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<b>let </b><font color="Maroon" title="c1">a</font> be    <a href="scmpds_2.html#M1" title="SCMPDS_2:mode.1">Int_position</a> ;<br/><b>let </b><font color="Maroon" title="c2">k1</font> be   <a href="int_1.html#NM1" title="INT_1:NM.1">Integer</a>;<br/>



<b>set </b><font color="Maroon" title="c3">k2</font> = 5;<br/>
<b>set </b><font color="Maroon" title="c4">i</font> = <font color="Maroon" title="c1">a</font>,<font color="Maroon" title="c2">k1</font> <a href="scmpds_2.html#K10" title="SCMPDS_2:func.10">&gt;=0_goto</a> 5;<br/>
<b>set </b><font color="Maroon" title="c5">X</font> = <span class="p1">{<span class="default"> <span class="p2">(<span class="default"><a href="amistd_1.html#K1" title="AMISTD_1:func.1">NIC</a> <span class="p3">(<span class="default"><font color="Maroon" title="c1">a</font>,<font color="Maroon" title="c2">k1</font> <a href="scmpds_2.html#K10" title="SCMPDS_2:func.10">&gt;=0_goto</a> 5</span>)</span>,<font color="Olive" title="b1">l</font></span>)</span> where <font color="Olive" title="b1">l</font> is    <a href="ami_1.html#M1" title="AMI_1:mode.1">Instruction-Location</a> of  <a href="scmpds_2.html#K1" title="SCMPDS_2:func.1">SCMPDS</a>  : verum </span>}</span> ;<br/>
<div><b>hereby </b> <i><font color="Red">:: according to </font></i><a class="ref" href="tarski.html#D3" title="TARSKI:def.3">TARSKI:def 3</a>,<a class="ref" href="xboole_0.html#D10" title="XBOOLE_0:def.10">XBOOLE_0:def 10</a>
<div class="add"><b>let </b><font color="Maroon" title="c6">x</font> be    <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a> ;<br/><b>assume </b><a NAME="E1:52_1"/><i><font color="Green" title="E38">A1</font></i>: 
<font color="Maroon" title="c6">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="amistd_1.html#K2" title="AMISTD_1:func.2">JUMP</a> <span class="p1">(<span class="default"><font color="Maroon" title="c1">a</font>,<font color="Maroon" title="c2">k1</font> <a href="scmpds_2.html#K10" title="SCMPDS_2:func.10">&gt;=0_goto</a> 5</span>)</span>
 ;<br/><b>set </b><font color="Maroon" title="c7">nl1</font> = 5;<br/><b>set </b><font color="Maroon" title="c8">nl2</font> = 8;<br/><b>set </b><font color="Maroon" title="c9">l1</font> =  <a href="scmpds_3.html#K2" title="SCMPDS_3:func.2">inspos</a> 5;<br/><a NAME="E2:52_1"/>
 <a href="amistd_1.html#K1" title="AMISTD_1:func.1">NIC</a> <span class="p1">(<span class="default"><font color="Maroon" title="c1">a</font>,<font color="Maroon" title="c2">k1</font> <a href="scmpds_2.html#K10" title="SCMPDS_2:func.10">&gt;=0_goto</a> 5</span>)</span>,<span class="p1">(<span class="default"><a href="scmpds_3.html#K2" title="SCMPDS_3:func.2">inspos</a> 5</span>)</span> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <span class="p1">{<span class="default"> <span class="p2">(<span class="default"><a href="amistd_1.html#K1" title="AMISTD_1:func.1">NIC</a> <span class="p3">(<span class="default"><font color="Maroon" title="c1">a</font>,<font color="Maroon" title="c2">k1</font> <a href="scmpds_2.html#K10" title="SCMPDS_2:func.10">&gt;=0_goto</a> 5</span>)</span>,<font color="Olive" title="b1">l</font></span>)</span> where <font color="Olive" title="b1">l</font> is    <a href="ami_1.html#M1" title="AMI_1:mode.1">Instruction-Location</a> of  <a href="scmpds_2.html#K1" title="SCMPDS_2:func.1">SCMPDS</a>  : verum </span>}</span> 
 ;<br/><a NAME="E3:52_1"/><b>then </b>
<font color="Maroon" title="c6">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="amistd_1.html#K1" title="AMISTD_1:func.1">NIC</a> <span class="p1">(<span class="default"><font color="Maroon" title="c1">a</font>,<font color="Maroon" title="c2">k1</font> <a href="scmpds_2.html#K10" title="SCMPDS_2:func.10">&gt;=0_goto</a> 5</span>)</span>,<span class="p1">(<span class="default"><a href="scmpds_3.html#K2" title="SCMPDS_3:func.2">inspos</a> 5</span>)</span>
 <b>by </b><i><a class="txt" href="scmpds_9.html#E1:52_1"><i><font color="Green" title="E38">A1</font></i></a>, <a class="ref" href="setfam_1.html#D1" title="SETFAM_1:def.1">SETFAM_1:def 1</a></i>;<br/><b>then consider </b><font color="Maroon" title="c10">s1</font> being   <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> <b> such that </b><br/><a NAME="E5:52_1"/><i><font color="Green" title="E39">A2</font></i>: 
<font color="Maroon" title="c6">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="ami_1.html#K6" title="AMI_1:func.6">IC</a> <span class="p1">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">Following</a> <font color="Maroon" title="c10">s1</font></span>)</span>
 <b>and </b><br/><a NAME="E6:52_1"/><i><font color="Green" title="E40">A3</font></i>: 
 <a href="ami_1.html#K6" title="AMI_1:func.6">IC</a> <font color="Maroon" title="c10">s1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="scmpds_3.html#K2" title="SCMPDS_3:func.2">inspos</a> 5
 <b>and </b><br/><a NAME="E7:52_1"/><i><font color="Green" title="E41">A4</font></i>: 
<font color="Maroon" title="c10">s1</font> <a href="ami_1.html#K12" title="AMI_1:func.12">.</a> <span class="p1">(<span class="default"><a href="scmpds_3.html#K2" title="SCMPDS_3:func.2">inspos</a> 5</span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c1">a</font>,<font color="Maroon" title="c2">k1</font> <a href="scmpds_2.html#K10" title="SCMPDS_2:func.10">&gt;=0_goto</a> 5
 ;<br/><b>consider </b><font color="Maroon" title="c11">m1</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="E9:52_1"/><i><font color="Green" title="E42">A5</font></i>: 
