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<div class="add">

<b>let </b><font color="Maroon" title="c1">I</font> be   <a href="ami_1.html#NM3" title="AMI_1:NM.3">Instruction</a> of <a href="scmfsa_2.html#K1" title="SCMFSA_2:func.1">SCM+FSA</a> ;<br/>

<b>assume </b><a NAME="E1:105"/><i><font color="Green" title="E72">A1</font></i>: 
 <a href="ami_5.html#K1" title="AMI_5:func.1">InsCode</a> <font color="Maroon" title="c1">I</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 0
 ;<br/>

<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="105_1"><b>now </b></a><div class="add"><b>assume </b><a NAME="E1:105_1"/>
<font color="Maroon" title="c1">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">K</font>,<span class="p3"><a href="finseq_4.html#K2" title="FINSEQ_4:func.2">&lt;*</a><span class="default"><font color="Olive" title="b2">dC</font>,<font color="Olive" title="b3">fB</font></span><a href="finseq_4.html#K2" title="FINSEQ_4:func.2">*&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#M2" title="SUBSET_1:mode.2">Element</a> of  <a href="gr_cy_1.html#K1" title="GR_CY_1:func.1">Segm</a> 13, <font color="Olive" title="b2">dC</font> is    <a href="subset_1.html#M2" title="SUBSET_1:mode.2">Element</a> of  <a href="scmfsa_1.html#K1" title="SCMFSA_1:func.1">SCM+FSA-Data-Loc</a> , <font color="Olive" title="b3">fB</font> is    <a href="subset_1.html#M2" title="SUBSET_1:mode.2">Element</a> of  <a href="scmfsa_1.html#K2" title="SCMFSA_1:func.2">SCM+FSA-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="tarski.html#K2" title="TARSKI:func.2">{</a><span class="default">11,12</span><a href="tarski.html#K2" title="TARSKI:func.2">}</a></span> </span>}</span> 
 ;<br/><b>then consider </b><font color="Maroon" title="c2">K</font> being    <a href="subset_1.html#M2" title="SUBSET_1:mode.2">Element</a> of  <a href="gr_cy_1.html#K1" title="GR_CY_1:func.1">Segm</a> 13, <font color="Maroon" title="c3">dC</font> being    <a href="subset_1.html#M2" title="SUBSET_1:mode.2">Element</a> of  <a href="scmfsa_1.html#K1" title="SCMFSA_1:func.1">SCM+FSA-Data-Loc</a> , <font color="Maroon" title="c4">fB</font> being    <a href="subset_1.html#M2" title="SUBSET_1:mode.2">Element</a> of  <a href="scmfsa_1.html#K2" title="SCMFSA_1:func.2">SCM+FSA-Data*-Loc</a> <b> such that </b><br/><a NAME="E3:105_1"/><i><font color="Green" title="E73">A2</font></i>: 
<font color="Maroon" title="c1">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="c2">K</font>,<span class="p2"><a href="finseq_4.html#K2" title="FINSEQ_4:func.2">&lt;*</a><span class="default"><font color="Maroon" title="c3">dC</font>,<font color="Maroon" title="c4">fB</font></span><a href="finseq_4.html#K2" title="FINSEQ_4:func.2">*&gt;</a></span></span><a href="tarski.html#K4" title="TARSKI:func.4">]</a></span>
 <b>and </b><br/><a NAME="E4:105_1"/><i><font color="Green" title="E74">A3</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="tarski.html#K2" title="TARSKI:func.2">{</a><span class="default">11,12</span><a href="tarski.html#K2" title="TARSKI:func.2">}</a></span>
 ;<br/><a NAME="E5:105_1"/>
( <font color="Maroon" title="c2">K</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 12 or <font color="Maroon" title="c2">K</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 11 )
 <b>by </b><i><a class="txt" href="scmfsa_2.html#E4:105_1"><i><font color="Green" title="E74">A3</font></i></a>, <a class="ref" href="tarski.html#D2" title="TARSKI:def.2">TARSKI:def 2</a></i>;<br/><b>hence </b><a NAME="E6:105_1"/>
