</span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p5">(<span class="default"><a href="scmpds_2.html#K12">AddTo</a> <a href="scmp_gcd.html#K2">GBP</a> ,1,2</span>)</span></span>)</span></span>)</span>,<span class="p3">(<span class="default"><a href="scmpds_4.html#K1">Load</a> <span class="p4">(<span class="default"><a href="scmpds_2.html#K12">AddTo</a> <a href="scmp_gcd.html#K2">GBP</a> ,1,<span class="p5">(<span class="default"><a href="xcmplx_0.html#K4">-</a> 2</span>)</span></span>)</span></span>)</span></span>)</span></span>)</span> <a href="scmpds_6.html#R2">is_halting_on</a>  <a href="scmpds_4.html#K9">IExec</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a>  <a href="scmpds_2.html#K6">:=</a> 0</span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p4">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a>  <a href="scmpds_2.html#K6">:=</a> 1</span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p3">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a> ,<span class="p4">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="scmpds_2.html#K11">:=</a> <span class="p4">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p2">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a> ,<span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span> <a href="scmpds_2.html#K11">:=</a> <span class="p3">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span></span>)</span></span>)</span>,<font color="Maroon">c<sub>47</sub></font> &amp;  <a href="scmpds_8.html#K3">while&gt;0</a> <a href="scmp_gcd.html#K2">GBP</a> ,1,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a> ,2 <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p4">(<span class="default"><span class="p5">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p3">(<span class="default"><a href="scmpds_2.html#K14">SubFrom</a> <a href="scmp_gcd.html#K2">GBP</a> ,2,<a href="scmp_gcd.html#K3">SBP</a> ,<span class="p4">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span></span>)</span></span>)</span> <a href="scmpds_4.html#K3">';'</a> <span class="p2">(<span class="default"><a href="scmpds_6.html#K3">if&gt;0</a> <a href="scmp_gcd.html#K2">GBP</a> ,2,<span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><span class="p0">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a> ,2 <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p1">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span></span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p0">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a> ,4 <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span> <a href="scmpds_4.html#K3">';'</a> <font color="Maroon">c<sub>50</sub></font></span>)</span> <a href="scmpds_4.html#K3">';'</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><span class="p0">(<span class="default"><span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a> ,<span class="p4">(<span class="default"><span class="p5">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 3</span>)</span> <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p4">(<span class="default"><span class="p5">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p3">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a> ,<span class="p4">(<span class="default"><span class="p5">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span> <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K2">GBP</a> ,4</span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p2">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a> ,<span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 2</span>)</span> <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K2">GBP</a> ,4</span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p1">(<span class="default"><a href="scmpds_2.html#K12">AddTo</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span>,<span class="p2">(<span class="default"><a href="xcmplx_0.html#K4">-</a> 1</span>)</span></span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p0">(<span class="default"><a href="scmpds_2.html#K12">AddTo</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 2</span>)</span>,1</span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p5">(<span class="default"><a href="scmpds_2.html#K12">AddTo</a> <a href="scmp_gcd.html#K2">GBP</a> ,1,2</span>)</span></span>)</span></span>)</span>,<span class="p3">(<span class="default"><a href="scmpds_4.html#K1">Load</a> <span class="p4">(<span class="default"><a href="scmpds_2.html#K12">AddTo</a> <a href="scmp_gcd.html#K2">GBP</a> ,1,<span class="p5">(<span class="default"><a href="xcmplx_0.html#K4">-</a> 2</span>)</span></span>)</span></span>)</span></span>)</span></span>)</span> <a href="scmpds_6.html#R1">is_closed_on</a>  <a href="scmpds_4.html#K9">IExec</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a>  <a href="scmpds_2.html#K6">:=</a> 0</span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p4">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a>  <a href="scmpds_2.html#K6">:=</a> 1</span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p3">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a> ,<span class="p4">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="scmpds_2.html#K11">:=</a> <span class="p4">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p2">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a> ,<span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span> <a href="scmpds_2.html#K11">:=</a> <span class="p3">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span></span>)</span></span>)</span>,<font color="Maroon">c<sub>47</sub></font> )
 
