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<span class="kw">let </span><font color="Maroon" title="c3">a</font> be    <a href="scmpds_2.html#M1" title="SCMPDS_2:mode.1">Int_position</a> ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> for <font color="Olive" title="b1">k1</font> being  <a href="int_1.html#NM1" title="INT_1:NM.1">Integer</a><br/> for <font color="Olive" title="b2">I</font>, <font color="Olive" title="b3">J</font> being  <a href="scmnorm.html#NM2" title="SCMNORM:NM.2">Program</a> of <a href="scmpds_2.html#K1" title="SCMPDS_2:func.1">SCMPDS</a>  holds <br/> (  <a href="numbers.html#K6" title="NUMBERS:func.6">0</a>  <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="afinsq_1.html#K2" title="AFINSQ_1:func.2">dom</a> <span class="p1">(<span class="default"><a href="scmpds_6.html#K4" title="SCMPDS_6:func.4">if&lt;0</a> <font color="Maroon" title="c3">a</font>,<font color="Olive" title="b1">k1</font>,<font color="Olive" title="b2">I</font>,<font color="Olive" title="b3">J</font></span>)</span> &amp; 1 <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="afinsq_1.html#K2" title="AFINSQ_1:func.2">dom</a> <span class="p1">(<span class="default"><a href="scmpds_6.html#K4" title="SCMPDS_6:func.4">if&lt;0</a> <font color="Maroon" title="c3">a</font>,<font color="Olive" title="b1">k1</font>,<font color="Olive" title="b2">I</font>,<font color="Olive" title="b3">J</font></span>)</span> )</span><br/><span class="kw">let </span><font color="Maroon" title="c4">k1</font> be   <a href="int_1.html#NM1" title="INT_1:NM.1">Integer</a>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> for <font color="Olive" title="b1">I</font>, <font color="Olive" title="b2">J</font> being  <a href="scmnorm.html#NM2" title="SCMNORM:NM.2">Program</a> of <a href="scmpds_2.html#K1" title="SCMPDS_2:func.1">SCMPDS</a>  holds <br/> (  <a href="numbers.html#K6" title="NUMBERS:func.6">0</a>  <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="afinsq_1.html#K2" title="AFINSQ_1:func.2">dom</a> <span class="p1">(<span class="default"><a href="scmpds_6.html#K4" title="SCMPDS_6:func.4">if&lt;0</a> <font color="Maroon" title="c3">a</font>,<font color="Maroon" title="c4">k1</font>,<font color="Olive" title="b1">I</font>,<font color="Olive" title="b2">J</font></span>)</span> &amp; 1 <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="afinsq_1.html#K2" title="AFINSQ_1:func.2">dom</a> <span class="p1">(<span class="default"><a href="scmpds_6.html#K4" title="SCMPDS_6:func.4">if&lt;0</a> <font color="Maroon" title="c3">a</font>,<font color="Maroon" title="c4">k1</font>,<font color="Olive" title="b1">I</font>,<font color="Olive" title="b2">J</font></span>)</span> )</span><br/><span class="kw">let </span><font color="Maroon" title="c5">I</font>, <font color="Maroon" title="c6">J</font> be   <a href="scmnorm.html#NM2" title="SCMNORM:NM.2">Program</a> of <a href="scmpds_2.html#K1" title="SCMPDS_2:func.1">SCMPDS</a> ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> (  <a href="numbers.html#K6" title="NUMBERS:func.6">0</a>  <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="afinsq_1.html#K2" title="AFINSQ_1:func.2">dom</a> <span class="p1">(<span class="default"><a href="scmpds_6.html#K4" title="SCMPDS_6:func.4">if&lt;0</a> <font color="Maroon" title="c3">a</font>,<font color="Maroon" title="c4">k1</font>,<font color="Maroon" title="c5">I</font>,<font color="Maroon" title="c6">J</font></span>)</span> &amp; 1 <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="afinsq_1.html#K2" title="AFINSQ_1:func.2">dom</a> <span class="p1">(<span class="default"><a href="scmpds_6.html#K4" title="SCMPDS_6:func.4">if&lt;0</a> <font color="Maroon" title="c3">a</font>,<font color="Maroon" title="c4">k1</font>,<font color="Maroon" title="c5">I</font>,<font color="Maroon" title="c6">J</font></span>)</span> )</span><br/>