contradiction
 <b>by </b><i><a class="txt" href="scmfsa_2.html#E1:105"><i><font color="Green" title="E72">A1</font></i></a>, <a class="txt" href="scmfsa_2.html#E3:105_1"><i><font color="Green" title="E73">A2</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="E3:105"/><b>then </b><i><font color="Green" title="E73">A4</font></i>: 
<font color="Maroon" title="c1">I</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <a href="ami_2.html#K6" title="AMI_2:func.6">SCM-Instr</a>  <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">L</font>,<span class="p3"><a href="finseq_4.html#K3" title="FINSEQ_4:func.3">&lt;*</a><span class="default"><font color="Olive" title="b2">dB</font>,<font color="Olive" title="b4">fA</font>,<font color="Olive" title="b3">dA</font></span><a href="finseq_4.html#K3" title="FINSEQ_4:func.3">*&gt;</a></span></span><a href="tarski.html#K4" title="TARSKI:func.4">]</a></span> where <font color="Olive" title="b1">L</font> is    <a href="subset_1.html#M2" title="SUBSET_1:mode.2">Element</a> of  <a href="gr_cy_1.html#K1" title="GR_CY_1:func.1">Segm</a> 13, <font color="Olive" title="b2">dB</font>, <font color="Olive" title="b3">dA</font> is    <a href="subset_1.html#M2" title="SUBSET_1:mode.2">Element</a> of  <a href="scmfsa_1.html#K1" title="SCMFSA_1:func.1">SCM+FSA-Data-Loc</a> , <font color="Olive" title="b4">fA</font> is    <a href="subset_1.html#M2" title="SUBSET_1:mode.2">Element</a> of  <a href="scmfsa_1.html#K2" title="SCMFSA_1:func.2">SCM+FSA-Data*-Loc</a>  : <font color="Olive" title="b1">L</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">9,10</span><a href="tarski.html#K2" title="TARSKI:func.2">}</a></span> </span>}</span> 
 
<b>by </b><i><a class="ref" href="scmfsa_1.html#D4" title="SCMFSA_1:def.4">SCMFSA_1:def 4</a>, <a class="ref" href="xboole_0.html#D2" title="XBOOLE_0:def.2">XBOOLE_0:def 2</a></i>;<br/>
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="105_2"><b>now </b></a><div class="add"><b>assume </b><a NAME="E1:105_2"/>
<font color="Maroon" title="c1">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">L</font>,<span class="p3"><a href="finseq_4.html#K3" title="FINSEQ_4:func.3">&lt;*</a><span class="default"><font color="Olive" title="b2">dB</font>,<font color="Olive" title="b4">fA</font>,<font color="Olive" title="b3">dA</font></span><a href="finseq_4.html#K3" title="FINSEQ_4:func.3">*&gt;</a></span></span><a href="tarski.html#K4" title="TARSKI:func.4">]</a></span> where <font color="Olive" title="b1">L</font> is    <a href="subset_1.html#M2" title="SUBSET_1:mode.2">Element</a> of  <a href="gr_cy_1.html#K1" title="GR_CY_1:func.1">Segm</a> 13, <font color="Olive" title="b2">dB</font>, <font color="Olive" title="b3">dA</font> is    <a href="subset_1.html#M2" title="SUBSET_1:mode.2">Element</a> of  <a href="scmfsa_1.html#K1" title="SCMFSA_1:func.1">SCM+FSA-Data-Loc</a> , <font color="Olive" title="b4">fA</font> is    <a href="subset_1.html#M2" title="SUBSET_1:mode.2">Element</a> of  <a href="scmfsa_1.html#K2" title="SCMFSA_1:func.2">SCM+FSA-Data*-Loc</a>  : <font color="Olive" title="b1">L</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">9,10</span><a href="tarski.html#K2" title="TARSKI:func.2">}</a></span> </span>}</span> 
