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<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>assume </b><a NAME="E1:24"/><i><font color="Green">E22</font></i>: 
( <font color="Maroon">c<sub>47</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>47</sub></font> <a href="scmpds_2.html#K2">.</a> <span class="p1">(<span class="default"><a href="scmp_gcd.html#K1">intpos</a> 5</span>)</span> <a href="xxreal_0.html#NR4" target="_self">&gt;</a> 0 &amp; <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> 4</span>)</span> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>48</sub></font> <a href="xcmplx_0.html#K2">+</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>47</sub></font> <a href="scmpds_2.html#K2">.</a> <span class="p2">(<span class="default"><a href="scmp_gcd.html#K1">intpos</a> 5</span>)</span></span>)</span> &amp; <font color="Maroon">c<sub>48</sub></font> <a href="xxreal_0.html#NR2" target="_self">&gt;=</a> 8 &amp; <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> 2</span>)</span> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>49</sub></font> &amp; <font color="Maroon">c<sub>49</sub></font> <a href="xxreal_0.html#NR2" target="_self">&gt;=</a> 8 )
 ;<br/>

<b>set </b><font color="Maroon">c<sub>50</sub></font> =  <a href="scmp_gcd.html#K2">GBP</a> ;<br/>
<b>set </b><font color="Maroon">c<sub>51</sub></font> =  <a href="scmpds_2.html#K3">DataLoc</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>47</sub></font> <a href="scmpds_2.html#K2">.</a> <a href="scmp_gcd.html#K2">GBP</a> </span>)</span>,5;<br/>
<a NAME="E2:24"/><i><font color="Green">E23</font></i>: 
 <a href="scmpds_2.html#K3">DataLoc</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>47</sub></font> <a href="scmpds_2.html#K2">.</a> <a href="scmp_gcd.html#K2">GBP</a> </span>)</span>,5 <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> 5</span>)</span>
 
<b>by </b><i><a class="txt" href="scpqsort.html#E1:24"><i><font color="Green">E22</font></i></a>, <a class="ref" href="scmp_gcd.html#T5">SCMP_GCD:5</a></i>;<br/>
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="24_1"><b>now </b></a><div class="add"><b>let </b><font color="Maroon">c<sub>52</sub></font> be   <a href="ami_1.html#NM4">State</a> of <a href="scmpds_2.html#K1">SCMPDS</a> ;<br/><b>assume </b><a NAME="E1:24_1"/><i><font color="Green">E24</font></i>: 
( <font color="Maroon">c<sub>52</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> <a href="xxreal_0.html#NR2" target="_self">&gt;=</a> <font color="Maroon">c<sub>48</sub></font> <a href="xcmplx_0.html#K2">+</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>52</sub></font> <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"><font color="Maroon">c<sub>47</sub></font> <a href="scmpds_2.html#K2">.</a> <a href="scmp_gcd.html#K2">GBP</a> </span>)</span>,5</span>)</span></span>)</span> &amp; <font color="Maroon">c<sub>52</sub></font> <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>47</sub></font> <a href="scmpds_2.html#K2">.</a> <span class="p1">(<span class="default"><a href="scmp_gcd.html#K1">intpos</a> 2</span>)</span> &amp; <font color="Maroon">c<sub>52</sub></font> <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>47</sub></font> <a href="scmpds_2.html#K2">.</a> <a href="scmp_gcd.html#K2">GBP</a>  &amp; <font color="Maroon">c<sub>52</sub></font> <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"><font color="Maroon">c<sub>47</sub></font> <a href="scmpds_2.html#K2">.</a> <a href="scmp_gcd.html#K2">GBP</a> </span>)</span>,5</span>)</span> <a href="xxreal_0.html#NR4" target="_self">&gt;</a> 0 )
 ;<br/><a NAME="E2:24_1"/><b>then </b><i><font color="Green">E25</font></i>: 
<font color="Maroon">c<sub>48</sub></font> <a href="xcmplx_0.html#K2">+</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>52</sub></font> <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"><font color="Maroon">c<sub>47</sub></font> <a href="scmpds_2.html#K2">.</a> <a href="scmp_gcd.html#K2">GBP</a> </span>)</span>,5</span>)</span></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> 0
 <b>by </b><i><a class="ref" href="xreal_1.html#T8">XREAL_1:8</a></i>;<br/><a NAME="E3:24_1"/><b>then </b><i><font color="Green">E26</font></i>: 
<font color="Maroon">c<sub>52</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> <a href="xxreal_0.html#NR2" target="_self">&gt;=</a> <font color="Maroon">c<sub>48</sub></font>
 <b>by </b><i><a class="txt" href="scpqsort.html#E1:24_1"><i><font color="Green">E24</font></i></a>, <a class="ref" href="xreal_1.html#T2">XREAL_1:2</a></i>;<br/><a NAME="E4:24_1"/>
<font color="Maroon">c<sub>52</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> <a href="xxreal_0.html#NR4" target="_self">&gt;</a> 0
 <b>by </b><i><a class="txt" href="scpqsort.html#E1:24_1"><i><font color="Green">E24</font></i></a>, <a class="txt" href="scpqsort.html#E2:24_1"><i><font color="Green">E25</font></i></a></i>;<br/><b>then reconsider </b><font color="Maroon">c<sub>53</sub></font> = <font color="Maroon">c<sub>52</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> as   <a href="nat_1.html#NM1">Nat</a> <b>by </b><i><a class="ref" href="int_1.html#T16">INT_1:16</a></i>;<br/><a NAME="E6:24_1"/><i><font color="Green">E27</font></i>: 
<font color="Maroon">c<sub>53</sub></font> <a href="xxreal_0.html#NR2" target="_self">&gt;=</a> 8
 <b>by </b><i><a class="txt" href="scpqsort.html#E1:24"><i><font color="Green">E22</font></i></a>, <a class="txt" href="scpqsort.html#E3:24_1"><i><font color="Green">E26</font></i></a>, <a class="ref" href="xreal_1.html#T2">XREAL_1:2</a></i>;<br/><a NAME="E7:24_1"/><b>then </b><i><font color="Green">E28</font></i>: 
