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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> be   <a href="struct_0.html#NM1">Element</a> of <font color="Maroon">c<sub>1</sub></font>;<br/><b>let </b><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="E1:49"/><i><font color="Green">E53</font></i>: 
 <a href="ami_5.html#K1">InsCode</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="scmring2.html#K8">:=</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="hidden.html#R1">=</a> 5
 
<b>by </b><i><a class="ref" href="scmring3.html#T13" target="_self">Th13</a></i>;<br/>
<a NAME="E2:49"/><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>3</sub></font> <a href="scmring2.html#K8">:=</a> <font color="Maroon">c<sub>2</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#T37" target="_self">Th37</a></i>;<br/>
<a NAME="E3:49"/><b>then </b><i><font color="Green">E54</font></i>: 
2 <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>3</sub></font> <a href="scmring2.html#K8">:=</a> <font color="Maroon">c<sub>2</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/>
<b>thus </b><a NAME="E4:49"/>
<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>3</sub></font> <a href="scmring2.html#K8">:=</a> <font color="Maroon">c<sub>2</sub></font></span>)</span></span>)</span></span>)</span></span>)</span> <a href="funct_1.html#K1">.</a> 2 <a href="tarski.html#R1">c=</a> the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">c<sub>1</sub></font>
  <i><font color="Red">:: according to </font></i><a class="ref" href="xboole_0.html#D10">XBOOLE_0:def 10</a><div><a class="txt" onclick="hs2(this)" href="javascript:()" title="49_1"><b>proof </b></a><div class="add">

<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="E1:49_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>3</sub></font> <a href="scmring2.html#K8">:=</a> <font color="Maroon">c<sub>2</sub></font></span>)</span></span>)</span></span>)</span></span>)</span> <a href="funct_1.html#K1">.</a> 2
 ;<br/>

<a NAME="E2:49_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>3</sub></font> <a href="scmring2.html#K8">:=</a> <font color="Maroon">c<sub>2</sub></font></span>)</span></span>)</span></span>)</span>,2
 
<b>by </b><i><a class="txt" href="scmring3.html#E3:49"><i><font color="Green">E54</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="E4:49_1"/><i><font color="Green">E55</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>3</sub></font> <a href="scmring2.html#K8">:=</a> <font color="Maroon">c<sub>2</sub></font></span>)</span></span>)</span>
 <b>and </b><br/><a NAME="E5:49_1"/><i><font color="Green">E56</font></i>: 
<font color="Maroon">c<sub>5</sub></font> <a href="funct_1.html#K1">.</a> 2 <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="E7:49_1"/><i><font color="Green">E57</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="E8:49_1"/><i><font color="Green">E58</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>3</sub></font> <a href="scmring2.html#K8">:=</a> <font color="Maroon">c<sub>2</sub></font></span>)</span>
 <b>by </b><i><a class="txt" href="scmring3.html#E4:49_1"><i><font color="Green">E55</font></i></a></i>;<br/>
<a NAME="E9:49_1"/>
 <a href="ami_5.html#K1">InsCode</a> <font color="Maroon">c<sub>6</sub></font> <a href="hidden.html#R1">=</a> 5
 
<b>by </b><i><a class="txt" href="scmring3.html#E8:49_1"><i><font color="Green">E58</font></i></a>, <a class="ref" href="scmring3.html#T13" target="_self">Th13</a></i>;<br/>
<b>then consider </b><font color="Maroon">c<sub>7</sub></font> being    <a href="scmring2.html#M1">Data-Location</a> of <font color="Maroon">c<sub>1</sub></font>, <font color="Maroon">c<sub>8</sub></font> being   <a href="struct_0.html#NM1">Element</a> of <font color="Maroon">c<sub>1</sub></font><b> such that </b><br/><a NAME="E11:49_1"/><i><font color="Green">E59</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#K8">:=</a> <font color="Maroon">c<sub>8</sub></font>
 <b>by </b><i><a class="ref" href="scmring3.html#T21" target="_self">Th21</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> 2
<b>by </b><i><a class="txt" href="scmring3.html#E5:49_1"><i><font color="Green">E56</font></i></a>, <a class="txt" href="scmring3.html#E7:49_1"><i><font color="Green">E57</font></i></a>, <a class="txt" href="scmring3.html#E11:49_1"><i><font color="Green">E59</font></i></a>, <a class="ref" href="scmring3.html#T29" target="_self">Th29</a></i>
<br/>.= 
<font color="Maroon">c<sub>8</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="E13:49_1"/>
<font color="Maroon">c<sub>4</sub></font> <a href="hidden.html#R2">in</a> the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">c<sub>1</sub></font>
 ;<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="E5:49"/>
<font color="Maroon">c<sub>4</sub></font> <a href="hidden.html#R2">in</a> the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">c<sub>1</sub></font>
 ;<br/>