 ;<br/><b>then consider </b><font color="Maroon" title="c2">L</font> being    <a href="subset_1.html#M2" title="SUBSET_1:mode.2">Element</a> of  <a href="gr_cy_1.html#K1" title="GR_CY_1:func.1">Segm</a> 13, <font color="Maroon" title="c3">dB</font>, <font color="Maroon" title="c4">dA</font> being    <a href="subset_1.html#M2" title="SUBSET_1:mode.2">Element</a> of  <a href="scmfsa_1.html#K1" title="SCMFSA_1:func.1">SCM+FSA-Data-Loc</a> , <font color="Maroon" title="c5">fA</font> being    <a href="subset_1.html#M2" title="SUBSET_1:mode.2">Element</a> of  <a href="scmfsa_1.html#K2" title="SCMFSA_1:func.2">SCM+FSA-Data*-Loc</a> <b> such that </b><br/><a NAME="E3:105_2"/><i><font color="Green" title="E74">A5</font></i>: 
<font color="Maroon" title="c1">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="c2">L</font>,<span class="p2"><a href="finseq_4.html#K3" title="FINSEQ_4:func.3">&lt;*</a><span class="default"><font color="Maroon" title="c3">dB</font>,<font color="Maroon" title="c5">fA</font>,<font color="Maroon" title="c4">dA</font></span><a href="finseq_4.html#K3" title="FINSEQ_4:func.3">*&gt;</a></span></span><a href="tarski.html#K4" title="TARSKI:func.4">]</a></span>
 <b>and </b><br/><a NAME="E4:105_2"/><i><font color="Green" title="E75">A6</font></i>: 
<font color="Maroon" title="c2">L</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">9,10</span><a href="tarski.html#K2" title="TARSKI:func.2">}</a></span>
 ;<br/><a NAME="E5:105_2"/>
( <font color="Maroon" title="c2">L</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 9 or <font color="Maroon" title="c2">L</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 10 )
 <b>by </b><i><a class="txt" href="scmfsa_2.html#E4:105_2"><i><font color="Green" title="E75">A6</font></i></a>, <a class="ref" href="tarski.html#D2" title="TARSKI:def.2">TARSKI:def 2</a></i>;<br/><b>hence </b><a NAME="E6:105_2"/>
contradiction
 <b>by </b><i><a class="txt" href="scmfsa_2.html#E1:105"><i><font color="Green" title="E72">A1</font></i></a>, <a class="txt" href="scmfsa_2.html#E3:105_2"><i><font color="Green" title="E74">A5</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="E5:105"/><b>then </b><i><font color="Green" title="E74">A7</font></i>: 
<font color="Maroon" title="c1">I</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="ami_2.html#K6" title="AMI_2:func.6">SCM-Instr</a> 
 
<b>by </b><i><a class="txt" href="scmfsa_2.html#E3:105"><i><font color="Green" title="E73">A4</font></i></a>, <a class="ref" href="xboole_0.html#D2" title="XBOOLE_0:def.2">XBOOLE_0:def 2</a></i>;<br/>
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="105_3"><b>now </b></a><div class="add"><b>assume </b><a NAME="E1:105_3"/>
<font color="Maroon" title="c1">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">R</font>,<span class="p3"><a href="finseq_4.html#K2" title="FINSEQ_4:func.2">&lt;*</a><span class="default"><font color="Olive" title="b2">DA</font>,<font color="Olive" title="b3">DC</font></span><a href="finseq_4.html#K2" title="FINSEQ_4:func.2">*&gt;</a></span></span><a href="tarski.html#K4" title="TARSKI:func.4">]</a></span> where <font color="Olive" title="b1">R</font> is    <a href="subset_1.html#M2" title="SUBSET_1:mode.2">Element</a> of  <a href="gr_cy_1.html#K1" title="GR_CY_1:func.1">Segm</a> 9, <font color="Olive" title="b2">DA</font>, <font color="Olive" title="b3">DC</font> is    <a href="subset_1.html#M2" title="SUBSET_1:mode.2">Element</a> of  <a href="ami_2.html#K4" title="AMI_2:func.4">SCM-Data-Loc</a>  : <font color="Olive" title="b1">R</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">1,2,3,4,5</span><a href="enumset1.html#K3" title="ENUMSET1:func.3">}</a></span> </span>}</span> 
