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

<b>set </b><font color="Maroon">D</font> = <a href="scmfsa_2.html#K2">Int-Locations</a>  <a href="subset_1.html#K4">\/</a> <a href="scmfsa_2.html#K3">FinSeq-Locations</a> ;<br/>
<b>let </b><font color="Maroon">s1</font> be   <a href="ami_1.html#NM4">State</a> of <a href="scmfsa_2.html#K1">SCM+FSA</a> , <font color="Maroon">s2</font> be   <a href="ami_1.html#NM4">State</a> of <a href="scmfsa_2.html#K1">SCM+FSA</a> ;<br/>

<b>assume </b><a NAME="E1:30"/><i><font color="Green">E31</font></i>: 
<font color="Maroon">s1</font> <a href="scmfsa_2.html#K20">.</a> <span class="p1">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> 0</span>)</span> <a href="hidden.html#R1">=</a> <font color="Maroon">s2</font> <a href="scmfsa_2.html#K20">.</a> <span class="p1">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> 0</span>)</span>
 ;<br/>

<b>assume </b><a NAME="E2:30"/><i><font color="Green">E32</font></i>: 
for <font color="Olive">a</font> being <a href="sf_mastr.html#V1">read-write</a>  <a href="scmfsa_2.html#M1">Int-Location</a>  holds  <font color="Maroon">s1</font> <a href="scmfsa_2.html#K20">.</a> <font color="Olive">a</font> <a href="hidden.html#R1">=</a> <font color="Maroon">s2</font> <a href="scmfsa_2.html#K20">.</a> <font color="Olive">a</font>
 ;<br/>

<b>assume </b><a NAME="E3:30"/><i><font color="Green">E33</font></i>: 
for <font color="Olive">f</font> being   <a href="scmfsa_2.html#M2">FinSeq-Location</a>  holds  <font color="Maroon">s1</font> <a href="scmfsa_2.html#K21">.</a> <font color="Olive">f</font> <a href="hidden.html#R1">=</a> <font color="Maroon">s2</font> <a href="scmfsa_2.html#K21">.</a> <font color="Olive">f</font>
 ;<br/>

<i><font color="Green">E41</font></i>:  <a href="relat_1.html#K1">dom</a> <span class="p1">(<span class="default"><font color="Maroon">s1</font> <a href="relat_1.html#K7">|</a> <span class="p2">(<span class="default"><a href="scmfsa_2.html#K2">Int-Locations</a>  <a href="subset_1.html#K4">\/</a> <a href="scmfsa_2.html#K3">FinSeq-Locations</a> </span>)</span></span>)</span> = 
<span class="p1">(<span class="default"><a href="relat_1.html#K1">dom</a> <font color="Maroon">s1</font></span>)</span> <a href="subset_1.html#K9">/\</a> <span class="p1">(<span class="default"><a href="scmfsa_2.html#K2">Int-Locations</a>  <a href="subset_1.html#K4">\/</a> <a href="scmfsa_2.html#K3">FinSeq-Locations</a> </span>)</span>
<b>by </b><i><a class="ref" href="relat_1.html#T90">RELAT_1:90</a></i>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="scmfsa_2.html#K2">Int-Locations</a>  <a href="subset_1.html#K4">\/</a> <a href="scmfsa_2.html#K3">FinSeq-Locations</a> </span>)</span> <a href="xboole_0.html#K2">\/</a> <span class="p3"><a href="tarski.html#K1">{</a><span class="default"><span class="p4">(<span class="default"><a href="ami_1.html#K2">IC</a> <a href="scmfsa_2.html#K1">SCM+FSA</a> </span>)</span></span><a href="tarski.html#K1">}</a></span></span>)</span> <a href="xboole_0.html#K2">\/</a> the <a href="ami_1.html#U2">Instruction-Locations</a> of <a href="scmfsa_2.html#K1">SCM+FSA</a> </span>)</span> <a href="subset_1.html#K9">/\</a> <span class="p1">(<span class="default"><a href="scmfsa_2.html#K2">Int-Locations</a>  <a href="subset_1.html#K4">\/</a> <a href="scmfsa_2.html#K3">FinSeq-Locations</a> </span>)</span>
