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<span class="kw">let </span><font color="Maroon" title="c17">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="firebrick">::  thesis: </font></span></a><span class="hide">  for <font color="Olive" title="b1">i</font> being   <a href="int_1.html#NM1" title="INT_1:NM.1">Integer</a><br/>  for <font color="Olive" title="b2">I</font> being   <a href="compos_1.html#NM5" title="COMPOS_1:NM.5">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="relat_1.html#NK2" title="RELAT_1:NK.2">dom</a> <span class="p1">(<span class="default"><a href="scpinvar.html#K4" title="SCPINVAR:func.4">while&lt;&gt;0</a> (<font color="Maroon" title="c17">a</font>,<font color="Olive" title="b1">i</font>,<font color="Olive" title="b2">I</font>)</span>)</span> &amp; 1 <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="relat_1.html#NK2" title="RELAT_1:NK.2">dom</a> <span class="p1">(<span class="default"><a href="scpinvar.html#K4" title="SCPINVAR:func.4">while&lt;&gt;0</a> (<font color="Maroon" title="c17">a</font>,<font color="Olive" title="b1">i</font>,<font color="Olive" title="b2">I</font>)</span>)</span> )</span><br/><span class="kw">let </span><font color="Maroon" title="c18">i</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="firebrick">::  thesis: </font></span></a><span class="hide">  for <font color="Olive" title="b1">I</font> being   <a href="compos_1.html#NM5" title="COMPOS_1:NM.5">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="relat_1.html#NK2" title="RELAT_1:NK.2">dom</a> <span class="p1">(<span class="default"><a href="scpinvar.html#K4" title="SCPINVAR:func.4">while&lt;&gt;0</a> (<font color="Maroon" title="c17">a</font>,<font color="Maroon" title="c18">i</font>,<font color="Olive" title="b1">I</font>)</span>)</span> &amp; 1 <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="relat_1.html#NK2" title="RELAT_1:NK.2">dom</a> <span class="p1">(<span class="default"><a href="scpinvar.html#K4" title="SCPINVAR:func.4">while&lt;&gt;0</a> (<font color="Maroon" title="c17">a</font>,<font color="Maroon" title="c18">i</font>,<font color="Olive" title="b1">I</font>)</span>)</span> )</span><br/><span class="kw">let </span><font color="Maroon" title="c19">I</font> be   <a href="compos_1.html#NM5" title="COMPOS_1:NM.5">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="firebrick">::  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="relat_1.html#NK2" title="RELAT_1:NK.2">dom</a> <span class="p1">(<span class="default"><a href="scpinvar.html#K4" title="SCPINVAR:func.4">while&lt;&gt;0</a> (<font color="Maroon" title="c17">a</font>,<font color="Maroon" title="c18">i</font>,<font color="Maroon" title="c19">I</font>)</span>)</span> &amp; 1 <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="relat_1.html#NK2" title="RELAT_1:NK.2">dom</a> <span class="p1">(<span class="default"><a href="scpinvar.html#K4" title="SCPINVAR:func.4">while&lt;&gt;0</a> (<font color="Maroon" title="c17">a</font>,<font color="Maroon" title="c18">i</font>,<font color="Maroon" title="c19">I</font>)</span>)</span> )</span><br/>





<a NAME="E1:23"/>
3 <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> <span class="p1">(<span class="default"><a href="card_1.html#K5" title="CARD_1:func.5">card</a> <font color="Maroon" title="c19">I</font></span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 3
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="nat_1.html#T11" title="NAT_1:th.11">NAT_1:11</a></span>;<br/>
<a NAME="E2:23"/><span class="kw">then </span>
(  <a href="numbers.html#K6" title="NUMBERS:func.6">0</a>  <a href="xxreal_0.html#NR3" title="XXREAL_0:NR.3">&lt;</a> <span class="p1">(<span class="default"><a href="card_1.html#K5" title="CARD_1:func.5">card</a> <font color="Maroon" title="c19">I</font></span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 3 &amp; 1 <a href="xxreal_0.html#NR3" title="XXREAL_0:NR.3">&lt;</a> <span class="p1">(<span class="default"><a href="card_1.html#K5" title="CARD_1:func.5">card</a> <font color="Maroon" title="c19">I</font></span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 3 )
 
<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="E3:23"/>
(  <a href="numbers.html#K6" title="NUMBERS:func.6">0</a>  <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="relat_1.html#NK2" title="RELAT_1:NK.2">dom</a> <span class="p1">(<span class="default"><a href="scpinvar.html#K4" title="SCPINVAR:func.4">while&lt;&gt;0</a> (<font color="Maroon" title="c17">a</font>,<font color="Maroon" title="c18">i</font>,<font color="Maroon" title="c19">I</font>)</span>)</span> &amp; 1 <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="relat_1.html#NK2" title="RELAT_1:NK.2">dom</a> <span class="p1">(<span class="default"><a href="scpinvar.html#K4" title="SCPINVAR:func.4">while&lt;&gt;0</a> (<font color="Maroon" title="c17">a</font>,<font color="Maroon" title="c18">i</font>,<font color="Maroon" title="c19">I</font>)</span>)</span> )
 <span class="kw">by</span> <span class="lab"><a class="ref" href="scpinvar.html#T9" target="_self" title="SCPINVAR:th.9">Th13</a></span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> verum</span><br/>


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