<b>by </b><i><a class="txt" href="scpqsort.html#E3:46"><i><font color="Green">E45</font></i></a>, <a class="txt" href="scpqsort.html#E19:46"><i><font color="Green">E59</font></i></a>, <a class="txt" href="scpqsort.html#E20:46"><i><font color="Green">E60</font></i></a>, <a class="txt" href="scpqsort.html#E21:46"><i><font color="Green">E61</font></i></a>, <a class="txt" href="scpqsort.html#E17"><i><font color="Green">Lemma17</font></i></a></i>;<br/>
<a NAME="E24:46"/><b>then </b>
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a>  <a href="scmpds_2.html#K6">:=</a> 0</span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p4">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a>  <a href="scmpds_2.html#K6">:=</a> 1</span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p3">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a> ,<span class="p4">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="scmpds_2.html#K11">:=</a> <span class="p4">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p2">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a> ,<span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span> <a href="scmpds_2.html#K11">:=</a> <span class="p3">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span></span>)</span></span>)</span> <a href="scmpds_4.html#K3">';'</a> <span class="p1">(<span class="default"><a href="scmpds_8.html#K3">while&gt;0</a> <a href="scmp_gcd.html#K2">GBP</a> ,1,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a> ,2 <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p5">(<span class="default"><span class="p0">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p4">(<span class="default"><a href="scmpds_2.html#K14">SubFrom</a> <a href="scmp_gcd.html#K2">GBP</a> ,2,<a href="scmp_gcd.html#K3">SBP</a> ,<span class="p5">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span></span>)</span></span>)</span> <a href="scmpds_4.html#K3">';'</a> <span class="p3">(<span class="default"><a href="scmpds_6.html#K3">if&gt;0</a> <a href="scmp_gcd.html#K2">GBP</a> ,2,<span class="p4">(<span class="default"><span class="p5">(<span class="default"><span class="p0">(<span class="default"><span class="p1">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a> ,2 <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p2">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span></span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p1">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a> ,4 <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span> <a href="scmpds_4.html#K3">';'</a> <font color="Maroon">c<sub>50</sub></font></span>)</span> <a href="scmpds_4.html#K3">';'</a> <span class="p5">(<span class="default"><span class="p0">(<span class="default"><span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a> ,<span class="p5">(<span class="default"><span class="p0">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 3</span>)</span> <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p5">(<span class="default"><span class="p0">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p4">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a> ,<span class="p5">(<span class="default"><span class="p0">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span> <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K2">GBP</a> ,4</span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p3">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a> ,<span class="p4">(<span class="default"><span class="p5">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 2</span>)</span> <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K2">GBP</a> ,4</span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p2">(<span class="default"><a href="scmpds_2.html#K12">AddTo</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span>,<span class="p3">(<span class="default"><a href="xcmplx_0.html#K4">-</a> 1</span>)</span></span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p1">(<span class="default"><a href="scmpds_2.html#K12">AddTo</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 2</span>)</span>,1</span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p0">(<span class="default"><a href="scmpds_2.html#K12">AddTo</a> <a href="scmp_gcd.html#K2">GBP</a> ,1,2</span>)</span></span>)</span></span>)</span>,<span class="p4">(<span class="default"><a href="scmpds_4.html#K1">Load</a> <span class="p5">(<span class="default"><a href="scmpds_2.html#K12">AddTo</a> <a href="scmp_gcd.html#K2">GBP</a> ,1,<span class="p0">(<span class="default"><a href="xcmplx_0.html#K4">-</a> 2</span>)</span></span>)</span></span>)</span></span>)</span></span>)</span></span>)</span> <a href="scmpds_6.html#R2">is_halting_on</a> <font color="Maroon">c<sub>47</sub></font>
 
