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<b>let </b><font color="Maroon" title="c1">I</font> be   <a href="scmpds_4.html#NM1" title="SCMPDS_4:NM.1">Program-block</a>;<br/><b>let </b><font color="Maroon" title="c2">s</font> be   <a href="ami_1.html#NM4" title="AMI_1:NM.4">State</a> of <a href="scmpds_2.html#K1" title="SCMPDS_2:func.1">SCMPDS</a> ;<br/>



<b>assume </b><a NAME="E1:75"/><i><font color="Green" title="E46">A1</font></i>: 
not  <a href="ami_1.html#K6" title="AMI_1:func.6">IC</a> <font color="Maroon" title="c2">s</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">I</font>
 ;<br/>

<b>consider </b><font color="Maroon" title="c3">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="E3:75"/><i><font color="Green" title="E47">A2</font></i>: 
 <a href="ami_1.html#K6" title="AMI_1:func.6">IC</a> <font color="Maroon" title="c2">s</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="c3">m</font>
 <b>by </b><i><a class="ref" href="scmpds_3.html#T32" title="SCMPDS_3:th.32">SCMPDS_3:32</a></i>;<br/>
<a NAME="E4:75"/><i><font color="Green" title="E48">A3</font></i>: 
<font color="Maroon" title="c3">m</font> <a href="xxreal_0.html#NR2" title="XXREAL_0:NR.2">&gt;=</a>  <a href="card_1.html#K4" title="CARD_1:func.4">card</a> <font color="Maroon" title="c1">I</font>
 
<b>by </b><i><a class="txt" href="scmpds_4.html#E1:75"><i><font color="Green" title="E46">A1</font></i></a>, <a class="txt" href="scmpds_4.html#E3:75"><i><font color="Green" title="E47">A2</font></i></a>, <a class="ref" href="scmpds_4.html#T1" target="_self" title="SCMPDS_4:th.1">Th1</a></i>;<br/>
<a NAME="E5:75"/><i><font color="Green" title="E49">A4</font></i>: 
 <a href="scmpds_2.html#K18" title="SCMPDS_2:func.18">Next</a> <span class="p1">(<span class="default"><a href="ami_1.html#K6" title="AMI_1:func.6">IC</a> <font color="Maroon" title="c2">s</font></span>)</span> <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="c3">m</font> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1</span>)</span>
 
<b>by </b><i><a class="txt" href="scmpds_4.html#E3:75"><i><font color="Green" title="E47">A2</font></i></a>, <a class="ref" href="scmpds_4.html#T70" target="_self" title="SCMPDS_4:th.70">Th70</a></i>;<br/>
<a NAME="E6:75"/>
<font color="Maroon" title="c3">m</font> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1 <a href="xxreal_0.html#NR2" title="XXREAL_0:NR.2">&gt;=</a> <font color="Maroon" title="c3">m</font>
 
<b>by </b><i><a class="ref" href="nat_1.html#T11" title="NAT_1:th.11">NAT_1:11</a></i>;<br/>
<a NAME="E7:75"/><b>then </b>
<font color="Maroon" title="c3">m</font> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1 <a href="xxreal_0.html#NR2" title="XXREAL_0:NR.2">&gt;=</a>  <a href="card_1.html#K4" title="CARD_1:func.4">card</a> <font color="Maroon" title="c1">I</font>
 
<b>by </b><i><a class="txt" href="scmpds_4.html#E4:75"><i><font color="Green" title="E48">A3</font></i></a>, <a class="ref" href="xxreal_0.html#T2" title="XXREAL_0:th.2">XXREAL_0:2</a></i>;<br/>
<b>hence </b><a NAME="E8:75"/>
not  <a href="scmpds_2.html#K18" title="SCMPDS_2:func.18">Next</a> <span class="p1">(<span class="default"><a href="ami_1.html#K6" title="AMI_1:func.6">IC</a> <font color="Maroon" title="c2">s</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> <font color="Maroon" title="c1">I</font>
 <b>by </b><i><a class="txt" href="scmpds_4.html#E5:75"><i><font color="Green" title="E49">A4</font></i></a>, <a class="ref" href="scmpds_4.html#T1" target="_self" title="SCMPDS_4:th.1">Th1</a></i>;<br/>


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