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<b>let </b><font color="Maroon" title="c16">s1</font>, <font color="Maroon" title="c17">s2</font> be   <a href="ami_1.html#NM5" title="AMI_1:NM.5">State</a> of <a href="scmpds_2.html#K1" title="SCMPDS_2:func.1">SCMPDS</a> ;<br/><b>let </b><font color="Maroon" title="c18">a</font> be    <a href="scmpds_2.html#M1" title="SCMPDS_2:mode.1">Int_position</a> ;<br/><b>let </b><font color="Maroon" title="c19">k</font> be    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of  <a href="ami_2.html#K5" title="AMI_2:func.5">NAT</a> ;<br/>





<b>set </b><font color="Maroon" title="c20">GA</font> =  <a href="scmp_gcd.html#K4" title="SCMP_GCD:func.4">GCD-Algorithm</a> ;<br/>
<b>assume </b><a NAME="E1:25"/><i><font color="Green" title="E23">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">s1</font> &amp;  <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="c17">s2</font> )
 ;<br/>

<b>assume </b><a NAME="E2:25"/><i><font color="Green" title="E24">A2</font></i>: 
( <font color="Maroon" title="c16">s1</font> <a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">.</a> <font color="Maroon" title="c18">a</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c17">s2</font> <a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">.</a> <font color="Maroon" title="c18">a</font> &amp; <font color="Maroon" title="c19">k</font> <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> 4 )
 ;<br/>

<a NAME="E3:25"/><i><font color="Green" title="E25">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">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="c17">s2</font> )
 
<b>by </b><i><a class="txt" href="scmp_gcd.html#E1:25"><i><font color="Green" title="E23">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="E4:25"/><i><font color="Green" title="E26">A4</font></i>: 
 <a href="ami_1.html#K7" title="AMI_1:func.7">IC</a> <font color="Maroon" title="c16">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> <a href="numbers.html#K6" title="NUMBERS:func.6">0</a> 
 
<b>by </b><i><a class="txt" href="scmp_gcd.html#E1:25"><i><font color="Green" title="E23">A1</font></i></a>, <a class="ref" href="scmpds_5.html#T18" title="SCMPDS_5:th.18">SCMPDS_5:18</a></i>;<br/>
<i><font color="Green" title="E27">A5</font></i>:  <a href="ami_1.html#K10" title="AMI_1:func.10">Computation</a> <font color="Maroon" title="c16">s1</font>,<span class="p1">(<span class="default"><a href="numbers.html#K6" title="NUMBERS:func.6">0</a>  <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span> = 
 <a href="ami_1.html#K9" title="AMI_1:func.9">Following</a> <span class="p1">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Computation</a> <font color="Maroon" title="c16">s1</font>,<a href="numbers.html#K6" title="NUMBERS:func.6">0</a> </span>)</span>
<b>by </b><i><a class="ref" href="ami_1.html#T14" title="AMI_1:th.14">AMI_1:14</a></i>
<br/>.= 
 <a href="ami_1.html#K9" title="AMI_1:func.9">Following</a> <font color="Maroon" title="c16">s1</font>
<b>by </b><i><a class="ref" href="ami_1.html#T13" title="AMI_1:th.13">AMI_1:13</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#K2" title="SCMP_GCD:func.2">GBP</a>  <a href="scmpds_2.html#K6" title="SCMPDS_2:func.6">:=</a> <a href="numbers.html#K6" title="NUMBERS:func.6">0</a> </span>)</span>,<font color="Maroon" title="c16">s1</font>
<b>by </b><i><a class="txt" href="scmp_gcd.html#E3:25"><i><font color="Green" title="E25">A3</font></i></a>, <a class="txt" href="scmp_gcd.html#E4:25"><i><font color="Green" title="E26">A4</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="E6:25"/><i><font color="Green" title="E28">A6</font></i>: 
 <a href="ami_1.html#K7" title="AMI_1:func.7">IC</a> <font color="Maroon" title="c17">s2</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="scmpds_3.html#K2" title="SCMPDS_3:func.2">inspos</a> <a href="numbers.html#K6" title="NUMBERS:func.6">0</a> 
 
<b>by </b><i><a class="txt" href="scmp_gcd.html#E1:25"><i><font color="Green" title="E23">A1</font></i></a>, <a class="ref" href="scmpds_5.html#T18" title="SCMPDS_5:th.18">SCMPDS_5:18</a></i>;<br/>
<i><font color="Green" title="E29">A7</font></i>:  <a href="ami_1.html#K10" title="AMI_1:func.10">Computation</a> <font color="Maroon" title="c17">s2</font>,<span class="p1">(<span class="default"><a href="numbers.html#K6" title="NUMBERS:func.6">0</a>  <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span> = 
 <a href="ami_1.html#K9" title="AMI_1:func.9">Following</a> <span class="p1">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Computation</a> <font color="Maroon" title="c17">s2</font>,<a href="numbers.html#K6" title="NUMBERS:func.6">0</a> </span>)</span>
<b>by </b><i><a class="ref" href="ami_1.html#T14" title="AMI_1:th.14">AMI_1:14</a></i>
<br/>.= 
 <a href="ami_1.html#K9" title="AMI_1:func.9">Following</a> <font color="Maroon" title="c17">s2</font>
<b>by </b><i><a class="ref" href="ami_1.html#T13" title="AMI_1:th.13">AMI_1:13</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#K2" title="SCMP_GCD:func.2">GBP</a>  <a href="scmpds_2.html#K6" title="SCMPDS_2:func.6">:=</a> <a href="numbers.html#K6" title="NUMBERS:func.6">0</a> </span>)</span>,<font color="Maroon" title="c17">s2</font>
<b>by </b><i><a class="txt" href="scmp_gcd.html#E3:25"><i><font color="Green" title="E25">A3</font></i></a>, <a class="txt" href="scmp_gcd.html#E6:25"><i><font color="Green" title="E28">A6</font></i></a>, <a class="txt" href="scmp_gcd.html#E19"><i><font color="Green" title="E11">Lm1</font></i></a></i>
;<br/>
<i><font color="Green" title="E30">A8</font></i>:  <a href="ami_1.html#K7" title="AMI_1:func.7">IC</a> <span class="p1">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Computation</a> <font color="Maroon" title="c16">s1</font>,1</span>)</span> = 
 <a href="scmnorm.html#K1" title="SCMNORM:func.1">Next</a> <span class="p1">(<span class="default"><a href="ami_1.html#K7" title="AMI_1:func.7">IC</a> <font color="Maroon" title="c16">s1</font></span>)</span>
<b>by </b><i><a class="txt" href="scmp_gcd.html#E5:25"><i><font color="Green" title="E27">A5</font></i></a>, <a class="ref" href="scmpds_2.html#T57" title="SCMPDS_2:th.57">SCMPDS_2:57</a></i>
<br/>.= 
