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<b>let </b><font color="Maroon">c<sub>16</sub></font> be   <a href="ami_1.html#NM4">State</a> of <a href="scmpds_2.html#K1">SCMPDS</a> ;<br/>

<b>set </b><font color="Maroon">c<sub>17</sub></font> =  <a href="scmp_gcd.html#K4" target="_self">GCD-Algorithm</a> ;<br/>
<b>assume </b><a NAME="E1:15"/><i><font color="Green">E15</font></i>: 
 <a href="scmp_gcd.html#K4" target="_self">GCD-Algorithm</a>  <a href="tarski.html#R1">c=</a> <font color="Maroon">c<sub>16</sub></font>
 ;<br/>

<a NAME="E2:15"/>
 <a href="scmpds_3.html#K2">inspos</a> 0 <a href="hidden.html#R2">in</a>  <a href="relat_1.html#K1">dom</a> <a href="scmp_gcd.html#K4" target="_self">GCD-Algorithm</a> 
 
<b>by </b><i><a class="ref" href="scmp_gcd.html#T12" target="_self">Th12</a>, <a class="ref" href="scmpds_4.html#T1">SCMPDS_4:1</a></i>;<br/>
<b>hence </b><a NAME="E3:15"/>
<font color="Maroon">c<sub>16</sub></font> <a href="ami_1.html#K13">.</a> <span class="p1">(<span class="default"><a href="scmpds_3.html#K2">inspos</a> 0</span>)</span> <a href="hidden.html#R1">=</a> <a href="scmp_gcd.html#K2" target="_self">GBP</a>  <a href="scmpds_2.html#K6">:=</a> 0
 <b>by </b><i><a class="txt" href="scmp_gcd.html#E1:15"><i><font color="Green">E15</font></i></a>, <a class="ref" href="scmp_gcd.html#T14" target="_self">Th14</a>, <a class="ref" href="grfunc_1.html#T8">GRFUNC_1:8</a></i>;<br/>

<a NAME="E4:15"/>
 <a href="scmpds_3.html#K2">inspos</a> 1 <a href="hidden.html#R2">in</a>  <a href="relat_1.html#K1">dom</a> <a href="scmp_gcd.html#K4" target="_self">GCD-Algorithm</a> 
 
<b>by </b><i><a class="ref" href="scmp_gcd.html#T12" target="_self">Th12</a>, <a class="ref" href="scmpds_4.html#T1">SCMPDS_4:1</a></i>;<br/>
<b>hence </b><a NAME="E5:15"/>
<font color="Maroon">c<sub>16</sub></font> <a href="ami_1.html#K13">.</a> <span class="p1">(<span class="default"><a href="scmpds_3.html#K2">inspos</a> 1</span>)</span> <a href="hidden.html#R1">=</a> <a href="scmp_gcd.html#K3" target="_self">SBP</a>  <a href="scmpds_2.html#K6">:=</a> 7
 <b>by </b><i><a class="txt" href="scmp_gcd.html#E1:15"><i><font color="Green">E15</font></i></a>, <a class="ref" href="scmp_gcd.html#T14" target="_self">Th14</a>, <a class="ref" href="grfunc_1.html#T8">GRFUNC_1:8</a></i>;<br/>

<a NAME="E6:15"/>
 <a href="scmpds_3.html#K2">inspos</a> 2 <a href="hidden.html#R2">in</a>  <a href="relat_1.html#K1">dom</a> <a href="scmp_gcd.html#K4" target="_self">GCD-Algorithm</a> 
 
