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<b>set </b><font color="Maroon" title="c16">GA</font> =  <a href="scmp_gcd.html#K4" title="SCMP_GCD:func.4">GCD-Algorithm</a> ;<br/>
<b>defpred </b><font color="Maroon">S<sub>1</sub></font>[   <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>means </b>for <font color="Olive" title="b1">s</font> being  <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>   st  <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="Olive" title="b1">s</font> &amp;  <a href="ami_1.html#K6" title="AMI_1:func.6">IC</a> <font color="Olive" title="b1">s</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 &amp; <font color="Olive" title="b1">s</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="xxreal_0.html#NR4" title="XXREAL_0:NR.4">&gt;</a> 0 &amp; <font color="Olive" title="b1">s</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 &amp; <font color="Olive" title="b1">s</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="Olive" title="b1">s</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#R1" title="XXREAL_0:pred.1">&lt;=</a> $1 &amp; <font color="Olive" title="b1">s</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="Olive" title="b1">s</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#NR2" title="XXREAL_0:NR.2">&gt;=</a> 0 &amp; <font color="Olive" title="b1">s</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="Olive" title="b1">s</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="xxreal_0.html#NR2" title="XXREAL_0:NR.2">&gt;=</a> <font color="Olive" title="b1">s</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="Olive" title="b1">s</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> holds <br/> ex <font color="Olive" title="b2">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>  st <br/>(  <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="Olive" title="b1">s</font></span>)</span> <a href="ami_1.html#K11" title="AMI_1:func.11">.</a> <font color="Olive" title="b2">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; <font color="Olive" title="b1">s</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> <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="Olive" title="b1">s</font></span>)</span> <a href="ami_1.html#K11" title="AMI_1:func.11">.</a> <font color="Olive" title="b2">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#K10" title="AMI_1:func.10">Computation</a> <font color="Olive" title="b1">s</font></span>)</span> <a href="ami_1.html#K11" title="AMI_1:func.11">.</a> <font color="Olive" title="b2">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"><font color="Olive" title="b1">s</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> <span class="p1">(<span class="default"><font color="Olive" title="b1">s</font> <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"><font color="Olive" title="b1">s</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></span>)</span> <a href="int_2.html#K3" title="INT_2:func.3">gcd</a> <span class="p1">(<span class="default"><font color="Olive" title="b1">s</font> <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"><font color="Olive" title="b1">s</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></span>)</span> &amp; ( for <font color="Olive" title="b3">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="b3">j</font> &amp; <font color="Olive" title="b3">j</font> <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> <span class="p1">(<span class="default"><font color="Olive" title="b1">s</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> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> 1 holds <br/><font color="Olive" title="b1">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> <font color="Olive" title="b3">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#K10" title="AMI_1:func.10">Computation</a> <font color="Olive" title="b1">s</font></span>)</span> <a href="ami_1.html#K11" title="AMI_1:func.11">.</a> <font color="Olive" title="b2">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="b3">j</font></span>)</span> ) );<br/>
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="20_1"><b>now </b></a><div class="add"><b>let </b><font color="Maroon" title="c17">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="c18">x</font> = <font color="Maroon" title="c17">s</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">s</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>;<br/><b>set </b><font color="Maroon" title="c19">y</font> = <font color="Maroon" title="c17">s</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">s</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/><b>set </b><font color="Maroon" title="c20">Cs</font> =  <a href="ami_1.html#K10" title="AMI_1:func.10">Computation</a> <font color="Maroon" title="c17">s</font>;<br/><b>assume </b><a NAME="E1:20_1"/><i><font color="Green" title="E21">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">s</font>
 ;<br/><b>assume </b><a NAME="E2:20_1"/><i><font color="Green" title="E22">A2</font></i>: 
 <a href="ami_1.html#K6" title="AMI_1:func.6">IC</a> <font color="Maroon" title="c17">s</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="E3:20_1"/>
<font color="Maroon" title="c17">s</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="xxreal_0.html#NR4" title="XXREAL_0:NR.4">&gt;</a> 0
 ;<br/><b>assume </b><a NAME="E4:20_1"/>
<font color="Maroon" title="c17">s</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="E5:20_1"/><i><font color="Green" title="E23">A3</font></i>: 
<font color="Maroon" title="c17">s</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">s</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#R1" title="XXREAL_0:pred.1">&lt;=</a> 0
 ;<br/><b>assume </b><a NAME="E6:20_1"/><i><font color="Green" title="E24">A4</font></i>: 
<font color="Maroon" title="c17">s</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">s</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#NR2" title="XXREAL_0:NR.2">&gt;=</a> 0
 ;<br/><b>assume </b><a NAME="E7:20_1"/><i><font color="Green" title="E25">A5</font></i>: 
<font color="Maroon" title="c17">s</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">s</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="xxreal_0.html#NR2" title="XXREAL_0:NR.2">&gt;=</a> <font color="Maroon" title="c17">s</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">s</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="E8:20_1"/><i><font color="Green" title="E26">A6</font></i>: 
 <a href="ami_1.html#K8" title="AMI_1:func.8">CurInstr</a> <font color="Maroon" title="c17">s</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#E2:20_1"><i><font color="Green" title="E22">A2</font></i></a>, <a class="txt" href="scmp_gcd.html#E1:20_1"><i><font color="Green" title="E21">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="E27">A7</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">s</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">s</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">s</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">s</font>
<b>by </b><i><a class="txt" href="scmp_gcd.html#E8:20_1"><i><font color="Green" title="E26">A6</font></i></a></i>
;<br/><i><font color="Green" title="E28">A8</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">s</font></span>)</span> <a href="ami_1.html#K11" title="AMI_1:func.11">.</a> 1</span>)</span> = 
 <a href="scmpds_2.html#K19" title="SCMPDS_2:func.19">ICplusConst</a> <font color="Maroon" title="c17">s</font>,9
<b>by </b><i><a class="txt" href="scmp_gcd.html#E5:20_1"><i><font color="Green" title="E23">A3</font></i></a>, <a class="txt" href="scmp_gcd.html#E9:20_1"><i><font color="Green" title="E27">A7</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> 9</span>)</span>
<b>by </b><i><a class="txt" href="scmp_gcd.html#E2:20_1"><i><font color="Green" title="E22">A2</font></i></a>, <a class="ref" href="scmpds_6.html#T23" title="SCMPDS_6:th.23">SCMPDS_6:23</a></i>
;<br/><b>take </b><font color="Maroon" title="c21">n</font> = 1;<br/><b>thus </b> <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">s</font></span>)</span> <a href="ami_1.html#K11" title="AMI_1:func.11">.</a> <font color="Maroon" title="c21">n</font></span>)</span> = 
<font color="Maroon" title="c17">s</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> 14</span>)</span>
<b>by </b><i><a class="txt" href="scmp_gcd.html#E10:20_1"><i><font color="Green" title="E28">A8</font></i></a>, <a class="ref" href="ami_1.html#T54" title="AMI_1:th.54">AMI_1:54</a></i>
<br/>.= 
 <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> 
<b>by </b><i><a class="txt" href="scmp_gcd.html#E1:20_1"><i><font color="Green" title="E21">A1</font></i></a>, <a class="txt" href="scmp_gcd.html#E21"><i><font color="Green" title="E14">Lm3</font></i></a></i>
;<br/><b>thus </b><a NAME="E12:20_1"/>
<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">s</font></span>)</span> <a href="ami_1.html#K11" title="AMI_1:func.11">.</a> <font color="Maroon" title="c21">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>  <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c17">s</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> 
 <b>by </b><i><a class="txt" href="scmp_gcd.html#E9:20_1"><i><font color="Green" title="E27">A7</font></i></a>, <a class="ref" href="scmpds_2.html#T68" title="SCMPDS_2:th.68">SCMPDS_2:68</a></i>;<br/><a NAME="E13:20_1"/><i><font color="Green" title="E29">A9</font></i>: 
<font color="Maroon" title="c17">s</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">s</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> 0
 <b>by </b><i><a class="txt" href="scmp_gcd.html#E5:20_1"><i><font color="Green" title="E23">A3</font></i></a>, <a class="txt" href="scmp_gcd.html#E6:20_1"><i><font color="Green" title="E24">A4</font></i></a>, <a class="ref" href="xxreal_0.html#T1" title="XXREAL_0:th.1">XXREAL_0:1</a></i>;<br/><a NAME="E14:20_1"/><b>then </b><i><font color="Green" title="E30">A10</font></i>: 
