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<b>let </b><font color="Maroon">s</font> be  <a href="ami_3.html#V1">programmed</a>  <a href="ami_1.html#M1">FinPartState</a> of  <a href="scmpds_2.html#K1">SCMPDS</a> ;<br/><b>let </b><font color="Maroon">f</font> be   <a href="funct_2.html#NM1">Function</a> of the <a href="ami_1.html#U4">Instructions</a> of <a href="scmpds_2.html#K1">SCMPDS</a> ,the <a href="ami_1.html#U4">Instructions</a> of <a href="scmpds_2.html#K1">SCMPDS</a> ;<br/><b>let </b><font color="Maroon">n</font> be    <a href="subset_1.html#M2">Element</a> of  <a href="numbers.html#K5">NAT</a> ;<br/>





<a NAME="E1:46"/><i><font color="Green">E33</font></i>: 
 <a href="relat_1.html#K1">dom</a> <span class="p1">(<span class="default"><font color="Maroon">f</font> <a href="scmfsa_4.html#K6">*</a> <font color="Maroon">s</font></span>)</span> <a href="hidden.html#R1">=</a>  <a href="relat_1.html#K1">dom</a> <font color="Maroon">s</font>
 
<b>by </b><i><a class="ref" href="scmfsa_4.html#T2">SCMFSA_4:2</a></i>;<br/>
<a NAME="E2:46"/><i><font color="Green">E35</font></i>: 
 <a href="relat_1.html#K1">dom</a> <span class="p1">(<span class="default"><font color="Maroon">f</font> <a href="scmfsa_4.html#K6">*</a> <span class="p2">(<span class="default"><a href="scmpds_3.html#K6" target="_self">Shift</a> <font color="Maroon">s</font>,<font color="Maroon">n</font></span>)</span></span>)</span> <a href="hidden.html#R1">=</a>  <a href="relat_1.html#K1">dom</a> <span class="p1">(<span class="default"><a href="scmpds_3.html#K6" target="_self">Shift</a> <font color="Maroon">s</font>,<font color="Maroon">n</font></span>)</span>
 
<b>by </b><i><a class="ref" href="scmfsa_4.html#T2">SCMFSA_4:2</a></i>;<br/>
<a NAME="E3:46"/><i><font color="Green">E36</font></i>: 
 <a href="relat_1.html#K1">dom</a> <span class="p1">(<span class="default"><a href="scmpds_3.html#K6" target="_self">Shift</a> <font color="Maroon">s</font>,<font color="Maroon">n</font></span>)</span> <a href="hidden.html#R1">=</a> <span class="p1">{<span class="default"> <span class="p2">(<span class="default"><a href="scmpds_3.html#K2" target="_self">inspos</a> <span class="p3">(<span class="default"><font color="Olive">m</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span></span>)</span> where <font color="Olive">m</font> is    <a href="subset_1.html#M2">Element</a> of  <a href="numbers.html#K5">NAT</a>  :  <a href="scmpds_3.html#K2" target="_self">inspos</a> <font color="Olive">m</font> <a href="hidden.html#R2">in</a>  <a href="relat_1.html#K1">dom</a> <span class="p1">(<span class="default"><font color="Maroon">f</font> <a href="scmfsa_4.html#K6">*</a> <font color="Maroon">s</font></span>)</span> </span>}</span> 
 
<b>by </b><i>, </i>;<br/>
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="46_1"><b>now </b></a><div class="add"><b>let </b><font color="Maroon">m</font> be    <a href="subset_1.html#M2">Element</a> of  <a href="numbers.html#K5">NAT</a> ;<br/><b>assume </b><a NAME="E1:46_1"/><i><font color="Green">E38</font></i>: 
 <a href="scmpds_3.html#K2" target="_self">inspos</a> <font color="Maroon">m</font> <a href="hidden.html#R2">in</a>  <a href="relat_1.html#K1">dom</a> <span class="p1">(<span class="default"><font color="Maroon">f</font> <a href="scmfsa_4.html#K6">*</a> <font color="Maroon">s</font></span>)</span>
 ;<br/><a NAME="E2:46_1"/><b>then </b>
 <a href="scmpds_3.html#K2" target="_self">inspos</a> <span class="p1">(<span class="default"><font color="Maroon">m</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="hidden.html#R2">in</a>  <a href="relat_1.html#K1">dom</a> <span class="p1">(<span class="default"><a href="scmpds_3.html#K6" target="_self">Shift</a> <font color="Maroon">s</font>,<font color="Maroon">n</font></span>)</span>
 <b>by </b><i/>;<br/><b>hence </b><span class="p1">(<span class="default"><font color="Maroon">f</font> <a href="scmfsa_4.html#K6">*</a> <span class="p2">(<span class="default"><a href="scmpds_3.html#K6" target="_self">Shift</a> <font color="Maroon">s</font>,<font color="Maroon">n</font></span>)</span></span>)</span> <a href="funct_1.html#K1">.</a> <span class="p1">(<span class="default"><a href="scmpds_3.html#K2" target="_self">inspos</a> <span class="p2">(<span class="default"><font color="Maroon">m</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span></span>)</span> = 
<font color="Maroon">f</font> <a href="funct_1.html#K1">.</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="scmpds_3.html#K6" target="_self">Shift</a> <font color="Maroon">s</font>,<font color="Maroon">n</font></span>)</span> <a href="funct_1.html#K1">.</a> <span class="p2">(<span class="default"><a href="scmpds_3.html#K2" target="_self">inspos</a> <span class="p3">(<span class="default"><font color="Maroon">m</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span></span>)</span></span>)</span>
<b>by </b><i><a class="ref" href="funct_1.html#T23">FUNCT_1:23</a></i>
<br/>.= 
<font color="Maroon">f</font> <a href="funct_1.html#K1">.</a> <span class="p1">(<span class="default"><font color="Maroon">s</font> <a href="funct_1.html#K1">.</a> <span class="p2">(<span class="default"><a href="scmpds_3.html#K2" target="_self">inspos</a> <font color="Maroon">m</font></span>)</span></span>)</span>
<b>by </b><i>, , </i>
<br/>.= 
<span class="p1">(<span class="default"><font color="Maroon">f</font> <a href="scmfsa_4.html#K6">*</a> <font color="Maroon">s</font></span>)</span> <a href="funct_1.html#K1">.</a> <span class="p1">(<span class="default"><a href="scmpds_3.html#K2" target="_self">inspos</a> <font color="Maroon">m</font></span>)</span>
<b>by </b><i>, , <a class="ref" href="funct_1.html#T23">FUNCT_1:23</a></i>
;<br/><br/></div><b>end;</b></div>
<b>hence </b><a NAME="E5:46"/>
 <a href="scmpds_3.html#K6" target="_self">Shift</a> <span class="p1">(<span class="default"><font color="Maroon">f</font> <a href="scmfsa_4.html#K6">*</a> <font color="Maroon">s</font></span>)</span>,<font color="Maroon">n</font> <a href="hidden.html#R1">=</a> <font color="Maroon">f</font> <a href="scmfsa_4.html#K6">*</a> <span class="p1">(<span class="default"><a href="scmpds_3.html#K6" target="_self">Shift</a> <font color="Maroon">s</font>,<font color="Maroon">n</font></span>)</span>
 <b>by </b><i>, , </i>;<br/>


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