 <a href="scmpds_3.html#K2" title="SCMPDS_3:func.2">inspos</a> <span class="p1">(<span class="default"><a href="numbers.html#K6" title="NUMBERS:func.6">0</a>  <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span>
<b>by </b><i><a class="txt" href="scmp_gcd.html#E4:25"><i><font color="Green" title="E26">A4</font></i></a></i>
;<br/>
<b>then </b><i><font color="Green" title="E31">A9</font></i>:  <a href="ami_1.html#K8" title="AMI_1:func.8">CurInstr</a> <span class="p1">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Computation</a> <font color="Maroon" title="c16">s1</font>,1</span>)</span> = 
<font color="Maroon" title="c16">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> 1</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>  <a href="scmpds_2.html#K6" title="SCMPDS_2:func.6">:=</a> 7
<b>by </b><i><a class="txt" href="scmp_gcd.html#E3:25"><i><font color="Green" title="E25">A3</font></i></a>, <a class="txt" href="scmp_gcd.html#E19"><i><font color="Green" title="E11">Lm1</font></i></a></i>
;<br/>
<i><font color="Green" title="E32">A10</font></i>:  <a href="ami_1.html#K10" title="AMI_1:func.10">Computation</a> <font color="Maroon" title="c16">s1</font>,<span class="p1">(<span class="default">1 <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span> = 
 <a href="ami_1.html#K9" title="AMI_1:func.9">Following</a> <span class="p1">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Computation</a> <font color="Maroon" title="c16">s1</font>,1</span>)</span>
<b>by </b><i><a class="ref" href="ami_1.html#T14" title="AMI_1:th.14">AMI_1:14</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>  <a href="scmpds_2.html#K6" title="SCMPDS_2:func.6">:=</a> 7</span>)</span>,<span class="p1">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Computation</a> <font color="Maroon" title="c16">s1</font>,1</span>)</span>
<b>by </b><i><a class="txt" href="scmp_gcd.html#E9:25"><i><font color="Green" title="E31">A9</font></i></a></i>
;<br/>
<i><font color="Green" title="E33">A11</font></i>:  <a href="ami_1.html#K7" title="AMI_1:func.7">IC</a> <span class="p1">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Computation</a> <font color="Maroon" title="c17">s2</font>,1</span>)</span> = 
 <a href="scmnorm.html#K1" title="SCMNORM:func.1">Next</a> <span class="p1">(<span class="default"><a href="ami_1.html#K7" title="AMI_1:func.7">IC</a> <font color="Maroon" title="c17">s2</font></span>)</span>
<b>by </b><i><a class="txt" href="scmp_gcd.html#E7:25"><i><font color="Green" title="E29">A7</font></i></a>, <a class="ref" href="scmpds_2.html#T57" title="SCMPDS_2:th.57">SCMPDS_2:57</a></i>
<br/>.= 
 <a href="scmpds_3.html#K2" title="SCMPDS_3:func.2">inspos</a> <span class="p1">(<span class="default"><a href="numbers.html#K6" title="NUMBERS:func.6">0</a>  <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span>
<b>by </b><i><a class="txt" href="scmp_gcd.html#E6:25"><i><font color="Green" title="E28">A6</font></i></a></i>
;<br/>
<b>then </b><i><font color="Green" title="E34">A12</font></i>:  <a href="ami_1.html#K8" title="AMI_1:func.8">CurInstr</a> <span class="p1">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Computation</a> <font color="Maroon" title="c17">s2</font>,1</span>)</span> = 
<font color="Maroon" title="c17">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> 1</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>  <a href="scmpds_2.html#K6" title="SCMPDS_2:func.6">:=</a> 7
<b>by </b><i><a class="txt" href="scmp_gcd.html#E3:25"><i><font color="Green" title="E25">A3</font></i></a>, <a class="txt" href="scmp_gcd.html#E19"><i><font color="Green" title="E11">Lm1</font></i></a></i>
;<br/>
<i><font color="Green" title="E35">A13</font></i>:  <a href="ami_1.html#K10" title="AMI_1:func.10">Computation</a> <font color="Maroon" title="c17">s2</font>,<span class="p1">(<span class="default">1 <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span> = 
 <a href="ami_1.html#K9" title="AMI_1:func.9">Following</a> <span class="p1">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Computation</a> <font color="Maroon" title="c17">s2</font>,1</span>)</span>
<b>by </b><i><a class="ref" href="ami_1.html#T14" title="AMI_1:th.14">AMI_1:14</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>  <a href="scmpds_2.html#K6" title="SCMPDS_2:func.6">:=</a> 7</span>)</span>,<span class="p1">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Computation</a> <font color="Maroon" title="c17">s2</font>,1</span>)</span>
<b>by </b><i><a class="txt" href="scmp_gcd.html#E12:25"><i><font color="Green" title="E34">A12</font></i></a></i>
;<br/>
<i><font color="Green" title="E36">A14</font></i>:  <a href="ami_1.html#K7" title="AMI_1:func.7">IC</a> <span class="p1">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Computation</a> <font color="Maroon" title="c16">s1</font>,2</span>)</span> = 
 <a href="scmnorm.html#K1" title="SCMNORM:func.1">Next</a> <span class="p1">(<span class="default"><a href="ami_1.html#K7" title="AMI_1:func.7">IC</a> <span class="p2">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Computation</a> <font color="Maroon" title="c16">s1</font>,1</span>)</span></span>)</span>
<b>by </b><i><a class="txt" href="scmp_gcd.html#E10:25"><i><font color="Green" title="E32">A10</font></i></a>, <a class="ref" href="scmpds_2.html#T57" title="SCMPDS_2:th.57">SCMPDS_2:57</a></i>
<br/>.= 
 <a href="scmpds_3.html#K2" title="SCMPDS_3:func.2">inspos</a> <span class="p1">(<span class="default">1 <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span>
<b>by </b><i><a class="txt" href="scmp_gcd.html#E8:25"><i><font color="Green" title="E30">A8</font></i></a></i>
;<br/>
<b>then </b><i><font color="Green" title="E37">A15</font></i>:  <a href="ami_1.html#K8" title="AMI_1:func.8">CurInstr</a> <span class="p1">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Computation</a> <font color="Maroon" title="c16">s1</font>,2</span>)</span> = 
<font color="Maroon" title="c16">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> 2</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#E3:25"><i><font color="Green" title="E25">A3</font></i></a>, <a class="txt" href="scmp_gcd.html#E19"><i><font color="Green" title="E11">Lm1</font></i></a></i>
;<br/>