<b>by </b><i><a class="ref" href="scmp_gcd.html#T12" target="_self">Th12</a>, <a class="ref" href="scmpds_4.html#T1">SCMPDS_4:1</a></i>;<br/>
<b>hence </b><a NAME="E7:15"/>
<font color="Maroon">c<sub>16</sub></font> <a href="ami_1.html#K13">.</a> <span class="p1">(<span class="default"><a href="scmpds_3.html#K2">inspos</a> 2</span>)</span> <a href="hidden.html#R1">=</a>  <a href="scmpds_2.html#K7">saveIC</a> <a href="scmp_gcd.html#K3" target="_self">SBP</a> ,<a href="scmpds_1.html#K23">RetIC</a> 
 <b>by </b><i><a class="txt" href="scmp_gcd.html#E1:15"><i><font color="Green">E15</font></i></a>, <a class="ref" href="scmp_gcd.html#T14" target="_self">Th14</a>, <a class="ref" href="grfunc_1.html#T8">GRFUNC_1:8</a></i>;<br/>

<a NAME="E8:15"/>
 <a href="scmpds_3.html#K2">inspos</a> 3 <a href="hidden.html#R2">in</a>  <a href="relat_1.html#K1">dom</a> <a href="scmp_gcd.html#K4" target="_self">GCD-Algorithm</a> 
 
<b>by </b><i><a class="ref" href="scmp_gcd.html#T12" target="_self">Th12</a>, <a class="ref" href="scmpds_4.html#T1">SCMPDS_4:1</a></i>;<br/>
<b>hence </b><a NAME="E9:15"/>
<font color="Maroon">c<sub>16</sub></font> <a href="ami_1.html#K13">.</a> <span class="p1">(<span class="default"><a href="scmpds_3.html#K2">inspos</a> 3</span>)</span> <a href="hidden.html#R1">=</a>  <a href="scmpds_2.html#K4">goto</a> 2
 <b>by </b><i><a class="txt" href="scmp_gcd.html#E1:15"><i><font color="Green">E15</font></i></a>, <a class="ref" href="scmp_gcd.html#T14" target="_self">Th14</a>, <a class="ref" href="grfunc_1.html#T8">GRFUNC_1:8</a></i>;<br/>

<a NAME="E10:15"/>
 <a href="scmpds_3.html#K2">inspos</a> 4 <a href="hidden.html#R2">in</a>  <a href="relat_1.html#K1">dom</a> <a href="scmp_gcd.html#K4" target="_self">GCD-Algorithm</a> 
 
<b>by </b><i><a class="ref" href="scmp_gcd.html#T12" target="_self">Th12</a>, <a class="ref" href="scmpds_4.html#T1">SCMPDS_4:1</a></i>;<br/>
<b>hence </b><a NAME="E11:15"/>
<font color="Maroon">c<sub>16</sub></font> <a href="ami_1.html#K13">.</a> <span class="p1">(<span class="default"><a href="scmpds_3.html#K2">inspos</a> 4</span>)</span> <a href="hidden.html#R1">=</a>  <a href="ami_1.html#K5">halt</a> <a href="scmpds_2.html#K1">SCMPDS</a> 
 <b>by </b><i><a class="txt" href="scmp_gcd.html#E1:15"><i><font color="Green">E15</font></i></a>, <a class="ref" href="scmp_gcd.html#T14" target="_self">Th14</a>, <a class="ref" href="grfunc_1.html#T8">GRFUNC_1:8</a></i>;<br/>

<a NAME="E12:15"/>
 <a href="scmpds_3.html#K2">inspos</a> 5 <a href="hidden.html#R2">in</a>  <a href="relat_1.html#K1">dom</a> <a href="scmp_gcd.html#K4" target="_self">GCD-Algorithm</a> 
 
<b>by </b><i><a class="ref" href="scmp_gcd.html#T12" target="_self">Th12</a>, <a class="ref" href="scmpds_4.html#T1">SCMPDS_4:1</a></i>;<br/>
<b>hence </b><a NAME="E13:15"/>
<font color="Maroon">c<sub>16</sub></font> <a href="ami_1.html#K13">.</a> <span class="p1">(<span class="default"><a href="scmpds_3.html#K2">inspos</a> 5</span>)</span> <a href="hidden.html#R1">=</a> <a href="scmp_gcd.html#K3" target="_self">SBP</a> ,3 <a href="scmpds_2.html#K9">&lt;=0_goto</a> 9
 <b>by </b><i><a class="txt" href="scmp_gcd.html#E1:15"><i><font color="Green">E15</font></i></a>, <a class="ref" href="scmp_gcd.html#T14" target="_self">Th14</a>, <a class="ref" href="grfunc_1.html#T8">GRFUNC_1:8</a></i>;<br/>

