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<span class="kw">let </span><font color="Maroon" title="c16">P</font> be   <a href="compos_1.html#NM2" title="COMPOS_1:NM.2">Instruction-Sequence</a> of <a href="scmpds_2.html#K1" title="SCMPDS_2:func.1">SCMPDS</a>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> (  <a href="scmp_gcd.html#K4" title="SCMP_GCD:func.4">GCD-Algorithm</a>  <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Maroon" title="c16">P</font> implies ( <font color="Maroon" title="c16">P</font> <a href="compos_1.html#K3" title="COMPOS_1:func.3">.</a> <a href="numbers.html#K6" title="NUMBERS:func.6">0</a> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <a href="scmp_gcd.html#K2" title="SCMP_GCD:func.2">GBP</a> <a href="scmpds_2.html#K6" title="SCMPDS_2:func.6">:=</a> <a href="numbers.html#K6" title="NUMBERS:func.6">0</a> &amp; <font color="Maroon" title="c16">P</font> <a href="compos_1.html#K3" title="COMPOS_1:func.3">.</a> 1 <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <a href="scmp_gcd.html#K3" title="SCMP_GCD:func.3">SBP</a> <a href="scmpds_2.html#K6" title="SCMPDS_2:func.6">:=</a> 7 &amp; <font color="Maroon" title="c16">P</font> <a href="compos_1.html#K3" title="COMPOS_1:func.3">.</a> 2 <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="scmpds_2.html#K7" title="SCMPDS_2:func.7">saveIC</a> (<a href="scmp_gcd.html#K3" title="SCMP_GCD:func.3">SBP</a>,<a href="scmpds_1.html#K23" title="SCMPDS_1:func.23">RetIC</a>) &amp; <font color="Maroon" title="c16">P</font> <a href="compos_1.html#K3" title="COMPOS_1:func.3">.</a> 3 <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="scmpds_2.html#K4" title="SCMPDS_2:func.4">goto</a> 2 &amp; <font color="Maroon" title="c16">P</font> <a href="compos_1.html#K3" title="COMPOS_1:func.3">.</a> 4 <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="compos_1.html#K2" title="COMPOS_1:func.2">halt</a> <a href="scmpds_2.html#K1" title="SCMPDS_2:func.1">SCMPDS</a> &amp; <font color="Maroon" title="c16">P</font> <a href="compos_1.html#K3" title="COMPOS_1:func.3">.</a> 5 <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 &amp; <font color="Maroon" title="c16">P</font> <a href="compos_1.html#K3" title="COMPOS_1:func.3">.</a> 6 <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> (<a href="scmp_gcd.html#K3" title="SCMP_GCD:func.3">SBP</a>,6) <a href="scmpds_2.html#K17" title="SCMPDS_2:func.17">:=</a> (<a href="scmp_gcd.html#K3" title="SCMP_GCD:func.3">SBP</a>,3) &amp; <font color="Maroon" title="c16">P</font> <a href="compos_1.html#K3" title="COMPOS_1:func.3">.</a> 7 <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="scmpds_2.html#K16" title="SCMPDS_2:func.16">Divide</a> (<a href="scmp_gcd.html#K3" title="SCMP_GCD:func.3">SBP</a>,2,<a href="scmp_gcd.html#K3" title="SCMP_GCD:func.3">SBP</a>,3) &amp; <font color="Maroon" title="c16">P</font> <a href="compos_1.html#K3" title="COMPOS_1:func.3">.</a> 8 <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> (<a href="scmp_gcd.html#K3" title="SCMP_GCD:func.3">SBP</a>,7) <a href="scmpds_2.html#K17" title="SCMPDS_2:func.17">:=</a> (<a href="scmp_gcd.html#K3" title="SCMP_GCD:func.3">SBP</a>,3) &amp; <font color="Maroon" title="c16">P</font> <a href="compos_1.html#K3" title="COMPOS_1:func.3">.</a> 9 <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> (<a href="scmp_gcd.html#K3" title="SCMP_GCD:func.3">SBP</a>,<span class="p1">(<span class="default">4 <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> <a href="scmpds_1.html#K22" title="SCMPDS_1:func.22">RetSP</a></span>)</span>) <a href="scmpds_2.html#K17" title="SCMPDS_2:func.17">:=</a> (<a href="scmp_gcd.html#K2" title="SCMP_GCD:func.2">GBP</a>,1) &amp; <font color="Maroon" title="c16">P</font> <a href="compos_1.html#K3" title="COMPOS_1:func.3">.</a> 10 <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="scmpds_2.html#K12" title="SCMPDS_2:func.12">AddTo</a> (<a href="scmp_gcd.html#K2" title="SCMP_GCD:func.2">GBP</a>,1,4) &amp; <font color="Maroon" title="c16">P</font> <a href="compos_1.html#K3" title="COMPOS_1:func.3">.</a> 11 <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="scmpds_2.html#K7" title="SCMPDS_2:func.7">saveIC</a> (<a href="scmp_gcd.html#K3" title="SCMP_GCD:func.3">SBP</a>,<a href="scmpds_1.html#K23" title="SCMPDS_1:func.23">RetIC</a>) &amp; <font color="Maroon" title="c16">P</font> <a href="compos_1.html#K3" title="COMPOS_1:func.3">.</a> 12 <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="scmpds_2.html#K4" title="SCMPDS_2:func.4">goto</a> <span class="p1">(<span class="default"><a href="xcmplx_0.html#K4" title="XCMPLX_0:func.4">-</a> 7</span>)</span> &amp; <font color="Maroon" title="c16">P</font> <a href="compos_1.html#K3" title="COMPOS_1:func.3">.</a> 13 <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> (<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) &amp; <font color="Maroon" title="c16">P</font> <a href="compos_1.html#K3" title="COMPOS_1:func.3">.</a> 14 <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> ) )</span><br/>