<b>by </b><i><a class="ref" href="scpisort.html#T10">SCPISORT:10</a></i>;<br/>
<b>hence </b><a NAME="E25:46"/>
 <a href="scpqsort.html#K2" target="_self">QuickSort</a> <font color="Maroon">c<sub>49</sub></font>,<font color="Maroon">c<sub>48</sub></font> <a href="scmpds_6.html#R2">is_halting_on</a> <font color="Maroon">c<sub>47</sub></font>
 ;<br/>

<b>consider </b><font color="Maroon">c<sub>76</sub></font> being    <a href="finseq_1.html#M2">FinSequence</a> of  <a href="numbers.html#K4">INT</a> <b> such that </b><br/><a NAME="E27:46"/><i><font color="Green">E64</font></i>: 
(  <a href="finseq_1.html#K3">len</a> <font color="Maroon">c<sub>76</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>49</sub></font> &amp; <font color="Maroon">c<sub>76</sub></font> <a href="scpisort.html#R1">is_FinSequence_on</a> <font color="Maroon">c<sub>47</sub></font>,<font color="Maroon">c<sub>48</sub></font> )
 <b>by </b><i><a class="ref" href="scpisort.html#T3">SCPISORT:3</a></i>;<br/>
<b>consider </b><font color="Maroon">c<sub>77</sub></font> being    <a href="finseq_1.html#M2">FinSequence</a> of  <a href="numbers.html#K4">INT</a> <b> such that </b><br/><a NAME="E29:46"/><i><font color="Green">E65</font></i>: 
(  <a href="finseq_1.html#K3">len</a> <font color="Maroon">c<sub>77</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>49</sub></font> &amp; <font color="Maroon">c<sub>77</sub></font> <a href="scpisort.html#R1">is_FinSequence_on</a>  <a href="scmpds_4.html#K9">IExec</a> <span class="p1">(<span class="default"><a href="scpqsort.html#K2" target="_self">QuickSort</a> <font color="Maroon">c<sub>49</sub></font>,<font color="Maroon">c<sub>48</sub></font></span>)</span>,<font color="Maroon">c<sub>47</sub></font>,<font color="Maroon">c<sub>48</sub></font> )
 <b>by </b><i><a class="ref" href="scpisort.html#T3">SCPISORT:3</a></i>;<br/>
<b>take </b>
<font color="Maroon">c<sub>76</sub></font>
;<br/>

<b>take </b>
<font color="Maroon">c<sub>77</sub></font>
;<br/>

<b>thus </b><a NAME="E30:46"/>
(  <a href="finseq_1.html#K3">len</a> <font color="Maroon">c<sub>76</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>49</sub></font> &amp; <font color="Maroon">c<sub>76</sub></font> <a href="scpisort.html#R1">is_FinSequence_on</a> <font color="Maroon">c<sub>47</sub></font>,<font color="Maroon">c<sub>48</sub></font> &amp;  <a href="finseq_1.html#K3">len</a> <font color="Maroon">c<sub>77</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>49</sub></font> &amp; <font color="Maroon">c<sub>77</sub></font> <a href="scpisort.html#R1">is_FinSequence_on</a>  <a href="scmpds_4.html#K9">IExec</a> <span class="p1">(<span class="default"><a href="scpqsort.html#K2" target="_self">QuickSort</a> <font color="Maroon">c<sub>49</sub></font>,<font color="Maroon">c<sub>48</sub></font></span>)</span>,<font color="Maroon">c<sub>47</sub></font>,<font color="Maroon">c<sub>48</sub></font> )
 <b>by </b><i><a class="txt" href="scpqsort.html#E27:46"><i><font color="Green">E64</font></i></a>, <a class="txt" href="scpqsort.html#E29:46"><i><font color="Green">E65</font></i></a></i>;<br/>

<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="46_15"><b>now </b></a><div class="add"><b>let </b><font color="Maroon">c<sub>78</sub></font> be   <a href="nat_1.html#NM1">Nat</a>;<br/><b>assume </b><a NAME="E1:46_15"/><i><font color="Green">E66</font></i>: 
( 1 <a href="xxreal_0.html#R1">&lt;=</a> <font color="Maroon">c<sub>78</sub></font> &amp; <font color="Maroon">c<sub>78</sub></font> <a href="xxreal_0.html#R1">&lt;=</a>  <a href="finseq_1.html#K3">len</a> <font color="Maroon">c<sub>76</sub></font> )
 ;<br/><a NAME="E2:46_15"/><b>then </b><i><font color="Green">E67</font></i>: 
<font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>78</sub></font> <a href="xxreal_0.html#NR2" target="_self">&gt;=</a> <font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> 1
 <b>by </b><i><a class="ref" href="xreal_1.html#T8">XREAL_1:8</a></i>;<br/><a NAME="E3:46_15"/>
<font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> 1 <a href="xxreal_0.html#NR2" target="_self">&gt;=</a> 7 <a href="nat_1.html#K1">+</a> 1
 <b>by </b><i><a class="txt" href="scpqsort.html#E5:46"><i><font color="Green">E46</font></i></a>, <a class="ref" href="xreal_1.html#T8">XREAL_1:8</a></i>;<br/><a NAME="E4:46_15"/><b>then </b><i><font color="Green">E68</font></i>: 
<font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>78</sub></font> <a href="xxreal_0.html#NR2" target="_self">&gt;=</a> 8
 <b>by </b><i><a class="txt" href="scpqsort.html#E2:46_15"><i><font color="Green">E67</font></i></a>, <a class="ref" href="xreal_1.html#T2">XREAL_1:2</a></i>;<br/><a NAME="E5:46_15"/><i><font color="Green">E69</font></i>: 
<font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>78</sub></font> <a href="xxreal_0.html#R1">&lt;=</a> <font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font>