<a NAME="E14:15"/>
 <a href="scmpds_3.html#K2">inspos</a> 6 <a href="hidden.html#R2">in</a>  <a href="relat_1.html#K1">dom</a> <a href="scmp_gcd.html#K4" target="_self">GCD-Algorithm</a> 
 
<b>by </b><i><a class="ref" href="scmp_gcd.html#T12" target="_self">Th12</a>, <a class="ref" href="scmpds_4.html#T1">SCMPDS_4:1</a></i>;<br/>
<b>hence </b><a NAME="E15:15"/>
<font color="Maroon">c<sub>16</sub></font> <a href="ami_1.html#K13">.</a> <span class="p1">(<span class="default"><a href="scmpds_3.html#K2">inspos</a> 6</span>)</span> <a href="hidden.html#R1">=</a> <a href="scmp_gcd.html#K3" target="_self">SBP</a> ,6 <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3" target="_self">SBP</a> ,3
 <b>by </b><i><a class="txt" href="scmp_gcd.html#E1:15"><i><font color="Green">E15</font></i></a>, <a class="ref" href="scmp_gcd.html#T14" target="_self">Th14</a>, <a class="ref" href="grfunc_1.html#T8">GRFUNC_1:8</a></i>;<br/>

<a NAME="E16:15"/>
 <a href="scmpds_3.html#K2">inspos</a> 7 <a href="hidden.html#R2">in</a>  <a href="relat_1.html#K1">dom</a> <a href="scmp_gcd.html#K4" target="_self">GCD-Algorithm</a> 
 
<b>by </b><i><a class="ref" href="scmp_gcd.html#T12" target="_self">Th12</a>, <a class="ref" href="scmpds_4.html#T1">SCMPDS_4:1</a></i>;<br/>
<b>hence </b><a NAME="E17:15"/>
<font color="Maroon">c<sub>16</sub></font> <a href="ami_1.html#K13">.</a> <span class="p1">(<span class="default"><a href="scmpds_3.html#K2">inspos</a> 7</span>)</span> <a href="hidden.html#R1">=</a>  <a href="scmpds_2.html#K16">Divide</a> <a href="scmp_gcd.html#K3" target="_self">SBP</a> ,2,<a href="scmp_gcd.html#K3" target="_self">SBP</a> ,3
 <b>by </b><i><a class="txt" href="scmp_gcd.html#E1:15"><i><font color="Green">E15</font></i></a>, <a class="ref" href="scmp_gcd.html#T14" target="_self">Th14</a>, <a class="ref" href="grfunc_1.html#T8">GRFUNC_1:8</a></i>;<br/>

<a NAME="E18:15"/>
 <a href="scmpds_3.html#K2">inspos</a> 8 <a href="hidden.html#R2">in</a>  <a href="relat_1.html#K1">dom</a> <a href="scmp_gcd.html#K4" target="_self">GCD-Algorithm</a> 
 
<b>by </b><i><a class="ref" href="scmp_gcd.html#T12" target="_self">Th12</a>, <a class="ref" href="scmpds_4.html#T1">SCMPDS_4:1</a></i>;<br/>
<b>hence </b><a NAME="E19:15"/>
<font color="Maroon">c<sub>16</sub></font> <a href="ami_1.html#K13">.</a> <span class="p1">(<span class="default"><a href="scmpds_3.html#K2">inspos</a> 8</span>)</span> <a href="hidden.html#R1">=</a> <a href="scmp_gcd.html#K3" target="_self">SBP</a> ,7 <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3" target="_self">SBP</a> ,3
 <b>by </b><i><a class="txt" href="scmp_gcd.html#E1:15"><i><font color="Green">E15</font></i></a>, <a class="ref" href="scmp_gcd.html#T14" target="_self">Th14</a>, <a class="ref" href="grfunc_1.html#T8">GRFUNC_1:8</a></i>;<br/>