<span class="kw">set </span><font color="Maroon" title="c17">GA</font> =  <a href="scmp_gcd.html#K4" title="SCMP_GCD:func.4">GCD-Algorithm</a> ;<br/>
<span class="kw">assume </span><a NAME="E1:12"/><span class="lab"><font color="Green" title="E10">A1</font></span>: 
 <a href="scmp_gcd.html#K4" title="SCMP_GCD:func.4">GCD-Algorithm</a>  <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Maroon" title="c16">P</font>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> ( <font color="Maroon" title="c16">P</font> <a href="compos_1.html#K3" title="COMPOS_1:func.3">.</a> <a href="numbers.html#K6" title="NUMBERS:func.6">0</a> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <a href="scmp_gcd.html#K2" title="SCMP_GCD:func.2">GBP</a> <a href="scmpds_2.html#K6" title="SCMPDS_2:func.6">:=</a> <a href="numbers.html#K6" title="NUMBERS:func.6">0</a> &amp; <font color="Maroon" title="c16">P</font> <a href="compos_1.html#K3" title="COMPOS_1:func.3">.</a> 1 <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <a href="scmp_gcd.html#K3" title="SCMP_GCD:func.3">SBP</a> <a href="scmpds_2.html#K6" title="SCMPDS_2:func.6">:=</a> 7 &amp; <font color="Maroon" title="c16">P</font> <a href="compos_1.html#K3" title="COMPOS_1:func.3">.</a> 2 <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="scmpds_2.html#K7" title="SCMPDS_2:func.7">saveIC</a> (<a href="scmp_gcd.html#K3" title="SCMP_GCD:func.3">SBP</a>,<a href="scmpds_1.html#K23" title="SCMPDS_1:func.23">RetIC</a>) &amp; <font color="Maroon" title="c16">P</font> <a href="compos_1.html#K3" title="COMPOS_1:func.3">.</a> 3 <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="scmpds_2.html#K4" title="SCMPDS_2:func.4">goto</a> 2 &amp; <font color="Maroon" title="c16">P</font> <a href="compos_1.html#K3" title="COMPOS_1:func.3">.</a> 4 <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="compos_1.html#K2" title="COMPOS_1:func.2">halt</a> <a href="scmpds_2.html#K1" title="SCMPDS_2:func.1">SCMPDS</a> &amp; <font color="Maroon" title="c16">P</font> <a href="compos_1.html#K3" title="COMPOS_1:func.3">.</a> 5 <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 &amp; <font color="Maroon" title="c16">P</font> <a href="compos_1.html#K3" title="COMPOS_1:func.3">.</a> 6 <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> (<a href="scmp_gcd.html#K3" title="SCMP_GCD:func.3">SBP</a>,6) <a href="scmpds_2.html#K17" title="SCMPDS_2:func.17">:=</a> (<a href="scmp_gcd.html#K3" title="SCMP_GCD:func.3">SBP</a>,3) &amp; <font color="Maroon" title="c16">P</font> <a href="compos_1.html#K3" title="COMPOS_1:func.3">.</a> 7 <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="scmpds_2.html#K16" title="SCMPDS_2:func.16">Divide</a> (<a href="scmp_gcd.html#K3" title="SCMP_GCD:func.3">SBP</a>,2,<a href="scmp_gcd.html#K3" title="SCMP_GCD:func.3">SBP</a>,3) &amp; <font color="Maroon" title="c16">P</font> <a href="compos_1.html#K3" title="COMPOS_1:func.3">.</a> 8 <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> (<a href="scmp_gcd.html#K3" title="SCMP_GCD:func.3">SBP</a>,7) <a href="scmpds_2.html#K17" title="SCMPDS_2:func.17">:=</a> (<a href="scmp_gcd.html#K3" title="SCMP_GCD:func.3">SBP</a>,3) &amp; <font color="Maroon" title="c16">P</font> <a href="compos_1.html#K3" title="COMPOS_1:func.3">.</a> 9 <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> (<a href="scmp_gcd.html#K3" title="SCMP_GCD:func.3">SBP</a>,<span class="p1">(<span class="default">4 <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> <a href="scmpds_1.html#K22" title="SCMPDS_1:func.22">RetSP</a></span>)</span>) <a href="scmpds_2.html#K17" title="SCMPDS_2:func.17">:=</a> (<a href="scmp_gcd.html#K2" title="SCMP_GCD:func.2">GBP</a>,1) &amp; <font color="Maroon" title="c16">P</font> <a href="compos_1.html#K3" title="COMPOS_1:func.3">.</a> 10 <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="scmpds_2.html#K12" title="SCMPDS_2:func.12">AddTo</a> (<a href="scmp_gcd.html#K2" title="SCMP_GCD:func.2">GBP</a>,1,4) &amp; <font color="Maroon" title="c16">P</font> <a href="compos_1.html#K3" title="COMPOS_1:func.3">.</a> 11 <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="scmpds_2.html#K7" title="SCMPDS_2:func.7">saveIC</a> (<a href="scmp_gcd.html#K3" title="SCMP_GCD:func.3">SBP</a>,<a href="scmpds_1.html#K23" title="SCMPDS_1:func.23">RetIC</a>) &amp; <font color="Maroon" title="c16">P</font> <a href="compos_1.html#K3" title="COMPOS_1:func.3">.</a> 12 <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="scmpds_2.html#K4" title="SCMPDS_2:func.4">goto</a> <span class="p1">(<span class="default"><a href="xcmplx_0.html#K4" title="XCMPLX_0:func.4">-</a> 7</span>)</span> &amp; <font color="Maroon" title="c16">P</font> <a href="compos_1.html#K3" title="COMPOS_1:func.3">.</a> 13 <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> (<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) &amp; <font color="Maroon" title="c16">P</font> <a href="compos_1.html#K3" title="COMPOS_1:func.3">.</a> 14 <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> )</span><br/>

<a NAME="E2:12"/>
 <a href="numbers.html#K6" title="NUMBERS:func.6">0</a>  <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="relat_1.html#NK2" title="RELAT_1:NK.2">dom</a> <a href="scmp_gcd.html#K4" title="SCMP_GCD:func.4">GCD-Algorithm</a>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="scmp_gcd.html#T8" target="_self" title="SCMP_GCD:th.8">Th12</a>, <a class="ref" href="afinsq_1.html#T66" title="AFINSQ_1:th.66">AFINSQ_1:66</a></span>;<br/>
<span class="kw">hence </span><a NAME="E3:12"/>
<font color="Maroon" title="c16">P</font> <a href="compos_1.html#K3" title="COMPOS_1:func.3">.</a> <a href="numbers.html#K6" title="NUMBERS:func.6">0</a> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <a href="scmp_gcd.html#K2" title="SCMP_GCD:func.2">GBP</a> <a href="scmpds_2.html#K6" title="SCMPDS_2:func.6">:=</a> <a href="numbers.html#K6" title="NUMBERS:func.6">0</a>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:12"><span class="lab"><font color="Green" title="E10">A1</font></span></a>, <a class="ref" href="scmp_gcd.html#T10" target="_self" title="SCMP_GCD:th.10">Th14</a>, <a class="ref" href="grfunc_1.html#T2" title="GRFUNC_1:th.2">GRFUNC_1:2</a></span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> ( <font color="Maroon" title="c16">P</font> <a href="compos_1.html#K3" title="COMPOS_1:func.3">.</a> 1 <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <a href="scmp_gcd.html#K3" title="SCMP_GCD:func.3">SBP</a> <a href="scmpds_2.html#K6" title="SCMPDS_2:func.6">:=</a> 7 &amp; <font color="Maroon" title="c16">P</font> <a href="compos_1.html#K3" title="COMPOS_1:func.3">.</a> 2 <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="scmpds_2.html#K7" title="SCMPDS_2:func.7">saveIC</a> (<a href="scmp_gcd.html#K3" title="SCMP_GCD:func.3">SBP</a>,<a href="scmpds_1.html#K23" title="SCMPDS_1:func.23">RetIC</a>) &amp; <font color="Maroon" title="c16">P</font> <a href="compos_1.html#K3" title="COMPOS_1:func.3">.</a> 3 <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="scmpds_2.html#K4" title="SCMPDS_2:func.4">goto</a> 2 &amp; <font color="Maroon" title="c16">P</font> <a href="compos_1.html#K3" title="COMPOS_1:func.3">.</a> 4 <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="compos_1.html#K2" title="COMPOS_1:func.2">halt</a> <a href="scmpds_2.html#K1" title="SCMPDS_2:func.1">SCMPDS</a> &amp; <font color="Maroon" title="c16">P</font> <a href="compos_1.html#K3" title="COMPOS_1:func.3">.</a> 5 <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 &amp; <font color="Maroon" title="c16">P</font> <a href="compos_1.html#K3" title="COMPOS_1:func.3">.</a> 6 <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> (<a href="scmp_gcd.html#K3" title="SCMP_GCD:func.3">SBP</a>,6) <a href="scmpds_2.html#K17" title="SCMPDS_2:func.17">:=</a> (<a href="scmp_gcd.html#K3" title="SCMP_GCD:func.3">SBP</a>,3) &amp; <font color="Maroon" title="c16">P</font> <a href="compos_1.html#K3" title="COMPOS_1:func.3">.</a> 7 <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="scmpds_2.html#K16" title="SCMPDS_2:func.16">Divide</a> (<a href="scmp_gcd.html#K3" title="SCMP_GCD:func.3">SBP</a>,2,<a href="scmp_gcd.html#K3" title="SCMP_GCD:func.3">SBP</a>,3) &amp; <font color="Maroon" title="c16">P</font> <a href="compos_1.html#K3" title="COMPOS_1:func.3">.</a> 8 <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> (<a href="scmp_gcd.html#K3" title="SCMP_GCD:func.3">SBP</a>,7) <a href="scmpds_2.html#K17" title="SCMPDS_2:func.17">:=</a> (<a href="scmp_gcd.html#K3" title="SCMP_GCD:func.3">SBP</a>,3) &amp; <font color="Maroon" title="c16">P</font> <a href="compos_1.html#K3" title="COMPOS_1:func.3">.</a> 9 <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> (<a href="scmp_gcd.html#K3" title="SCMP_GCD:func.3">SBP</a>,<span class="p1">(<span class="default">4 <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> <a href="scmpds_1.html#K22" title="SCMPDS_1:func.22">RetSP</a></span>)</span>) <a href="scmpds_2.html#K17" title="SCMPDS_2:func.17">:=</a> (<a href="scmp_gcd.html#K2" title="SCMP_GCD:func.2">GBP</a>,1) &amp; <font color="Maroon" title="c16">P</font> <a href="compos_1.html#K3" title="COMPOS_1:func.3">.</a> 10 <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="scmpds_2.html#K12" title="SCMPDS_2:func.12">AddTo</a> (<a href="scmp_gcd.html#K2" title="SCMP_GCD:func.2">GBP</a>,1,4) &amp; <font color="Maroon" title="c16">P</font> <a href="compos_1.html#K3" title="COMPOS_1:func.3">.</a> 11 <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="scmpds_2.html#K7" title="SCMPDS_2:func.7">saveIC</a> (<a href="scmp_gcd.html#K3" title="SCMP_GCD:func.3">SBP</a>,<a href="scmpds_1.html#K23" title="SCMPDS_1:func.23">RetIC</a>) &amp; <font color="Maroon" title="c16">P</font> <a href="compos_1.html#K3" title="COMPOS_1:func.3">.</a> 12 <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="scmpds_2.html#K4" title="SCMPDS_2:func.4">goto</a> <span class="p1">(<span class="default"><a href="xcmplx_0.html#K4" title="XCMPLX_0:func.4">-</a> 7</span>)</span> &amp; <font color="Maroon" title="c16">P</font> <a href="compos_1.html#K3" title="COMPOS_1:func.3">.</a> 13 <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> (<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) &amp; <font color="Maroon" title="c16">P</font> <a href="compos_1.html#K3" title="COMPOS_1:func.3">.</a> 14 <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> )</span><br/>

