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<b>let </b><font color="Maroon" title="c6">I</font> be   <a href="ami_1.html#NM3" title="AMI_1:NM.3">Instruction</a> of <a href="scmpds_2.html#K1" title="SCMPDS_2:func.1">SCMPDS</a> ;<br/>

<div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="12_1"><b>per </b></a><a class="txt" onclick="hs(this)" href="javascript:()"><b>cases </b></a><span class="hide"><a NAME="E1:12_1"/>
( <font color="Maroon" title="c6">I</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <span class="p1">{<span class="default"> <span class="p2"><a href="tarski.html#K4" title="TARSKI:func.4">[</a><span class="default">0,<span class="p3"><a href="finseq_1.html#K12" title="FINSEQ_1:func.12">&lt;*</a><span class="default"><font color="Olive" title="b1">k1</font></span><a href="finseq_1.html#K12" title="FINSEQ_1:func.12">*&gt;</a></span></span><a href="tarski.html#K4" title="TARSKI:func.4">]</a></span> where <font color="Olive" title="b1">k1</font> is    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of  <a href="numbers.html#K4" title="NUMBERS:func.4">INT</a>  : verum </span>}</span>  or <font color="Maroon" title="c6">I</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <span class="p1">{<span class="default"> <span class="p2"><a href="tarski.html#K4" title="TARSKI:func.4">[</a><span class="default">1,<span class="p3"><a href="finseq_1.html#K12" title="FINSEQ_1:func.12">&lt;*</a><span class="default"><font color="Olive" title="b1">d1</font></span><a href="finseq_1.html#K12" title="FINSEQ_1:func.12">*&gt;</a></span></span><a href="tarski.html#K4" title="TARSKI:func.4">]</a></span> where <font color="Olive" title="b1">d1</font> is    <a href="subset_1.html#M2" title="SUBSET_1:mode.2">Element</a> of  <a href="ami_2.html#K5" title="AMI_2:func.5">SCM-Data-Loc</a>  : verum </span>}</span>  or <font color="Maroon" title="c6">I</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <span class="p1">{<span class="default"> <span class="p2"><a href="tarski.html#K4" title="TARSKI:func.4">[</a><span class="default"><font color="Olive" title="b1">I1</font>,<span class="p3"><a href="scmpds_1.html#K9" title="SCMPDS_1:func.9">&lt;*</a><span class="default"><font color="Olive" title="b2">d2</font>,<font color="Olive" title="b3">k2</font></span><a href="scmpds_1.html#K9" title="SCMPDS_1:func.9">*&gt;</a></span></span><a href="tarski.html#K4" title="TARSKI:func.4">]</a></span> where <font color="Olive" title="b1">I1</font> is    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of  <a href="card_1.html#K6" title="CARD_1:func.6">Segm</a> 14, <font color="Olive" title="b2">d2</font> is    <a href="subset_1.html#M2" title="SUBSET_1:mode.2">Element</a> of  <a href="ami_2.html#K5" title="AMI_2:func.5">SCM-Data-Loc</a> , <font color="Olive" title="b3">k2</font> is    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of  <a href="numbers.html#K4" title="NUMBERS:func.4">INT</a>  : <font color="Olive" title="b1">I1</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <span class="p1"><a href="tarski.html#K2" title="TARSKI:func.2">{</a><span class="default">2,3</span><a href="tarski.html#K2" title="TARSKI:func.2">}</a></span> </span>}</span>  or <font color="Maroon" title="c6">I</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <span class="p1">{<span class="default"> <span class="p2"><a href="tarski.html#K4" title="TARSKI:func.4">[</a><span class="default"><font color="Olive" title="b1">I2</font>,<span class="p3"><a href="finseq_1.html#K11" title="FINSEQ_1:func.11">&lt;*</a><span class="default"><font color="Olive" title="b2">d3</font>,<font color="Olive" title="b3">k3</font>,<font color="Olive" title="b4">k4</font></span><a href="finseq_1.html#K11" title="FINSEQ_1:func.11">*&gt;</a></span></span><a href="tarski.html#K4" title="TARSKI:func.4">]</a></span> where <font color="Olive" title="b1">I2</font> is    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of  <a href="card_1.html#K6" title="CARD_1:func.6">Segm</a> 14, <font color="Olive" title="b2">d3</font> is    <a href="subset_1.html#M2" title="SUBSET_1:mode.2">Element</a> of  <a href="ami_2.html#K5" title="AMI_2:func.5">SCM-Data-Loc</a> , <font color="Olive" title="b3">k3</font>, <font color="Olive" title="b4">k4</font> is    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of  <a href="numbers.html#K4" title="NUMBERS:func.4">INT</a>  : <font color="Olive" title="b1">I2</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <span class="p1"><a href="enumset1.html#K3" title="ENUMSET1:func.3">{</a><span class="default">4,5,6,7,8</span><a href="enumset1.html#K3" title="ENUMSET1:func.3">}</a></span> </span>}</span>  or <font color="Maroon" title="c6">I</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <span class="p1">{<span class="default"> <span class="p2"><a href="tarski.html#K4" title="TARSKI:func.4">[</a><span class="default"><font color="Olive" title="b1">I3</font>,<span class="p3"><a href="finseq_4.html#K8" title="FINSEQ_4:func.8">&lt;*</a><span class="default"><font color="Olive" title="b2">d4</font>,<font color="Olive" title="b3">d5</font>,<font color="Olive" title="b4">k5</font>,<font color="Olive" title="b5">k6</font></span><a href="finseq_4.html#K8" title="FINSEQ_4:func.8">*&gt;</a></span></span><a href="tarski.html#K4" title="TARSKI:func.4">]</a></span> where <font color="Olive" title="b1">I3</font> is    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of  <a href="card_1.html#K6" title="CARD_1:func.6">Segm</a> 14, <font color="Olive" title="b2">d4</font>, <font color="Olive" title="b3">d5</font> is    <a href="subset_1.html#M2" title="SUBSET_1:mode.2">Element</a> of  <a href="ami_2.html#K5" title="AMI_2:func.5">SCM-Data-Loc</a> , <font color="Olive" title="b4">k5</font>, <font color="Olive" title="b5">k6</font> is    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of  <a href="numbers.html#K4" title="NUMBERS:func.4">INT</a>  : <font color="Olive" title="b1">I3</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <span class="p1"><a href="enumset1.html#K3" title="ENUMSET1:func.3">{</a><span class="default">9,10,11,12,13</span><a href="enumset1.html#K3" title="ENUMSET1:func.3">}</a></span> </span>}</span>  )
 </span><b>by </b><i><a class="txt" href="scmpds_2.html#E17"><i><font color="Green" title="E5">Lm1</font></i></a></i>;<br/><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="12_1_1"><b>suppose </b></a><a NAME="E1:12_1_1"/>
<font color="Maroon" title="c6">I</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <span class="p1">{<span class="default"> <span class="p2"><a href="tarski.html#K4" title="TARSKI:func.4">[</a><span class="default">0,<span class="p3"><a href="finseq_1.html#K12" title="FINSEQ_1:func.12">&lt;*</a><span class="default"><font color="Olive" title="b1">k1</font></span><a href="finseq_1.html#K12" title="FINSEQ_1:func.12">*&gt;</a></span></span><a href="tarski.html#K4" title="TARSKI:func.4">]</a></span> where <font color="Olive" title="b1">k1</font> is    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of  <a href="numbers.html#K4" title="NUMBERS:func.4">INT</a>  : verum </span>}</span> 
 ;<br/><div class="add"><b>then consider </b><font color="Maroon" title="c7">k1</font> being    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of  <a href="numbers.html#K4" title="NUMBERS:func.4">INT</a> <b> such that </b><br/><a NAME="E3:12_1_1"/><i><font color="Green" title="E6">A1</font></i>: 
<font color="Maroon" title="c6">I</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"><a href="tarski.html#K4" title="TARSKI:func.4">[</a><span class="default">0,<span class="p2"><a href="finseq_1.html#K12" title="FINSEQ_1:func.12">&lt;*</a><span class="default"><font color="Maroon" title="c7">k1</font></span><a href="finseq_1.html#K12" title="FINSEQ_1:func.12">*&gt;</a></span></span><a href="tarski.html#K4" title="TARSKI:func.4">]</a></span>
 ;<br/><a NAME="E4:12_1_1"/>
<font color="Maroon" title="c6">I</font> <a href="mcart_1.html#K1" title="MCART_1:func.1">`1</a>  <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 0
