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

<b>let </b><font color="Maroon">c<sub>1</sub></font>, <font color="Maroon">c<sub>2</sub></font> be    <a href="scmfsa_2.html#M1" target="_self">Int-Location</a> ;<br/><b>let </b><font color="Maroon">c<sub>3</sub></font> be   <a href="ami_1.html#NM4">State</a> of <a href="scmfsa_2.html#K1" target="_self">SCM+FSA</a> ;<br/>





<b>consider </b><font color="Maroon">c<sub>4</sub></font>, <font color="Maroon">c<sub>5</sub></font> being    <a href="ami_3.html#M1">Data-Location</a> <b> such that </b><br/><a NAME="E2:81"/><i><font color="Green">E49</font></i>: 
<font color="Maroon">c<sub>1</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>4</sub></font>
 <b>and </b><br/><a NAME="E3:81"/><i><font color="Green">E50</font></i>: 
<font color="Maroon">c<sub>2</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>5</sub></font>
 <b>and </b><br/><a NAME="E4:81"/><i><font color="Green">E51</font></i>: 
 <a href="scmfsa_2.html#K11" target="_self">MultBy</a> <font color="Maroon">c<sub>1</sub></font>,<font color="Maroon">c<sub>2</sub></font> <a href="hidden.html#R1">=</a>  <a href="ami_3.html#K6">MultBy</a> <font color="Maroon">c<sub>4</sub></font>,<font color="Maroon">c<sub>5</sub></font>
 <b>by </b><i><a class="ref" href="scmfsa_2.html#D14" target="_self">Def14</a></i>;<br/>
<b>reconsider </b><font color="Maroon">c<sub>6</sub></font> = <span class="p1">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="relat_1.html#K7">|</a> <a href="numbers.html#K5">NAT</a> </span>)</span> <a href="funct_4.html#K1">+*</a> <span class="p1">(<span class="default"><a href="ami_2.html#K3">SCM-Instr-Loc</a>  <a href="funcop_1.html#K2">--&gt;</a> <span class="p2">(<span class="default"><a href="ami_3.html#K6">MultBy</a> <font color="Maroon">c<sub>4</sub></font>,<font color="Maroon">c<sub>5</sub></font></span>)</span></span>)</span> as   <a href="ami_1.html#NM4">State</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>, <a class="ref" href="scmfsa_1.html#T18">SCMFSA_1:18</a></i>;<br/>
<a NAME="E6:81"/><i><font color="Green">E52</font></i>: 
 <a href="ami_1.html#K6">IC</a> <font color="Maroon">c<sub>3</sub></font> <a href="hidden.html#R1">=</a>  <a href="ami_1.html#K6">IC</a> <font color="Maroon">c<sub>6</sub></font>
 
<b>by </b><i><a class="ref" href="scmfsa_2.html#T88" target="_self">Th88</a></i>;<br/>
<a NAME="E7:81"/><i><font color="Green">E53</font></i>: 
 <a href="ami_1.html#K4">Exec</a> <span class="p1">(<span class="default"><a href="scmfsa_2.html#K11" target="_self">MultBy</a> <font color="Maroon">c<sub>1</sub></font>,<font color="Maroon">c<sub>2</sub></font></span>)</span>,<font color="Maroon">c<sub>3</sub></font> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="funct_4.html#K1">+*</a> <span class="p2">(<span class="default"><a href="ami_1.html#K4">Exec</a> <span class="p3">(<span class="default"><a href="ami_3.html#K6">MultBy</a> <font color="Maroon">c<sub>4</sub></font>,<font color="Maroon">c<sub>5</sub></font></span>)</span>,<font color="Maroon">c<sub>6</sub></font></span>)</span></span>)</span> <a href="funct_4.html#K1">+*</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="relat_1.html#K7">|</a> <a href="scmfsa_1.html#K3">SCM+FSA-Instr-Loc</a> </span>)</span>
 