 <a href="int_2.html#K1" title="INT_2:func.1">abs</a> <span class="p1">(<span class="default"><font color="Maroon" title="c17">s</font> <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"><font color="Maroon" title="c17">s</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></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 0
 <b>by </b><i><a class="ref" href="absvalue.html#D1" title="ABSVALUE:def.1">ABSVALUE:def 1</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">s</font></span>)</span> <a href="ami_1.html#K11" title="AMI_1:func.11">.</a> <font color="Maroon" title="c21">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"><font color="Maroon" title="c17">s</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> = 
<font color="Maroon" title="c17">s</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">s</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>
<b>by </b><i><a class="txt" href="scmp_gcd.html#E9:20_1"><i><font color="Green" title="E27">A7</font></i></a>, <a class="ref" href="scmpds_2.html#T68" title="SCMPDS_2:th.68">SCMPDS_2:68</a></i>
<br/>.= 
 <a href="int_2.html#K1" title="INT_2:func.1">abs</a> <span class="p1">(<span class="default"><font color="Maroon" title="c17">s</font> <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"><font color="Maroon" title="c17">s</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></span>)</span>
<b>by </b><i><a class="txt" href="scmp_gcd.html#E7:20_1"><i><font color="Green" title="E25">A5</font></i></a>, <a class="txt" href="scmp_gcd.html#E13:20_1"><i><font color="Green" title="E29">A9</font></i></a>, <a class="ref" href="absvalue.html#D1" title="ABSVALUE:def.1">ABSVALUE:def 1</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"><font color="Maroon" title="c17">s</font> <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"><font color="Maroon" title="c17">s</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></span>)</span></span>)</span> <a href="nat_d.html#K8" title="NAT_D:func.8">hcf</a> <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"><font color="Maroon" title="c17">s</font> <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"><font color="Maroon" title="c17">s</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></span>)</span></span>)</span>
<b>by </b><i><a class="txt" href="scmp_gcd.html#E14:20_1"><i><font color="Green" title="E30">A10</font></i></a>, <a class="ref" href="newton.html#T65" title="NEWTON:th.65">NEWTON:65</a></i>
<br/>.= 
<span class="p1">(<span class="default"><font color="Maroon" title="c17">s</font> <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"><font color="Maroon" title="c17">s</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></span>)</span> <a href="int_2.html#K3" title="INT_2:func.3">gcd</a> <span class="p1">(<span class="default"><font color="Maroon" title="c17">s</font> <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"><font color="Maroon" title="c17">s</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></span>)</span>
<b>by </b><i><a class="ref" href="int_2.html#D3" title="INT_2:def.3">INT_2:def 3</a></i>
;<br/><b>thus </b><a NAME="E16:20_1"/>
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"><font color="Maroon" title="c17">s</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> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> 1 holds <br/><font color="Maroon" title="c17">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> <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#K10" title="AMI_1:func.10">Computation</a> <font color="Maroon" title="c17">s</font></span>)</span> <a href="ami_1.html#K11" title="AMI_1:func.11">.</a> <font color="Maroon" title="c21">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#E9:20_1"><i><font color="Green" title="E27">A7</font></i></a>, <a class="ref" href="scmpds_2.html#T68" title="SCMPDS_2:th.68">SCMPDS_2:68</a></i>;<br/></div><b>end;</b></div>
<a NAME="E2:20"/><b>then </b><i><font color="Green" title="E21">A11</font></i>: 
<font color="Maroon">S<sub>1</sub></font>[0]
 
;<br/>
<div><i><font color="Green" title="E22">A12</font></i>: <a class="txt" onclick="hs2(this)" href="javascript:()" title="20_2"><b>now </b></a><div class="add"><b>let </b><font color="Maroon" title="c17">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>assume </b><a NAME="E1:20_2"/><i><font color="Green" title="E23">A13</font></i>: 
<font color="Maroon">S<sub>1</sub></font>[<font color="Maroon" title="c17">k</font>]
 ;<br/><div><a class="txt" onclick="hs2(this)" href="javascript:()" title="20_2_1"><b>now </b></a><div class="add"><b>let </b><font color="Maroon" title="c18">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="c19">x</font> = <font color="Maroon" title="c18">s</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="c18">s</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>;<br/><b>set </b><font color="Maroon" title="c20">y</font> = <font color="Maroon" title="c18">s</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="c18">s</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/><b>set </b><font color="Maroon" title="c21">yy</font> = <font color="Maroon" title="c18">s</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="c18">s</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/><b>set </b><font color="Maroon" title="c22">Cs</font> =  <a href="ami_1.html#K10" title="AMI_1:func.10">Computation</a> <font color="Maroon" title="c18">s</font>;<br/><b>assume </b><a NAME="E1:20_2_1"/><i><font color="Green" title="E24">A14</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="c18">s</font>
 ;<br/><b>assume </b><a NAME="E2:20_2_1"/><i><font color="Green" title="E25">A15</font></i>: 
 <a href="ami_1.html#K6" title="AMI_1:func.6">IC</a> <font color="Maroon" title="c18">s</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="E3:20_2_1"/><i><font color="Green" title="E26">A16</font></i>: 
<font color="Maroon" title="c18">s</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="xxreal_0.html#NR4" title="XXREAL_0:NR.4">&gt;</a> 0
 ;<br/><b>assume </b><a NAME="E4:20_2_1"/><i><font color="Green" title="E27">A17</font></i>: 
<font color="Maroon" title="c18">s</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="E5:20_2_1"/><i><font color="Green" title="E28">A18</font></i>: 
<font color="Maroon" title="c18">s</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="c18">s</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#R1" title="XXREAL_0:pred.1">&lt;=</a> <font color="Maroon" title="c17">k</font> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1
 ;<br/><b>assume </b><a NAME="E6:20_2_1"/><i><font color="Green" title="E29">A19</font></i>: 
<font color="Maroon" title="c18">s</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="c18">s</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#NR2" title="XXREAL_0:NR.2">&gt;=</a> 0
 ;<br/><b>assume </b><a NAME="E7:20_2_1"/><i><font color="Green" title="E30">A20</font></i>: 
<font color="Maroon" title="c18">s</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="c18">s</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="xxreal_0.html#NR2" title="XXREAL_0:NR.2">&gt;=</a> <font color="Maroon" title="c18">s</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="c18">s</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="E8:20_2_1"/><b>then </b><i><font color="Green" title="E31">A21</font></i>: 
<font color="Maroon" title="c18">s</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="c18">s</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="xxreal_0.html#NR2" title="XXREAL_0:NR.2">&gt;=</a> 0
 <b>by </b><i><a class="txt" href="scmp_gcd.html#E6:20_2_1"><i><font color="Green" title="E29">A19</font></i></a>, <a class="ref" href="xxreal_0.html#T2" title="XXREAL_0:th.2">XXREAL_0:2</a></i>;<br/><b>reconsider </b><font color="Maroon" title="c23">y</font> = <font color="Maroon" title="c18">s</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="c18">s</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> as    <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>by </b><i><a class="txt" href="scmp_gcd.html#E6:20_2_1"><i><font color="Green" title="E29">A19</font></i></a>, <a class="ref" href="int_1.html#T16" title="INT_1:th.16">INT_1:16</a></i>;<br/><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="20_2_1_1"><b>per </b></a><a class="txt" onclick="hs(this)" href="javascript:()"><b>cases </b></a><span class="hide"><a NAME="E1:20_2_1_1"/>
( <font color="Maroon" title="c23">y</font> <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> <font color="Maroon" title="c17">k</font> or <font color="Maroon" title="c23">y</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c17">k</font> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1 )
 </span><b>by </b><i><a class="txt" href="scmp_gcd.html#E5:20_2_1"><i><font color="Green" title="E28">A18</font></i></a>, <a class="ref" href="nat_1.html#T8" title="NAT_1:th.8">NAT_1:8</a></i>;<br/><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="20_2_1_1_1"><b>suppose </b></a><a NAME="E1:20_2_1_1_1"/>
<font color="Maroon" title="c23">y</font> <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> <font color="Maroon" title="c17">k</font>
 ;<br/><div class="add"><b>hence </b><a NAME="E2:20_2_1_1_1"/>
