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

<b>let </b><font color="Maroon" title="c16">s</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="c17">GA</font> =  <a href="scmp_gcd.html#K4" title="SCMP_GCD:func.4">GCD-Algorithm</a> ;<br/>
<b>assume </b><a NAME="E1:21"/><i><font color="Green" title="E19">A1</font></i>: 
 <a href="scmpds_4.html#K2" title="SCMPDS_4:func.2">Initialized</a> <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="c16">s</font>
 ;<br/>

<b>let </b><font color="Maroon" title="c18">x</font>, <font color="Maroon" title="c19">y</font> be   <a href="int_1.html#NM1" title="INT_1:NM.1">Integer</a>;<br/>

<b>assume </b><a NAME="E2:21"/><i><font color="Green" title="E20">A2</font></i>: 
( <font color="Maroon" title="c16">s</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> 9</span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c18">x</font> &amp; <font color="Maroon" title="c16">s</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> 10</span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c19">y</font> &amp; <font color="Maroon" title="c18">x</font> <a href="xxreal_0.html#NR2" title="XXREAL_0:NR.2">&gt;=</a> 0 &amp; <font color="Maroon" title="c19">y</font> <a href="xxreal_0.html#NR2" title="XXREAL_0:NR.2">&gt;=</a> 0 )
 ;<br/>

<b>set </b><font color="Maroon" title="c20">s4</font> = <span class="p1">(<span class="default"><a href="ami_1.html#K9" title="AMI_1:func.9">Computation</a> <font color="Maroon" title="c16">s</font></span>)</span> <a href="ami_1.html#K10" title="AMI_1:func.10">.</a> 4;<br/>
<a NAME="E3:21"/><i><font color="Green" title="E21">A3</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="c16">s</font>
 
<b>by </b><i><a class="txt" href="scmp_gcd.html#E1:21"><i><font color="Green" title="E19">A1</font></i></a>, <a class="ref" href="scmpds_4.html#T57" title="SCMPDS_4:th.57">SCMPDS_4:57</a></i>;<br/>
<a NAME="E4:21"/><b>then </b><i><font color="Green" title="E22">A4</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> <span class="p1">(<span class="default"><a href="ami_1.html#K9" title="AMI_1:func.9">Computation</a> <font color="Maroon" title="c16">s</font></span>)</span> <a href="ami_1.html#K10" title="AMI_1:func.10">.</a> 4
 
<b>by </b><i><a class="ref" href="ami_1.html#T81" title="AMI_1:th.81">AMI_1:81</a></i>;<br/>
<a NAME="E5:21"/><i><font color="Green" title="E23">A5</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#K9" title="AMI_1:func.9">Computation</a> <font color="Maroon" title="c16">s</font></span>)</span> <a href="ami_1.html#K10" title="AMI_1:func.10">.</a> 4</span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="scmpds_3.html#K2" title="SCMPDS_3:func.2">inspos</a> 5 &amp; <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K9" title="AMI_1:func.9">Computation</a> <font color="Maroon" title="c16">s</font></span>)</span> <a href="ami_1.html#K10" title="AMI_1:func.10">.</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 &amp; <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K9" title="AMI_1:func.9">Computation</a> <font color="Maroon" title="c16">s</font></span>)</span> <a href="ami_1.html#K10" title="AMI_1:func.10">.</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> 7 &amp; <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K9" title="AMI_1:func.9">Computation</a> <font color="Maroon" title="c16">s</font></span>)</span> <a href="ami_1.html#K10" title="AMI_1:func.10">.</a> 4</span>)</span> <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">7 <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> <a href="scmpds_1.html#K23" title="SCMPDS_1:func.23">RetIC</a> </span>)</span></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="scmpds_3.html#K2" title="SCMPDS_3:func.2">inspos</a> 2 &amp; <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K9" title="AMI_1:func.9">Computation</a> <font color="Maroon" title="c16">s</font></span>)</span> <a href="ami_1.html#K10" title="AMI_1:func.10">.</a> 4</span>)</span> <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> 9</span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c16">s</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> 9</span>)</span> &amp; <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K9" title="AMI_1:func.9">Computation</a> <font color="Maroon" title="c16">s</font></span>)</span> <a href="ami_1.html#K10" title="AMI_1:func.10">.</a> 4</span>)</span> <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> 10</span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c16">s</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> 10</span>)</span> )
 
