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<div class="add">

<b>let </b><font color="Maroon" title="c1">R</font> be  <a href="scmring1.html#V1" title="SCMRING1:attr.1">good</a> <a href="funcsdom.html#NM1" title="FUNCSDOM:NM.1">Ring</a>;<br/><b>let </b><font color="Maroon" title="c2">a</font>, <font color="Maroon" title="c3">b</font> be    <a href="scmring2.html#M1" title="SCMRING2:mode.1">Data-Location</a> of <font color="Maroon" title="c1">R</font>;<br/>





<a NAME="E1:33"/><i><font color="Green" title="E37">A1</font></i>: 
 <a href="ami_1.html#K20" title="AMI_1:func.20">InsCode</a> <span class="p1">(<span class="default"><a href="scmring2.html#K5" title="SCMRING2:func.5">AddTo</a> <font color="Maroon" title="c2">a</font>,<font color="Maroon" title="c3">b</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 2
 
<b>by </b><i><a class="ref" href="mcart_1.html#D1" title="MCART_1:def.1">MCART_1:def 1</a></i>;<br/>
<a NAME="E2:33"/>
 <a href="relat_1.html#NK2" title="RELAT_1:NK.2">dom</a> <span class="p1">(<span class="default"><a href="card_3.html#K10" title="CARD_3:func.10">product"</a> <span class="p2">(<span class="default"><a href="amistd_2.html#K4" title="AMISTD_2:func.4">AddressParts</a> <span class="p3">(<span class="default"><a href="ami_1.html#K20" title="AMI_1:func.20">InsCode</a> <span class="p4">(<span class="default"><a href="scmring2.html#K5" title="SCMRING2:func.5">AddTo</a> <font color="Maroon" title="c2">a</font>,<font color="Maroon" title="c3">b</font></span>)</span></span>)</span></span>)</span></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"><a href="tarski.html#K2" title="TARSKI:func.2">{</a><span class="default">1,2</span><a href="tarski.html#K2" title="TARSKI:func.2">}</a></span>
 
<b>by </b><i><a class="ref" href="scmring3.html#T10" target="_self" title="SCMRING3:th.10">Th10</a>, <a class="ref" href="scmring3.html#T34" target="_self" title="SCMRING3:th.34">Th34</a></i>;<br/>
<a NAME="E3:33"/><b>then </b><i><font color="Green" title="E38">A2</font></i>: 
1 <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="relat_1.html#NK2" title="RELAT_1:NK.2">dom</a> <span class="p1">(<span class="default"><a href="card_3.html#K10" title="CARD_3:func.10">product"</a> <span class="p2">(<span class="default"><a href="amistd_2.html#K4" title="AMISTD_2:func.4">AddressParts</a> <span class="p3">(<span class="default"><a href="ami_1.html#K20" title="AMI_1:func.20">InsCode</a> <span class="p4">(<span class="default"><a href="scmring2.html#K5" title="SCMRING2:func.5">AddTo</a> <font color="Maroon" title="c2">a</font>,<font color="Maroon" title="c3">b</font></span>)</span></span>)</span></span>)</span></span>)</span>
 