<b>by </b><i><a class="ref" href="scmfsa6a.html#T34">SCMFSA6A:34</a></i>
<br/>.= 
<span class="p1">(<span class="default"><a href="relat_1.html#K1">dom</a> <font color="Maroon">s2</font></span>)</span> <a href="subset_1.html#K9">/\</a> <span class="p1">(<span class="default"><a href="scmfsa_2.html#K2">Int-Locations</a>  <a href="subset_1.html#K4">\/</a> <a href="scmfsa_2.html#K3">FinSeq-Locations</a> </span>)</span>
<b>by </b><i><a class="ref" href="scmfsa6a.html#T34">SCMFSA6A:34</a></i>
<br/>.= 
 <a href="relat_1.html#K1">dom</a> <span class="p1">(<span class="default"><font color="Maroon">s2</font> <a href="relat_1.html#K7">|</a> <span class="p2">(<span class="default"><a href="scmfsa_2.html#K2">Int-Locations</a>  <a href="subset_1.html#K4">\/</a> <a href="scmfsa_2.html#K3">FinSeq-Locations</a> </span>)</span></span>)</span>
<b>by </b><i><a class="ref" href="relat_1.html#T90">RELAT_1:90</a></i>
;<br/>
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="30_2"><b>now </b></a><div class="add"><b>let </b><font color="Maroon">x</font> be    <a href="hidden.html#M1">set</a> ;<br/><b>assume </b><a NAME="E1:30_2"/><i><font color="Green">E44</font></i>: 
<font color="Maroon">x</font> <a href="hidden.html#R2">in</a>  <a href="relat_1.html#K1">dom</a> <span class="p1">(<span class="default"><font color="Maroon">s1</font> <a href="relat_1.html#K7">|</a> <span class="p2">(<span class="default"><a href="scmfsa_2.html#K2">Int-Locations</a>  <a href="subset_1.html#K4">\/</a> <a href="scmfsa_2.html#K3">FinSeq-Locations</a> </span>)</span></span>)</span>
 ;<br/><a NAME="E2:30_2"/><b>then </b><i><font color="Green">E45</font></i>: 
<font color="Maroon">x</font> <a href="hidden.html#R2">in</a> <span class="p1">(<span class="default"><a href="relat_1.html#K1">dom</a> <font color="Maroon">s1</font></span>)</span> <a href="subset_1.html#K9">/\</a> <span class="p1">(<span class="default"><a href="scmfsa_2.html#K2">Int-Locations</a>  <a href="subset_1.html#K4">\/</a> <a href="scmfsa_2.html#K3">FinSeq-Locations</a> </span>)</span>
 <b>by </b><i><a class="ref" href="relat_1.html#T90">RELAT_1:90</a></i>;<br/><a NAME="E3:30_2"/><b>then </b><i><font color="Green">E46</font></i>: 
( <font color="Maroon">x</font> <a href="hidden.html#R2">in</a>  <a href="relat_1.html#K1">dom</a> <font color="Maroon">s1</font> &amp; <font color="Maroon">x</font> <a href="hidden.html#R2">in</a> <a href="scmfsa_2.html#K2">Int-Locations</a>  <a href="subset_1.html#K4">\/</a> <a href="scmfsa_2.html#K3">FinSeq-Locations</a>  )
 <b>by </b><i><a class="ref" href="xboole_0.html#D3">XBOOLE_0:def 3</a></i>;<br/><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="30_2_1"><b>per </b></a><a class="txt" onclick="hs(this)" href="javascript:()"><b>cases </b></a><span class="hide"><a NAME="E1:30_2_1"/>
( <font color="Maroon">x</font> is    <a href="scmfsa_2.html#M1">Int-Location</a>  or <font color="Maroon">x</font> is    <a href="scmfsa_2.html#M2">FinSeq-Location</a>  or <font color="Maroon">x</font> <a href="hidden.html#R1">=</a>  <a href="ami_1.html#K2">IC</a> <a href="scmfsa_2.html#K1">SCM+FSA</a>  or <font color="Maroon">x</font> is   <a href="ami_1.html#NM2">Instruction-Location</a> of <a href="scmfsa_2.html#K1">SCM+FSA</a>  )