<b>by </b><i><a class="txt" href="scmp_gcd.html#E1:21"><i><font color="Green" title="E19">A1</font></i></a>, <a class="ref" href="scmp_gcd.html#T15" target="_self" title="SCMP_GCD:th.15">Th15</a></i>;<br/>
<b>then </b><i><font color="Green" title="E24">A6</font></i>: <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K9" title="AMI_1:func.9">Computation</a> <font color="Maroon" title="c16">s</font></span>)</span> <a href="ami_1.html#K10" title="AMI_1:func.10">.</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#K9" title="AMI_1:func.9">Computation</a> <font color="Maroon" title="c16">s</font></span>)</span> <a href="ami_1.html#K10" title="AMI_1:func.10">.</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>,3</span>)</span> = 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K9" title="AMI_1:func.9">Computation</a> <font color="Maroon" title="c16">s</font></span>)</span> <a href="ami_1.html#K10" title="AMI_1:func.10">.</a> 4</span>)</span> <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">7 <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 3</span>)</span></span>)</span>
<b>by </b><i><a class="ref" href="scmp_gcd.html#T5" target="_self" title="SCMP_GCD:th.5">Th5</a></i>
<br/>.= 
<font color="Maroon" title="c19">y</font>
<b>by </b><i><a class="txt" href="scmp_gcd.html#E1:21"><i><font color="Green" title="E19">A1</font></i></a>, <a class="txt" href="scmp_gcd.html#E2:21"><i><font color="Green" title="E20">A2</font></i></a>, <a class="ref" href="scmp_gcd.html#T15" target="_self" title="SCMP_GCD:th.15">Th15</a></i>
;<br/>
<a NAME="E7:21"/><i><font color="Green" title="E25">A7</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#K9" title="AMI_1:func.9">Computation</a> <font color="Maroon" title="c16">s</font></span>)</span> <a href="ami_1.html#K10" title="AMI_1:func.10">.</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>,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">7 <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#E5:21"><i><font color="Green" title="E23">A5</font></i></a>, <a class="ref" href="scmp_gcd.html#T5" target="_self" title="SCMP_GCD:th.5">Th5</a></i>;<br/>
<a NAME="E8:21"/><b>then </b><i><font color="Green" title="E26">A8</font></i>: 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K9" title="AMI_1:func.9">Computation</a> <font color="Maroon" title="c16">s</font></span>)</span> <a href="ami_1.html#K10" title="AMI_1:func.10">.</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#K9" title="AMI_1:func.9">Computation</a> <font color="Maroon" title="c16">s</font></span>)</span> <a href="ami_1.html#K10" title="AMI_1:func.10">.</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>,2</span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c18">x</font>
 