( ( <font color="Maroon">c<sub>52</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>49</sub></font></span>)</span> <a href="xxreal_0.html#NR3" target="_self">&lt;</a> <font color="Maroon">c<sub>52</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>53</sub></font></span>)</span> implies ( <span class="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> ,7 <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K2">GBP</a> ,5</span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p0">(<span class="default"><a href="scmpds_2.html#K12">AddTo</a> <a href="scmp_gcd.html#K2">GBP</a> ,5,<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="scmp_gcd.html#K2">GBP</a> ,6 <a href="scmpds_2.html#K17">:=</a> <span class="p0">(<span class="default"><a href="scmp_gcd.html#K1">intpos</a> 4</span>)</span>,0</span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p4">(<span class="default"><a href="scmpds_2.html#K14">SubFrom</a> <a href="scmp_gcd.html#K2">GBP</a> ,6,<span class="p5">(<span class="default"><a href="scmp_gcd.html#K1">intpos</a> 2</span>)</span>,0</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> ,6,<span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="scmpds_2.html#K12">AddTo</a> <a href="scmp_gcd.html#K2">GBP</a> ,4,<span class="p0">(<span class="default"><a href="xcmplx_0.html#K4">-</a> 1</span>)</span></span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p5">(<span class="default"><a href="scmpds_2.html#K12">AddTo</a> <a href="scmp_gcd.html#K2">GBP</a> ,7,<span class="p0">(<span class="default"><a href="xcmplx_0.html#K4">-</a> 1</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="scmp_gcd.html#K2">GBP</a> ,5 <a href="scmpds_2.html#K11">:=</a> 0</span>)</span></span>)</span></span>)</span></span>)</span>,<font color="Maroon">c<sub>52</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> 5</span>)</span> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>52</sub></font> <a href="scmpds_2.html#K2">.</a> <span class="p2">(<span class="default"><a href="scmp_gcd.html#K1">intpos</a> 5</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"><a href="scmp_gcd.html#K2">GBP</a> ,7 <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K2">GBP</a> ,5</span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p0">(<span class="default"><a href="scmpds_2.html#K12">AddTo</a> <a href="scmp_gcd.html#K2">GBP</a> ,5,<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="scmp_gcd.html#K2">GBP</a> ,6 <a href="scmpds_2.html#K17">:=</a> <span class="p0">(<span class="default"><a href="scmp_gcd.html#K1">intpos</a> 4</span>)</span>,0</span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p4">(<span class="default"><a href="scmpds_2.html#K14">SubFrom</a> <a href="scmp_gcd.html#K2">GBP</a> ,6,<span class="p5">(<span class="default"><a href="scmp_gcd.html#K1">intpos</a> 2</span>)</span>,0</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> ,6,<span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="scmpds_2.html#K12">AddTo</a> <a href="scmp_gcd.html#K2">GBP</a> ,4,<span class="p0">(<span class="default"><a href="xcmplx_0.html#K4">-</a> 1</span>)</span></span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p5">(<span class="default"><a href="scmpds_2.html#K12">AddTo</a> <a href="scmp_gcd.html#K2">GBP</a> ,7,<span class="p0">(<span class="default"><a href="xcmplx_0.html#K4">-</a> 1</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="scmp_gcd.html#K2">GBP</a> ,5 <a href="scmpds_2.html#K11">:=</a> 0</span>)</span></span>)</span></span>)</span></span>)</span>,<font color="Maroon">c<sub>52</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> <span class="p1">(<span class="default"><font color="Maroon">c<sub>52</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"><a href="scmp_gcd.html#K2">GBP</a> ,7 <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K2">GBP</a> ,5</span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p0">(<span class="default"><a href="scmpds_2.html#K12">AddTo</a> <a href="scmp_gcd.html#K2">GBP</a> ,5,<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="scmp_gcd.html#K2">GBP</a> ,6 <a href="scmpds_2.html#K17">:=</a> <span class="p0">(<span class="default"><a href="scmp_gcd.html#K1">intpos</a> 4</span>)</span>,0</span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p4">(<span class="default"><a href="scmpds_2.html#K14">SubFrom</a> <a href="scmp_gcd.html#K2">GBP</a> ,6,<span class="p5">(<span class="default"><a href="scmp_gcd.html#K1">intpos</a> 2</span>)</span>,0</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> ,6,<span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="scmpds_2.html#K12">AddTo</a> <a href="scmp_gcd.html#K2">GBP</a> ,4,<span class="p0">(<span class="default"><a href="xcmplx_0.html#K4">-</a> 1</span>)</span></span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p5">(<span class="default"><a href="scmpds_2.html#K12">AddTo</a> <a href="scmp_gcd.html#K2">GBP</a> ,7,<span class="p0">(<span class="default"><a href="xcmplx_0.html#K4">-</a> 1</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="scmp_gcd.html#K2">GBP</a> ,5 <a href="scmpds_2.html#K11">:=</a> 0</span>)</span></span>)</span></span>)</span></span>)</span>,<font color="Maroon">c<sub>52</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> 7</span>)</span> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>52</sub></font> <a href="scmpds_2.html#K2">.