<a NAME="E4:12"/>
1 <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="relat_1.html#NK2" title="RELAT_1:NK.2">dom</a> <a href="scmp_gcd.html#K4" title="SCMP_GCD:func.4">GCD-Algorithm</a>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="scmp_gcd.html#T8" target="_self" title="SCMP_GCD:th.8">Th12</a>, <a class="ref" href="afinsq_1.html#T66" title="AFINSQ_1:th.66">AFINSQ_1:66</a></span>;<br/>
<span class="kw">hence </span><a NAME="E5:12"/>
<font color="Maroon" title="c16">P</font> <a href="compos_1.html#K3" title="COMPOS_1:func.3">.</a> 1 <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <a href="scmp_gcd.html#K3" title="SCMP_GCD:func.3">SBP</a> <a href="scmpds_2.html#K6" title="SCMPDS_2:func.6">:=</a> 7
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:12"><span class="lab"><font color="Green" title="E10">A1</font></span></a>, <a class="ref" href="scmp_gcd.html#T10" target="_self" title="SCMP_GCD:th.10">Th14</a>, <a class="ref" href="grfunc_1.html#T2" title="GRFUNC_1:th.2">GRFUNC_1:2</a></span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> ( <font color="Maroon" title="c16">P</font> <a href="compos_1.html#K3" title="COMPOS_1:func.3">.</a> 2 <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="scmpds_2.html#K7" title="SCMPDS_2:func.7">saveIC</a> (<a href="scmp_gcd.html#K3" title="SCMP_GCD:func.3">SBP</a>,<a href="scmpds_1.html#K23" title="SCMPDS_1:func.23">RetIC</a>) &amp; <font color="Maroon" title="c16">P</font> <a href="compos_1.html#K3" title="COMPOS_1:func.3">.</a> 3 <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="scmpds_2.html#K4" title="SCMPDS_2:func.4">goto</a> 2 &amp; <font color="Maroon" title="c16">P</font> <a href="compos_1.html#K3" title="COMPOS_1:func.3">.</a> 4 <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="compos_1.html#K2" title="COMPOS_1:func.2">halt</a> <a href="scmpds_2.html#K1" title="SCMPDS_2:func.1">SCMPDS</a> &amp; <font color="Maroon" title="c16">P</font> <a href="compos_1.html#K3" title="COMPOS_1:func.3">.</a> 5 <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 &amp; <font color="Maroon" title="c16">P</font> <a href="compos_1.html#K3" title="COMPOS_1:func.3">.</a> 6 <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> (<a href="scmp_gcd.html#K3" title="SCMP_GCD:func.3">SBP</a>,6) <a href="scmpds_2.html#K17" title="SCMPDS_2:func.17">:=</a> (<a href="scmp_gcd.html#K3" title="SCMP_GCD:func.3">SBP</a>,3) &amp; <font color="Maroon" title="c16">P</font> <a href="compos_1.html#K3" title="COMPOS_1:func.3">.</a> 7 <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="scmpds_2.html#K16" title="SCMPDS_2:func.16">Divide</a> (<a href="scmp_gcd.html#K3" title="SCMP_GCD:func.3">SBP</a>,2,<a href="scmp_gcd.html#K3" title="SCMP_GCD:func.3">SBP</a>,3) &amp; <font color="Maroon" title="c16">P</font> <a href="compos_1.html#K3" title="COMPOS_1:func.3">.</a> 8 <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> (<a href="scmp_gcd.html#K3" title="SCMP_GCD:func.3">SBP</a>,7) <a href="scmpds_2.html#K17" title="SCMPDS_2:func.17">:=</a> (<a href="scmp_gcd.html#K3" title="SCMP_GCD:func.3">SBP</a>,3) &amp; <font color="Maroon" title="c16">P</font> <a href="compos_1.html#K3" title="COMPOS_1:func.3">.</a> 9 <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> (<a href="scmp_gcd.html#K3" title="SCMP_GCD:func.3">SBP</a>,<span class="p1">(<span class="default">4 <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> <a href="scmpds_1.html#K22" title="SCMPDS_1:func.22">RetSP</a></span>)</span>) <a href="scmpds_2.html#K17" title="SCMPDS_2:func.17">:=</a> (<a href="scmp_gcd.html#K2" title="SCMP_GCD:func.2">GBP</a>,1) &amp; <font color="Maroon" title="c16">P</font> <a href="compos_1.html#K3" title="COMPOS_1:func.3">.</a> 10 <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="scmpds_2.html#K12" title="SCMPDS_2:func.12">AddTo</a> (<a href="scmp_gcd.html#K2" title="SCMP_GCD:func.2">GBP</a>,1,4) &amp; <font color="Maroon" title="c16">P</font> <a href="compos_1.html#K3" title="COMPOS_1:func.3">.</a> 11 <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="scmpds_2.html#K7" title="SCMPDS_2:func.7">saveIC</a> (<a href="scmp_gcd.html#K3" title="SCMP_GCD:func.3">SBP</a>,<a href="scmpds_1.html#K23" title="SCMPDS_1:func.23">RetIC</a>) &amp; <font color="Maroon" title="c16">P</font> <a href="compos_1.html#K3" title="COMPOS_1:func.3">.</a> 12 <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="scmpds_2.html#K4" title="SCMPDS_2:func.4">goto</a> <span class="p1">(<span class="default"><a href="xcmplx_0.html#K4" title="XCMPLX_0:func.4">-</a> 7</span>)</span> &amp; <font color="Maroon" title="c16">P</font> <a href="compos_1.html#K3" title="COMPOS_1:func.3">.</a> 13 <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> (<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) &amp; <font color="Maroon" title="c16">P</font> <a href="compos_1.html#K3" title="COMPOS_1:func.3">.</a> 14 <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> )</span><br/>

