<?xml version="1.0"?>
<div class="add">

<b>let </b><font color="Maroon" title="c1">ins</font> be   <a href="ami_1.html#NM3" title="AMI_1:NM.3">Instruction</a> of <a href="ami_3.html#K1" title="AMI_3:func.1">SCM</a> ;<br/>

<b>assume </b><a NAME="E1:21"/><i><font color="Green" title="E15">A1</font></i>: 
 <a href="ami_1.html#K19" title="AMI_1:func.19">InsCode</a> <font color="Maroon" title="c1">ins</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 2
 ;<br/>

<a NAME="E2:21"/><i><font color="Green" title="E16">A2</font></i>: 
not <font color="Maroon" title="c1">ins</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <span class="p1"><a href="tarski.html#K1" title="TARSKI:func.1">{</a><span class="default"><span class="p2"><a href="tarski.html#K4" title="TARSKI:func.4">[</a><span class="default"><a href="ami_2.html#K1" title="AMI_2:func.1">SCM-Halt</a> ,<a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a> </span><a href="tarski.html#K4" title="TARSKI:func.4">]</a></span></span><a href="tarski.html#K1" title="TARSKI:func.1">}</a></span>
 
<b>by </b><i><a class="txt" href="ami_5.html#E1:21"><i><font color="Green" title="E15">A1</font></i></a>, <a class="ref" href="ami_5.html#T37" target="_self" title="AMI_5:th.37">Th37</a>, <a class="ref" href="ami_3.html#T71" title="AMI_3:th.71">AMI_3:71</a>, <a class="ref" href="tarski.html#D1" title="TARSKI:def.1">TARSKI:def 1</a></i>;<br/>
<div><i><font color="Green" title="E17">A3</font></i>: <a class="txt" onclick="hs2(this)" href="javascript:()" title="21_1"><b>now </b></a><div class="add"><b>assume </b><a NAME="E1:21_1"/>
<font color="Maroon" title="c1">ins</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">K</font>,<span class="p3"><a href="finseq_1.html#K10" title="FINSEQ_1:func.10">&lt;*</a><span class="default"><font color="Olive" title="b2">a1</font>,<font color="Olive" title="b3">b1</font></span><a href="finseq_1.html#K10" title="FINSEQ_1:func.10">*&gt;</a></span></span><a href="tarski.html#K4" title="TARSKI:func.4">]</a></span> where <font color="Olive" title="b1">K</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> 9, <font color="Olive" title="b2">a1</font> is    <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> , <font color="Olive" title="b3">b1</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="b1">K</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <span class="p1"><a href="domain_1.html#K7" title="DOMAIN_1:func.7">{</a><span class="default">7,8</span><a href="domain_1.html#K7" title="DOMAIN_1:func.7">}</a></span> </span>}</span> 
 ;<br/><b>then consider </b><font color="Maroon" title="c2">K</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> 9, <font color="Maroon" title="c3">a1</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> , <font color="Maroon" title="c4">b1</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="E3:21_1"/><i><font color="Green" title="E18">A4</font></i>: 
<font color="Maroon" title="c1">ins</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="c2">K</font>,<span class="p2"><a href="finseq_1.html#K10" title="FINSEQ_1:func.10">&lt;*</a><span class="default"><font color="Maroon" title="c3">a1</font>,<font color="Maroon" title="c4">b1</font></span><a href="finseq_1.html#K10" title="FINSEQ_1:func.10">*&gt;</a></span></span><a href="tarski.html#K4" title="TARSKI:func.4">]</a></span>
 <b>and </b><br/><a NAME="E4:21_1"/><i><font color="Green" title="E19">A5</font></i>: 
<font color="Maroon" title="c2">K</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <span class="p1"><a href="domain_1.html#K7" title="DOMAIN_1:func.7">{</a><span class="default">7,8</span><a href="domain_1.html#K7" title="DOMAIN_1:func.7">}</a></span>
 ;<br/><a NAME="E5:21_1"/>
 <a href="ami_1.html#K19" title="AMI_1:func.19">InsCode</a> <font color="Maroon" title="c1">ins</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c2">K</font>
 <b>by </b><i><a class="txt" href="ami_5.html#E3:21_1"><i><font color="Green" title="E18">A4</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="E6:21_1"/>
contradiction
 <b>by </b><i><a class="txt" href="ami_5.html#E1:21"><i><font color="Green" title="E15">A1</font></i></a>, <a class="txt" href="ami_5.html#E4:21_1"><i><font color="Green" title="E19">A5</font></i></a>, <a class="ref" href="tarski.html#D2" title="TARSKI:def.2">TARSKI:def 2</a></i>;<br/></div><b>end;</b></div>
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="21_2"><b>now </b></a><div class="add"><b>assume </b><a NAME="E1:21_2"/>
<font color="Maroon" title="c1">ins</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">J</font>,<span class="p3"><a href="finseq_1.html#K12" title="FINSEQ_1:func.12">&lt;*</a><span class="default"><font color="Olive" title="b2">a</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">J</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> 9, <font color="Olive" title="b2">a</font> is    <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>  : <font color="Olive" title="b1">J</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 6 </span>}</span> 
 ;<br/><b>then consider </b><font color="Maroon" title="c2">J</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> 9, <font color="Maroon" title="c3">a</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="E3:21_2"/><i><font color="Green" title="E18">A6</font></i>: 
<font color="Maroon" title="c1">ins</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="c2">J</font>,<span class="p2"><a href="finseq_1.html#K12" title="FINSEQ_1:func.12">&lt;*</a><span class="default"><font color="Maroon" title="c3">a</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>
 <b>and </b><br/><a NAME="E4:21_2"/><i><font color="Green" title="E19">A7</font></i>: 
<font color="Maroon" title="c2">J</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 6
 ;<br/><b>thus </b><a NAME="E5:21_2"/>
contradiction
 <b>by </b><i><a class="txt" href="ami_5.html#E1:21"><i><font color="Green" title="E15">A1</font></i></a>, <a class="txt" href="ami_5.html#E3:21_2"><i><font color="Green" title="E18">A6</font></i></a>, <a class="txt" href="ami_5.html#E4:21_2"><i><font color="Green" title="E19">A7</font></i></a>, <a class="ref" href="mcart_1.html#T7" title="MCART_1:th.7">MCART_1:7</a></i>;<br/></div><b>end;</b></div>
<a NAME="E5:21"/><b>then </b>
not <font color="Maroon" title="c1">ins</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <span class="p1"><a href="tarski.html#K1" title="TARSKI:func.1">{</a><span class="default"><span class="p2"><a href="tarski.html#K4" title="TARSKI:func.4">[</a><span class="default"><a href="ami_2.html#K1" title="AMI_2:func.1">SCM-Halt</a> ,<a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a> </span><a href="tarski.html#K4" title="TARSKI:func.4">]</a></span></span><a href="tarski.html#K1" title="TARSKI:func.1">}</a></span> <a href="xboole_0.html#K2" title="XBOOLE_0:func.2">\/</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">J</font>,<span class="p3"><a href="finseq_1.html#K12" title="FINSEQ_1:func.12">&lt;*</a><span class="default"><font color="Olive" title="b2">a</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">J</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> 9, <font color="Olive" title="b2">a</font> is    <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>  : <font color="Olive" title="b1">J</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 6 </span>}</span> 
 