 ;<br/><b>then consider </b><font color="Maroon" title="c2">R</font> being    <a href="subset_1.html#M2" title="SUBSET_1:mode.2">Element</a> of  <a href="gr_cy_1.html#K1" title="GR_CY_1:func.1">Segm</a> 9, <font color="Maroon" title="c3">DA</font>, <font color="Maroon" title="c4">DC</font> being    <a href="subset_1.html#M2" title="SUBSET_1:mode.2">Element</a> of  <a href="ami_2.html#K4" title="AMI_2:func.4">SCM-Data-Loc</a> <b> such that </b><br/><a NAME="E3:105_3"/><i><font color="Green" title="E75">A8</font></i>: 
<font color="Maroon" title="c1">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="c2">R</font>,<span class="p2"><a href="finseq_4.html#K2" title="FINSEQ_4:func.2">&lt;*</a><span class="default"><font color="Maroon" title="c3">DA</font>,<font color="Maroon" title="c4">DC</font></span><a href="finseq_4.html#K2" title="FINSEQ_4:func.2">*&gt;</a></span></span><a href="tarski.html#K4" title="TARSKI:func.4">]</a></span>
 <b>and </b><br/><a NAME="E4:105_3"/><i><font color="Green" title="E76">A9</font></i>: 
<font color="Maroon" title="c2">R</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">1,2,3,4,5</span><a href="enumset1.html#K3" title="ENUMSET1:func.3">}</a></span>
 ;<br/><a NAME="E5:105_3"/>
( <font color="Maroon" title="c2">R</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 1 or <font color="Maroon" title="c2">R</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 2 or <font color="Maroon" title="c2">R</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 3 or <font color="Maroon" title="c2">R</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 4 or <font color="Maroon" title="c2">R</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 5 )
 <b>by </b><i><a class="txt" href="scmfsa_2.html#E4:105_3"><i><font color="Green" title="E76">A9</font></i></a>, <a class="ref" href="enumset1.html#D3" title="ENUMSET1:def.3">ENUMSET1:def 3</a></i>;<br/><b>hence </b><a NAME="E6:105_3"/>
contradiction
 <b>by </b><i><a class="txt" href="scmfsa_2.html#E1:105"><i><font color="Green" title="E72">A1</font></i></a>, <a class="txt" href="scmfsa_2.html#E3:105_3"><i><font color="Green" title="E75">A8</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="E7:105"/><b>then </b><i><font color="Green" title="E75">A10</font></i>: 
<font color="Maroon" title="c1">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#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">O</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">LA</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">O</font> is    <a href="subset_1.html#M2" title="SUBSET_1:mode.2">Element</a> of  <a href="gr_cy_1.html#K1" title="GR_CY_1:func.1">Segm</a> 9, <font color="Olive" title="b2">LA</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-Instr-Loc</a>  : <font color="Olive" title="b1">O</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">P</font>,<span class="p3"><a href="finseq_4.html#K2" title="FINSEQ_4:func.2">&lt;*</a><span class="default"><font color="Olive" title="b2">LB</font>,<font color="Olive" title="b3">DB</font></span><a href="finseq_4.html#K2" title="FINSEQ_4:func.2">*&gt;</a></span></span><a href="tarski.html#K4" title="TARSKI:func.4">]</a></span> where <font color="Olive" title="b1">P</font> is    <a href="subset_1.html#M2" title="SUBSET_1:mode.2">Element</a> of  <a href="gr_cy_1.html#K1" title="GR_CY_1:func.1">Segm</a> 9, <font color="Olive" title="b2">LB</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-Instr-Loc</a> , <font color="Olive" title="b3">DB</font> is    <a href="subset_1.html#M2" title="SUBSET_1:mode.2">Element</a> of  <a href="ami_2.html#K4" title="AMI_2:func.4">SCM-Data-Loc</a>  : <font color="Olive" title="b1">P</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">7,8</span><a href="tarski.html#K2" title="TARSKI:func.2">}</a></span> </span>}</span> 
 