<i><font color="Green" title="E38">A16</font></i>:  <a href="ami_1.html#K10" title="AMI_1:func.10">Computation</a> <font color="Maroon" title="c16">s1</font>,<span class="p1">(<span class="default">2 <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span> = 
 <a href="ami_1.html#K9" title="AMI_1:func.9">Following</a> <span class="p1">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Computation</a> <font color="Maroon" title="c16">s1</font>,2</span>)</span>
<b>by </b><i><a class="ref" href="ami_1.html#T14" title="AMI_1:th.14">AMI_1:14</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"><a href="ami_1.html#K10" title="AMI_1:func.10">Computation</a> <font color="Maroon" title="c16">s1</font>,2</span>)</span>
<b>by </b><i><a class="txt" href="scmp_gcd.html#E15:25"><i><font color="Green" title="E37">A15</font></i></a></i>
;<br/>
<a NAME="E17:25"/><i><font color="Green" title="E39">A17</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="c16">s1</font>,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> 7
 
<b>by </b><i><a class="txt" href="scmp_gcd.html#E10:25"><i><font color="Green" title="E32">A10</font></i></a>, <a class="ref" href="scmpds_2.html#T57" title="SCMPDS_2:th.57">SCMPDS_2:57</a></i>;<br/>
<i><font color="Green" title="E40">A18</font></i>:  <a href="ami_1.html#K7" title="AMI_1:func.7">IC</a> <span class="p1">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Computation</a> <font color="Maroon" title="c17">s2</font>,2</span>)</span> = 
 <a href="scmnorm.html#K1" title="SCMNORM:func.1">Next</a> <span class="p1">(<span class="default"><a href="ami_1.html#K7" title="AMI_1:func.7">IC</a> <span class="p2">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Computation</a> <font color="Maroon" title="c17">s2</font>,1</span>)</span></span>)</span>
<b>by </b><i><a class="txt" href="scmp_gcd.html#E13:25"><i><font color="Green" title="E35">A13</font></i></a>, <a class="ref" href="scmpds_2.html#T57" title="SCMPDS_2:th.57">SCMPDS_2:57</a></i>
<br/>.= 
 <a href="scmpds_3.html#K2" title="SCMPDS_3:func.2">inspos</a> <span class="p1">(<span class="default">1 <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span>
<b>by </b><i><a class="txt" href="scmp_gcd.html#E11:25"><i><font color="Green" title="E33">A11</font></i></a></i>
;<br/>
<b>then </b><i><font color="Green" title="E41">A19</font></i>:  <a href="ami_1.html#K8" title="AMI_1:func.8">CurInstr</a> <span class="p1">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Computation</a> <font color="Maroon" title="c17">s2</font>,2</span>)</span> = 
<font color="Maroon" title="c17">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> 2</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#E3:25"><i><font color="Green" title="E25">A3</font></i></a>, <a class="txt" href="scmp_gcd.html#E19"><i><font color="Green" title="E11">Lm1</font></i></a></i>
;<br/>
<i><font color="Green" title="E42">A20</font></i>:  <a href="ami_1.html#K10" title="AMI_1:func.10">Computation</a> <font color="Maroon" title="c17">s2</font>,<span class="p1">(<span class="default">2 <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span> = 
 <a href="ami_1.html#K9" title="AMI_1:func.9">Following</a> <span class="p1">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Computation</a> <font color="Maroon" title="c17">s2</font>,2</span>)</span>
<b>by </b><i><a class="ref" href="ami_1.html#T14" title="AMI_1:th.14">AMI_1:14</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"><a href="ami_1.html#K10" title="AMI_1:func.10">Computation</a> <font color="Maroon" title="c17">s2</font>,2</span>)</span>
<b>by </b><i><a class="txt" href="scmp_gcd.html#E19:25"><i><font color="Green" title="E41">A19</font></i></a></i>
;<br/>
<a NAME="E21:25"/><i><font color="Green" title="E43">A21</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">s2</font>,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> 7
 
<b>by </b><i><a class="txt" href="scmp_gcd.html#E13:25"><i><font color="Green" title="E35">A13</font></i></a>, <a class="ref" href="scmpds_2.html#T57" title="SCMPDS_2:th.57">SCMPDS_2:57</a></i>;<br/>
<i><font color="Green" title="E44">A22</font></i>:  <a href="ami_1.html#K7" title="AMI_1:func.7">IC</a> <span class="p1">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Computation</a> <font color="Maroon" title="c16">s1</font>,3</span>)</span> = 
 <a href="scmnorm.html#K1" title="SCMNORM:func.1">Next</a> <span class="p1">(<span class="default"><a href="ami_1.html#K7" title="AMI_1:func.7">IC</a> <span class="p2">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Computation</a> <font color="Maroon" title="c16">s1</font>,2</span>)</span></span>)</span>
<b>by </b><i><a class="txt" href="scmp_gcd.html#E16:25"><i><font color="Green" title="E38">A16</font></i></a>, <a class="ref" href="scmpds_2.html#T71" title="SCMPDS_2:th.71">SCMPDS_2:71</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#K2" title="NAT_1:func.2">+</a> 1</span>)</span>
<b>by </b><i><a class="txt" href="scmp_gcd.html#E14:25"><i><font color="Green" title="E36">A14</font></i></a></i>
;<br/>
<b>then </b><i><font color="Green" title="E45">A23</font></i>:  <a href="ami_1.html#K8" title="AMI_1:func.8">CurInstr</a> <span class="p1">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Computation</a> <font color="Maroon" title="c16">s1</font>,3</span>)</span> = 
<font color="Maroon" title="c16">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> 3</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#K4" title="SCMPDS_2:func.4">goto</a> 2
<b>by </b><i><a class="txt" href="scmp_gcd.html#E3:25"><i><font color="Green" title="E25">A3</font></i></a>, <a class="txt" href="scmp_gcd.html#E19"><i><font color="Green" title="E11">Lm1</font></i></a></i>
;<br/>
<i><font color="Green" title="E46">A24</font></i>:  <a href="ami_1.html#K10" title="AMI_1:func.10">Computation</a> <font color="Maroon" title="c16">s1</font>,<span class="p1">(<span class="default">3 <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span> = 
 <a href="ami_1.html#K9" title="AMI_1:func.9">Following</a> <span class="p1">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Computation</a> <font color="Maroon" title="c16">s1</font>,3</span>)</span>