</a> <span class="p2">(<span class="default"><a href="scmp_gcd.html#K1">intpos</a> 5</span>)</span></span>)</span> <a href="xcmplx_0.html#K6">-</a> 1 ) ) &amp; ( <font color="Maroon">c<sub>52</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>49</sub></font></span>)</span> <a href="xxreal_0.html#NR2" target="_self">&gt;=</a> <font color="Maroon">c<sub>52</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>53</sub></font></span>)</span> implies ( <span class="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> ,7 <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K2">GBP</a> ,5</span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p0">(<span class="default"><a href="scmpds_2.html#K12">AddTo</a> <a href="scmp_gcd.html#K2">GBP</a> ,5,<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="scmp_gcd.html#K2">GBP</a> ,6 <a href="scmpds_2.html#K17">:=</a> <span class="p0">(<span class="default"><a href="scmp_gcd.html#K1">intpos</a> 4</span>)</span>,0</span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p4">(<span class="default"><a href="scmpds_2.html#K14">SubFrom</a> <a href="scmp_gcd.html#K2">GBP</a> ,6,<span class="p5">(<span class="default"><a href="scmp_gcd.html#K1">intpos</a> 2</span>)</span>,0</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> ,6,<span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="scmpds_2.html#K12">AddTo</a> <a href="scmp_gcd.html#K2">GBP</a> ,4,<span class="p0">(<span class="default"><a href="xcmplx_0.html#K4">-</a> 1</span>)</span></span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p5">(<span class="default"><a href="scmpds_2.html#K12">AddTo</a> <a href="scmp_gcd.html#K2">GBP</a> ,7,<span class="p0">(<span class="default"><a href="xcmplx_0.html#K4">-</a> 1</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="scmp_gcd.html#K2">GBP</a> ,5 <a href="scmpds_2.html#K11">:=</a> 0</span>)</span></span>)</span></span>)</span></span>)</span>,<font color="Maroon">c<sub>52</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> 5</span>)</span> <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"><a href="scmp_gcd.html#K2">GBP</a> ,7 <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K2">GBP</a> ,5</span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p0">(<span class="default"><a href="scmpds_2.html#K12">AddTo</a> <a href="scmp_gcd.html#K2">GBP</a> ,5,<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="scmp_gcd.html#K2">GBP</a> ,6 <a href="scmpds_2.html#K17">:=</a> <span class="p0">(<span class="default"><a href="scmp_gcd.html#K1">intpos</a> 4</span>)</span>,0</span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p4">(<span class="default"><a href="scmpds_2.html#K14">SubFrom</a> <a href="scmp_gcd.html#K2">GBP</a> ,6,<span class="p5">(<span class="default"><a href="scmp_gcd.html#K1">intpos</a> 2</span>)</span>,0</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> ,6,<span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="scmpds_2.html#K12">AddTo</a> <a href="scmp_gcd.html#K2">GBP</a> ,4,<span class="p0">(<span class="default"><a href="xcmplx_0.html#K4">-</a> 1</span>)</span></span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p5">(<span class="default"><a href="scmpds_2.html#K12">AddTo</a> <a href="scmp_gcd.html#K2">GBP</a> ,7,<span class="p0">(<span class="default"><a href="xcmplx_0.html#K4">-</a> 1</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="scmp_gcd.html#K2">GBP</a> ,5 <a href="scmpds_2.html#K11">:=</a> 0</span>)</span></span>)</span></span>)</span></span>)</span>,<font color="Maroon">c<sub>52</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>52</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> &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"><a href="scmp_gcd.html#K2">GBP</a> ,7 <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K2">GBP</a> ,5</span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p0">(<span class="default"><a href="scmpds_2.html#K12">AddTo</a> <a href="scmp_gcd.html#K2">GBP</a> ,5,<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="scmp_gcd.html#K2">GBP</a> ,6 <a href="scmpds_2.html#K17">:=</a> <span class="p0">(<span class="default"><a href="scmp_gcd.html#K1">intpos</a> 4</span>)</span>,0</span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p4">(<span class="default"><a href="scmpds_2.html#K14">SubFrom</a> <a href="scmp_gcd.html#K2">GBP</a> ,6,<span class="p5">(<span class="default"><a href="scmp_gcd.html#K1">intpos</a> 2</span>)</span>,0</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> ,6,<span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="scmpds_2.html#K12">AddTo</a> <a href="scmp_gcd.html#K2">GBP</a> ,4,<span class="p0">(<span class="default"><a href="xcmplx_0.html#K4">-</a> 1</span>)</span></span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p5">(<span class="default"><a href="scmpds_2.html#K12">AddTo</a> <a href="scmp_gcd.html#K2">GBP</a> ,7,<span class="p0">(<span class="default"><a href="xcmplx_0.html#K4">-</a> 1</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="scmp_gcd.html#K2">GBP</a> ,5 <a href="scmpds_2.html#K11">:=</a> 0</span>)</span></span>)</span></span>)</span></span>)</span>,<font color="Maroon">c<sub>52</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> 7</span>)</span> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>52</sub></font> <a href="scmpds_2.html#K2">.</a> <span class="p1">(<span class="default"><a href="scmp_gcd.html#K1">intpos</a> 5</span>)</span> ) ) )
 <b>by </b><i><a class="txt" href="scpqsort.html#E1:24"><i><font color="Green">E22</font></i></a>, <a class="txt" href="scpqsort.html#E2:24"><i><font color="Green">E23</font></i></a>, <a class="txt" href="scpqsort.html#E1:24_1"><i><font color="Green">E24</font></i></a>, <a class="txt" href="scpqsort.html#E21"><i><font color="Green">Lemma19</font></i></a></i>;<br/><b>thus </b><a NAME="E8:24_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"><span class="p5">(<span class="default"><span class="p0">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a> ,7 <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K2">GBP</a> ,5</span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p0">(<span class="default"><a href="scmpds_2.html#K12">AddTo</a> <a href="scmp_gcd.html#K2">GBP</a> ,5,<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="scmp_gcd.html#K2">GBP</a> ,6 <a href="scmpds_2.html#K17">:=</a> <span class="p0">(<span class="default"><a href="scmp_gcd.html#K1">intpos</a> 4</span>)</span>,0</span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p4">(<span class="default"><a href="scmpds_2.html#K14">SubFrom</a> <a href="scmp_gcd.html#K2">GBP</a> ,6,<span class="p5">(<span class="default"><a href="scmp_gcd.html#K1">intpos</a> 2</span>)</span>,0</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> ,6,<span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="scmpds_2.html#K12">AddTo</a> <a href="scmp_gcd.html#K2">GBP</a> ,4,<span class="p0">(<span class="default"><a href="xcmplx_0.html#K4">-</a> 1</span>)</span></span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p5">(<span class="default"><a href="scmpds_2.html#K12">AddTo</a> <a href="scmp_gcd.html#K2">GBP</a> ,7,<span class="p0">(<span class="default"><a href="xcmplx_0.html#K4">-</a> 1</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="scmp_gcd.html#K2">GBP</a> ,5 <a href="scmpds_2.html#K11">:=</a> 0</span>)</span></span>)</span></span>)</span></span>)</span>,<font color="Maroon">c<sub>52</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>52</sub></font> <a href="scmpds_2.html#K2">.</a> <a href="scmp_gcd.html#K2">GBP</a> 
