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<div class="add">

<b>let </b><font color="Maroon">R</font> be  <a href="scmring1.html#V1">good</a> <a href="funcsdom.html#NM1">Ring</a>;<br/><b>let </b><font color="Maroon">i1</font> be   <a href="ami_1.html#NM2">Instruction-Location</a> of <span class="p1">(<span class="default"><a href="scmring2.html#K1">SCM</a> <font color="Maroon">R</font></span>)</span>;<br/>



<a NAME="E1:50"/>
 <a href="ami_5.html#K1">InsCode</a> <span class="p1">(<span class="default"><a href="scmring2.html#K9">goto</a> <font color="Maroon">i1</font></span>)</span> <a href="hidden.html#R1">=</a> 6
 
<b>by </b><i/>;<br/>
<a NAME="E2:50"/><b>then </b>
 <a href="relat_1.html#K1">dom</a> <span class="p1">(<span class="default"><a href="amistd_2.html#K1">PA</a> <span class="p2">(<span class="default"><a href="amistd_2.html#K5">AddressParts</a> <span class="p3">(<span class="default"><a href="ami_5.html#K1">InsCode</a> <span class="p4">(<span class="default"><a href="scmring2.html#K9">goto</a> <font color="Maroon">i1</font></span>)</span></span>)</span></span>)</span></span>)</span> <a href="hidden.html#R1">=</a> <span class="p1"><a href="realset1.html#K5">{</a><span class="default">1</span><a href="realset1.html#K5">}</a></span>
 
<b>by </b><i/>;<br/>
<a NAME="E3:50"/><b>then </b><i><font color="Green">E50</font></i>: 
1 <a href="hidden.html#R2">in</a>  <a href="relat_1.html#K1">dom</a> <span class="p1">(<span class="default"><a href="amistd_2.html#K1">PA</a> <span class="p2">(<span class="default"><a href="amistd_2.html#K5">AddressParts</a> <span class="p3">(<span class="default"><a href="ami_5.html#K1">InsCode</a> <span class="p4">(<span class="default"><a href="scmring2.html#K9">goto</a> <font color="Maroon">i1</font></span>)</span></span>)</span></span>)</span></span>)</span>
 
<b>by </b><i><a class="ref" href="tarski.html#D1">TARSKI:def 1</a></i>;<br/>
<a NAME="E4:50"/><i><font color="Green">E51</font></i>: 
 <a href="ami_5.html#K1">InsCode</a> <span class="p1">(<span class="default"><a href="scmring2.html#K9">goto</a> <font color="Maroon">i1</font></span>)</span> <a href="hidden.html#R1">=</a> 6
 
