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

<b>let </b><font color="Maroon">c<sub>1</sub></font> be   <a href="ami_1.html#NM3">Instruction</a> of <a href="scmfsa_2.html#K1" target="_self">SCM+FSA</a> ;<br/>

<b>assume </b><a NAME="E1:52"/><i><font color="Green">E32</font></i>: 
 <a href="ami_5.html#K1">InsCode</a> <font color="Maroon">c<sub>1</sub></font> <a href="hidden.html#R1">=</a> 9
 ;<br/>

<a NAME="E2:52"/><i><font color="Green">E33</font></i>: 
( <font color="Maroon">c<sub>1</sub></font> <a href="hidden.html#R2">in</a> <a href="ami_2.html#K4">SCM-Instr</a>  <a href="xboole_0.html#K2">\/</a> <span class="p1">{<span class="default"> <span class="p2"><a href="tarski.html#K4">[</a><span class="default"><font color="Olive">b<sub>1</sub></font>,<span class="p3"><a href="finseq_4.html#K3">&lt;*</a><span class="default"><font color="Olive">b<sub>2</sub></font>,<font color="Olive">b<sub>4</sub></font>,<font color="Olive">b<sub>3</sub></font></span><a href="finseq_4.html#K3">*&gt;</a></span></span><a href="tarski.html#K4">]</a></span> where B is    <a href="subset_1.html#M2">Element</a> of  <a href="gr_cy_1.html#K1">Segm</a> 13, B is    <a href="subset_1.html#M2">Element</a> of  <a href="scmfsa_1.html#K1">SCM+FSA-Data-Loc</a> , B is    <a href="subset_1.html#M2">Element</a> of  <a href="scmfsa_1.html#K1">SCM+FSA-Data-Loc</a> , B is    <a href="subset_1.html#M2">Element</a> of  <a href="scmfsa_1.html#K2">SCM+FSA-Data*-Loc</a>  : <font color="Olive">b<sub>1</sub></font> <a href="hidden.html#R2">in</a> <span class="p1"><a href="tarski.html#K2">{</a><span class="default">9,10</span><a href="tarski.html#K2">}</a></span> </span>}</span>  or <font color="Maroon">c<sub>1</sub></font> <a href="hidden.html#R2">in</a> <span class="p1">{<span class="default"> <span class="p2"><a href="tarski.html#K4">[</a><span class="default"><font color="Olive">b<sub>1</sub></font>,<span class="p3"><a href="finseq_4.html#K2">&lt;*</a><span class="default"><font color="Olive">b<sub>2</sub></font>,<font color="Olive">b<sub>3</sub></font></span><a href="finseq_4.html#K2">*&gt;</a></span></span><a href="tarski.html#K4">]</a></span> where B is    <a href="subset_1.html#M2">Element</a> of  <a href="gr_cy_1.html#K1">Segm</a> 13, B is    <a href="subset_1.html#M2">Element</a> of  <a href="scmfsa_1.html#K1">SCM+FSA-Data-Loc</a> , B is    <a href="subset_1.html#M2">Element</a> of  <a href="scmfsa_1.html#K2">SCM+FSA-Data*-Loc</a>  : <font color="Olive">b<sub>1</sub></font> <a href="hidden.html#R2">in</a> <span class="p1"><a href="tarski.html#K2">{</a><span class="default">11,12</span><a href="tarski.html#K2">}</a></span> </span>}</span>  )
 