<b>by </b><i><a class="txt" href="scmp_gcd.html#E1:21"><i><font color="Green" title="E19">A1</font></i></a>, <a class="txt" href="scmp_gcd.html#E2:21"><i><font color="Green" title="E20">A2</font></i></a>, <a class="ref" href="scmp_gcd.html#T15" target="_self" title="SCMP_GCD:th.15">Th15</a></i>;<br/>
<b>set </b><font color="Maroon" title="c21">Cs4</font> =  <a href="ami_1.html#K9" title="AMI_1:func.9">Computation</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K9" title="AMI_1:func.9">Computation</a> <font color="Maroon" title="c16">s</font></span>)</span> <a href="ami_1.html#K10" title="AMI_1:func.10">.</a> 4</span>)</span>;<br/>
<b>consider </b><font color="Maroon" title="c22">n</font> being    <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> <b> such that </b><br/><a NAME="E10:21"/><i><font color="Green" title="E27">A9</font></i>: 
(  <a href="ami_1.html#K7" title="AMI_1:func.7">CurInstr</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K9" title="AMI_1:func.9">Computation</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="ami_1.html#K9" title="AMI_1:func.9">Computation</a> <font color="Maroon" title="c16">s</font></span>)</span> <a href="ami_1.html#K10" title="AMI_1:func.10">.</a> 4</span>)</span></span>)</span> <a href="ami_1.html#K10" title="AMI_1:func.10">.</a> <font color="Maroon" title="c22">n</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="scmpds_2.html#K5" title="SCMPDS_2:func.5">return</a> <a href="scmp_gcd.html#K3" title="SCMP_GCD:func.3">SBP</a>  &amp; <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K9" title="AMI_1:func.9">Computation</a> <font color="Maroon" title="c16">s</font></span>)</span> <a href="ami_1.html#K10" title="AMI_1:func.10">.</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> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K9" title="AMI_1:func.9">Computation</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="ami_1.html#K9" title="AMI_1:func.9">Computation</a> <font color="Maroon" title="c16">s</font></span>)</span> <a href="ami_1.html#K10" title="AMI_1:func.10">.</a> 4</span>)</span></span>)</span> <a href="ami_1.html#K10" title="AMI_1:func.10">.</a> <font color="Maroon" title="c22">n</font></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>  &amp; <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K9" title="AMI_1:func.9">Computation</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="ami_1.html#K9" title="AMI_1:func.9">Computation</a> <font color="Maroon" title="c16">s</font></span>)</span> <a href="ami_1.html#K10" title="AMI_1:func.10">.</a> 4</span>)</span></span>)</span> <a href="ami_1.html#K10" title="AMI_1:func.10">.</a> <font color="Maroon" title="c22">n</font></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#K9" title="AMI_1:func.9">Computation</a> <font color="Maroon" title="c16">s</font></span>)</span> <a href="ami_1.html#K10" title="AMI_1:func.10">.</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>,2</span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="ami_1.html#K9" title="AMI_1:func.9">Computation</a> <font color="Maroon" title="c16">s</font></span>)</span> <a href="ami_1.html#K10" title="AMI_1:func.10">.</a> 4</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#K9" title="AMI_1:func.9">Computation</a> <font color="Maroon" title="c16">s</font></span>)</span> <a href="ami_1.html#K10" title="AMI_1:func.10">.</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>,2</span>)</span></span>)</span> <a href="int_2.html#K3" title="INT_2:func.3">gcd</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="ami_1.html#K9" title="AMI_1:func.9">Computation</a> <font color="Maroon" title="c16">s</font></span>)</span> <a href="ami_1.html#K10" title="AMI_1:func.10">.</a> 4</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#K9" title="AMI_1:func.9">Computation</a> <font color="Maroon" title="c16">s</font></span>)</span> <a href="ami_1.html#K10" title="AMI_1:func.10">.</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>,3</span>)</span></span>)</span> &amp; ( for <font color="Olive" title="b1">j</font> being   <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>   st 1 <a href="xxreal_0.html#NR3" title="XXREAL_0:NR.3">&lt;</a> <font color="Olive" title="b1">j</font> &amp; <font color="Olive" title="b1">j</font> <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="ami_1.html#K9" title="AMI_1:func.9">Computation</a> <font color="Maroon" title="c16">s</font></span>)</span> <a href="ami_1.html#K10" title="AMI_1:func.10">.</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> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> 1 holds <br/><span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K9" title="AMI_1:func.9">Computation</a> <font color="Maroon" title="c16">s</font></span>)</span> <a href="ami_1.html#K10" title="AMI_1:func.10">.</a> 4</span>)</span> <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> <font color="Olive" title="b1">j</font></span>)</span> <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#K9" title="AMI_1:func.9">Computation</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="ami_1.html#K9" title="AMI_1:func.9">Computation</a> <font color="Maroon" title="c16">s</font></span>)</span> <a href="ami_1.html#K10" title="AMI_1:func.10">.</a> 4</span>)</span></span>)</span> <a href="ami_1.html#K10" title="AMI_1:func.10">.</a> <font color="Maroon" title="c22">n</font></span>)</span> <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> <font color="Olive" title="b1">j</font></span>)</span> ) )
 <b>by </b><i><a class="txt" href="scmp_gcd.html#E2:21"><i><font color="Green" title="E20">A2</font></i></a>, <a class="txt" href="scmp_gcd.html#E4:21"><i><font color="Green" title="E22">A4</font></i></a>, <a class="txt" href="scmp_gcd.html#E5:21"><i><font color="Green" title="E23">A5</font></i></a>, <a class="txt" href="scmp_gcd.html#E6:21"><i><font color="Green" title="E24">A6</font></i></a>, <a class="txt" href="scmp_gcd.html#E7:21"><i><font color="Green" title="E25">A7</font></i></a>, <a class="ref" href="scmp_gcd.html#T17" target="_self" title="SCMP_GCD:th.17">Th17</a></i>;<br/>
<a NAME="E11:21"/><i><font color="Green" title="E28">A10</font></i>: 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K9" title="AMI_1:func.9">Computation</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="ami_1.html#K9" title="AMI_1:func.9">Computation</a> <font color="Maroon" title="c16">s</font></span>)</span> <a href="ami_1.html#K10" title="AMI_1:func.10">.</a> 4</span>)</span></span>)</span> <a href="ami_1.html#K10" title="AMI_1:func.10">.</a> <font color="Maroon" title="c22">n</font></span>)</span> <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> 8</span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="scmpds_3.html#K2" title="SCMPDS_3:func.2">inspos</a> 2
 