<b>by </b><i><a class="ref" href="ami_1.html#T14" title="AMI_1:th.14">AMI_1:14</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#K4" title="SCMPDS_2:func.4">goto</a> 2</span>)</span>,<span class="p1">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Computation</a> <font color="Maroon" title="c16">s1</font>,3</span>)</span>
<b>by </b><i><a class="txt" href="scmp_gcd.html#E23:25"><i><font color="Green" title="E45">A23</font></i></a></i>
;<br/>
<i><font color="Green" title="E47">A25</font></i>:  <a href="ami_1.html#K7" title="AMI_1:func.7">IC</a> <span class="p1">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Computation</a> <font color="Maroon" title="c17">s2</font>,3</span>)</span> = 
 <a href="scmnorm.html#K1" title="SCMNORM:func.1">Next</a> <span class="p1">(<span class="default"><a href="ami_1.html#K7" title="AMI_1:func.7">IC</a> <span class="p2">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Computation</a> <font color="Maroon" title="c17">s2</font>,2</span>)</span></span>)</span>
<b>by </b><i><a class="txt" href="scmp_gcd.html#E20:25"><i><font color="Green" title="E42">A20</font></i></a>, <a class="ref" href="scmpds_2.html#T71" title="SCMPDS_2:th.71">SCMPDS_2:71</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#K2" title="NAT_1:func.2">+</a> 1</span>)</span>
<b>by </b><i><a class="txt" href="scmp_gcd.html#E18:25"><i><font color="Green" title="E40">A18</font></i></a></i>
;<br/>
<b>then </b><i><font color="Green" title="E48">A26</font></i>:  <a href="ami_1.html#K8" title="AMI_1:func.8">CurInstr</a> <span class="p1">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Computation</a> <font color="Maroon" title="c17">s2</font>,3</span>)</span> = 
<font color="Maroon" title="c17">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> 3</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#K4" title="SCMPDS_2:func.4">goto</a> 2
<b>by </b><i><a class="txt" href="scmp_gcd.html#E3:25"><i><font color="Green" title="E25">A3</font></i></a>, <a class="txt" href="scmp_gcd.html#E19"><i><font color="Green" title="E11">Lm1</font></i></a></i>
;<br/>
<i><font color="Green" title="E49">A27</font></i>:  <a href="ami_1.html#K10" title="AMI_1:func.10">Computation</a> <font color="Maroon" title="c17">s2</font>,<span class="p1">(<span class="default">3 <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span> = 
 <a href="ami_1.html#K9" title="AMI_1:func.9">Following</a> <span class="p1">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Computation</a> <font color="Maroon" title="c17">s2</font>,3</span>)</span>
<b>by </b><i><a class="ref" href="ami_1.html#T14" title="AMI_1:th.14">AMI_1:14</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#K4" title="SCMPDS_2:func.4">goto</a> 2</span>)</span>,<span class="p1">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Computation</a> <font color="Maroon" title="c17">s2</font>,3</span>)</span>
<b>by </b><i><a class="txt" href="scmp_gcd.html#E26:25"><i><font color="Green" title="E48">A26</font></i></a></i>
;<br/>
<div><i><font color="Green" title="E50">A28</font></i>: <a class="txt" onclick="hs2(this)" href="javascript:()" title="25_21"><b>now </b></a><div class="add"><b>let </b><font color="Maroon" title="c21">b</font> be    <a href="scmpds_2.html#M1" title="SCMPDS_2:mode.1">Int_position</a> ;<br/><b>assume </b><a NAME="E1:25_21"/><i><font color="Green" title="E51">A29</font></i>: 
<font color="Maroon" title="c16">s1</font> <a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">.</a> <font color="Maroon" title="c21">b</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c17">s2</font> <a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">.</a> <font color="Maroon" title="c21">b</font>
 ;<br/><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="25_21_1"><b>per </b></a><a class="txt" onclick="hs(this)" href="javascript:()"><b>cases </b></a><span class="hide"><a NAME="E1:25_21_1"/>
( <font color="Maroon" title="c21">b</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="scmp_gcd.html#K2" title="SCMP_GCD:func.2">GBP</a>  or <font color="Maroon" title="c21">b</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a>  <a href="scmp_gcd.html#K2" title="SCMP_GCD:func.2">GBP</a>  )
 </span>;<br/><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="25_21_1_1"><b>suppose </b></a><a NAME="E1:25_21_1_1"/><i><font color="Green" title="E52">A30</font></i>: 
<font color="Maroon" title="c21">b</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="scmp_gcd.html#K2" title="SCMP_GCD:func.2">GBP</a> 
 ;<br/><div class="add"><b>hence </b><span class="p1">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Computation</a> <font color="Maroon" title="c16">s1</font>,1</span>)</span> <a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">.</a> <font color="Maroon" title="c21">b</font> = 
 <a href="numbers.html#K6" title="NUMBERS:func.6">0</a> 
<b>by </b><i><a class="txt" href="scmp_gcd.html#E5:25"><i><font color="Green" title="E27">A5</font></i></a>, <a class="ref" href="scmpds_2.html#T57" title="SCMPDS_2:th.57">SCMPDS_2:57</a></i>
<br/>.= 
<span class="p1">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Computation</a> <font color="Maroon" title="c17">s2</font>,1</span>)</span> <a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">.</a> <font color="Maroon" title="c21">b</font>
<b>by </b><i><a class="txt" href="scmp_gcd.html#E7:25"><i><font color="Green" title="E29">A7</font></i></a>, <a class="txt" href="scmp_gcd.html#E1:25_21_1_1"><i><font color="Green" title="E52">A30</font></i></a>, <a class="ref" href="scmpds_2.html#T57" title="SCMPDS_2:th.57">SCMPDS_2:57</a></i>
;<br/><br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="25_21_1_2"><b>suppose </b></a><a NAME="E1:25_21_1_2"/><i><font color="Green" title="E52">A31</font></i>: 
<font color="Maroon" title="c21">b</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a>  <a href="scmp_gcd.html#K2" title="SCMP_GCD:func.2">GBP</a> 
 ;<br/><div class="add"><b>hence </b><span class="p1">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Computation</a> <font color="Maroon" title="c16">s1</font>,1</span>)</span> <a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">.</a> <font color="Maroon" title="c21">b</font> = 
<font color="Maroon" title="c16">s1</font> <a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">.</a> <font color="Maroon" title="c21">b</font>