 <b>by </b><i><a class="txt" href="scpqsort.html#E27:46"><i><font color="Green">E64</font></i></a>, <a class="txt" href="scpqsort.html#E1:46_15"><i><font color="Green">E66</font></i></a>, <a class="ref" href="xreal_1.html#T8">XREAL_1:8</a></i>;<br/><b>thus </b><font color="Maroon">c<sub>76</sub></font> <a href="funct_1.html#K1">.</a> <font color="Maroon">c<sub>78</sub></font> = 
<font color="Maroon">c<sub>47</sub></font> <a href="scmpds_2.html#K2">.</a> <span class="p1">(<span class="default"><a href="scmp_gcd.html#K1">intpos</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>78</sub></font></span>)</span></span>)</span>
<b>by </b><i><a class="txt" href="scpqsort.html#E27:46"><i><font color="Green">E64</font></i></a>, <a class="txt" href="scpqsort.html#E1:46_15"><i><font color="Green">E66</font></i></a>, <a class="ref" href="scpisort.html#D1">SCPISORT:def 1</a></i>
<br/>.= 
<span class="p1">(<span class="default"><a href="scmpds_4.html#K9">IExec</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a>  <a href="scmpds_2.html#K6">:=</a> 0</span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p5">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a>  <a href="scmpds_2.html#K6">:=</a> 1</span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p4">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a> ,<span class="p5">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="scmpds_2.html#K11">:=</a> <span class="p5">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p3">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a> ,<span class="p4">(<span class="default"><span class="p5">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span> <a href="scmpds_2.html#K11">:=</a> <span class="p4">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span></span>)</span></span>)</span>,<font color="Maroon">c<sub>47</sub></font></span>)</span> <a href="scmpds_2.html#K2">.</a> <span class="p1">(<span class="default"><a href="scmp_gcd.html#K1">intpos</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>78</sub></font></span>)</span></span>)</span>
<b>by </b><i><a class="txt" href="scpqsort.html#E21:46"><i><font color="Green">E61</font></i></a>, <a class="txt" href="scpqsort.html#E4:46_15"><i><font color="Green">E68</font></i></a>, <a class="txt" href="scpqsort.html#E5:46_15"><i><font color="Green">E69</font></i></a></i>
;<br/></div><b>end;</b></div>
<a NAME="E32:46"/><b>then </b><i><font color="Green">E66</font></i>: 
<font color="Maroon">c<sub>76</sub></font> <a href="scpisort.html#R1">is_FinSequence_on</a>  <a href="scmpds_4.html#K9">IExec</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a>  <a href="scmpds_2.html#K6">:=</a> 0</span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p4">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a>  <a href="scmpds_2.html#K6">:=</a> 1</span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p3">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a> ,<span class="p4">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="scmpds_2.html#K11">:=</a> <span class="p4">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p2">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a> ,<span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span> <a href="scmpds_2.html#K11">:=</a> <span class="p3">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span></span>)</span></span>)</span>,<font color="Maroon">c<sub>47</sub></font>,<font color="Maroon">c<sub>48</sub></font>
 
<b>by </b><i><a class="ref" href="scpisort.html#D1">SCPISORT:def 1</a></i>;<br/>
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="46_16"><b>now </b></a><div class="add"><b>let </b><font color="Maroon">c<sub>78</sub></font> be   <a href="nat_1.html#NM1">Nat</a>;<br/><b>assume </b><a NAME="E1:46_16"/>
( 1 <a href="xxreal_0.html#R1">&lt;=</a> <font color="Maroon">c<sub>78</sub></font> &amp; <font color="Maroon">c<sub>78</sub></font> <a href="xxreal_0.html#R1">&lt;=</a>  <a href="finseq_1.html#K3">len</a> <font color="Maroon">c<sub>77</sub></font> )
 ;<br/><b>hence </b><font color="Maroon">c<sub>77</sub></font> <a href="funct_1.html#K1">.</a> <font color="Maroon">c<sub>78</sub></font> = 
<span class="p1">(<span class="default"><a href="scmpds_4.html#K9">IExec</a> <span class="p2">(<span class="default"><a href="scpqsort.html#K2" target="_self">QuickSort</a> <font color="Maroon">c<sub>49</sub></font>,<font color="Maroon">c<sub>48</sub></font></span>)</span>,<font color="Maroon">c<sub>47</sub></font></span>)</span> <a href="scmpds_2.html#K2">.</a> <span class="p1">(<span class="default"><a href="scmp_gcd.html#K1">intpos</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>78</sub></font></span>)</span></span>)</span>
<b>by </b><i><a class="txt" href="scpqsort.html#E29:46"><i><font color="Green">E65</font></i></a>, <a class="ref" href="scpisort.html#D1">SCPISORT:def 1</a></i>
<br/>.= 