 </span><b>by </b><i><a class="txt" href="scmfsa8c.html#E2:30"><i><font color="Green">E32</font></i></a>, <a class="ref" href="scmfsa6a.html#T35">SCMFSA6A:35</a></i>;<br/><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="30_2_1_1"><b>suppose </b></a><a NAME="E1:30_2_1_1"/><i><font color="Green">E48</font></i>: 
<font color="Maroon">x</font> is    <a href="scmfsa_2.html#M1">Int-Location</a> 
 ;<br/><div class="add"><div><b>hereby </b>
<div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="30_2_1_1_1_1"><b>per </b></a><a class="txt" onclick="hs(this)" href="javascript:()"><b>cases </b></a><span class="hide"><a NAME="E1:30_2_1_1_1_1"/>
( <font color="Maroon">x</font> is  <a href="sf_mastr.html#V1">read-write</a>  <a href="scmfsa_2.html#M1">Int-Location</a>  or  not <font color="Maroon">x</font> is  <a href="sf_mastr.html#V1">read-write</a>  <a href="scmfsa_2.html#M1">Int-Location</a>  )
 </span>;<br/><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="30_2_1_1_1_1_1"><b>suppose </b></a><a NAME="E1:30_2_1_1_1_1_1"/><i><font color="Green">E49</font></i>: 
<font color="Maroon">x</font> is  <a href="sf_mastr.html#V1">read-write</a>  <a href="scmfsa_2.html#M1">Int-Location</a> 
 ;<br/><div class="add"><b>thus </b><span class="p1">(<span class="default"><font color="Maroon">s1</font> <a href="relat_1.html#K7">|</a> <span class="p2">(<span class="default"><a href="scmfsa_2.html#K2">Int-Locations</a>  <a href="subset_1.html#K4">\/</a> <a href="scmfsa_2.html#K3">FinSeq-Locations</a> </span>)</span></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">x</font> = 
<font color="Maroon">s1</font> <a href="funct_1.html#K1">.</a> <font color="Maroon">x</font>
<b>by </b><i>, <a class="ref" href="funct_1.html#T70">FUNCT_1:70</a></i>
<br/>.= 
<font color="Maroon">s2</font> <a href="funct_1.html#K1">.</a> <font color="Maroon">x</font>
<b>by </b><i>, <a class="ref" href="scmfsa8c.html#T6" target="_self">Th6</a></i>
<br/>.= 
<span class="p1">(<span class="default"><font color="Maroon">s2</font> <a href="relat_1.html#K7">|</a> <span class="p2">(<span class="default"><a href="scmfsa_2.html#K2">Int-Locations</a>  <a href="subset_1.html#K4">\/</a> <a href="scmfsa_2.html#K3">FinSeq-Locations</a> </span>)</span></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">x</font>
<b>by </b><i>, , <a class="ref" href="funct_1.html#T70">FUNCT_1:70</a></i>
;<br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="30_2_1_1_1_1_2"><b>suppose </b></a><a NAME="E1:30_2_1_1_1_1_2"/><i><font color="Green">E50</font></i>: 
<font color="Maroon">x</font> is  not  <a href="sf_mastr.html#V1">read-write</a>  <a href="scmfsa_2.html#M1">Int-Location</a> 
 ;<br/><div class="add"><b>reconsider </b><font color="Maroon">a</font> = <font color="Maroon">x</font> as    <a href="scmfsa_2.html#M1">Int-Location</a>  <b>by </b><i><a class="txt" href="scmfsa8c.html#E3:30"><i><font color="Green">E33</font></i></a></i>;<br/><a NAME="E3:30_2_1_1_1_1_2"/>
<font color="Maroon">a</font> <a href="hidden.html#R1">=</a>  <a href="scmfsa_2.html#K4">intloc</a> 0