<b>by </b><i><a class="ref" href="scmfsa_1.html#D4">SCMFSA_1:def 4</a>, <a class="ref" href="xboole_0.html#D2">XBOOLE_0:def 2</a></i>;<br/>
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="52_1"><b>now </b></a><div class="add"><b>assume </b><a NAME="E1:52_1"/>
<font color="Maroon">c<sub>1</sub></font> <a href="hidden.html#R2">in</a> <span class="p1">{<span class="default"> <span class="p2"><a href="tarski.html#K4">[</a><span class="default"><font color="Olive">b<sub>1</sub></font>,<span class="p3"><a href="finseq_4.html#K2">&lt;*</a><span class="default"><font color="Olive">b<sub>2</sub></font>,<font color="Olive">b<sub>3</sub></font></span><a href="finseq_4.html#K2">*&gt;</a></span></span><a href="tarski.html#K4">]</a></span> where B is    <a href="subset_1.html#M2">Element</a> of  <a href="gr_cy_1.html#K1">Segm</a> 13, B is    <a href="subset_1.html#M2">Element</a> of  <a href="scmfsa_1.html#K1">SCM+FSA-Data-Loc</a> , B is    <a href="subset_1.html#M2">Element</a> of  <a href="scmfsa_1.html#K2">SCM+FSA-Data*-Loc</a>  : <font color="Olive">b<sub>1</sub></font> <a href="hidden.html#R2">in</a> <span class="p1"><a href="tarski.html#K2">{</a><span class="default">11,12</span><a href="tarski.html#K2">}</a></span> </span>}</span> 
 ;<br/><b>then consider </b><font color="Maroon">c<sub>2</sub></font> being    <a href="subset_1.html#M2">Element</a> of  <a href="gr_cy_1.html#K1">Segm</a> 13, <font color="Maroon">c<sub>3</sub></font> being    <a href="subset_1.html#M2">Element</a> of  <a href="scmfsa_1.html#K1">SCM+FSA-Data-Loc</a> , <font color="Maroon">c<sub>4</sub></font> being    <a href="subset_1.html#M2">Element</a> of  <a href="scmfsa_1.html#K2">SCM+FSA-Data*-Loc</a> <b> such that </b><br/><a NAME="E3:52_1"/><i><font color="Green">E34</font></i>: 
<font color="Maroon">c<sub>1</sub></font> <a href="hidden.html#R1">=</a> <span class="p1"><a href="tarski.html#K4">[</a><span class="default"><font color="Maroon">c<sub>2</sub></font>,<span class="p2"><a href="finseq_4.html#K2">&lt;*</a><span class="default"><font color="Maroon">c<sub>3</sub></font>,<font color="Maroon">c<sub>4</sub></font></span><a href="finseq_4.html#K2">*&gt;</a></span></span><a href="tarski.html#K4">]</a></span>
 <b>and </b><br/><a NAME="E4:52_1"/><i><font color="Green">E35</font></i>: 
<font color="Maroon">c<sub>2</sub></font> <a href="hidden.html#R2">in</a> <span class="p1"><a href="tarski.html#K2">{</a><span class="default">11,12</span><a href="tarski.html#K2">}</a></span>
 ;<br/><a NAME="E5:52_1"/><i><font color="Green">E36</font></i>: 
( <font color="Maroon">c<sub>2</sub></font> <a href="hidden.html#R1">=</a> 11 or <font color="Maroon">c<sub>2</sub></font> <a href="hidden.html#R1">=</a> 12 )
 <b>by </b><i><a class="txt" href="scmfsa_2.html#E4:52_1"><i><font color="Green">E35</font></i></a>, <a class="ref" href="tarski.html#D2">TARSKI:def 2</a></i>;<br/><a NAME="E6:52_1"/>
<font color="Maroon">c<sub>1</sub></font> <a href="mcart_1.html#K1">`1</a>  <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>2</sub></font>
 <b>by </b><i><a class="txt" href="scmfsa_2.html#E3:52_1"><i><font color="Green">E34</font></i></a>, <a class="ref" href="mcart_1.html#T7">MCART_1:7</a></i>;<br/><b>hence </b><a NAME="E7:52_1"/>
contradiction
 <b>by </b><i><a class="txt" href="scmfsa_2.html#E1:52"><i><font color="Green">E32</font></i></a>, <a class="txt" href="scmfsa_2.html#E5:52_1"><i><font color="Green">E36</font></i></a>, <a class="ref" href="ami_5.html#D1">AMI_5:def 1</a></i>;<br/></div><b>end;</b></div>
<a NAME="E4:52"/><b>then </b><i><font color="Green">E34</font></i>: 
( <font color="Maroon">c<sub>1</sub></font> <a href="hidden.html#R2">in</a>  <a href="ami_2.html#K4">SCM-Instr</a>  or <font color="Maroon">c<sub>1</sub></font> <a href="hidden.html#R2">in</a> <span class="p1">{<span class="default"> <span class="p2"><a href="tarski.html#K4">[</a><span class="default"><font color="Olive">b<sub>1</sub></font>,<span class="p3"><a href="finseq_4.html#K3">&lt;*</a><span class="default"><font color="Olive">b<sub>2</sub></font>,<font color="Olive">b<sub>4</sub></font>,<font color="Olive">b<sub>3</sub></font></span><a href="finseq_4.html#K3">*&gt;</a></span></span><a href="tarski.html#K4">]</a></span> where B is    <a href="subset_1.html#M2">Element</a> of  <a href="gr_cy_1.html#K1">Segm</a> 13, B is    <a href="subset_1.html#M2">Element</a> of  <a href="scmfsa_1.html#K1">SCM+FSA-Data-Loc</a> , B is    <a href="subset_1.html#M2">Element</a> of  <a href="scmfsa_1.html#K1">SCM+FSA-Data-Loc</a> , B is    <a href="subset_1.html#M2">Element</a> of  <a href="scmfsa_1.html#K2">SCM+FSA-Data*-Loc</a>  : <font color="Olive">b<sub>1</sub></font> <a href="hidden.html#R2">in</a> <span class="p1"><a href="tarski.html#K2">{</a><span class="default">9,10</span><a href="tarski.html#K2">}</a></span> </span>}</span>  )
 