<a NAME="E6:12"/>
2 <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="relat_1.html#NK2" title="RELAT_1:NK.2">dom</a> <a href="scmp_gcd.html#K4" title="SCMP_GCD:func.4">GCD-Algorithm</a>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="scmp_gcd.html#T8" target="_self" title="SCMP_GCD:th.8">Th12</a>, <a class="ref" href="afinsq_1.html#T66" title="AFINSQ_1:th.66">AFINSQ_1:66</a></span>;<br/>
<span class="kw">hence </span><a NAME="E7:12"/>
<font color="Maroon" title="c16">P</font> <a href="compos_1.html#K3" title="COMPOS_1:func.3">.</a> 2 <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="scmpds_2.html#K7" title="SCMPDS_2:func.7">saveIC</a> (<a href="scmp_gcd.html#K3" title="SCMP_GCD:func.3">SBP</a>,<a href="scmpds_1.html#K23" title="SCMPDS_1:func.23">RetIC</a>)
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:12"><span class="lab"><font color="Green" title="E10">A1</font></span></a>, <a class="ref" href="scmp_gcd.html#T10" target="_self" title="SCMP_GCD:th.10">Th14</a>, <a class="ref" href="grfunc_1.html#T2" title="GRFUNC_1:th.2">GRFUNC_1:2</a></span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> ( <font color="Maroon" title="c16">P</font> <a href="compos_1.html#K3" title="COMPOS_1:func.3">.</a> 3 <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="scmpds_2.html#K4" title="SCMPDS_2:func.4">goto</a> 2 &amp; <font color="Maroon" title="c16">P</font> <a href="compos_1.html#K3" title="COMPOS_1:func.3">.</a> 4 <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="compos_1.html#K2" title="COMPOS_1:func.2">halt</a> <a href="scmpds_2.html#K1" title="SCMPDS_2:func.1">SCMPDS</a> &amp; <font color="Maroon" title="c16">P</font> <a href="compos_1.html#K3" title="COMPOS_1:func.3">.</a> 5 <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 &amp; <font color="Maroon" title="c16">P</font> <a href="compos_1.html#K3" title="COMPOS_1:func.3">.</a> 6 <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> (<a href="scmp_gcd.html#K3" title="SCMP_GCD:func.3">SBP</a>,6) <a href="scmpds_2.html#K17" title="SCMPDS_2:func.17">:=</a> (<a href="scmp_gcd.html#K3" title="SCMP_GCD:func.3">SBP</a>,3) &amp; <font color="Maroon" title="c16">P</font> <a href="compos_1.html#K3" title="COMPOS_1:func.3">.</a> 7 <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="scmpds_2.html#K16" title="SCMPDS_2:func.16">Divide</a> (<a href="scmp_gcd.html#K3" title="SCMP_GCD:func.3">SBP</a>,2,<a href="scmp_gcd.html#K3" title="SCMP_GCD:func.3">SBP</a>,3) &amp; <font color="Maroon" title="c16">P</font> <a href="compos_1.html#K3" title="COMPOS_1:func.3">.</a> 8 <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> (<a href="scmp_gcd.html#K3" title="SCMP_GCD:func.3">SBP</a>,7) <a href="scmpds_2.html#K17" title="SCMPDS_2:func.17">:=</a> (<a href="scmp_gcd.html#K3" title="SCMP_GCD:func.3">SBP</a>,3) &amp; <font color="Maroon" title="c16">P</font> <a href="compos_1.html#K3" title="COMPOS_1:func.3">.</a> 9 <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> (<a href="scmp_gcd.html#K3" title="SCMP_GCD:func.3">SBP</a>,<span class="p1">(<span class="default">4 <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> <a href="scmpds_1.html#K22" title="SCMPDS_1:func.22">RetSP</a></span>)</span>) <a href="scmpds_2.html#K17" title="SCMPDS_2:func.17">:=</a> (<a href="scmp_gcd.html#K2" title="SCMP_GCD:func.2">GBP</a>,1) &amp; <font color="Maroon" title="c16">P</font> <a href="compos_1.html#K3" title="COMPOS_1:func.3">.</a> 10 <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="scmpds_2.html#K12" title="SCMPDS_2:func.12">AddTo</a> (<a href="scmp_gcd.html#K2" title="SCMP_GCD:func.2">GBP</a>,1,4) &amp; <font color="Maroon" title="c16">P</font> <a href="compos_1.html#K3" title="COMPOS_1:func.3">.</a> 11 <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="scmpds_2.html#K7" title="SCMPDS_2:func.7">saveIC</a> (<a href="scmp_gcd.html#K3" title="SCMP_GCD:func.3">SBP</a>,<a href="scmpds_1.html#K23" title="SCMPDS_1:func.23">RetIC</a>) &amp; <font color="Maroon" title="c16">P</font> <a href="compos_1.html#K3" title="COMPOS_1:func.3">.</a> 12 <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="scmpds_2.html#K4" title="SCMPDS_2:func.4">goto</a> <span class="p1">(<span class="default"><a href="xcmplx_0.html#K4" title="XCMPLX_0:func.4">-</a> 7</span>)</span> &amp; <font color="Maroon" title="c16">P</font> <a href="compos_1.html#K3" title="COMPOS_1:func.3">.</a> 13 <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> (<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) &amp; <font color="Maroon" title="c16">P</font> <a href="compos_1.html#K3" title="COMPOS_1:func.3">.</a> 14 <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> )</span><br/>

<a NAME="E8:12"/>
3 <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="relat_1.html#NK2" title="RELAT_1:NK.2">dom</a> <a href="scmp_gcd.html#K4" title="SCMP_GCD:func.4">GCD-Algorithm</a>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="scmp_gcd.html#T8" target="_self" title="SCMP_GCD:th.8">Th12</a>, <a class="ref" href="afinsq_1.html#T66" title="AFINSQ_1:th.66">AFINSQ_1:66</a></span>;<br/>
<span class="kw">hence </span><a NAME="E9:12"/>
<font color="Maroon" title="c16">P</font> <a href="compos_1.html#K3" title="COMPOS_1:func.3">.</a> 3 <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="scmpds_2.html#K4" title="SCMPDS_2:func.4">goto</a> 2
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:12"><span class="lab"><font color="Green" title="E10">A1</font></span></a>, <a class="ref" href="scmp_gcd.html#T10" target="_self" title="SCMP_GCD:th.10">Th14</a>, <a class="ref" href="grfunc_1.html#T2" title="GRFUNC_1:th.2">GRFUNC_1:2</a></span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> ( <font color="Maroon" title="c16">P</font> <a href="compos_1.html#K3" title="COMPOS_1:func.3">.</a> 4 <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="compos_1.html#K2" title="COMPOS_1:func.2">halt</a> <a href="scmpds_2.html#K1" title="SCMPDS_2:func.1">SCMPDS</a> &amp; <font color="Maroon" title="c16">P</font> <a href="compos_1.html#K3" title="COMPOS_1:func.3">.</a> 5 <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 &amp; <font color="Maroon" title="c16">P</font> <a href="compos_1.html#K3" title="COMPOS_1:func.3">.</a> 6 <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> (<a href="scmp_gcd.html#K3" title="SCMP_GCD:func.3">SBP</a>,6) <a href="scmpds_2.html#K17" title="SCMPDS_2:func.17">:=</a> (<a href="scmp_gcd.html#K3" title="SCMP_GCD:func.3">SBP</a>,3) &amp; <font color="Maroon" title="c16">P</font> <a href="compos_1.html#K3" title="COMPOS_1:func.3">.</a> 7 <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="scmpds_2.html#K16" title="SCMPDS_2:func.16">Divide</a> (<a href="scmp_gcd.html#K3" title="SCMP_GCD:func.3">SBP</a>,2,<a href="scmp_gcd.html#K3" title="SCMP_GCD:func.3">SBP</a>,3) &amp; <font color="Maroon" title="c16">P</font> <a href="compos_1.html#K3" title="COMPOS_1:func.3">.</a> 8 <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> (<a href="scmp_gcd.html#K3" title="SCMP_GCD:func.3">SBP</a>,7) <a href="scmpds_2.html#K17" title="SCMPDS_2:func.17">:=</a> (<a href="scmp_gcd.html#K3" title="SCMP_GCD:func.3">SBP</a>,3) &amp; <font color="Maroon" title="c16">P</font> <a href="compos_1.html#K3" title="COMPOS_1:func.3">.</a> 9 <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> (<a href="scmp_gcd.html#K3" title="SCMP_GCD:func.3">SBP</a>,<span class="p1">(<span class="default">4 <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> <a href="scmpds_1.html#K22" title="SCMPDS_1:func.22">RetSP</a></span>)</span>) <a href="scmpds_2.html#K17" title="SCMPDS_2:func.17">:=</a> (<a href="scmp_gcd.html#K2" title="SCMP_GCD:func.2">GBP</a>,1) &amp; <font color="Maroon" title="c16">P</font> <a href="compos_1.html#K3" title="COMPOS_1:func.3">.</a> 10 <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="scmpds_2.html#K12" title="SCMPDS_2:func.12">AddTo</a> (<a href="scmp_gcd.html#K2" title="SCMP_GCD:func.2">GBP</a>,1,4) &amp; <font color="Maroon" title="c16">P</font> <a href="compos_1.html#K3" title="COMPOS_1:func.3">.</a> 11 <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="scmpds_2.html#K7" title="SCMPDS_2:func.7">saveIC</a> (<a href="scmp_gcd.html#K3" title="SCMP_GCD:func.3">SBP</a>,<a href="scmpds_1.html#K23" title="SCMPDS_1:func.23">RetIC</a>) &amp; <font color="Maroon" title="c16">P</font> <a href="compos_1.html#K3" title="COMPOS_1:func.3">.</a> 12 <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="scmpds_2.html#K4" title="SCMPDS_2:func.4">goto</a> <span class="p1">(<span class="default"><a href="xcmplx_0.html#K4" title="XCMPLX_0:func.4">-</a> 7</span>)</span> &amp; <font color="Maroon" title="c16">P</font> <a href="compos_1.html#K3" title="COMPOS_1:func.3">.</a> 13 <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> (<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) &amp; <font color="Maroon" title="c16">P</font> <a href="compos_1.html#K3" title="COMPOS_1:func.3">.</a> 14 <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> )</span><br/>