 ex <font color="Olive" title="b1">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>  st <br/>(  <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">s</font></span>)</span> <a href="ami_1.html#K11" title="AMI_1:func.11">.</a> <font color="Olive" title="b1">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; <font color="Maroon" title="c18">s</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> <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">s</font></span>)</span> <a href="ami_1.html#K11" title="AMI_1:func.11">.</a> <font color="Olive" title="b1">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#K10" title="AMI_1:func.10">Computation</a> <font color="Maroon" title="c18">s</font></span>)</span> <a href="ami_1.html#K11" title="AMI_1:func.11">.</a> <font color="Olive" title="b1">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"><font color="Maroon" title="c18">s</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> <span class="p1">(<span class="default"><font color="Maroon" title="c18">s</font> <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"><font color="Maroon" title="c18">s</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></span>)</span> <a href="int_2.html#K3" title="INT_2:func.3">gcd</a> <span class="p1">(<span class="default"><font color="Maroon" title="c18">s</font> <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"><font color="Maroon" title="c18">s</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></span>)</span> &amp; ( for <font color="Olive" title="b2">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="b2">j</font> &amp; <font color="Olive" title="b2">j</font> <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> <span class="p1">(<span class="default"><font color="Maroon" title="c18">s</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> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> 1 holds <br/><font color="Maroon" title="c18">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> <font color="Olive" title="b2">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#K10" title="AMI_1:func.10">Computation</a> <font color="Maroon" title="c18">s</font></span>)</span> <a href="ami_1.html#K11" title="AMI_1:func.11">.</a> <font color="Olive" title="b1">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="b2">j</font></span>)</span> ) )
 <b>by </b><i><a class="txt" href="scmp_gcd.html#E1:20_2"><i><font color="Green" title="E23">A13</font></i></a>, <a class="txt" href="scmp_gcd.html#E1:20_2_1"><i><font color="Green" title="E24">A14</font></i></a>, <a class="txt" href="scmp_gcd.html#E2:20_2_1"><i><font color="Green" title="E25">A15</font></i></a>, <a class="txt" href="scmp_gcd.html#E3:20_2_1"><i><font color="Green" title="E26">A16</font></i></a>, <a class="txt" href="scmp_gcd.html#E4:20_2_1"><i><font color="Green" title="E27">A17</font></i></a>, <a class="txt" href="scmp_gcd.html#E6:20_2_1"><i><font color="Green" title="E29">A19</font></i></a>, <a class="txt" href="scmp_gcd.html#E7:20_2_1"><i><font color="Green" title="E30">A20</font></i></a></i>;<br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="20_2_1_1_2"><b>suppose </b></a><a NAME="E1:20_2_1_1_2"/><i><font color="Green" title="E32">A22</font></i>: 
<font color="Maroon" title="c23">y</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c17">k</font> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1
 ;<br/><div class="add"><a NAME="E2:20_2_1_1_2"/><b>then </b>
<font color="Maroon" title="c23">y</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> 0
 <b>by </b><i><a class="ref" href="nat_1.html#T5" title="NAT_1:th.5">NAT_1:5</a></i>;<br/><a NAME="E3:20_2_1_1_2"/><b>then </b><i><font color="Green" title="E33">A23</font></i>: 
<font color="Maroon" title="c23">y</font> <a href="xxreal_0.html#NR4" title="XXREAL_0:NR.4">&gt;</a> 0
 <b>by </b><i><a class="ref" href="nat_1.html#T3" title="NAT_1:th.3">NAT_1:3</a></i>;<br/><b>reconsider </b><font color="Maroon" title="c24">pn</font> = <font color="Maroon" title="c18">s</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>  as    <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>by </b><i><a class="txt" href="scmp_gcd.html#E3:20_2_1"><i><font color="Green" title="E26">A16</font></i></a>, <a class="ref" href="int_1.html#T16" title="INT_1:th.16">INT_1:16</a></i>;<br/><a NAME="E5:20_2_1_1_2"/><i><font color="Green" title="E34">A24</font></i>: 
<font color="Maroon" title="c24">pn</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c18">s</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/><a NAME="E6:20_2_1_1_2"/><b>then </b><i><font color="Green" title="E35">A25</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">s</font></span>)</span> <a href="ami_1.html#K11" title="AMI_1:func.11">.</a> 7</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> <span class="p1">(<span class="default">5 <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 7</span>)</span> &amp; <span class="p1">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Computation</a> <font color="Maroon" title="c18">s</font></span>)</span> <a href="ami_1.html#K11" title="AMI_1:func.11">.</a> 8 <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <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> <span class="p2">(<span class="default"><a href="xcmplx_0.html#K4" title="XCMPLX_0:func.4">-</a> 7</span>)</span></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">s</font></span>)</span> <a href="ami_1.html#K11" title="AMI_1:func.11">.</a> 7</span>)</span> &amp; <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">s</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> <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="c24">pn</font> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 4 &amp; <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">s</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> <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#K10" title="AMI_1:func.10">Computation</a> <font color="Maroon" title="c18">s</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> <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"><font color="Maroon" title="c24">pn</font> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 7</span>)</span></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><font color="Maroon" title="c18">s</font> <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"><font color="Maroon" title="c18">s</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></span>)</span> <a href="int_1.html#K6" title="INT_1:func.6">mod</a> <font color="Maroon" title="c23">y</font> &amp; <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">s</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> <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"><font color="Maroon" title="c24">pn</font> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 6</span>)</span></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c23">y</font> &amp; <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">s</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> <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"><font color="Maroon" title="c24">pn</font> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 4</span>)</span></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c24">pn</font> &amp; <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">s</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> <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"><font color="Maroon" title="c24">pn</font> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 5</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> 11 )
 <b>by </b><i><a class="txt" href="scmp_gcd.html#E1:20_2_1"><i><font color="Green" title="E24">A14</font></i></a>, <a class="txt" href="scmp_gcd.html#E2:20_2_1"><i><font color="Green" title="E25">A15</font></i></a>, <a class="txt" href="scmp_gcd.html#E4:20_2_1"><i><font color="Green" title="E27">A17</font></i></a>, <a class="txt" href="scmp_gcd.html#E3:20_2_1_1_2"><i><font color="Green" title="E33">A23</font></i></a>, <a class="txt" href="scmp_gcd.html#E25"><i><font color="Green" title="E18">Lm6</font></i></a></i>;<br/><b>set </b><font color="Maroon" title="c25">s8</font> = <span class="p1">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Computation</a> <font color="Maroon" title="c18">s</font></span>)</span> <a href="ami_1.html#K11" title="AMI_1:func.11">.</a> 8;<br/><i><font color="Green" title="E36">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">s</font></span>)</span> <a href="ami_1.html#K11" title="AMI_1:func.11">.</a> 8</span>)</span> = 
 <a href="scmpds_2.html#K19" title="SCMPDS_2:func.19">ICplusConst</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">s</font></span>)</span> <a href="ami_1.html#K11" title="AMI_1:func.11">.</a> 7</span>)</span>,<span class="p1">(<span class="default"><a href="xcmplx_0.html#K4" title="XCMPLX_0:func.4">-</a> 7</span>)</span>
<b>by </b><i><a class="txt" href="scmp_gcd.html#E6:20_2_1_1_2"><i><font color="Green" title="E35">A25</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> 5
<b>by </b><i><a class="txt" href="scmp_gcd.html#E6:20_2_1_1_2"><i><font color="Green" title="E35">A25</font></i></a>, <a class="ref" href="scmp_gcd.html#T6" target="_self" title="SCMP_GCD:th.6">Th6</a></i>
;<br/><a NAME="E8:20_2_1_1_2"/><i><font color="Green" title="E37">A27</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#K10" title="AMI_1:func.10">Computation</a> <font color="Maroon" title="c18">s</font></span>)</span> <a href="ami_1.html#K11" title="AMI_1:func.11">.</a> 8
 <b>by </b><i><a class="txt" href="scmp_gcd.html#E1:20_2_1"><i><font color="Green" title="E24">A14</font></i></a>, <a class="ref" href="ami_3.html#T38" title="AMI_3:th.38">AMI_3:38</a></i>;<br/><a NAME="E9:20_2_1_1_2"/><i><font color="Green" title="E38">A28</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="c18">s</font></span>)</span> <a href="ami_1.html#K11" title="AMI_1:func.11">.</a> 8</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="c24">pn</font> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 4
 <b>by </b><i><a class="txt" href="scmp_gcd.html#E6:20_2_1_1_2"><i><font color="Green" title="E35">A25</font></i></a>, <a class="ref" href="scmpds_2.html#T66" title="SCMPDS_2:th.66">SCMPDS_2:66</a></i>;<br/><a NAME="E10:20_2_1_1_2"/><i><font color="Green" title="E39">A29</font></i>: 
4 <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> <font color="Maroon" title="c24">pn</font> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 4
 <b>by </b><i><a class="ref" href="nat_1.html#T11" title="NAT_1:th.11">NAT_1:11</a></i>;<br/><a NAME="E11:20_2_1_1_2"/><b>then </b><i><font color="Green" title="E40">A30</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="c18">s</font></span>)</span> <a href="ami_1.html#K11" title="AMI_1:func.11">.</a> 8</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="xxreal_0.html#NR4" title="XXREAL_0:NR.4">&gt;</a> 0