<font color="Maroon" title="c11">m1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="ami_1.html#K6" title="AMI_1:func.6">IC</a> <font color="Maroon" title="c10">s1</font>
 <b>and </b><br/><a NAME="E10:52_1"/><i><font color="Green" title="E43">A6</font></i>: 
 <a href="scmpds_2.html#K19" title="SCMPDS_2:func.19">ICplusConst</a> <font color="Maroon" title="c10">s1</font>,5 <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="int_2.html#K1" title="INT_2:func.1">abs</a> <span class="p1">(<span class="default"><font color="Maroon" title="c11">m1</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 5</span>)</span>
 <b>by </b><i><a class="ref" href="scmpds_2.html#D20" title="SCMPDS_2:def.20">SCMPDS_2:def 20</a></i>;<br/><i><font color="Green" title="E44">A7</font></i>: <font color="Maroon" title="c11">m1</font> = 
 <a href="ami_3.html#K13" title="AMI_3:func.13">il.</a> 5
<b>by </b><i><a class="txt" href="scmpds_9.html#E6:52_1"><i><font color="Green" title="E40">A3</font></i></a>, <a class="txt" href="scmpds_9.html#E9:52_1"><i><font color="Green" title="E42">A5</font></i></a>, <a class="ref" href="scmpds_3.html#D2" title="SCMPDS_3:def.2">SCMPDS_3:def 2</a></i>
<br/>.= 
5
<b>by </b><i><a class="ref" href="ami_3.html#D20" title="AMI_3:def.20">AMI_3:def 20</a></i>
;<br/><b>set </b><font color="Maroon" title="c12">l2</font> =  <a href="scmpds_3.html#K2" title="SCMPDS_3:func.2">inspos</a> 8;<br/><a NAME="E12:52_1"/>
 <a href="amistd_1.html#K1" title="AMISTD_1:func.1">NIC</a> <span class="p1">(<span class="default"><font color="Maroon" title="c1">a</font>,<font color="Maroon" title="c2">k1</font> <a href="scmpds_2.html#K10" title="SCMPDS_2:func.10">&gt;=0_goto</a> 5</span>)</span>,<span class="p1">(<span class="default"><a href="scmpds_3.html#K2" title="SCMPDS_3:func.2">inspos</a> 8</span>)</span> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <span class="p1">{<span class="default"> <span class="p2">(<span class="default"><a href="amistd_1.html#K1" title="AMISTD_1:func.1">NIC</a> <span class="p3">(<span class="default"><font color="Maroon" title="c1">a</font>,<font color="Maroon" title="c2">k1</font> <a href="scmpds_2.html#K10" title="SCMPDS_2:func.10">&gt;=0_goto</a> 5</span>)</span>,<font color="Olive" title="b1">l</font></span>)</span> where <font color="Olive" title="b1">l</font> is    <a href="ami_1.html#M1" title="AMI_1:mode.1">Instruction-Location</a> of  <a href="scmpds_2.html#K1" title="SCMPDS_2:func.1">SCMPDS</a>  : verum </span>}</span> 
 ;<br/><a NAME="E13:52_1"/><b>then </b>
<font color="Maroon" title="c6">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="amistd_1.html#K1" title="AMISTD_1:func.1">NIC</a> <span class="p1">(<span class="default"><font color="Maroon" title="c1">a</font>,<font color="Maroon" title="c2">k1</font> <a href="scmpds_2.html#K10" title="SCMPDS_2:func.10">&gt;=0_goto</a> 5</span>)</span>,<span class="p1">(<span class="default"><a href="scmpds_3.html#K2" title="SCMPDS_3:func.2">inspos</a> 8</span>)</span>
 <b>by </b><i><a class="txt" href="scmpds_9.html#E1:52_1"><i><font color="Green" title="E38">A1</font></i></a>, <a class="ref" href="setfam_1.html#D1" title="SETFAM_1:def.1">SETFAM_1:def 1</a></i>;<br/><b>then consider </b><font color="Maroon" title="c13">s2</font> being   <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> <b> such that </b><br/><a NAME="E15:52_1"/><i><font color="Green" title="E45">A8</font></i>: 
<font color="Maroon" title="c6">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="ami_1.html#K6" title="AMI_1:func.6">IC</a> <span class="p1">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">Following</a> <font color="Maroon" title="c13">s2</font></span>)</span>
 <b>and </b><br/><a NAME="E16:52_1"/><i><font color="Green" title="E46">A9</font></i>: 
 <a href="ami_1.html#K6" title="AMI_1:func.6">IC</a> <font color="Maroon" title="c13">s2</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="scmpds_3.html#K2" title="SCMPDS_3:func.2">inspos</a> 8
 <b>and </b><br/><a NAME="E17:52_1"/><i><font color="Green" title="E47">A10</font></i>: 
<font color="Maroon" title="c13">s2</font> <a href="ami_1.html#K12" title="AMI_1:func.12">.</a> <span class="p1">(<span class="default"><a href="scmpds_3.html#K2" title="SCMPDS_3:func.2">inspos</a> 8</span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c1">a</font>,<font color="Maroon" title="c2">k1</font> <a href="scmpds_2.html#K10" title="SCMPDS_2:func.10">&gt;=0_goto</a> 5
 ;<br/><b>consider </b><font color="Maroon" title="c14">m2</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="E19:52_1"/><i><font color="Green" title="E48">A11</font></i>: 
<font color="Maroon" title="c14">m2</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="ami_1.html#K6" title="AMI_1:func.6">IC</a> <font color="Maroon" title="c13">s2</font>
 <b>and </b><br/><a NAME="E20:52_1"/><i><font color="Green" title="E49">A12</font></i>: 
 <a href="scmpds_2.html#K19" title="SCMPDS_2:func.19">ICplusConst</a> <font color="Maroon" title="c13">s2</font>,5 <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="int_2.html#K1" title="INT_2:func.1">abs</a> <span class="p1">(<span class="default"><font color="Maroon" title="c14">m2</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 5</span>)</span>
 <b>by </b><i><a class="ref" href="scmpds_2.html#D20" title="SCMPDS_2:def.20">SCMPDS_2:def 20</a></i>;<br/><i><font color="Green" title="E50">A13</font></i>: <font color="Maroon" title="c14">m2</font> = 