<b>by </b><i><a class="txt" href="scmp_gcd.html#E5:25"><i><font color="Green" title="E27">A5</font></i></a>, <a class="ref" href="scmpds_2.html#T57" title="SCMPDS_2:th.57">SCMPDS_2:57</a></i>
<br/>.= 
<span class="p1">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Computation</a> <font color="Maroon" title="c17">s2</font>,1</span>)</span> <a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">.</a> <font color="Maroon" title="c21">b</font>
<b>by </b><i><a class="txt" href="scmp_gcd.html#E7:25"><i><font color="Green" title="E29">A7</font></i></a>, <a class="txt" href="scmp_gcd.html#E1:25_21"><i><font color="Green" title="E51">A29</font></i></a>, <a class="txt" href="scmp_gcd.html#E1:25_21_1_2"><i><font color="Green" title="E52">A31</font></i></a>, <a class="ref" href="scmpds_2.html#T57" title="SCMPDS_2:th.57">SCMPDS_2:57</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="E51">A32</font></i>: <a class="txt" onclick="hs2(this)" href="javascript:()" title="25_22"><b>now </b></a><div class="add"><b>let </b><font color="Maroon" title="c21">b</font> be    <a href="scmpds_2.html#M1" title="SCMPDS_2:mode.1">Int_position</a> ;<br/><b>assume </b><a NAME="E1:25_22"/><i><font color="Green" title="E52">A33</font></i>: 
<font color="Maroon" title="c16">s1</font> <a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">.</a> <font color="Maroon" title="c21">b</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c17">s2</font> <a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">.</a> <font color="Maroon" title="c21">b</font>
 ;<br/><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="25_22_1"><b>per </b></a><a class="txt" onclick="hs(this)" href="javascript:()"><b>cases </b></a><span class="hide"><a NAME="E1:25_22_1"/>
( <font color="Maroon" title="c21">b</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="scmp_gcd.html#K3" title="SCMP_GCD:func.3">SBP</a>  or <font color="Maroon" title="c21">b</font> <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>  )
 </span>;<br/><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="25_22_1_1"><b>suppose </b></a><a NAME="E1:25_22_1_1"/><i><font color="Green" title="E53">A34</font></i>: 
<font color="Maroon" title="c21">b</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="scmp_gcd.html#K3" title="SCMP_GCD:func.3">SBP</a> 
 ;<br/><div class="add"><b>hence </b><span class="p1">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Computation</a> <font color="Maroon" title="c16">s1</font>,2</span>)</span> <a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">.</a> <font color="Maroon" title="c21">b</font> = 
7
<b>by </b><i><a class="txt" href="scmp_gcd.html#E10:25"><i><font color="Green" title="E32">A10</font></i></a>, <a class="ref" href="scmpds_2.html#T57" title="SCMPDS_2:th.57">SCMPDS_2:57</a></i>
<br/>.= 
<span class="p1">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Computation</a> <font color="Maroon" title="c17">s2</font>,2</span>)</span> <a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">.</a> <font color="Maroon" title="c21">b</font>
<b>by </b><i><a class="txt" href="scmp_gcd.html#E13:25"><i><font color="Green" title="E35">A13</font></i></a>, <a class="txt" href="scmp_gcd.html#E1:25_22_1_1"><i><font color="Green" title="E53">A34</font></i></a>, <a class="ref" href="scmpds_2.html#T57" title="SCMPDS_2:th.57">SCMPDS_2:57</a></i>
;<br/><br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="25_22_1_2"><b>suppose </b></a><a NAME="E1:25_22_1_2"/><i><font color="Green" title="E53">A35</font></i>: 
<font color="Maroon" title="c21">b</font> <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> 
 ;<br/><div class="add"><b>hence </b><span class="p1">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Computation</a> <font color="Maroon" title="c16">s1</font>,2</span>)</span> <a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">.</a> <font color="Maroon" title="c21">b</font> = 
<span class="p1">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Computation</a> <font color="Maroon" title="c16">s1</font>,1</span>)</span> <a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">.</a> <font color="Maroon" title="c21">b</font>
<b>by </b><i><a class="txt" href="scmp_gcd.html#E10:25"><i><font color="Green" title="E32">A10</font></i></a>, <a class="ref" href="scmpds_2.html#T57" title="SCMPDS_2:th.57">SCMPDS_2:57</a></i>
<br/>.= 
<span class="p1">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Computation</a> <font color="Maroon" title="c17">s2</font>,1</span>)</span> <a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">.</a> <font color="Maroon" title="c21">b</font>
<b>by </b><i><a class="txt" href="scmp_gcd.html#E28:25"><i><font color="Green" title="E50">A28</font></i></a>, <a class="txt" href="scmp_gcd.html#E1:25_22"><i><font color="Green" title="E52">A33</font></i></a></i>
<br/>.= 
<span class="p1">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Computation</a> <font color="Maroon" title="c17">s2</font>,2</span>)</span> <a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">.</a> <font color="Maroon" title="c21">b</font>
<b>by </b><i><a class="txt" href="scmp_gcd.html#E13:25"><i><font color="Green" title="E35">A13</font></i></a>, <a class="txt" href="scmp_gcd.html#E1:25_22_1_2"><i><font color="Green" title="E53">A35</font></i></a>, <a class="ref" href="scmpds_2.html#T57" title="SCMPDS_2:th.57">SCMPDS_2:57</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="E52">A36</font></i>: <a class="txt" onclick="hs2(this)" href="javascript:()" title="25_23"><b>now </b></a><div class="add"><b>let </b><font color="Maroon" title="c21">b</font> be    <a href="scmpds_2.html#M1" title="SCMPDS_2:mode.1">Int_position</a> ;<br/><b>assume </b><a NAME="E1:25_23"/><i><font color="Green" title="E53">A37</font></i>: 
<font color="Maroon" title="c16">s1</font> <a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">.</a> <font color="Maroon" title="c21">b</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c17">s2</font> <a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">.</a> <font color="Maroon" title="c21">b</font>
 ;<br/><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="25_23_1"><b>per </b></a><a class="txt" onclick="hs(this)" href="javascript:()"><b>cases </b></a><span class="hide"><a NAME="E1:25_23_1"/>