<b>then reconsider </b><font color="Maroon">c<sub>5</sub></font> = <font color="Maroon">c<sub>4</sub></font> as   <a href="struct_0.html#NM1">Element</a> of <font color="Maroon">c<sub>1</sub></font> ;<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/>
<b>set </b><font color="Maroon">c<sub>7</sub></font> = <font color="Maroon">c<sub>6</sub></font> <a href="scmring2.html#K8">:=</a> <font color="Maroon">c<sub>5</sub></font>;<br/>
<a NAME="E8:49"/><i><font color="Green">E55</font></i>: 
 <a href="amistd_2.html#K4">AddressPart</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>6</sub></font> <a href="scmring2.html#K8">:=</a> <font color="Maroon">c<sub>5</sub></font></span>)</span> <a href="hidden.html#R1">=</a> <span class="p1"><a href="finseq_1.html#K10">&lt;*</a><span class="default"><font color="Maroon">c<sub>6</sub></font>,<font color="Maroon">c<sub>5</sub></font></span><a href="finseq_1.html#K10">*&gt;</a></span>
 
<b>by </b><i><a class="ref" href="scmring3.html#T29" target="_self">Th29</a></i>;<br/>
<a NAME="E9:49"/>
 <a href="ami_5.html#K1">InsCode</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>6</sub></font> <a href="scmring2.html#K8">:=</a> <font color="Maroon">c<sub>5</sub></font></span>)</span> <a href="hidden.html#R1">=</a> 5
 
<b>by </b><i><a class="ref" href="scmring3.html#T13" target="_self">Th13</a></i>;<br/>
<a NAME="E10:49"/><b>then </b>
 <a href="amistd_2.html#K4">AddressPart</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>6</sub></font> <a href="scmring2.html#K8">:=</a> <font color="Maroon">c<sub>5</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>3</sub></font> <a href="scmring2.html#K8">:=</a> <font color="Maroon">c<sub>2</sub></font></span>)</span></span>)</span>
 
<b>by </b><i><a class="txt" href="scmring3.html#E1:49"><i><font color="Green">E53</font></i></a></i>;<br/>
<a NAME="E11:49"/><b>then </b><i><font color="Green">E56</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>6</sub></font> <a href="scmring2.html#K8">:=</a> <font color="Maroon">c<sub>5</sub></font></span>)</span></span>)</span> <a href="funct_1.html#K1">.</a> 2 <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>3</sub></font> <a href="scmring2.html#K8">:=</a> <font color="Maroon">c<sub>2</sub></font></span>)</span></span>)</span></span>)</span>,2
 
<b>by </b><i><a class="ref" href="card_3.html#D6">CARD_3:def 6</a></i>;<br/>
<a NAME="E12:49"/>
<font color="Maroon">c<sub>5</sub></font> <a href="hidden.html#R1">=</a> <span class="p1"><a href="finseq_1.html#K10">&lt;*</a><span class="default"><font color="Maroon">c<sub>6</sub></font>,<font color="Maroon">c<sub>5</sub></font></span><a href="finseq_1.html#K10">*&gt;</a></span> <a href="funct_1.html#K1">.</a> 2
 
<b>by </b><i><a class="ref" href="finseq_1.html#T61">FINSEQ_1:61</a></i>;<br/>
<b>hence </b><a NAME="E13:49"/>
<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>3</sub></font> <a href="scmring2.html#K8">:=</a> <font color="Maroon">c<sub>2</sub></font></span>)</span></span>)</span></span>)</span></span>)</span> <a href="funct_1.html#K1">.</a> 2
 <b>by </b><i><a class="txt" href="scmring3.html#E3:49"><i><font color="Green">E54</font></i></a>, <a class="txt" href="scmring3.html#E8:49"><i><font color="Green">E55</font></i></a>, <a class="txt" href="scmring3.html#E11:49"><i><font color="Green">E56</font></i></a>, <a class="ref" href="amistd_2.html#D1">AMISTD_2:def 1</a></i>;<br/>


</div>