<b>by </b><i><a class="txt" href="scmp_gcd.html#E5:21"><i><font color="Green" title="E23">A5</font></i></a>, <a class="txt" href="scmp_gcd.html#E10:21"><i><font color="Green" title="E27">A9</font></i></a>, <a class="ref" href="scmpds_1.html#D23" title="SCMPDS_1:def.23">SCMPDS_1:def 23</a></i>;<br/>
<a NAME="E12:21"/><i><font color="Green" title="E29">A11</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#K9" title="AMI_1:func.9">Computation</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="ami_1.html#K9" title="AMI_1:func.9">Computation</a> <font color="Maroon" title="c16">s</font></span>)</span> <a href="ami_1.html#K10" title="AMI_1:func.10">.</a> 4</span>)</span></span>)</span> <a href="ami_1.html#K10" title="AMI_1:func.10">.</a> <font color="Maroon" title="c22">n</font></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>  <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">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#E5:21"><i><font color="Green" title="E23">A5</font></i></a>, <a class="txt" href="scmp_gcd.html#E10:21"><i><font color="Green" title="E27">A9</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#D23" title="SCMPDS_1:def.23">SCMPDS_1:def 23</a></i>;<br/>
<i><font color="Green" title="E30">A12</font></i>: <span class="p1">(<span class="default"><a href="ami_1.html#K9" title="AMI_1:func.9">Computation</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="ami_1.html#K9" title="AMI_1:func.9">Computation</a> <font color="Maroon" title="c16">s</font></span>)</span> <a href="ami_1.html#K10" title="AMI_1:func.10">.</a> 4</span>)</span></span>)</span> <a href="ami_1.html#K10" title="AMI_1:func.10">.</a> <span class="p1">(<span class="default"><font color="Maroon" title="c22">n</font> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1</span>)</span> = 
 <a href="ami_1.html#K8" title="AMI_1:func.8">Following</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K9" title="AMI_1:func.9">Computation</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="ami_1.html#K9" title="AMI_1:func.9">Computation</a> <font color="Maroon" title="c16">s</font></span>)</span> <a href="ami_1.html#K10" title="AMI_1:func.10">.</a> 4</span>)</span></span>)</span> <a href="ami_1.html#K10" title="AMI_1:func.10">.</a> <font color="Maroon" title="c22">n</font></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#K5" title="SCMPDS_2:func.5">return</a> <a href="scmp_gcd.html#K3" title="SCMP_GCD:func.3">SBP</a> </span>)</span>,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K9" title="AMI_1:func.9">Computation</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="ami_1.html#K9" title="AMI_1:func.9">Computation</a> <font color="Maroon" title="c16">s</font></span>)</span> <a href="ami_1.html#K10" title="AMI_1:func.10">.</a> 4</span>)</span></span>)</span> <a href="ami_1.html#K10" title="AMI_1:func.10">.</a> <font color="Maroon" title="c22">n</font></span>)</span>
<b>by </b><i><a class="txt" href="scmp_gcd.html#E10:21"><i><font color="Green" title="E27">A9</font></i></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#K9" title="AMI_1:func.9">Computation</a> <font color="Maroon" title="c16">s</font></span>)</span> <a href="ami_1.html#K10" title="AMI_1:func.10">.</a> <span class="p2">(<span class="default">4 <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> <span class="p3">(<span class="default"><font color="Maroon" title="c22">n</font> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1</span>)</span></span>)</span></span>)</span> = 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K9" title="AMI_1:func.9">Computation</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="ami_1.html#K9" title="AMI_1:func.9">Computation</a> <font color="Maroon" title="c16">s</font></span>)</span> <a href="ami_1.html#K10" title="AMI_1:func.10">.