<b>by </b><i><a class="txt" href="scmfsa_2.html#E5:105"><i><font color="Green" title="E74">A7</font></i></a>, <a class="ref" href="ami_2.html#D4" title="AMI_2:def.4">AMI_2:def 4</a>, <a class="ref" href="xboole_0.html#D2" title="XBOOLE_0:def.2">XBOOLE_0:def 2</a></i>;<br/>
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="105_4"><b>now </b></a><div class="add"><b>assume </b><a NAME="E1:105_4"/>
<font color="Maroon" title="c1">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">P</font>,<span class="p3"><a href="finseq_4.html#K2" title="FINSEQ_4:func.2">&lt;*</a><span class="default"><font color="Olive" title="b2">LB</font>,<font color="Olive" title="b3">DB</font></span><a href="finseq_4.html#K2" title="FINSEQ_4:func.2">*&gt;</a></span></span><a href="tarski.html#K4" title="TARSKI:func.4">]</a></span> where <font color="Olive" title="b1">P</font> is    <a href="subset_1.html#M2" title="SUBSET_1:mode.2">Element</a> of  <a href="gr_cy_1.html#K1" title="GR_CY_1:func.1">Segm</a> 9, <font color="Olive" title="b2">LB</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-Instr-Loc</a> , <font color="Olive" title="b3">DB</font> is    <a href="subset_1.html#M2" title="SUBSET_1:mode.2">Element</a> of  <a href="ami_2.html#K4" title="AMI_2:func.4">SCM-Data-Loc</a>  : <font color="Olive" title="b1">P</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">7,8</span><a href="tarski.html#K2" title="TARSKI:func.2">}</a></span> </span>}</span> 
 ;<br/><b>then consider </b><font color="Maroon" title="c2">P</font> being    <a href="subset_1.html#M2" title="SUBSET_1:mode.2">Element</a> of  <a href="gr_cy_1.html#K1" title="GR_CY_1:func.1">Segm</a> 9, <font color="Maroon" title="c3">LB</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-Instr-Loc</a> , <font color="Maroon" title="c4">DB</font> being    <a href="subset_1.html#M2" title="SUBSET_1:mode.2">Element</a> of  <a href="ami_2.html#K4" title="AMI_2:func.4">SCM-Data-Loc</a> <b> such that </b><br/><a NAME="E3:105_4"/><i><font color="Green" title="E76">A11</font></i>: 
<font color="Maroon" title="c1">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="c2">P</font>,<span class="p2"><a href="finseq_4.html#K2" title="FINSEQ_4:func.2">&lt;*</a><span class="default"><font color="Maroon" title="c3">LB</font>,<font color="Maroon" title="c4">DB</font></span><a href="finseq_4.html#K2" title="FINSEQ_4:func.2">*&gt;</a></span></span><a href="tarski.html#K4" title="TARSKI:func.4">]</a></span>
 <b>and </b><br/><a NAME="E4:105_4"/><i><font color="Green" title="E77">A12</font></i>: 
<font color="Maroon" title="c2">P</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">7,8</span><a href="tarski.html#K2" title="TARSKI:func.2">}</a></span>
 ;<br/><a NAME="E5:105_4"/>
( <font color="Maroon" title="c2">P</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 7 or <font color="Maroon" title="c2">P</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 8 )
 <b>by </b><i><a class="txt" href="scmfsa_2.html#E4:105_4"><i><font color="Green" title="E77">A12</font></i></a>, <a class="ref" href="tarski.html#D2" title="TARSKI:def.2">TARSKI:def 2</a></i>;<br/><b>hence </b><a NAME="E6:105_4"/>
contradiction