<span class="kw">set </span><font color="Maroon" title="c7">ci</font> =  <a href="card_1.html#K5" title="CARD_1:func.5">card</a> <span class="p1">(<span class="default"><a href="scmpds_6.html#K4" title="SCMPDS_6:func.4">if&lt;0</a> <font color="Maroon" title="c3">a</font>,<font color="Maroon" title="c4">k1</font>,<font color="Maroon" title="c5">I</font>,<font color="Maroon" title="c6">J</font></span>)</span>;<br/>
<a NAME="E1:120"/>
 <a href="card_1.html#K5" title="CARD_1:func.5">card</a> <span class="p1">(<span class="default"><a href="scmpds_6.html#K4" title="SCMPDS_6:func.4">if&lt;0</a> <font color="Maroon" title="c3">a</font>,<font color="Maroon" title="c4">k1</font>,<font color="Maroon" title="c5">I</font>,<font color="Maroon" title="c6">J</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="card_1.html#K5" title="CARD_1:func.5">card</a> <font color="Maroon" title="c5">I</font></span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> <span class="p2">(<span class="default"><a href="card_1.html#K5" title="CARD_1:func.5">card</a> <font color="Maroon" title="c6">J</font></span>)</span></span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 2
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="scmpds_6.html#E64"><span class="lab"><font color="Green" title="E45">Lm3</font></span></a></span>;<br/>
<a NAME="E2:120"/><span class="kw">then </span>
2 <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a>  <a href="card_1.html#K5" title="CARD_1:func.5">card</a> <span class="p1">(<span class="default"><a href="scmpds_6.html#K4" title="SCMPDS_6:func.4">if&lt;0</a> <font color="Maroon" title="c3">a</font>,<font color="Maroon" title="c4">k1</font>,<font color="Maroon" title="c5">I</font>,<font color="Maroon" title="c6">J</font></span>)</span>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="nat_1.html#T12" title="NAT_1:th.12">NAT_1:12</a></span>;<br/>
<a NAME="E3:120"/><span class="kw">then </span>
1 <a href="xxreal_0.html#NR3" title="XXREAL_0:NR.3">&lt;</a>  <a href="card_1.html#K5" title="CARD_1:func.5">card</a> <span class="p1">(<span class="default"><a href="scmpds_6.html#K4" title="SCMPDS_6:func.4">if&lt;0</a> <font color="Maroon" title="c3">a</font>,<font color="Maroon" title="c4">k1</font>,<font color="Maroon" title="c5">I</font>,<font color="Maroon" title="c6">J</font></span>)</span>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="xxreal_0.html#T2" title="XXREAL_0:th.2">XXREAL_0:2</a></span>;<br/>
<span class="kw">hence </span><a NAME="E4:120"/>
(  <a href="numbers.html#K6" title="NUMBERS:func.6">0</a>  <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="afinsq_1.html#K2" title="AFINSQ_1:func.2">dom</a> <span class="p1">(<span class="default"><a href="scmpds_6.html#K4" title="SCMPDS_6:func.4">if&lt;0</a> <font color="Maroon" title="c3">a</font>,<font color="Maroon" title="c4">k1</font>,<font color="Maroon" title="c5">I</font>,<font color="Maroon" title="c6">J</font></span>)</span> &amp; 1 <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="afinsq_1.html#K2" title="AFINSQ_1:func.2">dom</a> <span class="p1">(<span class="default"><a href="scmpds_6.html#K4" title="SCMPDS_6:func.4">if&lt;0</a> <font color="Maroon" title="c3">a</font>,<font color="Maroon" title="c4">k1</font>,<font color="Maroon" title="c5">I</font>,<font color="Maroon" title="c6">J</font></span>)</span> )
 <span class="kw">by</span> <span class="lab"><a class="ref" href="afinsq_1.html#T70" title="AFINSQ_1:th.70">AFINSQ_1:70</a></span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> verum</span><br/>


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