<span class="p1">(<span class="default"><a href="scmpds_4.html#K9">IExec</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><span class="p0">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a>  <a href="scmpds_2.html#K6">:=</a> 0</span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p0">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a>  <a href="scmpds_2.html#K6">:=</a> 1</span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p5">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a> ,<span class="p0">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="scmpds_2.html#K11">:=</a> <span class="p0">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p4">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a> ,<span class="p5">(<span class="default"><span class="p0">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span> <a href="scmpds_2.html#K11">:=</a> <span class="p5">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span></span>)</span></span>)</span> <a href="scmpds_4.html#K3">';'</a> <span class="p3">(<span class="default"><a href="scmpds_8.html#K3">while&gt;0</a> <a href="scmp_gcd.html#K2">GBP</a> ,1,<span class="p4">(<span class="default"><span class="p5">(<span class="default"><span class="p0">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a> ,2 <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p0">(<span class="default"><a href="scmpds_2.html#K14">SubFrom</a> <a href="scmp_gcd.html#K2">GBP</a> ,2,<a href="scmp_gcd.html#K3">SBP</a> ,<span class="p1">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span></span>)</span></span>)</span> <a href="scmpds_4.html#K3">';'</a> <span class="p5">(<span class="default"><a href="scmpds_6.html#K3">if&gt;0</a> <a href="scmp_gcd.html#K2">GBP</a> ,2,<span class="p0">(<span class="default"><span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a> ,2 <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p4">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span></span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p3">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a> ,4 <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p4">(<span class="default"><span class="p5">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span> <a href="scmpds_4.html#K3">';'</a> <font color="Maroon">c<sub>50</sub></font></span>)</span> <a href="scmpds_4.html#K3">';'</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><span class="p0">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a> ,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 3</span>)</span> <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p0">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a> ,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span> <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K2">GBP</a> ,4</span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p5">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a> ,<span class="p0">(<span class="default"><span class="p1">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 2</span>)</span> <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K2">GBP</a> ,4</span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p4">(<span class="default"><a href="scmpds_2.html#K12">AddTo</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p5">(<span class="default"><span class="p0">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span>,<span class="p5">(<span class="default"><a href="xcmplx_0.html#K4">-</a> 1</span>)</span></span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p3">(<span class="default"><a href="scmpds_2.html#K12">AddTo</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p4">(<span class="default"><span class="p5">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 2</span>)</span>,1</span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p2">(<span class="default"><a href="scmpds_2.html#K12">AddTo</a> <a href="scmp_gcd.html#K2">GBP</a> ,1,2</span>)</span></span>)</span></span>)</span>,<span class="p0">(<span class="default"><a href="scmpds_4.html#K1">Load</a> <span class="p1">(<span class="default"><a href="scmpds_2.html#K12">AddTo</a> <a href="scmp_gcd.html#K2">GBP</a> ,1,<span class="p2">(<span class="default"><a href="xcmplx_0.html#K4">-</a> 2</span>)</span></span>)</span></span>)</span></span>)</span></span>)</span></span>)</span></span>)</span>,<font color="Maroon">c<sub>47</sub></font></span>)</span> <a href="scmpds_2.html#K2">.</a> <span class="p1">(<span class="default"><a href="scmp_gcd.html#K1">intpos</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>78</sub></font></span>)</span></span>)</span>

<br/>.= 