 <b>by </b><i><a class="txt" href="scmfsa_2.html#E1:105"><i><font color="Green" title="E72">A1</font></i></a>, <a class="txt" href="scmfsa_2.html#E3:105_4"><i><font color="Green" title="E76">A11</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="E9:105"/><b>then </b><i><font color="Green" title="E76">A13</font></i>: 
<font color="Maroon" title="c1">I</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">O</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">LA</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">O</font> is    <a href="subset_1.html#M2" title="SUBSET_1:mode.2">Element</a> of  <a href="gr_cy_1.html#K1" title="GR_CY_1:func.1">Segm</a> 9, <font color="Olive" title="b2">LA</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-Instr-Loc</a>  : <font color="Olive" title="b1">O</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 6 </span>}</span> 
 
<b>by </b><i><a class="txt" href="scmfsa_2.html#E7:105"><i><font color="Green" title="E75">A10</font></i></a>, <a class="ref" href="xboole_0.html#D2" title="XBOOLE_0:def.2">XBOOLE_0:def 2</a></i>;<br/>
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="105_5"><b>now </b></a><div class="add"><b>assume </b><a NAME="E1:105_5"/>
<font color="Maroon" title="c1">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">O</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">LA</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">O</font> is    <a href="subset_1.html#M2" title="SUBSET_1:mode.2">Element</a> of  <a href="gr_cy_1.html#K1" title="GR_CY_1:func.1">Segm</a> 9, <font color="Olive" title="b2">LA</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-Instr-Loc</a>  : <font color="Olive" title="b1">O</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 6 </span>}</span> 
 ;<br/><b>then consider </b><font color="Maroon" title="c2">O</font> being    <a href="subset_1.html#M2" title="SUBSET_1:mode.2">Element</a> of  <a href="gr_cy_1.html#K1" title="GR_CY_1:func.1">Segm</a> 9, <font color="Maroon" title="c3">LA</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-Instr-Loc</a> <b> such that </b><br/><a NAME="E3:105_5"/><i><font color="Green" title="E77">A14</font></i>: 
<font color="Maroon" title="c1">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="c2">O</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">LA</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="E4:105_5"/><i><font color="Green" title="E78">A15</font></i>: 
<font color="Maroon" title="c2">O</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 6
 ;<br/><b>thus </b><a NAME="E5:105_5"/>
contradiction
 <b>by </b><i><a class="txt" href="scmfsa_2.html#E1:105"><i><font color="Green" title="E72">A1</font></i></a>, <a class="txt" href="scmfsa_2.html#E3:105_5"><i><font color="Green" title="E77">A14</font></i></a>, <a class="txt" href="scmfsa_2.html#E4:105_5"><i><font color="Green" title="E78">A15</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="E11:105"/><b>then </b>
<font color="Maroon" title="c1">I</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="scmfsa_2.html#E9:105"><i><font color="Green" title="E76">A13</font></i></a>, <a class="ref" href="xboole_0.html#D2" title="XBOOLE_0:def.2">XBOOLE_0:def 2</a></i>;<br/>
<b>hence </b><a NAME="E12:105"/>
<font color="Maroon" title="c1">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,<a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a> </span><a href="tarski.html#K4" title="TARSKI:func.4">]</a></span>
 <b>by </b><i><a class="ref" href="tarski.html#D1" title="TARSKI:def.1">TARSKI:def 1</a></i>;<br/>


</div>