<b>by </b><i><a class="txt" href="scmfsa_2.html#E4:81"><i><font color="Green">E51</font></i></a>, <a class="ref" href="scmfsa_2.html#T75" target="_self">Th75</a></i>;<br/>
<b>hence </b><span class="p1">(<span class="default"><a href="ami_1.html#K4">Exec</a> <span class="p2">(<span class="default"><a href="scmfsa_2.html#K11" target="_self">MultBy</a> <font color="Maroon">c<sub>1</sub></font>,<font color="Maroon">c<sub>2</sub></font></span>)</span>,<font color="Maroon">c<sub>3</sub></font></span>)</span> <a href="funct_1.html#K1">.</a> <span class="p1">(<span class="default"><a href="ami_1.html#K2">IC</a> <a href="scmfsa_2.html#K1" target="_self">SCM+FSA</a> </span>)</span> = 
<span class="p1">(<span class="default"><a href="ami_1.html#K4">Exec</a> <span class="p2">(<span class="default"><a href="ami_3.html#K6">MultBy</a> <font color="Maroon">c<sub>4</sub></font>,<font color="Maroon">c<sub>5</sub></font></span>)</span>,<font color="Maroon">c<sub>6</sub></font></span>)</span> <a href="funct_1.html#K1">.</a> <span class="p1">(<span class="default"><a href="ami_1.html#K2">IC</a> <a href="ami_3.html#K1">SCM</a> </span>)</span>
<b>by </b><i><a class="ref" href="scmfsa_2.html#T78" target="_self">Th78</a></i>
<br/>.= 
 <a href="ami_3.html#K11">Next</a> <span class="p1">(<span class="default"><a href="ami_1.html#K6">IC</a> <font color="Maroon">c<sub>6</sub></font></span>)</span>
<b>by </b><i><a class="ref" href="ami_3.html#T11">AMI_3:11</a></i>
<br/>.= 
 <a href="scmfsa_2.html#K7" target="_self">Next</a> <span class="p1">(<span class="default"><a href="ami_1.html#K6">IC</a> <font color="Maroon">c<sub>3</sub></font></span>)</span>
<b>by </b><i><a class="txt" href="scmfsa_2.html#E6:81"><i><font color="Green">E52</font></i></a>, <a class="ref" href="scmfsa_2.html#T33" target="_self">Th33</a></i>
;<br/><br/>

<b>thus </b><span class="p1">(<span class="default"><a href="ami_1.html#K4">Exec</a> <span class="p2">(<span class="default"><a href="scmfsa_2.html#K11" target="_self">MultBy</a> <font color="Maroon">c<sub>1</sub></font>,<font color="Maroon">c<sub>2</sub></font></span>)</span>,<font color="Maroon">c<sub>3</sub></font></span>)</span> <a href="scmfsa_2.html#K20" target="_self">.</a> <font color="Maroon">c<sub>1</sub></font> = 
<span class="p1">(<span class="default"><a href="ami_1.html#K4">Exec</a> <span class="p2">(<span class="default"><a href="ami_3.html#K6">MultBy</a> <font color="Maroon">c<sub>4</sub></font>,<font color="Maroon">c<sub>5</sub></font></span>)</span>,<font color="Maroon">c<sub>6</sub></font></span>)</span> <a href="ami_3.html#K2">.</a> <font color="Maroon">c<sub>4</sub></font>
<b>by </b><i><a class="txt" href="scmfsa_2.html#E2:81"><i><font color="Green">E49</font></i></a>, <a class="txt" href="scmfsa_2.html#E7:81"><i><font color="Green">E53</font></i></a>, <a class="ref" href="scmfsa_2.html#T79" target="_self">Th79</a></i>
<br/>.= 
<span class="p1">(<span class="default"><font color="Maroon">c<sub>6</sub></font> <a href="ami_3.html#K2">.</a> <font color="Maroon">c<sub>4</sub></font></span>)</span> <a href="xcmplx_0.html#K3">*</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>6</sub></font> <a href="ami_3.html#K2">.</a> <font color="Maroon">c<sub>5</sub></font></span>)</span>
<b>by </b><i><a class="ref" href="ami_3.html#T11">AMI_3:11</a></i>
<br/>.= 
<span class="p1">(<span class="default"><font color="Maroon">c<sub>6</sub></font> <a href="ami_3.html#K2">.</a> <font color="Maroon">c<sub>4</sub></font></span>)</span> <a href="xcmplx_0.html#K3">*</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="scmfsa_2.html#K20" target="_self">.</a> <font color="Maroon">c<sub>2</sub></font></span>)</span>
<b>by </b><i><a class="txt" href="scmfsa_2.html#E3:81"><i><font color="Green">E50</font></i></a>, <a class="ref" href="scmfsa_2.html#T80" target="_self">Th80</a></i>
<br/>.= 
<span class="p1">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="scmfsa_2.html#K20" target="_self">.</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="xcmplx_0.html#K3">*</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="scmfsa_2.html#K20" target="_self">.</a> <font color="Maroon">c<sub>2</sub></font></span>)</span>
<b>by </b><i><a class="txt" href="scmfsa_2.html#E2:81"><i><font color="Green">E49</font></i></a>, <a class="ref" href="scmfsa_2.html#T80" target="_self">Th80</a></i>
;<br/>