<a NAME="E10:12"/>
4 <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="relat_1.html#NK2" title="RELAT_1:NK.2">dom</a> <a href="scmp_gcd.html#K4" title="SCMP_GCD:func.4">GCD-Algorithm</a>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="scmp_gcd.html#T8" target="_self" title="SCMP_GCD:th.8">Th12</a>, <a class="ref" href="afinsq_1.html#T66" title="AFINSQ_1:th.66">AFINSQ_1:66</a></span>;<br/>
<span class="kw">hence </span><a NAME="E11:12"/>
<font color="Maroon" title="c16">P</font> <a href="compos_1.html#K3" title="COMPOS_1:func.3">.</a> 4 <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="compos_1.html#K2" title="COMPOS_1:func.2">halt</a> <a href="scmpds_2.html#K1" title="SCMPDS_2:func.1">SCMPDS</a>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:12"><span class="lab"><font color="Green" title="E10">A1</font></span></a>, <a class="ref" href="scmp_gcd.html#T10" target="_self" title="SCMP_GCD:th.10">Th14</a>, <a class="ref" href="grfunc_1.html#T2" title="GRFUNC_1:th.2">GRFUNC_1:2</a></span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> ( <font color="Maroon" title="c16">P</font> <a href="compos_1.html#K3" title="COMPOS_1:func.3">.</a> 5 <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 &amp; <font color="Maroon" title="c16">P</font> <a href="compos_1.html#K3" title="COMPOS_1:func.3">.</a> 6 <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> (<a href="scmp_gcd.html#K3" title="SCMP_GCD:func.3">SBP</a>,6) <a href="scmpds_2.html#K17" title="SCMPDS_2:func.17">:=</a> (<a href="scmp_gcd.html#K3" title="SCMP_GCD:func.3">SBP</a>,3) &amp; <font color="Maroon" title="c16">P</font> <a href="compos_1.html#K3" title="COMPOS_1:func.3">.</a> 7 <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="scmpds_2.html#K16" title="SCMPDS_2:func.16">Divide</a> (<a href="scmp_gcd.html#K3" title="SCMP_GCD:func.3">SBP</a>,2,<a href="scmp_gcd.html#K3" title="SCMP_GCD:func.3">SBP</a>,3) &amp; <font color="Maroon" title="c16">P</font> <a href="compos_1.html#K3" title="COMPOS_1:func.3">.</a> 8 <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> (<a href="scmp_gcd.html#K3" title="SCMP_GCD:func.3">SBP</a>,7) <a href="scmpds_2.html#K17" title="SCMPDS_2:func.17">:=</a> (<a href="scmp_gcd.html#K3" title="SCMP_GCD:func.3">SBP</a>,3) &amp; <font color="Maroon" title="c16">P</font> <a href="compos_1.html#K3" title="COMPOS_1:func.3">.</a> 9 <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> (<a href="scmp_gcd.html#K3" title="SCMP_GCD:func.3">SBP</a>,<span class="p1">(<span class="default">4 <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> <a href="scmpds_1.html#K22" title="SCMPDS_1:func.22">RetSP</a></span>)</span>) <a href="scmpds_2.html#K17" title="SCMPDS_2:func.17">:=</a> (<a href="scmp_gcd.html#K2" title="SCMP_GCD:func.2">GBP</a>,1) &amp; <font color="Maroon" title="c16">P</font> <a href="compos_1.html#K3" title="COMPOS_1:func.3">.</a> 10 <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="scmpds_2.html#K12" title="SCMPDS_2:func.12">AddTo</a> (<a href="scmp_gcd.html#K2" title="SCMP_GCD:func.2">GBP</a>,1,4) &amp; <font color="Maroon" title="c16">P</font> <a href="compos_1.html#K3" title="COMPOS_1:func.3">.</a> 11 <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="scmpds_2.html#K7" title="SCMPDS_2:func.7">saveIC</a> (<a href="scmp_gcd.html#K3" title="SCMP_GCD:func.3">SBP</a>,<a href="scmpds_1.html#K23" title="SCMPDS_1:func.23">RetIC</a>) &amp; <font color="Maroon" title="c16">P</font> <a href="compos_1.html#K3" title="COMPOS_1:func.3">.</a> 12 <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="scmpds_2.html#K4" title="SCMPDS_2:func.4">goto</a> <span class="p1">(<span class="default"><a href="xcmplx_0.html#K4" title="XCMPLX_0:func.4">-</a> 7</span>)</span> &amp; <font color="Maroon" title="c16">P</font> <a href="compos_1.html#K3" title="COMPOS_1:func.3">.</a> 13 <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> (<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) &amp; <font color="Maroon" title="c16">P</font> <a href="compos_1.html#K3" title="COMPOS_1:func.3">.</a> 14 <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> )</span><br/>

<a NAME="E12:12"/>
5 <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="relat_1.html#NK2" title="RELAT_1:NK.2">dom</a> <a href="scmp_gcd.html#K4" title="SCMP_GCD:func.4">GCD-Algorithm</a>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="scmp_gcd.html#T8" target="_self" title="SCMP_GCD:th.8">Th12</a>, <a class="ref" href="afinsq_1.html#T66" title="AFINSQ_1:th.66">AFINSQ_1:66</a></span>;<br/>
<span class="kw">hence </span><a NAME="E13:12"/>
<font color="Maroon" title="c16">P</font> <a href="compos_1.html#K3" title="COMPOS_1:func.3">.</a> 5 <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
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:12"><span class="lab"><font color="Green" title="E10">A1</font></span></a>, <a class="ref" href="scmp_gcd.html#T10" target="_self" title="SCMP_GCD:th.10">Th14</a>, <a class="ref" href="grfunc_1.html#T2" title="GRFUNC_1:th.2">GRFUNC_1:2</a></span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> ( <font color="Maroon" title="c16">P</font> <a href="compos_1.html#K3" title="COMPOS_1:func.3">.</a> 6 <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> (<a href="scmp_gcd.html#K3" title="SCMP_GCD:func.3">SBP</a>,6) <a href="scmpds_2.html#K17" title="SCMPDS_2:func.17">:=</a> (<a href="scmp_gcd.html#K3" title="SCMP_GCD:func.3">SBP</a>,3) &amp; <font color="Maroon" title="c16">P</font> <a href="compos_1.html#K3" title="COMPOS_1:func.3">.</a> 7 <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="scmpds_2.html#K16" title="SCMPDS_2:func.16">Divide</a> (<a href="scmp_gcd.html#K3" title="SCMP_GCD:func.3">SBP</a>,2,<a href="scmp_gcd.html#K3" title="SCMP_GCD:func.3">SBP</a>,3) &amp; <font color="Maroon" title="c16">P</font> <a href="compos_1.html#K3" title="COMPOS_1:func.3">.</a> 8 <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> (<a href="scmp_gcd.html#K3" title="SCMP_GCD:func.3">SBP</a>,7) <a href="scmpds_2.html#K17" title="SCMPDS_2:func.17">:=</a> (<a href="scmp_gcd.html#K3" title="SCMP_GCD:func.3">SBP</a>,3) &amp; <font color="Maroon" title="c16">P</font> <a href="compos_1.html#K3" title="COMPOS_1:func.3">.</a> 9 <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> (<a href="scmp_gcd.html#K3" title="SCMP_GCD:func.3">SBP</a>,<span class="p1">(<span class="default">4 <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> <a href="scmpds_1.html#K22" title="SCMPDS_1:func.22">RetSP</a></span>)</span>) <a href="scmpds_2.html#K17" title="SCMPDS_2:func.17">:=</a> (<a href="scmp_gcd.html#K2" title="SCMP_GCD:func.2">GBP</a>,1) &amp; <font color="Maroon" title="c16">P</font> <a href="compos_1.html#K3" title="COMPOS_1:func.3">.</a> 10 <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="scmpds_2.html#K12" title="SCMPDS_2:func.12">AddTo</a> (<a href="scmp_gcd.html#K2" title="SCMP_GCD:func.2">GBP</a>,1,4) &amp; <font color="Maroon" title="c16">P</font> <a href="compos_1.html#K3" title="COMPOS_1:func.3">.</a> 11 <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="scmpds_2.html#K7" title="SCMPDS_2:func.7">saveIC</a> (<a href="scmp_gcd.html#K3" title="SCMP_GCD:func.3">SBP</a>,<a href="scmpds_1.html#K23" title="SCMPDS_1:func.23">RetIC</a>) &amp; <font color="Maroon" title="c16">P</font> <a href="compos_1.html#K3" title="COMPOS_1:func.3">.</a> 12 <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="scmpds_2.html#K4" title="SCMPDS_2:func.4">goto</a> <span class="p1">(<span class="default"><a href="xcmplx_0.html#K4" title="XCMPLX_0:func.4">-</a> 7</span>)</span> &amp; <font color="Maroon" title="c16">P</font> <a href="compos_1.html#K3" title="COMPOS_1:func.3">.</a> 13 <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> (<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) &amp; <font color="Maroon" title="c16">P</font> <a href="compos_1.html#K3" title="COMPOS_1:func.3">.</a> 14 <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> )</span><br/>