 <a href="ami_3.html#K13" title="AMI_3:func.13">il.</a> 8
<b>by </b><i><a class="txt" href="scmpds_9.html#E16:52_1"><i><font color="Green" title="E46">A9</font></i></a>, <a class="txt" href="scmpds_9.html#E19:52_1"><i><font color="Green" title="E48">A11</font></i></a>, <a class="ref" href="scmpds_3.html#D2" title="SCMPDS_3:def.2">SCMPDS_3:def 2</a></i>
<br/>.= 
8
<b>by </b><i><a class="ref" href="ami_3.html#D20" title="AMI_3:def.20">AMI_3:def 20</a></i>
;<br/><a NAME="E22:52_1"/><i><font color="Green" title="E51">A14</font></i>: 
 <a href="scmpds_3.html#K2" title="SCMPDS_3:func.2">inspos</a> 5 <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a>  <a href="scmpds_3.html#K2" title="SCMPDS_3:func.2">inspos</a> 8
 <b>by </b><i><a class="ref" href="scmpds_3.html#T31" title="SCMPDS_3:th.31">SCMPDS_3:31</a></i>;<br/><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="52_1_3"><b>per </b></a><a class="txt" onclick="hs(this)" href="javascript:()"><b>cases </b></a><span class="hide"><a NAME="E1:52_1_3"/>
( ( <font color="Maroon" title="c10">s1</font> <a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">.</a> <span class="p1">(<span class="default"><a href="scmpds_2.html#K3" title="SCMPDS_2:func.3">DataLoc</a> <span class="p2">(<span class="default"><font color="Maroon" title="c10">s1</font> <a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">.</a> <font color="Maroon" title="c1">a</font></span>)</span>,<font color="Maroon" title="c2">k1</font></span>)</span> <a href="xxreal_0.html#NR2" title="XXREAL_0:NR.2">&gt;=</a>  <a href="numbers.html#K6" title="NUMBERS:func.6">0</a>  &amp; <font color="Maroon" title="c13">s2</font> <a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">.</a> <span class="p1">(<span class="default"><a href="scmpds_2.html#K3" title="SCMPDS_2:func.3">DataLoc</a> <span class="p2">(<span class="default"><font color="Maroon" title="c13">s2</font> <a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">.</a> <font color="Maroon" title="c1">a</font></span>)</span>,<font color="Maroon" title="c2">k1</font></span>)</span> <a href="xxreal_0.html#NR2" title="XXREAL_0:NR.2">&gt;=</a>  <a href="numbers.html#K6" title="NUMBERS:func.6">0</a>  ) or ( <font color="Maroon" title="c10">s1</font> <a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">.</a> <span class="p1">(<span class="default"><a href="scmpds_2.html#K3" title="SCMPDS_2:func.3">DataLoc</a> <span class="p2">(<span class="default"><font color="Maroon" title="c10">s1</font> <a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">.</a> <font color="Maroon" title="c1">a</font></span>)</span>,<font color="Maroon" title="c2">k1</font></span>)</span> <a href="xxreal_0.html#NR3" title="XXREAL_0:NR.3">&lt;</a>  <a href="numbers.html#K6" title="NUMBERS:func.6">0</a>  &amp; <font color="Maroon" title="c13">s2</font> <a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">.</a> <span class="p1">(<span class="default"><a href="scmpds_2.html#K3" title="SCMPDS_2:func.3">DataLoc</a> <span class="p2">(<span class="default"><font color="Maroon" title="c13">s2</font> <a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">.</a> <font color="Maroon" title="c1">a</font></span>)</span>,<font color="Maroon" title="c2">k1</font></span>)</span> <a href="xxreal_0.html#NR3" title="XXREAL_0:NR.3">&lt;</a>  <a href="numbers.html#K6" title="NUMBERS:func.6">0</a>  ) or ( <font color="Maroon" title="c10">s1</font> <a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">.</a> <span class="p1">(<span class="default"><a href="scmpds_2.html#K3" title="SCMPDS_2:func.3">DataLoc</a> <span class="p2">(<span class="default"><font color="Maroon" title="c10">s1</font> <a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">.</a> <font color="Maroon" title="c1">a</font></span>)</span>,<font color="Maroon" title="c2">k1</font></span>)</span> <a href="xxreal_0.html#NR3" title="XXREAL_0:NR.3">&lt;</a>  <a href="numbers.html#K6" title="NUMBERS:func.6">0</a>  &amp; <font color="Maroon" title="c13">s2</font> <a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">.</a> <span class="p1">(<span class="default"><a href="scmpds_2.html#K3" title="SCMPDS_2:func.3">DataLoc</a> <span class="p2">(<span class="default"><font color="Maroon" title="c13">s2</font> <a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">.</a> <font color="Maroon" title="c1">a</font></span>)</span>,<font color="Maroon" title="c2">k1</font></span>)</span> <a href="xxreal_0.html#NR2" title="XXREAL_0:NR.2">&gt;=</a>  <a href="numbers.html#K6" title="NUMBERS:func.6">0</a>  ) or ( <font color="Maroon" title="c10">s1</font> <a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">.</a> <span class="p1">(<span class="default"><a href="scmpds_2.html#K3" title="SCMPDS_2:func.3">DataLoc</a> <span class="p2">(<span class="default"><font color="Maroon" title="c10">s1</font> <a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">.</a> <font color="Maroon" title="c1">a</font></span>)</span>,<font color="Maroon" title="c2">k1</font></span>)</span> <a href="xxreal_0.html#NR2" title="XXREAL_0:NR.2">&gt;=</a>  <a href="numbers.html#K6" title="NUMBERS:func.6">0</a>  &amp; <font color="Maroon" title="c13">s2</font> <a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">.</a> <span class="p1">(<span class="default"><a href="scmpds_2.html#K3" title="SCMPDS_2:func.3">DataLoc</a> <span class="p2">(<span class="default"><font color="Maroon" title="c13">s2</font> <a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">.</a> <font color="Maroon" title="c1">a</font></span>)</span>,<font color="Maroon" title="c2">k1</font></span>)</span> <a href="xxreal_0.html#NR3" title="XXREAL_0:NR.3">&lt;</a>  <a href="numbers.html#K6" title="NUMBERS:func.6">0</a>  ) )