 <b>by </b><i><a class="txt" href="scpqsort.html#E1:24"><i><font color="Green">E22</font></i></a>, <a class="txt" href="scpqsort.html#E2:24"><i><font color="Green">E23</font></i></a>, <a class="txt" href="scpqsort.html#E1:24_1"><i><font color="Green">E24</font></i></a>, <a class="txt" href="scpqsort.html#E6:24_1"><i><font color="Green">E27</font></i></a>, <a class="txt" href="scpqsort.html#E21"><i><font color="Green">Lemma19</font></i></a></i>;<br/><b>thus </b><a NAME="E9:24_1"/>
( <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> ,7 <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K2">GBP</a> ,5</span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p4">(<span class="default"><a href="scmpds_2.html#K12">AddTo</a> <a href="scmp_gcd.html#K2">GBP</a> ,5,<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="scmp_gcd.html#K2">GBP</a> ,6 <a href="scmpds_2.html#K17">:=</a> <span class="p4">(<span class="default"><a href="scmp_gcd.html#K1">intpos</a> 4</span>)</span>,0</span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p2">(<span class="default"><a href="scmpds_2.html#K14">SubFrom</a> <a href="scmp_gcd.html#K2">GBP</a> ,6,<span class="p3">(<span class="default"><a href="scmp_gcd.html#K1">intpos</a> 2</span>)</span>,0</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> ,6,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="scmpds_2.html#K12">AddTo</a> <a href="scmp_gcd.html#K2">GBP</a> ,4,<span class="p4">(<span class="default"><a href="xcmplx_0.html#K4">-</a> 1</span>)</span></span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p3">(<span class="default"><a href="scmpds_2.html#K12">AddTo</a> <a href="scmp_gcd.html#K2">GBP</a> ,7,<span class="p4">(<span class="default"><a href="xcmplx_0.html#K4">-</a> 1</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="scmp_gcd.html#K2">GBP</a> ,5 <a href="scmpds_2.html#K11">:=</a> 0</span>)</span></span>)</span></span>)</span> <a href="scmpds_6.html#R1">is_closed_on</a> <font color="Maroon">c<sub>52</sub></font> &amp; <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> ,7 <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K2">GBP</a> ,5</span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p4">(<span class="default"><a href="scmpds_2.html#K12">AddTo</a> <a href="scmp_gcd.html#K2">GBP</a> ,5,<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="scmp_gcd.html#K2">GBP</a> ,6 <a href="scmpds_2.html#K17">:=</a> <span class="p4">(<span class="default"><a href="scmp_gcd.html#K1">intpos</a> 4</span>)</span>,0</span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p2">(<span class="default"><a href="scmpds_2.html#K14">SubFrom</a> <a href="scmp_gcd.html#K2">GBP</a> ,6,<span class="p3">(<span class="default"><a href="scmp_gcd.html#K1">intpos</a> 2</span>)</span>,0</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> ,6,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="scmpds_2.html#K12">AddTo</a> <a href="scmp_gcd.html#K2">GBP</a> ,4,<span class="p4">(<span class="default"><a href="xcmplx_0.html#K4">-</a> 1</span>)</span></span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p3">(<span class="default"><a href="scmpds_2.html#K12">AddTo</a> <a href="scmp_gcd.html#K2">GBP</a> ,7,<span class="p4">(<span class="default"><a href="xcmplx_0.html#K4">-</a> 1</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="scmp_gcd.html#K2">GBP</a> ,5 <a href="scmpds_2.html#K11">:=</a> 0</span>)</span></span>)</span></span>)</span> <a href="scmpds_6.html#R2">is_halting_on</a> <font color="Maroon">c<sub>52</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/><div><b>hereby </b>
<div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="24_1_1_1"><b>per </b></a><a class="txt" onclick="hs(this)" href="javascript:()"><b>cases </b></a><span class="hide"><a NAME="E1:24_1_1_1"/>
( <font color="Maroon">c<sub>52</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>49</sub></font></span>)</span> <a href="xxreal_0.html#NR3" target="_self">&lt;</a> <font color="Maroon">c<sub>52</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>53</sub></font></span>)</span> or <font color="Maroon">c<sub>52</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>49</sub></font></span>)</span> <a href="xxreal_0.html#NR2" target="_self">&gt;=</a> <font color="Maroon">c<sub>52</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>53</sub></font></span>)</span> )
 </span>;<br/><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="24_1_1_1_1"><b>suppose </b></a><a NAME="E1:24_1_1_1_1"/><i><font color="Green">E29</font></i>: 
<font color="Maroon">c<sub>52</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>49</sub></font></span>)</span> <a href="xxreal_0.html#NR3" target="_self">&lt;</a> <font color="Maroon">c<sub>52</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>53</sub></font></span>)</span>