</a> 4</span>)</span></span>)</span> <a href="ami_1.html#K10" title="AMI_1:func.10">.</a> <span class="p2">(<span class="default"><font color="Maroon" title="c22">n</font> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1</span>)</span></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p1">(<span class="default"><a href="ami_1.html#K2" title="AMI_1:func.2">IC</a> <a href="scmpds_2.html#K1" title="SCMPDS_2:func.1">SCMPDS</a> </span>)</span>
<b>by </b><i><a class="ref" href="ami_1.html#T51" title="AMI_1:th.51">AMI_1:51</a></i>
<br/>.= 
<span class="p1">(<span class="default"><a href="int_2.html#K1" title="INT_2:func.1">abs</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="ami_1.html#K9" title="AMI_1:func.9">Computation</a> <span class="p5">(<span class="default"><span class="p0">(<span class="default"><a href="ami_1.html#K9" title="AMI_1:func.9">Computation</a> <font color="Maroon" title="c16">s</font></span>)</span> <a href="ami_1.html#K10" title="AMI_1:func.10">.</a> 4</span>)</span></span>)</span> <a href="ami_1.html#K10" title="AMI_1:func.10">.</a> <font color="Maroon" title="c22">n</font></span>)</span> <a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">.</a> <span class="p3">(<span class="default"><a href="scmpds_2.html#K3" title="SCMPDS_2:func.3">DataLoc</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><span class="p0">(<span class="default"><a href="ami_1.html#K9" title="AMI_1:func.9">Computation</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K9" title="AMI_1:func.9">Computation</a> <font color="Maroon" title="c16">s</font></span>)</span> <a href="ami_1.html#K10" title="AMI_1:func.10">.</a> 4</span>)</span></span>)</span> <a href="ami_1.html#K10" title="AMI_1:func.10">.</a> <font color="Maroon" title="c22">n</font></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>)</span></span>)</span></span>)</span> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 2
<b>by </b><i><a class="txt" href="scmp_gcd.html#E13:21"><i><font color="Green" title="E30">A12</font></i></a>, <a class="ref" href="scmpds_2.html#T70" title="SCMPDS_2:th.70">SCMPDS_2:70</a></i>
<br/>.= 
 <a href="scmpds_3.html#K2" title="SCMPDS_3:func.2">inspos</a> <span class="p1">(<span class="default">2 <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#E11:21"><i><font color="Green" title="E28">A10</font></i></a>, <a class="txt" href="scmp_gcd.html#E12:21"><i><font color="Green" title="E29">A11</font></i></a>, <a class="ref" href="scmp_gcd.html#T3" target="_self" title="SCMP_GCD:th.3">Th3</a></i>
;<br/>
<a NAME="E15:21"/><b>then </b><i><font color="Green" title="E31">A13</font></i>: 
<font color="Maroon" title="c16">s</font> <a href="ami_1.html#K12" title="AMI_1:func.12">.</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#K9" title="AMI_1:func.9">Computation</a> <font color="Maroon" title="c16">s</font></span>)</span> <a href="ami_1.html#K10" title="AMI_1:func.10">.</a> <span class="p3">(<span class="default">4 <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> <span class="p4">(<span class="default"><font color="Maroon" title="c22">n</font> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1</span>)</span></span>)</span></span>)</span></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="ami_1.html#K5" title="AMI_1:func.5">halt</a> <a href="scmpds_2.html#K1" title="SCMPDS_2:func.1">SCMPDS</a> 
 