 </span>;<br/><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="52_1_3_1"><b>suppose </b></a><b>that </b><a NAME="E1:52_1_3_1"/><i><font color="Green" title="E52">A15</font></i>: 
<font color="Maroon" title="c10">s1</font> <a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">.</a> <span class="p1">(<span class="default"><a href="scmpds_2.html#K3" title="SCMPDS_2:func.3">DataLoc</a> <span class="p2">(<span class="default"><font color="Maroon" title="c10">s1</font> <a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">.</a> <font color="Maroon" title="c1">a</font></span>)</span>,<font color="Maroon" title="c2">k1</font></span>)</span> <a href="xxreal_0.html#NR2" title="XXREAL_0:NR.2">&gt;=</a>  <a href="numbers.html#K6" title="NUMBERS:func.6">0</a> 
 <b>and </b><br/><a NAME="E2:52_1_3_1"/><i><font color="Green" title="E53">A16</font></i>: 
<font color="Maroon" title="c13">s2</font> <a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">.</a> <span class="p1">(<span class="default"><a href="scmpds_2.html#K3" title="SCMPDS_2:func.3">DataLoc</a> <span class="p2">(<span class="default"><font color="Maroon" title="c13">s2</font> <a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">.</a> <font color="Maroon" title="c1">a</font></span>)</span>,<font color="Maroon" title="c2">k1</font></span>)</span> <a href="xxreal_0.html#NR2" title="XXREAL_0:NR.2">&gt;=</a>  <a href="numbers.html#K6" title="NUMBERS:func.6">0</a> 
 ;<br/><div class="add"><i><font color="Green" title="E54">A17</font></i>: <font color="Maroon" title="c6">x</font> = 
<span class="p1">(<span class="default"><a href="ami_1.html#K4" title="AMI_1:func.4">Exec</a> <span class="p2">(<span class="default"><font color="Maroon" title="c1">a</font>,<font color="Maroon" title="c2">k1</font> <a href="scmpds_2.html#K10" title="SCMPDS_2:func.10">&gt;=0_goto</a> 5</span>)</span>,<font color="Maroon" title="c10">s1</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p1">(<span class="default"><a href="ami_1.html#K2" title="AMI_1:func.2">IC</a> <a href="scmpds_2.html#K1" title="SCMPDS_2:func.1">SCMPDS</a> </span>)</span>
<b>by </b><i><a class="txt" href="scmpds_9.html#E5:52_1"><i><font color="Green" title="E39">A2</font></i></a>, <a class="txt" href="scmpds_9.html#E6:52_1"><i><font color="Green" title="E40">A3</font></i></a>, <a class="txt" href="scmpds_9.html#E7:52_1"><i><font color="Green" title="E41">A4</font></i></a>, <a class="txt" href="scmpds_9.html#E6"><i><font color="Green" title="E6">Lm1</font></i></a></i>
<br/>.= 
 <a href="int_2.html#K1" title="INT_2:func.1">abs</a> <span class="p1">(<span class="default"><font color="Maroon" title="c11">m1</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 5</span>)</span>
<b>by </b><i><a class="txt" href="scmpds_9.html#E10:52_1"><i><font color="Green" title="E43">A6</font></i></a>, <a class="txt" href="scmpds_9.html#E1:52_1_3_1"><i><font color="Green" title="E52">A15</font></i></a>, <a class="ref" href="scmpds_2.html#T69" title="SCMPDS_2:th.69">SCMPDS_2:69</a></i>
;<br/><font color="Maroon" title="c6">x</font> = 
<span class="p1">(<span class="default"><a href="ami_1.html#K4" title="AMI_1:func.4">Exec</a> <span class="p2">(<span class="default"><font color="Maroon" title="c1">a</font>,<font color="Maroon" title="c2">k1</font> <a href="scmpds_2.html#K10" title="SCMPDS_2:func.10">&gt;=0_goto</a> 5</span>)</span>,<font color="Maroon" title="c13">s2</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p1">(<span class="default"><a href="ami_1.html#K2" title="AMI_1:func.2">IC</a> <a href="scmpds_2.html#K1" title="SCMPDS_2:func.1">SCMPDS</a> </span>)</span>
<b>by </b><i><a class="txt" href="scmpds_9.html#E15:52_1"><i><font color="Green" title="E45">A8</font></i></a>, <a class="txt" href="scmpds_9.html#E16:52_1"><i><font color="Green" title="E46">A9</font></i></a>, <a class="txt" href="scmpds_9.html#E17:52_1"><i><font color="Green" title="E47">A10</font></i></a>, <a class="txt" href="scmpds_9.html#E6"><i><font color="Green" title="E6">Lm1</font></i></a></i>
<br/>.= 
 <a href="int_2.html#K1" title="INT_2:func.1">abs</a> <span class="p1">(<span class="default"><font color="Maroon" title="c14">m2</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 5</span>)</span>
<b>by </b><i><a class="txt" href="scmpds_9.html#E20:52_1"><i><font color="Green" title="E49">A12</font></i></a>, <a class="txt" href="scmpds_9.html#E2:52_1_3_1"><i><font color="Green" title="E53">A16</font></i></a>, <a class="ref" href="scmpds_2.html#T69" title="SCMPDS_2:th.69">SCMPDS_2:69</a></i>
;<br/><a NAME="E5:52_1_3_1"/><b>then </b>
( <span class="p1">(<span class="default"><span class="p2">(<span class="default">5 <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 2</span>)</span> <a href="xcmplx_0.html#K6" title="XCMPLX_0:func.6">-</a> 2</span>)</span> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> 5 <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default">8 <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 2</span>)</span> <a href="xcmplx_0.html#K6" title="XCMPLX_0:func.6">-</a> 2</span>)</span> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> 5 or <span class="p1">(<span class="default"><span class="p2">(<span class="default">5 <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 2</span>)</span> <a href="xcmplx_0.html#K6" title="XCMPLX_0:func.6">-</a> 2</span>)</span> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> 5 <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="xcmplx_0.html#K4" title="XCMPLX_0:func.4">-</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default">8 <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 2</span>)</span> <a href="xcmplx_0.html#K6" title="XCMPLX_0:func.6">-</a> 2</span>)</span> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> 5</span>)</span> )
