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<b>let </b><font color="Maroon">c<sub>1</sub></font> be  <a href="scmring1.html#V1">good</a> <a href="funcsdom.html#NM1">Ring</a>;<br/><b>let </b><font color="Maroon">c<sub>2</sub></font>, <font color="Maroon">c<sub>3</sub></font> be    <a href="scmring2.html#M1">Data-Location</a> of <font color="Maroon">c<sub>1</sub></font>;<br/>





<a NAME="E1:40"/><i><font color="Green">E44</font></i>: 
 <a href="ami_5.html#K1">InsCode</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="scmring2.html#K4">:=</a> <font color="Maroon">c<sub>3</sub></font></span>)</span> <a href="hidden.html#R1">=</a> 1
 
<b>by </b><i><a class="ref" href="scmring3.html#T9" target="_self">Th9</a></i>;<br/>
<a NAME="E2:40"/><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"><font color="Maroon">c<sub>2</sub></font> <a href="scmring2.html#K4">:=</a> <font color="Maroon">c<sub>3</sub></font></span>)</span></span>)</span></span>)</span></span>)</span> <a href="hidden.html#R1">=</a> <span class="p1"><a href="tarski.html#K2">{</a><span class="default">1,2</span><a href="tarski.html#K2">}</a></span>
 
<b>by </b><i><a class="ref" href="scmring3.html#T33" target="_self">Th33</a></i>;<br/>
<a NAME="E3:40"/><b>then </b><i><font color="Green">E45</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"><font color="Maroon">c<sub>2</sub></font> <a href="scmring2.html#K4">:=</a> <font color="Maroon">c<sub>3</sub></font></span>)</span></span>)</span></span>)</span></span>)</span>
 
<b>by </b><i><a class="ref" href="tarski.html#D2">TARSKI:def 2</a></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">c<sub>4</sub></font> be    <a href="hidden.html#M1">set</a> ;<br/><b>assume </b><a NAME="E1:40_1"/>
<font color="Maroon">c<sub>4</sub></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"><font color="Maroon">c<sub>2</sub></font> <a href="scmring2.html#K4">:=</a> <font color="Maroon">c<sub>3</sub></font></span>)</span></span>)</span></span>)</span></span>)</span> <a href="funct_1.html#K1">.</a> 1
 ;<br/><a NAME="E2:40_1"/><b>then </b>
<font color="Maroon">c<sub>4</sub></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"><font color="Maroon">c<sub>2</sub></font> <a href="scmring2.html#K4">:=</a> <font color="Maroon">c<sub>3</sub></font></span>)</span></span>)</span></span>)</span>,1
 <b>by </b><i><a class="txt" href="scmring3.html#E3:40"><i><font color="Green">E45</font></i></a>, <a class="ref" href="amistd_2.html#D1">AMISTD_2:def 1</a></i>;<br/><b>then consider </b><font color="Maroon">c<sub>5</sub></font> being   <a href="funct_1.html#NM1">Function</a><b> such that </b><br/><a NAME="E4:40_1"/><i><font color="Green">E46</font></i>: 
<font color="Maroon">c<sub>5</sub></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"><font color="Maroon">c<sub>2</sub></font> <a href="scmring2.html#K4">:=</a> <font color="Maroon">c<sub>3</sub></font></span>)</span></span>)</span>
 <b>and </b><br/><a NAME="E5:40_1"/><i><font color="Green">E47</font></i>: 
<font color="Maroon">c<sub>5</sub></font> <a href="funct_1.html#K1">.</a> 1 <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>4</sub></font>
 <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">c<sub>6</sub></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">c<sub>1</sub></font></span>)</span><b> such that </b><br/><a NAME="E7:40_1"/><i><font color="Green">E48</font></i>: 
<font color="Maroon">c<sub>5</sub></font> <a href="hidden.html#R1">=</a>  <a href="amistd_2.html#K4">AddressPart</a> <font color="Maroon">c<sub>6</sub></font>
 <b>and </b><br/><a NAME="E8:40_1"/><i><font color="Green">E49</font></i>: 
 <a href="ami_5.html#K1">InsCode</a> <font color="Maroon">c<sub>6</sub></font> <a href="hidden.html#R1">=</a>  <a href="ami_5.html#K1">InsCode</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="scmring2.html#K4">:=</a> <font color="Maroon">c<sub>3</sub></font></span>)</span>
 <b>by </b><i><a class="txt" href="scmring3.html#E4:40_1"><i><font color="Green">E46</font></i></a></i>;<br/><a NAME="E9:40_1"/>
 <a href="ami_5.html#K1">InsCode</a> <font color="Maroon">c<sub>6</sub></font> <a href="hidden.html#R1">=</a> 1
 <b>by </b><i><a class="txt" href="scmring3.html#E8:40_1"><i><font color="Green">E49</font></i></a>, <a class="ref" href="scmring3.html#T9" target="_self">Th9</a></i>;<br/><b>then consider </b><font color="Maroon">c<sub>7</sub></font>, <font color="Maroon">c<sub>8</sub></font> being    <a href="scmring2.html#M1">Data-Location</a> of <font color="Maroon">c<sub>1</sub></font><b> such that </b><br/><a NAME="E11:40_1"/><i><font color="Green">E50</font></i>: 
<font color="Maroon">c<sub>6</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>7</sub></font> <a href="scmring2.html#K4">:=</a> <font color="Maroon">c<sub>8</sub></font>
 <b>by </b><i><a class="ref" href="scmring3.html#T17" target="_self">Th17</a></i>;<br/><font color="Maroon">c<sub>4</sub></font> = 
<span class="p1"><a href="finseq_1.html#K10">&lt;*</a><span class="default"><font color="Maroon">c<sub>7</sub></font>,<font color="Maroon">c<sub>8</sub></font></span><a href="finseq_1.html#K10">*&gt;</a></span> <a href="funct_1.html#K1">.</a> 1
<b>by </b><i><a class="txt" href="scmring3.html#E5:40_1"><i><font color="Green">E47</font></i></a>, <a class="txt" href="scmring3.html#E7:40_1"><i><font color="Green">E48</font></i></a>, <a class="txt" href="scmring3.html#E11:40_1"><i><font color="Green">E50</font></i></a>, <a class="ref" href="scmring3.html#T25" target="_self">Th25</a></i>
<br/>.= 
<font color="Maroon">c<sub>7</sub></font>
<b>by </b><i><a class="ref" href="finseq_1.html#T61">FINSEQ_1:61</a></i>
;<br/><b>hence </b><a NAME="E13:40_1"/>
<font color="Maroon">c<sub>4</sub></font> <a href="hidden.html#R2">in</a>  <a href="ami_2.html#K2">SCM-Data-Loc</a> 
 <b>by </b><i><a class="ref" href="scmring2.html#T1">SCMRING2:1</a></i>;<br/></div>
<b>end;</b></div>