 <b>by </b><i><a class="ref" href="scmfsa8c.html#T6" target="_self">Th6</a>, <a class="ref" href="sf_mastr.html#D5">SF_MASTR:def 5</a></i>;<br/><b>hence </b><span class="p1">(<span class="default"><font color="Maroon">s1</font> <a href="relat_1.html#K7">|</a> <span class="p2">(<span class="default"><a href="scmfsa_2.html#K2">Int-Locations</a>  <a href="subset_1.html#K4">\/</a> <a href="scmfsa_2.html#K3">FinSeq-Locations</a> </span>)</span></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">x</font> = 
<font color="Maroon">s2</font> <a href="scmfsa_2.html#K20">.</a> <font color="Maroon">a</font>
<b>by </b><i><a class="ref" href="scmfsa8c.html#T2" target="_self">Th2</a>, , <a class="ref" href="funct_1.html#T70">FUNCT_1:70</a></i>
<br/>.= 
<span class="p1">(<span class="default"><font color="Maroon">s2</font> <a href="relat_1.html#K7">|</a> <span class="p2">(<span class="default"><a href="scmfsa_2.html#K2">Int-Locations</a>  <a href="subset_1.html#K4">\/</a> <a href="scmfsa_2.html#K3">FinSeq-Locations</a> </span>)</span></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">x</font>
<b>by </b><i>, , <a class="ref" href="funct_1.html#T70">FUNCT_1:70</a></i>
;<br/><br/></div><b>end;</b></div></div><b>end;</b></div></div>
<b>end;</b></div></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="30_2_1_2"><b>suppose </b></a><a NAME="E1:30_2_1_2"/><i><font color="Green">E51</font></i>: 
<font color="Maroon">x</font> is    <a href="scmfsa_2.html#M2">FinSeq-Location</a> 
 ;<br/><div class="add"><b>thus </b><span class="p1">(<span class="default"><font color="Maroon">s1</font> <a href="relat_1.html#K7">|</a> <span class="p2">(<span class="default"><a href="scmfsa_2.html#K2">Int-Locations</a>  <a href="subset_1.html#K4">\/</a> <a href="scmfsa_2.html#K3">FinSeq-Locations</a> </span>)</span></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">x</font> = 
<font color="Maroon">s1</font> <a href="funct_1.html#K1">.</a> <font color="Maroon">x</font>
<b>by </b><i>, <a class="ref" href="funct_1.html#T70">FUNCT_1:70</a></i>
<br/>.= 
<font color="Maroon">s2</font> <a href="funct_1.html#K1">.</a> <font color="Maroon">x</font>
<b>by </b><i>, <a class="txt" href="scmfsa8c.html#E3:30"><i><font color="Green">E33</font></i></a></i>
<br/>.= 
<span class="p1">(<span class="default"><font color="Maroon">s2</font> <a href="relat_1.html#K7">|</a> <span class="p2">(<span class="default"><a href="scmfsa_2.html#K2">Int-Locations</a>  <a href="subset_1.html#K4">\/</a> <a href="scmfsa_2.html#K3">FinSeq-Locations</a> </span>)</span></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">x</font>
<b>by </b><i>, , <a class="ref" href="funct_1.html#T70">FUNCT_1:70</a></i>
;<br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="30_2_1_3"><b>suppose </b></a><a NAME="E1:30_2_1_3"/><i><font color="Green">E52</font></i>: 
<font color="Maroon">x</font> <a href="hidden.html#R1">=</a>  <a href="ami_1.html#K2">IC</a> <a href="scmfsa_2.html#K1">SCM+FSA</a> 
 ;<br/><div class="add"><b>assume </b><a NAME="E2:30_2_1_3"/>
not <span class="p1">(<span class="default"><font color="Maroon">s1</font> <a href="relat_1.html#K7">|</a> <span class="p2">(<span class="default"><a href="scmfsa_2.html#K2">Int-Locations</a>  <a href="subset_1.html#K4">\/</a> <a href="scmfsa_2.html#K3">FinSeq-Locations</a> </span>)</span></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">x</font> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><font color="Maroon">s2</font> <a href="relat_1.html#K7">|</a> <span class="p2">(<span class="default"><a href="scmfsa_2.html#K2">Int-Locations</a>  <a href="subset_1.html#K4">\/</a> <a href="scmfsa_2.html#K3">FinSeq-Locations</a> </span>)</span></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">x</font>