<b>by </b><i><a class="txt" href="scmp_gcd.html#E3:21"><i><font color="Green" title="E21">A3</font></i></a>, <a class="txt" href="scmp_gcd.html#E19"><i><font color="Green" title="E11">Lm1</font></i></a></i>;<br/>
<a NAME="E16:21"/><i><font color="Green" title="E32">A14</font></i>: 
 <a href="scmp_gcd.html#K1" title="SCMP_GCD:func.1">intpos</a> 9 <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a>  <a href="scmp_gcd.html#K3" title="SCMP_GCD:func.3">SBP</a> 
 
<b>by </b><i><a class="ref" href="ami_3.html#T52" title="AMI_3:th.52">AMI_3:52</a></i>;<br/>
 <a href="ami_1.html#K11" title="AMI_1:func.11">Result</a> <font color="Maroon" title="c16">s</font> = 
<span class="p1">(<span class="default"><a href="ami_1.html#K9" title="AMI_1:func.9">Computation</a> <font color="Maroon" title="c16">s</font></span>)</span> <a href="ami_1.html#K10" title="AMI_1:func.10">.</a> <span class="p1">(<span class="default">4 <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> <span class="p2">(<span class="default"><font color="Maroon" title="c22">n</font> <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#E15:21"><i><font color="Green" title="E31">A13</font></i></a>, <a class="ref" href="ami_1.html#T56" title="AMI_1:th.56">AMI_1:56</a></i>
<br/>.= 
<span class="p1">(<span class="default"><a href="ami_1.html#K9" title="AMI_1:func.9">Computation</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="ami_1.html#K9" title="AMI_1:func.9">Computation</a> <font color="Maroon" title="c16">s</font></span>)</span> <a href="ami_1.html#K10" title="AMI_1:func.10">.</a> 4</span>)</span></span>)</span> <a href="ami_1.html#K10" title="AMI_1:func.10">.</a> <span class="p1">(<span class="default"><font color="Maroon" title="c22">n</font> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1</span>)</span>
<b>by </b><i><a class="ref" href="ami_1.html#T51" title="AMI_1:th.51">AMI_1:51</a></i>
;<br/>
<b>hence </b><a NAME="E18:21"/>
<span class="p1">(<span class="default"><a href="ami_1.html#K11" title="AMI_1:func.11">Result</a> <font color="Maroon" title="c16">s</font></span>)</span> <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> 9</span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c18">x</font> <a href="int_2.html#K3" title="INT_2:func.3">gcd</a> <font color="Maroon" title="c19">y</font>
 <b>by </b><i><a class="txt" href="scmp_gcd.html#E6:21"><i><font color="Green" title="E24">A6</font></i></a>, <a class="txt" href="scmp_gcd.html#E7:21"><i><font color="Green" title="E25">A7</font></i></a>, <a class="txt" href="scmp_gcd.html#E8:21"><i><font color="Green" title="E26">A8</font></i></a>, <a class="txt" href="scmp_gcd.html#E10:21"><i><font color="Green" title="E27">A9</font></i></a>, <a class="txt" href="scmp_gcd.html#E13:21"><i><font color="Green" title="E30">A12</font></i></a>, <a class="txt" href="scmp_gcd.html#E16:21"><i><font color="Green" title="E32">A14</font></i></a>, <a class="ref" href="scmpds_2.html#T70" title="SCMPDS_2:th.70">SCMPDS_2:70</a></i>;<br/>


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