<b>by </b><i/>;<br/>
<div><b>hereby </b> <i><font color="Red">:: according to </font></i><a class="ref" href="tarski.html#D3">TARSKI:def 3</a>,<a class="ref" href="xboole_0.html#D10">XBOOLE_0:def 10</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="E1:50_1"/>
<font color="Maroon">x</font> <a href="hidden.html#R2">in</a> <span class="p1">(<span class="default"><a href="amistd_2.html#K1">PA</a> <span class="p2">(<span class="default"><a href="amistd_2.html#K5">AddressParts</a> <span class="p3">(<span class="default"><a href="ami_5.html#K1">InsCode</a> <span class="p4">(<span class="default"><a href="scmring2.html#K9">goto</a> <font color="Maroon">i1</font></span>)</span></span>)</span></span>)</span></span>)</span> <a href="funct_1.html#K1">.</a> 1
 ;<br/><a NAME="E2:50_1"/><b>then </b>
<font color="Maroon">x</font> <a href="hidden.html#R2">in</a>  <a href="card_3.html#K5">pi</a> <span class="p1">(<span class="default"><a href="amistd_2.html#K5">AddressParts</a> <span class="p2">(<span class="default"><a href="ami_5.html#K1">InsCode</a> <span class="p3">(<span class="default"><a href="scmring2.html#K9">goto</a> <font color="Maroon">i1</font></span>)</span></span>)</span></span>)</span>,1
 <b>by </b><i>, <a class="ref" href="amistd_2.html#T8">AMISTD_2:8</a></i>;<br/><b>then consider </b><font color="Maroon">g</font> being   <a href="funct_1.html#NM1">Function</a><b> such that </b><br/><a NAME="E4:50_1"/><i><font color="Green">E64</font></i>: 
<font color="Maroon">g</font> <a href="hidden.html#R2">in</a>  <a href="amistd_2.html#K5">AddressParts</a> <span class="p1">(<span class="default"><a href="ami_5.html#K1">InsCode</a> <span class="p2">(<span class="default"><a href="scmring2.html#K9">goto</a> <font color="Maroon">i1</font></span>)</span></span>)</span>
 <b>and </b><br/><a NAME="E5:50_1"/><i><font color="Green">E67</font></i>: 
<font color="Maroon">x</font> <a href="hidden.html#R1">=</a> <font color="Maroon">g</font> <a href="funct_1.html#K1">.</a> 1
 <b>by </b><i><a class="ref" href="card_3.html#D6">CARD_3:def 6</a></i>;<br/><b>consider </b><font color="Maroon">I</font> being   <a href="ami_1.html#NM3">Instruction</a> of <span class="p1">(<span class="default"><a href="scmring2.html#K1">SCM</a> <font color="Maroon">R</font></span>)</span><b> such that </b><br/><a NAME="E7:50_1"/><i><font color="Green">E68</font></i>: 
<font color="Maroon">g</font> <a href="hidden.html#R1">=</a>  <a href="amistd_2.html#K4">AddressPart</a> <font color="Maroon">I</font>
 <b>and </b><br/><a NAME="E8:50_1"/><i><font color="Green">E69</font></i>: 
 <a href="ami_5.html#K1">InsCode</a> <font color="Maroon">I</font> <a href="hidden.html#R1">=</a>  <a href="ami_5.html#K1">InsCode</a> <span class="p1">(<span class="default"><a href="scmring2.html#K9">goto</a> <font color="Maroon">i1</font></span>)</span>
 <b>by </b><i><a class="ref" href="scmring3.html#T2" target="_self">Th2</a></i>;<br/><b>consider </b><font color="Maroon">i2</font> being   <a href="ami_1.html#NM2">Instruction-Location</a> of <span class="p1">(<span class="default"><a href="scmring2.html#K1">SCM</a> <font color="Maroon">R</font></span>)</span><b> such that </b><br/><a NAME="E10:50_1"/><i><font color="Green">E104</font></i>: 
<font color="Maroon">I</font> <a href="hidden.html#R1">=</a>  <a href="scmring2.html#K9">goto</a> <font color="Maroon">i2</font>
 <b>by </b><i>, <a class="ref" href="scmring3.html#T5" target="_self">Th5</a>, </i>;<br/><a NAME="E11:50_1"/>
<font color="Maroon">g</font> <a href="hidden.html#R1">=</a> <span class="p1"><a href="finseq_1.html#K12">&lt;*</a><span class="default"><font color="Maroon">i2</font></span><a href="finseq_1.html#K12">*&gt;</a></span>
 <b>by </b><i><a class="ref" href="scmring3.html#T4" target="_self">Th4</a>, , <a class="ref" href="mcart_1.html#D2">MCART_1:def 2</a></i>;<br/><a NAME="E12:50_1"/><b>then </b>
<font color="Maroon">x</font> <a href="hidden.html#R1">=</a> <font color="Maroon">i2</font>
 <b>by </b><i><a class="ref" href="scmring3.html#T3" target="_self">Th3</a>, <a class="ref" href="finseq_1.html#D8">FINSEQ_1:def 8</a></i>;<br/><b>hence </b><a NAME="E13:50_1"/>
<font color="Maroon">x</font> <a href="hidden.html#R2">in</a> the <a href="ami_1.html#U2">Instruction-Locations</a> of <span class="p1">(<span class="default"><a href="scmring2.html#K1">SCM</a> <font color="Maroon">R</font></span>)</span>
 ;<br/></div>
<b>end;</b></div>

<b>let </b><font color="Maroon">x</font> be    <a href="hidden.html#M1">set</a> ; <i><font color="Red">:: according to </font></i><a class="ref" href="tarski.html#D3">TARSKI:def 3</a><br/>

<b>assume </b><a NAME="E6:50"/>
<font color="Maroon">x</font> <a href="hidden.html#R2">in</a> the <a href="ami_1.html#U2">Instruction-Locations</a> of <span class="p1">(<span class="default"><a href="scmring2.html#K1">SCM</a> <font color="Maroon">R</font></span>)</span>
 ;<br/>