( <font color="Maroon" title="c21">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"><a href="ami_1.html#K10" title="AMI_1:func.10">Computation</a> <font color="Maroon" title="c16">s1</font>,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>,<a href="scmpds_1.html#K23" title="SCMPDS_1:func.23">RetIC</a>  or <font color="Maroon" title="c21">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"><a href="ami_1.html#K10" title="AMI_1:func.10">Computation</a> <font color="Maroon" title="c16">s1</font>,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>,<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="25_23_1_1"><b>suppose </b></a><a NAME="E1:25_23_1_1"/><i><font color="Green" title="E54">A38</font></i>: 
<font color="Maroon" title="c21">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"><a href="ami_1.html#K10" title="AMI_1:func.10">Computation</a> <font color="Maroon" title="c16">s1</font>,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>,<a href="scmpds_1.html#K23" title="SCMPDS_1:func.23">RetIC</a> 
 ;<br/><div class="add"><b>hence </b><span class="p1">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Computation</a> <font color="Maroon" title="c16">s1</font>,3</span>)</span> <a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">.</a> <font color="Maroon" title="c21">b</font> = 
 <a href="ami_1.html#K7" title="AMI_1:func.7">IC</a> <span class="p1">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Computation</a> <font color="Maroon" title="c16">s1</font>,2</span>)</span>
<b>by </b><i><a class="txt" href="scmp_gcd.html#E16:25"><i><font color="Green" title="E38">A16</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"><a href="ami_1.html#K10" title="AMI_1:func.10">Computation</a> <font color="Maroon" title="c17">s2</font>,3</span>)</span> <a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">.</a> <font color="Maroon" title="c21">b</font>
<b>by </b><i><a class="txt" href="scmp_gcd.html#E14:25"><i><font color="Green" title="E36">A14</font></i></a>, <a class="txt" href="scmp_gcd.html#E17:25"><i><font color="Green" title="E39">A17</font></i></a>, <a class="txt" href="scmp_gcd.html#E18:25"><i><font color="Green" title="E40">A18</font></i></a>, <a class="txt" href="scmp_gcd.html#E20:25"><i><font color="Green" title="E42">A20</font></i></a>, <a class="txt" href="scmp_gcd.html#E21:25"><i><font color="Green" title="E43">A21</font></i></a>, <a class="txt" href="scmp_gcd.html#E1:25_23_1_1"><i><font color="Green" title="E54">A38</font></i></a>, <a class="ref" href="scmpds_2.html#T71" title="SCMPDS_2:th.71">SCMPDS_2:71</a></i>
;<br/><br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="25_23_1_2"><b>suppose </b></a><a NAME="E1:25_23_1_2"/><i><font color="Green" title="E54">A39</font></i>: 
<font color="Maroon" title="c21">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"><a href="ami_1.html#K10" title="AMI_1:func.10">Computation</a> <font color="Maroon" title="c16">s1</font>,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>,<a href="scmpds_1.html#K23" title="SCMPDS_1:func.23">RetIC</a> 
 ;<br/><div class="add"><b>hence </b><span class="p1">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Computation</a> <font color="Maroon" title="c16">s1</font>,3</span>)</span> <a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">.</a> <font color="Maroon" title="c21">b</font> = 
<span class="p1">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Computation</a> <font color="Maroon" title="c16">s1</font>,2</span>)</span> <a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">.</a> <font color="Maroon" title="c21">b</font>
<b>by </b><i><a class="txt" href="scmp_gcd.html#E16:25"><i><font color="Green" title="E38">A16</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"><a href="ami_1.html#K10" title="AMI_1:func.10">Computation</a> <font color="Maroon" title="c17">s2</font>,2</span>)</span> <a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">.</a> <font color="Maroon" title="c21">b</font>
<b>by </b><i><a class="txt" href="scmp_gcd.html#E29:25"><i><font color="Green" title="E51">A32</font></i></a>, <a class="txt" href="scmp_gcd.html#E1:25_23"><i><font color="Green" title="E53">A37</font></i></a></i>
<br/>.= 
<span class="p1">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Computation</a> <font color="Maroon" title="c17">s2</font>,3</span>)</span> <a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">.</a> <font color="Maroon" title="c21">b</font>
<b>by </b><i><a class="txt" href="scmp_gcd.html#E17:25"><i><font color="Green" title="E39">A17</font></i></a>, <a class="txt" href="scmp_gcd.html#E20:25"><i><font color="Green" title="E42">A20</font></i></a>, <a class="txt" href="scmp_gcd.html#E21:25"><i><font color="Green" title="E43">A21</font></i></a>, <a class="txt" href="scmp_gcd.html#E1:25_23_1_2"><i><font color="Green" title="E54">A39</font></i></a>, <a class="ref" href="scmpds_2.html#T71" title="SCMPDS_2:th.71">SCMPDS_2:71</a></i>
;<br/><br/></div><b>end;</b></div></div><b>end;</b></div></div><b>end;</b></div>
<div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="25_24"><b>per </b></a><a class="txt" onclick="hs(this)" href="javascript:()"><b>cases </b></a><span class="hide"><a NAME="E1:25_24"/>
( <font color="Maroon" title="c19">k</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="numbers.html#K6" title="NUMBERS:func.6">0</a>  or <font color="Maroon" title="c19">k</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 1 or <font color="Maroon" title="c19">k</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 2 or <font color="Maroon" title="c19">k</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 3 or <font color="Maroon" title="c19">k</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 4 )
 </span><b>by </b><i><a class="txt" href="scmp_gcd.html#E2:25"><i><font color="Green" title="E24">A2</font></i></a>, <a class="ref" href="nat_1.html#T29" title="NAT_1:th.29">NAT_1:29</a></i>;<br/><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="25_24_1"><b>suppose </b></a><a NAME="E1:25_24_1"/><i><font color="Green" title="E53">A40</font></i>: 
<font color="Maroon" title="c19">k</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="numbers.html#K6" title="NUMBERS:func.6">0</a> 