<b>let </b><font color="Maroon">c<sub>4</sub></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="E5:40"/>
<font color="Maroon">c<sub>4</sub></font> <a href="hidden.html#R2">in</a>  <a href="ami_2.html#K2">SCM-Data-Loc</a> 
 ;<br/>

<b>then reconsider </b><font color="Maroon">c<sub>5</sub></font> = <font color="Maroon">c<sub>4</sub></font> as    <a href="scmring2.html#M1">Data-Location</a> of <font color="Maroon">c<sub>1</sub></font> <b>by </b><i><a class="ref" href="scmring2.html#T1">SCMRING2:1</a></i>;<br/>
<b>consider </b><font color="Maroon">c<sub>6</sub></font> being    <a href="scmring2.html#M1">Data-Location</a> of <font color="Maroon">c<sub>1</sub></font>;<br/>
<a NAME="E8:40"/>
 <a href="ami_5.html#K1">InsCode</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>5</sub></font> <a href="scmring2.html#K4">:=</a> <font color="Maroon">c<sub>6</sub></font></span>)</span> <a href="hidden.html#R1">=</a> 1
 
<b>by </b><i><a class="ref" href="scmring3.html#T9" target="_self">Th9</a></i>;<br/>
<a NAME="E9:40"/><b>then </b>
 <a href="amistd_2.html#K4">AddressPart</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>5</sub></font> <a href="scmring2.html#K4">:=</a> <font color="Maroon">c<sub>6</sub></font></span>)</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"><font color="Maroon">c<sub>2</sub></font> <a href="scmring2.html#K4">:=</a> <font color="Maroon">c<sub>3</sub></font></span>)</span></span>)</span>
 
<b>by </b><i><a class="txt" href="scmring3.html#E1:40"><i><font color="Green">E44</font></i></a></i>;<br/>
<a NAME="E10:40"/><b>then </b><i><font color="Green">E46</font></i>: 
<span class="p1">(<span class="default"><a href="amistd_2.html#K4">AddressPart</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>5</sub></font> <a href="scmring2.html#K4">:=</a> <font color="Maroon">c<sub>6</sub></font></span>)</span></span>)</span> <a href="funct_1.html#K1">.</a> 1 <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"><font color="Maroon">c<sub>2</sub></font> <a href="scmring2.html#K4">:=</a> <font color="Maroon">c<sub>3</sub></font></span>)</span></span>)</span></span>)</span>,1
 
<b>by </b><i><a class="ref" href="card_3.html#D6">CARD_3:def 6</a></i>;<br/>
<span class="p1">(<span class="default"><a href="amistd_2.html#K4">AddressPart</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>5</sub></font> <a href="scmring2.html#K4">:=</a> <font color="Maroon">c<sub>6</sub></font></span>)</span></span>)</span> <a href="funct_1.html#K1">.</a> 1 = 
<span class="p1"><a href="finseq_1.html#K10">&lt;*</a><span class="default"><font color="Maroon">c<sub>5</sub></font>,<font color="Maroon">c<sub>6</sub></font></span><a href="finseq_1.html#K10">*&gt;</a></span> <a href="funct_1.html#K1">.</a> 1
<b>by </b><i><a class="ref" href="scmring3.html#T25" target="_self">Th25</a></i>
<br/>.= 
<font color="Maroon">c<sub>5</sub></font>
<b>by </b><i><a class="ref" href="finseq_1.html#T61">FINSEQ_1:61</a></i>
;<br/>
<b>hence </b><a NAME="E12:40"/>
<font color="Maroon">c<sub>4</sub></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"><font color="Maroon">c<sub>2</sub></font> <a href="scmring2.html#K4">:=</a> <font color="Maroon">c<sub>3</sub></font></span>)</span></span>)</span></span>)</span></span>)</span> <a href="funct_1.html#K1">.</a> 1
 <b>by </b><i><a class="txt" href="scmring3.html#E3:40"><i><font color="Green">E45</font></i></a>, <a class="txt" href="scmring3.html#E10:40"><i><font color="Green">E46</font></i></a>, <a class="ref" href="amistd_2.html#D1">AMISTD_2:def 1</a></i>;<br/>


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