<a NAME="E14:12"/>
6 <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="relat_1.html#NK2" title="RELAT_1:NK.2">dom</a> <a href="scmp_gcd.html#K4" title="SCMP_GCD:func.4">GCD-Algorithm</a>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="scmp_gcd.html#T8" target="_self" title="SCMP_GCD:th.8">Th12</a>, <a class="ref" href="afinsq_1.html#T66" title="AFINSQ_1:th.66">AFINSQ_1:66</a></span>;<br/>
<span class="kw">hence </span><a NAME="E15:12"/>
<font color="Maroon" title="c16">P</font> <a href="compos_1.html#K3" title="COMPOS_1:func.3">.</a> 6 <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> (<a href="scmp_gcd.html#K3" title="SCMP_GCD:func.3">SBP</a>,6) <a href="scmpds_2.html#K17" title="SCMPDS_2:func.17">:=</a> (<a href="scmp_gcd.html#K3" title="SCMP_GCD:func.3">SBP</a>,3)
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:12"><span class="lab"><font color="Green" title="E10">A1</font></span></a>, <a class="ref" href="scmp_gcd.html#T10" target="_self" title="SCMP_GCD:th.10">Th14</a>, <a class="ref" href="grfunc_1.html#T2" title="GRFUNC_1:th.2">GRFUNC_1:2</a></span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> ( <font color="Maroon" title="c16">P</font> <a href="compos_1.html#K3" title="COMPOS_1:func.3">.</a> 7 <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="scmpds_2.html#K16" title="SCMPDS_2:func.16">Divide</a> (<a href="scmp_gcd.html#K3" title="SCMP_GCD:func.3">SBP</a>,2,<a href="scmp_gcd.html#K3" title="SCMP_GCD:func.3">SBP</a>,3) &amp; <font color="Maroon" title="c16">P</font> <a href="compos_1.html#K3" title="COMPOS_1:func.3">.</a> 8 <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> (<a href="scmp_gcd.html#K3" title="SCMP_GCD:func.3">SBP</a>,7) <a href="scmpds_2.html#K17" title="SCMPDS_2:func.17">:=</a> (<a href="scmp_gcd.html#K3" title="SCMP_GCD:func.3">SBP</a>,3) &amp; <font color="Maroon" title="c16">P</font> <a href="compos_1.html#K3" title="COMPOS_1:func.3">.</a> 9 <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> (<a href="scmp_gcd.html#K3" title="SCMP_GCD:func.3">SBP</a>,<span class="p1">(<span class="default">4 <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> <a href="scmpds_1.html#K22" title="SCMPDS_1:func.22">RetSP</a></span>)</span>) <a href="scmpds_2.html#K17" title="SCMPDS_2:func.17">:=</a> (<a href="scmp_gcd.html#K2" title="SCMP_GCD:func.2">GBP</a>,1) &amp; <font color="Maroon" title="c16">P</font> <a href="compos_1.html#K3" title="COMPOS_1:func.3">.</a> 10 <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="scmpds_2.html#K12" title="SCMPDS_2:func.12">AddTo</a> (<a href="scmp_gcd.html#K2" title="SCMP_GCD:func.2">GBP</a>,1,4) &amp; <font color="Maroon" title="c16">P</font> <a href="compos_1.html#K3" title="COMPOS_1:func.3">.</a> 11 <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="scmpds_2.html#K7" title="SCMPDS_2:func.7">saveIC</a> (<a href="scmp_gcd.html#K3" title="SCMP_GCD:func.3">SBP</a>,<a href="scmpds_1.html#K23" title="SCMPDS_1:func.23">RetIC</a>) &amp; <font color="Maroon" title="c16">P</font> <a href="compos_1.html#K3" title="COMPOS_1:func.3">.</a> 12 <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="scmpds_2.html#K4" title="SCMPDS_2:func.4">goto</a> <span class="p1">(<span class="default"><a href="xcmplx_0.html#K4" title="XCMPLX_0:func.4">-</a> 7</span>)</span> &amp; <font color="Maroon" title="c16">P</font> <a href="compos_1.html#K3" title="COMPOS_1:func.3">.</a> 13 <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> (<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) &amp; <font color="Maroon" title="c16">P</font> <a href="compos_1.html#K3" title="COMPOS_1:func.3">.</a> 14 <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> )</span><br/>

