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

<b>let </b><font color="Maroon" title="c16">n</font> be    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of  <a href="numbers.html#K5" title="NUMBERS:func.5">NAT</a> ;<br/><b>let </b><font color="Maroon" title="c17">s1</font>, <font color="Maroon" title="c18">s2</font> be   <a href="ami_1.html#NM4" title="AMI_1:NM.4">State</a> of <a href="scmpds_2.html#K1" title="SCMPDS_2:func.1">SCMPDS</a> ;<br/>





<b>set </b><font color="Maroon" title="c19">GA</font> =  <a href="scmp_gcd.html#K4" title="SCMP_GCD:func.4">GCD-Algorithm</a> ;<br/>
<b>set </b><font color="Maroon" title="c20">Cs1</font> =  <a href="ami_1.html#K10" title="AMI_1:func.10">Computation</a> <font color="Maroon" title="c17">s1</font>;<br/>
<b>set </b><font color="Maroon" title="c21">Cs2</font> =  <a href="ami_1.html#K10" title="AMI_1:func.10">Computation</a> <font color="Maroon" title="c18">s2</font>;<br/>
<b>assume </b><a NAME="E1:24"/><i><font color="Green" title="E24">A1</font></i>: 
(  <a href="scmp_gcd.html#K4" title="SCMP_GCD:func.4">GCD-Algorithm</a>  <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Maroon" title="c17">s1</font> &amp;  <a href="scmp_gcd.html#K4" title="SCMP_GCD:func.4">GCD-Algorithm</a>  <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Maroon" title="c18">s2</font> )
 ;<br/>

<b>assume </b><a NAME="E2:24"/><i><font color="Green" title="E25">A2</font></i>: 
 <a href="ami_1.html#K6" title="AMI_1:func.6">IC</a> <font color="Maroon" title="c17">s1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="scmpds_3.html#K2" title="SCMPDS_3:func.2">inspos</a> 5
 ;<br/>

<b>assume </b><a NAME="E3:24"/><i><font color="Green" title="E26">A3</font></i>: 
<font color="Maroon" title="c16">n</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c17">s1</font> <a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">.</a> <a href="scmp_gcd.html#K3" title="SCMP_GCD:func.3">SBP</a> 
 ;<br/>

<b>assume </b><a NAME="E4:24"/><i><font color="Green" title="E27">A4</font></i>: 
<font color="Maroon" title="c17">s1</font> <a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">.</a> <a href="scmp_gcd.html#K2" title="SCMP_GCD:func.2">GBP</a>  <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 0
 ;<br/>

<b>assume </b><a NAME="E5:24"/><i><font color="Green" title="E28">A5</font></i>: 
<font color="Maroon" title="c17">s1</font> <a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">.</a> <span class="p1">(<span class="default"><a href="scmpds_2.html#K3" title="SCMPDS_2:func.3">DataLoc</a> <span class="p2">(<span class="default"><font color="Maroon" title="c17">s1</font> <a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">.</a> <a href="scmp_gcd.html#K3" title="SCMP_GCD:func.3">SBP</a> </span>)</span>,3</span>)</span> <a href="xxreal_0.html#NR4" title="XXREAL_0:NR.4">&gt;</a> 0
 ;<br/>

<b>assume </b><a NAME="E6:24"/><i><font color="Green" title="E29">A6</font></i>: 
(  <a href="ami_1.html#K6" title="AMI_1:func.6">IC</a> <font color="Maroon" title="c18">s2</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="ami_1.html#K6" title="AMI_1:func.6">IC</a> <font color="Maroon" title="c17">s1</font> &amp; <font color="Maroon" title="c18">s2</font> <a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">.</a> <a href="scmp_gcd.html#K3" title="SCMP_GCD:func.3">SBP</a>  <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c17">s1</font> <a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">.</a> <a href="scmp_gcd.html#K3" title="SCMP_GCD:func.3">SBP</a>  &amp; <font color="Maroon" title="c18">s2</font> <a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">.</a> <a href="scmp_gcd.html#K2" title="SCMP_GCD:func.2">GBP</a>  <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 0 )
 ;<br/>

<b>assume </b><a NAME="E7:24"/><i><font color="Green" title="E30">A7</font></i>: 
( <font color="Maroon" title="c18">s2</font> <a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">.</a> <span class="p1">(<span class="default"><a href="scmpds_2.html#K3" title="SCMPDS_2:func.3">DataLoc</a> <span class="p2">(<span class="default"><font color="Maroon" title="c17">s1</font> <a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">.</a> <a href="scmp_gcd.html#K3" title="SCMP_GCD:func.3">SBP</a> </span>)</span>,2</span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c17">s1</font> <a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">.</a> <span class="p1">(<span class="default"><a href="scmpds_2.html#K3" title="SCMPDS_2:func.3">DataLoc</a> <span class="p2">(<span class="default"><font color="Maroon" title="c17">s1</font> <a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">.</a> <a href="scmp_gcd.html#K3" title="SCMP_GCD:func.3">SBP</a> </span>)</span>,2</span>)</span> &amp; <font color="Maroon" title="c18">s2</font> <a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">.</a> <span class="p1">(<span class="default"><a href="scmpds_2.html#K3" title="SCMPDS_2:func.3">DataLoc</a> <span class="p2">(<span class="default"><font color="Maroon" title="c17">s1</font> <a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">.</a> <a href="scmp_gcd.html#K3" title="SCMP_GCD:func.3">SBP</a> </span>)</span>,3</span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c17">s1</font> <a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">.</a> <span class="p1">(<span class="default"><a href="scmpds_2.html#K3" title="SCMPDS_2:func.3">DataLoc</a> <span class="p2">(<span class="default"><font color="Maroon" title="c17">s1</font> <a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">.</a> <a href="scmp_gcd.html#K3" title="SCMP_GCD:func.3">SBP</a> </span>)</span>,3</span>)</span> )
 ;<br/>

<a NAME="E8:24"/><i><font color="Green" title="E31">A8</font></i>: 
 <a href="ami_1.html#K8" title="AMI_1:func.8">CurInstr</a> <font color="Maroon" title="c17">s1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <a href="scmp_gcd.html#K3" title="SCMP_GCD:func.3">SBP</a> ,3 <a href="scmpds_2.html#K9" title="SCMPDS_2:func.9">&lt;=0_goto</a> 9
 
<b>by </b><i><a class="txt" href="scmp_gcd.html#E2:24"><i><font color="Green" title="E25">A2</font></i></a>, <a class="txt" href="scmp_gcd.html#E1:24"><i><font color="Green" title="E24">A1</font></i></a>, <a class="txt" href="scmp_gcd.html#E21"><i><font color="Green" title="E14">Lm3</font></i></a></i>;<br/>
<i><font color="Green" title="E32">A9</font></i>: <span class="p1">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Computation</a> <font color="Maroon" title="c17">s1</font></span>)</span> <a href="ami_1.html#K11" title="AMI_1:func.11">.</a> <span class="p1">(<span class="default">1 <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 0</span>)</span> = 
 <a href="ami_1.html#K9" title="AMI_1:func.9">Following</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Computation</a> <font color="Maroon" title="c17">s1</font></span>)</span> <a href="ami_1.html#K11" title="AMI_1:func.11">.</a> 0</span>)</span>
<b>by </b><i><a class="ref" href="ami_1.html#D19" title="AMI_1:def.19">AMI_1:def 19</a></i>
<br/>.= 
 <a href="ami_1.html#K9" title="AMI_1:func.9">Following</a> <font color="Maroon" title="c17">s1</font>
<b>by </b><i><a class="ref" href="ami_1.html#D19" title="AMI_1:def.19">AMI_1:def 19</a></i>
<br/>.= 
 <a href="ami_1.html#K4" title="AMI_1:func.4">Exec</a> <span class="p1">(<span class="default"><a href="scmp_gcd.html#K3" title="SCMP_GCD:func.3">SBP</a> ,3 <a href="scmpds_2.html#K9" title="SCMPDS_2:func.9">&lt;=0_goto</a> 9</span>)</span>,<font color="Maroon" title="c17">s1</font>
<b>by </b><i><a class="txt" href="scmp_gcd.html#E8:24"><i><font color="Green" title="E31">A8</font></i></a></i>
;<br/>
<a NAME="E10:24"/><i><font color="Green" title="E33">A10</font></i>: 
 <a href="ami_1.html#K8" title="AMI_1:func.8">CurInstr</a> <font color="Maroon" title="c18">s2</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <a href="scmp_gcd.html#K3" title="SCMP_GCD:func.3">SBP</a> ,3 <a href="scmpds_2.html#K9" title="SCMPDS_2:func.9">&lt;=0_goto</a> 9
 
<b>by </b><i><a class="txt" href="scmp_gcd.html#E2:24"><i><font color="Green" title="E25">A2</font></i></a>, <a class="txt" href="scmp_gcd.html#E6:24"><i><font color="Green" title="E29">A6</font></i></a>, <a class="txt" href="scmp_gcd.html#E1:24"><i><font color="Green" title="E24">A1</font></i></a>, <a class="txt" href="scmp_gcd.html#E21"><i><font color="Green" title="E14">Lm3</font></i></a></i>;<br/>
<i><font color="Green" title="E34">A11</font></i>: <span class="p1">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Computation</a> <font color="Maroon" title="c18">s2</font></span>)</span> <a href="ami_1.html#K11" title="AMI_1:func.11">.</a> <span class="p1">(<span class="default">1 <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 0</span>)</span> = 
 <a href="ami_1.html#K9" title="AMI_1:func.9">Following</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Computation</a> <font color="Maroon" title="c18">s2</font></span>)</span> <a href="ami_1.html#K11" title="AMI_1:func.11">.</a> 0</span>)</span>
<b>by </b><i><a class="ref" href="ami_1.html#D19" title="AMI_1:def.19">AMI_1:def 19</a></i>
<br/>.= 
 <a href="ami_1.html#K9" title="AMI_1:func.9">Following</a> <font color="Maroon" title="c18">s2</font>
<b>by </b><i><a class="ref" href="ami_1.html#D19" title="AMI_1:def.19">AMI_1:def 19</a></i>
<br/>.= 
 <a href="ami_1.html#K4" title="AMI_1:func.4">Exec</a> <span class="p1">(<span class="default"><a href="scmp_gcd.html#K3" title="SCMP_GCD:func.3">SBP</a> ,3 <a href="scmpds_2.html#K9" title="SCMPDS_2:func.9">&lt;=0_goto</a> 9</span>)</span>,<font color="Maroon" title="c18">s2</font>
<b>by </b><i><a class="txt" href="scmp_gcd.html#E10:24"><i><font color="Green" title="E33">A10</font></i></a></i>
;<br/>
<i><font color="Green" title="E35">A12</font></i>:  <a href="ami_1.html#K6" title="AMI_1:func.6">IC</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Computation</a> <font color="Maroon" title="c17">s1</font></span>)</span> <a href="ami_1.html#K11" title="AMI_1:func.11">.</a> 1</span>)</span> = 
 <a href="scmpds_2.html#K18" title="SCMPDS_2:func.18">Next</a> <span class="p1">(<span class="default"><a href="ami_1.html#K6" title="AMI_1:func.6">IC</a> <font color="Maroon" title="c17">s1</font></span>)</span>
<b>by </b><i><a class="txt" href="scmp_gcd.html#E5:24"><i><font color="Green" title="E28">A5</font></i></a>, <a class="txt" href="scmp_gcd.html#E9:24"><i><font color="Green" title="E32">A9</font></i></a>, <a class="ref" href="scmpds_2.html#T68" title="SCMPDS_2:th.68">SCMPDS_2:68</a></i>
<br/>.= 
 <a href="scmpds_3.html#K2" title="SCMPDS_3:func.2">inspos</a> <span class="p1">(<span class="default">5 <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1</span>)</span>
<b>by </b><i><a class="txt" href="scmp_gcd.html#E2:24"><i><font color="Green" title="E25">A2</font></i></a>, <a class="ref" href="scmpds_4.html#T70" title="SCMPDS_4:th.70">SCMPDS_4:70</a></i>
;<br/>
<b>then </b><i><font color="Green" title="E36">A13</font></i>:  <a href="ami_1.html#K8" title="AMI_1:func.8">CurInstr</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Computation</a> <font color="Maroon" title="c17">s1</font></span>)</span> <a href="ami_1.html#K11" title="AMI_1:func.11">.</a> 1</span>)</span> = 
<font color="Maroon" title="c17">s1</font> <a href="ami_1.html#K13" title="AMI_1:func.13">.</a> <span class="p1">(<span class="default"><a href="scmpds_3.html#K2" title="SCMPDS_3:func.2">inspos</a> 6</span>)</span>
<b>by </b><i><a class="ref" href="ami_1.html#T54" title="AMI_1:th.54">AMI_1:54</a></i>
<br/>.= 
<a href="scmp_gcd.html#K3" title="SCMP_GCD:func.3">SBP</a> ,6 <a href="scmpds_2.html#K17" title="SCMPDS_2:func.17">:=</a> <a href="scmp_gcd.html#K3" title="SCMP_GCD:func.3">SBP</a> ,3
<b>by </b><i><a class="txt" href="scmp_gcd.html#E1:24"><i><font color="Green" title="E24">A1</font></i></a>, <a class="txt" href="scmp_gcd.html#E21"><i><font color="Green" title="E14">Lm3</font></i></a></i>
;<br/>
<i><font color="Green" title="E37">A14</font></i>: <span class="p1">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Computation</a> <font color="Maroon" title="c17">s1</font></span>)</span> <a href="ami_1.html#K11" title="AMI_1:func.11">.</a> <span class="p1">(<span class="default">1 <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1</span>)</span> = 
 <a href="ami_1.html#K9" title="AMI_1:func.9">Following</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Computation</a> <font color="Maroon" title="c17">s1</font></span>)</span> <a href="ami_1.html#K11" title="AMI_1:func.11">.</a> 1</span>)</span>
<b>by </b><i><a class="ref" href="ami_1.html#D19" title="AMI_1:def.19">AMI_1:def 19</a></i>
<br/>.= 
 <a href="ami_1.html#K4" title="AMI_1:func.4">Exec</a> <span class="p1">(<span class="default"><a href="scmp_gcd.html#K3" title="SCMP_GCD:func.3">SBP</a> ,6 <a href="scmpds_2.html#K17" title="SCMPDS_2:func.17">:=</a> <a href="scmp_gcd.html#K3" title="SCMP_GCD:func.3">SBP</a> ,3</span>)</span>,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Computation</a> <font color="Maroon" title="c17">s1</font></span>)</span> <a href="ami_1.html#K11" title="AMI_1:func.11">.</a> 1</span>)</span>
<b>by </b><i><a class="txt" href="scmp_gcd.html#E13:24"><i><font color="Green" title="E36">A13</font></i></a></i>
;<br/>
<a NAME="E15:24"/><i><font color="Green" title="E38">A15</font></i>: 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Computation</a> <font color="Maroon" title="c17">s1</font></span>)</span> <a href="ami_1.html#K11" title="AMI_1:func.11">.</a> 1</span>)</span> <a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">.</a> <a href="scmp_gcd.html#K3" title="SCMP_GCD:func.3">SBP</a>  <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c16">n</font>
 
<b>by </b><i><a class="txt" href="scmp_gcd.html#E3:24"><i><font color="Green" title="E26">A3</font></i></a>, <a class="txt" href="scmp_gcd.html#E9:24"><i><font color="Green" title="E32">A9</font></i></a>, <a class="ref" href="scmpds_2.html#T68" title="SCMPDS_2:th.68">SCMPDS_2:68</a></i>;<br/>
<a NAME="E16:24"/><i><font color="Green" title="E39">A16</font></i>: 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Computation</a> <font color="Maroon" title="c17">s1</font></span>)</span> <a href="ami_1.html#K11" title="AMI_1:func.11">.</a> 1</span>)</span> <a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">.</a> <a href="scmp_gcd.html#K2" title="SCMP_GCD:func.2">GBP</a>  <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 0
 
<b>by </b><i><a class="txt" href="scmp_gcd.html#E4:24"><i><font color="Green" title="E27">A4</font></i></a>, <a class="txt" href="scmp_gcd.html#E9:24"><i><font color="Green" title="E32">A9</font></i></a>, <a class="ref" href="scmpds_2.html#T68" title="SCMPDS_2:th.68">SCMPDS_2:68</a></i>;<br/>
<i><font color="Green" title="E40">A17</font></i>:  <a href="ami_1.html#K6" title="AMI_1:func.6">IC</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Computation</a> <font color="Maroon" title="c18">s2</font></span>)</span> <a href="ami_1.html#K11" title="AMI_1:func.11">.</a> 1</span>)</span> = 
 <a href="scmpds_2.html#K18" title="SCMPDS_2:func.18">Next</a> <span class="p1">(<span class="default"><a href="ami_1.html#K6" title="AMI_1:func.6">IC</a> <font color="Maroon" title="c18">s2</font></span>)</span>
<b>by </b><i><a class="txt" href="scmp_gcd.html#E5:24"><i><font color="Green" title="E28">A5</font></i></a>, <a class="txt" href="scmp_gcd.html#E6:24"><i><font color="Green" title="E29">A6</font></i></a>, <a class="txt" href="scmp_gcd.html#E7:24"><i><font color="Green" title="E30">A7</font></i></a>, <a class="txt" href="scmp_gcd.html#E11:24"><i><font color="Green" title="E34">A11</font></i></a>, <a class="ref" href="scmpds_2.html#T68" title="SCMPDS_2:th.68">SCMPDS_2:68</a></i>
<br/>.= 
 <a href="scmpds_3.html#K2" title="SCMPDS_3:func.2">inspos</a> <span class="p1">(<span class="default">5 <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1</span>)</span>
<b>by </b><i><a class="txt" href="scmp_gcd.html#E2:24"><i><font color="Green" title="E25">A2</font></i></a>, <a class="txt" href="scmp_gcd.html#E6:24"><i><font color="Green" title="E29">A6</font></i></a>, <a class="ref" href="scmpds_4.html#T70" title="SCMPDS_4:th.70">SCMPDS_4:70</a></i>
;<br/>
<b>then </b><i><font color="Green" title="E41">A18</font></i>:  <a href="ami_1.html#K8" title="AMI_1:func.8">CurInstr</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Computation</a> <font color="Maroon" title="c18">s2</font></span>)</span> <a href="ami_1.html#K11" title="AMI_1:func.11">.</a> 1</span>)</span> = 
<font color="Maroon" title="c18">s2</font> <a href="ami_1.html#K13" title="AMI_1:func.13">.</a> <span class="p1">(<span class="default"><a href="scmpds_3.html#K2" title="SCMPDS_3:func.2">inspos</a> 6</span>)</span>
<b>by </b><i><a class="ref" href="ami_1.html#T54" title="AMI_1:th.54">AMI_1:54</a></i>
<br/>.= 
<a href="scmp_gcd.html#K3" title="SCMP_GCD:func.3">SBP</a> ,6 <a href="scmpds_2.html#K17" title="SCMPDS_2:func.17">:=</a> <a href="scmp_gcd.html#K3" title="SCMP_GCD:func.3">SBP</a> ,3
<b>by </b><i><a class="txt" href="scmp_gcd.html#E1:24"><i><font color="Green" title="E24">A1</font></i></a>, <a class="txt" href="scmp_gcd.html#E21"><i><font color="Green" title="E14">Lm3</font></i></a></i>
;<br/>
<i><font color="Green" title="E42">A19</font></i>: <span class="p1">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Computation</a> <font color="Maroon" title="c18">s2</font></span>)</span> <a href="ami_1.html#K11" title="AMI_1:func.11">.</a> <span class="p1">(<span class="default">1 <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1</span>)</span> = 
 <a href="ami_1.html#K9" title="AMI_1:func.9">Following</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Computation</a> <font color="Maroon" title="c18">s2</font></span>)</span> <a href="ami_1.html#K11" title="AMI_1:func.11">.</a> 1</span>)</span>
<b>by </b><i><a class="ref" href="ami_1.html#D19" title="AMI_1:def.19">AMI_1:def 19</a></i>
<br/>.= 
 <a href="ami_1.html#K4" title="AMI_1:func.4">Exec</a> <span class="p1">(<span class="default"><a href="scmp_gcd.html#K3" title="SCMP_GCD:func.3">SBP</a> ,6 <a href="scmpds_2.html#K17" title="SCMPDS_2:func.17">:=</a> <a href="scmp_gcd.html#K3" title="SCMP_GCD:func.3">SBP</a> ,3</span>)</span>,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Computation</a> <font color="Maroon" title="c18">s2</font></span>)</span> <a href="ami_1.html#K11" title="AMI_1:func.11">.</a> 1</span>)</span>
<b>by </b><i><a class="txt" href="scmp_gcd.html#E18:24"><i><font color="Green" title="E41">A18</font></i></a></i>
;<br/>
<i><font color="Green" title="E43">A20</font></i>:  <a href="ami_1.html#K6" title="AMI_1:func.6">IC</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Computation</a> <font color="Maroon" title="c17">s1</font></span>)</span> <a href="ami_1.html#K11" title="AMI_1:func.11">.</a> 2</span>)</span> = 
 <a href="scmpds_2.html#K18" title="SCMPDS_2:func.18">Next</a> <span class="p1">(<span class="default"><a href="ami_1.html#K6" title="AMI_1:func.6">IC</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Computation</a> <font color="Maroon" title="c17">s1</font></span>)</span> <a href="ami_1.html#K11" title="AMI_1:func.11">.</a> 1</span>)</span></span>)</span>
<b>by </b><i><a class="txt" href="scmp_gcd.html#E14:24"><i><font color="Green" title="E37">A14</font></i></a>, <a class="ref" href="scmpds_2.html#T59" title="SCMPDS_2:th.59">SCMPDS_2:59</a></i>
<br/>.= 
 <a href="scmpds_3.html#K2" title="SCMPDS_3:func.2">inspos</a> <span class="p1">(<span class="default">6 <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1</span>)</span>
<b>by </b><i><a class="txt" href="scmp_gcd.html#E12:24"><i><font color="Green" title="E35">A12</font></i></a>, <a class="ref" href="scmpds_4.html#T70" title="SCMPDS_4:th.70">SCMPDS_4:70</a></i>
;<br/>
<b>then </b><i><font color="Green" title="E44">A21</font></i>:  <a href="ami_1.html#K8" title="AMI_1:func.8">CurInstr</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Computation</a> <font color="Maroon" title="c17">s1</font></span>)</span> <a href="ami_1.html#K11" title="AMI_1:func.11">.</a> 2</span>)</span> = 
<font color="Maroon" title="c17">s1</font> <a href="ami_1.html#K13" title="AMI_1:func.13">.</a> <span class="p1">(<span class="default"><a href="scmpds_3.html#K2" title="SCMPDS_3:func.2">inspos</a> 7</span>)</span>
<b>by </b><i><a class="ref" href="ami_1.html#T54" title="AMI_1:th.54">AMI_1:54</a></i>
<br/>.= 
 <a href="scmpds_2.html#K16" title="SCMPDS_2:func.16">Divide</a> <a href="scmp_gcd.html#K3" title="SCMP_GCD:func.3">SBP</a> ,2,<a href="scmp_gcd.html#K3" title="SCMP_GCD:func.3">SBP</a> ,3
<b>by </b><i><a class="txt" href="scmp_gcd.html#E1:24"><i><font color="Green" title="E24">A1</font></i></a>, <a class="txt" href="scmp_gcd.html#E21"><i><font color="Green" title="E14">Lm3</font></i></a></i>
;<br/>
<i><font color="Green" title="E45">A22</font></i>: <span class="p1">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Computation</a> <font color="Maroon" title="c17">s1</font></span>)</span> <a href="ami_1.html#K11" title="AMI_1:func.11">.</a> <span class="p1">(<span class="default">2 <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1</span>)</span> = 
 <a href="ami_1.html#K9" title="AMI_1:func.9">Following</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Computation</a> <font color="Maroon" title="c17">s1</font></span>)</span> <a href="ami_1.html#K11" title="AMI_1:func.11">.</a> 2</span>)</span>
<b>by </b><i><a class="ref" href="ami_1.html#D19" title="AMI_1:def.19">AMI_1:def 19</a></i>
<br/>.= 
 <a href="ami_1.html#K4" title="AMI_1:func.4">Exec</a> <span class="p1">(<span class="default"><a href="scmpds_2.html#K16" title="SCMPDS_2:func.16">Divide</a> <a href="scmp_gcd.html#K3" title="SCMP_GCD:func.3">SBP</a> ,2,<a href="scmp_gcd.html#K3" title="SCMP_GCD:func.3">SBP</a> ,3</span>)</span>,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Computation</a> <font color="Maroon" title="c17">s1</font></span>)</span> <a href="ami_1.html#K11" title="AMI_1:func.11">.</a> 2</span>)</span>
<b>by </b><i><a class="txt" href="scmp_gcd.html#E21:24"><i><font color="Green" title="E44">A21</font></i></a></i>
;<br/>
<a NAME="E23:24"/><i><font color="Green" title="E46">A23</font></i>: 
 <a href="scmpds_2.html#K3" title="SCMPDS_2:func.3">DataLoc</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Computation</a> <font color="Maroon" title="c17">s1</font></span>)</span> <a href="ami_1.html#K11" title="AMI_1:func.11">.</a> 1</span>)</span> <a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">.</a> <a href="scmp_gcd.html#K3" title="SCMP_GCD:func.3">SBP</a> </span>)</span>,6 <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="scmp_gcd.html#K1" title="SCMP_GCD:func.1">intpos</a> <span class="p1">(<span class="default"><font color="Maroon" title="c16">n</font> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 6</span>)</span>
 