 <b>by </b><i><a class="txt" href="scmp_gcd.html#E9:20_2_1_1_2"><i><font color="Green" title="E38">A28</font></i></a>, <a class="ref" href="xxreal_0.html#T2" title="XXREAL_0:th.2">XXREAL_0:2</a></i>;<br/><a NAME="E12:20_2_1_1_2"/><i><font color="Green" title="E41">A31</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="c18">s</font></span>)</span> <a href="ami_1.html#K11" title="AMI_1:func.11">.</a> 8</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#E6:20_2_1_1_2"><i><font color="Green" title="E35">A25</font></i></a>, <a class="ref" href="scmpds_2.html#T66" title="SCMPDS_2:th.66">SCMPDS_2:66</a></i>;<br/><b>set </b><font color="Maroon" title="c26">x1</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="c18">s</font></span>)</span> <a href="ami_1.html#K11" title="AMI_1:func.11">.</a> 8</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">s</font></span>)</span> <a href="ami_1.html#K11" title="AMI_1:func.11">.</a> 8</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>;<br/><b>set </b><font color="Maroon" title="c27">y1</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="c18">s</font></span>)</span> <a href="ami_1.html#K11" title="AMI_1:func.11">.</a> 8</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">s</font></span>)</span> <a href="ami_1.html#K11" title="AMI_1:func.11">.</a> 8</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>;<br/><i><font color="Green" title="E42">A32</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="c18">s</font></span>)</span> <a href="ami_1.html#K11" title="AMI_1:func.11">.</a> 8</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">s</font></span>)</span> <a href="ami_1.html#K11" title="AMI_1:func.11">.</a> 8</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 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">s</font></span>)</span> <a href="ami_1.html#K11" title="AMI_1:func.11">.</a> 8</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"><span class="p3">(<span class="default"><font color="Maroon" title="c24">pn</font> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 4</span>)</span> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 2</span>)</span></span>)</span>
<b>by </b><i><a class="txt" href="scmp_gcd.html#E9:20_2_1_1_2"><i><font color="Green" title="E38">A28</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="c23">y</font>
<b>by </b><i><a class="txt" href="scmp_gcd.html#E6:20_2_1_1_2"><i><font color="Green" title="E35">A25</font></i></a>, <a class="ref" href="scmpds_2.html#T66" title="SCMPDS_2:th.66">SCMPDS_2:66</a></i>
;<br/><i><font color="Green" title="E43">A33</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="c18">s</font></span>)</span> <a href="ami_1.html#K11" title="AMI_1:func.11">.</a> 8</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">s</font></span>)</span> <a href="ami_1.html#K11" title="AMI_1:func.11">.</a> 8</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#K10" title="AMI_1:func.10">Computation</a> <font color="Maroon" title="c18">s</font></span>)</span> <a href="ami_1.html#K11" title="AMI_1:func.11">.</a> 8</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"><span class="p3">(<span class="default"><font color="Maroon" title="c24">pn</font> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 4</span>)</span> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 3</span>)</span></span>)</span>
<b>by </b><i><a class="txt" href="scmp_gcd.html#E9:20_2_1_1_2"><i><font color="Green" title="E38">A28</font></i></a>, <a class="ref" href="scmp_gcd.html#T5" target="_self" title="SCMP_GCD:th.5">Th5</a></i>
<br/>.= 
<span class="p1">(<span class="default"><font color="Maroon" title="c18">s</font> <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"><font color="Maroon" title="c18">s</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></span>)</span> <a href="int_1.html#K6" title="INT_1:func.6">mod</a> <font color="Maroon" title="c23">y</font>
<b>by </b><i><a class="txt" href="scmp_gcd.html#E6:20_2_1_1_2"><i><font color="Green" title="E35">A25</font></i></a>, <a class="ref" href="scmpds_2.html#T66" title="SCMPDS_2:th.66">SCMPDS_2:66</a></i>
;<br/><a NAME="E15:20_2_1_1_2"/><b>then </b><i><font color="Green" title="E44">A34</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="c18">s</font></span>)</span> <a href="ami_1.html#K11" title="AMI_1:func.11">.</a> 8</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">s</font></span>)</span> <a href="ami_1.html#K11" title="AMI_1:func.11">.</a> 8</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> <a href="xxreal_0.html#NR3" title="XXREAL_0:NR.3">&lt;</a> <font color="Maroon" title="c23">y</font>
 <b>by </b><i><a class="txt" href="scmp_gcd.html#E3:20_2_1_1_2"><i><font color="Green" title="E33">A23</font></i></a>, <a class="ref" href="newton.html#T79" title="NEWTON:th.79">NEWTON:79</a></i>;<br/><a NAME="E16:20_2_1_1_2"/><b>then </b><i><font color="Green" title="E45">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="c18">s</font></span>)</span> <a href="ami_1.html#K11" title="AMI_1:func.11">.</a> 8</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">s</font></span>)</span> <a href="ami_1.html#K11" title="AMI_1:func.11">.</a> 8</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> <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> <font color="Maroon" title="c17">k</font>
 <b>by </b><i><a class="txt" href="scmp_gcd.html#E1:20_2_1_1_2"><i><font color="Green" title="E32">A22</font></i></a>, <a class="ref" href="int_1.html#T20" title="INT_1:th.20">INT_1:20</a></i>;<br/><a NAME="E17:20_2_1_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="c18">s</font></span>)</span> <a href="ami_1.html#K11" title="AMI_1:func.11">.</a> 8</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">s</font></span>)</span> <a href="ami_1.html#K11" title="AMI_1:func.11">.</a> 8</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> <a href="xxreal_0.html#NR2" title="XXREAL_0:NR.2">&gt;=</a> 0
 <b>by </b><i><a class="txt" href="scmp_gcd.html#E3:20_2_1_1_2"><i><font color="Green" title="E33">A23</font></i></a>, <a class="txt" href="scmp_gcd.html#E14:20_2_1_1_2"><i><font color="Green" title="E43">A33</font></i></a>, <a class="ref" href="newton.html#T78" title="NEWTON:th.78">NEWTON:78</a></i>;<br/><b>then consider </b><font color="Maroon" title="c28">m</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="E19:20_2_1_1_2"/><i><font color="Green" title="E46">A36</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> <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">s</font></span>)</span> <a href="ami_1.html#K11" title="AMI_1:func.11">.</a> 8</span>)</span></span>)</span> <a href="ami_1.html#K11" title="AMI_1:func.11">.</a> <font color="Maroon" title="c28">m</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#K10" title="AMI_1:func.10">Computation</a> <font color="Maroon" title="c18">s</font></span>)</span> <a href="ami_1.html#K11" title="AMI_1:func.11">.</a> 8</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#K10" title="AMI_1:func.10">Computation</a> <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">s</font></span>)</span> <a href="ami_1.html#K11" title="AMI_1:func.11">.</a> 8</span>)</span></span>)</span> <a href="ami_1.html#K11" title="AMI_1:func.11">.</a> <font color="Maroon" title="c28">m</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#K10" title="AMI_1:func.10">Computation</a> <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">s</font></span>)</span> <a href="ami_1.html#K11" title="AMI_1:func.11">.</a> 8</span>)</span></span>)</span> <a href="ami_1.html#K11" title="AMI_1:func.11">.</a> <font color="Maroon" title="c28">m</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#K10" title="AMI_1:func.10">Computation</a> <font color="Maroon" title="c18">s</font></span>)</span> <a href="ami_1.html#K11" title="AMI_1:func.11">.</a> 8</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#K10" title="AMI_1:func.10">Computation</a> <font color="Maroon" title="c18">s</font></span>)</span> <a href="ami_1.html#K11" title="AMI_1:func.11">.</a> 8</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">s</font></span>)</span> <a href="ami_1.html#K11" title="AMI_1:func.11">.</a> 8</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#K10" title="AMI_1:func.10">Computation</a> <font color="Maroon" title="c18">s</font></span>)</span> <a href="ami_1.html#K11" title="AMI_1:func.11">.</a> 8</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">s</font></span>)</span> <a href="ami_1.html#K11" title="AMI_1:func.11">.</a> 8</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#K10" title="AMI_1:func.10">Computation</a> <font color="Maroon" title="c18">s</font></span>)</span> <a href="ami_1.html#K11" title="AMI_1:func.11">.</a> 8</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#K10" title="AMI_1:func.10">Computation</a> <font color="Maroon" title="c18">s</font></span>)</span> <a href="ami_1.html#K11" title="AMI_1:func.11">.</a> 8</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#K10" title="AMI_1:func.10">Computation</a> <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">s</font></span>)</span> <a href="ami_1.html#K11" title="AMI_1:func.11">.</a> 8</span>)</span></span>)</span> <a href="ami_1.html#K11" title="AMI_1:func.11">.</a> <font color="Maroon" title="c28">m</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#E1:20_2"><i><font color="Green" title="E23">A13</font></i></a>, <a class="txt" href="scmp_gcd.html#E7:20_2_1_1_2"><i><font color="Green" title="E36">A26</font></i></a>, <a class="txt" href="scmp_gcd.html#E8:20_2_1_1_2"><i><font color="Green" title="E37">A27</font></i></a>, <a class="txt" href="scmp_gcd.html#E11:20_2_1_1_2"><i><font color="Green" title="E40">A30</font></i></a>, <a class="txt" href="scmp_gcd.html#E12:20_2_1_1_2"><i><font color="Green" title="E41">A31</font></i></a>, <a class="txt" href="scmp_gcd.html#E13:20_2_1_1_2"><i><font color="Green" title="E42">A32</font></i></a>, <a class="txt" href="scmp_gcd.html#E15:20_2_1_1_2"><i><font color="Green" title="E44">A34</font></i></a>, <a class="txt" href="scmp_gcd.html#E16:20_2_1_1_2"><i><font color="Green" title="E45">A35</font></i></a></i>;<br/><b>set </b><font color="Maroon" title="c29">s9</font> = <span class="p1">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Computation</a> <font color="Maroon" title="c18">s</font></span>)</span> <a href="ami_1.html#K11" title="AMI_1:func.11">.</a> <span class="p1">(<span class="default"><font color="Maroon" title="c28">m</font> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 8</span>)</span>;<br/><a NAME="E20:20_2_1_1_2"/><i><font color="Green" title="E47">A37</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">s</font></span>)</span> <a href="ami_1.html#K11" title="AMI_1:func.11">.</a> <span class="p2">(<span class="default"><font color="Maroon" title="c28">m</font> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 8</span>)</span></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> 