<b>by </b><i><a class="txt" href="scmfsa_2.html#E2:52"><i><font color="Green">E33</font></i></a>, <a class="ref" href="xboole_0.html#D2">XBOOLE_0:def 2</a></i>;<br/>
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="52_2"><b>now </b></a><div class="add"><b>assume </b><a NAME="E1:52_2"/>
<font color="Maroon">c<sub>1</sub></font> <a href="hidden.html#R2">in</a>  <a href="ami_2.html#K4">SCM-Instr</a> 
 ;<br/><b>then reconsider </b><font color="Maroon">c<sub>2</sub></font> = <font color="Maroon">c<sub>1</sub></font> as   <a href="ami_1.html#NM3">Instruction</a> of <a href="ami_3.html#K1">SCM</a>  <b>by </b><i><a class="ref" href="ami_3.html#D1">AMI_3:def 1</a></i>;<br/><a NAME="E3:52_2"/>
 <a href="ami_5.html#K1">InsCode</a> <font color="Maroon">c<sub>2</sub></font> <a href="hidden.html#R1">=</a> 9
 <b>by </b><i><a class="txt" href="scmfsa_2.html#E1:52"><i><font color="Green">E32</font></i></a>, <a class="ref" href="scmfsa_2.html#T37" target="_self">Th37</a></i>;<br/><b>hence </b><a NAME="E4:52_2"/>
contradiction
 <b>by </b><i><a class="ref" href="ami_5.html#T36">AMI_5:36</a></i>;<br/></div><b>end;</b></div>
<b>then consider </b><font color="Maroon">c<sub>2</sub></font> being    <a href="subset_1.html#M2">Element</a> of  <a href="gr_cy_1.html#K1">Segm</a> 13, <font color="Maroon">c<sub>3</sub></font>, <font color="Maroon">c<sub>4</sub></font> being    <a href="subset_1.html#M2">Element</a> of  <a href="scmfsa_1.html#K1">SCM+FSA-Data-Loc</a> , <font color="Maroon">c<sub>5</sub></font> being    <a href="subset_1.html#M2">Element</a> of  <a href="scmfsa_1.html#K2">SCM+FSA-Data*-Loc</a> <b> such that </b><br/><a NAME="E7:52"/><i><font color="Green">E35</font></i>: 
<font color="Maroon">c<sub>1</sub></font> <a href="hidden.html#R1">=</a> <span class="p1"><a href="tarski.html#K4">[</a><span class="default"><font color="Maroon">c<sub>2</sub></font>,<span class="p2"><a href="finseq_4.html#K3">&lt;*</a><span class="default"><font color="Maroon">c<sub>3</sub></font>,<font color="Maroon">c<sub>5</sub></font>,<font color="Maroon">c<sub>4</sub></font></span><a href="finseq_4.html#K3">*&gt;</a></span></span><a href="tarski.html#K4">]</a></span>
 <b>and </b><br/><a NAME="E8:52"/>
<font color="Maroon">c<sub>2</sub></font> <a href="hidden.html#R2">in</a> <span class="p1"><a href="tarski.html#K2">{</a><span class="default">9,10</span><a href="tarski.html#K2">}</a></span>
 <b>by </b><i><a class="txt" href="scmfsa_2.html#E4:52"><i><font color="Green">E34</font></i></a></i>;<br/>
<i><font color="Green">E36</font></i>: <font color="Maroon">c<sub>2</sub></font> = 
<font color="Maroon">c<sub>1</sub></font> <a href="mcart_1.html#K1">`1</a> 
<b>by </b><i><a class="txt" href="scmfsa_2.html#E7:52"><i><font color="Green">E35</font></i></a>, <a class="ref" href="mcart_1.html#T7">MCART_1:7</a></i>
<br/>.= 
9
<b>by </b><i><a class="txt" href="scmfsa_2.html#E1:52"><i><font color="Green">E32</font></i></a>, <a class="ref" href="ami_5.html#D1">AMI_5:def 1</a></i>
;<br/>
<b>reconsider </b><font color="Maroon">c<sub>6</sub></font> = <font color="Maroon">c<sub>3</sub></font>, <font color="Maroon">c<sub>7</sub></font> = <font color="Maroon">c<sub>4</sub></font> as    <a href="scmfsa_2.html#M1" target="_self">Int-Location</a>  <b>by </b><i><a class="ref" href="scmfsa_2.html#D4" target="_self">Def4</a></i>;<br/>
<b>reconsider </b><font color="Maroon">c<sub>8</sub></font> = <font color="Maroon">c<sub>5</sub></font> as    <a href="scmfsa_2.html#M2" target="_self">FinSeq-Location</a>  <b>by </b><i><a class="ref" href="scmfsa_2.html#D5" target="_self">Def5</a></i>;<br/>
<b>take </b>
<font color="Maroon">c<sub>7</sub></font>
;<br/>

<b>take </b>
<font color="Maroon">c<sub>6</sub></font>
;<br/>

<b>take </b>
<font color="Maroon">c<sub>8</sub></font>
;<br/>

<b>thus </b><a NAME="E12:52"/>
<font color="Maroon">c<sub>1</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>6</sub></font> <a href="scmfsa_2.html#K16" target="_self">:=</a> <font color="Maroon">c<sub>8</sub></font>,<font color="Maroon">c<sub>7</sub></font>
 <b>by </b><i><a class="txt" href="scmfsa_2.html#E7:52"><i><font color="Green">E35</font></i></a>, <a class="txt" href="scmfsa_2.html#E9:52"><i><font color="Green">E36</font></i></a></i>;<br/>


</div>