<div><b>hereby </b>
<div class="add"><b>let </b><font color="Maroon">c<sub>7</sub></font> be    <a href="scmfsa_2.html#M1" target="_self">Int-Location</a> ;<br/><b>assume </b><a NAME="E1:81_3"/><i><font color="Green">E54</font></i>: 
<font color="Maroon">c<sub>7</sub></font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <font color="Maroon">c<sub>1</sub></font>
 ;<br/><b>reconsider </b><font color="Maroon">c<sub>8</sub></font> = <font color="Maroon">c<sub>7</sub></font> as    <a href="ami_3.html#M1">Data-Location</a>  <b>by </b><i><a class="ref" href="scmfsa_2.html#T25" target="_self">Th25</a></i>;<br/><b>thus </b><span class="p1">(<span class="default"><a href="ami_1.html#K4">Exec</a> <span class="p2">(<span class="default"><a href="scmfsa_2.html#K11" target="_self">MultBy</a> <font color="Maroon">c<sub>1</sub></font>,<font color="Maroon">c<sub>2</sub></font></span>)</span>,<font color="Maroon">c<sub>3</sub></font></span>)</span> <a href="scmfsa_2.html#K20" target="_self">.</a> <font color="Maroon">c<sub>7</sub></font> = 
<span class="p1">(<span class="default"><a href="ami_1.html#K4">Exec</a> <span class="p2">(<span class="default"><a href="ami_3.html#K6">MultBy</a> <font color="Maroon">c<sub>4</sub></font>,<font color="Maroon">c<sub>5</sub></font></span>)</span>,<font color="Maroon">c<sub>6</sub></font></span>)</span> <a href="ami_3.html#K2">.</a> <font color="Maroon">c<sub>8</sub></font>
<b>by </b><i><a class="txt" href="scmfsa_2.html#E7:81"><i><font color="Green">E53</font></i></a>, <a class="ref" href="scmfsa_2.html#T79" target="_self">Th79</a></i>
<br/>.= 
<font color="Maroon">c<sub>6</sub></font> <a href="ami_3.html#K2">.</a> <font color="Maroon">c<sub>8</sub></font>
<b>by </b><i><a class="txt" href="scmfsa_2.html#E2:81"><i><font color="Green">E49</font></i></a>, <a class="txt" href="scmfsa_2.html#E1:81_3"><i><font color="Green">E54</font></i></a>, <a class="ref" href="ami_3.html#T11">AMI_3:11</a></i>
<br/>.= 
<font color="Maroon">c<sub>3</sub></font> <a href="scmfsa_2.html#K20" target="_self">.</a> <font color="Maroon">c<sub>7</sub></font>
<b>by </b><i><a class="ref" href="scmfsa_2.html#T80" target="_self">Th80</a></i>
;<br/></div>
<b>end;</b></div>

<b>let </b><font color="Maroon">c<sub>7</sub></font> be    <a href="scmfsa_2.html#M2" target="_self">FinSeq-Location</a> ;<br/>

<a NAME="E11:81"/><i><font color="Green">E54</font></i>: 
 <a href="relat_1.html#K1">dom</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="relat_1.html#K7">|</a> <a href="scmfsa_1.html#K3">SCM+FSA-Instr-Loc</a> </span>)</span> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><a href="relat_1.html#K1">dom</a> <font color="Maroon">c<sub>3</sub></font></span>)</span> <a href="subset_1.html#K9">/\</a> <a href="scmfsa_1.html#K3">SCM+FSA-Instr-Loc</a> 
 