 <b>by </b><i><a class="txt" href="scmp_gcd.html#E19:20_2_1_1_2"><i><font color="Green" title="E46">A36</font></i></a>, <a class="ref" href="ami_1.html#T51" title="AMI_1:th.51">AMI_1:51</a></i>;<br/><a NAME="E21:20_2_1_1_2"/><i><font color="Green" title="E48">A38</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="c18">s</font></span>)</span> <a href="ami_1.html#K11" title="AMI_1:func.11">.</a> 8</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#K10" title="AMI_1:func.10">Computation</a> <font color="Maroon" title="c18">s</font></span>)</span> <a href="ami_1.html#K11" title="AMI_1:func.11">.</a> <span class="p2">(<span class="default"><font color="Maroon" title="c28">m</font> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 8</span>)</span></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> 
 <b>by </b><i><a class="txt" href="scmp_gcd.html#E19:20_2_1_1_2"><i><font color="Green" title="E46">A36</font></i></a>, <a class="ref" href="ami_1.html#T51" title="AMI_1:th.51">AMI_1:51</a></i>;<br/><i><font color="Green" title="E49">A39</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">s</font></span>)</span> <a href="ami_1.html#K11" title="AMI_1:func.11">.</a> <span class="p1">(<span class="default"><font color="Maroon" title="c28">m</font> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> <span class="p2">(<span class="default">8 <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1</span>)</span></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="c18">s</font></span>)</span> <a href="ami_1.html#K11" title="AMI_1:func.11">.</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c28">m</font> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 8</span>)</span> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1</span>)</span>

<br/>.= 
 <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">s</font></span>)</span> <a href="ami_1.html#K11" title="AMI_1:func.11">.</a> <span class="p2">(<span class="default"><font color="Maroon" title="c28">m</font> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 8</span>)</span></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#K10" title="AMI_1:func.10">Computation</a> <font color="Maroon" title="c18">s</font></span>)</span> <a href="ami_1.html#K11" title="AMI_1:func.11">.</a> <span class="p2">(<span class="default"><font color="Maroon" title="c28">m</font> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 8</span>)</span></span>)</span>
<b>by </b><i><a class="txt" href="scmp_gcd.html#E20:20_2_1_1_2"><i><font color="Green" title="E47">A37</font></i></a></i>
;<br/><a NAME="E23:20_2_1_1_2"/><i><font color="Green" title="E50">A40</font></i>: 
1 <a href="xxreal_0.html#NR3" title="XXREAL_0:NR.3">&lt;</a> <font color="Maroon" title="c24">pn</font> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 4
 <b>by </b><i><a class="txt" href="scmp_gcd.html#E10:20_2_1_1_2"><i><font color="Green" title="E39">A29</font></i></a>, <a class="ref" href="xxreal_0.html#T2" title="XXREAL_0:th.2">XXREAL_0:2</a></i>;<br/><a NAME="E24:20_2_1_1_2"/>
<font color="Maroon" title="c24">pn</font> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 4 <a href="xxreal_0.html#NR3" title="XXREAL_0:NR.3">&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#K10" title="AMI_1:func.10">Computation</a> <font color="Maroon" title="c18">s</font></span>)</span> <a href="ami_1.html#K11" title="AMI_1:func.11">.</a> 8</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
 <b>by </b><i><a class="txt" href="scmp_gcd.html#E9:20_2_1_1_2"><i><font color="Green" title="E38">A28</font></i></a>, <a class="ref" href="xreal_1.html#T31" title="XREAL_1:th.31">XREAL_1:31</a></i>;<br/><b>then </b><i><font color="Green" title="E51">A41</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="c18">s</font></span>)</span> <a href="ami_1.html#K11" title="AMI_1:func.11">.</a> 8</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"><font color="Maroon" title="c24">pn</font> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 4</span>)</span></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> <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">s</font></span>)</span> <a href="ami_1.html#K11" title="AMI_1:func.11">.</a> 8</span>)</span></span>)</span> <a href="ami_1.html#K11" title="AMI_1:func.11">.</a> <font color="Maroon" title="c28">m</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> <span class="p2">(<span class="default"><font color="Maroon" title="c24">pn</font> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 4</span>)</span></span>)</span>
<b>by </b><i><a class="txt" href="scmp_gcd.html#E19:20_2_1_1_2"><i><font color="Green" title="E46">A36</font></i></a>, <a class="txt" href="scmp_gcd.html#E23:20_2_1_1_2"><i><font color="Green" title="E50">A40</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">s</font></span>)</span> <a href="ami_1.html#K11" title="AMI_1:func.11">.</a> <span class="p2">(<span class="default"><font color="Maroon" title="c28">m</font> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 8</span>)</span></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"><font color="Maroon" title="c24">pn</font> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 4</span>)</span></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/><a NAME="E26:20_2_1_1_2"/>
5 <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> <font color="Maroon" title="c24">pn</font> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 5
 <b>by </b><i><a class="ref" href="nat_1.html#T11" title="NAT_1:th.11">NAT_1:11</a></i>;<br/><a NAME="E27:20_2_1_1_2"/><b>then </b><i><font color="Green" title="E52">A42</font></i>: 
1 <a href="xxreal_0.html#NR3" title="XXREAL_0:NR.3">&lt;</a> <font color="Maroon" title="c24">pn</font> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 5
 <b>by </b><i><a class="ref" href="xxreal_0.html#T2" title="XXREAL_0:th.2">XXREAL_0:2</a></i>;<br/><i><font color="Green" title="E53">A43</font></i>:  <a href="scmpds_3.html#K2" title="SCMPDS_3:func.2">inspos</a> 11 = 
<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">s</font></span>)</span> <a href="ami_1.html#K11" title="AMI_1:func.11">.</a> 8</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"><font color="Maroon" title="c24">pn</font> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 5</span>)</span></span>)</span>
<b>by </b><i><a class="txt" href="scmp_gcd.html#E6:20_2_1_1_2"><i><font color="Green" title="E35">A25</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"><span class="p2">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Computation</a> <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">s</font></span>)</span> <a href="ami_1.html#K11" title="AMI_1:func.11">.</a> 8</span>)</span></span>)</span> <a href="ami_1.html#K11" title="AMI_1:func.11">.</a> <font color="Maroon" title="c28">m</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> <span class="p2">(<span class="default"><font color="Maroon" title="c24">pn</font> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 5</span>)</span></span>)</span>
<b>by </b><i><a class="txt" href="scmp_gcd.html#E19:20_2_1_1_2"><i><font color="Green" title="E46">A36</font></i></a>, <a class="txt" href="scmp_gcd.html#E27:20_2_1_1_2"><i><font color="Green" title="E52">A42</font></i></a>, <a class="txt" href="scmp_gcd.html#E9:20_2_1_1_2"><i><font color="Green" title="E38">A28</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">s</font></span>)</span> <a href="ami_1.html#K11" title="AMI_1:func.11">.</a> <span class="p2">(<span class="default"><font color="Maroon" title="c28">m</font> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 8</span>)</span></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"><span class="p3">(<span class="default"><font color="Maroon" title="c24">pn</font> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 4</span>)</span> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1</span>)</span></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"><span class="p2">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Computation</a> <font color="Maroon" title="c18">s</font></span>)</span> <a href="ami_1.html#K11" title="AMI_1:func.11">.</a> <span class="p2">(<span class="default"><font color="Maroon" title="c28">m</font> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 8</span>)</span></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">s</font></span>)</span> <a href="ami_1.html#K11" title="AMI_1:func.11">.</a> <span class="p4">(<span class="default"><font color="Maroon" title="c28">m</font> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 8</span>)</span></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>
<b>by </b><i><a class="txt" href="scmp_gcd.html#E9:20_2_1_1_2"><i><font color="Green" title="E38">A28</font></i></a>, <a class="txt" href="scmp_gcd.html#E21:20_2_1_1_2"><i><font color="Green" title="E48">A38</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="E54">A44</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">s</font></span>)</span> <a href="ami_1.html#K11" title="AMI_1:func.11">.</a> <span class="p2">(<span class="default"><font color="Maroon" title="c28">m</font> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 9</span>)</span></span>)</span> = 