 ;<br/><div class="add"><b>hence </b> <a href="ami_1.html#K7" title="AMI_1:func.7">IC</a> <span class="p1">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Computation</a> <font color="Maroon" title="c16">s1</font>,<font color="Maroon" title="c19">k</font></span>)</span> = 
 <a href="ami_1.html#K7" title="AMI_1:func.7">IC</a> <font color="Maroon" title="c16">s1</font>
<b>by </b><i><a class="ref" href="ami_1.html#T13" title="AMI_1:th.13">AMI_1:13</a></i>
<br/>.= 
 <a href="ami_1.html#K7" title="AMI_1:func.7">IC</a> <span class="p1">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Computation</a> <font color="Maroon" title="c17">s2</font>,<font color="Maroon" title="c19">k</font></span>)</span>
<b>by </b><i><a class="txt" href="scmp_gcd.html#E4:25"><i><font color="Green" title="E26">A4</font></i></a>, <a class="txt" href="scmp_gcd.html#E6:25"><i><font color="Green" title="E28">A6</font></i></a>, <a class="txt" href="scmp_gcd.html#E1:25_24_1"><i><font color="Green" title="E53">A40</font></i></a>, <a class="ref" href="ami_1.html#T13" title="AMI_1:th.13">AMI_1:13</a></i>
;<br/><br/><b>thus </b><span class="p1">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Computation</a> <font color="Maroon" title="c16">s1</font>,<font color="Maroon" title="c19">k</font></span>)</span> <a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">.</a> <font color="Maroon" title="c18">a</font> = 
<font color="Maroon" title="c16">s1</font> <a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">.</a> <font color="Maroon" title="c18">a</font>
<b>by </b><i><a class="txt" href="scmp_gcd.html#E1:25_24_1"><i><font color="Green" title="E53">A40</font></i></a>, <a class="ref" href="ami_1.html#T13" title="AMI_1:th.13">AMI_1:13</a></i>
<br/>.= 
<span class="p1">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Computation</a> <font color="Maroon" title="c17">s2</font>,<font color="Maroon" title="c19">k</font></span>)</span> <a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">.</a> <font color="Maroon" title="c18">a</font>
<b>by </b><i><a class="txt" href="scmp_gcd.html#E2:25"><i><font color="Green" title="E24">A2</font></i></a>, <a class="txt" href="scmp_gcd.html#E1:25_24_1"><i><font color="Green" title="E53">A40</font></i></a>, <a class="ref" href="ami_1.html#T13" title="AMI_1:th.13">AMI_1:13</a></i>
;<br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="25_24_2"><b>suppose </b></a><a NAME="E1:25_24_2"/><i><font color="Green" title="E53">A41</font></i>: 
<font color="Maroon" title="c19">k</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 1
 ;<br/><div class="add"><b>hence </b><a NAME="E2:25_24_2"/>
 <a href="ami_1.html#K7" title="AMI_1:func.7">IC</a> <span class="p1">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Computation</a> <font color="Maroon" title="c16">s1</font>,<font color="Maroon" title="c19">k</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="ami_1.html#K7" title="AMI_1:func.7">IC</a> <span class="p1">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Computation</a> <font color="Maroon" title="c17">s2</font>,<font color="Maroon" title="c19">k</font></span>)</span>
 <b>by </b><i><a class="txt" href="scmp_gcd.html#E8:25"><i><font color="Green" title="E30">A8</font></i></a>, <a class="txt" href="scmp_gcd.html#E11:25"><i><font color="Green" title="E33">A11</font></i></a></i>;<br/><b>thus </b><a NAME="E3:25_24_2"/>
<span class="p1">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Computation</a> <font color="Maroon" title="c16">s1</font>,<font color="Maroon" title="c19">k</font></span>)</span> <a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">.</a> <font color="Maroon" title="c18">a</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Computation</a> <font color="Maroon" title="c17">s2</font>,<font color="Maroon" title="c19">k</font></span>)</span> <a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">.</a> <font color="Maroon" title="c18">a</font>
 <b>by </b><i><a class="txt" href="scmp_gcd.html#E2:25"><i><font color="Green" title="E24">A2</font></i></a>, <a class="txt" href="scmp_gcd.html#E28:25"><i><font color="Green" title="E50">A28</font></i></a>, <a class="txt" href="scmp_gcd.html#E1:25_24_2"><i><font color="Green" title="E53">A41</font></i></a></i>;<br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="25_24_3"><b>suppose </b></a><a NAME="E1:25_24_3"/><i><font color="Green" title="E53">A42</font></i>: 
<font color="Maroon" title="c19">k</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 2
 ;<br/><div class="add"><b>hence </b><a NAME="E2:25_24_3"/>
 <a href="ami_1.html#K7" title="AMI_1:func.7">IC</a> <span class="p1">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Computation</a> <font color="Maroon" title="c16">s1</font>,<font color="Maroon" title="c19">k</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="ami_1.html#K7" title="AMI_1:func.7">IC</a> <span class="p1">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Computation</a> <font color="Maroon" title="c17">s2</font>,<font color="Maroon" title="c19">k</font></span>)</span>
 <b>by </b><i><a class="txt" href="scmp_gcd.html#E14:25"><i><font color="Green" title="E36">A14</font></i></a>, <a class="txt" href="scmp_gcd.html#E18:25"><i><font color="Green" title="E40">A18</font></i></a></i>;<br/><b>thus </b><a NAME="E3:25_24_3"/>
<span class="p1">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Computation</a> <font color="Maroon" title="c16">s1</font>,<font color="Maroon" title="c19">k</font></span>)</span> <a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">.</a> <font color="Maroon" title="c18">a</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Computation</a> <font color="Maroon" title="c17">s2</font>,<font color="Maroon" title="c19">k</font></span>)</span> <a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">.</a> <font color="Maroon" title="c18">a</font>
 <b>by </b><i><a class="txt" href="scmp_gcd.html#E2:25"><i><font color="Green" title="E24">A2</font></i></a>, <a class="txt" href="scmp_gcd.html#E29:25"><i><font color="Green" title="E51">A32</font></i></a>, <a class="txt" href="scmp_gcd.html#E1:25_24_3"><i><font color="Green" title="E53">A42</font></i></a></i>;<br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="25_24_4"><b>suppose </b></a><a NAME="E1:25_24_4"/><i><font color="Green" title="E53">A43</font></i>: 