<b>by </b><i><a class="txt" href="scmp_gcd.html#E15:24"><i><font color="Green" title="E38">A15</font></i></a>, <a class="ref" href="scmp_gcd.html#T5" target="_self" title="SCMP_GCD:th.5">Th5</a></i>;<br/>
<a NAME="E24:24"/><b>then </b>
 <a href="scmp_gcd.html#K3" title="SCMP_GCD:func.3">SBP</a>  <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a>  <a href="scmpds_2.html#K3" title="SCMPDS_2:func.3">DataLoc</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Computation</a> <font color="Maroon" title="c17">s1</font></span>)</span> <a href="ami_1.html#K11" title="AMI_1:func.11">.</a> 1</span>)</span> <a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">.</a> <a href="scmp_gcd.html#K3" title="SCMP_GCD:func.3">SBP</a> </span>)</span>,6
 
<b>by </b><i><a class="txt" href="scmp_gcd.html#E24"><i><font color="Green" title="E17">Lm5</font></i></a></i>;<br/>
<a NAME="E25:24"/><b>then </b><i><font color="Green" title="E47">A24</font></i>: 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Computation</a> <font color="Maroon" title="c17">s1</font></span>)</span> <a href="ami_1.html#K11" title="AMI_1:func.11">.</a> 2</span>)</span> <a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">.</a> <a href="scmp_gcd.html#K3" title="SCMP_GCD:func.3">SBP</a>  <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c16">n</font>
 
<b>by </b><i><a class="txt" href="scmp_gcd.html#E14:24"><i><font color="Green" title="E37">A14</font></i></a>, <a class="txt" href="scmp_gcd.html#E15:24"><i><font color="Green" title="E38">A15</font></i></a>, <a class="ref" href="scmpds_2.html#T59" title="SCMPDS_2:th.59">SCMPDS_2:59</a></i>;<br/>
<a NAME="E26:24"/>
 <a href="scmp_gcd.html#K2" title="SCMP_GCD:func.2">GBP</a>  <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a>  <a href="scmpds_2.html#K3" title="SCMPDS_2:func.3">DataLoc</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Computation</a> <font color="Maroon" title="c17">s1</font></span>)</span> <a href="ami_1.html#K11" title="AMI_1:func.11">.</a> 1</span>)</span> <a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">.</a> <a href="scmp_gcd.html#K3" title="SCMP_GCD:func.3">SBP</a> </span>)</span>,6
 
<b>by </b><i><a class="txt" href="scmp_gcd.html#E23:24"><i><font color="Green" title="E46">A23</font></i></a>, <a class="txt" href="scmp_gcd.html#E23"><i><font color="Green" title="E16">Lm4</font></i></a></i>;<br/>
<a NAME="E27:24"/><b>then </b><i><font color="Green" title="E48">A25</font></i>: 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Computation</a> <font color="Maroon" title="c17">s1</font></span>)</span> <a href="ami_1.html#K11" title="AMI_1:func.11">.</a> 2</span>)</span> <a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">.</a> <a href="scmp_gcd.html#K2" title="SCMP_GCD:func.2">GBP</a>  <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 0
 
<b>by </b><i><a class="txt" href="scmp_gcd.html#E14:24"><i><font color="Green" title="E37">A14</font></i></a>, <a class="txt" href="scmp_gcd.html#E16:24"><i><font color="Green" title="E39">A16</font></i></a>, <a class="ref" href="scmpds_2.html#T59" title="SCMPDS_2:th.59">SCMPDS_2:59</a></i>;<br/>
<i><font color="Green" title="E49">A26</font></i>:  <a href="ami_1.html#K6" title="AMI_1:func.6">IC</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Computation</a> <font color="Maroon" title="c18">s2</font></span>)</span> <a href="ami_1.html#K11" title="AMI_1:func.11">.</a> 2</span>)</span> = 
 <a href="scmpds_2.html#K18" title="SCMPDS_2:func.18">Next</a> <span class="p1">(<span class="default"><a href="ami_1.html#K6" title="AMI_1:func.6">IC</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Computation</a> <font color="Maroon" title="c18">s2</font></span>)</span> <a href="ami_1.html#K11" title="AMI_1:func.11">.</a> 1</span>)</span></span>)</span>
<b>by </b><i><a class="txt" href="scmp_gcd.html#E19:24"><i><font color="Green" title="E42">A19</font></i></a>, <a class="ref" href="scmpds_2.html#T59" title="SCMPDS_2:th.59">SCMPDS_2:59</a></i>
<br/>.= 
 <a href="scmpds_3.html#K2" title="SCMPDS_3:func.2">inspos</a> <span class="p1">(<span class="default">6 <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1</span>)</span>
<b>by </b><i><a class="txt" href="scmp_gcd.html#E17:24"><i><font color="Green" title="E40">A17</font></i></a>, <a class="ref" href="scmpds_4.html#T70" title="SCMPDS_4:th.70">SCMPDS_4:70</a></i>
;<br/>
<b>then </b><i><font color="Green" title="E50">A27</font></i>:  <a href="ami_1.html#K8" title="AMI_1:func.8">CurInstr</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Computation</a> <font color="Maroon" title="c18">s2</font></span>)</span> <a href="ami_1.html#K11" title="AMI_1:func.11">.</a> 2</span>)</span> = 
<font color="Maroon" title="c18">s2</font> <a href="ami_1.html#K13" title="AMI_1:func.13">.</a> <span class="p1">(<span class="default"><a href="scmpds_3.html#K2" title="SCMPDS_3:func.2">inspos</a> 7</span>)</span>
<b>by </b><i><a class="ref" href="ami_1.html#T54" title="AMI_1:th.54">AMI_1:54</a></i>
<br/>.= 
 <a href="scmpds_2.html#K16" title="SCMPDS_2:func.16">Divide</a> <a href="scmp_gcd.html#K3" title="SCMP_GCD:func.3">SBP</a> ,2,<a href="scmp_gcd.html#K3" title="SCMP_GCD:func.3">SBP</a> ,3
<b>by </b><i><a class="txt" href="scmp_gcd.html#E1:24"><i><font color="Green" title="E24">A1</font></i></a>, <a class="txt" href="scmp_gcd.html#E21"><i><font color="Green" title="E14">Lm3</font></i></a></i>
;<br/>
<i><font color="Green" title="E51">A28</font></i>: <span class="p1">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Computation</a> <font color="Maroon" title="c18">s2</font></span>)</span> <a href="ami_1.html#K11" title="AMI_1:func.11">.</a> <span class="p1">(<span class="default">2 <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1</span>)</span> = 
 <a href="ami_1.html#K9" title="AMI_1:func.9">Following</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Computation</a> <font color="Maroon" title="c18">s2</font></span>)</span> <a href="ami_1.html#K11" title="AMI_1:func.11">.</a> 2</span>)</span>
<b>by </b><i><a class="ref" href="ami_1.html#D19" title="AMI_1:def.19">AMI_1:def 19</a></i>
<br/>.= 
 <a href="ami_1.html#K4" title="AMI_1:func.4">Exec</a> <span class="p1">(<span class="default"><a href="scmpds_2.html#K16" title="SCMPDS_2:func.16">Divide</a> <a href="scmp_gcd.html#K3" title="SCMP_GCD:func.3">SBP</a> ,2,<a href="scmp_gcd.html#K3" title="SCMP_GCD:func.3">SBP</a> ,3</span>)</span>,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Computation</a> <font color="Maroon" title="c18">s2</font></span>)</span> <a href="ami_1.html#K11" title="AMI_1:func.11">.</a> 2</span>)</span>
<b>by </b><i><a class="txt" href="scmp_gcd.html#E29:24"><i><font color="Green" title="E50">A27</font></i></a></i>
;<br/>
<i><font color="Green" title="E52">A29</font></i>:  <a href="ami_1.html#K6" title="AMI_1:func.6">IC</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Computation</a> <font color="Maroon" title="c17">s1</font></span>)</span> <a href="ami_1.html#K11" title="AMI_1:func.11">.</a> 3</span>)</span> = 
 <a href="scmpds_2.html#K18" title="SCMPDS_2:func.18">Next</a> <span class="p1">(<span class="default"><a href="ami_1.html#K6" title="AMI_1:func.6">IC</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Computation</a> <font color="Maroon" title="c17">s1</font></span>)</span> <a href="ami_1.html#K11" title="AMI_1:func.11">.</a> 2</span>)</span></span>)</span>
<b>by </b><i><a class="txt" href="scmp_gcd.html#E22:24"><i><font color="Green" title="E45">A22</font></i></a>, <a class="ref" href="scmpds_2.html#T64" title="SCMPDS_2:th.64">SCMPDS_2:64</a></i>
<br/>.= 
 <a href="scmpds_3.html#K2" title="SCMPDS_3:func.2">inspos</a> <span class="p1">(<span class="default">7 <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1</span>)</span>
<b>by </b><i><a class="txt" href="scmp_gcd.html#E20:24"><i><font color="Green" title="E43">A20</font></i></a>, <a class="ref" href="scmpds_4.html#T70" title="SCMPDS_4:th.70">SCMPDS_4:70</a></i>
;<br/>
<b>then </b><i><font color="Green" title="E53">A30</font></i>:  <a href="ami_1.html#K8" title="AMI_1:func.8">CurInstr</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Computation</a> <font color="Maroon" title="c17">s1</font></span>)</span> <a href="ami_1.html#K11" title="AMI_1:func.11">.</a> 3</span>)</span> = 
<font color="Maroon" title="c17">s1</font> <a href="ami_1.html#K13" title="AMI_1:func.13">.</a> <span class="p1">(<span class="default"><a href="scmpds_3.html#K2" title="SCMPDS_3:func.2">inspos</a> 8</span>)</span>
<b>by </b><i><a class="ref" href="ami_1.html#T54" title="AMI_1:th.54">AMI_1:54</a></i>
<br/>.= 
<a href="scmp_gcd.html#K3" title="SCMP_GCD:func.3">SBP</a> ,7 <a href="scmpds_2.html#K17" title="SCMPDS_2:func.17">:=</a> <a href="scmp_gcd.html#K3" title="SCMP_GCD:func.3">SBP</a> ,3
<b>by </b><i><a class="txt" href="scmp_gcd.html#E1:24"><i><font color="Green" title="E24">A1</font></i></a>, <a class="txt" href="scmp_gcd.html#E21"><i><font color="Green" title="E14">Lm3</font></i></a></i>
;<br/>
<i><font color="Green" title="E54">A31</font></i>: <span class="p1">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Computation</a> <font color="Maroon" title="c17">s1</font></span>)</span> <a href="ami_1.html#K11" title="AMI_1:func.11">.</a> <span class="p1">(<span class="default">3 <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1</span>)</span> = 
 <a href="ami_1.html#K9" title="AMI_1:func.9">Following</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Computation</a> <font color="Maroon" title="c17">s1</font></span>)</span> <a href="ami_1.html#K11" title="AMI_1:func.11">.</a> 3</span>)</span>
<b>by </b><i><a class="ref" href="ami_1.html#D19" title="AMI_1:def.19">AMI_1:def 19</a></i>
<br/>.= 
 <a href="ami_1.html#K4" title="AMI_1:func.4">Exec</a> <span class="p1">(<span class="default"><a href="scmp_gcd.html#K3" title="SCMP_GCD:func.3">SBP</a> ,7 <a href="scmpds_2.html#K17" title="SCMPDS_2:func.17">:=</a> <a href="scmp_gcd.html#K3" title="SCMP_GCD:func.3">SBP</a> ,3</span>)</span>,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Computation</a> <font color="Maroon" title="c17">s1</font></span>)</span> <a href="ami_1.html#K11" title="AMI_1:func.11">.</a> 3</span>)</span>
<b>by </b><i><a class="txt" href="scmp_gcd.html#E32:24"><i><font color="Green" title="E53">A30</font></i></a></i>
;<br/>
<a NAME="E34:24"/><i><font color="Green" title="E55">A32</font></i>: 
 <a href="scmpds_2.html#K3" title="SCMPDS_2:func.3">DataLoc</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Computation</a> <font color="Maroon" title="c17">s1</font></span>)</span> <a href="ami_1.html#K11" title="AMI_1:func.11">.</a> 2</span>)</span> <a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">.</a> <a href="scmp_gcd.html#K3" title="SCMP_GCD:func.3">SBP</a> </span>)</span>,2 <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="scmp_gcd.html#K1" title="SCMP_GCD:func.1">intpos</a> <span class="p1">(<span class="default"><font color="Maroon" title="c16">n</font> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 2</span>)</span>
 
<b>by </b><i><a class="txt" href="scmp_gcd.html#E25:24"><i><font color="Green" title="E47">A24</font></i></a>, <a class="ref" href="scmp_gcd.html#T5" target="_self" title="SCMP_GCD:th.5">Th5</a></i>;<br/>
<a NAME="E35:24"/><b>then </b><i><font color="Green" title="E56">A33</font></i>: 
 <a href="scmp_gcd.html#K3" title="SCMP_GCD:func.3">SBP</a>  <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a>  <a href="scmpds_2.html#K3" title="SCMPDS_2:func.3">DataLoc</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Computation</a> <font color="Maroon" title="c17">s1</font></span>)</span> <a href="ami_1.html#K11" title="AMI_1:func.11">.</a> 2</span>)</span> <a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">.</a> <a href="scmp_gcd.html#K3" title="SCMP_GCD:func.3">SBP</a> </span>)</span>,2
 
<b>by </b><i><a class="txt" href="scmp_gcd.html#E24"><i><font color="Green" title="E17">Lm5</font></i></a></i>;<br/>
<a NAME="E36:24"/><i><font color="Green" title="E57">A34</font></i>: 
 <a href="scmpds_2.html#K3" title="SCMPDS_2:func.3">DataLoc</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Computation</a> <font color="Maroon" title="c17">s1</font></span>)</span> <a href="ami_1.html#K11" title="AMI_1:func.11">.</a> 2</span>)</span> <a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">.</a> <a href="scmp_gcd.html#K3" title="SCMP_GCD:func.3">SBP</a> </span>)</span>,3 <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="scmp_gcd.html#K1" title="SCMP_GCD:func.1">intpos</a> <span class="p1">(<span class="default"><font color="Maroon" title="c16">n</font> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 3</span>)</span>
 
<b>by </b><i><a class="txt" href="scmp_gcd.html#E25:24"><i><font color="Green" title="E47">A24</font></i></a>, <a class="ref" href="scmp_gcd.html#T5" target="_self" title="SCMP_GCD:th.5">Th5</a></i>;<br/>
<a NAME="E37:24"/><b>then </b>
 <a href="scmp_gcd.html#K3" title="SCMP_GCD:func.3">SBP</a>  <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a>  <a href="scmpds_2.html#K3" title="SCMPDS_2:func.3">DataLoc</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Computation</a> <font color="Maroon" title="c17">s1</font></span>)</span> <a href="ami_1.html#K11" title="AMI_1:func.11">.</a> 2</span>)</span> <a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">.</a> <a href="scmp_gcd.html#K3" title="SCMP_GCD:func.3">SBP</a> </span>)</span>,3
 
<b>by </b><i><a class="txt" href="scmp_gcd.html#E24"><i><font color="Green" title="E17">Lm5</font></i></a></i>;<br/>
<a NAME="E38:24"/><b>then </b><i><font color="Green" title="E58">A35</font></i>: 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Computation</a> <font color="Maroon" title="c17">s1</font></span>)</span> <a href="ami_1.html#K11" title="AMI_1:func.11">.</a> 3</span>)</span> <a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">.</a> <a href="scmp_gcd.html#K3" title="SCMP_GCD:func.3">SBP</a>  <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c16">n</font>
 
<b>by </b><i><a class="txt" href="scmp_gcd.html#E22:24"><i><font color="Green" title="E45">A22</font></i></a>, <a class="txt" href="scmp_gcd.html#E25:24"><i><font color="Green" title="E47">A24</font></i></a>, <a class="txt" href="scmp_gcd.html#E35:24"><i><font color="Green" title="E56">A33</font></i></a>, <a class="ref" href="scmpds_2.html#T64" title="SCMPDS_2:th.64">SCMPDS_2:64</a></i>;<br/>
<a NAME="E39:24"/><i><font color="Green" title="E59">A36</font></i>: 
 <a href="scmp_gcd.html#K2" title="SCMP_GCD:func.2">GBP</a>  <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a>  <a href="scmpds_2.html#K3" title="SCMPDS_2:func.3">DataLoc</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Computation</a> <font color="Maroon" title="c17">s1</font></span>)</span> <a href="ami_1.html#K11" title="AMI_1:func.11">.</a> 2</span>)</span> <a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">.</a> <a href="scmp_gcd.html#K3" title="SCMP_GCD:func.3">SBP</a> </span>)</span>,2
 
<b>by </b><i><a class="txt" href="scmp_gcd.html#E34:24"><i><font color="Green" title="E55">A32</font></i></a>, <a class="txt" href="scmp_gcd.html#E23"><i><font color="Green" title="E16">Lm4</font></i></a></i>;<br/>
<a NAME="E40:24"/>
 <a href="scmp_gcd.html#K2" title="SCMP_GCD:func.2">GBP</a>  <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a>  <a href="scmpds_2.html#K3" title="SCMPDS_2:func.3">DataLoc</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Computation</a> <font color="Maroon" title="c17">s1</font></span>)</span> <a href="ami_1.html#K11" title="AMI_1:func.11">.</a> 2</span>)</span> <a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">.</a> <a href="scmp_gcd.html#K3" title="SCMP_GCD:func.3">SBP</a> </span>)</span>,3
 
<b>by </b><i><a class="txt" href="scmp_gcd.html#E36:24"><i><font color="Green" title="E57">A34</font></i></a>, <a class="txt" href="scmp_gcd.html#E23"><i><font color="Green" title="E16">Lm4</font></i></a></i>;<br/>
<a NAME="E41:24"/><b>then </b><i><font color="Green" title="E60">A37</font></i>: 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Computation</a> <font color="Maroon" title="c17">s1</font></span>)</span> <a href="ami_1.html#K11" title="AMI_1:func.11">.</a> 3</span>)</span> <a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">.</a> <a href="scmp_gcd.html#K2" title="SCMP_GCD:func.2">GBP</a>  <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 0
 