<span class="p1">(<span class="default">2 <a href="nat_1.html#K2" title="NAT_1:func.2">*</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="int_2.html#K1" title="INT_2:func.1">abs</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><span class="p0">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Computation</a> <font color="Maroon" title="c18">s</font></span>)</span> <a href="ami_1.html#K11" title="AMI_1:func.11">.</a> <span class="p0">(<span class="default"><font color="Maroon" title="c28">m</font> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 8</span>)</span></span>)</span> <a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">.</a> <span class="p5">(<span class="default"><a href="scmpds_2.html#K3" title="SCMPDS_2:func.3">DataLoc</a> <span class="p0">(<span class="default"><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">s</font></span>)</span> <a href="ami_1.html#K11" title="AMI_1:func.11">.</a> <span class="p2">(<span class="default"><font color="Maroon" title="c28">m</font> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 8</span>)</span></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_d.html#K3" title="NAT_D:func.3">div</a> 2</span>)</span></span>)</span> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 4
<b>by </b><i><a class="txt" href="scmp_gcd.html#E22:20_2_1_1_2"><i><font color="Green" title="E49">A39</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">11 <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#E28:20_2_1_1_2"><i><font color="Green" title="E53">A43</font></i></a>, <a class="ref" href="scmp_gcd.html#T3" target="_self" title="SCMP_GCD:th.3">Th3</a></i>
;<br/><b>then </b><i><font color="Green" title="E55">A45</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">s</font></span>)</span> <a href="ami_1.html#K11" title="AMI_1:func.11">.</a> <span class="p2">(<span class="default"><font color="Maroon" title="c28">m</font> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 9</span>)</span></span>)</span> = 
<font color="Maroon" title="c18">s</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> 13</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> ,2 <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> ,6
<b>by </b><i><a class="txt" href="scmp_gcd.html#E1:20_2_1"><i><font color="Green" title="E24">A14</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="E56">A46</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">s</font></span>)</span> <a href="ami_1.html#K11" title="AMI_1:func.11">.</a> <span class="p1">(<span class="default"><font color="Maroon" title="c28">m</font> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> <span class="p2">(<span class="default">9 <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1</span>)</span></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="c18">s</font></span>)</span> <a href="ami_1.html#K11" title="AMI_1:func.11">.</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c28">m</font> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 9</span>)</span> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1</span>)</span>

<br/>.= 
 <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">s</font></span>)</span> <a href="ami_1.html#K11" title="AMI_1:func.11">.</a> <span class="p2">(<span class="default"><font color="Maroon" title="c28">m</font> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 9</span>)</span></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> ,2 <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> ,6</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">s</font></span>)</span> <a href="ami_1.html#K11" title="AMI_1:func.11">.</a> <span class="p2">(<span class="default"><font color="Maroon" title="c28">m</font> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 9</span>)</span></span>)</span>
<b>by </b><i><a class="txt" href="scmp_gcd.html#E30:20_2_1_1_2"><i><font color="Green" title="E55">A45</font></i></a></i>
;<br/><i><font color="Green" title="E57">A47</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="c18">s</font></span>)</span> <a href="ami_1.html#K11" title="AMI_1:func.11">.</a> <span class="p2">(<span class="default"><font color="Maroon" title="c28">m</font> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 9</span>)</span></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 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">s</font></span>)</span> <a href="ami_1.html#K11" title="AMI_1:func.11">.</a> <span class="p2">(<span class="default"><font color="Maroon" title="c28">m</font> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 8</span>)</span></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="c24">pn</font> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 4</span>)</span>,<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#E9:20_2_1_1_2"><i><font color="Green" title="E38">A28</font></i></a>, <a class="txt" href="scmp_gcd.html#E21:20_2_1_1_2"><i><font color="Green" title="E48">A38</font></i></a>, <a class="txt" href="scmp_gcd.html#E22:20_2_1_1_2"><i><font color="Green" title="E49">A39</font></i></a>, <a class="ref" href="scmpds_2.html#T70" title="SCMPDS_2:th.70">SCMPDS_2:70</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">s</font></span>)</span> <a href="ami_1.html#K11" title="AMI_1:func.11">.</a> <span class="p2">(<span class="default"><font color="Maroon" title="c28">m</font> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 8</span>)</span></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"><span class="p3">(<span class="default"><font color="Maroon" title="c24">pn</font> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 4</span>)</span> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 0</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>, <a class="ref" href="scmpds_1.html#D22" title="SCMPDS_1:def.22">SCMPDS_1:def 22</a></i>
<br/>.= 
<font color="Maroon" title="c24">pn</font>
<b>by </b><i><a class="txt" href="scmp_gcd.html#E6:20_2_1_1_2"><i><font color="Green" title="E35">A25</font></i></a>, <a class="txt" href="scmp_gcd.html#E25:20_2_1_1_2"><i><font color="Green" title="E51">A41</font></i></a>, <a class="ref" href="scmpds_2.html#T66" title="SCMPDS_2:th.66">SCMPDS_2:66</a></i>
;<br/><a NAME="E33:20_2_1_1_2"/>
 <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="scmp_gcd.html#K1" title="SCMP_GCD:func.1">intpos</a> <span class="p1">(<span class="default"><font color="Maroon" title="c24">pn</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#E24"><i><font color="Green" title="E17">Lm5</font></i></a></i>;<br/><b>then </b><i><font color="Green" title="E58">A48</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="c18">s</font></span>)</span> <a href="ami_1.html#K11" title="AMI_1:func.11">.</a> <span class="p2">(<span class="default"><font color="Maroon" title="c28">m</font> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 9</span>)</span></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"><font color="Maroon" title="c24">pn</font> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 6</span>)</span></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">s</font></span>)</span> <a href="ami_1.html#K11" title="AMI_1:func.11">.</a> <span class="p2">(<span class="default"><font color="Maroon" title="c28">m</font> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 8</span>)</span></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"><span class="p3">(<span class="default"><font color="Maroon" title="c24">pn</font> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 4</span>)</span> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 2</span>)</span></span>)</span>
<b>by </b><i><a class="txt" href="scmp_gcd.html#E22:20_2_1_1_2"><i><font color="Green" title="E49">A39</font></i></a>, <a class="ref" href="scmpds_2.html#T70" title="SCMPDS_2:th.70">SCMPDS_2:70</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">s</font></span>)</span> <a href="ami_1.html#K11" title="AMI_1:func.11">.</a> <span class="p2">(<span class="default"><font color="Maroon" title="c28">m</font> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 8</span>)</span></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">s</font></span>)</span> <a href="ami_1.html#K11" title="AMI_1:func.11">.</a> 8</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>
<b>by </b><i><a class="txt" href="scmp_gcd.html#E9:20_2_1_1_2"><i><font color="Green" title="E38">A28</font></i></a>, <a class="ref" href="scmp_gcd.html#T5" target="_self" title="SCMP_GCD:th.5">Th5</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">s</font></span>)</span> <a href="ami_1.html#K11" title="AMI_1:func.11">.</a> 8</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">s</font></span>)</span> <a href="ami_1.html#K11" title="AMI_1:func.11">.</a> 8</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#K10" title="AMI_1:func.10">Computation</a> <font color="Maroon" title="c18">s</font></span>)</span> <a href="ami_1.html#K11" title="AMI_1:func.11">.</a> 8</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">s</font></span>)</span> <a href="ami_1.html#K11" title="AMI_1:func.11">.</a> 8</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#E19:20_2_1_1_2"><i><font color="Green" title="E46">A36</font></i></a>, <a class="ref" href="ami_1.html#T51" title="AMI_1:th.51">AMI_1:51</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">s</font></span>)</span> <a href="ami_1.html#K11" title="AMI_1:func.11">.</a> <span class="p2">(<span class="default"><font color="Maroon" title="c28">m</font> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 10</span>)</span></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">s</font></span>)</span> <a href="ami_1.html#K11" title="AMI_1:func.11">.</a> <span class="p3">(<span class="default"><font color="Maroon" title="c28">m</font> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 9</span>)</span></span>)</span></span>)</span>