 <b>by </b><i><a class="txt" href="scmpds_2.html#E3:12_1_1"><i><font color="Green" title="E6">A1</font></i></a>, <a class="ref" href="mcart_1.html#T7" title="MCART_1:th.7">MCART_1:7</a></i>;<br/><b>hence </b><a NAME="E5:12_1_1"/>
 <a href="ami_1.html#K19" title="AMI_1:func.19">InsCode</a> <font color="Maroon" title="c6">I</font> <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> 13
 ;<br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="12_1_2"><b>suppose </b></a><a NAME="E1:12_1_2"/>
<font color="Maroon" title="c6">I</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <span class="p1">{<span class="default"> <span class="p2"><a href="tarski.html#K4" title="TARSKI:func.4">[</a><span class="default">1,<span class="p3"><a href="finseq_1.html#K12" title="FINSEQ_1:func.12">&lt;*</a><span class="default"><font color="Olive" title="b1">d1</font></span><a href="finseq_1.html#K12" title="FINSEQ_1:func.12">*&gt;</a></span></span><a href="tarski.html#K4" title="TARSKI:func.4">]</a></span> where <font color="Olive" title="b1">d1</font> is    <a href="subset_1.html#M2" title="SUBSET_1:mode.2">Element</a> of  <a href="ami_2.html#K5" title="AMI_2:func.5">SCM-Data-Loc</a>  : verum </span>}</span> 
 ;<br/><div class="add"><b>then consider </b><font color="Maroon" title="c7">d1</font> being    <a href="subset_1.html#M2" title="SUBSET_1:mode.2">Element</a> of  <a href="ami_2.html#K5" title="AMI_2:func.5">SCM-Data-Loc</a> <b> such that </b><br/><a NAME="E3:12_1_2"/><i><font color="Green" title="E6">A2</font></i>: 
<font color="Maroon" title="c6">I</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"><a href="tarski.html#K4" title="TARSKI:func.4">[</a><span class="default">1,<span class="p2"><a href="finseq_1.html#K12" title="FINSEQ_1:func.12">&lt;*</a><span class="default"><font color="Maroon" title="c7">d1</font></span><a href="finseq_1.html#K12" title="FINSEQ_1:func.12">*&gt;</a></span></span><a href="tarski.html#K4" title="TARSKI:func.4">]</a></span>
 ;<br/><a NAME="E4:12_1_2"/>
<font color="Maroon" title="c6">I</font> <a href="mcart_1.html#K1" title="MCART_1:func.1">`1</a>  <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 1
 <b>by </b><i><a class="txt" href="scmpds_2.html#E3:12_1_2"><i><font color="Green" title="E6">A2</font></i></a>, <a class="ref" href="mcart_1.html#T7" title="MCART_1:th.7">MCART_1:7</a></i>;<br/><b>hence </b><a NAME="E5:12_1_2"/>
 <a href="ami_1.html#K19" title="AMI_1:func.19">InsCode</a> <font color="Maroon" title="c6">I</font> <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> 13
 ;<br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="12_1_3"><b>suppose </b></a><a NAME="E1:12_1_3"/>
<font color="Maroon" title="c6">I</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <span class="p1">{<span class="default"> <span class="p2"><a href="tarski.html#K4" title="TARSKI:func.4">[</a><span class="default"><font color="Olive" title="b1">I1</font>,<span class="p3"><a href="scmpds_1.html#K9" title="SCMPDS_1:func.9">&lt;*</a><span class="default"><font color="Olive" title="b2">d2</font>,<font color="Olive" title="b3">k2</font></span><a href="scmpds_1.html#K9" title="SCMPDS_1:func.9">*&gt;</a></span></span><a href="tarski.html#K4" title="TARSKI:func.4">]</a></span> where <font color="Olive" title="b1">I1</font> is    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of  <a href="card_1.html#K6" title="CARD_1:func.6">Segm</a> 14, <font color="Olive" title="b2">d2</font> is    <a href="subset_1.html#M2" title="SUBSET_1:mode.2">Element</a> of  <a href="ami_2.html#K5" title="AMI_2:func.5">SCM-Data-Loc</a> , <font color="Olive" title="b3">k2</font> is    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of  <a href="numbers.html#K4" title="NUMBERS:func.4">INT</a>  : <font color="Olive" title="b1">I1</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <span class="p1"><a href="tarski.html#K2" title="TARSKI:func.2">{</a><span class="default">2,3</span><a href="tarski.html#K2" title="TARSKI:func.2">}</a></span> </span>}</span> 