<b>by </b><i><a class="txt" href="scmp_gcd.html#E22:24"><i><font color="Green" title="E45">A22</font></i></a>, <a class="txt" href="scmp_gcd.html#E27:24"><i><font color="Green" title="E48">A25</font></i></a>, <a class="txt" href="scmp_gcd.html#E39:24"><i><font color="Green" title="E59">A36</font></i></a>, <a class="ref" href="scmpds_2.html#T64" title="SCMPDS_2:th.64">SCMPDS_2:64</a></i>;<br/>
<i><font color="Green" title="E61">A38</font></i>:  <a href="ami_1.html#K6" title="AMI_1:func.6">IC</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Computation</a> <font color="Maroon" title="c18">s2</font></span>)</span> <a href="ami_1.html#K11" title="AMI_1:func.11">.</a> 3</span>)</span> = 
 <a href="scmpds_2.html#K18" title="SCMPDS_2:func.18">Next</a> <span class="p1">(<span class="default"><a href="ami_1.html#K6" title="AMI_1:func.6">IC</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Computation</a> <font color="Maroon" title="c18">s2</font></span>)</span> <a href="ami_1.html#K11" title="AMI_1:func.11">.</a> 2</span>)</span></span>)</span>
<b>by </b><i><a class="txt" href="scmp_gcd.html#E30:24"><i><font color="Green" title="E51">A28</font></i></a>, <a class="ref" href="scmpds_2.html#T64" title="SCMPDS_2:th.64">SCMPDS_2:64</a></i>
<br/>.= 
 <a href="scmpds_3.html#K2" title="SCMPDS_3:func.2">inspos</a> <span class="p1">(<span class="default">7 <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1</span>)</span>
<b>by </b><i><a class="txt" href="scmp_gcd.html#E28:24"><i><font color="Green" title="E49">A26</font></i></a>, <a class="ref" href="scmpds_4.html#T70" title="SCMPDS_4:th.70">SCMPDS_4:70</a></i>
;<br/>
<b>then </b><i><font color="Green" title="E62">A39</font></i>:  <a href="ami_1.html#K8" title="AMI_1:func.8">CurInstr</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Computation</a> <font color="Maroon" title="c18">s2</font></span>)</span> <a href="ami_1.html#K11" title="AMI_1:func.11">.</a> 3</span>)</span> = 
<font color="Maroon" title="c18">s2</font> <a href="ami_1.html#K13" title="AMI_1:func.13">.</a> <span class="p1">(<span class="default"><a href="scmpds_3.html#K2" title="SCMPDS_3:func.2">inspos</a> 8</span>)</span>
<b>by </b><i><a class="ref" href="ami_1.html#T54" title="AMI_1:th.54">AMI_1:54</a></i>
<br/>.= 
<a href="scmp_gcd.html#K3" title="SCMP_GCD:func.3">SBP</a> ,7 <a href="scmpds_2.html#K17" title="SCMPDS_2:func.17">:=</a> <a href="scmp_gcd.html#K3" title="SCMP_GCD:func.3">SBP</a> ,3
<b>by </b><i><a class="txt" href="scmp_gcd.html#E1:24"><i><font color="Green" title="E24">A1</font></i></a>, <a class="txt" href="scmp_gcd.html#E21"><i><font color="Green" title="E14">Lm3</font></i></a></i>
;<br/>
<i><font color="Green" title="E63">A40</font></i>: <span class="p1">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Computation</a> <font color="Maroon" title="c18">s2</font></span>)</span> <a href="ami_1.html#K11" title="AMI_1:func.11">.</a> <span class="p1">(<span class="default">3 <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1</span>)</span> = 
 <a href="ami_1.html#K9" title="AMI_1:func.9">Following</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Computation</a> <font color="Maroon" title="c18">s2</font></span>)</span> <a href="ami_1.html#K11" title="AMI_1:func.11">.</a> 3</span>)</span>
<b>by </b><i><a class="ref" href="ami_1.html#D19" title="AMI_1:def.19">AMI_1:def 19</a></i>
<br/>.= 
 <a href="ami_1.html#K4" title="AMI_1:func.4">Exec</a> <span class="p1">(<span class="default"><a href="scmp_gcd.html#K3" title="SCMP_GCD:func.3">SBP</a> ,7 <a href="scmpds_2.html#K17" title="SCMPDS_2:func.17">:=</a> <a href="scmp_gcd.html#K3" title="SCMP_GCD:func.3">SBP</a> ,3</span>)</span>,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Computation</a> <font color="Maroon" title="c18">s2</font></span>)</span> <a href="ami_1.html#K11" title="AMI_1:func.11">.</a> 3</span>)</span>
<b>by </b><i><a class="txt" href="scmp_gcd.html#E43:24"><i><font color="Green" title="E62">A39</font></i></a></i>
;<br/>
<i><font color="Green" title="E64">A41</font></i>:  <a href="ami_1.html#K6" title="AMI_1:func.6">IC</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Computation</a> <font color="Maroon" title="c17">s1</font></span>)</span> <a href="ami_1.html#K11" title="AMI_1:func.11">.</a> 4</span>)</span> = 
 <a href="scmpds_2.html#K18" title="SCMPDS_2:func.18">Next</a> <span class="p1">(<span class="default"><a href="ami_1.html#K6" title="AMI_1:func.6">IC</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Computation</a> <font color="Maroon" title="c17">s1</font></span>)</span> <a href="ami_1.html#K11" title="AMI_1:func.11">.</a> 3</span>)</span></span>)</span>
<b>by </b><i><a class="txt" href="scmp_gcd.html#E33:24"><i><font color="Green" title="E54">A31</font></i></a>, <a class="ref" href="scmpds_2.html#T59" title="SCMPDS_2:th.59">SCMPDS_2:59</a></i>
<br/>.= 
 <a href="scmpds_3.html#K2" title="SCMPDS_3:func.2">inspos</a> <span class="p1">(<span class="default">8 <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1</span>)</span>
<b>by </b><i><a class="txt" href="scmp_gcd.html#E31:24"><i><font color="Green" title="E52">A29</font></i></a>, <a class="ref" href="scmpds_4.html#T70" title="SCMPDS_4:th.70">SCMPDS_4:70</a></i>
;<br/>
<b>then </b><i><font color="Green" title="E65">A42</font></i>:  <a href="ami_1.html#K8" title="AMI_1:func.8">CurInstr</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Computation</a> <font color="Maroon" title="c17">s1</font></span>)</span> <a href="ami_1.html#K11" title="AMI_1:func.11">.</a> 4</span>)</span> = 
<font color="Maroon" title="c17">s1</font> <a href="ami_1.html#K13" title="AMI_1:func.13">.</a> <span class="p1">(<span class="default"><a href="scmpds_3.html#K2" title="SCMPDS_3:func.2">inspos</a> 9</span>)</span>
<b>by </b><i><a class="ref" href="ami_1.html#T54" title="AMI_1:th.54">AMI_1:54</a></i>
<br/>.= 
<a href="scmp_gcd.html#K3" title="SCMP_GCD:func.3">SBP</a> ,<span class="p1">(<span class="default">4 <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> <a href="scmpds_1.html#K22" title="SCMPDS_1:func.22">RetSP</a> </span>)</span> <a href="scmpds_2.html#K17" title="SCMPDS_2:func.17">:=</a> <a href="scmp_gcd.html#K2" title="SCMP_GCD:func.2">GBP</a> ,1
<b>by </b><i><a class="txt" href="scmp_gcd.html#E1:24"><i><font color="Green" title="E24">A1</font></i></a>, <a class="txt" href="scmp_gcd.html#E21"><i><font color="Green" title="E14">Lm3</font></i></a></i>
;<br/>
<i><font color="Green" title="E66">A43</font></i>: <span class="p1">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Computation</a> <font color="Maroon" title="c17">s1</font></span>)</span> <a href="ami_1.html#K11" title="AMI_1:func.11">.</a> <span class="p1">(<span class="default">4 <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1</span>)</span> = 
 <a href="ami_1.html#K9" title="AMI_1:func.9">Following</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Computation</a> <font color="Maroon" title="c17">s1</font></span>)</span> <a href="ami_1.html#K11" title="AMI_1:func.11">.</a> 4</span>)</span>
<b>by </b><i><a class="ref" href="ami_1.html#D19" title="AMI_1:def.19">AMI_1:def 19</a></i>
<br/>.= 
 <a href="ami_1.html#K4" title="AMI_1:func.4">Exec</a> <span class="p1">(<span class="default"><a href="scmp_gcd.html#K3" title="SCMP_GCD:func.3">SBP</a> ,<span class="p2">(<span class="default">4 <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> <a href="scmpds_1.html#K22" title="SCMPDS_1:func.22">RetSP</a> </span>)</span> <a href="scmpds_2.html#K17" title="SCMPDS_2:func.17">:=</a> <a href="scmp_gcd.html#K2" title="SCMP_GCD:func.2">GBP</a> ,1</span>)</span>,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Computation</a> <font color="Maroon" title="c17">s1</font></span>)</span> <a href="ami_1.html#K11" title="AMI_1:func.11">.</a> 4</span>)</span>
<b>by </b><i><a class="txt" href="scmp_gcd.html#E46:24"><i><font color="Green" title="E65">A42</font></i></a></i>
;<br/>
<a NAME="E48:24"/><i><font color="Green" title="E67">A44</font></i>: 
 <a href="scmpds_2.html#K3" title="SCMPDS_2:func.3">DataLoc</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Computation</a> <font color="Maroon" title="c17">s1</font></span>)</span> <a href="ami_1.html#K11" title="AMI_1:func.11">.</a> 3</span>)</span> <a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">.</a> <a href="scmp_gcd.html#K3" title="SCMP_GCD:func.3">SBP</a> </span>)</span>,7 <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="scmp_gcd.html#K1" title="SCMP_GCD:func.1">intpos</a> <span class="p1">(<span class="default"><font color="Maroon" title="c16">n</font> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 7</span>)</span>
 
<b>by </b><i><a class="txt" href="scmp_gcd.html#E38:24"><i><font color="Green" title="E58">A35</font></i></a>, <a class="ref" href="scmp_gcd.html#T5" target="_self" title="SCMP_GCD:th.5">Th5</a></i>;<br/>
<a NAME="E49:24"/><b>then </b>
 <a href="scmp_gcd.html#K3" title="SCMP_GCD:func.3">SBP</a>  <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a>  <a href="scmpds_2.html#K3" title="SCMPDS_2:func.3">DataLoc</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Computation</a> <font color="Maroon" title="c17">s1</font></span>)</span> <a href="ami_1.html#K11" title="AMI_1:func.11">.</a> 3</span>)</span> <a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">.</a> <a href="scmp_gcd.html#K3" title="SCMP_GCD:func.3">SBP</a> </span>)</span>,7
 
<b>by </b><i><a class="txt" href="scmp_gcd.html#E24"><i><font color="Green" title="E17">Lm5</font></i></a></i>;<br/>
<a NAME="E50:24"/><b>then </b><i><font color="Green" title="E68">A45</font></i>: 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Computation</a> <font color="Maroon" title="c17">s1</font></span>)</span> <a href="ami_1.html#K11" title="AMI_1:func.11">.</a> 4</span>)</span> <a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">.</a> <a href="scmp_gcd.html#K3" title="SCMP_GCD:func.3">SBP</a>  <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c16">n</font>
 
<b>by </b><i><a class="txt" href="scmp_gcd.html#E33:24"><i><font color="Green" title="E54">A31</font></i></a>, <a class="txt" href="scmp_gcd.html#E38:24"><i><font color="Green" title="E58">A35</font></i></a>, <a class="ref" href="scmpds_2.html#T59" title="SCMPDS_2:th.59">SCMPDS_2:59</a></i>;<br/>
<a NAME="E51:24"/>
 <a href="scmp_gcd.html#K2" title="SCMP_GCD:func.2">GBP</a>  <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a>  <a href="scmpds_2.html#K3" title="SCMPDS_2:func.3">DataLoc</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Computation</a> <font color="Maroon" title="c17">s1</font></span>)</span> <a href="ami_1.html#K11" title="AMI_1:func.11">.</a> 3</span>)</span> <a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">.</a> <a href="scmp_gcd.html#K3" title="SCMP_GCD:func.3">SBP</a> </span>)</span>,7
 
<b>by </b><i><a class="txt" href="scmp_gcd.html#E48:24"><i><font color="Green" title="E67">A44</font></i></a>, <a class="txt" href="scmp_gcd.html#E23"><i><font color="Green" title="E16">Lm4</font></i></a></i>;<br/>
<a NAME="E52:24"/><b>then </b><i><font color="Green" title="E69">A46</font></i>: 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Computation</a> <font color="Maroon" title="c17">s1</font></span>)</span> <a href="ami_1.html#K11" title="AMI_1:func.11">.</a> 4</span>)</span> <a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">.</a> <a href="scmp_gcd.html#K2" title="SCMP_GCD:func.2">GBP</a>  <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 0
 
<b>by </b><i><a class="txt" href="scmp_gcd.html#E33:24"><i><font color="Green" title="E54">A31</font></i></a>, <a class="txt" href="scmp_gcd.html#E41:24"><i><font color="Green" title="E60">A37</font></i></a>, <a class="ref" href="scmpds_2.html#T59" title="SCMPDS_2:th.59">SCMPDS_2:59</a></i>;<br/>
<i><font color="Green" title="E70">A47</font></i>:  <a href="ami_1.html#K6" title="AMI_1:func.6">IC</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Computation</a> <font color="Maroon" title="c18">s2</font></span>)</span> <a href="ami_1.html#K11" title="AMI_1:func.11">.</a> 4</span>)</span> = 
 <a href="scmpds_2.html#K18" title="SCMPDS_2:func.18">Next</a> <span class="p1">(<span class="default"><a href="ami_1.html#K6" title="AMI_1:func.6">IC</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Computation</a> <font color="Maroon" title="c18">s2</font></span>)</span> <a href="ami_1.html#K11" title="AMI_1:func.11">.</a> 3</span>)</span></span>)</span>
<b>by </b><i><a class="txt" href="scmp_gcd.html#E44:24"><i><font color="Green" title="E63">A40</font></i></a>, <a class="ref" href="scmpds_2.html#T59" title="SCMPDS_2:th.59">SCMPDS_2:59</a></i>
<br/>.= 
 <a href="scmpds_3.html#K2" title="SCMPDS_3:func.2">inspos</a> <span class="p1">(<span class="default">8 <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1</span>)</span>
<b>by </b><i><a class="txt" href="scmp_gcd.html#E42:24"><i><font color="Green" title="E61">A38</font></i></a>, <a class="ref" href="scmpds_4.html#T70" title="SCMPDS_4:th.70">SCMPDS_4:70</a></i>
;<br/>
<b>then </b><i><font color="Green" title="E71">A48</font></i>:  <a href="ami_1.html#K8" title="AMI_1:func.8">CurInstr</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Computation</a> <font color="Maroon" title="c18">s2</font></span>)</span> <a href="ami_1.html#K11" title="AMI_1:func.11">.</a> 4</span>)</span> = 
<font color="Maroon" title="c18">s2</font> <a href="ami_1.html#K13" title="AMI_1:func.13">.</a> <span class="p1">(<span class="default"><a href="scmpds_3.html#K2" title="SCMPDS_3:func.2">inspos</a> 9</span>)</span>
<b>by </b><i><a class="ref" href="ami_1.html#T54" title="AMI_1:th.54">AMI_1:54</a></i>
<br/>.= 
<a href="scmp_gcd.html#K3" title="SCMP_GCD:func.3">SBP</a> ,<span class="p1">(<span class="default">4 <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> <a href="scmpds_1.html#K22" title="SCMPDS_1:func.22">RetSP</a> </span>)</span> <a href="scmpds_2.html#K17" title="SCMPDS_2:func.17">:=</a> <a href="scmp_gcd.html#K2" title="SCMP_GCD:func.2">GBP</a> ,1
<b>by </b><i><a class="txt" href="scmp_gcd.html#E1:24"><i><font color="Green" title="E24">A1</font></i></a>, <a class="txt" href="scmp_gcd.html#E21"><i><font color="Green" title="E14">Lm3</font></i></a></i>
;<br/>
<i><font color="Green" title="E72">A49</font></i>: <span class="p1">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Computation</a> <font color="Maroon" title="c18">s2</font></span>)</span> <a href="ami_1.html#K11" title="AMI_1:func.11">.</a> <span class="p1">(<span class="default">4 <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1</span>)</span> = 
 <a href="ami_1.html#K9" title="AMI_1:func.9">Following</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Computation</a> <font color="Maroon" title="c18">s2</font></span>)</span> <a href="ami_1.html#K11" title="AMI_1:func.11">.</a> 4</span>)</span>
<b>by </b><i><a class="ref" href="ami_1.html#D19" title="AMI_1:def.19">AMI_1:def 19</a></i>
<br/>.= 
 <a href="ami_1.html#K4" title="AMI_1:func.4">Exec</a> <span class="p1">(<span class="default"><a href="scmp_gcd.html#K3" title="SCMP_GCD:func.3">SBP</a> ,<span class="p2">(<span class="default">4 <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> <a href="scmpds_1.html#K22" title="SCMPDS_1:func.22">RetSP</a> </span>)</span> <a href="scmpds_2.html#K17" title="SCMPDS_2:func.17">:=</a> <a href="scmp_gcd.html#K2" title="SCMP_GCD:func.2">GBP</a> ,1</span>)</span>,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Computation</a> <font color="Maroon" title="c18">s2</font></span>)</span> <a href="ami_1.html#K11" title="AMI_1:func.11">.</a> 4</span>)</span>
<b>by </b><i><a class="txt" href="scmp_gcd.html#E54:24"><i><font color="Green" title="E71">A48</font></i></a></i>
;<br/>
<i><font color="Green" title="E73">A50</font></i>:  <a href="ami_1.html#K6" title="AMI_1:func.6">IC</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Computation</a> <font color="Maroon" title="c17">s1</font></span>)</span> <a href="ami_1.html#K11" title="AMI_1:func.11">.</a> 5</span>)</span> = 
 <a href="scmpds_2.html#K18" title="SCMPDS_2:func.18">Next</a> <span class="p1">(<span class="default"><a href="ami_1.html#K6" title="AMI_1:func.6">IC</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Computation</a> <font color="Maroon" title="c17">s1</font></span>)</span> <a href="ami_1.html#K11" title="AMI_1:func.11">.</a> 4</span>)</span></span>)</span>
<b>by </b><i><a class="txt" href="scmp_gcd.html#E47:24"><i><font color="Green" title="E66">A43</font></i></a>, <a class="ref" href="scmpds_2.html#T59" title="SCMPDS_2:th.59">SCMPDS_2:59</a></i>
<br/>.= 
 <a href="scmpds_3.html#K2" title="SCMPDS_3:func.2">inspos</a> <span class="p1">(<span class="default">9 <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1</span>)</span>
<b>by </b><i><a class="txt" href="scmp_gcd.html#E45:24"><i><font color="Green" title="E64">A41</font></i></a>, <a class="ref" href="scmpds_4.html#T70" title="SCMPDS_4:th.70">SCMPDS_4:70</a></i>
;<br/>
<b>then </b><i><font color="Green" title="E74">A51</font></i>:  <a href="ami_1.html#K8" title="AMI_1:func.8">CurInstr</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Computation</a> <font color="Maroon" title="c17">s1</font></span>)</span> <a href="ami_1.html#K11" title="AMI_1:func.11">.</a> 5</span>)</span> = 
<font color="Maroon" title="c17">s1</font> <a href="ami_1.html#K13" title="AMI_1:func.13">.</a> <span class="p1">(<span class="default"><a href="scmpds_3.html#K2" title="SCMPDS_3:func.2">inspos</a> 10</span>)</span>
<b>by </b><i><a class="ref" href="ami_1.html#T54" title="AMI_1:th.54">AMI_1:54</a></i>
<br/>.= 
 <a href="scmpds_2.html#K12" title="SCMPDS_2:func.12">AddTo</a> <a href="scmp_gcd.html#K2" title="SCMP_GCD:func.2">GBP</a> ,1,4
<b>by </b><i><a class="txt" href="scmp_gcd.html#E1:24"><i><font color="Green" title="E24">A1</font></i></a>, <a class="txt" href="scmp_gcd.html#E21"><i><font color="Green" title="E14">Lm3</font></i></a></i>
;<br/>
<i><font color="Green" title="E75">A52</font></i>: <span class="p1">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Computation</a> <font color="Maroon" title="c17">s1</font></span>)</span> <a href="ami_1.html#K11" title="AMI_1:func.11">.</a> <span class="p1">(<span class="default">5 <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1</span>)</span> = 
 <a href="ami_1.html#K9" title="AMI_1:func.9">Following</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Computation</a> <font color="Maroon" title="c17">s1</font></span>)</span> <a href="ami_1.html#K11" title="AMI_1:func.11">.</a> 5</span>)</span>
<b>by </b><i><a class="ref" href="ami_1.html#D19" title="AMI_1:def.19">AMI_1:def 19</a></i>
<br/>.= 
 <a href="ami_1.html#K4" title="AMI_1:func.4">Exec</a> <span class="p1">(<span class="default"><a href="scmpds_2.html#K12" title="SCMPDS_2:func.12">AddTo</a> <a href="scmp_gcd.html#K2" title="SCMP_GCD:func.2">GBP</a> ,1,4</span>)</span>,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Computation</a> <font color="Maroon" title="c17">s1</font></span>)</span> <a href="ami_1.html#K11" title="AMI_1:func.11">.</a> 5</span>)</span>
<b>by </b><i><a class="txt" href="scmp_gcd.html#E57:24"><i><font color="Green" title="E74">A51</font></i></a></i>
;<br/>
<a NAME="E59:24"/>
 <a href="scmpds_2.html#K3" title="SCMPDS_2:func.3">DataLoc</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Computation</a> <font color="Maroon" title="c17">s1</font></span>)</span> <a href="ami_1.html#K11" title="AMI_1:func.11">.</a> 4</span>)</span> <a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">.</a> <a href="scmp_gcd.html#K3" title="SCMP_GCD:func.3">SBP</a> </span>)</span>,<span class="p1">(<span class="default">4 <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> <a href="scmpds_1.html#K22" title="SCMPDS_1:func.22">RetSP</a> </span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="scmp_gcd.html#K1" title="SCMP_GCD:func.1">intpos</a> <span class="p1">(<span class="default"><font color="Maroon" title="c16">n</font> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> <span class="p2">(<span class="default">4 <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 0</span>)</span></span>)</span>
 
<b>by </b><i><a class="txt" href="scmp_gcd.html#E50:24"><i><font color="Green" title="E68">A45</font></i></a>, <a class="ref" href="scmp_gcd.html#T5" target="_self" title="SCMP_GCD:th.5">Th5</a>, <a class="ref" href="scmpds_1.html#D22" title="SCMPDS_1:def.22">SCMPDS_1:def 22</a></i>;<br/>
<a NAME="E60:24"/><b>then </b>
 <a href="scmp_gcd.html#K2" title="SCMP_GCD:func.2">GBP</a>  <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a>  <a href="scmpds_2.html#K3" title="SCMPDS_2:func.3">DataLoc</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Computation</a> <font color="Maroon" title="c17">s1</font></span>)</span> <a href="ami_1.html#K11" title="AMI_1:func.11">.</a> 4</span>)</span> <a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">.</a> <a href="scmp_gcd.html#K3" title="SCMP_GCD:func.3">SBP</a> </span>)</span>,<span class="p1">(<span class="default">4 <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> <a href="scmpds_1.html#K22" title="SCMPDS_1:func.22">RetSP</a> </span>)</span>
 
<b>by </b><i><a class="txt" href="scmp_gcd.html#E23"><i><font color="Green" title="E16">Lm4</font></i></a></i>;<br/>
<a NAME="E61:24"/><b>then </b><i><font color="Green" title="E76">A53</font></i>: 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Computation</a> <font color="Maroon" title="c17">s1</font></span>)</span> <a href="ami_1.html#K11" title="AMI_1:func.11">.</a> 5</span>)</span> <a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">.</a> <a href="scmp_gcd.html#K2" title="SCMP_GCD:func.2">GBP</a>  <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 0
 
