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<b>let </b><font color="Maroon" title="c1">p</font> be  <a href="ami_1.html#V15" title="AMI_1:attr.15">programmed</a> <a href="ami_1.html#NM5" title="AMI_1:NM.5">FinPartState</a> of <a href="scmpds_2.html#K1" title="SCMPDS_2:func.1">SCMPDS</a> ;<br/><b>let </b><font color="Maroon" title="c2">k</font> be    <a href="subset_1.html#M2" title="SUBSET_1:mode.2">Element</a> of  <a href="numbers.html#K5" title="NUMBERS:func.5">NAT</a> ;<br/>



<a NAME="E1:43"/><i><font color="Green" title="E19">A1</font></i>: 
 <a href="relat_1.html#K1" title="RELAT_1:func.1">dom</a> <span class="p1">(<span class="default"><a href="scmpds_3.html#K6" title="SCMPDS_3:func.6">Shift</a> <font color="Maroon" title="c1">p</font>,<font color="Maroon" title="c2">k</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="scmpds_3.html#K2" title="SCMPDS_3:func.2">inspos</a> <span class="p3">(<span class="default"><font color="Olive" title="b1">m</font> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> <font color="Maroon" title="c2">k</font></span>)</span></span>)</span> where <font color="Olive" title="b1">m</font> is    <a href="subset_1.html#M2" title="SUBSET_1:mode.2">Element</a> of  <a href="numbers.html#K5" title="NUMBERS:func.5">NAT</a>  :  <a href="scmpds_3.html#K2" title="SCMPDS_3:func.2">inspos</a> <font color="Olive" title="b1">m</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="relat_1.html#K1" title="RELAT_1:func.1">dom</a> <font color="Maroon" title="c1">p</font> </span>}</span> 
 
<b>by </b><i><a class="ref" href="scmpds_3.html#D7" target="_self" title="SCMPDS_3:def.7">Def7</a></i>;<br/>
<div><b>hereby </b> <i><font color="Red">:: according to </font></i><a class="ref" href="tarski.html#D3" title="TARSKI:def.3">TARSKI:def 3</a>,<a class="ref" href="xboole_0.html#D10" title="XBOOLE_0:def.10">XBOOLE_0:def 10</a>
<div class="add"><b>let </b><font color="Maroon" title="c3">e</font> be    <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a> ;<br/><b>assume </b><a NAME="E1:43_1"/>
<font color="Maroon" title="c3">e</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="relat_1.html#K1" title="RELAT_1:func.1">dom</a> <span class="p1">(<span class="default"><a href="scmpds_3.html#K6" title="SCMPDS_3:func.6">Shift</a> <font color="Maroon" title="c1">p</font>,<font color="Maroon" title="c2">k</font></span>)</span>
 ;<br/><b>then consider </b><font color="Maroon" title="c4">m</font> being    <a href="subset_1.html#M2" title="SUBSET_1:mode.2">Element</a> of  <a href="numbers.html#K5" title="NUMBERS:func.5">NAT</a> <b> such that </b><br/><a NAME="E3:43_1"/><i><font color="Green" title="E20">A2</font></i>: 
<font color="Maroon" title="c3">e</font> <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"><font color="Maroon" title="c4">m</font> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> <font color="Maroon" title="c2">k</font></span>)</span>
 <b>and </b><br/><a NAME="E4:43_1"/><i><font color="Green" title="E21">A3</font></i>: 
 <a href="scmpds_3.html#K2" title="SCMPDS_3:func.2">inspos</a> <font color="Maroon" title="c4">m</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="relat_1.html#K1" title="RELAT_1:func.1">dom</a> <font color="Maroon" title="c1">p</font>
 <b>by </b><i><a class="txt" href="scmpds_3.html#E1:43"><i><font color="Green" title="E19">A1</font></i></a></i>;<br/><a NAME="E5:43_1"/>
<span class="p1">(<span class="default"><a href="scmpds_3.html#K2" title="SCMPDS_3:func.2">inspos</a> <font color="Maroon" title="c4">m</font></span>)</span> <a href="scmpds_3.html#K3" title="SCMPDS_3:func.3">+</a> <font color="Maroon" title="c2">k</font> <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"><font color="Maroon" title="c4">m</font> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> <font color="Maroon" title="c2">k</font></span>)</span>
 <b>by </b><i><a class="ref" href="scmpds_3.html#D3" target="_self" title="SCMPDS_3:def.3">Def3</a></i>;<br/><b>hence </b><a NAME="E6:43_1"/>
<font color="Maroon" title="c3">e</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <span class="p1">{<span class="default"> <span class="p2">(<span class="default"><font color="Olive" title="b1">il</font> <a href="scmpds_3.html#K3" title="SCMPDS_3:func.3">+</a> <font color="Maroon" title="c2">k</font></span>)</span> where <font color="Olive" title="b1">il</font> is    <a href="ami_1.html#M1" title="AMI_1:mode.1">Instruction-Location</a> of  <a href="scmpds_2.html#K1" title="SCMPDS_2:func.1">SCMPDS</a>  : <font color="Olive" title="b1">il</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="relat_1.html#K1" title="RELAT_1:func.1">dom</a> <font color="Maroon" title="c1">p</font> </span>}</span> 
 <b>by </b><i><a class="txt" href="scmpds_3.html#E3:43_1"><i><font color="Green" title="E20">A2</font></i></a>, <a class="txt" href="scmpds_3.html#E4:43_1"><i><font color="Green" title="E21">A3</font></i></a></i>;<br/></div>
<b>end;</b></div>

