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<b>let </b><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:()"><i><font color="Red">::  thesis: </font></i></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="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="scmpds_3.html#K2" title="SCMPDS_3:func.2">inspos</a> <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#K3" title="SCPINVAR:func.3">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;  <a href="scmpds_3.html#K2" title="SCMPDS_3:func.2">inspos</a> 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#K3" title="SCPINVAR:func.3">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/><b>let </b><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:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> for <font color="Olive" title="b1">I</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="scmpds_3.html#K2" title="SCMPDS_3:func.2">inspos</a> <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#K3" title="SCPINVAR:func.3">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;  <a href="scmpds_3.html#K2" title="SCMPDS_3:func.2">inspos</a> 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#K3" title="SCPINVAR:func.3">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/><b>let </b><font color="Maroon" title="c19">I</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:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> (  <a href="scmpds_3.html#K2" title="SCMPDS_3:func.2">inspos</a> <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#K3" title="SCPINVAR:func.3">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;  <a href="scmpds_3.html#K2" title="SCMPDS_3:func.2">inspos</a> 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#K3" title="SCPINVAR:func.3">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="E1:24"/><i><font color="Green" title="E18">A1</font></i>: 
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
 
<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="E2:24"/><b>then </b><i><font color="Green" title="E19">A2</font></i>: 
 <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
 
<b>by </b><i><a class="ref" href="xxreal_0.html#T2" title="XXREAL_0:th.2">XXREAL_0:2</a></i>;<br/>
<a NAME="E3:24"/>
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
 
<b>by </b><i><a class="txt" href="#E1:24"><i><font color="Green" title="E18">A1</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="E4:24"/>
(  <a href="scmpds_3.html#K2" title="SCMPDS_3:func.2">inspos</a> <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#K3" title="SCPINVAR:func.3">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;  <a href="scmpds_3.html#K2" title="SCMPDS_3:func.2">inspos</a> 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#K3" title="SCPINVAR:func.3">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> )
 <b>by </b><i><a class="txt" href="#E2:24"><i><font color="Green" title="E19">A2</font></i></a>, <a class="ref" href="scpinvar.html#T13" target="_self" title="SCPINVAR:th.13">Th13</a></i>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> verum</span><br/>


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