 <b>by </b><i><a class="txt" href="scmpds_9.html#E11:52_1"><i><font color="Green" title="E44">A7</font></i></a>, <a class="txt" href="scmpds_9.html#E21:52_1"><i><font color="Green" title="E50">A13</font></i></a>, <a class="txt" href="scmpds_9.html#E3:52_1_3_1"><i><font color="Green" title="E54">A17</font></i></a>, <a class="ref" href="scmpds_9.html#T3" target="_self" title="SCMPDS_9:th.3">Th3</a></i>;<br/><b>hence </b><a NAME="E6:52_1_3_1"/>
<font color="Maroon" title="c6">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a> 
 ;<br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="52_1_3_2"><b>suppose </b></a><b>that </b><a NAME="E1:52_1_3_2"/><i><font color="Green" title="E52">A18</font></i>: 
<font color="Maroon" title="c10">s1</font> <a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">.</a> <span class="p1">(<span class="default"><a href="scmpds_2.html#K3" title="SCMPDS_2:func.3">DataLoc</a> <span class="p2">(<span class="default"><font color="Maroon" title="c10">s1</font> <a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">.</a> <font color="Maroon" title="c1">a</font></span>)</span>,<font color="Maroon" title="c2">k1</font></span>)</span> <a href="xxreal_0.html#NR3" title="XXREAL_0:NR.3">&lt;</a>  <a href="numbers.html#K6" title="NUMBERS:func.6">0</a> 
 <b>and </b><br/><a NAME="E2:52_1_3_2"/><i><font color="Green" title="E53">A19</font></i>: 
<font color="Maroon" title="c13">s2</font> <a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">.</a> <span class="p1">(<span class="default"><a href="scmpds_2.html#K3" title="SCMPDS_2:func.3">DataLoc</a> <span class="p2">(<span class="default"><font color="Maroon" title="c13">s2</font> <a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">.</a> <font color="Maroon" title="c1">a</font></span>)</span>,<font color="Maroon" title="c2">k1</font></span>)</span> <a href="xxreal_0.html#NR3" title="XXREAL_0:NR.3">&lt;</a>  <a href="numbers.html#K6" title="NUMBERS:func.6">0</a> 
 ;<br/><div class="add"><i><font color="Green" title="E54">A20</font></i>: <font color="Maroon" title="c6">x</font> = 
<span class="p1">(<span class="default"><a href="ami_1.html#K4" title="AMI_1:func.4">Exec</a> <span class="p2">(<span class="default"><font color="Maroon" title="c1">a</font>,<font color="Maroon" title="c2">k1</font> <a href="scmpds_2.html#K10" title="SCMPDS_2:func.10">&gt;=0_goto</a> 5</span>)</span>,<font color="Maroon" title="c10">s1</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p1">(<span class="default"><a href="ami_1.html#K2" title="AMI_1:func.2">IC</a> <a href="scmpds_2.html#K1" title="SCMPDS_2:func.1">SCMPDS</a> </span>)</span>
<b>by </b><i><a class="txt" href="scmpds_9.html#E5:52_1"><i><font color="Green" title="E39">A2</font></i></a>, <a class="txt" href="scmpds_9.html#E6:52_1"><i><font color="Green" title="E40">A3</font></i></a>, <a class="txt" href="scmpds_9.html#E7:52_1"><i><font color="Green" title="E41">A4</font></i></a>, <a class="txt" href="scmpds_9.html#E6"><i><font color="Green" title="E6">Lm1</font></i></a></i>
<br/>.= 
 <a href="scmpds_2.html#K18" title="SCMPDS_2:func.18">Next</a> <span class="p1">(<span class="default"><a href="scmpds_3.html#K2" title="SCMPDS_3:func.2">inspos</a> 5</span>)</span>
<b>by </b><i><a class="txt" href="scmpds_9.html#E6:52_1"><i><font color="Green" title="E40">A3</font></i></a>, <a class="txt" href="scmpds_9.html#E1:52_1_3_2"><i><font color="Green" title="E52">A18</font></i></a>, <a class="ref" href="scmpds_2.html#T69" title="SCMPDS_2:th.69">SCMPDS_2:69</a></i>
;<br/><font color="Maroon" title="c6">x</font> = 
<span class="p1">(<span class="default"><a href="ami_1.html#K4" title="AMI_1:func.4">Exec</a> <span class="p2">(<span class="default"><font color="Maroon" title="c1">a</font>,<font color="Maroon" title="c2">k1</font> <a href="scmpds_2.html#K10" title="SCMPDS_2:func.10">&gt;=0_goto</a> 5</span>)</span>,<font color="Maroon" title="c13">s2</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p1">(<span class="default"><a href="ami_1.html#K2" title="AMI_1:func.2">IC</a> <a href="scmpds_2.html#K1" title="SCMPDS_2:func.1">SCMPDS</a> </span>)</span>
<b>by </b><i><a class="txt" href="scmpds_9.html#E15:52_1"><i><font color="Green" title="E45">A8</font></i></a>, <a class="txt" href="scmpds_9.html#E16:52_1"><i><font color="Green" title="E46">A9</font></i></a>, <a class="txt" href="scmpds_9.html#E17:52_1"><i><font color="Green" title="E47">A10</font></i></a>, <a class="txt" href="scmpds_9.html#E6"><i><font color="Green" title="E6">Lm1</font></i></a></i>
<br/>.= 
 <a href="scmpds_2.html#K18" title="SCMPDS_2:func.18">Next</a> <span class="p1">(<span class="default"><a href="scmpds_3.html#K2" title="SCMPDS_3:func.2">inspos</a> 8</span>)</span>
<b>by </b><i><a class="txt" href="scmpds_9.html#E16:52_1"><i><font color="Green" title="E46">A9</font></i></a>, <a class="txt" href="scmpds_9.html#E2:52_1_3_2"><i><font color="Green" title="E53">A19</font></i></a>, <a class="ref" href="scmpds_2.html#T69" title="SCMPDS_2:th.69">SCMPDS_2:69</a></i>