<b>by </b><i><a class="txt" href="ami_5.html#E2:21"><i><font color="Green" title="E16">A2</font></i></a>, <a class="ref" href="xboole_0.html#D2" title="XBOOLE_0:def.2">XBOOLE_0:def 2</a></i>;<br/>
<a NAME="E6:21"/><b>then </b>
not <font color="Maroon" title="c1">ins</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#K1" title="TARSKI:func.1">{</a><span class="default"><span class="p3"><a href="tarski.html#K4" title="TARSKI:func.4">[</a><span class="default"><a href="ami_2.html#K1" title="AMI_2:func.1">SCM-Halt</a> ,<a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a> </span><a href="tarski.html#K4" title="TARSKI:func.4">]</a></span></span><a href="tarski.html#K1" title="TARSKI:func.1">}</a></span> <a href="xboole_0.html#K2" title="XBOOLE_0:func.2">\/</a> <span class="p2">{<span class="default"> <span class="p3"><a href="tarski.html#K4" title="TARSKI:func.4">[</a><span class="default"><font color="Olive" title="b1">J</font>,<span class="p4"><a href="finseq_1.html#K12" title="FINSEQ_1:func.12">&lt;*</a><span class="default"><font color="Olive" title="b2">a</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">J</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> 9, <font color="Olive" title="b2">a</font> is    <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>  : <font color="Olive" title="b1">J</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 6 </span>}</span> </span>)</span> <a href="xboole_0.html#K2" title="XBOOLE_0:func.2">\/</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">K</font>,<span class="p3"><a href="finseq_1.html#K10" title="FINSEQ_1:func.10">&lt;*</a><span class="default"><font color="Olive" title="b2">a1</font>,<font color="Olive" title="b3">b1</font></span><a href="finseq_1.html#K10" title="FINSEQ_1:func.10">*&gt;</a></span></span><a href="tarski.html#K4" title="TARSKI:func.4">]</a></span> where <font color="Olive" title="b1">K</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> 9, <font color="Olive" title="b2">a1</font> is    <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> , <font color="Olive" title="b3">b1</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="b1">K</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <span class="p1"><a href="domain_1.html#K7" title="DOMAIN_1:func.7">{</a><span class="default">7,8</span><a href="domain_1.html#K7" title="DOMAIN_1:func.7">}</a></span> </span>}</span> 
 