 ;<br/><div class="add"><b>hence </b><a NAME="E2:24_1_1_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"><span class="p5">(<span class="default"><span class="p0">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a> ,7 <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K2">GBP</a> ,5</span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p0">(<span class="default"><a href="scmpds_2.html#K12">AddTo</a> <a href="scmp_gcd.html#K2">GBP</a> ,5,<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="scmp_gcd.html#K2">GBP</a> ,6 <a href="scmpds_2.html#K17">:=</a> <span class="p0">(<span class="default"><a href="scmp_gcd.html#K1">intpos</a> 4</span>)</span>,0</span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p4">(<span class="default"><a href="scmpds_2.html#K14">SubFrom</a> <a href="scmp_gcd.html#K2">GBP</a> ,6,<span class="p5">(<span class="default"><a href="scmp_gcd.html#K1">intpos</a> 2</span>)</span>,0</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> ,6,<span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="scmpds_2.html#K12">AddTo</a> <a href="scmp_gcd.html#K2">GBP</a> ,4,<span class="p0">(<span class="default"><a href="xcmplx_0.html#K4">-</a> 1</span>)</span></span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p5">(<span class="default"><a href="scmpds_2.html#K12">AddTo</a> <a href="scmp_gcd.html#K2">GBP</a> ,7,<span class="p0">(<span class="default"><a href="xcmplx_0.html#K4">-</a> 1</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="scmp_gcd.html#K2">GBP</a> ,5 <a href="scmpds_2.html#K11">:=</a> 0</span>)</span></span>)</span></span>)</span></span>)</span>,<font color="Maroon">c<sub>52</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"><font color="Maroon">c<sub>47</sub></font> <a href="scmpds_2.html#K2">.</a> <a href="scmp_gcd.html#K2">GBP</a> </span>)</span>,5</span>)</span> <a href="xxreal_0.html#NR3" target="_self">&lt;</a> <font color="Maroon">c<sub>52</sub></font> <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"><font color="Maroon">c<sub>47</sub></font> <a href="scmpds_2.html#K2">.</a> <a href="scmp_gcd.html#K2">GBP</a> </span>)</span>,5</span>)</span>
 <b>by </b><i><a class="txt" href="scpqsort.html#E2:24"><i><font color="Green">E23</font></i></a>, <a class="txt" href="scpqsort.html#E7:24_1"><i><font color="Green">E28</font></i></a>, <a class="ref" href="xreal_1.html#T148">XREAL_1:148</a></i>;<br/><a NAME="E3:24_1_1_1_1"/>
<span class="p1">(<span class="default"><font color="Maroon">c<sub>48</sub></font> <a href="xcmplx_0.html#K2">+</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>52</sub></font> <a href="scmpds_2.html#K2">.</a> <span class="p3">(<span class="default"><a href="scmpds_2.html#K3">DataLoc</a> <span class="p4">(<span class="default"><font color="Maroon">c<sub>47</sub></font> <a href="scmpds_2.html#K2">.</a> <a href="scmp_gcd.html#K2">GBP</a> </span>)</span>,5</span>)</span></span>)</span></span>)</span> <a href="xcmplx_0.html#K6">-</a> 1 <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>48</sub></font> <a href="xcmplx_0.html#K2">+</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#K2">GBP</a> ,7 <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K2">GBP</a> ,5</span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p1">(<span class="default"><a href="scmpds_2.html#K12">AddTo</a> <a href="scmp_gcd.html#K2">GBP</a> ,5,<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="scmp_gcd.html#K2">GBP</a> ,6 <a href="scmpds_2.html#K17">:=</a> <span class="p1">(<span class="default"><a href="scmp_gcd.html#K1">intpos</a> 4</span>)</span>,0</span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p5">(<span class="default"><a href="scmpds_2.html#K14">SubFrom</a> <a href="scmp_gcd.html#K2">GBP</a> ,6,<span class="p0">(<span class="default"><a href="scmp_gcd.html#K1">intpos</a> 2</span>)</span>,0</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> ,6,<span class="p5">(<span class="default"><span class="p0">(<span class="default"><a href="scmpds_2.html#K12">AddTo</a> <a href="scmp_gcd.html#K2">GBP</a> ,4,<span class="p1">(<span class="default"><a href="xcmplx_0.html#K4">-</a> 1</span>)</span></span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p0">(<span class="default"><a href="scmpds_2.html#K12">AddTo</a> <a href="scmp_gcd.html#K2">GBP</a> ,7,<span class="p1">(<span class="default"><a href="xcmplx_0.html#K4">-</a> 1</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="scmp_gcd.html#K2">GBP</a> ,5 <a href="scmpds_2.html#K11">:=</a> 0</span>)</span></span>)</span></span>)</span></span>)</span>,<font color="Maroon">c<sub>52</sub></font></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"><font color="Maroon">c<sub>47</sub></font> <a href="scmpds_2.html#K2">.</a> <a href="scmp_gcd.html#K2">GBP</a> </span>)</span>,5</span>)</span></span>)</span>
 <b>by </b><i><a class="txt" href="scpqsort.html#E2:24"><i><font color="Green">E23</font></i></a>, <a class="txt" href="scpqsort.html#E7:24_1"><i><font color="Green">E28</font></i></a>, <a class="txt" href="scpqsort.html#E1:24_1_1_1_1"><i><font color="Green">E29</font></i></a></i>;<br/><b>hence </b><a NAME="E4:24_1_1_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"><span class="p5">(<span class="default"><span class="p0">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a> ,7 <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K2">GBP</a> ,5</span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p0">(<span class="default"><a href="scmpds_2.html#K12">AddTo</a> <a href="scmp_gcd.html#K2">GBP</a> ,5,<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="scmp_gcd.html#K2">GBP</a> ,6 <a href="scmpds_2.html#K17">:=</a> <span class="p0">(<span class="default"><a href="scmp_gcd.html#K1">intpos</a> 4</span>)</span>,0</span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p4">(<span class="default"><a href="scmpds_2.html#K14">SubFrom</a> <a href="scmp_gcd.html#K2">GBP</a> ,6,<span class="p5">(<span class="default"><a href="scmp_gcd.html#K1">intpos</a> 2</span>)</span>,0</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> ,6,<span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="scmpds_2.html#K12">AddTo</a> <a href="scmp_gcd.html#K2">GBP</a> ,4,<span class="p0">(<span class="default"><a href="xcmplx_0.html#K4">-</a> 1</span>)</span></span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p5">(<span