;<br/><b>hence </b><a NAME="E5:52_1_3_2"/>
<font color="Maroon" title="c6">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a> 
 <b>by </b><i><a class="txt" href="scmpds_9.html#E22:52_1"><i><font color="Green" title="E51">A14</font></i></a>, <a class="txt" href="scmpds_9.html#E3:52_1_3_2"><i><font color="Green" title="E54">A20</font></i></a>, <a class="ref" href="scmpds_9.html#T10" target="_self" title="SCMPDS_9:th.10">Th10</a></i>;<br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="52_1_3_3"><b>suppose </b></a><b>that </b><a NAME="E1:52_1_3_3"/><i><font color="Green" title="E52">A21</font></i>: 
<font color="Maroon" title="c10">s1</font> <a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">.</a> <span class="p1">(<span class="default"><a href="scmpds_2.html#K3" title="SCMPDS_2:func.3">DataLoc</a> <span class="p2">(<span class="default"><font color="Maroon" title="c10">s1</font> <a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">.</a> <font color="Maroon" title="c1">a</font></span>)</span>,<font color="Maroon" title="c2">k1</font></span>)</span> <a href="xxreal_0.html#NR3" title="XXREAL_0:NR.3">&lt;</a>  <a href="numbers.html#K6" title="NUMBERS:func.6">0</a> 
 <b>and </b><br/><a NAME="E2:52_1_3_3"/><i><font color="Green" title="E53">A22</font></i>: 
<font color="Maroon" title="c13">s2</font> <a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">.</a> <span class="p1">(<span class="default"><a href="scmpds_2.html#K3" title="SCMPDS_2:func.3">DataLoc</a> <span class="p2">(<span class="default"><font color="Maroon" title="c13">s2</font> <a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">.</a> <font color="Maroon" title="c1">a</font></span>)</span>,<font color="Maroon" title="c2">k1</font></span>)</span> <a href="xxreal_0.html#NR2" title="XXREAL_0:NR.2">&gt;=</a>  <a href="numbers.html#K6" title="NUMBERS:func.6">0</a> 
 ;<br/><div class="add"><b>consider </b><font color="Maroon" title="c15">n1</font> being    <a href="subset_1.html#M2" title="SUBSET_1:mode.2">Element</a> of  <a href="ami_2.html#K6" title="AMI_2:func.6">SCM-Instr-Loc</a> <b> such that </b><br/><a NAME="E4:52_1_3_3"/><i><font color="Green" title="E54">A23</font></i>: 
( <font color="Maroon" title="c15">n1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="scmpds_3.html#K2" title="SCMPDS_3:func.2">inspos</a> 5 &amp;  <a href="scmpds_2.html#K18" title="SCMPDS_2:func.18">Next</a> <span class="p1">(<span class="default"><a href="scmpds_3.html#K2" title="SCMPDS_3:func.2">inspos</a> 5</span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="ami_2.html#K18" title="AMI_2:func.18">Next</a> <font color="Maroon" title="c15">n1</font> )
 <b>by </b><i><a class="ref" href="scmpds_2.html#D19" title="SCMPDS_2:def.19">SCMPDS_2:def 19</a></i>;<br/><b>consider </b><font color="Maroon" title="c16">w1</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="E6:52_1_3_3"/><i><font color="Green" title="E55">A24</font></i>: 
<font color="Maroon" title="c15">n1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c16">w1</font>
 <b>by </b><i><a class="ref" href="scmpds_2.html#T1" title="SCMPDS_2:th.1">SCMPDS_2:1</a></i>;<br/><i><font color="Green" title="E56">A25</font></i>: <font color="Maroon" title="c6">x</font> = 
<span class="p1">(<span class="default"><a href="ami_1.html#K4" title="AMI_1:func.4">Exec</a> <span class="p2">(<span class="default"><font color="Maroon" title="c1">a</font>,<font color="Maroon" title="c2">k1</font> <a href="scmpds_2.html#K10" title="SCMPDS_2:func.10">&gt;=0_goto</a> 5</span>)</span>,<font color="Maroon" title="c10">s1</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p1">(<span class="default"><a href="ami_1.html#K2" title="AMI_1:func.2">IC</a> <a href="scmpds_2.html#K1" title="SCMPDS_2:func.1">SCMPDS</a> </span>)</span>
<b>by </b><i><a class="txt" href="scmpds_9.html#E5:52_1"><i><font color="Green" title="E39">A2</font></i></a>, <a class="txt" href="scmpds_9.html#E6:52_1"><i><font color="Green" title="E40">A3</font></i></a>, <a class="txt" href="scmpds_9.html#E7:52_1"><i><font color="Green" title="E41">A4</font></i></a>, <a class="txt" href="scmpds_9.html#E6"><i><font color="Green" title="E6">Lm1</font></i></a></i>
<br/>.= 
 <a href="ami_2.html#K18" title="AMI_2:func.18">Next</a> <font color="Maroon" title="c15">n1</font>
<b>by </b><i><a class="txt" href="scmpds_9.html#E6:52_1"><i><font color="Green" title="E40">A3</font></i></a>, <a class="txt" href="scmpds_9.html#E1:52_1_3_3"><i><font color="Green" title="E52">A21</font></i></a>, <a class="txt" href="scmpds_9.html#E4:52_1_3_3"><i><font color="Green" title="E54">A23</font></i></a>, <a class="ref" href="scmpds_2.html#T69" title="SCMPDS_2:th.69">SCMPDS_2:69</a></i>
<br/>.= 
<font color="Maroon" title="c15">n1</font> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1
<b>by </b><i><a class="ref" href="ami_2.html#D15" title="AMI_2:def.15">AMI_2:def 15</a></i>
;<br/><font color="Maroon" title="c6">x</font> = 
<span class="p1">(<span class="default"><a href="ami_1.html#K4" title="AMI_1:func.4">Exec</a> <span class="p2">(<span class="default"><font color="Maroon" title="c1">a</font>,<font color="Maroon" title="c2">k1</font> <a href="scmpds_2.html#K10" title="SCMPDS_2:func.10">&gt;=0_goto</a> 5</span>)</span>,<font color="Maroon" title="c13">s2</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p1">(<span class="default"><a href="ami_1.html#K2" title="AMI_1:func.2">IC</a> <a href="scmpds_2.html#K1" title="SCMPDS_2:func.1">SCMPDS</a> </span>)</span>