<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="81_4"><b>now </b></a><div class="add"><b>assume </b><a NAME="E1:81_4"/>
<font color="Maroon">c<sub>7</sub></font> <a href="hidden.html#R2">in</a>  <a href="scmfsa_1.html#K3">SCM+FSA-Instr-Loc</a> 
 ;<br/><a NAME="E2:81_4"/><b>then </b><i><font color="Green">E55</font></i>: 
<a href="scmfsa_1.html#K6">SCM+FSA-OK</a>  <a href="funct_1.html#K1">.</a> <font color="Maroon">c<sub>7</sub></font> <a href="hidden.html#R1">=</a>  <a href="scmfsa_1.html#K4">SCM+FSA-Instr</a> 
 <b>by </b><i><a class="ref" href="scmfsa_1.html#T11">SCMFSA_1:11</a></i>;<br/><a NAME="E3:81_4"/>
<font color="Maroon">c<sub>7</sub></font> <a href="hidden.html#R2">in</a>  <a href="scmfsa_1.html#K2">SCM+FSA-Data*-Loc</a> 
 <b>by </b><i><a class="ref" href="scmfsa_2.html#D5" target="_self">Def5</a></i>;<br/><b>hence </b><a NAME="E4:81_4"/>
contradiction
 <b>by </b><i><a class="txt" href="scmfsa_2.html#E2:81_4"><i><font color="Green">E55</font></i></a>, <a class="ref" href="scmfsa_1.html#T12">SCMFSA_1:12</a>, <a class="ref" href="scmfsa_1.html#T13">SCMFSA_1:13</a></i>;<br/></div><b>end;</b></div>
<a NAME="E13:81"/><b>then </b><i><font color="Green">E55</font></i>: 
not <font color="Maroon">c<sub>7</sub></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">c<sub>3</sub></font> <a href="relat_1.html#K7">|</a> <a href="scmfsa_1.html#K3">SCM+FSA-Instr-Loc</a> </span>)</span>
 
<b>by </b><i><a class="txt" href="scmfsa_2.html#E11:81"><i><font color="Green">E54</font></i></a>, <a class="ref" href="xboole_0.html#D3">XBOOLE_0:def 3</a></i>;<br/>
<a NAME="E14:81"/><i><font color="Green">E56</font></i>: 
not <font color="Maroon">c<sub>7</sub></font> <a href="hidden.html#R2">in</a>  <a href="relat_1.html#K1">dom</a> <span class="p1">(<span class="default"><a href="ami_1.html#K4">Exec</a> <span class="p2">(<span class="default"><a href="ami_3.html#K6">MultBy</a> <font color="Maroon">c<sub>4</sub></font>,<font color="Maroon">c<sub>5</sub></font></span>)</span>,<font color="Maroon">c<sub>6</sub></font></span>)</span>
 
<b>by </b><i><a class="ref" href="scmfsa_2.html#T68" target="_self">Th68</a></i>;<br/>
<b>thus </b><span class="p1">(<span class="default"><a href="ami_1.html#K4">Exec</a> <span class="p2">(<span class="default"><a href="scmfsa_2.html#K11" target="_self">MultBy</a> <font color="Maroon">c<sub>1</sub></font>,<font color="Maroon">c<sub>2</sub></font></span>)</span>,<font color="Maroon">c<sub>3</sub></font></span>)</span> <a href="scmfsa_2.html#K21" target="_self">.</a> <font color="Maroon">c<sub>7</sub></font> = 
<span class="p1">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="funct_4.html#K1">+*</a> <span class="p2">(<span class="default"><a href="ami_1.html#K4">Exec</a> <span class="p3">(<span class="default"><a href="ami_3.html#K6">MultBy</a> <font color="Maroon">c<sub>4</sub></font>,<font color="Maroon">c<sub>5</sub></font></span>)</span>,<font color="Maroon">c<sub>6</sub></font></span>)</span></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">c<sub>7</sub></font>
<b>by </b><i><a class="txt" href="scmfsa_2.html#E7:81"><i><font color="Green">E53</font></i></a>, <a class="txt" href="scmfsa_2.html#E13:81"><i><font color="Green">E55</font></i></a>, <a class="ref" href="funct_4.html#T12">FUNCT_4:12</a></i>
<br/>.= 
<font color="Maroon">c<sub>3</sub></font> <a href="scmfsa_2.html#K21" target="_self">.</a> <font color="Maroon">c<sub>7</sub></font>
<b>by </b><i><a class="txt" href="scmfsa_2.html#E14:81"><i><font color="Green">E56</font></i></a>, <a class="ref" href="funct_4.html#T12">FUNCT_4:12</a></i>
;<br/>


</div>