<b>by </b><i><a class="txt" href="scmp_gcd.html#E47:24"><i><font color="Green" title="E66">A43</font></i></a>, <a class="txt" href="scmp_gcd.html#E52:24"><i><font color="Green" title="E69">A46</font></i></a>, <a class="ref" href="scmpds_2.html#T59" title="SCMPDS_2:th.59">SCMPDS_2:59</a></i>;<br/>
<i><font color="Green" title="E77">A54</font></i>:  <a href="ami_1.html#K6" title="AMI_1:func.6">IC</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Computation</a> <font color="Maroon" title="c18">s2</font></span>)</span> <a href="ami_1.html#K11" title="AMI_1:func.11">.</a> 5</span>)</span> = 
 <a href="scmpds_2.html#K18" title="SCMPDS_2:func.18">Next</a> <span class="p1">(<span class="default"><a href="ami_1.html#K6" title="AMI_1:func.6">IC</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Computation</a> <font color="Maroon" title="c18">s2</font></span>)</span> <a href="ami_1.html#K11" title="AMI_1:func.11">.</a> 4</span>)</span></span>)</span>
<b>by </b><i><a class="txt" href="scmp_gcd.html#E55:24"><i><font color="Green" title="E72">A49</font></i></a>, <a class="ref" href="scmpds_2.html#T59" title="SCMPDS_2:th.59">SCMPDS_2:59</a></i>
<br/>.= 
 <a href="scmpds_3.html#K2" title="SCMPDS_3:func.2">inspos</a> <span class="p1">(<span class="default">9 <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1</span>)</span>
<b>by </b><i><a class="txt" href="scmp_gcd.html#E53:24"><i><font color="Green" title="E70">A47</font></i></a>, <a class="ref" href="scmpds_4.html#T70" title="SCMPDS_4:th.70">SCMPDS_4:70</a></i>
;<br/>
<b>then </b><i><font color="Green" title="E78">A55</font></i>:  <a href="ami_1.html#K8" title="AMI_1:func.8">CurInstr</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Computation</a> <font color="Maroon" title="c18">s2</font></span>)</span> <a href="ami_1.html#K11" title="AMI_1:func.11">.</a> 5</span>)</span> = 
<font color="Maroon" title="c18">s2</font> <a href="ami_1.html#K13" title="AMI_1:func.13">.</a> <span class="p1">(<span class="default"><a href="scmpds_3.html#K2" title="SCMPDS_3:func.2">inspos</a> 10</span>)</span>
<b>by </b><i><a class="ref" href="ami_1.html#T54" title="AMI_1:th.54">AMI_1:54</a></i>
<br/>.= 
 <a href="scmpds_2.html#K12" title="SCMPDS_2:func.12">AddTo</a> <a href="scmp_gcd.html#K2" title="SCMP_GCD:func.2">GBP</a> ,1,4
<b>by </b><i><a class="txt" href="scmp_gcd.html#E1:24"><i><font color="Green" title="E24">A1</font></i></a>, <a class="txt" href="scmp_gcd.html#E21"><i><font color="Green" title="E14">Lm3</font></i></a></i>
;<br/>
<i><font color="Green" title="E79">A56</font></i>: <span class="p1">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Computation</a> <font color="Maroon" title="c18">s2</font></span>)</span> <a href="ami_1.html#K11" title="AMI_1:func.11">.</a> <span class="p1">(<span class="default">5 <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1</span>)</span> = 
 <a href="ami_1.html#K9" title="AMI_1:func.9">Following</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Computation</a> <font color="Maroon" title="c18">s2</font></span>)</span> <a href="ami_1.html#K11" title="AMI_1:func.11">.</a> 5</span>)</span>
<b>by </b><i><a class="ref" href="ami_1.html#D19" title="AMI_1:def.19">AMI_1:def 19</a></i>
<br/>.= 
 <a href="ami_1.html#K4" title="AMI_1:func.4">Exec</a> <span class="p1">(<span class="default"><a href="scmpds_2.html#K12" title="SCMPDS_2:func.12">AddTo</a> <a href="scmp_gcd.html#K2" title="SCMP_GCD:func.2">GBP</a> ,1,4</span>)</span>,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Computation</a> <font color="Maroon" title="c18">s2</font></span>)</span> <a href="ami_1.html#K11" title="AMI_1:func.11">.</a> 5</span>)</span>
<b>by </b><i><a class="txt" href="scmp_gcd.html#E63:24"><i><font color="Green" title="E78">A55</font></i></a></i>
;<br/>
<i><font color="Green" title="E80">A57</font></i>:  <a href="ami_1.html#K6" title="AMI_1:func.6">IC</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Computation</a> <font color="Maroon" title="c17">s1</font></span>)</span> <a href="ami_1.html#K11" title="AMI_1:func.11">.</a> 6</span>)</span> = 
 <a href="scmpds_2.html#K18" title="SCMPDS_2:func.18">Next</a> <span class="p1">(<span class="default"><a href="ami_1.html#K6" title="AMI_1:func.6">IC</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Computation</a> <font color="Maroon" title="c17">s1</font></span>)</span> <a href="ami_1.html#K11" title="AMI_1:func.11">.</a> 5</span>)</span></span>)</span>
<b>by </b><i><a class="txt" href="scmp_gcd.html#E58:24"><i><font color="Green" title="E75">A52</font></i></a>, <a class="ref" href="scmpds_2.html#T60" title="SCMPDS_2:th.60">SCMPDS_2:60</a></i>
<br/>.= 
 <a href="scmpds_3.html#K2" title="SCMPDS_3:func.2">inspos</a> <span class="p1">(<span class="default">10 <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1</span>)</span>
<b>by </b><i><a class="txt" href="scmp_gcd.html#E56:24"><i><font color="Green" title="E73">A50</font></i></a>, <a class="ref" href="scmpds_4.html#T70" title="SCMPDS_4:th.70">SCMPDS_4:70</a></i>
;<br/>
<b>then </b><i><font color="Green" title="E81">A58</font></i>:  <a href="ami_1.html#K8" title="AMI_1:func.8">CurInstr</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Computation</a> <font color="Maroon" title="c17">s1</font></span>)</span> <a href="ami_1.html#K11" title="AMI_1:func.11">.</a> 6</span>)</span> = 
<font color="Maroon" title="c17">s1</font> <a href="ami_1.html#K13" title="AMI_1:func.13">.</a> <span class="p1">(<span class="default"><a href="scmpds_3.html#K2" title="SCMPDS_3:func.2">inspos</a> 11</span>)</span>
<b>by </b><i><a class="ref" href="ami_1.html#T54" title="AMI_1:th.54">AMI_1:54</a></i>
<br/>.= 
 <a href="scmpds_2.html#K7" title="SCMPDS_2:func.7">saveIC</a> <a href="scmp_gcd.html#K3" title="SCMP_GCD:func.3">SBP</a> ,<a href="scmpds_1.html#K23" title="SCMPDS_1:func.23">RetIC</a> 
<b>by </b><i><a class="txt" href="scmp_gcd.html#E1:24"><i><font color="Green" title="E24">A1</font></i></a>, <a class="txt" href="scmp_gcd.html#E21"><i><font color="Green" title="E14">Lm3</font></i></a></i>
;<br/>
<i><font color="Green" title="E82">A59</font></i>: <span class="p1">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Computation</a> <font color="Maroon" title="c17">s1</font></span>)</span> <a href="ami_1.html#K11" title="AMI_1:func.11">.</a> <span class="p1">(<span class="default">6 <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1</span>)</span> = 
 <a href="ami_1.html#K9" title="AMI_1:func.9">Following</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Computation</a> <font color="Maroon" title="c17">s1</font></span>)</span> <a href="ami_1.html#K11" title="AMI_1:func.11">.</a> 6</span>)</span>
<b>by </b><i><a class="ref" href="ami_1.html#D19" title="AMI_1:def.19">AMI_1:def 19</a></i>
<br/>.= 
 <a href="ami_1.html#K4" title="AMI_1:func.4">Exec</a> <span class="p1">(<span class="default"><a href="scmpds_2.html#K7" title="SCMPDS_2:func.7">saveIC</a> <a href="scmp_gcd.html#K3" title="SCMP_GCD:func.3">SBP</a> ,<a href="scmpds_1.html#K23" title="SCMPDS_1:func.23">RetIC</a> </span>)</span>,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Computation</a> <font color="Maroon" title="c17">s1</font></span>)</span> <a href="ami_1.html#K11" title="AMI_1:func.11">.</a> 6</span>)</span>
<b>by </b><i><a class="txt" href="scmp_gcd.html#E66:24"><i><font color="Green" title="E81">A58</font></i></a></i>
;<br/>
<i><font color="Green" title="E83">A60</font></i>:  <a href="ami_1.html#K6" title="AMI_1:func.6">IC</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Computation</a> <font color="Maroon" title="c18">s2</font></span>)</span> <a href="ami_1.html#K11" title="AMI_1:func.11">.</a> 6</span>)</span> = 
 <a href="scmpds_2.html#K18" title="SCMPDS_2:func.18">Next</a> <span class="p1">(<span class="default"><a href="ami_1.html#K6" title="AMI_1:func.6">IC</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Computation</a> <font color="Maroon" title="c18">s2</font></span>)</span> <a href="ami_1.html#K11" title="AMI_1:func.11">.</a> 5</span>)</span></span>)</span>
<b>by </b><i><a class="txt" href="scmp_gcd.html#E64:24"><i><font color="Green" title="E79">A56</font></i></a>, <a class="ref" href="scmpds_2.html#T60" title="SCMPDS_2:th.60">SCMPDS_2:60</a></i>
<br/>.= 
 <a href="scmpds_3.html#K2" title="SCMPDS_3:func.2">inspos</a> <span class="p1">(<span class="default">10 <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1</span>)</span>
<b>by </b><i><a class="txt" href="scmp_gcd.html#E62:24"><i><font color="Green" title="E77">A54</font></i></a>, <a class="ref" href="scmpds_4.html#T70" title="SCMPDS_4:th.70">SCMPDS_4:70</a></i>
;<br/>
<b>then </b><i><font color="Green" title="E84">A61</font></i>:  <a href="ami_1.html#K8" title="AMI_1:func.8">CurInstr</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Computation</a> <font color="Maroon" title="c18">s2</font></span>)</span> <a href="ami_1.html#K11" title="AMI_1:func.11">.</a> 6</span>)</span> = 
<font color="Maroon" title="c18">s2</font> <a href="ami_1.html#K13" title="AMI_1:func.13">.</a> <span class="p1">(<span class="default"><a href="scmpds_3.html#K2" title="SCMPDS_3:func.2">inspos</a> 11</span>)</span>
<b>by </b><i><a class="ref" href="ami_1.html#T54" title="AMI_1:th.54">AMI_1:54</a></i>
<br/>.= 
 <a href="scmpds_2.html#K7" title="SCMPDS_2:func.7">saveIC</a> <a href="scmp_gcd.html#K3" title="SCMP_GCD:func.3">SBP</a> ,<a href="scmpds_1.html#K23" title="SCMPDS_1:func.23">RetIC</a> 
<b>by </b><i><a class="txt" href="scmp_gcd.html#E1:24"><i><font color="Green" title="E24">A1</font></i></a>, <a class="txt" href="scmp_gcd.html#E21"><i><font color="Green" title="E14">Lm3</font></i></a></i>
;<br/>
<i><font color="Green" title="E85">A62</font></i>: <span class="p1">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Computation</a> <font color="Maroon" title="c18">s2</font></span>)</span> <a href="ami_1.html#K11" title="AMI_1:func.11">.</a> <span class="p1">(<span class="default">6 <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1</span>)</span> = 
 <a href="ami_1.html#K9" title="AMI_1:func.9">Following</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Computation</a> <font color="Maroon" title="c18">s2</font></span>)</span> <a href="ami_1.html#K11" title="AMI_1:func.11">.</a> 6</span>)</span>
<b>by </b><i><a class="ref" href="ami_1.html#D19" title="AMI_1:def.19">AMI_1:def 19</a></i>
<br/>.= 
 <a href="ami_1.html#K4" title="AMI_1:func.4">Exec</a> <span class="p1">(<span class="default"><a href="scmpds_2.html#K7" title="SCMPDS_2:func.7">saveIC</a> <a href="scmp_gcd.html#K3" title="SCMP_GCD:func.3">SBP</a> ,<a href="scmpds_1.html#K23" title="SCMPDS_1:func.23">RetIC</a> </span>)</span>,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Computation</a> <font color="Maroon" title="c18">s2</font></span>)</span> <a href="ami_1.html#K11" title="AMI_1:func.11">.</a> 6</span>)</span>
<b>by </b><i><a class="txt" href="scmp_gcd.html#E69:24"><i><font color="Green" title="E84">A61</font></i></a></i>
;<br/>
<div><i><font color="Green" title="E86">A63</font></i>: <a class="txt" onclick="hs2(this)" href="javascript:()" title="24_39"><b>now </b></a><div class="add"><b>let </b><font color="Maroon" title="c22">b</font> be    <a href="scmpds_2.html#M1" title="SCMPDS_2:mode.1">Int_position</a> ;<br/><b>assume </b><a NAME="E1:24_39"/>
<font color="Maroon" title="c17">s1</font> <a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">.</a> <font color="Maroon" title="c22">b</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c18">s2</font> <a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">.</a> <font color="Maroon" title="c22">b</font>
 ;<br/><b>hence </b><span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Computation</a> <font color="Maroon" title="c17">s1</font></span>)</span> <a href="ami_1.html#K11" title="AMI_1:func.11">.</a> 1</span>)</span> <a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">.</a> <font color="Maroon" title="c22">b</font> = 
<font color="Maroon" title="c18">s2</font> <a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">.</a> <font color="Maroon" title="c22">b</font>
<b>by </b><i><a class="txt" href="scmp_gcd.html#E9:24"><i><font color="Green" title="E32">A9</font></i></a>, <a class="ref" href="scmpds_2.html#T68" title="SCMPDS_2:th.68">SCMPDS_2:68</a></i>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Computation</a> <font color="Maroon" title="c18">s2</font></span>)</span> <a href="ami_1.html#K11" title="AMI_1:func.11">.</a> 1</span>)</span> <a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">.</a> <font color="Maroon" title="c22">b</font>
<b>by </b><i><a class="txt" href="scmp_gcd.html#E11:24"><i><font color="Green" title="E34">A11</font></i></a>, <a class="ref" href="scmpds_2.html#T68" title="SCMPDS_2:th.68">SCMPDS_2:68</a></i>
;<br/><br/></div><b>end;</b></div>
<a NAME="E72:24"/><i><font color="Green" title="E87">A64</font></i>: 
for <font color="Olive" title="b1">b</font> being   <a href="scmpds_2.html#M1" title="SCMPDS_2:mode.1">Int_position</a>   st <font color="Maroon" title="c17">s1</font> <a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">.</a> <font color="Olive" title="b1">b</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c18">s2</font> <a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">.</a> <font color="Olive" title="b1">b</font> holds <br/><span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Computation</a> <font color="Maroon" title="c17">s1</font></span>)</span> <a href="ami_1.html#K11" title="AMI_1:func.11">.</a> 2</span>)</span> <a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">.</a> <font color="Olive" title="b1">b</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Computation</a> <font color="Maroon" title="c18">s2</font></span>)</span> <a href="ami_1.html#K11" title="AMI_1:func.11">.</a> 2</span>)</span> <a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">.</a> <font color="Olive" title="b1">b</font>
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="24_40"><b>proof </b></a><div class="add">

<b>let </b><font color="Maroon" title="c22">b</font> be    <a href="scmpds_2.html#M1" title="SCMPDS_2:mode.1">Int_position</a> ;<br/>

<b>assume </b><a NAME="E1:24_40"/><i><font color="Green" title="E88">A65</font></i>: 
<font color="Maroon" title="c17">s1</font> <a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">.</a> <font color="Maroon" title="c22">b</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c18">s2</font> <a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">.</a> <font color="Maroon" title="c22">b</font>
 ;<br/>

<div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="24_40_1"><b>per </b></a><a class="txt" onclick="hs(this)" href="javascript:()"><b>cases </b></a><span class="hide"><a NAME="E1:24_40_1"/>
( <font color="Maroon" title="c22">b</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="scmpds_2.html#K3" title="SCMPDS_2:func.3">DataLoc</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Computation</a> <font color="Maroon" title="c17">s1</font></span>)</span> <a href="ami_1.html#K11" title="AMI_1:func.11">.</a> 1</span>)</span> <a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">.</a> <a href="scmp_gcd.html#K3" title="SCMP_GCD:func.3">SBP</a> </span>)</span>,6 or <font color="Maroon" title="c22">b</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a>  <a href="scmpds_2.html#K3" title="SCMPDS_2:func.3">DataLoc</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Computation</a> <font color="Maroon" title="c17">s1</font></span>)</span> <a href="ami_1.html#K11" title="AMI_1:func.11">.</a> 1</span>)</span> <a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">.</a> <a href="scmp_gcd.html#K3" title="SCMP_GCD:func.3">SBP</a> </span>)</span>,6 )
 </span>;<br/><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="24_40_1_1"><b>suppose </b></a><a NAME="E1:24_40_1_1"/><i><font color="Green" title="E89">A66</font></i>: 
<font color="Maroon" title="c22">b</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="scmpds_2.html#K3" title="SCMPDS_2:func.3">DataLoc</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Computation</a> <font color="Maroon" title="c17">s1</font></span>)</span> <a href="ami_1.html#K11" title="AMI_1:func.11">.</a> 1</span>)</span> <a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">.</a> <a href="scmp_gcd.html#K3" title="SCMP_GCD:func.3">SBP</a> </span>)</span>,6
 ;<br/><div class="add"><a NAME="E2:24_40_1_1"/><b>then </b><i><font color="Green" title="E90">A67</font></i>: 
<font color="Maroon" title="c22">b</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="scmpds_2.html#K3" title="SCMPDS_2:func.3">DataLoc</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Computation</a> <font color="Maroon" title="c18">s2</font></span>)</span> <a href="ami_1.html#K11" title="AMI_1:func.11">.</a> 1</span>)</span> <a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">.</a> <a href="scmp_gcd.html#K3" title="SCMP_GCD:func.3">SBP</a> </span>)</span>,6
 <b>by </b><i><a class="txt" href="scmp_gcd.html#E6:24"><i><font color="Green" title="E29">A6</font></i></a>, <a class="txt" href="scmp_gcd.html#E71:24"><i><font color="Green" title="E86">A63</font></i></a></i>;<br/><b>thus </b><span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Computation</a> <font color="Maroon" title="c17">s1</font></span>)</span> <a href="ami_1.html#K11" title="AMI_1:func.11">.</a> 2</span>)</span> <a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">.</a> <font color="Maroon" title="c22">b</font> = 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Computation</a> <font color="Maroon" title="c17">s1</font></span>)</span> <a href="ami_1.html#K11" title="AMI_1:func.11">.</a> 1</span>)</span> <a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">.</a> <span class="p1">(<span class="default"><a href="scmpds_2.html#K3" title="SCMPDS_2:func.3">DataLoc</a> <span class="p2">(<span class="default"><font color="Maroon" title="c17">s1</font> <a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">.</a> <a href="scmp_gcd.html#K3" title="SCMP_GCD:func.3">SBP</a> </span>)</span>,3</span>)</span>
<b>by </b><i><a class="txt" href="scmp_gcd.html#E3:24"><i><font color="Green" title="E26">A3</font></i></a>, <a class="txt" href="scmp_gcd.html#E14:24"><i><font color="Green" title="E37">A14</font></i></a>, <a class="txt" href="scmp_gcd.html#E15:24"><i><font color="Green" title="E38">A15</font></i></a>, <a class="txt" href="scmp_gcd.html#E1:24_40_1_1"><i><font color="Green" title="E89">A66</font></i></a>, <a class="ref" href="scmpds_2.html#T59" title="SCMPDS_2:th.59">SCMPDS_2:59</a></i>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Computation</a> <font color="Maroon" title="c18">s2</font></span>)</span> <a href="ami_1.html#K11" title="AMI_1:func.11">.</a> 1</span>)</span> <a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">.</a> <span class="p1">(<span class="default"><a href="scmpds_2.html#K3" title="SCMPDS_2:func.3">DataLoc</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Computation</a> <font color="Maroon" title="c17">s1</font></span>)</span> <a href="ami_1.html#K11" title="AMI_1:func.11">.</a> 1</span>)</span> <a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">.</a> <a href="scmp_gcd.html#K3" title="SCMP_GCD:func.3">SBP</a> </span>)</span>,3</span>)</span>
<b>by </b><i><a class="txt" href="scmp_gcd.html#E3:24"><i><font color="Green" title="E26">A3</font></i></a>, <a class="txt" href="scmp_gcd.html#E7:24"><i><font color="Green" title="E30">A7</font></i></a>, <a class="txt" href="scmp_gcd.html#E15:24"><i><font color="Green" title="E38">A15</font></i></a>, <a class="txt" href="scmp_gcd.html#E71:24"><i><font color="Green" title="E86">A63</font></i></a></i>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Computation</a> <font color="Maroon" title="c18">s2</font></span>)</span> <a href="ami_1.html#K11" title="AMI_1:func.11">.</a> 1</span>)</span> <a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">.</a> <span class="p1">(<span class="default"><a href="scmpds_2.html#K3" title="SCMPDS_2:func.3">DataLoc</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Computation</a> <font color="Maroon" title="c18">s2</font></span>)</span> <a href="ami_1.html#K11" title="AMI_1:func.11">.</a> 1</span>)</span> <a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">.</a> <a href="scmp_gcd.html#K3" title="SCMP_GCD:func.3">SBP</a> </span>)</span>,3</span>)</span>
<b>by </b><i><a class="txt" href="scmp_gcd.html#E6:24"><i><font color="Green" title="E29">A6</font></i></a>, <a class="txt" href="scmp_gcd.html#E71:24"><i><font color="Green" title="E86">A63</font></i></a></i>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Computation</a> <font color="Maroon" title="c18">s2</font></span>)</span> <a href="ami_1.html#K11" title="AMI_1:func.11">.</a> 2</span>)</span> <a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">.</a> <font color="Maroon" title="c22">b</font>
<b>by </b><i><a class="txt" href="scmp_gcd.html#E19:24"><i><font color="Green" title="E42">A19</font></i></a>, <a class="txt" href="scmp_gcd.html#E2:24_40_1_1"><i><font color="Green" title="E90">A67</font></i></a>, <a class="ref" href="scmpds_2.html#T59" title="SCMPDS_2:th.59">SCMPDS_2:59</a></i>
;<br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="24_40_1_2"><b>suppose </b></a><a NAME="E1:24_40_1_2"/><i><font color="Green" title="E89">A68</font></i>: 
<font color="Maroon" title="c22">b</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a>  <a href="scmpds_2.html#K3" title="SCMPDS_2:func.3">DataLoc</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Computation</a> <font color="Maroon" title="c17">s1</font></span>)</span> <a href="ami_1.html#K11" title="AMI_1:func.11">.</a> 1</span>)</span> <a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">.</a> <a href="scmp_gcd.html#K3" title="SCMP_GCD:func.3">SBP</a> </span>)</span>,6
 ;<br/><div class="add"><a NAME="E2:24_40_1_2"/><b>then </b><i><font color="Green" title="E90">A69</font></i>: 
<font color="Maroon" title="c22">b</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a>  <a href="scmpds_2.html#K3" title="SCMPDS_2:func.3">DataLoc</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Computation</a> <font color="Maroon" title="c18">s2</font></span>)</span> <a href="ami_1.html#K11" title="AMI_1:func.11">.</a> 1</span>)</span> <a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">.</a> <a href="scmp_gcd.html#K3" title="SCMP_GCD:func.3">SBP</a> </span>)</span>,6
 <b>by </b><i><a class="txt" href="scmp_gcd.html#E6:24"><i><font color="Green" title="E29">A6</font></i></a>, <a class="txt" href="scmp_gcd.html#E71:24"><i><font color="Green" title="E86">A63</font></i></a></i>;<br/><b>thus </b><span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Computation</a> <font color="Maroon" title="c17">s1</font></span>)</span> <a href="ami_1.html#K11" title="AMI_1:func.11">.</a> 2</span>)</span> <a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">.</a> <font color="Maroon" title="c22">b</font> = 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Computation</a> <font color="Maroon" title="c17">s1</font></span>)</span> <a href="ami_1.html#K11" title="AMI_1:func.11">.</a> 1</span>)</span> <a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">.</a> <font color="Maroon" title="c22">b</font>
<b>by </b><i><a class="txt" href="scmp_gcd.html#E14:24"><i><font color="Green" title="E37">A14</font></i></a>, <a class="txt" href="scmp_gcd.html#E1:24_40_1_2"><i><font color="Green" title="E89">A68</font></i></a>, <a class="ref" href="scmpds_2.html#T59" title="SCMPDS_2:th.59">SCMPDS_2:59</a></i>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Computation</a> <font color="Maroon" title="c18">s2</font></span>)</span> <a href="ami_1.html#K11" title="AMI_1:func.11">.</a> 1</span>)</span> <a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">.</a> <font color="Maroon" title="c22">b</font>
<b>by </b><i><a class="txt" href="scmp_gcd.html#E71:24"><i><font color="Green" title="E86">A63</font></i></a>, <a class="txt" href="scmp_gcd.html#E1:24_40"><i><font color="Green" title="E88">A65</font></i></a></i>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Computation</a> <font color="Maroon" title="c18">s2</font></span>)</span> <a href="ami_1.html#K11" title="AMI_1:func.11">.</a> 2</span>)</span> <a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">.</a> <font color="Maroon" title="c22">b</font>
<b>by </b><i><a class="txt" href="scmp_gcd.html#E19:24"><i><font color="Green" title="E42">A19</font></i></a>, <a class="txt" href="scmp_gcd.html#E2:24_40_1_2"><i><font color="Green" title="E90">A69</font></i></a>, <a class="ref" href="scmpds_2.html#T59" title="SCMPDS_2:th.59">SCMPDS_2:59</a></i>
;<br/></div><b>end;</b></div></div><b>end;</b></div>