<b>by </b><i><a class="txt" href="scmpds_9.html#E15:52_1"><i><font color="Green" title="E45">A8</font></i></a>, <a class="txt" href="scmpds_9.html#E16:52_1"><i><font color="Green" title="E46">A9</font></i></a>, <a class="txt" href="scmpds_9.html#E17:52_1"><i><font color="Green" title="E47">A10</font></i></a>, <a class="txt" href="scmpds_9.html#E6"><i><font color="Green" title="E6">Lm1</font></i></a></i>
<br/>.= 
 <a href="int_2.html#K1" title="INT_2:func.1">abs</a> <span class="p1">(<span class="default"><font color="Maroon" title="c14">m2</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 5</span>)</span>
<b>by </b><i><a class="txt" href="scmpds_9.html#E20:52_1"><i><font color="Green" title="E49">A12</font></i></a>, <a class="txt" href="scmpds_9.html#E2:52_1_3_3"><i><font color="Green" title="E53">A22</font></i></a>, <a class="ref" href="scmpds_2.html#T69" title="SCMPDS_2:th.69">SCMPDS_2:69</a></i>
;<br/><a NAME="E9:52_1_3_3"/><b>then </b>
( <font color="Maroon" title="c16">w1</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1 <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c14">m2</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 5 or <font color="Maroon" title="c16">w1</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1 <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="xcmplx_0.html#K4" title="XCMPLX_0:func.4">-</a> <span class="p1">(<span class="default"><font color="Maroon" title="c14">m2</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 5</span>)</span> )
 <b>by </b><i><a class="txt" href="scmpds_9.html#E6:52_1_3_3"><i><font color="Green" title="E55">A24</font></i></a>, <a class="txt" href="scmpds_9.html#E7:52_1_3_3"><i><font color="Green" title="E56">A25</font></i></a>, <a class="ref" href="absvalue.html#T1" title="ABSVALUE:th.1">ABSVALUE:1</a></i>;<br/><b>hence </b><a NAME="E10:52_1_3_3"/>
<font color="Maroon" title="c6">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a> 
 <b>by </b><i><a class="txt" href="scmpds_9.html#E6:52_1"><i><font color="Green" title="E40">A3</font></i></a>, <a class="txt" href="scmpds_9.html#E9:52_1"><i><font color="Green" title="E42">A5</font></i></a>, <a class="txt" href="scmpds_9.html#E11:52_1"><i><font color="Green" title="E44">A7</font></i></a>, <a class="txt" href="scmpds_9.html#E21:52_1"><i><font color="Green" title="E50">A13</font></i></a>, <a class="txt" href="scmpds_9.html#E4:52_1_3_3"><i><font color="Green" title="E54">A23</font></i></a>, <a class="txt" href="scmpds_9.html#E6:52_1_3_3"><i><font color="Green" title="E55">A24</font></i></a></i>;<br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="52_1_3_4"><b>suppose </b></a><b>that </b><a NAME="E1:52_1_3_4"/><i><font color="Green" title="E52">A26</font></i>: 
<font color="Maroon" title="c10">s1</font> <a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">.</a> <span class="p1">(<span class="default"><a href="scmpds_2.html#K3" title="SCMPDS_2:func.3">DataLoc</a> <span class="p2">(<span class="default"><font color="Maroon" title="c10">s1</font> <a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">.</a> <font color="Maroon" title="c1">a</font></span>)</span>,<font color="Maroon" title="c2">k1</font></span>)</span> <a href="xxreal_0.html#NR2" title="XXREAL_0:NR.2">&gt;=</a>  <a href="numbers.html#K6" title="NUMBERS:func.6">0</a> 
 <b>and </b><br/><a NAME="E2:52_1_3_4"/><i><font color="Green" title="E53">A27</font></i>: 
<font color="Maroon" title="c13">s2</font> <a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">.</a> <span class="p1">(<span class="default"><a href="scmpds_2.html#K3" title="SCMPDS_2:func.3">DataLoc</a> <span class="p2">(<span class="default"><font color="Maroon" title="c13">s2</font> <a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">.</a> <font color="Maroon" title="c1">a</font></span>)</span>,<font color="Maroon" title="c2">k1</font></span>)</span> <a href="xxreal_0.html#NR3" title="XXREAL_0:NR.3">&lt;</a>  <a href="numbers.html#K6" title="NUMBERS:func.6">0</a> 
 ;<br/><div class="add"><b>consider </b><font color="Maroon" title="c15">n2</font> being    <a href="subset_1.html#M2" title="SUBSET_1:mode.2">Element</a> of  <a href="ami_2.html#K6" title="AMI_2:func.6">SCM-Instr-Loc</a> <b> such that </b><br/><a NAME="E4:52_1_3_4"/><i><font color="Green" title="E54">A28</font></i>: 
( <font color="Maroon" title="c15">n2</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="scmpds_3.html#K2" title="SCMPDS_3:func.2">inspos</a> 8 &amp;  <a href="scmpds_2.html#K18" title="SCMPDS_2:func.18">Next</a> <span class="p1">(<span class="default"><a href="scmpds_3.html#K2" title="SCMPDS_3:func.2">inspos</a> 8</span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="ami_2.html#K18" title="AMI_2:func.18">Next</a> <font color="Maroon" title="c15">n2</font> )
 <b>by </b><i><a class="ref" href="scmpds_2.html#D19" title="SCMPDS_2:def.19">SCMPDS_2:def 19</a></i>;<br/><b>consider </b><font color="Maroon" title="c16">w2</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="E6:52_1_3_4"/><i><font color="Green" title="E55">A29</font></i>: 
<font color="Maroon" title="c15">n2</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c16">w2</font>
 <b>by </b><i><a class="ref" href="scmpds_2.html#T1" title="SCMPDS_2:th.1">SCMPDS_2:1</a></i>;<br/><i><font color="Green" title="E56">A30</font></i>: <font color="Maroon" title="c6">x</font> = 