class="default"><a href="scmpds_2.html#K12">AddTo</a> <a href="scmp_gcd.html#K2">GBP</a> ,7,<span class="p0">(<span class="default"><a href="xcmplx_0.html#K4">-</a> 1</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="scmp_gcd.html#K2">GBP</a> ,5 <a href="scmpds_2.html#K11">:=</a> 0</span>)</span></span>)</span></span>)</span></span>)</span>,<font color="Maroon">c<sub>52</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="xxreal_0.html#NR2" target="_self">&gt;=</a> <font color="Maroon">c<sub>48</sub></font> <a href="xcmplx_0.html#K2">+</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#K2">GBP</a> ,7 <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K2">GBP</a> ,5</span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p1">(<span class="default"><a href="scmpds_2.html#K12">AddTo</a> <a href="scmp_gcd.html#K2">GBP</a> ,5,<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="scmp_gcd.html#K2">GBP</a> ,6 <a href="scmpds_2.html#K17">:=</a> <span class="p1">(<span class="default"><a href="scmp_gcd.html#K1">intpos</a> 4</span>)</span>,0</span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p5">(<span class="default"><a href="scmpds_2.html#K14">SubFrom</a> <a href="scmp_gcd.html#K2">GBP</a> ,6,<span class="p0">(<span class="default"><a href="scmp_gcd.html#K1">intpos</a> 2</span>)</span>,0</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> ,6,<span class="p5">(<span class="default"><span class="p0">(<span class="default"><a href="scmpds_2.html#K12">AddTo</a> <a href="scmp_gcd.html#K2">GBP</a> ,4,<span class="p1">(<span class="default"><a href="xcmplx_0.html#K4">-</a> 1</span>)</span></span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p0">(<span class="default"><a href="scmpds_2.html#K12">AddTo</a> <a href="scmp_gcd.html#K2">GBP</a> ,7,<span class="p1">(<span class="default"><a href="xcmplx_0.html#K4">-</a> 1</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="scmp_gcd.html#K2">GBP</a> ,5 <a href="scmpds_2.html#K11">:=</a> 0</span>)</span></span>)</span></span>)</span></span>)</span>,<font color="Maroon">c<sub>52</sub></font></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"><font color="Maroon">c<sub>47</sub></font> <a href="scmpds_2.html#K2">.</a> <a href="scmp_gcd.html#K2">GBP</a> </span>)</span>,5</span>)</span></span>)</span>
 <b>by </b><i><a class="txt" href="scpqsort.html#E1:24_1"><i><font color="Green">E24</font></i></a>, <a class="txt" href="scpqsort.html#E7:24_1"><i><font color="Green">E28</font></i></a>, <a class="txt" href="scpqsort.html#E1:24_1_1_1_1"><i><font color="Green">E29</font></i></a>, <a class="ref" href="xreal_1.html#T11">XREAL_1:11</a></i>;<br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="24_1_1_1_2"><b>suppose </b></a><a NAME="E1:24_1_1_1_2"/><i><font color="Green">E29</font></i>: 
<font color="Maroon">c<sub>52</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>49</sub></font></span>)</span> <a href="xxreal_0.html#NR2" target="_self">&gt;=</a> <font color="Maroon">c<sub>52</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>53</sub></font></span>)</span>
 ;<br/><div class="add"><b>hence </b><a NAME="E2:24_1_1_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"><span class="p5">(<span class="default"><span class="p0">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a> ,7 <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K2">GBP</a> ,5</span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p0">(<span class="default"><a href="scmpds_2.html#K12">AddTo</a> <a href="scmp_gcd.html#K2">GBP</a> ,5,<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="scmp_gcd.html#K2">GBP</a> ,6 <a href="scmpds_2.html#K17">:=</a> <span class="p0">(<span class="default"><a href="scmp_gcd.html#K1">intpos</a> 4</span>)</span>,0</span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p4">(<span class="default"><a href="scmpds_2.html#K14">SubFrom</a> <a href="scmp_gcd.html#K2">GBP</a> ,6,<span class="p5">(<span class="default"><a href="scmp_gcd.html#K1">intpos</a> 2</span>)</span>,0</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> ,6,<span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="scmpds_2.html#K12">AddTo</a> <a href="scmp_gcd.html#K2">GBP</a> ,4,<span class="p0">(<span class="default"><a href="xcmplx_0.html#K4">-</a> 1</span>)</span></span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p5">(<span class="default"><a href="scmpds_2.html#K12">AddTo</a> <a href="scmp_gcd.html#K2">GBP</a> ,7,<span class="p0">(<span class="default"><a href="xcmplx_0.html#K4">-</a> 1</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="scmp_gcd.html#K2">GBP</a> ,5 <a href="scmpds_2.html#K11">:=</a> 0</span>)</span></span>)</span></span>)</span></span>)</span>,<font color="Maroon">c<sub>52</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"><font color="Maroon">c<sub>47</sub></font> <a href="scmpds_2.html#K2">.</a> <a href="scmp_gcd.html#K2">GBP</a> </span>)</span>,5</span>)</span> <a href="xxreal_0.html#NR3" target="_self">&lt;</a> <font color="Maroon">c<sub>52</sub></font> <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"><font color="Maroon">c<sub>47</sub></font> <a href="scmpds_2.html#K2">.</a> <a href="scmp_gcd.html#K2">GBP</a> </span>)</span>,5</span>)</span>
 <b>by </b><i><a class="txt" href="scpqsort.html#E1:24"><i><font color="Green">E22</font></i></a>, <a class="txt" href="scpqsort.html#E2:24"><i><font color="Green">E23</font></i></a>, <a class="txt" href="scpqsort.html#E1:24_1"><i><font color="Green">E24</font></i></a>, <a class="txt" href="scpqsort.html#E6:24_1"><i><font color="Green">E27</font></i></a>, <a class="txt" href="scpqsort.html#E21"><i><font color="Green">Lemma19</font></i></a></i>;<br/><a NAME="E3:24_1_1_1_2"/>