</div><b>end;</b></div>
<div><i><font color="Green" title="E88">A70</font></i>: <a class="txt" onclick="hs2(this)" href="javascript:()" title="24_41"><b>now </b></a><div class="add"><b>let </b><font color="Maroon" title="c22">b</font> be    <a href="scmpds_2.html#M1" title="SCMPDS_2:mode.1">Int_position</a> ;<br/><b>assume </b><a NAME="E1:24_41"/><i><font color="Green" title="E89">A71</font></i>: 
<font color="Maroon" title="c17">s1</font> <a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">.</a> <font color="Maroon" title="c22">b</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c18">s2</font> <a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">.</a> <font color="Maroon" title="c22">b</font>
 ;<br/><b>set </b><font color="Maroon" title="c23">x1</font> =  <a href="scmpds_2.html#K3" title="SCMPDS_2:func.3">DataLoc</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Computation</a> <font color="Maroon" title="c17">s1</font></span>)</span> <a href="ami_1.html#K11" title="AMI_1:func.11">.</a> 2</span>)</span> <a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">.</a> <a href="scmp_gcd.html#K3" title="SCMP_GCD:func.3">SBP</a> </span>)</span>,2;<br/><b>set </b><font color="Maroon" title="c24">x2</font> =  <a href="scmpds_2.html#K3" title="SCMPDS_2:func.3">DataLoc</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Computation</a> <font color="Maroon" title="c17">s1</font></span>)</span> <a href="ami_1.html#K11" title="AMI_1:func.11">.</a> 2</span>)</span> <a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">.</a> <a href="scmp_gcd.html#K3" title="SCMP_GCD:func.3">SBP</a> </span>)</span>,3;<br/><b>set </b><font color="Maroon" title="c25">y1</font> =  <a href="scmpds_2.html#K3" title="SCMPDS_2:func.3">DataLoc</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Computation</a> <font color="Maroon" title="c18">s2</font></span>)</span> <a href="ami_1.html#K11" title="AMI_1:func.11">.</a> 2</span>)</span> <a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">.</a> <a href="scmp_gcd.html#K3" title="SCMP_GCD:func.3">SBP</a> </span>)</span>,2;<br/><b>set </b><font color="Maroon" title="c26">y2</font> =  <a href="scmpds_2.html#K3" title="SCMPDS_2:func.3">DataLoc</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Computation</a> <font color="Maroon" title="c18">s2</font></span>)</span> <a href="ami_1.html#K11" title="AMI_1:func.11">.</a> 2</span>)</span> <a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">.</a> <a href="scmp_gcd.html#K3" title="SCMP_GCD:func.3">SBP</a> </span>)</span>,3;<br/><a NAME="E2:24_41"/><i><font color="Green" title="E90">A72</font></i>: 
 <a href="scmpds_2.html#K3" title="SCMPDS_2:func.3">DataLoc</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Computation</a> <font color="Maroon" title="c17">s1</font></span>)</span> <a href="ami_1.html#K11" title="AMI_1:func.11">.</a> 2</span>)</span> <a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">.</a> <a href="scmp_gcd.html#K3" title="SCMP_GCD:func.3">SBP</a> </span>)</span>,2 <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="scmpds_2.html#K3" title="SCMPDS_2:func.3">DataLoc</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Computation</a> <font color="Maroon" title="c18">s2</font></span>)</span> <a href="ami_1.html#K11" title="AMI_1:func.11">.</a> 2</span>)</span> <a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">.</a> <a href="scmp_gcd.html#K3" title="SCMP_GCD:func.3">SBP</a> </span>)</span>,2
 <b>by </b><i><a class="txt" href="scmp_gcd.html#E6:24"><i><font color="Green" title="E29">A6</font></i></a>, <a class="txt" href="scmp_gcd.html#E72:24"><i><font color="Green" title="E87">A64</font></i></a></i>;<br/><a NAME="E3:24_41"/><i><font color="Green" title="E91">A73</font></i>: 
 <a href="scmpds_2.html#K3" title="SCMPDS_2:func.3">DataLoc</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Computation</a> <font color="Maroon" title="c17">s1</font></span>)</span> <a href="ami_1.html#K11" title="AMI_1:func.11">.</a> 2</span>)</span> <a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">.</a> <a href="scmp_gcd.html#K3" title="SCMP_GCD:func.3">SBP</a> </span>)</span>,3 <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="scmpds_2.html#K3" title="SCMPDS_2:func.3">DataLoc</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Computation</a> <font color="Maroon" title="c18">s2</font></span>)</span> <a href="ami_1.html#K11" title="AMI_1:func.11">.</a> 2</span>)</span> <a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">.</a> <a href="scmp_gcd.html#K3" title="SCMP_GCD:func.3">SBP</a> </span>)</span>,3
 <b>by </b><i><a class="txt" href="scmp_gcd.html#E6:24"><i><font color="Green" title="E29">A6</font></i></a>, <a class="txt" href="scmp_gcd.html#E72:24"><i><font color="Green" title="E87">A64</font></i></a></i>;<br/><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="24_41_1"><b>per </b></a><a class="txt" onclick="hs(this)" href="javascript:()"><b>cases </b></a><span class="hide"><a NAME="E1:24_41_1"/>
( ( <font color="Maroon" title="c22">b</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a>  <a href="scmpds_2.html#K3" title="SCMPDS_2:func.3">DataLoc</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Computation</a> <font color="Maroon" title="c17">s1</font></span>)</span> <a href="ami_1.html#K11" title="AMI_1:func.11">.</a> 2</span>)</span> <a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">.</a> <a href="scmp_gcd.html#K3" title="SCMP_GCD:func.3">SBP</a> </span>)</span>,2 &amp; <font color="Maroon" title="c22">b</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a>  <a href="scmpds_2.html#K3" title="SCMPDS_2:func.3">DataLoc</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Computation</a> <font color="Maroon" title="c17">s1</font></span>)</span> <a href="ami_1.html#K11" title="AMI_1:func.11">.</a> 2</span>)</span> <a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">.</a> <a href="scmp_gcd.html#K3" title="SCMP_GCD:func.3">SBP</a> </span>)</span>,3 ) or <font color="Maroon" title="c22">b</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="scmpds_2.html#K3" title="SCMPDS_2:func.3">DataLoc</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Computation</a> <font color="Maroon" title="c17">s1</font></span>)</span> <a href="ami_1.html#K11" title="AMI_1:func.11">.</a> 2</span>)</span> <a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">.</a> <a href="scmp_gcd.html#K3" title="SCMP_GCD:func.3">SBP</a> </span>)</span>,2 or <font color="Maroon" title="c22">b</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="scmpds_2.html#K3" title="SCMPDS_2:func.3">DataLoc</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Computation</a> <font color="Maroon" title="c17">s1</font></span>)</span> <a href="ami_1.html#K11" title="AMI_1:func.11">.</a> 2</span>)</span> <a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">.</a> <a href="scmp_gcd.html#K3" title="SCMP_GCD:func.3">SBP</a> </span>)</span>,3 )
 </span>;<br/><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="24_41_1_1"><b>suppose </b></a><a NAME="E1:24_41_1_1"/><i><font color="Green" title="E92">A74</font></i>: 
( <font color="Maroon" title="c22">b</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a>  <a href="scmpds_2.html#K3" title="SCMPDS_2:func.3">DataLoc</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Computation</a> <font color="Maroon" title="c17">s1</font></span>)</span> <a href="ami_1.html#K11" title="AMI_1:func.11">.</a> 2</span>)</span> <a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">.</a> <a href="scmp_gcd.html#K3" title="SCMP_GCD:func.3">SBP</a> </span>)</span>,2 &amp; <font color="Maroon" title="c22">b</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a>  <a href="scmpds_2.html#K3" title="SCMPDS_2:func.3">DataLoc</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Computation</a> <font color="Maroon" title="c17">s1</font></span>)</span> <a href="ami_1.html#K11" title="AMI_1:func.11">.</a> 2</span>)</span> <a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">.</a> <a href="scmp_gcd.html#K3" title="SCMP_GCD:func.3">SBP</a> </span>)</span>,3 )
 ;<br/><div class="add"><b>hence </b><span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Computation</a> <font color="Maroon" title="c17">s1</font></span>)</span> <a href="ami_1.html#K11" title="AMI_1:func.11">.</a> 3</span>)</span> <a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">.</a> <font color="Maroon" title="c22">b</font> = 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Computation</a> <font color="Maroon" title="c17">s1</font></span>)</span> <a href="ami_1.html#K11" title="AMI_1:func.11">.</a> 2</span>)</span> <a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">.</a> <font color="Maroon" title="c22">b</font>
<b>by </b><i><a class="txt" href="scmp_gcd.html#E22:24"><i><font color="Green" title="E45">A22</font></i></a>, <a class="ref" href="scmpds_2.html#T64" title="SCMPDS_2:th.64">SCMPDS_2:64</a></i>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Computation</a> <font color="Maroon" title="c18">s2</font></span>)</span> <a href="ami_1.html#K11" title="AMI_1:func.11">.</a> 2</span>)</span> <a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">.</a> <font color="Maroon" title="c22">b</font>
<b>by </b><i><a class="txt" href="scmp_gcd.html#E72:24"><i><font color="Green" title="E87">A64</font></i></a>, <a class="txt" href="scmp_gcd.html#E1:24_41"><i><font color="Green" title="E89">A71</font></i></a></i>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Computation</a> <font color="Maroon" title="c18">s2</font></span>)</span> <a href="ami_1.html#K11" title="AMI_1:func.11">.</a> 3</span>)</span> <a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">.</a> <font color="Maroon" title="c22">b</font>
<b>by </b><i><a class="txt" href="scmp_gcd.html#E30:24"><i><font color="Green" title="E51">A28</font></i></a>, <a class="txt" href="scmp_gcd.html#E2:24_41"><i><font color="Green" title="E90">A72</font></i></a>, <a class="txt" href="scmp_gcd.html#E3:24_41"><i><font color="Green" title="E91">A73</font></i></a>, <a class="txt" href="scmp_gcd.html#E1:24_41_1_1"><i><font color="Green" title="E92">A74</font></i></a>, <a class="ref" href="scmpds_2.html#T64" title="SCMPDS_2:th.64">SCMPDS_2:64</a></i>
;<br/><br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="24_41_1_2"><b>suppose </b></a><a NAME="E1:24_41_1_2"/><i><font color="Green" title="E92">A75</font></i>: 
<font color="Maroon" title="c22">b</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="scmpds_2.html#K3" title="SCMPDS_2:func.3">DataLoc</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Computation</a> <font color="Maroon" title="c17">s1</font></span>)</span> <a href="ami_1.html#K11" title="AMI_1:func.11">.</a> 2</span>)</span> <a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">.</a> <a href="scmp_gcd.html#K3" title="SCMP_GCD:func.3">SBP</a> </span>)</span>,2
 ;<br/><div class="add"><a NAME="E2:24_41_1_2"/><i><font color="Green" title="E93">A76</font></i>: 
<font color="Maroon" title="c16">n</font> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 2 <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c16">n</font> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 3
 ;<br/><a NAME="E3:24_41_1_2"/><b>then </b><i><font color="Green" title="E94">A77</font></i>: 
 <a href="scmpds_2.html#K3" title="SCMPDS_2:func.3">DataLoc</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Computation</a> <font color="Maroon" title="c17">s1</font></span>)</span> <a href="ami_1.html#K11" title="AMI_1:func.11">.</a> 2</span>)</span> <a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">.</a> <a href="scmp_gcd.html#K3" title="SCMP_GCD:func.3">SBP</a> </span>)</span>,2 <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a>  <a href="scmpds_2.html#K3" title="SCMPDS_2:func.3">DataLoc</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Computation</a> <font color="Maroon" title="c17">s1</font></span>)</span> <a href="ami_1.html#K11" title="AMI_1:func.11">.</a> 2</span>)</span> <a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">.</a> <a href="scmp_gcd.html#K3" title="SCMP_GCD:func.3">SBP</a> </span>)</span>,3
 <b>by </b><i><a class="txt" href="scmp_gcd.html#E34:24"><i><font color="Green" title="E55">A32</font></i></a>, <a class="txt" href="scmp_gcd.html#E36:24"><i><font color="Green" title="E57">A34</font></i></a>, <a class="txt" href="scmp_gcd.html#E6"><i><font color="Green" title="E4">Lm2</font></i></a></i>;<br/><a NAME="E4:24_41_1_2"/><i><font color="Green" title="E95">A78</font></i>: 
 <a href="scmpds_2.html#K3" title="SCMPDS_2:func.3">DataLoc</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Computation</a> <font color="Maroon" title="c18">s2</font></span>)</span> <a href="ami_1.html#K11" title="AMI_1:func.11">.</a> 2</span>)</span> <a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">.</a> <a href="scmp_gcd.html#K3" title="SCMP_GCD:func.3">SBP</a> </span>)</span>,2 <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a>  <a href="scmpds_2.html#K3" title="SCMPDS_2:func.3">DataLoc</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Computation</a> <font color="Maroon" title="c18">s2</font></span>)</span> <a href="ami_1.html#K11" title="AMI_1:func.11">.</a> 2</span>)</span> <a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">.</a> <a href="scmp_gcd.html#K3" title="SCMP_GCD:func.3">SBP</a> </span>)</span>,3
 <b>by </b><i><a class="txt" href="scmp_gcd.html#E34:24"><i><font color="Green" title="E55">A32</font></i></a>, <a class="txt" href="scmp_gcd.html#E36:24"><i><font color="Green" title="E57">A34</font></i></a>, <a class="txt" href="scmp_gcd.html#E2:24_41"><i><font color="Green" title="E90">A72</font></i></a>, <a class="txt" href="scmp_gcd.html#E3:24_41"><i><font color="Green" title="E91">A73</font></i></a>, <a class="txt" href="scmp_gcd.html#E2:24_41_1_2"><i><font color="Green" title="E93">A76</font></i></a>, <a class="txt" href="scmp_gcd.html#E6"><i><font color="Green" title="E4">Lm2</font></i></a></i>;<br/><b>thus </b><span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Computation</a> <font color="Maroon" title="c17">s1</font></span>)</span> <a href="ami_1.html#K11" title="AMI_1:func.11">.</a> 3</span>)</span> <a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">.</a> <font color="Maroon" title="c22">b</font> = 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Computation</a> <font color="Maroon" title="c17">s1</font></span>)</span> <a href="ami_1.html#K11" title="AMI_1:func.11">.</a> 2</span>)</span> <a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">.</a> <span class="p2">(<span class="default"><a href="scmpds_2.html#K3" title="SCMPDS_2:func.3">DataLoc</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Computation</a> <font color="Maroon" title="c17">s1</font></span>)</span> <a href="ami_1.html#K11" title="AMI_1:func.11">.</a> 2</span>)</span> <a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">.</a> <a href="scmp_gcd.html#K3" title="SCMP_GCD:func.3">SBP</a> </span>)</span>,2</span>)</span></span>)</span> <a href="int_1.html#K5" title="INT_1:func.5">div</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Computation</a> <font color="Maroon" title="c17">s1</font></span>)</span> <a href="ami_1.html#K11" title="AMI_1:func.11">.</a> 2</span>)</span> <a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">.</a> <span class="p2">(<span class="default"><a href="scmpds_2.html#K3" title="SCMPDS_2:func.3">DataLoc</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Computation</a> <font color="Maroon" title="c17">s1</font></span>)</span> <a href="ami_1.html#K11" title="AMI_1:func.11">.</a> 2</span>)</span> <a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">.</a> <a href="scmp_gcd.html#K3" title="SCMP_GCD:func.3">SBP</a> </span>)</span>,3</span>)</span></span>)</span>
<b>by </b><i><a class="txt" href="scmp_gcd.html#E22:24"><i><font color="Green" title="E45">A22</font></i></a>, <a class="txt" href="scmp_gcd.html#E1:24_41_1_2"><i><font color="Green" title="E92">A75</font></i></a>, <a class="txt" href="scmp_gcd.html#E3:24_41_1_2"><i><font color="Green" title="E94">A77</font></i></a>, <a class="ref" href="scmpds_2.html#T64" title="SCMPDS_2:th.64">SCMPDS_2:64</a></i>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Computation</a> <font color="Maroon" title="c18">s2</font></span>)</span> <a href="ami_1.html#K11" title="AMI_1:func.11">.</a> 2</span>)</span> <a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">.</a> <span class="p2">(<span class="default"><a href="scmpds_2.html#K3" title="SCMPDS_2:func.3">DataLoc</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Computation</a> <font color="Maroon" title="c17">s1</font></span>)</span> <a href="ami_1.html#K11" title="AMI_1:func.11">.</a> 2</span>)</span> <a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">.</a> <a href="scmp_gcd.html#K3" title="SCMP_GCD:func.3">SBP</a> </span>)</span>,2</span>)</span></span>)</span> <a href="int_1.html#K5" title="INT_1:func.5">div</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Computation</a> <font color="Maroon" title="c17">s1</font></span>)</span> <a href="ami_1.html#K11" title="AMI_1:func.11">.</a> 2</span>)</span> <a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">.</a> <span class="p2">(<span class="default"><a href="scmpds_2.html#K3" title="SCMPDS_2:func.3">DataLoc</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Computation</a> <font color="Maroon" title="c17">s1</font></span>)</span> <a href="ami_1.html#K11" title="AMI_1:func.11">.</a> 2</span>)</span> <a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">.</a> <a href="scmp_gcd.html#K3" title="SCMP_GCD:func.3">SBP</a> </span>)</span>,3</span>)</span></span>)</span>
<b>by </b><i><a class="txt" href="scmp_gcd.html#E3:24"><i><font color="Green" title="E26">A3</font></i></a>, <a class="txt" href="scmp_gcd.html#E7:24"><i><font color="Green" title="E30">A7</font></i></a>, <a class="txt" href="scmp_gcd.html#E25:24"><i><font color="Green" title="E47">A24</font></i></a>, <a class="txt" href="scmp_gcd.html#E72:24"><i><font color="Green" title="E87">A64</font></i></a></i>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Computation</a> <font color="Maroon" title="c18">s2</font></span>)</span> <a href="ami_1.html#K11" title="AMI_1:func.11">.</a> 2</span>)</span> <a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">.</a> <span class="p2">(<span class="default"><a href="scmpds_2.html#K3" title="SCMPDS_2:func.3">DataLoc</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Computation</a> <font color="Maroon" title="c17">s1</font></span>)</span> <a href="ami_1.html#K11" title="AMI_1:func.11">.</a> 2</span>)</span> <a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">.</a> <a href="scmp_gcd.html#K3" title="SCMP_GCD:func.3">SBP</a> </span>)</span>,2</span>)</span></span>)</span> <a href="int_1.html#K5" title="INT_1:func.5">div</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Computation</a> <font color="Maroon" title="c18">s2</font></span>)</span> <a href="ami_1.html#K11" title="AMI_1:func.11">.</a> 2</span>)</span> <a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">.</a> <span class="p2">(<span class="default"><a href="scmpds_2.html#K3" title="SCMPDS_2:func.3">DataLoc</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Computation</a> <font color="Maroon" title="c17">s1</font></span>)</span> <a href="ami_1.html#K11" title="AMI_1:func.11">.</a> 2</span>)</span> <a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">.</a> <a href="scmp_gcd.html#K3" title="SCMP_GCD:func.3">SBP</a> </span>)</span>,3</span>)</span></span>)</span>
<b>by </b><i><a class="txt" href="scmp_gcd.html#E3:24"><i><font color="Green" title="E26">A3</font></i></a>, <a class="txt" href="scmp_gcd.html#E7:24"><i><font color="Green" title="E30">A7</font></i></a>, <a class="txt" href="scmp_gcd.html#E25:24"><i><font color="Green" title="E47">A24</font></i></a>, <a class="txt" href="scmp_gcd.html#E72:24"><i><font color="Green" title="E87">A64</font></i></a></i>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Computation</a> <font color="Maroon" title="c18">s2</font></span>)</span> <a href="ami_1.html#K11" title="AMI_1:func.11">.</a> 3</span>)</span> <a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">.</a> <font color="Maroon" title="c22">b</font>
<b>by </b><i><a class="txt" href="scmp_gcd.html#E30:24"><i><font color="Green" title="E51">A28</font></i></a>, <a class="txt" href="scmp_gcd.html#E2:24_41"><i><font color="Green" title="E90">A72</font></i></a>, <a class="txt" href="scmp_gcd.html#E3:24_41"><i><font color="Green" title="E91">A73</font></i></a>, <a class="txt" href="scmp_gcd.html#E1:24_41_1_2"><i><font color="Green" title="E92">A75</font></i></a>, <a class="txt" href="scmp_gcd.html#E4:24_41_1_2"><i><font color="Green" title="E95">A78</font></i></a>, <a class="ref" href="scmpds_2.html#T64" title="SCMPDS_2:th.64">SCMPDS_2:64</a></i>
;<br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="24_41_1_3"><b>suppose </b></a><a NAME="E1:24_41_1_3"/><i><font color="Green" title="E92">A79</font></i>: 
<font color="Maroon" title="c22">b</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="scmpds_2.html#K3" title="SCMPDS_2:func.3">DataLoc</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Computation</a> <font color="Maroon" title="c17">s1</font></span>)</span> <a href="ami_1.html#K11" title="AMI_1:func.11">.</a> 2</span>)</span> <a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">.</a> <a href="scmp_gcd.html#K3" title="SCMP_GCD:func.3">SBP</a> </span>)</span>,3
 ;<br/><div class="add"><b>hence </b><span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Computation</a> <font color="Maroon" title="c17">s1</font></span>)</span> <a href="ami_1.html#K11" title="AMI_1:func.11">.</a> 3</span>)</span> <a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">.</a> <font color="Maroon" title="c22">b</font> = 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Computation</a> <font color="Maroon" title="c17">s1</font></span>)</span> <a href="ami_1.html#K11" title="AMI_1:func.11">.</a> 2</span>)</span> <a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">.</a> <span class="p2">(<span class="default"><a href="scmpds_2.html#K3" title="SCMPDS_2:func.3">DataLoc</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Computation</a> <font color="Maroon" title="c17">s1</font></span>)</span> <a href="ami_1.html#K11" title="AMI_1:func.11">.</a> 2</span>)</span> <a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">.</a> <a href="scmp_gcd.html#K3" title="SCMP_GCD:func.3">SBP</a> </span>)</span>,2</span>)</span></span>)</span> <a href="int_1.html#K6" title="INT_1:func.6">mod</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Computation</a> <font color="Maroon" title="c17">s1</font></span>)</span> <a href="ami_1.html#K11" title="AMI_1:func.11">.</a> 2</span>)</span> <a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">.</a> <span class="p2">(<span class="default"><a href="scmpds_2.html#K3" title="SCMPDS_2:func.3">DataLoc</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Computation</a> <font color="Maroon" title="c17">s1</font></span>)</span> <a href="ami_1.html#K11" title="AMI_1:func.11">.</a> 2</span>)</span> <a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">.</a> <a href="scmp_gcd.html#K3" title="SCMP_GCD:func.3">SBP</a> </span>)</span>,3</span>)</span></span>)</span>