<b>let </b><font color="Maroon" title="c3">e</font> be    <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a> ; <i><font color="Red">:: according to </font></i><a class="ref" href="tarski.html#D3" title="TARSKI:def.3">TARSKI:def 3</a><br/>

<b>assume </b><a NAME="E3:43"/>
<font color="Maroon" title="c3">e</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <span class="p1">{<span class="default"> <span class="p2">(<span class="default"><font color="Olive" title="b1">il</font> <a href="scmpds_3.html#K3" title="SCMPDS_3:func.3">+</a> <font color="Maroon" title="c2">k</font></span>)</span> where <font color="Olive" title="b1">il</font> is    <a href="ami_1.html#M1" title="AMI_1:mode.1">Instruction-Location</a> of  <a href="scmpds_2.html#K1" title="SCMPDS_2:func.1">SCMPDS</a>  : <font color="Olive" title="b1">il</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="relat_1.html#K1" title="RELAT_1:func.1">dom</a> <font color="Maroon" title="c1">p</font> </span>}</span> 
 ;<br/>

<b>then consider </b><font color="Maroon" title="c4">il</font> being    <a href="ami_1.html#M1" title="AMI_1:mode.1">Instruction-Location</a> of  <a href="scmpds_2.html#K1" title="SCMPDS_2:func.1">SCMPDS</a> <b> such that </b><br/><a NAME="E5:43"/><i><font color="Green" title="E20">A4</font></i>: 
<font color="Maroon" title="c3">e</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c4">il</font> <a href="scmpds_3.html#K3" title="SCMPDS_3:func.3">+</a> <font color="Maroon" title="c2">k</font>
 <b>and </b><br/><a NAME="E6:43"/><i><font color="Green" title="E21">A5</font></i>: 
<font color="Maroon" title="c4">il</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="relat_1.html#K1" title="RELAT_1:func.1">dom</a> <font color="Maroon" title="c1">p</font>
 ;<br/>
<b>consider </b><font color="Maroon" title="c5">m</font> being    <a href="subset_1.html#M2" title="SUBSET_1:mode.2">Element</a> of  <a href="numbers.html#K5" title="NUMBERS:func.5">NAT</a> <b> such that </b><br/><a NAME="E8:43"/><i><font color="Green" title="E22">A6</font></i>: 
<font color="Maroon" title="c4">il</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="scmpds_3.html#K2" title="SCMPDS_3:func.2">inspos</a> <font color="Maroon" title="c5">m</font>
 <b>and </b><br/><a NAME="E9:43"/><i><font color="Green" title="E23">A7</font></i>: 
<font color="Maroon" title="c4">il</font> <a href="scmpds_3.html#K3" title="SCMPDS_3:func.3">+</a> <font color="Maroon" title="c2">k</font> <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"><font color="Maroon" title="c5">m</font> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> <font color="Maroon" title="c2">k</font></span>)</span>
 <b>by </b><i><a class="ref" href="scmpds_3.html#D3" target="_self" title="SCMPDS_3:def.3">Def3</a></i>;<br/>
<b>thus </b><a NAME="E10:43"/>
<font color="Maroon" title="c3">e</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="relat_1.html#K1" title="RELAT_1:func.1">dom</a> <span class="p1">(<span class="default"><a href="scmpds_3.html#K6" title="SCMPDS_3:func.6">Shift</a> <font color="Maroon" title="c1">p</font>,<font color="Maroon" title="c2">k</font></span>)</span>
 <b>by </b><i><a class="txt" href="scmpds_3.html#E1:43"><i><font color="Green" title="E19">A1</font></i></a>, <a class="txt" href="scmpds_3.html#E5:43"><i><font color="Green" title="E20">A4</font></i></a>, <a class="txt" href="scmpds_3.html#E6:43"><i><font color="Green" title="E21">A5</font></i></a>, <a class="txt" href="scmpds_3.html#E8:43"><i><font color="Green" title="E22">A6</font></i></a>, <a class="txt" href="scmpds_3.html#E9:43"><i><font color="Green" title="E23">A7</font></i></a></i>;<br/>


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