<b>by </b><i><a class="txt" href="scmp_gcd.html#E31:20_2_1_1_2"><i><font color="Green" title="E56">A46</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">13 <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#E29:20_2_1_1_2"><i><font color="Green" title="E54">A44</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="E59">A49</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">s</font></span>)</span> <a href="ami_1.html#K11" title="AMI_1:func.11">.</a> <span class="p2">(<span class="default"><font color="Maroon" title="c28">m</font> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 10</span>)</span></span>)</span> = 
<font color="Maroon" title="c18">s</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> 14</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#K5" title="SCMPDS_2:func.5">return</a> <a href="scmp_gcd.html#K3" title="SCMP_GCD:func.3">SBP</a> 
<b>by </b><i><a class="txt" href="scmp_gcd.html#E1:20_2_1"><i><font color="Green" title="E24">A14</font></i></a>, <a class="txt" href="scmp_gcd.html#E21"><i><font color="Green" title="E14">Lm3</font></i></a></i>
;<br/><div><b>hereby </b>
<div class="add"><b>take </b><font color="Maroon" title="c30">n</font> = <font color="Maroon" title="c28">m</font> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 10;<br/><b>thus </b><a NAME="E1:20_2_1_1_2_14"/>
 <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">s</font></span>)</span> <a href="ami_1.html#K11" title="AMI_1:func.11">.</a> <font color="Maroon" title="c30">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> 
 <b>by </b><i><a class="txt" href="scmp_gcd.html#E36:20_2_1_1_2"><i><font color="Green" title="E59">A49</font></i></a></i>;<br/><a NAME="E2:20_2_1_1_2_14"/><i><font color="Green" title="E60">A50</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">s</font></span>)</span> <a href="ami_1.html#K11" title="AMI_1:func.11">.</a> <span class="p3">(<span class="default"><font color="Maroon" title="c28">m</font> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 9</span>)</span></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="c24">pn</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#E32:20_2_1_1_2"><i><font color="Green" title="E57">A47</font></i></a>, <a class="ref" href="scmp_gcd.html#T5" target="_self" title="SCMP_GCD:th.5">Th5</a></i>;<br/><a NAME="E3:20_2_1_1_2_14"/><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="c18">s</font></span>)</span> <a href="ami_1.html#K11" title="AMI_1:func.11">.</a> <span class="p3">(<span class="default"><font color="Maroon" title="c28">m</font> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 9</span>)</span></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/><b>hence </b><a NAME="E4:20_2_1_1_2_14"/>
<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">s</font></span>)</span> <a href="ami_1.html#K11" title="AMI_1:func.11">.</a> <font color="Maroon" title="c30">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>  <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c18">s</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> 
 <b>by </b><i><a class="txt" href="scmp_gcd.html#E31:20_2_1_1_2"><i><font color="Green" title="E56">A46</font></i></a>, <a class="txt" href="scmp_gcd.html#E32:20_2_1_1_2"><i><font color="Green" title="E57">A47</font></i></a>, <a class="ref" href="scmpds_2.html#T59" title="SCMPDS_2:th.59">SCMPDS_2:59</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="c18">s</font></span>)</span> <a href="ami_1.html#K11" title="AMI_1:func.11">.</a> <font color="Maroon" title="c30">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"><font color="Maroon" title="c18">s</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> = 
<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">s</font></span>)</span> <a href="ami_1.html#K11" title="AMI_1:func.11">.</a> <span class="p2">(<span class="default"><font color="Maroon" title="c28">m</font> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 9</span>)</span></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> <font color="Maroon" title="c24">pn</font>,6</span>)</span>
<b>by </b><i><a class="txt" href="scmp_gcd.html#E31:20_2_1_1_2"><i><font color="Green" title="E56">A46</font></i></a>, <a class="txt" href="scmp_gcd.html#E32:20_2_1_1_2"><i><font color="Green" title="E57">A47</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"><font color="Maroon" title="c18">s</font> <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"><font color="Maroon" title="c18">s</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></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"><font color="Maroon" title="c18">s</font> <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"><font color="Maroon" title="c18">s</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></span>)</span> <a href="int_1.html#K6" title="INT_1:func.6">mod</a> <span class="p2">(<span class="default"><font color="Maroon" title="c18">s</font> <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"><font color="Maroon" title="c18">s</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></span>)</span></span>)</span>
<b>by </b><i><a class="txt" href="scmp_gcd.html#E13:20_2_1_1_2"><i><font color="Green" title="E42">A32</font></i></a>, <a class="txt" href="scmp_gcd.html#E14:20_2_1_1_2"><i><font color="Green" title="E43">A33</font></i></a>, <a class="txt" href="scmp_gcd.html#E34:20_2_1_1_2"><i><font color="Green" title="E58">A48</font></i></a>, <a class="ref" href="scmp_gcd.html#T5" target="_self" title="SCMP_GCD:th.5">Th5</a></i>
<br/>.= 
<span class="p1">(<span class="default"><font color="Maroon" title="c18">s</font> <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"><font color="Maroon" title="c18">s</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></span>)</span> <a href="int_2.html#K3" title="INT_2:func.3">gcd</a> <span class="p1">(<span class="default"><font color="Maroon" title="c18">s</font> <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"><font color="Maroon" title="c18">s</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></span>)</span>
<b>by </b><i><a class="txt" href="scmp_gcd.html#E8:20_2_1"><i><font color="Green" title="E31">A21</font></i></a>, <a class="txt" href="scmp_gcd.html#E3:20_2_1_1_2"><i><font color="Green" title="E33">A23</font></i></a>, <a class="ref" href="scmp_gcd.html#T2" target="_self" title="SCMP_GCD:th.2">Th2</a></i>
;<br/><div><b>hereby </b>
<div class="add"><b>let </b><font color="Maroon" title="c31">j</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>assume </b><a NAME="E1:20_2_1_1_2_14_2"/><i><font color="Green" title="E61">A51</font></i>: 
( 1 <a href="xxreal_0.html#NR3" title="XXREAL_0:NR.3">&lt;</a> <font color="Maroon" title="c31">j</font> &amp; <font color="Maroon" title="c31">j</font> <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> <span class="p1">(<span class="default"><font color="Maroon" title="c18">s</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> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> 1 )
 ;<br/><a NAME="E2:20_2_1_1_2_14_2"/>
<font color="Maroon" title="c18">s</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="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</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">s</font></span>)</span> <a href="ami_1.html#K11" title="AMI_1:func.11">.</a> 8</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> 
 <b>by </b><i><a class="txt" href="scmp_gcd.html#E9:20_2_1_1_2"><i><font color="Green" title="E38">A28</font></i></a>, <a class="ref" href="nat_1.html#T11" title="NAT_1:th.11">NAT_1:11</a></i>;<br/><a NAME="E3:20_2_1_1_2_14_2"/><b>then </b>
<span class="p1">(<span class="default"><font color="Maroon" title="c18">s</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> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> 1 <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#K10" title="AMI_1:func.10">Computation</a> <font color="Maroon" title="c18">s</font></span>)</span> <a href="ami_1.html#K11" title="AMI_1:func.11">.</a> 8</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
 <b>by </b><i><a class="ref" href="xreal_1.html#T8" title="XREAL_1:th.8">XREAL_1:8</a></i>;<br/><a NAME="E4:20_2_1_1_2_14_2"/><b>then </b><i><font color="Green" title="E62">A52</font></i>: 
<font color="Maroon" title="c31">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#K10" title="AMI_1:func.10">Computation</a> <font color="Maroon" title="c18">s</font></span>)</span> <a href="ami_1.html#K11" title="AMI_1:func.11">.</a> 8</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
 <b>by </b><i><a class="txt" href="scmp_gcd.html#E1:20_2_1_1_2_14_2"><i><font color="Green" title="E61">A51</font></i></a>, <a class="ref" href="xxreal_0.html#T2" title="XXREAL_0:th.2">XXREAL_0:2</a></i>;<br/><a NAME="E5:20_2_1_1_2_14_2"/>
 <a href="scmp_gcd.html#K1" title="SCMP_GCD:func.1">intpos</a> <font color="Maroon" title="c31">j</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> 
 <b>by </b><i><a class="txt" href="scmp_gcd.html#E1:20_2_1_1_2_14_2"><i><font color="Green" title="E61">A51</font></i></a>, <a class="txt" href="scmp_gcd.html#E6"><i><font color="Green" title="E4">Lm2</font></i></a></i>;<br/><b>then </b><i><font color="Green" title="E63">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="c18">s</font></span>)</span> <a href="ami_1.html#K11" title="AMI_1:func.11">.</a> <span class="p2">(<span class="default"><font color="Maroon" title="c28">m</font> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 9</span>)</span></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="Maroon" title="c31">j</font></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">s</font></span>)</span> <a href="ami_1.html#K11" title="AMI_1:func.11">.</a> <span class="p2">(<span class="default"><font color="Maroon" title="c28">m</font> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 8</span>)</span></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="Maroon" title="c31">j</font></span>)</span>