<b>by </b><i><a class="txt" href="scmp_gcd.html#E22:24"><i><font color="Green" title="E45">A22</font></i></a>, <a class="ref" href="scmpds_2.html#T64" title="SCMPDS_2:th.64">SCMPDS_2:64</a></i>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Computation</a> <font color="Maroon" title="c18">s2</font></span>)</span> <a href="ami_1.html#K11" title="AMI_1:func.11">.</a> 2</span>)</span> <a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">.</a> <span class="p2">(<span class="default"><a href="scmpds_2.html#K3" title="SCMPDS_2:func.3">DataLoc</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Computation</a> <font color="Maroon" title="c17">s1</font></span>)</span> <a href="ami_1.html#K11" title="AMI_1:func.11">.</a> 2</span>)</span> <a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">.</a> <a href="scmp_gcd.html#K3" title="SCMP_GCD:func.3">SBP</a> </span>)</span>,2</span>)</span></span>)</span> <a href="int_1.html#K6" title="INT_1:func.6">mod</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Computation</a> <font color="Maroon" title="c17">s1</font></span>)</span> <a href="ami_1.html#K11" title="AMI_1:func.11">.</a> 2</span>)</span> <a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">.</a> <span class="p2">(<span class="default"><a href="scmpds_2.html#K3" title="SCMPDS_2:func.3">DataLoc</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Computation</a> <font color="Maroon" title="c17">s1</font></span>)</span> <a href="ami_1.html#K11" title="AMI_1:func.11">.</a> 2</span>)</span> <a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">.</a> <a href="scmp_gcd.html#K3" title="SCMP_GCD:func.3">SBP</a> </span>)</span>,3</span>)</span></span>)</span>
<b>by </b><i><a class="txt" href="scmp_gcd.html#E3:24"><i><font color="Green" title="E26">A3</font></i></a>, <a class="txt" href="scmp_gcd.html#E7:24"><i><font color="Green" title="E30">A7</font></i></a>, <a class="txt" href="scmp_gcd.html#E25:24"><i><font color="Green" title="E47">A24</font></i></a>, <a class="txt" href="scmp_gcd.html#E72:24"><i><font color="Green" title="E87">A64</font></i></a></i>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Computation</a> <font color="Maroon" title="c18">s2</font></span>)</span> <a href="ami_1.html#K11" title="AMI_1:func.11">.</a> 2</span>)</span> <a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">.</a> <span class="p2">(<span class="default"><a href="scmpds_2.html#K3" title="SCMPDS_2:func.3">DataLoc</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Computation</a> <font color="Maroon" title="c17">s1</font></span>)</span> <a href="ami_1.html#K11" title="AMI_1:func.11">.</a> 2</span>)</span> <a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">.</a> <a href="scmp_gcd.html#K3" title="SCMP_GCD:func.3">SBP</a> </span>)</span>,2</span>)</span></span>)</span> <a href="int_1.html#K6" title="INT_1:func.6">mod</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Computation</a> <font color="Maroon" title="c18">s2</font></span>)</span> <a href="ami_1.html#K11" title="AMI_1:func.11">.</a> 2</span>)</span> <a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">.</a> <span class="p2">(<span class="default"><a href="scmpds_2.html#K3" title="SCMPDS_2:func.3">DataLoc</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Computation</a> <font color="Maroon" title="c17">s1</font></span>)</span> <a href="ami_1.html#K11" title="AMI_1:func.11">.</a> 2</span>)</span> <a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">.</a> <a href="scmp_gcd.html#K3" title="SCMP_GCD:func.3">SBP</a> </span>)</span>,3</span>)</span></span>)</span>
<b>by </b><i><a class="txt" href="scmp_gcd.html#E3:24"><i><font color="Green" title="E26">A3</font></i></a>, <a class="txt" href="scmp_gcd.html#E7:24"><i><font color="Green" title="E30">A7</font></i></a>, <a class="txt" href="scmp_gcd.html#E25:24"><i><font color="Green" title="E47">A24</font></i></a>, <a class="txt" href="scmp_gcd.html#E72:24"><i><font color="Green" title="E87">A64</font></i></a></i>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Computation</a> <font color="Maroon" title="c18">s2</font></span>)</span> <a href="ami_1.html#K11" title="AMI_1:func.11">.</a> 3</span>)</span> <a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">.</a> <font color="Maroon" title="c22">b</font>
<b>by </b><i><a class="txt" href="scmp_gcd.html#E30:24"><i><font color="Green" title="E51">A28</font></i></a>, <a class="txt" href="scmp_gcd.html#E2:24_41"><i><font color="Green" title="E90">A72</font></i></a>, <a class="txt" href="scmp_gcd.html#E3:24_41"><i><font color="Green" title="E91">A73</font></i></a>, <a class="txt" href="scmp_gcd.html#E1:24_41_1_3"><i><font color="Green" title="E92">A79</font></i></a>, <a class="ref" href="scmpds_2.html#T64" title="SCMPDS_2:th.64">SCMPDS_2:64</a></i>
;<br/><br/></div><b>end;</b></div></div><b>end;</b></div></div><b>end;</b></div>
<div><i><font color="Green" title="E89">A80</font></i>: <a class="txt" onclick="hs2(this)" href="javascript:()" title="24_42"><b>now </b></a><div class="add"><b>let </b><font color="Maroon" title="c22">b</font> be    <a href="scmpds_2.html#M1" title="SCMPDS_2:mode.1">Int_position</a> ;<br/><b>assume </b><a NAME="E1:24_42"/><i><font color="Green" title="E90">A81</font></i>: 
<font color="Maroon" title="c17">s1</font> <a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">.</a> <font color="Maroon" title="c22">b</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c18">s2</font> <a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">.</a> <font color="Maroon" title="c22">b</font>
 ;<br/><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="24_42_1"><b>per </b></a><a class="txt" onclick="hs(this)" href="javascript:()"><b>cases </b></a><span class="hide"><a NAME="E1:24_42_1"/>
( <font color="Maroon" title="c22">b</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="scmpds_2.html#K3" title="SCMPDS_2:func.3">DataLoc</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Computation</a> <font color="Maroon" title="c17">s1</font></span>)</span> <a href="ami_1.html#K11" title="AMI_1:func.11">.</a> 3</span>)</span> <a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">.</a> <a href="scmp_gcd.html#K3" title="SCMP_GCD:func.3">SBP</a> </span>)</span>,7 or <font color="Maroon" title="c22">b</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a>  <a href="scmpds_2.html#K3" title="SCMPDS_2:func.3">DataLoc</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Computation</a> <font color="Maroon" title="c17">s1</font></span>)</span> <a href="ami_1.html#K11" title="AMI_1:func.11">.</a> 3</span>)</span> <a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">.</a> <a href="scmp_gcd.html#K3" title="SCMP_GCD:func.3">SBP</a> </span>)</span>,7 )
 </span>;<br/><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="24_42_1_1"><b>suppose </b></a><a NAME="E1:24_42_1_1"/><i><font color="Green" title="E91">A82</font></i>: 
<font color="Maroon" title="c22">b</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="scmpds_2.html#K3" title="SCMPDS_2:func.3">DataLoc</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Computation</a> <font color="Maroon" title="c17">s1</font></span>)</span> <a href="ami_1.html#K11" title="AMI_1:func.11">.</a> 3</span>)</span> <a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">.</a> <a href="scmp_gcd.html#K3" title="SCMP_GCD:func.3">SBP</a> </span>)</span>,7
 ;<br/><div class="add"><a NAME="E2:24_42_1_1"/><b>then </b><i><font color="Green" title="E92">A83</font></i>: 
<font color="Maroon" title="c22">b</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="scmpds_2.html#K3" title="SCMPDS_2:func.3">DataLoc</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Computation</a> <font color="Maroon" title="c18">s2</font></span>)</span> <a href="ami_1.html#K11" title="AMI_1:func.11">.</a> 3</span>)</span> <a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">.</a> <a href="scmp_gcd.html#K3" title="SCMP_GCD:func.3">SBP</a> </span>)</span>,7
 <b>by </b><i><a class="txt" href="scmp_gcd.html#E6:24"><i><font color="Green" title="E29">A6</font></i></a>, <a class="txt" href="scmp_gcd.html#E73:24"><i><font color="Green" title="E88">A70</font></i></a></i>;<br/><b>thus </b><span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Computation</a> <font color="Maroon" title="c17">s1</font></span>)</span> <a href="ami_1.html#K11" title="AMI_1:func.11">.</a> 4</span>)</span> <a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">.</a> <font color="Maroon" title="c22">b</font> = 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Computation</a> <font color="Maroon" title="c17">s1</font></span>)</span> <a href="ami_1.html#K11" title="AMI_1:func.11">.</a> 3</span>)</span> <a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">.</a> <span class="p1">(<span class="default"><a href="scmpds_2.html#K3" title="SCMPDS_2:func.3">DataLoc</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Computation</a> <font color="Maroon" title="c17">s1</font></span>)</span> <a href="ami_1.html#K11" title="AMI_1:func.11">.</a> 3</span>)</span> <a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">.</a> <a href="scmp_gcd.html#K3" title="SCMP_GCD:func.3">SBP</a> </span>)</span>,3</span>)</span>
<b>by </b><i><a class="txt" href="scmp_gcd.html#E33:24"><i><font color="Green" title="E54">A31</font></i></a>, <a class="txt" href="scmp_gcd.html#E1:24_42_1_1"><i><font color="Green" title="E91">A82</font></i></a>, <a class="ref" href="scmpds_2.html#T59" title="SCMPDS_2:th.59">SCMPDS_2:59</a></i>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Computation</a> <font color="Maroon" title="c18">s2</font></span>)</span> <a href="ami_1.html#K11" title="AMI_1:func.11">.</a> 3</span>)</span> <a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">.</a> <span class="p1">(<span class="default"><a href="scmpds_2.html#K3" title="SCMPDS_2:func.3">DataLoc</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Computation</a> <font color="Maroon" title="c17">s1</font></span>)</span> <a href="ami_1.html#K11" title="AMI_1:func.11">.</a> 3</span>)</span> <a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">.</a> <a href="scmp_gcd.html#K3" title="SCMP_GCD:func.3">SBP</a> </span>)</span>,3</span>)</span>
<b>by </b><i><a class="txt" href="scmp_gcd.html#E3:24"><i><font color="Green" title="E26">A3</font></i></a>, <a class="txt" href="scmp_gcd.html#E7:24"><i><font color="Green" title="E30">A7</font></i></a>, <a class="txt" href="scmp_gcd.html#E38:24"><i><font color="Green" title="E58">A35</font></i></a>, <a class="txt" href="scmp_gcd.html#E73:24"><i><font color="Green" title="E88">A70</font></i></a></i>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Computation</a> <font color="Maroon" title="c18">s2</font></span>)</span> <a href="ami_1.html#K11" title="AMI_1:func.11">.</a> 3</span>)</span> <a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">.</a> <span class="p1">(<span class="default"><a href="scmpds_2.html#K3" title="SCMPDS_2:func.3">DataLoc</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Computation</a> <font color="Maroon" title="c18">s2</font></span>)</span> <a href="ami_1.html#K11" title="AMI_1:func.11">.</a> 3</span>)</span> <a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">.</a> <a href="scmp_gcd.html#K3" title="SCMP_GCD:func.3">SBP</a> </span>)</span>,3</span>)</span>
<b>by </b><i><a class="txt" href="scmp_gcd.html#E6:24"><i><font color="Green" title="E29">A6</font></i></a>, <a class="txt" href="scmp_gcd.html#E73:24"><i><font color="Green" title="E88">A70</font></i></a></i>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Computation</a> <font color="Maroon" title="c18">s2</font></span>)</span> <a href="ami_1.html#K11" title="AMI_1:func.11">.</a> 4</span>)</span> <a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">.</a> <font color="Maroon" title="c22">b</font>
<b>by </b><i><a class="txt" href="scmp_gcd.html#E44:24"><i><font color="Green" title="E63">A40</font></i></a>, <a class="txt" href="scmp_gcd.html#E2:24_42_1_1"><i><font color="Green" title="E92">A83</font></i></a>, <a class="ref" href="scmpds_2.html#T59" title="SCMPDS_2:th.59">SCMPDS_2:59</a></i>
;<br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="24_42_1_2"><b>suppose </b></a><a NAME="E1:24_42_1_2"/><i><font color="Green" title="E91">A84</font></i>: 
<font color="Maroon" title="c22">b</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a>  <a href="scmpds_2.html#K3" title="SCMPDS_2:func.3">DataLoc</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Computation</a> <font color="Maroon" title="c17">s1</font></span>)</span> <a href="ami_1.html#K11" title="AMI_1:func.11">.</a> 3</span>)</span> <a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">.</a> <a href="scmp_gcd.html#K3" title="SCMP_GCD:func.3">SBP</a> </span>)</span>,7
 ;<br/><div class="add"><a NAME="E2:24_42_1_2"/><b>then </b><i><font color="Green" title="E92">A85</font></i>: 
<font color="Maroon" title="c22">b</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a>  <a href="scmpds_2.html#K3" title="SCMPDS_2:func.3">DataLoc</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Computation</a> <font color="Maroon" title="c18">s2</font></span>)</span> <a href="ami_1.html#K11" title="AMI_1:func.11">.</a> 3</span>)</span> <a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">.</a> <a href="scmp_gcd.html#K3" title="SCMP_GCD:func.3">SBP</a> </span>)</span>,7
 <b>by </b><i><a class="txt" href="scmp_gcd.html#E6:24"><i><font color="Green" title="E29">A6</font></i></a>, <a class="txt" href="scmp_gcd.html#E73:24"><i><font color="Green" title="E88">A70</font></i></a></i>;<br/><b>thus </b><span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Computation</a> <font color="Maroon" title="c17">s1</font></span>)</span> <a href="ami_1.html#K11" title="AMI_1:func.11">.</a> 4</span>)</span> <a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">.</a> <font color="Maroon" title="c22">b</font> = 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Computation</a> <font color="Maroon" title="c17">s1</font></span>)</span> <a href="ami_1.html#K11" title="AMI_1:func.11">.</a> 3</span>)</span> <a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">.</a> <font color="Maroon" title="c22">b</font>
<b>by </b><i><a class="txt" href="scmp_gcd.html#E33:24"><i><font color="Green" title="E54">A31</font></i></a>, <a class="txt" href="scmp_gcd.html#E1:24_42_1_2"><i><font color="Green" title="E91">A84</font></i></a>, <a class="ref" href="scmpds_2.html#T59" title="SCMPDS_2:th.59">SCMPDS_2:59</a></i>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Computation</a> <font color="Maroon" title="c18">s2</font></span>)</span> <a href="ami_1.html#K11" title="AMI_1:func.11">.</a> 3</span>)</span> <a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">.</a> <font color="Maroon" title="c22">b</font>
<b>by </b><i><a class="txt" href="scmp_gcd.html#E73:24"><i><font color="Green" title="E88">A70</font></i></a>, <a class="txt" href="scmp_gcd.html#E1:24_42"><i><font color="Green" title="E90">A81</font></i></a></i>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Computation</a> <font color="Maroon" title="c18">s2</font></span>)</span> <a href="ami_1.html#K11" title="AMI_1:func.11">.</a> 4</span>)</span> <a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">.</a> <font color="Maroon" title="c22">b</font>
<b>by </b><i><a class="txt" href="scmp_gcd.html#E44:24"><i><font color="Green" title="E63">A40</font></i></a>, <a class="txt" href="scmp_gcd.html#E2:24_42_1_2"><i><font color="Green" title="E92">A85</font></i></a>, <a class="ref" href="scmpds_2.html#T59" title="SCMPDS_2:th.59">SCMPDS_2:59</a></i>
;<br/></div><b>end;</b></div></div><b>end;</b></div></div><b>end;</b></div>
<div><i><font color="Green" title="E90">A86</font></i>: <a class="txt" onclick="hs2(this)" href="javascript:()" title="24_43"><b>now </b></a><div class="add"><b>let </b><font color="Maroon" title="c22">b</font> be    <a href="scmpds_2.html#M1" title="SCMPDS_2:mode.1">Int_position</a> ;<br/><b>assume </b><a NAME="E1:24_43"/><i><font color="Green" title="E91">A87</font></i>: 
<font color="Maroon" title="c17">s1</font> <a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">.</a> <font color="Maroon" title="c22">b</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c18">s2</font> <a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">.</a> <font color="Maroon" title="c22">b</font>
 ;<br/><i><font color="Green" title="E92">A88</font></i>: <font color="Maroon" title="c17">s1</font> <a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">.</a> <span class="p1">(<span class="default"><a href="scmpds_2.html#K3" title="SCMPDS_2:func.3">DataLoc</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Computation</a> <font color="Maroon" title="c17">s1</font></span>)</span> <a href="ami_1.html#K11" title="AMI_1:func.11">.</a> 4</span>)</span> <a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">.</a> <a href="scmp_gcd.html#K2" title="SCMP_GCD:func.2">GBP</a> </span>)</span>,1</span>)</span> = 
<font color="Maroon" title="c18">s2</font> <a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">.</a> <span class="p1">(<span class="default"><a href="scmp_gcd.html#K1" title="SCMP_GCD:func.1">intpos</a> <span class="p2">(<span class="default">0 <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1</span>)</span></span>)</span>
<b>by </b><i><a class="txt" href="scmp_gcd.html#E6:24"><i><font color="Green" title="E29">A6</font></i></a>, <a class="txt" href="scmp_gcd.html#E52:24"><i><font color="Green" title="E69">A46</font></i></a>, <a class="ref" href="scmp_gcd.html#T5" target="_self" title="SCMP_GCD:th.5">Th5</a></i>
<br/>.= 
<font color="Maroon" title="c18">s2</font> <a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">.</a> <span class="p1">(<span class="default"><a href="scmpds_2.html#K3" title="SCMPDS_2:func.3">DataLoc</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Computation</a> <font color="Maroon" title="c17">s1</font></span>)</span> <a href="ami_1.html#K11" title="AMI_1:func.11">.</a> 4</span>)</span> <a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">.</a> <a href="scmp_gcd.html#K2" title="SCMP_GCD:func.2">GBP</a> </span>)</span>,1</span>)</span>
<b>by </b><i><a class="txt" href="scmp_gcd.html#E52:24"><i><font color="Green" title="E69">A46</font></i></a>, <a class="ref" href="scmp_gcd.html#T5" target="_self" title="SCMP_GCD:th.5">Th5</a></i>
;<br/><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="24_43_2"><b>per </b></a><a class="txt" onclick="hs(this)" href="javascript:()"><b>cases </b></a><span class="hide"><a NAME="E1:24_43_2"/>
( <font color="Maroon" title="c22">b</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="scmpds_2.html#K3" title="SCMPDS_2:func.3">DataLoc</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Computation</a> <font color="Maroon" title="c17">s1</font></span>)</span> <a href="ami_1.html#K11" title="AMI_1:func.11">.</a> 4</span>)</span> <a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">.</a> <a href="scmp_gcd.html#K3" title="SCMP_GCD:func.3">SBP</a> </span>)</span>,<span class="p1">(<span class="default">4 <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> <a href="scmpds_1.html#K22" title="SCMPDS_1:func.22">RetSP</a> </span>)</span> or <font color="Maroon" title="c22">b</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a>  <a href="scmpds_2.html#K3" title="SCMPDS_2:func.3">DataLoc</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Computation</a> <font color="Maroon" title="c17">s1</font></span>)</span> <a href="ami_1.html#K11" title="AMI_1:func.11">.</a> 4</span>)</span> <a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">.</a> <a href="scmp_gcd.html#K3" title="SCMP_GCD:func.3">SBP</a> </span>)</span>,<span class="p1">(<span class="default">4 <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> <a href="scmpds_1.html#K22" title="SCMPDS_1:func.22">RetSP</a> </span>)</span> )
 </span>;<br/><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="24_43_2_1"><b>suppose </b></a><a NAME="E1:24_43_2_1"/><i><font color="Green" title="E93">A89</font></i>: 
<font color="Maroon" title="c22">b</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="scmpds_2.html#K3" title="SCMPDS_2:func.3">DataLoc</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Computation</a> <font color="Maroon" title="c17">s1</font></span>)</span> <a href="ami_1.html#K11" title="AMI_1:func.11">.</a> 4</span>)</span> <a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">.</a> <a href="scmp_gcd.html#K3" title="SCMP_GCD:func.3">SBP</a> </span>)</span>,<span class="p1">(<span class="default">4 <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> <a href="scmpds_1.html#K22" title="SCMPDS_1:func.22">RetSP</a> </span>)</span>
 ;<br/><div class="add"><a NAME="E2:24_43_2_1"/><b>then </b><i><font color="Green" title="E94">A90</font></i>: 
<font color="Maroon" title="c22">b</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="scmpds_2.html#K3" title="SCMPDS_2:func.3">DataLoc</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Computation</a> <font color="Maroon" title="c18">s2</font></span>)</span> <a href="ami_1.html#K11" title="AMI_1:func.11">.</a> 4</span>)</span> <a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">.</a> <a href="scmp_gcd.html#K3" title="SCMP_GCD:func.3">SBP</a> </span>)</span>,<span class="p1">(<span class="default">4 <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> <a href="scmpds_1.html#K22" title="SCMPDS_1:func.22">RetSP</a> </span>)</span>
 <b>by </b><i><a class="txt" href="scmp_gcd.html#E6:24"><i><font color="Green" title="E29">A6</font></i></a>, <a class="txt" href="scmp_gcd.html#E74:24"><i><font color="Green" title="E89">A80</font></i></a></i>;<br/><b>thus </b><span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Computation</a> <font color="Maroon" title="c17">s1</font></span>)</span> <a href="ami_1.html#K11" title="AMI_1:func.11">.</a> 5</span>)</span> <a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">.</a> <font color="Maroon" title="c22">b</font> = 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Computation</a> <font color="Maroon" title="c17">s1</font></span>)</span> <a href="ami_1.html#K11" title="AMI_1:func.11">.</a> 4</span>)</span> <a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">.</a> <span class="p1">(<span class="default"><a href="scmpds_2.html#K3" title="SCMPDS_2:func.3">DataLoc</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Computation</a> <font color="Maroon" title="c17">s1</font></span>)</span> <a href="ami_1.html#K11" title="AMI_1:func.11">.</a> 4</span>)</span> <a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">.</a> <a href="scmp_gcd.html#K2" title="SCMP_GCD:func.2">GBP</a> </span>)</span>,1</span>)</span>
<b>by </b><i><a class="txt" href="scmp_gcd.html#E47:24"><i><font color="Green" title="E66">A43</font></i></a>, <a class="txt" href="scmp_gcd.html#E1:24_43_2_1"><i><font color="Green" title="E93">A89</font></i></a>, <a class="ref" href="scmpds_2.html#T59" title="SCMPDS_2:th.59">SCMPDS_2:59</a></i>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Computation</a> <font color="Maroon" title="c18">s2</font></span>)</span> <a href="ami_1.html#K11" title="AMI_1:func.11">.</a> 4</span>)</span> <a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">.</a> <span class="p1">(<span class="default"><a href="scmpds_2.html#K3" title="SCMPDS_2:func.3">DataLoc</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Computation</a> <font color="Maroon" title="c17">s1</font></span>)</span> <a href="ami_1.html#K11" title="AMI_1:func.11">.</a> 4</span>)</span> <a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">.</a> <a href="scmp_gcd.html#K2" title="SCMP_GCD:func.2">GBP</a> </span>)</span>,1</span>)</span>
<b>by </b><i><a class="txt" href="scmp_gcd.html#E74:24"><i><font color="Green" title="E89">A80</font></i></a>, <a class="txt" href="scmp_gcd.html#E2:24_43"><i><font color="Green" title="E92">A88</font></i></a></i>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Computation</a> <font color="Maroon" title="c18">s2</font></span>)</span> <a href="ami_1.html#K11" title="AMI_1:func.11">.</a> 4</span>)</span> <a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">.</a> <span class="p1">(<span class="default"><a href="scmpds_2.html#K3" title="SCMPDS_2:func.3">DataLoc</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Computation</a> <font color="Maroon" title="c18">s2</font></span>)</span> <a href="ami_1.html#K11" title="AMI_1:func.11">.</a> 4</span>)</span> <a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">.</a> <a href="scmp_gcd.html#K2" title="SCMP_GCD:func.2">GBP</a> </span>)</span>,1</span>)</span>