<a NAME="E20:15"/>
 <a href="scmpds_3.html#K2">inspos</a> 9 <a href="hidden.html#R2">in</a>  <a href="relat_1.html#K1">dom</a> <a href="scmp_gcd.html#K4" target="_self">GCD-Algorithm</a> 
 
<b>by </b><i><a class="ref" href="scmp_gcd.html#T12" target="_self">Th12</a>, <a class="ref" href="scmpds_4.html#T1">SCMPDS_4:1</a></i>;<br/>
<b>hence </b><a NAME="E21:15"/>
<font color="Maroon">c<sub>16</sub></font> <a href="ami_1.html#K13">.</a> <span class="p1">(<span class="default"><a href="scmpds_3.html#K2">inspos</a> 9</span>)</span> <a href="hidden.html#R1">=</a> <a href="scmp_gcd.html#K3" target="_self">SBP</a> ,<span class="p1">(<span class="default">4 <a href="nat_1.html#K1">+</a> <a href="scmpds_1.html#K22">RetSP</a> </span>)</span> <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K2" target="_self">GBP</a> ,1
 <b>by </b><i><a class="txt" href="scmp_gcd.html#E1:15"><i><font color="Green">E15</font></i></a>, <a class="ref" href="scmp_gcd.html#T14" target="_self">Th14</a>, <a class="ref" href="grfunc_1.html#T8">GRFUNC_1:8</a></i>;<br/>

<a NAME="E22:15"/>
 <a href="scmpds_3.html#K2">inspos</a> 10 <a href="hidden.html#R2">in</a>  <a href="relat_1.html#K1">dom</a> <a href="scmp_gcd.html#K4" target="_self">GCD-Algorithm</a> 
 
<b>by </b><i><a class="ref" href="scmp_gcd.html#T12" target="_self">Th12</a>, <a class="ref" href="scmpds_4.html#T1">SCMPDS_4:1</a></i>;<br/>
<b>hence </b><a NAME="E23:15"/>
<font color="Maroon">c<sub>16</sub></font> <a href="ami_1.html#K13">.</a> <span class="p1">(<span class="default"><a href="scmpds_3.html#K2">inspos</a> 10</span>)</span> <a href="hidden.html#R1">=</a>  <a href="scmpds_2.html#K12">AddTo</a> <a href="scmp_gcd.html#K2" target="_self">GBP</a> ,1,4
 <b>by </b><i><a class="txt" href="scmp_gcd.html#E1:15"><i><font color="Green">E15</font></i></a>, <a class="ref" href="scmp_gcd.html#T14" target="_self">Th14</a>, <a class="ref" href="grfunc_1.html#T8">GRFUNC_1:8</a></i>;<br/>

<a NAME="E24:15"/>
 <a href="scmpds_3.html#K2">inspos</a> 11 <a href="hidden.html#R2">in</a>  <a href="relat_1.html#K1">dom</a> <a href="scmp_gcd.html#K4" target="_self">GCD-Algorithm</a> 
 
<b>by </b><i><a class="ref" href="scmp_gcd.html#T12" target="_self">Th12</a>, <a class="ref" href="scmpds_4.html#T1">SCMPDS_4:1</a></i>;<br/>
<b>hence </b><a NAME="E25:15"/>
<font color="Maroon">c<sub>16</sub></font> <a href="ami_1.html#K13">.</a> <span class="p1">(<span class="default"><a href="scmpds_3.html#K2">inspos</a> 11</span>)</span> <a href="hidden.html#R1">=</a>  <a href="scmpds_2.html#K7">saveIC</a> <a href="scmp_gcd.html#K3" target="_self">SBP</a> ,<a href="scmpds_1.html#K23">RetIC</a> 
 <b>by </b><i><a class="txt" href="scmp_gcd.html#E1:15"><i><font color="Green">E15</font></i></a>, <a class="ref" href="scmp_gcd.html#T14" target="_self">Th14</a>, <a class="ref" href="grfunc_1.html#T8">GRFUNC_1:8</a></i>;<br/>