<font color="Maroon">c<sub>48</sub></font> <a href="xcmplx_0.html#K2">+</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#K2">GBP</a> ,7 <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K2">GBP</a> ,5</span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p1">(<span class="default"><a href="scmpds_2.html#K12">AddTo</a> <a href="scmp_gcd.html#K2">GBP</a> ,5,<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="scmp_gcd.html#K2">GBP</a> ,6 <a href="scmpds_2.html#K17">:=</a> <span class="p1">(<span class="default"><a href="scmp_gcd.html#K1">intpos</a> 4</span>)</span>,0</span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p5">(<span class="default"><a href="scmpds_2.html#K14">SubFrom</a> <a href="scmp_gcd.html#K2">GBP</a> ,6,<span class="p0">(<span class="default"><a href="scmp_gcd.html#K1">intpos</a> 2</span>)</span>,0</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> ,6,<span class="p5">(<span class="default"><span class="p0">(<span class="default"><a href="scmpds_2.html#K12">AddTo</a> <a href="scmp_gcd.html#K2">GBP</a> ,4,<span class="p1">(<span class="default"><a href="xcmplx_0.html#K4">-</a> 1</span>)</span></span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p0">(<span class="default"><a href="scmpds_2.html#K12">AddTo</a> <a href="scmp_gcd.html#K2">GBP</a> ,7,<span class="p1">(<span class="default"><a href="xcmplx_0.html#K4">-</a> 1</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="scmp_gcd.html#K2">GBP</a> ,5 <a href="scmpds_2.html#K11">:=</a> 0</span>)</span></span>)</span></span>)</span></span>)</span>,<font color="Maroon">c<sub>52</sub></font></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"><font color="Maroon">c<sub>47</sub></font> <a href="scmpds_2.html#K2">.</a> <a href="scmp_gcd.html#K2">GBP</a> </span>)</span>,5</span>)</span></span>)</span> <a href="xxreal_0.html#NR3" target="_self">&lt;</a> <font color="Maroon">c<sub>48</sub></font> <a href="xcmplx_0.html#K2">+</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>52</sub></font> <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"><font color="Maroon">c<sub>47</sub></font> <a href="scmpds_2.html#K2">.</a> <a href="scmp_gcd.html#K2">GBP</a> </span>)</span>,5</span>)</span></span>)</span>
 <b>by </b><i><a class="txt" href="scpqsort.html#E2:24"><i><font color="Green">E23</font></i></a>, <a class="txt" href="scpqsort.html#E1:24_1"><i><font color="Green">E24</font></i></a>, <a class="txt" href="scpqsort.html#E7:24_1"><i><font color="Green">E28</font></i></a>, <a class="txt" href="scpqsort.html#E1:24_1_1_1_2"><i><font color="Green">E29</font></i></a>, <a class="ref" href="xreal_1.html#T8">XREAL_1:8</a></i>;<br/><b>hence </b><a NAME="E4:24_1_1_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"><span class="p5">(<span class="default"><span class="p0">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a> ,7 <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K2">GBP</a> ,5</span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p0">(<span class="default"><a href="scmpds_2.html#K12">AddTo</a> <a href="scmp_gcd.html#K2">GBP</a> ,5,<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="scmp_gcd.html#K2">GBP</a> ,6 <a href="scmpds_2.html#K17">:=</a> <span class="p0">(<span class="default"><a href="scmp_gcd.html#K1">intpos</a> 4</span>)</span>,0</span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p4">(<span class="default"><a href="scmpds_2.html#K14">SubFrom</a> <a href="scmp_gcd.html#K2">GBP</a> ,6,<span class="p5">(<span class="default"><a href="scmp_gcd.html#K1">intpos</a> 2</span>)</span>,0</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> ,6,<span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="scmpds_2.html#K12">AddTo</a> <a href="scmp_gcd.html#K2">GBP</a> ,4,<span class="p0">(<span class="default"><a href="xcmplx_0.html#K4">-</a> 1</span>)</span></span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p5">(<span class="default"><a href="scmpds_2.html#K12">AddTo</a> <a href="scmp_gcd.html#K2">GBP</a> ,7,<span class="p0">(<span class="default"><a href="xcmplx_0.html#K4">-</a> 1</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="scmp_gcd.html#K2">GBP</a> ,5 <a href="scmpds_2.html#K11">:=</a> 0</span>)</span></span>)</span></span>)</span></span>)</span>,<font color="Maroon">c<sub>52</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="xxreal_0.html#NR2" target="_self">&gt;=</a> <font color="Maroon">c<sub>48</sub></font> <a href="xcmplx_0.html#K2">+</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#K2">GBP</a> ,7 <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K2">GBP</a> ,5</span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p1">(<span class="default"><a href="scmpds_2.html#K12">AddTo</a> <a href="scmp_gcd.html#K2">GBP</a> ,5,<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="scmp_gcd.html#K2">GBP</a> ,6 <a href="scmpds_2.html#K17">:=</a> <span class="p1">(<span class="default"><a href="scmp_gcd.html#K1">intpos</a> 4</span>)</span>,0</span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p5">(<span class="default"><a href="scmpds_2.html#K14">SubFrom</a> <a href="scmp_gcd.html#K2">GBP</a> ,6,<span class="p0">(<span class="default"><a href="scmp_gcd.html#K1">intpos</a> 2</span>)</span>,0</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> ,6,<span class="p5">(<span class="default"><span class="p0">(<span class="default"><a href="scmpds_2.html#K12">AddTo</a> <a href="scmp_gcd.html#K2">GBP</a> ,4,<span class="p1">(<span class="default"><a href="xcmplx_0.html#K4">-</a> 1</span>)</span></span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p0">(<span class="default"><a href="scmpds_2.html#K12">AddTo</a> <a href="scmp_gcd.html#K2">GBP</a> ,7,<span class="p1">(<span class="default"><a href="xcmplx_0.html#K4">-</a> 1</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="scmp_gcd.html#K2">GBP</a> ,5 <a href="scmpds_2.html#K11">:=</a> 0</span>)</span></span>)</span></span>)</span></span>)</span>,<font color="Maroon">c<sub>52</sub></font></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"><font color="Maroon">c<sub>47</sub></font> <a href="scmpds_2.html#K2">.</a> <a href="scmp_gcd.html#K2">GBP</a> </span>)</span>,5</span>)</span></span>)</span>