<b>by </b><i><a class="txt" href="ami_5.html#E3:21"><i><font color="Green" title="E17">A3</font></i></a>, <a class="ref" href="xboole_0.html#D2" title="XBOOLE_0:def.2">XBOOLE_0:def 2</a></i>;<br/>
<a NAME="E7:21"/><b>then </b>
<font color="Maroon" title="c1">ins</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">I</font>,<span class="p3"><a href="finseq_1.html#K10" title="FINSEQ_1:func.10">&lt;*</a><span class="default"><font color="Olive" title="b2">b</font>,<font color="Olive" title="b3">c</font></span><a href="finseq_1.html#K10" title="FINSEQ_1:func.10">*&gt;</a></span></span><a href="tarski.html#K4" title="TARSKI:func.4">]</a></span> where <font color="Olive" title="b1">I</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> 9, <font color="Olive" title="b2">b</font>, <font color="Olive" title="b3">c</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="b1">I</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <span class="p1"><a href="domain_1.html#K10" title="DOMAIN_1:func.10">{</a><span class="default">1,2,3,4,5</span><a href="domain_1.html#K10" title="DOMAIN_1:func.10">}</a></span> </span>}</span> 
 
<b>by </b><i><a class="ref" href="xboole_0.html#D2" title="XBOOLE_0:def.2">XBOOLE_0:def 2</a></i>;<br/>
<b>then consider </b><font color="Maroon" title="c2">I</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> 9, <font color="Maroon" title="c3">b</font>, <font color="Maroon" title="c4">c</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="E9:21"/><i><font color="Green" title="E18">A8</font></i>: 
<font color="Maroon" title="c1">ins</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="c2">I</font>,<span class="p2"><a href="finseq_1.html#K10" title="FINSEQ_1:func.10">&lt;*</a><span class="default"><font color="Maroon" title="c3">b</font>,<font color="Maroon" title="c4">c</font></span><a href="finseq_1.html#K10" title="FINSEQ_1:func.10">*&gt;</a></span></span><a href="tarski.html#K4" title="TARSKI:func.4">]</a></span>
 <b>and </b><br/><a NAME="E10:21"/>
<font color="Maroon" title="c2">I</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <span class="p1"><a href="domain_1.html#K10" title="DOMAIN_1:func.10">{</a><span class="default">1,2,3,4,5</span><a href="domain_1.html#K10" title="DOMAIN_1:func.10">}</a></span>
 ;<br/>
<b>reconsider </b><font color="Maroon" title="c5">da</font> = <font color="Maroon" title="c3">b</font> <a href="ami_5.html#K3" title="AMI_5:func.3">@</a> , <font color="Maroon" title="c6">db</font> = <font color="Maroon" title="c4">c</font> <a href="ami_5.html#K3" title="AMI_5:func.3">@</a>  as    <a href="ami_3.html#M1" title="AMI_3:mode.1">Data-Location</a>  ;<br/>
<b>take </b>
<font color="Maroon" title="c5">da</font>
;<br/>

<b>take </b>
<font color="Maroon" title="c6">db</font>
;<br/>

<b>thus </b><a NAME="E12:21"/>
<font color="Maroon" title="c1">ins</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="ami_3.html#K4" title="AMI_3:func.4">AddTo</a> <font color="Maroon" title="c5">da</font>,<font color="Maroon" title="c6">db</font>
 <b>by </b><i><a class="txt" href="ami_5.html#E1:21"><i><font color="Green" title="E15">A1</font></i></a>, <a class="txt" href="ami_5.html#E9:21"><i><font color="Green" title="E18">A8</font></i></a>, <a class="ref" href="mcart_1.html#T7" title="MCART_1:th.7">MCART_1:7</a></i>;<br/>


</div>