 ;<br/><div class="add"><b>then consider </b><font color="Maroon" title="c7">I1</font> being    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of  <a href="card_1.html#K6" title="CARD_1:func.6">Segm</a> 14, <font color="Maroon" title="c8">d1</font> being    <a href="subset_1.html#M2" title="SUBSET_1:mode.2">Element</a> of  <a href="ami_2.html#K5" title="AMI_2:func.5">SCM-Data-Loc</a> , <font color="Maroon" title="c9">k1</font> being    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of  <a href="numbers.html#K4" title="NUMBERS:func.4">INT</a> <b> such that </b><br/><a NAME="E3:12_1_3"/><i><font color="Green" title="E6">A3</font></i>: 
<font color="Maroon" title="c6">I</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"><a href="tarski.html#K4" title="TARSKI:func.4">[</a><span class="default"><font color="Maroon" title="c7">I1</font>,<span class="p2"><a href="scmpds_1.html#K9" title="SCMPDS_1:func.9">&lt;*</a><span class="default"><font color="Maroon" title="c8">d1</font>,<font color="Maroon" title="c9">k1</font></span><a href="scmpds_1.html#K9" title="SCMPDS_1:func.9">*&gt;</a></span></span><a href="tarski.html#K4" title="TARSKI:func.4">]</a></span>
 <b>and </b><br/><a NAME="E4:12_1_3"/><i><font color="Green" title="E7">A4</font></i>: 
<font color="Maroon" title="c7">I1</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <span class="p1"><a href="tarski.html#K2" title="TARSKI:func.2">{</a><span class="default">2,3</span><a href="tarski.html#K2" title="TARSKI:func.2">}</a></span>
 ;<br/><a NAME="E5:12_1_3"/><i><font color="Green" title="E8">A5</font></i>: 
( <font color="Maroon" title="c7">I1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 2 or <font color="Maroon" title="c7">I1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 3 )
 <b>by </b><i><a class="txt" href="scmpds_2.html#E4:12_1_3"><i><font color="Green" title="E7">A4</font></i></a>, <a class="ref" href="tarski.html#D2" title="TARSKI:def.2">TARSKI:def 2</a></i>;<br/><a NAME="E6:12_1_3"/>
<font color="Maroon" title="c6">I</font> <a href="mcart_1.html#K1" title="MCART_1:func.1">`1</a>  <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c7">I1</font>
 <b>by </b><i><a class="txt" href="scmpds_2.html#E3:12_1_3"><i><font color="Green" title="E6">A3</font></i></a>, <a class="ref" href="mcart_1.html#T7" title="MCART_1:th.7">MCART_1:7</a></i>;<br/><b>hence </b><a NAME="E7:12_1_3"/>
 <a href="ami_1.html#K19" title="AMI_1:func.19">InsCode</a> <font color="Maroon" title="c6">I</font> <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> 13
 <b>by </b><i><a class="txt" href="scmpds_2.html#E5:12_1_3"><i><font color="Green" title="E8">A5</font></i></a></i>;<br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="12_1_4"><b>suppose </b></a><a NAME="E1:12_1_4"/>
<font color="Maroon" title="c6">I</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <span class="p1">{<span class="default"> <span class="p2"><a href="tarski.html#K4" title="TARSKI:func.4">[</a><span class="default"><font color="Olive" title="b1">I2</font>,<span class="p3"><a href="finseq_1.html#K11" title="FINSEQ_1:func.11">&lt;*</a><span class="default"><font color="Olive" title="b2">d3</font>,<font color="Olive" title="b3">k3</font>,<font color="Olive" title="b4">k4</font></span><a href="finseq_1.html#K11" title="FINSEQ_1:func.11">*&gt;</a></span></span><a href="tarski.html#K4" title="TARSKI:func.4">]</a></span> where <font color="Olive" title="b1">I2</font> is    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of  <a href="card_1.html#K6" title="CARD_1:func.6">Segm</a> 14, <font color="Olive" title="b2">d3</font> is    <a href="subset_1.html#M2" title="SUBSET_1:mode.2">Element</a> of  <a href="ami_2.html#K5" title="AMI_2:func.5">SCM-Data-Loc</a> , <font color="Olive" title="b3">k3</font>, <font color="Olive" title="b4">k4</font> is    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of  <a href="numbers.html#K4" title="NUMBERS:func.4">INT</a>  : <font color="Olive" title="b1">I2</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <span class="p1"><a href="enumset1.html#K3" title="ENUMSET1:func.3">{</a><span class="default">4,5,6,7,8</span><a href="enumset1.html#K3" title="ENUMSET1:func.3">}</a></span> </span>}</span> 
