<?xml version="1.0"?>
<div class="add">

<b>let </b><font color="Maroon" title="c1">i</font> be   <a href="ami_1.html#NM3" title="AMI_1:NM.3">Instruction</a> of <a href="scmpds_2.html#K1" title="SCMPDS_2:func.1">SCMPDS</a> ;<br/><b>let </b><font color="Maroon" title="c2">I</font> be   <a href="scmpds_4.html#NM1" title="SCMPDS_4:NM.1">Program-block</a>;<br/>



<a NAME="E1:9"/><i><font color="Green" title="E11">A1</font></i>: 
 <a href="scmpds_3.html#K2" title="SCMPDS_3:func.2">inspos</a> 0 <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_4.html#K1" title="SCMPDS_4:func.1">Load</a> <font color="Maroon" title="c1">i</font></span>)</span>
 
<b>by </b><i><a class="ref" href="scmpds_5.html#T2" title="SCMPDS_5:th.2">SCMPDS_5:2</a></i>;<br/>
<b>thus </b><span class="p1">(<span class="default"><font color="Maroon" title="c2">I</font> <a href="scmpds_4.html#K5" title="SCMPDS_4:func.5">';'</a> <font color="Maroon" title="c1">i</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p1">(<span class="default"><a href="scmpds_3.html#K2" title="SCMPDS_3:func.2">inspos</a> <span class="p2">(<span class="default"><a href="card_1.html#K4" title="CARD_1:func.4">card</a> <font color="Maroon" title="c2">I</font></span>)</span></span>)</span> = 
<span class="p1">(<span class="default"><font color="Maroon" title="c2">I</font> <a href="scmpds_4.html#K5" title="SCMPDS_4:func.5">';'</a> <font color="Maroon" title="c1">i</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p1">(<span class="default"><a href="scmpds_3.html#K2" title="SCMPDS_3:func.2">inspos</a> <span class="p2">(<span class="default">0 <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> <span class="p3">(<span class="default"><a href="card_1.html#K4" title="CARD_1:func.4">card</a> <font color="Maroon" title="c2">I</font></span>)</span></span>)</span></span>)</span>

<br/>.= 
<span class="p1">(<span class="default"><font color="Maroon" title="c2">I</font> <a href="scmpds_4.html#K5" title="SCMPDS_4:func.5">';'</a> <font color="Maroon" title="c1">i</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.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> 0</span>)</span> <a href="scmpds_3.html#K3" title="SCMPDS_3:func.3">+</a> <span class="p2">(<span class="default"><a href="card_1.html#K4" title="CARD_1:func.4">card</a> <font color="Maroon" title="c2">I</font></span>)</span></span>)</span>
<b>by </b><i><a class="ref" href="scmpds_3.html#D3" title="SCMPDS_3:def.3">SCMPDS_3:def 3</a></i>
<br/>.= 
<span class="p1">(<span class="default"><font color="Maroon" title="c2">I</font> <a href="scmpds_4.html#K3" title="SCMPDS_4:func.3">';'</a> <span class="p2">(<span class="default"><a href="scmpds_4.html#K1" title="SCMPDS_4:func.1">Load</a> <font color="Maroon" title="c1">i</font></span>)</span></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.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> 0</span>)</span> <a href="scmpds_3.html#K3" title="SCMPDS_3:func.3">+</a> <span class="p2">(<span class="default"><a href="card_1.html#K4" title="CARD_1:func.4">card</a> <font color="Maroon" title="c2">I</font></span>)</span></span>)</span>
<b>by </b><i><a class="ref" href="scmpds_4.html#D5" title="SCMPDS_4:def.5">SCMPDS_4:def 5</a></i>
<br/>.= 
<span class="p1">(<span class="default"><a href="scmpds_4.html#K1" title="SCMPDS_4:func.1">Load</a> <font color="Maroon" title="c1">i</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p1">(<span class="default"><a href="scmpds_3.html#K2" title="SCMPDS_3:func.2">inspos</a> 0</span>)</span>
<b>by </b><i><a class="txt" href="scmp_gcd.html#E1:9"><i><font color="Green" title="E11">A1</font></i></a>, <a class="ref" href="scmpds_4.html#T38" title="SCMPDS_4:th.38">SCMPDS_4:38</a></i>
<br/>.= 
<font color="Maroon" title="c1">i</font>
<b>by </b><i><a class="ref" href="scmpds_5.html#T4" title="SCMPDS_5:th.4">SCMPDS_5:4</a></i>
;<br/>

<a NAME="E3:9"/>
 <a href="card_1.html#K4" title="CARD_1:func.4">card</a> <span class="p1">(<span class="default"><font color="Maroon" title="c2">I</font> <a href="scmpds_4.html#K5" title="SCMPDS_4:func.5">';'</a> <font color="Maroon" title="c1">i</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="card_1.html#K4" title="CARD_1:func.4">card</a> <font color="Maroon" title="c2">I</font></span>)</span> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1
 
<b>by </b><i><a class="ref" href="scmp_gcd.html#T8" target="_self" title="SCMP_GCD:th.8">Th8</a></i>;<br/>
<a NAME="E4:9"/><b>then </b>
 <a href="card_1.html#K4" title="CARD_1:func.4">card</a> <font color="Maroon" title="c2">I</font> <a href="xxreal_0.html#NR3" title="XXREAL_0:NR.3">&lt;</a>  <a href="card_1.html#K4" title="CARD_1:func.4">card</a> <span class="p1">(<span class="default"><font color="Maroon" title="c2">I</font> <a href="scmpds_4.html#K5" title="SCMPDS_4:func.5">';'</a> <font color="Maroon" title="c1">i</font></span>)</span>
 
<b>by </b><i><a class="ref" href="xreal_1.html#T31" title="XREAL_1:th.31">XREAL_1:31</a></i>;<br/>
<b>hence </b><a NAME="E5:9"/>
 <a href="scmpds_3.html#K2" title="SCMPDS_3:func.2">inspos</a> <span class="p1">(<span class="default"><a href="card_1.html#K4" title="CARD_1:func.4">card</a> <font color="Maroon" title="c2">I</font></span>)</span> <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"><font color="Maroon" title="c2">I</font> <a href="scmpds_4.html#K5" title="SCMPDS_4:func.5">';'</a> <font color="Maroon" title="c1">i</font></span>)</span>
 <b>by </b><i><a class="ref" href="scmpds_4.html#T1" title="SCMPDS_4:th.1">SCMPDS_4:1</a></i>;<br/>


</div>