<a NAME="E26:15"/>
 <a href="scmpds_3.html#K2">inspos</a> 12 <a href="hidden.html#R2">in</a>  <a href="relat_1.html#K1">dom</a> <a href="scmp_gcd.html#K4" target="_self">GCD-Algorithm</a> 
 
<b>by </b><i><a class="ref" href="scmp_gcd.html#T12" target="_self">Th12</a>, <a class="ref" href="scmpds_4.html#T1">SCMPDS_4:1</a></i>;<br/>
<b>hence </b><a NAME="E27:15"/>
<font color="Maroon">c<sub>16</sub></font> <a href="ami_1.html#K13">.</a> <span class="p1">(<span class="default"><a href="scmpds_3.html#K2">inspos</a> 12</span>)</span> <a href="hidden.html#R1">=</a>  <a href="scmpds_2.html#K4">goto</a> <span class="p1">(<span class="default"><a href="xcmplx_0.html#K4">-</a> 7</span>)</span>
 <b>by </b><i><a class="txt" href="scmp_gcd.html#E1:15"><i><font color="Green">E15</font></i></a>, <a class="ref" href="scmp_gcd.html#T14" target="_self">Th14</a>, <a class="ref" href="grfunc_1.html#T8">GRFUNC_1:8</a></i>;<br/>

<a NAME="E28:15"/>
 <a href="scmpds_3.html#K2">inspos</a> 13 <a href="hidden.html#R2">in</a>  <a href="relat_1.html#K1">dom</a> <a href="scmp_gcd.html#K4" target="_self">GCD-Algorithm</a> 
 
<b>by </b><i><a class="ref" href="scmp_gcd.html#T12" target="_self">Th12</a>, <a class="ref" href="scmpds_4.html#T1">SCMPDS_4:1</a></i>;<br/>
<b>hence </b><a NAME="E29:15"/>
<font color="Maroon">c<sub>16</sub></font> <a href="ami_1.html#K13">.</a> <span class="p1">(<span class="default"><a href="scmpds_3.html#K2">inspos</a> 13</span>)</span> <a href="hidden.html#R1">=</a> <a href="scmp_gcd.html#K3" target="_self">SBP</a> ,2 <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3" target="_self">SBP</a> ,6
 <b>by </b><i><a class="txt" href="scmp_gcd.html#E1:15"><i><font color="Green">E15</font></i></a>, <a class="ref" href="scmp_gcd.html#T14" target="_self">Th14</a>, <a class="ref" href="grfunc_1.html#T8">GRFUNC_1:8</a></i>;<br/>

<a NAME="E30:15"/>
 <a href="scmpds_3.html#K2">inspos</a> 14 <a href="hidden.html#R2">in</a>  <a href="relat_1.html#K1">dom</a> <a href="scmp_gcd.html#K4" target="_self">GCD-Algorithm</a> 
 
<b>by </b><i><a class="ref" href="scmp_gcd.html#T12" target="_self">Th12</a>, <a class="ref" href="scmpds_4.html#T1">SCMPDS_4:1</a></i>;<br/>
<b>hence </b><a NAME="E31:15"/>
<font color="Maroon">c<sub>16</sub></font> <a href="ami_1.html#K13">.</a> <span class="p1">(<span class="default"><a href="scmpds_3.html#K2">inspos</a> 14</span>)</span> <a href="hidden.html#R1">=</a>  <a href="scmpds_2.html#K5">return</a> <a href="scmp_gcd.html#K3" target="_self">SBP</a> 
 <b>by </b><i><a class="txt" href="scmp_gcd.html#E1:15"><i><font color="Green">E15</font></i></a>, <a class="ref" href="scmp_gcd.html#T14" target="_self">Th14</a>, <a class="ref" href="grfunc_1.html#T8">GRFUNC_1:8</a></i>;<br/>


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