<span class="p1">(<span class="default"><a href="scmpds_4.html#K9">IExec</a> <span class="p2">(<span class="default"><a href="scmpds_8.html#K3">while&gt;0</a> <a href="scmp_gcd.html#K2">GBP</a> ,1,<span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a> ,2 <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p0">(<span class="default"><span class="p1">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p5">(<span class="default"><a href="scmpds_2.html#K14">SubFrom</a> <a href="scmp_gcd.html#K2">GBP</a> ,2,<a href="scmp_gcd.html#K3">SBP</a> ,<span class="p0">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span></span>)</span></span>)</span> <a href="scmpds_4.html#K3">';'</a> <span class="p4">(<span class="default"><a href="scmpds_6.html#K3">if&gt;0</a> <a href="scmp_gcd.html#K2">GBP</a> ,2,<span class="p5">(<span class="default"><span class="p0">(<span class="default"><span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a> ,2 <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p3">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span></span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p2">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a> ,4 <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span> <a href="scmpds_4.html#K3">';'</a> <font color="Maroon">c<sub>50</sub></font></span>)</span> <a href="scmpds_4.html#K3">';'</a> <span class="p0">(<span class="default"><span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a> ,<span class="p0">(<span class="default"><span class="p1">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 3</span>)</span> <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p0">(<span class="default"><span class="p1">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p5">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a> ,<span class="p0">(<span class="default"><span class="p1">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span> <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K2">GBP</a> ,4</span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p4">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a> ,<span class="p5">(<span class="default"><span class="p0">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 2</span>)</span> <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K2">GBP</a> ,4</span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p3">(<span class="default"><a href="scmpds_2.html#K12">AddTo</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p4">(<span class="default"><span class="p5">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span>,<span class="p4">(<span class="default"><a href="xcmplx_0.html#K4">-</a> 1</span>)</span></span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p2">(<span class="default"><a href="scmpds_2.html#K12">AddTo</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 2</span>)</span>,1</span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p1">(<span class="default"><a href="scmpds_2.html#K12">AddTo</a> <a href="scmp_gcd.html#K2">GBP</a> ,1,2</span>)</span></span>)</span></span>)</span>,<span class="p5">(<span class="default"><a href="scmpds_4.html#K1">Load</a> <span class="p0">(<span class="default"><a href="scmpds_2.html#K12">AddTo</a> <a href="scmp_gcd.html#K2">GBP</a> ,1,<span class="p1">(<span class="default"><a href="xcmplx_0.html#K4">-</a> 2</span>)</span></span>)</span></span>)</span></span>)</span></span>)</span></span>)</span>,<span class="p2">(<span class="default"><a href="scmpds_4.html#K9">IExec</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><span class="p0">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a>  <a href="scmpds_2.html#K6">:=</a> 0</span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p0">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a>  <a href="scmpds_2.html#K6">:=</a> 1</span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p5">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a> ,<span class="p0">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="scmpds_2.html#K11">:=</a> <span class="p0">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p4">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a> ,<span class="p5">(<span class="default"><span class="p0">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span> <a href="scmpds_2.html#K11">:=</a> <span class="p5">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span></span>)</span></span>)</span>,<font color="Maroon">c<sub>47</sub></font></span>)</span></span>)</span> <a href="scmpds_2.html#K2">.</a> <span class="p1">(<span class="default"><a href="scmp_gcd.html#K1">intpos</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>78</sub></font></span>)</span></span>)</span>
<b>by </b><i><a class="txt" href="scpqsort.html#E23:46"><i><font color="Green">E63</font></i></a>, <a class="ref" href="scpisort.html#T8">SCPISORT:8</a></i>
;<br/><br/></div><b>end;</b></div>
<a NAME="E34:46"/><b>then </b>