<font color="Maroon" title="c19">k</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 3
 ;<br/><div class="add"><b>hence </b><a NAME="E2:25_24_4"/>
 <a href="ami_1.html#K7" title="AMI_1:func.7">IC</a> <span class="p1">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Computation</a> <font color="Maroon" title="c16">s1</font>,<font color="Maroon" title="c19">k</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="ami_1.html#K7" title="AMI_1:func.7">IC</a> <span class="p1">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Computation</a> <font color="Maroon" title="c17">s2</font>,<font color="Maroon" title="c19">k</font></span>)</span>
 <b>by </b><i><a class="txt" href="scmp_gcd.html#E22:25"><i><font color="Green" title="E44">A22</font></i></a>, <a class="txt" href="scmp_gcd.html#E25:25"><i><font color="Green" title="E47">A25</font></i></a></i>;<br/><b>thus </b><a NAME="E3:25_24_4"/>
<span class="p1">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Computation</a> <font color="Maroon" title="c16">s1</font>,<font color="Maroon" title="c19">k</font></span>)</span> <a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">.</a> <font color="Maroon" title="c18">a</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Computation</a> <font color="Maroon" title="c17">s2</font>,<font color="Maroon" title="c19">k</font></span>)</span> <a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">.</a> <font color="Maroon" title="c18">a</font>
 <b>by </b><i><a class="txt" href="scmp_gcd.html#E2:25"><i><font color="Green" title="E24">A2</font></i></a>, <a class="txt" href="scmp_gcd.html#E30:25"><i><font color="Green" title="E52">A36</font></i></a>, <a class="txt" href="scmp_gcd.html#E1:25_24_4"><i><font color="Green" title="E53">A43</font></i></a></i>;<br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="25_24_5"><b>suppose </b></a><a NAME="E1:25_24_5"/><i><font color="Green" title="E53">A44</font></i>: 
<font color="Maroon" title="c19">k</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 4
 ;<br/><div class="add"><b>hence </b> <a href="ami_1.html#K7" title="AMI_1:func.7">IC</a> <span class="p1">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Computation</a> <font color="Maroon" title="c16">s1</font>,<font color="Maroon" title="c19">k</font></span>)</span> = 
 <a href="scmpds_2.html#K18" title="SCMPDS_2:func.18">ICplusConst</a> <span class="p1">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Computation</a> <font color="Maroon" title="c16">s1</font>,3</span>)</span>,2
<b>by </b><i><a class="txt" href="scmp_gcd.html#E24:25"><i><font color="Green" title="E46">A24</font></i></a>, <a class="ref" href="scmpds_2.html#T66" title="SCMPDS_2:th.66">SCMPDS_2:66</a></i>
<br/>.= 
 <a href="scmpds_3.html#K2" title="SCMPDS_3:func.2">inspos</a> <span class="p1">(<span class="default">3 <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 2</span>)</span>
<b>by </b><i><a class="txt" href="scmp_gcd.html#E22:25"><i><font color="Green" title="E44">A22</font></i></a>, <a class="ref" href="scmpds_6.html#T23" title="SCMPDS_6:th.23">SCMPDS_6:23</a></i>
<br/>.= 
 <a href="scmpds_2.html#K18" title="SCMPDS_2:func.18">ICplusConst</a> <span class="p1">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Computation</a> <font color="Maroon" title="c17">s2</font>,3</span>)</span>,2
<b>by </b><i><a class="txt" href="scmp_gcd.html#E25:25"><i><font color="Green" title="E47">A25</font></i></a>, <a class="ref" href="scmpds_6.html#T23" title="SCMPDS_6:th.23">SCMPDS_6:23</a></i>
<br/>.= 
 <a href="ami_1.html#K7" title="AMI_1:func.7">IC</a> <span class="p1">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Computation</a> <font color="Maroon" title="c17">s2</font>,<font color="Maroon" title="c19">k</font></span>)</span>
<b>by </b><i><a class="txt" href="scmp_gcd.html#E27:25"><i><font color="Green" title="E49">A27</font></i></a>, <a class="txt" href="scmp_gcd.html#E1:25_24_5"><i><font color="Green" title="E53">A44</font></i></a>, <a class="ref" href="scmpds_2.html#T66" title="SCMPDS_2:th.66">SCMPDS_2:66</a></i>
;<br/><br/><b>thus </b><span class="p1">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Computation</a> <font color="Maroon" title="c16">s1</font>,<font color="Maroon" title="c19">k</font></span>)</span> <a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">.</a> <font color="Maroon" title="c18">a</font> = 
<span class="p1">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Computation</a> <font color="Maroon" title="c16">s1</font>,3</span>)</span> <a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">.</a> <font color="Maroon" title="c18">a</font>
<b>by </b><i><a class="txt" href="scmp_gcd.html#E24:25"><i><font color="Green" title="E46">A24</font></i></a>, <a class="txt" href="scmp_gcd.html#E1:25_24_5"><i><font color="Green" title="E53">A44</font></i></a>, <a class="ref" href="scmpds_2.html#T66" title="SCMPDS_2:th.66">SCMPDS_2:66</a></i>
<br/>.= 
<span class="p1">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Computation</a> <font color="Maroon" title="c17">s2</font>,3</span>)</span> <a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">.</a> <font color="Maroon" title="c18">a</font>
<b>by </b><i><a class="txt" href="scmp_gcd.html#E2:25"><i><font color="Green" title="E24">A2</font></i></a>, <a class="txt" href="scmp_gcd.html#E30:25"><i><font color="Green" title="E52">A36</font></i></a></i>
<br/>.= 
<span class="p1">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Computation</a> <font color="Maroon" title="c17">s2</font>,<font color="Maroon" title="c19">k</font></span>)</span> <a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">.</a> <font color="Maroon" title="c18">a</font>
<b>by </b><i><a class="txt" href="scmp_gcd.html#E27:25"><i><font color="Green" title="E49">A27</font></i></a>, <a class="txt" href="scmp_gcd.html#E1:25_24_5"><i><font color="Green" title="E53">A44</font></i></a>, <a class="ref" href="scmpds_2.html#T66" title="SCMPDS_2:th.66">SCMPDS_2:66</a></i>
;<br/></div><b>end;</b></div></div><b>end;</b></div>

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