<b>by </b><i><a class="txt" href="scmp_gcd.html#E4:24"><i><font color="Green" title="E27">A4</font></i></a>, <a class="txt" href="scmp_gcd.html#E6:24"><i><font color="Green" title="E29">A6</font></i></a>, <a class="txt" href="scmp_gcd.html#E74:24"><i><font color="Green" title="E89">A80</font></i></a></i>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Computation</a> <font color="Maroon" title="c18">s2</font></span>)</span> <a href="ami_1.html#K11" title="AMI_1:func.11">.</a> 5</span>)</span> <a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">.</a> <font color="Maroon" title="c22">b</font>
<b>by </b><i><a class="txt" href="scmp_gcd.html#E55:24"><i><font color="Green" title="E72">A49</font></i></a>, <a class="txt" href="scmp_gcd.html#E2:24_43_2_1"><i><font color="Green" title="E94">A90</font></i></a>, <a class="ref" href="scmpds_2.html#T59" title="SCMPDS_2:th.59">SCMPDS_2:59</a></i>
;<br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="24_43_2_2"><b>suppose </b></a><a NAME="E1:24_43_2_2"/><i><font color="Green" title="E93">A91</font></i>: 
<font color="Maroon" title="c22">b</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a>  <a href="scmpds_2.html#K3" title="SCMPDS_2:func.3">DataLoc</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Computation</a> <font color="Maroon" title="c17">s1</font></span>)</span> <a href="ami_1.html#K11" title="AMI_1:func.11">.</a> 4</span>)</span> <a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">.</a> <a href="scmp_gcd.html#K3" title="SCMP_GCD:func.3">SBP</a> </span>)</span>,<span class="p1">(<span class="default">4 <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> <a href="scmpds_1.html#K22" title="SCMPDS_1:func.22">RetSP</a> </span>)</span>
 ;<br/><div class="add"><a NAME="E2:24_43_2_2"/><b>then </b><i><font color="Green" title="E94">A92</font></i>: 
<font color="Maroon" title="c22">b</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a>  <a href="scmpds_2.html#K3" title="SCMPDS_2:func.3">DataLoc</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Computation</a> <font color="Maroon" title="c18">s2</font></span>)</span> <a href="ami_1.html#K11" title="AMI_1:func.11">.</a> 4</span>)</span> <a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">.</a> <a href="scmp_gcd.html#K3" title="SCMP_GCD:func.3">SBP</a> </span>)</span>,<span class="p1">(<span class="default">4 <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> <a href="scmpds_1.html#K22" title="SCMPDS_1:func.22">RetSP</a> </span>)</span>
 <b>by </b><i><a class="txt" href="scmp_gcd.html#E6:24"><i><font color="Green" title="E29">A6</font></i></a>, <a class="txt" href="scmp_gcd.html#E74:24"><i><font color="Green" title="E89">A80</font></i></a></i>;<br/><b>thus </b><span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Computation</a> <font color="Maroon" title="c17">s1</font></span>)</span> <a href="ami_1.html#K11" title="AMI_1:func.11">.</a> 5</span>)</span> <a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">.</a> <font color="Maroon" title="c22">b</font> = 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Computation</a> <font color="Maroon" title="c17">s1</font></span>)</span> <a href="ami_1.html#K11" title="AMI_1:func.11">.</a> 4</span>)</span> <a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">.</a> <font color="Maroon" title="c22">b</font>
<b>by </b><i><a class="txt" href="scmp_gcd.html#E47:24"><i><font color="Green" title="E66">A43</font></i></a>, <a class="txt" href="scmp_gcd.html#E1:24_43_2_2"><i><font color="Green" title="E93">A91</font></i></a>, <a class="ref" href="scmpds_2.html#T59" title="SCMPDS_2:th.59">SCMPDS_2:59</a></i>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Computation</a> <font color="Maroon" title="c18">s2</font></span>)</span> <a href="ami_1.html#K11" title="AMI_1:func.11">.</a> 4</span>)</span> <a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">.</a> <font color="Maroon" title="c22">b</font>
<b>by </b><i><a class="txt" href="scmp_gcd.html#E74:24"><i><font color="Green" title="E89">A80</font></i></a>, <a class="txt" href="scmp_gcd.html#E1:24_43"><i><font color="Green" title="E91">A87</font></i></a></i>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Computation</a> <font color="Maroon" title="c18">s2</font></span>)</span> <a href="ami_1.html#K11" title="AMI_1:func.11">.</a> 5</span>)</span> <a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">.</a> <font color="Maroon" title="c22">b</font>
<b>by </b><i><a class="txt" href="scmp_gcd.html#E55:24"><i><font color="Green" title="E72">A49</font></i></a>, <a class="txt" href="scmp_gcd.html#E2:24_43_2_2"><i><font color="Green" title="E94">A92</font></i></a>, <a class="ref" href="scmpds_2.html#T59" title="SCMPDS_2:th.59">SCMPDS_2:59</a></i>
;<br/></div><b>end;</b></div></div><b>end;</b></div></div><b>end;</b></div>
<div><i><font color="Green" title="E91">A93</font></i>: <a class="txt" onclick="hs2(this)" href="javascript:()" title="24_44"><b>now </b></a><div class="add"><b>let </b><font color="Maroon" title="c22">b</font> be    <a href="scmpds_2.html#M1" title="SCMPDS_2:mode.1">Int_position</a> ;<br/><b>assume </b><a NAME="E1:24_44"/><i><font color="Green" title="E92">A94</font></i>: 
<font color="Maroon" title="c17">s1</font> <a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">.</a> <font color="Maroon" title="c22">b</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c18">s2</font> <a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">.</a> <font color="Maroon" title="c22">b</font>
 ;<br/><i><font color="Green" title="E93">A95</font></i>: <font color="Maroon" title="c17">s1</font> <a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">.</a> <span class="p1">(<span class="default"><a href="scmpds_2.html#K3" title="SCMPDS_2:func.3">DataLoc</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Computation</a> <font color="Maroon" title="c17">s1</font></span>)</span> <a href="ami_1.html#K11" title="AMI_1:func.11">.</a> 5</span>)</span> <a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">.</a> <a href="scmp_gcd.html#K2" title="SCMP_GCD:func.2">GBP</a> </span>)</span>,1</span>)</span> = 
<font color="Maroon" title="c18">s2</font> <a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">.</a> <span class="p1">(<span class="default"><a href="scmp_gcd.html#K1" title="SCMP_GCD:func.1">intpos</a> <span class="p2">(<span class="default">0 <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1</span>)</span></span>)</span>
<b>by </b><i><a class="txt" href="scmp_gcd.html#E6:24"><i><font color="Green" title="E29">A6</font></i></a>, <a class="txt" href="scmp_gcd.html#E61:24"><i><font color="Green" title="E76">A53</font></i></a>, <a class="ref" href="scmp_gcd.html#T5" target="_self" title="SCMP_GCD:th.5">Th5</a></i>
<br/>.= 
<font color="Maroon" title="c18">s2</font> <a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">.</a> <span class="p1">(<span class="default"><a href="scmpds_2.html#K3" title="SCMPDS_2:func.3">DataLoc</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Computation</a> <font color="Maroon" title="c17">s1</font></span>)</span> <a href="ami_1.html#K11" title="AMI_1:func.11">.</a> 5</span>)</span> <a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">.</a> <a href="scmp_gcd.html#K2" title="SCMP_GCD:func.2">GBP</a> </span>)</span>,1</span>)</span>
<b>by </b><i><a class="txt" href="scmp_gcd.html#E61:24"><i><font color="Green" title="E76">A53</font></i></a>, <a class="ref" href="scmp_gcd.html#T5" target="_self" title="SCMP_GCD:th.5">Th5</a></i>
;<br/><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="24_44_2"><b>per </b></a><a class="txt" onclick="hs(this)" href="javascript:()"><b>cases </b></a><span class="hide"><a NAME="E1:24_44_2"/>
( <font color="Maroon" title="c22">b</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="scmpds_2.html#K3" title="SCMPDS_2:func.3">DataLoc</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Computation</a> <font color="Maroon" title="c17">s1</font></span>)</span> <a href="ami_1.html#K11" title="AMI_1:func.11">.</a> 5</span>)</span> <a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">.</a> <a href="scmp_gcd.html#K2" title="SCMP_GCD:func.2">GBP</a> </span>)</span>,1 or <font color="Maroon" title="c22">b</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a>  <a href="scmpds_2.html#K3" title="SCMPDS_2:func.3">DataLoc</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Computation</a> <font color="Maroon" title="c17">s1</font></span>)</span> <a href="ami_1.html#K11" title="AMI_1:func.11">.</a> 5</span>)</span> <a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">.</a> <a href="scmp_gcd.html#K2" title="SCMP_GCD:func.2">GBP</a> </span>)</span>,1 )
 </span>;<br/><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="24_44_2_1"><b>suppose </b></a><a NAME="E1:24_44_2_1"/><i><font color="Green" title="E94">A96</font></i>: 
<font color="Maroon" title="c22">b</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="scmpds_2.html#K3" title="SCMPDS_2:func.3">DataLoc</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Computation</a> <font color="Maroon" title="c17">s1</font></span>)</span> <a href="ami_1.html#K11" title="AMI_1:func.11">.</a> 5</span>)</span> <a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">.</a> <a href="scmp_gcd.html#K2" title="SCMP_GCD:func.2">GBP</a> </span>)</span>,1
 ;<br/><div class="add"><a NAME="E2:24_44_2_1"/><b>then </b><i><font color="Green" title="E95">A97</font></i>: 
<font color="Maroon" title="c22">b</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="scmpds_2.html#K3" title="SCMPDS_2:func.3">DataLoc</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Computation</a> <font color="Maroon" title="c18">s2</font></span>)</span> <a href="ami_1.html#K11" title="AMI_1:func.11">.</a> 5</span>)</span> <a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">.</a> <a href="scmp_gcd.html#K2" title="SCMP_GCD:func.2">GBP</a> </span>)</span>,1
 <b>by </b><i><a class="txt" href="scmp_gcd.html#E4:24"><i><font color="Green" title="E27">A4</font></i></a>, <a class="txt" href="scmp_gcd.html#E6:24"><i><font color="Green" title="E29">A6</font></i></a>, <a class="txt" href="scmp_gcd.html#E75:24"><i><font color="Green" title="E90">A86</font></i></a></i>;<br/><b>thus </b><span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Computation</a> <font color="Maroon" title="c17">s1</font></span>)</span> <a href="ami_1.html#K11" title="AMI_1:func.11">.</a> 6</span>)</span> <a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">.</a> <font color="Maroon" title="c22">b</font> = 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Computation</a> <font color="Maroon" title="c17">s1</font></span>)</span> <a href="ami_1.html#K11" title="AMI_1:func.11">.</a> 5</span>)</span> <a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">.</a> <span class="p2">(<span class="default"><a href="scmpds_2.html#K3" title="SCMPDS_2:func.3">DataLoc</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Computation</a> <font color="Maroon" title="c17">s1</font></span>)</span> <a href="ami_1.html#K11" title="AMI_1:func.11">.</a> 5</span>)</span> <a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">.</a> <a href="scmp_gcd.html#K2" title="SCMP_GCD:func.2">GBP</a> </span>)</span>,1</span>)</span></span>)</span> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> 4
<b>by </b><i><a class="txt" href="scmp_gcd.html#E58:24"><i><font color="Green" title="E75">A52</font></i></a>, <a class="txt" href="scmp_gcd.html#E1:24_44_2_1"><i><font color="Green" title="E94">A96</font></i></a>, <a class="ref" href="scmpds_2.html#T60" title="SCMPDS_2:th.60">SCMPDS_2:60</a></i>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Computation</a> <font color="Maroon" title="c18">s2</font></span>)</span> <a href="ami_1.html#K11" title="AMI_1:func.11">.</a> 5</span>)</span> <a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">.</a> <span class="p2">(<span class="default"><a href="scmpds_2.html#K3" title="SCMPDS_2:func.3">DataLoc</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Computation</a> <font color="Maroon" title="c17">s1</font></span>)</span> <a href="ami_1.html#K11" title="AMI_1:func.11">.</a> 5</span>)</span> <a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">.</a> <a href="scmp_gcd.html#K2" title="SCMP_GCD:func.2">GBP</a> </span>)</span>,1</span>)</span></span>)</span> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> 4
<b>by </b><i><a class="txt" href="scmp_gcd.html#E75:24"><i><font color="Green" title="E90">A86</font></i></a>, <a class="txt" href="scmp_gcd.html#E2:24_44"><i><font color="Green" title="E93">A95</font></i></a></i>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Computation</a> <font color="Maroon" title="c18">s2</font></span>)</span> <a href="ami_1.html#K11" title="AMI_1:func.11">.</a> 5</span>)</span> <a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">.</a> <span class="p2">(<span class="default"><a href="scmpds_2.html#K3" title="SCMPDS_2:func.3">DataLoc</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Computation</a> <font color="Maroon" title="c18">s2</font></span>)</span> <a href="ami_1.html#K11" title="AMI_1:func.11">.</a> 5</span>)</span> <a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">.</a> <a href="scmp_gcd.html#K2" title="SCMP_GCD:func.2">GBP</a> </span>)</span>,1</span>)</span></span>)</span> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> 4
<b>by </b><i><a class="txt" href="scmp_gcd.html#E4:24"><i><font color="Green" title="E27">A4</font></i></a>, <a class="txt" href="scmp_gcd.html#E6:24"><i><font color="Green" title="E29">A6</font></i></a>, <a class="txt" href="scmp_gcd.html#E75:24"><i><font color="Green" title="E90">A86</font></i></a></i>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Computation</a> <font color="Maroon" title="c18">s2</font></span>)</span> <a href="ami_1.html#K11" title="AMI_1:func.11">.</a> 6</span>)</span> <a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">.</a> <font color="Maroon" title="c22">b</font>
<b>by </b><i><a class="txt" href="scmp_gcd.html#E64:24"><i><font color="Green" title="E79">A56</font></i></a>, <a class="txt" href="scmp_gcd.html#E2:24_44_2_1"><i><font color="Green" title="E95">A97</font></i></a>, <a class="ref" href="scmpds_2.html#T60" title="SCMPDS_2:th.60">SCMPDS_2:60</a></i>
;<br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="24_44_2_2"><b>suppose </b></a><a NAME="E1:24_44_2_2"/><i><font color="Green" title="E94">A98</font></i>: 
<font color="Maroon" title="c22">b</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a>  <a href="scmpds_2.html#K3" title="SCMPDS_2:func.3">DataLoc</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Computation</a> <font color="Maroon" title="c17">s1</font></span>)</span> <a href="ami_1.html#K11" title="AMI_1:func.11">.</a> 5</span>)</span> <a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">.</a> <a href="scmp_gcd.html#K2" title="SCMP_GCD:func.2">GBP</a> </span>)</span>,1
 ;<br/><div class="add"><a NAME="E2:24_44_2_2"/><b>then </b><i><font color="Green" title="E95">A99</font></i>: 
<font color="Maroon" title="c22">b</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a>  <a href="scmpds_2.html#K3" title="SCMPDS_2:func.3">DataLoc</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Computation</a> <font color="Maroon" title="c18">s2</font></span>)</span> <a href="ami_1.html#K11" title="AMI_1:func.11">.</a> 5</span>)</span> <a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">.</a> <a href="scmp_gcd.html#K2" title="SCMP_GCD:func.2">GBP</a> </span>)</span>,1
 <b>by </b><i><a class="txt" href="scmp_gcd.html#E4:24"><i><font color="Green" title="E27">A4</font></i></a>, <a class="txt" href="scmp_gcd.html#E6:24"><i><font color="Green" title="E29">A6</font></i></a>, <a class="txt" href="scmp_gcd.html#E75:24"><i><font color="Green" title="E90">A86</font></i></a></i>;<br/><b>thus </b><span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Computation</a> <font color="Maroon" title="c17">s1</font></span>)</span> <a href="ami_1.html#K11" title="AMI_1:func.11">.</a> 6</span>)</span> <a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">.</a> <font color="Maroon" title="c22">b</font> = 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Computation</a> <font color="Maroon" title="c17">s1</font></span>)</span> <a href="ami_1.html#K11" title="AMI_1:func.11">.</a> 5</span>)</span> <a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">.</a> <font color="Maroon" title="c22">b</font>
<b>by </b><i><a class="txt" href="scmp_gcd.html#E58:24"><i><font color="Green" title="E75">A52</font></i></a>, <a class="txt" href="scmp_gcd.html#E1:24_44_2_2"><i><font color="Green" title="E94">A98</font></i></a>, <a class="ref" href="scmpds_2.html#T60" title="SCMPDS_2:th.60">SCMPDS_2:60</a></i>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Computation</a> <font color="Maroon" title="c18">s2</font></span>)</span> <a href="ami_1.html#K11" title="AMI_1:func.11">.</a> 5</span>)</span> <a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">.</a> <font color="Maroon" title="c22">b</font>
<b>by </b><i><a class="txt" href="scmp_gcd.html#E75:24"><i><font color="Green" title="E90">A86</font></i></a>, <a class="txt" href="scmp_gcd.html#E1:24_44"><i><font color="Green" title="E92">A94</font></i></a></i>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Computation</a> <font color="Maroon" title="c18">s2</font></span>)</span> <a href="ami_1.html#K11" title="AMI_1:func.11">.</a> 6</span>)</span> <a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">.</a> <font color="Maroon" title="c22">b</font>
<b>by </b><i><a class="txt" href="scmp_gcd.html#E64:24"><i><font color="Green" title="E79">A56</font></i></a>, <a class="txt" href="scmp_gcd.html#E2:24_44_2_2"><i><font color="Green" title="E95">A99</font></i></a>, <a class="ref" href="scmpds_2.html#T60" title="SCMPDS_2:th.60">SCMPDS_2:60</a></i>
;<br/></div><b>end;</b></div></div><b>end;</b></div></div><b>end;</b></div>
<div><i><font color="Green" title="E92">A100</font></i>: <a class="txt" onclick="hs2(this)" href="javascript:()" title="24_45"><b>now </b></a><div class="add"><b>let </b><font color="Maroon" title="c22">b</font> be    <a href="scmpds_2.html#M1" title="SCMPDS_2:mode.1">Int_position</a> ;<br/><b>assume </b><a NAME="E1:24_45"/><i><font color="Green" title="E93">A101</font></i>: 
<font color="Maroon" title="c17">s1</font> <a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">.</a> <font color="Maroon" title="c22">b</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c18">s2</font> <a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">.</a> <font color="Maroon" title="c22">b</font>
 ;<br/><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="24_45_1"><b>per </b></a><a class="txt" onclick="hs(this)" href="javascript:()"><b>cases </b></a><span class="hide"><a NAME="E1:24_45_1"/>
( <font color="Maroon" title="c22">b</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="scmpds_2.html#K3" title="SCMPDS_2:func.3">DataLoc</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Computation</a> <font color="Maroon" title="c17">s1</font></span>)</span> <a href="ami_1.html#K11" title="AMI_1:func.11">.</a> 6</span>)</span> <a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">.</a> <a href="scmp_gcd.html#K3" title="SCMP_GCD:func.3">SBP</a> </span>)</span>,<a href="scmpds_1.html#K23" title="SCMPDS_1:func.23">RetIC</a>  or <font color="Maroon" title="c22">b</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a>  <a href="scmpds_2.html#K3" title="SCMPDS_2:func.3">DataLoc</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Computation</a> <font color="Maroon" title="c17">s1</font></span>)</span> <a href="ami_1.html#K11" title="AMI_1:func.11">.</a> 6</span>)</span> <a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">.</a> <a href="scmp_gcd.html#K3" title="SCMP_GCD:func.3">SBP</a> </span>)</span>,<a href="scmpds_1.html#K23" title="SCMPDS_1:func.23">RetIC</a>  )
 </span>;<br/><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="24_45_1_1"><b>suppose </b></a><a NAME="E1:24_45_1_1"/><i><font color="Green" title="E94">A102</font></i>: 
<font color="Maroon" title="c22">b</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="scmpds_2.html#K3" title="SCMPDS_2:func.3">DataLoc</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Computation</a> <font color="Maroon" title="c17">s1</font></span>)</span> <a href="ami_1.html#K11" title="AMI_1:func.11">.</a> 6</span>)</span> <a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">.</a> <a href="scmp_gcd.html#K3" title="SCMP_GCD:func.3">SBP</a> </span>)</span>,<a href="scmpds_1.html#K23" title="SCMPDS_1:func.23">RetIC</a> 
 ;<br/><div class="add"><a NAME="E2:24_45_1_1"/><b>then </b><i><font color="Green" title="E95">A103</font></i>: 
<font color="Maroon" title="c22">b</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="scmpds_2.html#K3" title="SCMPDS_2:func.3">DataLoc</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Computation</a> <font color="Maroon" title="c18">s2</font></span>)</span> <a href="ami_1.html#K11" title="AMI_1:func.11">.</a> 6</span>)</span> <a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">.</a> <a href="scmp_gcd.html#K3" title="SCMP_GCD:func.3">SBP</a> </span>)</span>,<a href="scmpds_1.html#K23" title="SCMPDS_1:func.23">RetIC</a> 
 <b>by </b><i><a class="txt" href="scmp_gcd.html#E6:24"><i><font color="Green" title="E29">A6</font></i></a>, <a class="txt" href="scmp_gcd.html#E76:24"><i><font color="Green" title="E91">A93</font></i></a></i>;<br/><b>thus </b><span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Computation</a> <font color="Maroon" title="c17">s1</font></span>)</span> <a href="ami_1.html#K11" title="AMI_1:func.11">.</a> 7</span>)</span> <a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">.</a> <font color="Maroon" title="c22">b</font> = 
 <a href="ami_1.html#K6" title="AMI_1:func.6">IC</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Computation</a> <font color="Maroon" title="c17">s1</font></span>)</span> <a href="ami_1.html#K11" title="AMI_1:func.11">.</a> 6</span>)</span>
<b>by </b><i><a class="txt" href="scmp_gcd.html#E67:24"><i><font color="Green" title="E82">A59</font></i></a>, <a class="txt" href="scmp_gcd.html#E1:24_45_1_1"><i><font color="Green" title="E94">A102</font></i></a>, <a class="ref" href="scmpds_2.html#T71" title="SCMPDS_2:th.71">SCMPDS_2:71</a></i>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Computation</a> <font color="Maroon" title="c18">s2</font></span>)</span> <a href="ami_1.html#K11" title="AMI_1:func.11">.</a> 7</span>)</span> <a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">.</a> <font color="Maroon" title="c22">b</font>
<b>by </b><i><a class="txt" href="scmp_gcd.html#E65:24"><i><font color="Green" title="E80">A57</font></i></a>, <a class="txt" href="scmp_gcd.html#E68:24"><i><font color="Green" title="E83">A60</font></i></a>, <a class="txt" href="scmp_gcd.html#E70:24"><i><font color="Green" title="E85">A62</font></i></a>, <a class="txt" href="scmp_gcd.html#E2:24_45_1_1"><i><font color="Green" title="E95">A103</font></i></a>, <a class="ref" href="scmpds_2.html#T71" title="SCMPDS_2:th.71">SCMPDS_2:71</a></i>
;<br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="24_45_1_2"><b>suppose </b></a><a NAME="E1:24_45_1_2"/><i><font color="Green" title="E94">A104</font></i>: 
<font color="Maroon" title="c22">b</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a>  <a href="scmpds_2.html#K3" title="SCMPDS_2:func.3">DataLoc</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Computation</a> <font color="Maroon" title="c17">s1</font></span>)</span> <a href="ami_1.html#K11" title="AMI_1:func.11">.</a> 6</span>)</span> <a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">.</a> <a href="scmp_gcd.html#K3" title="SCMP_GCD:func.3">SBP</a> </span>)</span>,<a href="scmpds_1.html#K23" title="SCMPDS_1:func.23">RetIC</a> 