 ;<br/><b>thus </b><a NAME="E3:30_2_1_3"/>
contradiction
 <b>by </b><i><a class="txt" href="scmfsa8c.html#E1:30"><i><font color="Green">E31</font></i></a>, <a class="txt" href="scmfsa8c.html#E3:30"><i><font color="Green">E33</font></i></a>, <a class="ref" href="scmfsa6a.html#T37">SCMFSA6A:37</a>, <a class="ref" href="xboole_0.html#D3">XBOOLE_0:def 3</a></i>;<br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="30_2_1_4"><b>suppose </b></a><a NAME="E1:30_2_1_4"/><i><font color="Green">E53</font></i>: 
<font color="Maroon">x</font> is   <a href="ami_1.html#NM2">Instruction-Location</a> of <a href="scmfsa_2.html#K1">SCM+FSA</a> 
 ;<br/><div class="add"><b>assume </b><a NAME="E2:30_2_1_4"/>
not <span class="p1">(<span class="default"><font color="Maroon">s1</font> <a href="relat_1.html#K7">|</a> <span class="p2">(<span class="default"><a href="scmfsa_2.html#K2">Int-Locations</a>  <a href="subset_1.html#K4">\/</a> <a href="scmfsa_2.html#K3">FinSeq-Locations</a> </span>)</span></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">x</font> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><font color="Maroon">s2</font> <a href="relat_1.html#K7">|</a> <span class="p2">(<span class="default"><a href="scmfsa_2.html#K2">Int-Locations</a>  <a href="subset_1.html#K4">\/</a> <a href="scmfsa_2.html#K3">FinSeq-Locations</a> </span>)</span></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">x</font>
 ;<br/><b>thus </b><a NAME="E3:30_2_1_4"/>
contradiction
 <b>by </b><i><a class="txt" href="scmfsa8c.html#E2:30"><i><font color="Green">E32</font></i></a>, <a class="txt" href="scmfsa8c.html#E3:30"><i><font color="Green">E33</font></i></a>, <a class="ref" href="scmfsa6a.html#T37">SCMFSA6A:37</a></i>;<br/></div><b>end;</b></div></div><b>end;</b></div></div><b>end;</b></div>
<a NAME="E6:30"/><b>then </b>
<font color="Maroon">s1</font> <a href="relat_1.html#K7">|</a> <span class="p1">(<span class="default"><a href="scmfsa_2.html#K2">Int-Locations</a>  <a href="subset_1.html#K4">\/</a> <a href="scmfsa_2.html#K3">FinSeq-Locations</a> </span>)</span> <a href="tarski.html#R1">c=</a> <font color="Maroon">s2</font> <a href="relat_1.html#K7">|</a> <span class="p1">(<span class="default"><a href="scmfsa_2.html#K2">Int-Locations</a>  <a href="subset_1.html#K4">\/</a> <a href="scmfsa_2.html#K3">FinSeq-Locations</a> </span>)</span>
 
<b>by </b><i>, <a class="ref" href="grfunc_1.html#T8">GRFUNC_1:8</a></i>;<br/>
<b>hence </b><a NAME="E7:30"/>
<font color="Maroon">s1</font> <a href="relat_1.html#K7">|</a> <span class="p1">(<span class="default"><a href="scmfsa_2.html#K2">Int-Locations</a>  <a href="subset_1.html#K4">\/</a> <a href="scmfsa_2.html#K3">FinSeq-Locations</a> </span>)</span> <a href="hidden.html#R1">=</a> <font color="Maroon">s2</font> <a href="relat_1.html#K7">|</a> <span class="p1">(<span class="default"><a href="scmfsa_2.html#K2">Int-Locations</a>  <a href="subset_1.html#K4">\/</a> <a href="scmfsa_2.html#K3">FinSeq-Locations</a> </span>)</span>
 <b>by </b><i>, <a class="ref" href="grfunc_1.html#T9">GRFUNC_1:9</a></i>;<br/>


</div>