<b>by </b><i><a class="txt" href="scmp_gcd.html#E22:20_2_1_1_2"><i><font color="Green" title="E49">A39</font></i></a>, <a class="ref" href="scmpds_2.html#T70" title="SCMPDS_2:th.70">SCMPDS_2:70</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> <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">s</font></span>)</span> <a href="ami_1.html#K11" title="AMI_1:func.11">.</a> 8</span>)</span></span>)</span> <a href="ami_1.html#K11" title="AMI_1:func.11">.</a> <font color="Maroon" title="c28">m</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="Maroon" title="c31">j</font></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"><span class="p2">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Computation</a> <font color="Maroon" title="c18">s</font></span>)</span> <a href="ami_1.html#K11" title="AMI_1:func.11">.</a> 8</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="Maroon" title="c31">j</font></span>)</span>
<b>by </b><i><a class="txt" href="scmp_gcd.html#E19:20_2_1_1_2"><i><font color="Green" title="E46">A36</font></i></a>, <a class="txt" href="scmp_gcd.html#E1:20_2_1_1_2_14_2"><i><font color="Green" title="E61">A51</font></i></a>, <a class="txt" href="scmp_gcd.html#E4:20_2_1_1_2_14_2"><i><font color="Green" title="E62">A52</font></i></a></i>
;<br/><a NAME="E7:20_2_1_1_2_14_2"/>
<font color="Maroon" title="c24">pn</font> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1 <a href="xxreal_0.html#NR3" title="XXREAL_0:NR.3">&lt;</a> <font color="Maroon" title="c24">pn</font> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 2
 <b>by </b><i><a class="ref" href="xreal_1.html#T8" title="XREAL_1:th.8">XREAL_1:8</a></i>;<br/><a NAME="E8:20_2_1_1_2_14_2"/><b>then </b><i><font color="Green" title="E64">A54</font></i>: 
 <a href="scmp_gcd.html#K1" title="SCMP_GCD:func.1">intpos</a> <font color="Maroon" title="c31">j</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">s</font></span>)</span> <a href="ami_1.html#K11" title="AMI_1:func.11">.</a> <span class="p3">(<span class="default"><font color="Maroon" title="c28">m</font> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 9</span>)</span></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#E2:20_2_1_1_2_14"><i><font color="Green" title="E60">A50</font></i></a>, <a class="txt" href="scmp_gcd.html#E1:20_2_1_1_2_14_2"><i><font color="Green" title="E61">A51</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="E9:20_2_1_1_2_14_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="c18">s</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> <span class="p1">(<span class="default"><a href="scmp_gcd.html#K1" title="SCMP_GCD:func.1">intpos</a> <font color="Maroon" title="c31">j</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c18">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> <font color="Maroon" title="c31">j</font></span>)</span>
 <b>by </b><i><a class="txt" href="scmp_gcd.html#E1:20_2_1"><i><font color="Green" title="E24">A14</font></i></a>, <a class="txt" href="scmp_gcd.html#E2:20_2_1"><i><font color="Green" title="E25">A15</font></i></a>, <a class="txt" href="scmp_gcd.html#E4:20_2_1"><i><font color="Green" title="E27">A17</font></i></a>, <a class="txt" href="scmp_gcd.html#E3:20_2_1_1_2"><i><font color="Green" title="E33">A23</font></i></a>, <a class="txt" href="scmp_gcd.html#E5:20_2_1_1_2"><i><font color="Green" title="E34">A24</font></i></a>, <a class="txt" href="scmp_gcd.html#E1:20_2_1_1_2_14_2"><i><font color="Green" title="E61">A51</font></i></a>, <a class="txt" href="scmp_gcd.html#E26"><i><font color="Green" title="E19">Lm7</font></i></a></i>;<br/><b>hence </b><font color="Maroon" title="c18">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> <font color="Maroon" title="c31">j</font></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">s</font></span>)</span> <a href="ami_1.html#K11" title="AMI_1:func.11">.</a> 8</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="Maroon" title="c31">j</font></span>)</span>
<b>by </b><i><a class="txt" href="scmp_gcd.html#E6:20_2_1_1_2"><i><font color="Green" title="E35">A25</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"><span class="p2">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Computation</a> <font color="Maroon" title="c18">s</font></span>)</span> <a href="ami_1.html#K11" title="AMI_1:func.11">.</a> <font color="Maroon" title="c30">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="Maroon" title="c31">j</font></span>)</span>
<b>by </b><i><a class="txt" href="scmp_gcd.html#E31:20_2_1_1_2"><i><font color="Green" title="E56">A46</font></i></a>, <a class="txt" href="scmp_gcd.html#E6:20_2_1_1_2_14_2"><i><font color="Green" title="E63">A53</font></i></a>, <a class="txt" href="scmp_gcd.html#E8:20_2_1_1_2_14_2"><i><font color="Green" title="E64">A54</font></i></a>, <a class="ref" href="scmpds_2.html#T59" title="SCMPDS_2:th.59">SCMPDS_2:59</a></i>
;<br/><br/></div>
<b>end;</b></div></div>
<b>end;</b></div></div><b>end;</b></div></div><b>end;</b></div></div><b>end;</b></div><b>hence </b><a NAME="E3:20_2"/>
<font color="Maroon">S<sub>1</sub></font>[<font color="Maroon" title="c17">k</font> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1]
 ;<br/></div><b>end;</b></div>
<a NAME="E4:20"/><i><font color="Green" title="E23">A55</font></i>: 
for <font color="Olive" title="b1">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>  holds  <font color="Maroon">S<sub>1</sub></font>[<font color="Olive" title="b1">n</font>]
 
<b>from </b><i><a class="ref" href="nat_1.html#S1" title="NAT_1:sch.1">NAT_1:sch 1</a>(<a class="txt" href="scmp_gcd.html#E2:20"><i><font color="Green" title="E21">A11</font></i></a>, <a class="txt" href="scmp_gcd.html#E3:20"><i><font color="Green" title="E22">A12</font></i></a>);<br/></i>
<b>let </b><font color="Maroon" title="c17">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>assume </b><a NAME="E5:20"/><i><font color="Green" title="E24">A56</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">s</font> &amp;  <a href="ami_1.html#K6" title="AMI_1:func.6">IC</a> <font color="Maroon" title="c17">s</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 &amp; <font color="Maroon" title="c17">s</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="xxreal_0.html#NR4" title="XXREAL_0:NR.4">&gt;</a> 0 &amp; <font color="Maroon" title="c17">s</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 &amp; <font color="Maroon" title="c17">s</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">s</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#NR2" title="XXREAL_0:NR.2">&gt;=</a> 0 &amp; <font color="Maroon" title="c17">s</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">s</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="xxreal_0.html#NR2" title="XXREAL_0:NR.2">&gt;=</a> <font color="Maroon" title="c17">s</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">s</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/>

<b>then reconsider </b><font color="Maroon" title="c18">m</font> = <font color="Maroon" title="c17">s</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">s</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> as    <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>by </b><i><a class="ref" href="int_1.html#T16" title="INT_1:th.16">INT_1:16</a></i>;<br/>
<a NAME="E7:20"/>
<font color="Maroon">S<sub>1</sub></font>[<font color="Maroon" title="c18">m</font>]
 
<b>by </b><i><a class="txt" href="scmp_gcd.html#E4:20"><i><font color="Green" title="E23">A55</font></i></a></i>;<br/>
<b>hence </b><a NAME="E8:20"/>
 ex <font color="Olive" title="b1">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>  st <br/>(  <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">s</font></span>)</span> <a href="ami_1.html#K11" title="AMI_1:func.11">.</a> <font color="Olive" title="b1">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; <font color="Maroon" title="c17">s</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> <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">s</font></span>)</span> <a href="ami_1.html#K11" title="AMI_1:func.11">.</a> <font color="Olive" title="b1">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#K10" title="AMI_1:func.10">Computation</a> <font color="Maroon" title="c17">s</font></span>)</span> <a href="ami_1.html#K11" title="AMI_1:func.11">.</a> <font color="Olive" title="b1">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"><font color="Maroon" title="c17">s</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> <span class="p1">(<span class="default"><font color="Maroon" title="c17">s</font> <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"><font color="Maroon" title="c17">s</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></span>)</span> <a href="int_2.html#K3" title="INT_2:func.3">gcd</a> <span class="p1">(<span class="default"><font color="Maroon" title="c17">s</font> <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"><font color="Maroon" title="c17">s</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></span>)</span> &amp; ( for <font color="Olive" title="b2">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="b2">j</font> &amp; <font color="Olive" title="b2">j</font> <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> <span class="p1">(<span class="default"><font color="Maroon" title="c17">s</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> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> 1 holds <br/><font color="Maroon" title="c17">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> <font color="Olive" title="b2">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#K10" title="AMI_1:func.10">Computation</a> <font color="Maroon" title="c17">s</font></span>)</span> <a href="ami_1.html#K11" title="AMI_1:func.11">.</a> <font color="Olive" title="b1">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="b2">j</font></span>)</span> ) )
 <b>by </b><i><a class="txt" href="scmp_gcd.html#E5:20"><i><font color="Green" title="E24">A56</font></i></a></i>;<br/>


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