 ;<br/><div class="add"><a NAME="E2:24_45_1_2"/><b>then </b><i><font color="Green" title="E95">A105</font></i>: 
<font color="Maroon" title="c22">b</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a>  <a href="scmpds_2.html#K3" title="SCMPDS_2:func.3">DataLoc</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Computation</a> <font color="Maroon" title="c18">s2</font></span>)</span> <a href="ami_1.html#K11" title="AMI_1:func.11">.</a> 6</span>)</span> <a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">.</a> <a href="scmp_gcd.html#K3" title="SCMP_GCD:func.3">SBP</a> </span>)</span>,<a href="scmpds_1.html#K23" title="SCMPDS_1:func.23">RetIC</a> 
 <b>by </b><i><a class="txt" href="scmp_gcd.html#E6:24"><i><font color="Green" title="E29">A6</font></i></a>, <a class="txt" href="scmp_gcd.html#E76:24"><i><font color="Green" title="E91">A93</font></i></a></i>;<br/><b>thus </b><span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Computation</a> <font color="Maroon" title="c17">s1</font></span>)</span> <a href="ami_1.html#K11" title="AMI_1:func.11">.</a> 7</span>)</span> <a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">.</a> <font color="Maroon" title="c22">b</font> = 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Computation</a> <font color="Maroon" title="c17">s1</font></span>)</span> <a href="ami_1.html#K11" title="AMI_1:func.11">.</a> 6</span>)</span> <a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">.</a> <font color="Maroon" title="c22">b</font>
<b>by </b><i><a class="txt" href="scmp_gcd.html#E67:24"><i><font color="Green" title="E82">A59</font></i></a>, <a class="txt" href="scmp_gcd.html#E1:24_45_1_2"><i><font color="Green" title="E94">A104</font></i></a>, <a class="ref" href="scmpds_2.html#T71" title="SCMPDS_2:th.71">SCMPDS_2:71</a></i>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Computation</a> <font color="Maroon" title="c18">s2</font></span>)</span> <a href="ami_1.html#K11" title="AMI_1:func.11">.</a> 6</span>)</span> <a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">.</a> <font color="Maroon" title="c22">b</font>
<b>by </b><i><a class="txt" href="scmp_gcd.html#E76:24"><i><font color="Green" title="E91">A93</font></i></a>, <a class="txt" href="scmp_gcd.html#E1:24_45"><i><font color="Green" title="E93">A101</font></i></a></i>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Computation</a> <font color="Maroon" title="c18">s2</font></span>)</span> <a href="ami_1.html#K11" title="AMI_1:func.11">.</a> 7</span>)</span> <a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">.</a> <font color="Maroon" title="c22">b</font>
<b>by </b><i><a class="txt" href="scmp_gcd.html#E70:24"><i><font color="Green" title="E85">A62</font></i></a>, <a class="txt" href="scmp_gcd.html#E2:24_45_1_2"><i><font color="Green" title="E95">A105</font></i></a>, <a class="ref" href="scmpds_2.html#T71" title="SCMPDS_2:th.71">SCMPDS_2:71</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>let </b><font color="Maroon" title="c22">k</font> be    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of  <a href="numbers.html#K5" title="NUMBERS:func.5">NAT</a> ;<br/><b>let </b><font color="Maroon" title="c23">a</font> be    <a href="scmpds_2.html#M1" title="SCMPDS_2:mode.1">Int_position</a> ;<br/><b>assume </b><a NAME="E1:24_46"/><i><font color="Green" title="E93">A106</font></i>: 
( <font color="Maroon" title="c22">k</font> <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> 7 &amp; <font color="Maroon" title="c17">s1</font> <a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">.</a> <font color="Maroon" title="c23">a</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c18">s2</font> <a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">.</a> <font color="Maroon" title="c23">a</font> )
 ;<br/><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="24_46_1"><b>per </b></a><a class="txt" onclick="hs(this)" href="javascript:()"><b>cases </b></a><span class="hide"><a NAME="E1:24_46_1"/>
( <font color="Maroon" title="c22">k</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 0 or <font color="Maroon" title="c22">k</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 1 or <font color="Maroon" title="c22">k</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 2 or <font color="Maroon" title="c22">k</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 3 or <font color="Maroon" title="c22">k</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 4 or <font color="Maroon" title="c22">k</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 5 or <font color="Maroon" title="c22">k</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 6 or <font color="Maroon" title="c22">k</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 7 )
 </span><b>by </b><i><a class="txt" href="scmp_gcd.html#E1:24_46"><i><font color="Green" title="E93">A106</font></i></a>, <a class="ref" href="nat_1.html#T32" title="NAT_1:th.32">NAT_1:32</a></i>;<br/><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="24_46_1_1"><b>suppose </b></a><a NAME="E1:24_46_1_1"/><i><font color="Green" title="E94">A107</font></i>: 
<font color="Maroon" title="c22">k</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 0
 ;<br/><div class="add"><b>hence </b> <a href="ami_1.html#K6" title="AMI_1:func.6">IC</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Computation</a> <font color="Maroon" title="c17">s1</font></span>)</span> <a href="ami_1.html#K11" title="AMI_1:func.11">.</a> <font color="Maroon" title="c22">k</font></span>)</span> = 
 <a href="ami_1.html#K6" title="AMI_1:func.6">IC</a> <font color="Maroon" title="c17">s1</font>
<b>by </b><i><a class="ref" href="ami_1.html#D19" title="AMI_1:def.19">AMI_1:def 19</a></i>
<br/>.= 
 <a href="ami_1.html#K6" title="AMI_1:func.6">IC</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Computation</a> <font color="Maroon" title="c18">s2</font></span>)</span> <a href="ami_1.html#K11" title="AMI_1:func.11">.</a> <font color="Maroon" title="c22">k</font></span>)</span>
<b>by </b><i><a class="txt" href="scmp_gcd.html#E6:24"><i><font color="Green" title="E29">A6</font></i></a>, <a class="txt" href="scmp_gcd.html#E1:24_46_1_1"><i><font color="Green" title="E94">A107</font></i></a>, <a class="ref" href="ami_1.html#D19" title="AMI_1:def.19">AMI_1:def 19</a></i>
;<br/><br/><b>thus </b><span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Computation</a> <font color="Maroon" title="c17">s1</font></span>)</span> <a href="ami_1.html#K11" title="AMI_1:func.11">.</a> <font color="Maroon" title="c22">k</font></span>)</span> <a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">.</a> <font color="Maroon" title="c23">a</font> = 
<font color="Maroon" title="c17">s1</font> <a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">.</a> <font color="Maroon" title="c23">a</font>
<b>by </b><i><a class="txt" href="scmp_gcd.html#E1:24_46_1_1"><i><font color="Green" title="E94">A107</font></i></a>, <a class="ref" href="ami_1.html#D19" title="AMI_1:def.19">AMI_1:def 19</a></i>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Computation</a> <font color="Maroon" title="c18">s2</font></span>)</span> <a href="ami_1.html#K11" title="AMI_1:func.11">.</a> <font color="Maroon" title="c22">k</font></span>)</span> <a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">.</a> <font color="Maroon" title="c23">a</font>
<b>by </b><i><a class="txt" href="scmp_gcd.html#E1:24_46"><i><font color="Green" title="E93">A106</font></i></a>, <a class="txt" href="scmp_gcd.html#E1:24_46_1_1"><i><font color="Green" title="E94">A107</font></i></a>, <a class="ref" href="ami_1.html#D19" title="AMI_1:def.19">AMI_1:def 19</a></i>
;<br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="24_46_1_2"><b>suppose </b></a><a NAME="E1:24_46_1_2"/><i><font color="Green" title="E94">A108</font></i>: 
<font color="Maroon" title="c22">k</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 1
 ;<br/><div class="add"><b>hence </b><a NAME="E2:24_46_1_2"/>
 <a href="ami_1.html#K6" title="AMI_1:func.6">IC</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Computation</a> <font color="Maroon" title="c17">s1</font></span>)</span> <a href="ami_1.html#K11" title="AMI_1:func.11">.</a> <font color="Maroon" title="c22">k</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="ami_1.html#K6" title="AMI_1:func.6">IC</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Computation</a> <font color="Maroon" title="c18">s2</font></span>)</span> <a href="ami_1.html#K11" title="AMI_1:func.11">.</a> <font color="Maroon" title="c22">k</font></span>)</span>
 <b>by </b><i><a class="txt" href="scmp_gcd.html#E12:24"><i><font color="Green" title="E35">A12</font></i></a>, <a class="txt" href="scmp_gcd.html#E17:24"><i><font color="Green" title="E40">A17</font></i></a></i>;<br/><b>thus </b><a NAME="E3:24_46_1_2"/>
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Computation</a> <font color="Maroon" title="c17">s1</font></span>)</span> <a href="ami_1.html#K11" title="AMI_1:func.11">.</a> <font color="Maroon" title="c22">k</font></span>)</span> <a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">.</a> <font color="Maroon" title="c23">a</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Computation</a> <font color="Maroon" title="c18">s2</font></span>)</span> <a href="ami_1.html#K11" title="AMI_1:func.11">.</a> <font color="Maroon" title="c22">k</font></span>)</span> <a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">.</a> <font color="Maroon" title="c23">a</font>
 <b>by </b><i><a class="txt" href="scmp_gcd.html#E71:24"><i><font color="Green" title="E86">A63</font></i></a>, <a class="txt" href="scmp_gcd.html#E1:24_46"><i><font color="Green" title="E93">A106</font></i></a>, <a class="txt" href="scmp_gcd.html#E1:24_46_1_2"><i><font color="Green" title="E94">A108</font></i></a></i>;<br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="24_46_1_3"><b>suppose </b></a><a NAME="E1:24_46_1_3"/><i><font color="Green" title="E94">A109</font></i>: 
<font color="Maroon" title="c22">k</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 2
 ;<br/><div class="add"><b>hence </b><a NAME="E2:24_46_1_3"/>
 <a href="ami_1.html#K6" title="AMI_1:func.6">IC</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Computation</a> <font color="Maroon" title="c17">s1</font></span>)</span> <a href="ami_1.html#K11" title="AMI_1:func.11">.</a> <font color="Maroon" title="c22">k</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="ami_1.html#K6" title="AMI_1:func.6">IC</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Computation</a> <font color="Maroon" title="c18">s2</font></span>)</span> <a href="ami_1.html#K11" title="AMI_1:func.11">.</a> <font color="Maroon" title="c22">k</font></span>)</span>
 <b>by </b><i><a class="txt" href="scmp_gcd.html#E20:24"><i><font color="Green" title="E43">A20</font></i></a>, <a class="txt" href="scmp_gcd.html#E28:24"><i><font color="Green" title="E49">A26</font></i></a></i>;<br/><b>thus </b><a NAME="E3:24_46_1_3"/>
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Computation</a> <font color="Maroon" title="c17">s1</font></span>)</span> <a href="ami_1.html#K11" title="AMI_1:func.11">.</a> <font color="Maroon" title="c22">k</font></span>)</span> <a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">.</a> <font color="Maroon" title="c23">a</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Computation</a> <font color="Maroon" title="c18">s2</font></span>)</span> <a href="ami_1.html#K11" title="AMI_1:func.11">.</a> <font color="Maroon" title="c22">k</font></span>)</span> <a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">.</a> <font color="Maroon" title="c23">a</font>
 <b>by </b><i><a class="txt" href="scmp_gcd.html#E72:24"><i><font color="Green" title="E87">A64</font></i></a>, <a class="txt" href="scmp_gcd.html#E1:24_46"><i><font color="Green" title="E93">A106</font></i></a>, <a class="txt" href="scmp_gcd.html#E1:24_46_1_3"><i><font color="Green" title="E94">A109</font></i></a></i>;<br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="24_46_1_4"><b>suppose </b></a><a NAME="E1:24_46_1_4"/><i><font color="Green" title="E94">A110</font></i>: 
<font color="Maroon" title="c22">k</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 3
 ;<br/><div class="add"><b>hence </b><a NAME="E2:24_46_1_4"/>
 <a href="ami_1.html#K6" title="AMI_1:func.6">IC</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Computation</a> <font color="Maroon" title="c17">s1</font></span>)</span> <a href="ami_1.html#K11" title="AMI_1:func.11">.</a> <font color="Maroon" title="c22">k</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="ami_1.html#K6" title="AMI_1:func.6">IC</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Computation</a> <font color="Maroon" title="c18">s2</font></span>)</span> <a href="ami_1.html#K11" title="AMI_1:func.11">.</a> <font color="Maroon" title="c22">k</font></span>)</span>
 <b>by </b><i><a class="txt" href="scmp_gcd.html#E31:24"><i><font color="Green" title="E52">A29</font></i></a>, <a class="txt" href="scmp_gcd.html#E42:24"><i><font color="Green" title="E61">A38</font></i></a></i>;<br/><b>thus </b><a NAME="E3:24_46_1_4"/>
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Computation</a> <font color="Maroon" title="c17">s1</font></span>)</span> <a href="ami_1.html#K11" title="AMI_1:func.11">.</a> <font color="Maroon" title="c22">k</font></span>)</span> <a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">.</a> <font color="Maroon" title="c23">a</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Computation</a> <font color="Maroon" title="c18">s2</font></span>)</span> <a href="ami_1.html#K11" title="AMI_1:func.11">.</a> <font color="Maroon" title="c22">k</font></span>)</span> <a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">.</a> <font color="Maroon" title="c23">a</font>
 <b>by </b><i><a class="txt" href="scmp_gcd.html#E73:24"><i><font color="Green" title="E88">A70</font></i></a>, <a class="txt" href="scmp_gcd.html#E1:24_46"><i><font color="Green" title="E93">A106</font></i></a>, <a class="txt" href="scmp_gcd.html#E1:24_46_1_4"><i><font color="Green" title="E94">A110</font></i></a></i>;<br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="24_46_1_5"><b>suppose </b></a><a NAME="E1:24_46_1_5"/><i><font color="Green" title="E94">A111</font></i>: 
<font color="Maroon" title="c22">k</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 4
 ;<br/><div class="add"><b>hence </b><a NAME="E2:24_46_1_5"/>
 <a href="ami_1.html#K6" title="AMI_1:func.6">IC</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Computation</a> <font color="Maroon" title="c17">s1</font></span>)</span> <a href="ami_1.html#K11" title="AMI_1:func.11">.</a> <font color="Maroon" title="c22">k</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="ami_1.html#K6" title="AMI_1:func.6">IC</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Computation</a> <font color="Maroon" title="c18">s2</font></span>)</span> <a href="ami_1.html#K11" title="AMI_1:func.11">.</a> <font color="Maroon" title="c22">k</font></span>)</span>
 <b>by </b><i><a class="txt" href="scmp_gcd.html#E45:24"><i><font color="Green" title="E64">A41</font></i></a>, <a class="txt" href="scmp_gcd.html#E53:24"><i><font color="Green" title="E70">A47</font></i></a></i>;<br/><b>thus </b><a NAME="E3:24_46_1_5"/>
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Computation</a> <font color="Maroon" title="c17">s1</font></span>)</span> <a href="ami_1.html#K11" title="AMI_1:func.11">.</a> <font color="Maroon" title="c22">k</font></span>)</span> <a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">.</a> <font color="Maroon" title="c23">a</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Computation</a> <font color="Maroon" title="c18">s2</font></span>)</span> <a href="ami_1.html#K11" title="AMI_1:func.11">.</a> <font color="Maroon" title="c22">k</font></span>)</span> <a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">.</a> <font color="Maroon" title="c23">a</font>
 <b>by </b><i><a class="txt" href="scmp_gcd.html#E74:24"><i><font color="Green" title="E89">A80</font></i></a>, <a class="txt" href="scmp_gcd.html#E1:24_46"><i><font color="Green" title="E93">A106</font></i></a>, <a class="txt" href="scmp_gcd.html#E1:24_46_1_5"><i><font color="Green" title="E94">A111</font></i></a></i>;<br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="24_46_1_6"><b>suppose </b></a><a NAME="E1:24_46_1_6"/><i><font color="Green" title="E94">A112</font></i>: 
<font color="Maroon" title="c22">k</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 5
 ;<br/><div class="add"><b>hence </b><a NAME="E2:24_46_1_6"/>
 <a href="ami_1.html#K6" title="AMI_1:func.6">IC</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Computation</a> <font color="Maroon" title="c17">s1</font></span>)</span> <a href="ami_1.html#K11" title="AMI_1:func.11">.</a> <font color="Maroon" title="c22">k</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="ami_1.html#K6" title="AMI_1:func.6">IC</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Computation</a> <font color="Maroon" title="c18">s2</font></span>)</span> <a href="ami_1.html#K11" title="AMI_1:func.11">.</a> <font color="Maroon" title="c22">k</font></span>)</span>
 <b>by </b><i><a class="txt" href="scmp_gcd.html#E56:24"><i><font color="Green" title="E73">A50</font></i></a>, <a class="txt" href="scmp_gcd.html#E62:24"><i><font color="Green" title="E77">A54</font></i></a></i>;<br/><b>thus </b><a NAME="E3:24_46_1_6"/>
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Computation</a> <font color="Maroon" title="c17">s1</font></span>)</span> <a href="ami_1.html#K11" title="AMI_1:func.11">.</a> <font color="Maroon" title="c22">k</font></span>)</span> <a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">.</a> <font color="Maroon" title="c23">a</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Computation</a> <font color="Maroon" title="c18">s2</font></span>)</span> <a href="ami_1.html#K11" title="AMI_1:func.11">.</a> <font color="Maroon" title="c22">k</font></span>)</span> <a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">.</a> <font color="Maroon" title="c23">a</font>
 <b>by </b><i><a class="txt" href="scmp_gcd.html#E75:24"><i><font color="Green" title="E90">A86</font></i></a>, <a class="txt" href="scmp_gcd.html#E1:24_46"><i><font color="Green" title="E93">A106</font></i></a>, <a class="txt" href="scmp_gcd.html#E1:24_46_1_6"><i><font color="Green" title="E94">A112</font></i></a></i>;<br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="24_46_1_7"><b>suppose </b></a><a NAME="E1:24_46_1_7"/><i><font color="Green" title="E94">A113</font></i>: 
<font color="Maroon" title="c22">k</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 6
 ;<br/><div class="add"><b>hence </b><a NAME="E2:24_46_1_7"/>
 <a href="ami_1.html#K6" title="AMI_1:func.6">IC</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Computation</a> <font color="Maroon" title="c17">s1</font></span>)</span> <a href="ami_1.html#K11" title="AMI_1:func.11">.</a> <font color="Maroon" title="c22">k</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="ami_1.html#K6" title="AMI_1:func.6">IC</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Computation</a> <font color="Maroon" title="c18">s2</font></span>)</span> <a href="ami_1.html#K11" title="AMI_1:func.11">.</a> <font color="Maroon" title="c22">k</font></span>)</span>
 <b>by </b><i><a class="txt" href="scmp_gcd.html#E65:24"><i><font color="Green" title="E80">A57</font></i></a>, <a class="txt" href="scmp_gcd.html#E68:24"><i><font color="Green" title="E83">A60</font></i></a></i>;<br/><b>thus </b><a NAME="E3:24_46_1_7"/>
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Computation</a> <font color="Maroon" title="c17">s1</font></span>)</span> <a href="ami_1.html#K11" title="AMI_1:func.11">.</a> <font color="Maroon" title="c22">k</font></span>)</span> <a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">.</a> <font color="Maroon" title="c23">a</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Computation</a> <font color="Maroon" title="c18">s2</font></span>)</span> <a href="ami_1.html#K11" title="AMI_1:func.11">.</a> <font color="Maroon" title="c22">k</font></span>)</span> <a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">.</a> <font color="Maroon" title="c23">a</font>
 <b>by </b><i><a class="txt" href="scmp_gcd.html#E76:24"><i><font color="Green" title="E91">A93</font></i></a>, <a class="txt" href="scmp_gcd.html#E1:24_46"><i><font color="Green" title="E93">A106</font></i></a>, <a class="txt" href="scmp_gcd.html#E1:24_46_1_7"><i><font color="Green" title="E94">A113</font></i></a></i>;<br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="24_46_1_8"><b>suppose </b></a><a NAME="E1:24_46_1_8"/><i><font color="Green" title="E94">A114</font></i>: 
<font color="Maroon" title="c22">k</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 7
 ;<br/><div class="add"><b>thus </b> <a href="ami_1.html#K6" title="AMI_1:func.6">IC</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Computation</a> <font color="Maroon" title="c17">s1</font></span>)</span> <a href="ami_1.html#K11" title="AMI_1:func.11">.</a> <font color="Maroon" title="c22">k</font></span>)</span> = 
 <a href="scmpds_2.html#K18" title="SCMPDS_2:func.18">Next</a> <span class="p1">(<span class="default"><a href="ami_1.html#K6" title="AMI_1:func.6">IC</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Computation</a> <font color="Maroon" title="c18">s2</font></span>)</span> <a href="ami_1.html#K11" title="AMI_1:func.11">.</a> 6</span>)</span></span>)</span>
<b>by </b><i><a class="txt" href="scmp_gcd.html#E65:24"><i><font color="Green" title="E80">A57</font></i></a>, <a class="txt" href="scmp_gcd.html#E67:24"><i><font color="Green" title="E82">A59</font></i></a>, <a class="txt" href="scmp_gcd.html#E68:24"><i><font color="Green" title="E83">A60</font></i></a>, <a class="txt" href="scmp_gcd.html#E1:24_46_1_8"><i><font color="Green" title="E94">A114</font></i></a>, <a class="ref" href="scmpds_2.html#T71" title="SCMPDS_2:th.71">SCMPDS_2:71</a></i>
<br/>.= 
 <a href="ami_1.html#K6" title="AMI_1:func.6">IC</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Computation</a> <font color="Maroon" title="c18">s2</font></span>)</span> <a href="ami_1.html#K11" title="AMI_1:func.11">.</a> <font color="Maroon" title="c22">k</font></span>)</span>
<b>by </b><i><a class="txt" href="scmp_gcd.html#E70:24"><i><font color="Green" title="E85">A62</font></i></a>, <a class="txt" href="scmp_gcd.html#E1:24_46_1_8"><i><font color="Green" title="E94">A114</font></i></a>, <a class="ref" href="scmpds_2.html#T71" title="SCMPDS_2:th.71">SCMPDS_2:71</a></i>
;<br/><b>thus </b><a NAME="E3:24_46_1_8"/>
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Computation</a> <font color="Maroon" title="c17">s1</font></span>)</span> <a href="ami_1.html#K11" title="AMI_1:func.11">.</a> <font color="Maroon" title="c22">k</font></span>)</span> <a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">.</a> <font color="Maroon" title="c23">a</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Computation</a> <font color="Maroon" title="c18">s2</font></span>)</span> <a href="ami_1.html#K11" title="AMI_1:func.11">.</a> <font color="Maroon" title="c22">k</font></span>)</span> <a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">.</a> <font color="Maroon" title="c23">a</font>
 <b>by </b><i><a class="txt" href="scmp_gcd.html#E77:24"><i><font color="Green" title="E92">A100</font></i></a>, <a class="txt" href="scmp_gcd.html#E1:24_46"><i><font color="Green" title="E93">A106</font></i></a>, <a class="txt" href="scmp_gcd.html#E1:24_46_1_8"><i><font color="Green" title="E94">A114</font></i></a></i>;<br/></div><b>end;</b></div></div><b>end;</b></div></div>
<b>end;</b></div>


</div>