<font color="Maroon">c<sub>77</sub></font> <a href="scpisort.html#R1">is_FinSequence_on</a>  <a href="scmpds_4.html#K9">IExec</a> <span class="p1">(<span class="default"><a href="scmpds_8.html#K3">while&gt;0</a> <a href="scmp_gcd.html#K2">GBP</a> ,1,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a> ,2 <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p5">(<span class="default"><span class="p0">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p4">(<span class="default"><a href="scmpds_2.html#K14">SubFrom</a> <a href="scmp_gcd.html#K2">GBP</a> ,2,<a href="scmp_gcd.html#K3">SBP</a> ,<span class="p5">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span></span>)</span></span>)</span> <a href="scmpds_4.html#K3">';'</a> <span class="p3">(<span class="default"><a href="scmpds_6.html#K3">if&gt;0</a> <a href="scmp_gcd.html#K2">GBP</a> ,2,<span class="p4">(<span class="default"><span class="p5">(<span class="default"><span class="p0">(<span class="default"><span class="p1">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a> ,2 <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p2">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span></span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p1">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a> ,4 <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span> <a href="scmpds_4.html#K3">';'</a> <font color="Maroon">c<sub>50</sub></font></span>)</span> <a href="scmpds_4.html#K3">';'</a> <span class="p5">(<span class="default"><span class="p0">(<span class="default"><span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a> ,<span class="p5">(<span class="default"><span class="p0">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 3</span>)</span> <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p5">(<span class="default"><span class="p0">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p4">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a> ,<span class="p5">(<span class="default"><span class="p0">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span> <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K2">GBP</a> ,4</span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p3">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a> ,<span class="p4">(<span class="default"><span class="p5">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 2</span>)</span> <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K2">GBP</a> ,4</span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p2">(<span class="default"><a href="scmpds_2.html#K12">AddTo</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span>,<span class="p3">(<span class="default"><a href="xcmplx_0.html#K4">-</a> 1</span>)</span></span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p1">(<span class="default"><a href="scmpds_2.html#K12">AddTo</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 2</span>)</span>,1</span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p0">(<span class="default"><a href="scmpds_2.html#K12">AddTo</a> <a href="scmp_gcd.html#K2">GBP</a> ,1,2</span>)</span></span>)</span></span>)</span>,<span class="p4">(<span class="default"><a href="scmpds_4.html#K1">Load</a> <span class="p5">(<span class="default"><a href="scmpds_2.html#K12">AddTo</a> <a href="scmp_gcd.html#K2">GBP</a> ,1,<span class="p0">(<span class="default"><a href="xcmplx_0.html#K4">-</a> 2</span>)</span></span>)</span></span>)</span></span>)</span></span>)</span></span>)</span>,<span class="p1">(<span class="default"><a href="scmpds_4.html#K9">IExec</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a>  <a href="scmpds_2.html#K6">:=</a> 0</span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p5">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a>  <a href="scmpds_2.html#K6">:=</a> 1</span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p4">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a> ,<span class="p5">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="scmpds_2.html#K11">:=</a> <span class="p5">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p3">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a> ,<span class="p4">(<span class="default"><span class="p5">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span> <a href="scmpds_2.html#K11">:=</a> <span class="p4">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>49</sub></font></span>)</span></span>)</span></span>)</span>,<font color="Maroon">c<sub>47</sub></font></span>)</span>,<font color="Maroon">c<sub>48</sub></font>
 
<b>by </b><i><a class="ref" href="scpisort.html#D1">SCPISORT:def 1</a></i>;<br/>
<b>hence </b><a NAME="E35:46"/>
( <font color="Maroon">c<sub>76</sub></font>,<font color="Maroon">c<sub>77</sub></font> <a href="rfinseq.html#R1">are_fiberwise_equipotent</a>  &amp; <font color="Maroon">c<sub>77</sub></font> <a href="sfmastr3.html#R1">is_non_decreasing_on</a> 1,<font color="Maroon">c<sub>49</sub></font> )
 <b>by </b><i><a class="txt" href="scpqsort.html#E3:46"><i><font color="Green">E45</font></i></a>, <a class="txt" href="scpqsort.html#E19:46"><i><font color="Green">E59</font></i></a>, <a class="txt" href="scpqsort.html#E20:46"><i><font color="Green">E60</font></i></a>, <a class="txt" href="scpqsort.html#E21:46"><i><font color="Green">E61</font></i></a>, <a class="txt" href="scpqsort.html#E22:46"><i><font color="Green">E62</font></i></a>, <a class="txt" href="scpqsort.html#E27:46"><i><font color="Green">E64</font></i></a>, <a class="txt" href="scpqsort.html#E29:46"><i><font color="Green">E65</font></i></a>, <a class="txt" href="scpqsort.html#E32:46"><i><font color="Green">E66</font></i></a>, <a class="txt" href="scpqsort.html#E15"><i><font color="Green">Lemma15</font></i></a></i>;<br/>


</div>