<a NAME="E16:12"/>
7 <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="relat_1.html#NK2" title="RELAT_1:NK.2">dom</a> <a href="scmp_gcd.html#K4" title="SCMP_GCD:func.4">GCD-Algorithm</a>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="scmp_gcd.html#T8" target="_self" title="SCMP_GCD:th.8">Th12</a>, <a class="ref" href="afinsq_1.html#T66" title="AFINSQ_1:th.66">AFINSQ_1:66</a></span>;<br/>
<span class="kw">hence </span><a NAME="E17:12"/>
<font color="Maroon" title="c16">P</font> <a href="compos_1.html#K3" title="COMPOS_1:func.3">.</a> 7 <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="scmpds_2.html#K16" title="SCMPDS_2:func.16">Divide</a> (<a href="scmp_gcd.html#K3" title="SCMP_GCD:func.3">SBP</a>,2,<a href="scmp_gcd.html#K3" title="SCMP_GCD:func.3">SBP</a>,3)
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:12"><span class="lab"><font color="Green" title="E10">A1</font></span></a>, <a class="ref" href="scmp_gcd.html#T10" target="_self" title="SCMP_GCD:th.10">Th14</a>, <a class="ref" href="grfunc_1.html#T2" title="GRFUNC_1:th.2">GRFUNC_1:2</a></span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> ( <font color="Maroon" title="c16">P</font> <a href="compos_1.html#K3" title="COMPOS_1:func.3">.</a> 8 <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> (<a href="scmp_gcd.html#K3" title="SCMP_GCD:func.3">SBP</a>,7) <a href="scmpds_2.html#K17" title="SCMPDS_2:func.17">:=</a> (<a href="scmp_gcd.html#K3" title="SCMP_GCD:func.3">SBP</a>,3) &amp; <font color="Maroon" title="c16">P</font> <a href="compos_1.html#K3" title="COMPOS_1:func.3">.</a> 9 <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> (<a href="scmp_gcd.html#K3" title="SCMP_GCD:func.3">SBP</a>,<span class="p1">(<span class="default">4 <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> <a href="scmpds_1.html#K22" title="SCMPDS_1:func.22">RetSP</a></span>)</span>) <a href="scmpds_2.html#K17" title="SCMPDS_2:func.17">:=</a> (<a href="scmp_gcd.html#K2" title="SCMP_GCD:func.2">GBP</a>,1) &amp; <font color="Maroon" title="c16">P</font> <a href="compos_1.html#K3" title="COMPOS_1:func.3">.</a> 10 <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="scmpds_2.html#K12" title="SCMPDS_2:func.12">AddTo</a> (<a href="scmp_gcd.html#K2" title="SCMP_GCD:func.2">GBP</a>,1,4) &amp; <font color="Maroon" title="c16">P</font> <a href="compos_1.html#K3" title="COMPOS_1:func.3">.</a> 11 <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="scmpds_2.html#K7" title="SCMPDS_2:func.7">saveIC</a> (<a href="scmp_gcd.html#K3" title="SCMP_GCD:func.3">SBP</a>,<a href="scmpds_1.html#K23" title="SCMPDS_1:func.23">RetIC</a>) &amp; <font color="Maroon" title="c16">P</font> <a href="compos_1.html#K3" title="COMPOS_1:func.3">.</a> 12 <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="scmpds_2.html#K4" title="SCMPDS_2:func.4">goto</a> <span class="p1">(<span class="default"><a href="xcmplx_0.html#K4" title="XCMPLX_0:func.4">-</a> 7</span>)</span> &amp; <font color="Maroon" title="c16">P</font> <a href="compos_1.html#K3" title="COMPOS_1:func.3">.</a> 13 <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> (<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) &amp; <font color="Maroon" title="c16">P</font> <a href="compos_1.html#K3" title="COMPOS_1:func.3">.</a> 14 <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> )</span><br/>

<a NAME="E18:12"/>
8 <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="relat_1.html#NK2" title="RELAT_1:NK.2">dom</a> <a href="scmp_gcd.html#K4" title="SCMP_GCD:func.4">GCD-Algorithm</a>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="scmp_gcd.html#T8" target="_self" title="SCMP_GCD:th.8">Th12</a>, <a class="ref" href="afinsq_1.html#T66" title="AFINSQ_1:th.66">AFINSQ_1:66</a></span>;<br/>
<span class="kw">hence </span><a NAME="E19:12"/>
<font color="Maroon" title="c16">P</font> <a href="compos_1.html#K3" title="COMPOS_1:func.3">.</a> 8 <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> (<a href="scmp_gcd.html#K3" title="SCMP_GCD:func.3">SBP</a>,7) <a href="scmpds_2.html#K17" title="SCMPDS_2:func.17">:=</a> (<a href="scmp_gcd.html#K3" title="SCMP_GCD:func.3">SBP</a>,3)
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:12"><span class="lab"><font color="Green" title="E10">A1</font></span></a>, <a class="ref" href="scmp_gcd.html#T10" target="_self" title="SCMP_GCD:th.10">Th14</a>, <a class="ref" href="grfunc_1.html#T2" title="GRFUNC_1:th.2">GRFUNC_1:2</a></span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> ( <font color="Maroon" title="c16">P</font> <a href="compos_1.html#K3" title="COMPOS_1:func.3">.</a> 9 <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> (<a href="scmp_gcd.html#K3" title="SCMP_GCD:func.3">SBP</a>,<span class="p1">(<span class="default">4 <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> <a href="scmpds_1.html#K22" title="SCMPDS_1:func.22">RetSP</a></span>)</span>) <a href="scmpds_2.html#K17" title="SCMPDS_2:func.17">:=</a> (<a href="scmp_gcd.html#K2" title="SCMP_GCD:func.2">GBP</a>,1) &amp; <font color="Maroon" title="c16">P</font> <a href="compos_1.html#K3" title="COMPOS_1:func.3">.</a> 10 <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="scmpds_2.html#K12" title="SCMPDS_2:func.12">AddTo</a> (<a href="scmp_gcd.html#K2" title="SCMP_GCD:func.2">GBP</a>,1,4) &amp; <font color="Maroon" title="c16">P</font> <a href="compos_1.html#K3" title="COMPOS_1:func.3">.</a> 11 <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="scmpds_2.html#K7" title="SCMPDS_2:func.7">saveIC</a> (<a href="scmp_gcd.html#K3" title="SCMP_GCD:func.3">SBP</a>,<a href="scmpds_1.html#K23" title="SCMPDS_1:func.23">RetIC</a>) &amp; <font color="Maroon" title="c16">P</font> <a href="compos_1.html#K3" title="COMPOS_1:func.3">.</a> 12 <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="scmpds_2.html#K4" title="SCMPDS_2:func.4">goto</a> <span class="p1">(<span class="default"><a href="xcmplx_0.html#K4" title="XCMPLX_0:func.4">-</a> 7</span>)</span> &amp; <font color="Maroon" title="c16">P</font> <a href="compos_1.html#K3" title="COMPOS_1:func.3">.</a> 13 <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> (<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) &amp; <font color="Maroon" title="c16">P</font> <a href="compos_1.html#K3" title="COMPOS_1:func.3">.</a> 14 <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> )</span><br/>

<a NAME="E20:12"/>
9 <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="relat_1.html#NK2" title="RELAT_1:NK.2">dom</a> <a href="scmp_gcd.html#K4" title="SCMP_GCD:func.4">GCD-Algorithm</a>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="scmp_gcd.html#T8" target="_self" title="SCMP_GCD:th.8">Th12</a>, <a class="ref" href="afinsq_1.html#T66" title="AFINSQ_1:th.66">AFINSQ_1:66</a></span>;<br/>
<span class="kw">hence </span><a NAME="E21:12"/>
<font color="Maroon" title="c16">P</font> <a href="compos_1.html#K3" title="COMPOS_1:func.3">.</a> 9 <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> (<a href="scmp_gcd.html#K3" title="SCMP_GCD:func.3">SBP</a>,<span class="p1">(<span class="default">4 <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> <a href="scmpds_1.html#K22" title="SCMPDS_1:func.22">RetSP</a></span>)</span>) <a href="scmpds_2.html#K17" title="SCMPDS_2:func.17">:=</a> (<a href="scmp_gcd.html#K2" title="SCMP_GCD:func.2">GBP</a>,1)
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:12"><span class="lab"><font color="Green" title="E10">A1</font></span></a>, <a class="ref" href="scmp_gcd.html#T10" target="_self" title="SCMP_GCD:th.10">Th14</a>, <a class="ref" href="grfunc_1.html#T2" title="GRFUNC_1:th.2">GRFUNC_1:2</a></span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> ( <font color="Maroon" title="c16">P</font> <a href="compos_1.html#K3" title="COMPOS_1:func.3">.</a> 10 <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="scmpds_2.html#K12" title="SCMPDS_2:func.12">AddTo</a> (<a href="scmp_gcd.html#K2" title="SCMP_GCD:func.2">GBP</a>,1,4) &amp; <font color="Maroon" title="c16">P</font> <a href="compos_1.html#K3" title="COMPOS_1:func.3">.</a> 11 <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="scmpds_2.html#K7" title="SCMPDS_2:func.7">saveIC</a> (<a href="scmp_gcd.html#K3" title="SCMP_GCD:func.3">SBP</a>,<a href="scmpds_1.html#K23" title="SCMPDS_1:func.23">RetIC</a>) &amp; <font color="Maroon" title="c16">P</font> <a href="compos_1.html#K3" title="COMPOS_1:func.3">.</a> 12 <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="scmpds_2.html#K4" title="SCMPDS_2:func.4">goto</a> <span class="p1">(<span class="default"><a href="xcmplx_0.html#K4" title="XCMPLX_0:func.4">-</a> 7</span>)</span> &amp; <font color="Maroon" title="c16">P</font> <a href="compos_1.html#K3" title="COMPOS_1:func.3">.</a> 13 <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> (<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) &amp; <font color="Maroon" title="c16">P</font> <a href="compos_1.html#K3" title="COMPOS_1:func.3">.</a> 14 <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> )</span><br/>