 <b>by </b><i><a class="txt" href="scpqsort.html#E1:24_1"><i><font color="Green">E24</font></i></a>, <a class="txt" href="scpqsort.html#E7:24_1"><i><font color="Green">E28</font></i></a>, <a class="txt" href="scpqsort.html#E1:24_1_1_1_2"><i><font color="Green">E29</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><b>thus </b><a NAME="E11:24_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"><span class="p5">(<span class="default"><span class="p0">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a> ,7 <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K2">GBP</a> ,5</span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p0">(<span class="default"><a href="scmpds_2.html#K12">AddTo</a> <a href="scmp_gcd.html#K2">GBP</a> ,5,<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="scmp_gcd.html#K2">GBP</a> ,6 <a href="scmpds_2.html#K17">:=</a> <span class="p0">(<span class="default"><a href="scmp_gcd.html#K1">intpos</a> 4</span>)</span>,0</span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p4">(<span class="default"><a href="scmpds_2.html#K14">SubFrom</a> <a href="scmp_gcd.html#K2">GBP</a> ,6,<span class="p5">(<span class="default"><a href="scmp_gcd.html#K1">intpos</a> 2</span>)</span>,0</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> ,6,<span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="scmpds_2.html#K12">AddTo</a> <a href="scmp_gcd.html#K2">GBP</a> ,4,<span class="p0">(<span class="default"><a href="xcmplx_0.html#K4">-</a> 1</span>)</span></span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p5">(<span class="default"><a href="scmpds_2.html#K12">AddTo</a> <a href="scmp_gcd.html#K2">GBP</a> ,7,<span class="p0">(<span class="default"><a href="xcmplx_0.html#K4">-</a> 1</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="scmp_gcd.html#K2">GBP</a> ,5 <a href="scmpds_2.html#K11">:=</a> 0</span>)</span></span>)</span></span>)</span></span>)</span>,<font color="Maroon">c<sub>52</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>52</sub></font> <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="txt" href="scpqsort.html#E1:24"><i><font color="Green">E22</font></i></a>, <a class="txt" href="scpqsort.html#E2:24"><i><font color="Green">E23</font></i></a>, <a class="txt" href="scpqsort.html#E1:24_1"><i><font color="Green">E24</font></i></a>, <a class="txt" href="scpqsort.html#E6:24_1"><i><font color="Green">E27</font></i></a>, <a class="txt" href="scpqsort.html#E21"><i><font color="Green">Lemma19</font></i></a></i>;<br/></div><b>end;</b></div>
<b>hence </b><a NAME="E4:24"/>
(  <a href="scmpds_8.html#K3">while&gt;0</a> <a href="scmp_gcd.html#K2">GBP</a> ,5,<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> ,7 <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K2">GBP</a> ,5</span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p5">(<span class="default"><a href="scmpds_2.html#K12">AddTo</a> <a href="scmp_gcd.html#K2">GBP</a> ,5,<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="scmp_gcd.html#K2">GBP</a> ,6 <a href="scmpds_2.html#K17">:=</a> <span class="p5">(<span class="default"><a href="scmp_gcd.html#K1">intpos</a> 4</span>)</span>,0</span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p3">(<span class="default"><a href="scmpds_2.html#K14">SubFrom</a> <a href="scmp_gcd.html#K2">GBP</a> ,6,<span class="p4">(<span class="default"><a href="scmp_gcd.html#K1">intpos</a> 2</span>)</span>,0</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> ,6,<span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="scmpds_2.html#K12">AddTo</a> <a href="scmp_gcd.html#K2">GBP</a> ,4,<span class="p5">(<span class="default"><a href="xcmplx_0.html#K4">-</a> 1</span>)</span></span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p4">(<span class="default"><a href="scmpds_2.html#K12">AddTo</a> <a href="scmp_gcd.html#K2">GBP</a> ,7,<span class="p5">(<span class="default"><a href="xcmplx_0.html#K4">-</a> 1</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="scmp_gcd.html#K2">GBP</a> ,5 <a href="scmpds_2.html#K11">:=</a> 0</span>)</span></span>)</span></span>)</span></span>)</span> <a href="scmpds_6.html#R1">is_closed_on</a> <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> ,5,<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> ,7 <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K2">GBP</a> ,5</span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p5">(<span class="default"><a href="scmpds_2.html#K12">AddTo</a> <a href="scmp_gcd.html#K2">GBP</a> ,5,<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="scmp_gcd.html#K2">GBP</a> ,6 <a href="scmpds_2.html#K17">:=</a> <span class="p5">(<span class="default"><a href="scmp_gcd.html#K1">intpos</a> 4</span>)</span>,0</span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p3">(<span class="default"><a href="scmpds_2.html#K14">SubFrom</a> <a href="scmp_gcd.html#K2">GBP</a> ,6,<span class="p4">(<span class="default"><a href="scmp_gcd.html#K1">intpos</a> 2</span>)</span>,0</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> ,6,<span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="scmpds_2.html#K12">AddTo</a> <a href="scmp_gcd.html#K2">GBP</a> ,4,<span class="p5">(<span class="default"><a href="xcmplx_0.html#K4">-</a> 1</span>)</span></span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p4">(<span class="default"><a href="scmpds_2.html#K12">AddTo</a> <a href="scmp_gcd.html#K2">GBP</a> ,7,<span class="p5">(<span class="default"><a href="xcmplx_0.html#K4">-</a> 1</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="scmp_gcd.html#K2">GBP</a> ,5 <a href="scmpds_2.html#K11">:=</a> 0</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="txt" href="scpqsort.html#E1:24"><i><font color="Green">E22</font></i></a>, <a class="txt" href="scpqsort.html#E2:24"><i><font color="Green">E23</font></i></a>, <a class="txt" href="scpqsort.html#E20"><i><font color="Green">Lemma18</font></i></a>, <a class="ref" href="scpqsort.html#T5" target="_self">Th5</a></i>;<br/>


</div>