 ;<br/><div class="add"><b>then consider </b><font color="Maroon" title="c7">I1</font> being    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of  <a href="card_1.html#K6" title="CARD_1:func.6">Segm</a> 14, <font color="Maroon" title="c8">d1</font> being    <a href="subset_1.html#M2" title="SUBSET_1:mode.2">Element</a> of  <a href="ami_2.html#K5" title="AMI_2:func.5">SCM-Data-Loc</a> , <font color="Maroon" title="c9">k1</font>, <font color="Maroon" title="c10">k2</font> being    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of  <a href="numbers.html#K4" title="NUMBERS:func.4">INT</a> <b> such that </b><br/><a NAME="E3:12_1_4"/><i><font color="Green" title="E6">A6</font></i>: 
<font color="Maroon" title="c6">I</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"><a href="tarski.html#K4" title="TARSKI:func.4">[</a><span class="default"><font color="Maroon" title="c7">I1</font>,<span class="p2"><a href="finseq_1.html#K11" title="FINSEQ_1:func.11">&lt;*</a><span class="default"><font color="Maroon" title="c8">d1</font>,<font color="Maroon" title="c9">k1</font>,<font color="Maroon" title="c10">k2</font></span><a href="finseq_1.html#K11" title="FINSEQ_1:func.11">*&gt;</a></span></span><a href="tarski.html#K4" title="TARSKI:func.4">]</a></span>
 <b>and </b><br/><a NAME="E4:12_1_4"/><i><font color="Green" title="E7">A7</font></i>: 
<font color="Maroon" title="c7">I1</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <span class="p1"><a href="enumset1.html#K3" title="ENUMSET1:func.3">{</a><span class="default">4,5,6,7,8</span><a href="enumset1.html#K3" title="ENUMSET1:func.3">}</a></span>
 ;<br/><a NAME="E5:12_1_4"/><i><font color="Green" title="E8">A8</font></i>: 
( <font color="Maroon" title="c7">I1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 4 or <font color="Maroon" title="c7">I1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 5 or <font color="Maroon" title="c7">I1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 6 or <font color="Maroon" title="c7">I1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 7 or <font color="Maroon" title="c7">I1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 8 )
 <b>by </b><i><a class="txt" href="scmpds_2.html#E4:12_1_4"><i><font color="Green" title="E7">A7</font></i></a>, <a class="ref" href="enumset1.html#D3" title="ENUMSET1:def.3">ENUMSET1:def 3</a></i>;<br/><a NAME="E6:12_1_4"/>
<font color="Maroon" title="c6">I</font> <a href="mcart_1.html#K1" title="MCART_1:func.1">`1</a>  <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c7">I1</font>
 <b>by </b><i><a class="txt" href="scmpds_2.html#E3:12_1_4"><i><font color="Green" title="E6">A6</font></i></a>, <a class="ref" href="mcart_1.html#T7" title="MCART_1:th.7">MCART_1:7</a></i>;<br/><b>hence </b><a NAME="E7:12_1_4"/>
 <a href="ami_1.html#K19" title="AMI_1:func.19">InsCode</a> <font color="Maroon" title="c6">I</font> <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> 13
 <b>by </b><i><a class="txt" href="scmpds_2.html#E5:12_1_4"><i><font color="Green" title="E8">A8</font></i></a></i>;<br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="12_1_5"><b>suppose </b></a><a NAME="E1:12_1_5"/>
<font color="Maroon" title="c6">I</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <span class="p1">{<span class="default"> <span class="p2"><a href="tarski.html#K4" title="TARSKI:func.4">[</a><span class="default"><font color="Olive" title="b1">I3</font>,<span class="p3"><a href="finseq_4.html#K8" title="FINSEQ_4:func.8">&lt;*</a><span class="default"><font color="Olive" title="b2">d4</font>,<font color="Olive" title="b3">d5</font>,<font color="Olive" title="b4">k5</font>,<font color="Olive" title="b5">k6</font></span><a href="finseq_4.html#K8" title="FINSEQ_4:func.8">*&gt;</a></span></span><a href="tarski.html#K4" title="TARSKI:func.4">]</a></span> where <font color="Olive" title="b1">I3</font> is    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of  <a href="card_1.html#K6" title="CARD_1:func.6">Segm</a> 14, <font color="Olive" title="b2">d4</font>, <font color="Olive" title="b3">d5</font> is    <a href="subset_1.html#M2" title="SUBSET_1:mode.2">Element</a> of  <a href="ami_2.html#K5" title="AMI_2:func.5">SCM-Data-Loc</a> , <font color="Olive" title="b4">k5</font>, <font color="Olive" title="b5">k6</font> is    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of  <a href="numbers.html#K4" title="NUMBERS:func.4">INT</a>  : <font color="Olive" title="b1">I3</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <span class="p1"><a href="enumset1.html#K3" title="ENUMSET1:func.3">{</a><span class="default">9,10,11,12,13</span><a href="enumset1.html#K3" title="ENUMSET1:func.3">}</a></span> </span>}</span> 
 ;<br/><div class="add"><b>then consider </b><font color="Maroon" title="c7">I1</font> being    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of  <a href="card_1.html#K6" title="CARD_1:func.6">Segm</a> 14, <font color="Maroon" title="c8">d1</font>, <font color="Maroon" title="c9">d2</font> being    <a href="subset_1.html#M2" title="SUBSET_1:mode.2">Element</a> of  <a href="ami_2.html#K5" title="AMI_2:func.5">SCM-Data-Loc</a> , <font color="Maroon" title="c10">k1</font>, <font color="Maroon" title="c11">k2</font> being    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of  <a href="numbers.html#K4" title="NUMBERS:func.4">INT</a> <b> such that </b><br/><a NAME="E3:12_1_5"/><i><font color="Green" title="E6">A9</font></i>: 
<font color="Maroon" title="c6">I</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"><a href="tarski.html#K4" title="TARSKI:func.4">[</a><span class="default"><font color="Maroon" title="c7">I1</font>,<span class="p2"><a href="finseq_4.html#K8" title="FINSEQ_4:func.8">&lt;*</a><span class="default"><font color="Maroon" title="c8">d1</font>,<font color="Maroon" title="c9">d2</font>,<font color="Maroon" title="c10">k1</font>,<font color="Maroon" title="c11">k2</font></span><a href="finseq_4.html#K8" title="FINSEQ_4:func.8">*&gt;</a></span></span><a href="tarski.html#K4" title="TARSKI:func.4">]</a></span>
 <b>and </b><br/><a NAME="E4:12_1_5"/><i><font color="Green" title="E7">A10</font></i>: 
<font color="Maroon" title="c7">I1</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <span class="p1"><a href="enumset1.html#K3" title="ENUMSET1:func.3">{</a><span class="default">9,10,11,12,13</span><a href="enumset1.html#K3" title="ENUMSET1:func.3">}</a></span>
 ;<br/><a NAME="E5:12_1_5"/><i><font color="Green" title="E8">A11</font></i>: 
( <font color="Maroon" title="c7">I1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 9 or <font color="Maroon" title="c7">I1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 10 or <font color="Maroon" title="c7">I1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 11 or <font color="Maroon" title="c7">I1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 12 or <font color="Maroon" title="c7">I1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 13 )
 <b>by </b><i><a class="txt" href="scmpds_2.html#E4:12_1_5"><i><font color="Green" title="E7">A10</font></i></a>, <a class="ref" href="enumset1.html#D3" title="ENUMSET1:def.3">ENUMSET1:def 3</a></i>;<br/><a NAME="E6:12_1_5"/>
<font color="Maroon" title="c6">I</font> <a href="mcart_1.html#K1" title="MCART_1:func.1">`1</a>  <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c7">I1</font>
 <b>by </b><i><a class="txt" href="scmpds_2.html#E3:12_1_5"><i><font color="Green" title="E6">A9</font></i></a>, <a class="ref" href="mcart_1.html#T7" title="MCART_1:th.7">MCART_1:7</a></i>;<br/><b>hence </b><a NAME="E7:12_1_5"/>
 <a href="ami_1.html#K19" title="AMI_1:func.19">InsCode</a> <font color="Maroon" title="c6">I</font> <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> 13
 <b>by </b><i><a class="txt" href="scmpds_2.html#E5:12_1_5"><i><font color="Green" title="E8">A11</font></i></a></i>;<br/></div><b>end;</b></div></div><b>end;</b></div>

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