<span class="p1">(<span class="default"><a href="ami_1.html#K4" title="AMI_1:func.4">Exec</a> <span class="p2">(<span class="default"><font color="Maroon" title="c1">a</font>,<font color="Maroon" title="c2">k1</font> <a href="scmpds_2.html#K10" title="SCMPDS_2:func.10">&gt;=0_goto</a> 5</span>)</span>,<font color="Maroon" title="c10">s1</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p1">(<span class="default"><a href="ami_1.html#K2" title="AMI_1:func.2">IC</a> <a href="scmpds_2.html#K1" title="SCMPDS_2:func.1">SCMPDS</a> </span>)</span>
<b>by </b><i><a class="txt" href="scmpds_9.html#E5:52_1"><i><font color="Green" title="E39">A2</font></i></a>, <a class="txt" href="scmpds_9.html#E6:52_1"><i><font color="Green" title="E40">A3</font></i></a>, <a class="txt" href="scmpds_9.html#E7:52_1"><i><font color="Green" title="E41">A4</font></i></a>, <a class="txt" href="scmpds_9.html#E6"><i><font color="Green" title="E6">Lm1</font></i></a></i>
<br/>.= 
 <a href="int_2.html#K1" title="INT_2:func.1">abs</a> <span class="p1">(<span class="default"><font color="Maroon" title="c11">m1</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 5</span>)</span>
<b>by </b><i><a class="txt" href="scmpds_9.html#E10:52_1"><i><font color="Green" title="E43">A6</font></i></a>, <a class="txt" href="scmpds_9.html#E1:52_1_3_4"><i><font color="Green" title="E52">A26</font></i></a>, <a class="ref" href="scmpds_2.html#T69" title="SCMPDS_2:th.69">SCMPDS_2:69</a></i>
;<br/><font color="Maroon" title="c6">x</font> = 
<span class="p1">(<span class="default"><a href="ami_1.html#K4" title="AMI_1:func.4">Exec</a> <span class="p2">(<span class="default"><font color="Maroon" title="c1">a</font>,<font color="Maroon" title="c2">k1</font> <a href="scmpds_2.html#K10" title="SCMPDS_2:func.10">&gt;=0_goto</a> 5</span>)</span>,<font color="Maroon" title="c13">s2</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p1">(<span class="default"><a href="ami_1.html#K2" title="AMI_1:func.2">IC</a> <a href="scmpds_2.html#K1" title="SCMPDS_2:func.1">SCMPDS</a> </span>)</span>
<b>by </b><i><a class="txt" href="scmpds_9.html#E15:52_1"><i><font color="Green" title="E45">A8</font></i></a>, <a class="txt" href="scmpds_9.html#E16:52_1"><i><font color="Green" title="E46">A9</font></i></a>, <a class="txt" href="scmpds_9.html#E17:52_1"><i><font color="Green" title="E47">A10</font></i></a>, <a class="txt" href="scmpds_9.html#E6"><i><font color="Green" title="E6">Lm1</font></i></a></i>
<br/>.= 
 <a href="ami_2.html#K18" title="AMI_2:func.18">Next</a> <font color="Maroon" title="c15">n2</font>
<b>by </b><i><a class="txt" href="scmpds_9.html#E16:52_1"><i><font color="Green" title="E46">A9</font></i></a>, <a class="txt" href="scmpds_9.html#E2:52_1_3_4"><i><font color="Green" title="E53">A27</font></i></a>, <a class="txt" href="scmpds_9.html#E4:52_1_3_4"><i><font color="Green" title="E54">A28</font></i></a>, <a class="ref" href="scmpds_2.html#T69" title="SCMPDS_2:th.69">SCMPDS_2:69</a></i>
<br/>.= 
<font color="Maroon" title="c15">n2</font> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1
<b>by </b><i><a class="ref" href="ami_2.html#D15" title="AMI_2:def.15">AMI_2:def 15</a></i>
;<br/><a NAME="E9:52_1_3_4"/><b>then </b>
( <font color="Maroon" title="c16">w2</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1 <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c11">m1</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 5 or <font color="Maroon" title="c16">w2</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1 <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="xcmplx_0.html#K4" title="XCMPLX_0:func.4">-</a> <span class="p1">(<span class="default"><font color="Maroon" title="c11">m1</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 5</span>)</span> )
 <b>by </b><i><a class="txt" href="scmpds_9.html#E6:52_1_3_4"><i><font color="Green" title="E55">A29</font></i></a>, <a class="txt" href="scmpds_9.html#E7:52_1_3_4"><i><font color="Green" title="E56">A30</font></i></a>, <a class="ref" href="absvalue.html#T1" title="ABSVALUE:th.1">ABSVALUE:1</a></i>;<br/><b>hence </b><a NAME="E10:52_1_3_4"/>
<font color="Maroon" title="c6">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a> 
 <b>by </b><i><a class="txt" href="scmpds_9.html#E11:52_1"><i><font color="Green" title="E44">A7</font></i></a>, <a class="txt" href="scmpds_9.html#E16:52_1"><i><font color="Green" title="E46">A9</font></i></a>, <a class="txt" href="scmpds_9.html#E19:52_1"><i><font color="Green" title="E48">A11</font></i></a>, <a class="txt" href="scmpds_9.html#E21:52_1"><i><font color="Green" title="E50">A13</font></i></a>, <a class="txt" href="scmpds_9.html#E4:52_1_3_4"><i><font color="Green" title="E54">A28</font></i></a>, <a class="txt" href="scmpds_9.html#E6:52_1_3_4"><i><font color="Green" title="E55">A29</font></i></a></i>;<br/></div><b>end;</b></div></div><b>end;</b></div></div>
<b>end;</b></div>

<b>thus </b><a NAME="E2:52"/>
 <a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a>  <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a>  <a href="amistd_1.html#K2" title="AMISTD_1:func.2">JUMP</a> <span class="p1">(<span class="default"><font color="Maroon" title="c1">a</font>,<font color="Maroon" title="c2">k1</font> <a href="scmpds_2.html#K10" title="SCMPDS_2:func.10">&gt;=0_goto</a> 5</span>)</span>
 <b>by </b><i><a class="ref" href="xboole_1.html#T2" title="XBOOLE_1:th.2">XBOOLE_1:2</a></i>;<br/>


</div>