<a NAME="E22:12"/>
10 <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="relat_1.html#NK2" title="RELAT_1:NK.2">dom</a> <a href="scmp_gcd.html#K4" title="SCMP_GCD:func.4">GCD-Algorithm</a>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="scmp_gcd.html#T8" target="_self" title="SCMP_GCD:th.8">Th12</a>, <a class="ref" href="afinsq_1.html#T66" title="AFINSQ_1:th.66">AFINSQ_1:66</a></span>;<br/>
<span class="kw">hence </span><a NAME="E23:12"/>
<font color="Maroon" title="c16">P</font> <a href="compos_1.html#K3" title="COMPOS_1:func.3">.</a> 10 <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="scmpds_2.html#K12" title="SCMPDS_2:func.12">AddTo</a> (<a href="scmp_gcd.html#K2" title="SCMP_GCD:func.2">GBP</a>,1,4)
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:12"><span class="lab"><font color="Green" title="E10">A1</font></span></a>, <a class="ref" href="scmp_gcd.html#T10" target="_self" title="SCMP_GCD:th.10">Th14</a>, <a class="ref" href="grfunc_1.html#T2" title="GRFUNC_1:th.2">GRFUNC_1:2</a></span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> ( <font color="Maroon" title="c16">P</font> <a href="compos_1.html#K3" title="COMPOS_1:func.3">.</a> 11 <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="scmpds_2.html#K7" title="SCMPDS_2:func.7">saveIC</a> (<a href="scmp_gcd.html#K3" title="SCMP_GCD:func.3">SBP</a>,<a href="scmpds_1.html#K23" title="SCMPDS_1:func.23">RetIC</a>) &amp; <font color="Maroon" title="c16">P</font> <a href="compos_1.html#K3" title="COMPOS_1:func.3">.</a> 12 <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="scmpds_2.html#K4" title="SCMPDS_2:func.4">goto</a> <span class="p1">(<span class="default"><a href="xcmplx_0.html#K4" title="XCMPLX_0:func.4">-</a> 7</span>)</span> &amp; <font color="Maroon" title="c16">P</font> <a href="compos_1.html#K3" title="COMPOS_1:func.3">.</a> 13 <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> (<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) &amp; <font color="Maroon" title="c16">P</font> <a href="compos_1.html#K3" title="COMPOS_1:func.3">.</a> 14 <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> )</span><br/>

<a NAME="E24:12"/>
11 <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="relat_1.html#NK2" title="RELAT_1:NK.2">dom</a> <a href="scmp_gcd.html#K4" title="SCMP_GCD:func.4">GCD-Algorithm</a>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="scmp_gcd.html#T8" target="_self" title="SCMP_GCD:th.8">Th12</a>, <a class="ref" href="afinsq_1.html#T66" title="AFINSQ_1:th.66">AFINSQ_1:66</a></span>;<br/>
<span class="kw">hence </span><a NAME="E25:12"/>
<font color="Maroon" title="c16">P</font> <a href="compos_1.html#K3" title="COMPOS_1:func.3">.</a> 11 <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="scmpds_2.html#K7" title="SCMPDS_2:func.7">saveIC</a> (<a href="scmp_gcd.html#K3" title="SCMP_GCD:func.3">SBP</a>,<a href="scmpds_1.html#K23" title="SCMPDS_1:func.23">RetIC</a>)
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:12"><span class="lab"><font color="Green" title="E10">A1</font></span></a>, <a class="ref" href="scmp_gcd.html#T10" target="_self" title="SCMP_GCD:th.10">Th14</a>, <a class="ref" href="grfunc_1.html#T2" title="GRFUNC_1:th.2">GRFUNC_1:2</a></span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> ( <font color="Maroon" title="c16">P</font> <a href="compos_1.html#K3" title="COMPOS_1:func.3">.</a> 12 <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="scmpds_2.html#K4" title="SCMPDS_2:func.4">goto</a> <span class="p1">(<span class="default"><a href="xcmplx_0.html#K4" title="XCMPLX_0:func.4">-</a> 7</span>)</span> &amp; <font color="Maroon" title="c16">P</font> <a href="compos_1.html#K3" title="COMPOS_1:func.3">.</a> 13 <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> (<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) &amp; <font color="Maroon" title="c16">P</font> <a href="compos_1.html#K3" title="COMPOS_1:func.3">.</a> 14 <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> )</span><br/>

<a NAME="E26:12"/>
12 <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="relat_1.html#NK2" title="RELAT_1:NK.2">dom</a> <a href="scmp_gcd.html#K4" title="SCMP_GCD:func.4">GCD-Algorithm</a>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="scmp_gcd.html#T8" target="_self" title="SCMP_GCD:th.8">Th12</a>, <a class="ref" href="afinsq_1.html#T66" title="AFINSQ_1:th.66">AFINSQ_1:66</a></span>;<br/>
<span class="kw">hence </span><a NAME="E27:12"/>
<font color="Maroon" title="c16">P</font> <a href="compos_1.html#K3" title="COMPOS_1:func.3">.</a> 12 <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="scmpds_2.html#K4" title="SCMPDS_2:func.4">goto</a> <span class="p1">(<span class="default"><a href="xcmplx_0.html#K4" title="XCMPLX_0:func.4">-</a> 7</span>)</span>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:12"><span class="lab"><font color="Green" title="E10">A1</font></span></a>, <a class="ref" href="scmp_gcd.html#T10" target="_self" title="SCMP_GCD:th.10">Th14</a>, <a class="ref" href="grfunc_1.html#T2" title="GRFUNC_1:th.2">GRFUNC_1:2</a></span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> ( <font color="Maroon" title="c16">P</font> <a href="compos_1.html#K3" title="COMPOS_1:func.3">.</a> 13 <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> (<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) &amp; <font color="Maroon" title="c16">P</font> <a href="compos_1.html#K3" title="COMPOS_1:func.3">.</a> 14 <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> )</span><br/>

<a NAME="E28:12"/>
13 <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="relat_1.html#NK2" title="RELAT_1:NK.2">dom</a> <a href="scmp_gcd.html#K4" title="SCMP_GCD:func.4">GCD-Algorithm</a>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="scmp_gcd.html#T8" target="_self" title="SCMP_GCD:th.8">Th12</a>, <a class="ref" href="afinsq_1.html#T66" title="AFINSQ_1:th.66">AFINSQ_1:66</a></span>;<br/>
<span class="kw">hence </span><a NAME="E29:12"/>
<font color="Maroon" title="c16">P</font> <a href="compos_1.html#K3" title="COMPOS_1:func.3">.</a> 13 <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> (<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 class="kw">by</span> <span class="lab"><a class="txt" href="#E1:12"><span class="lab"><font color="Green" title="E10">A1</font></span></a>, <a class="ref" href="scmp_gcd.html#T10" target="_self" title="SCMP_GCD:th.10">Th14</a>, <a class="ref" href="grfunc_1.html#T2" title="GRFUNC_1:th.2">GRFUNC_1:2</a></span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> <font color="Maroon" title="c16">P</font> <a href="compos_1.html#K3" title="COMPOS_1:func.3">.</a> 14 <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></span><br/>

<a NAME="E30:12"/>
14 <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="relat_1.html#NK2" title="RELAT_1:NK.2">dom</a> <a href="scmp_gcd.html#K4" title="SCMP_GCD:func.4">GCD-Algorithm</a>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="scmp_gcd.html#T8" target="_self" title="SCMP_GCD:th.8">Th12</a>, <a class="ref" href="afinsq_1.html#T66" title="AFINSQ_1:th.66">AFINSQ_1:66</a></span>;<br/>
<span class="kw">hence </span><a NAME="E31:12"/>
<font color="Maroon" title="c16">P</font> <a href="compos_1.html#K3" title="COMPOS_1:func.3">.</a> 14 <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>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:12"><span class="lab"><font color="Green" title="E10">A1</font></span></a>, <a class="ref" href="scmp_gcd.html#T10" target="_self" title="SCMP_GCD:th.10">Th14</a>, <a class="ref" href="grfunc_1.html#T2" title="GRFUNC_1:th.2">GRFUNC_1:2</a></span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> verum</span><br/>


</div>