<b>then reconsider </b><font color="Maroon">x</font> = <font color="Maroon">x</font> as   <a href="ami_1.html#NM2">Instruction-Location</a> of <span class="p1">(<span class="default"><a href="scmring2.html#K1">SCM</a> <font color="Maroon">R</font></span>)</span> ;<br/>
<a NAME="E8:50"/><i><font color="Green">E112</font></i>: 
 <a href="amistd_2.html#K4">AddressPart</a> <span class="p1">(<span class="default"><a href="scmring2.html#K9">goto</a> <font color="Maroon">x</font></span>)</span> <a href="hidden.html#R1">=</a> <span class="p1"><a href="finseq_1.html#K12">&lt;*</a><span class="default"><font color="Maroon">x</font></span><a href="finseq_1.html#K12">*&gt;</a></span>
 
<b>by </b><i><a class="ref" href="mcart_1.html#D2">MCART_1:def 2</a></i>;<br/>
<a NAME="E9:50"/>
 <a href="ami_5.html#K1">InsCode</a> <span class="p1">(<span class="default"><a href="scmring2.html#K9">goto</a> <font color="Maroon">i1</font></span>)</span> <a href="hidden.html#R1">=</a>  <a href="ami_5.html#K1">InsCode</a> <span class="p1">(<span class="default"><a href="scmring2.html#K9">goto</a> <font color="Maroon">x</font></span>)</span>
 
<b>by </b><i>, </i>;<br/>
<a NAME="E10:50"/><b>then </b><i><font color="Green">E126</font></i>: 
<span class="p1"><a href="finseq_1.html#K12">&lt;*</a><span class="default"><font color="Maroon">x</font></span><a href="finseq_1.html#K12">*&gt;</a></span> <a href="hidden.html#R2">in</a>  <a href="amistd_2.html#K5">AddressParts</a> <span class="p1">(<span class="default"><a href="ami_5.html#K1">InsCode</a> <span class="p2">(<span class="default"><a href="scmring2.html#K9">goto</a> <font color="Maroon">i1</font></span>)</span></span>)</span>
 
<b>by </b><i><a class="ref" href="scmring3.html#T2" target="_self">Th2</a></i>;<br/>
<a NAME="E11:50"/>
<span class="p1"><a href="finseq_1.html#K12">&lt;*</a><span class="default"><font color="Maroon">x</font></span><a href="finseq_1.html#K12">*&gt;</a></span> <a href="funct_1.html#K1">.</a> 1 <a href="hidden.html#R1">=</a> <font color="Maroon">x</font>
 
<b>by </b><i><a class="ref" href="finseq_1.html#D8">FINSEQ_1:def 8</a></i>;<br/>
<a NAME="E12:50"/><b>then </b>
<font color="Maroon">x</font> <a href="hidden.html#R2">in</a>  <a href="card_3.html#K5">pi</a> <span class="p1">(<span class="default"><a href="amistd_2.html#K5">AddressParts</a> <span class="p2">(<span class="default"><a href="ami_5.html#K1">InsCode</a> <span class="p3">(<span class="default"><a href="scmring2.html#K9">goto</a> <font color="Maroon">i1</font></span>)</span></span>)</span></span>)</span>,1
 
<b>by </b><i><a class="ref" href="scmring3.html#T3" target="_self">Th3</a>, <a class="ref" href="card_3.html#D6">CARD_3:def 6</a></i>;<br/>
<b>hence </b><a NAME="E13:50"/>
<font color="Maroon">x</font> <a href="hidden.html#R2">in</a> <span class="p1">(<span class="default"><a href="amistd_2.html#K1">PA</a> <span class="p2">(<span class="default"><a href="amistd_2.html#K5">AddressParts</a> <span class="p3">(<span class="default"><a href="ami_5.html#K1">InsCode</a> <span class="p4">(<span class="default"><a href="scmring2.html#K9">goto</a> <font color="Maroon">i1</font></span>)</span></span>)</span></span>)</span></span>)</span> <a href="funct_1.html#K1">.</a> 1
 <b>by </b><i>, <a class="ref" href="amistd_2.html#T8">AMISTD_2:8</a></i>;<br/>


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