<b>by </b><i><a class="ref" href="tarski.html#D2" title="TARSKI:def.2">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" title="TARSKI:def.3">TARSKI:def 3</a>,<a class="ref" href="xboole_0.html#D10" title="XBOOLE_0:def.10">XBOOLE_0:def 10</a>
<div class="add"><b>let </b><font color="Maroon" title="c4">x</font> be    <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a> ;<br/><b>assume </b><a NAME="E1:33_1"/>
<font color="Maroon" title="c4">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <span class="p1">(<span class="default"><a href="card_3.html#K10" title="CARD_3:func.10">product"</a> <span class="p2">(<span class="default"><a href="amistd_2.html#K4" title="AMISTD_2:func.4">AddressParts</a> <span class="p3">(<span class="default"><a href="ami_1.html#K20" title="AMI_1:func.20">InsCode</a> <span class="p4">(<span class="default"><a href="scmring2.html#K5" title="SCMRING2:func.5">AddTo</a> <font color="Maroon" title="c2">a</font>,<font color="Maroon" title="c3">b</font></span>)</span></span>)</span></span>)</span></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> 1
 ;<br/><a NAME="E2:33_1"/><b>then </b>
<font color="Maroon" title="c4">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="card_3.html#K5" title="CARD_3:func.5">pi</a> <span class="p1">(<span class="default"><a href="amistd_2.html#K4" title="AMISTD_2:func.4">AddressParts</a> <span class="p2">(<span class="default"><a href="ami_1.html#K20" title="AMI_1:func.20">InsCode</a> <span class="p3">(<span class="default"><a href="scmring2.html#K5" title="SCMRING2:func.5">AddTo</a> <font color="Maroon" title="c2">a</font>,<font color="Maroon" title="c3">b</font></span>)</span></span>)</span></span>)</span>,1
 <b>by </b><i><a class="txt" href="scmring3.html#E3:33"><i><font color="Green" title="E38">A2</font></i></a>, <a class="ref" href="card_3.html#D13" title="CARD_3:def.13">CARD_3:def 13</a></i>;<br/><b>then consider </b><font color="Maroon" title="c5">f</font> being   <a href="funct_1.html#NM1" title="FUNCT_1:NM.1">Function</a><b> such that </b><br/><a NAME="E4:33_1"/><i><font color="Green" title="E39">A3</font></i>: 
<font color="Maroon" title="c5">f</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="amistd_2.html#K4" title="AMISTD_2:func.4">AddressParts</a> <span class="p1">(<span class="default"><a href="ami_1.html#K20" title="AMI_1:func.20">InsCode</a> <span class="p2">(<span class="default"><a href="scmring2.html#K5" title="SCMRING2:func.5">AddTo</a> <font color="Maroon" title="c2">a</font>,<font color="Maroon" title="c3">b</font></span>)</span></span>)</span>
 <b>and </b><br/><a NAME="E5:33_1"/><i><font color="Green" title="E40">A4</font></i>: 
<font color="Maroon" title="c5">f</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> 1 <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c4">x</font>
 <b>by </b><i><a class="ref" href="card_3.html#D6" title="CARD_3:def.6">CARD_3:def 6</a></i>;<br/><b>consider </b><font color="Maroon" title="c6">I</font> being   <a href="ami_1.html#NM4" title="AMI_1:NM.4">Instruction</a> of <span class="p1">(<span class="default"><a href="scmring2.html#K1" title="SCMRING2:func.1">SCM</a> <font color="Maroon" title="c1">R</font></span>)</span><b> such that </b><br/><a NAME="E7:33_1"/><i><font color="Green" title="E41">A5</font></i>: 
<font color="Maroon" title="c5">f</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="amistd_2.html#K3" title="AMISTD_2:func.3">AddressPart</a> <font color="Maroon" title="c6">I</font>
 <b>and </b><br/><a NAME="E8:33_1"/><i><font color="Green" title="E42">A6</font></i>: 
 <a href="ami_1.html#K20" title="AMI_1:func.20">InsCode</a> <font color="Maroon" title="c6">I</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="ami_1.html#K20" title="AMI_1:func.20">InsCode</a> <span class="p1">(<span class="default"><a href="scmring2.html#K5" title="SCMRING2:func.5">AddTo</a> <font color="Maroon" title="c2">a</font>,<font color="Maroon" title="c3">b</font></span>)</span>
 <b>by </b><i><a class="txt" href="scmring3.html#E4:33_1"><i><font color="Green" title="E39">A3</font></i></a></i>;<br/><a NAME="E9:33_1"/>
 <a href="ami_1.html#K20" title="AMI_1:func.20">InsCode</a> <font color="Maroon" title="c6">I</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 2
 <b>by </b><i><a class="txt" href="scmring3.html#E8:33_1"><i><font color="Green" title="E42">A6</font></i></a>, <a class="ref" href="mcart_1.html#D1" title="MCART_1:def.1">MCART_1:def 1</a></i>;<br/><b>then consider </b><font color="Maroon" title="c7">d1</font>, <font color="Maroon" title="c8">d2</font> being    <a href="scmring2.html#M1" title="SCMRING2:mode.1">Data-Location</a> of <font color="Maroon" title="c1">R</font><b> such that </b><br/><a NAME="E11:33_1"/><i><font color="Green" title="E43">A7</font></i>: 
<font color="Maroon" title="c6">I</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="scmring2.html#K5" title="SCMRING2:func.5">AddTo</a> <font color="Maroon" title="c7">d1</font>,<font color="Maroon" title="c8">d2</font>
 <b>by </b><i><a class="ref" href="scmring3.html#T18" target="_self" title="SCMRING3:th.18">Th18</a></i>;<br/><font color="Maroon" title="c4">x</font> = 
<span class="p1"><a href="finseq_1.html#K10" title="FINSEQ_1:func.10">&lt;*</a><span class="default"><font color="Maroon" title="c7">d1</font>,<font color="Maroon" title="c8">d2</font></span><a href="finseq_1.html#K10" title="FINSEQ_1:func.10">*&gt;</a></span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> 1
<b>by </b><i><a class="txt" href="scmring3.html#E5:33_1"><i><font color="Green" title="E40">A4</font></i></a>, <a class="txt" href="scmring3.html#E7:33_1"><i><font color="Green" title="E41">A5</font></i></a>, <a class="txt" href="scmring3.html#E11:33_1"><i><font color="Green" title="E43">A7</font></i></a>, <a class="ref" href="mcart_1.html#D2" title="MCART_1:def.2">MCART_1:def 2</a></i>
<br/>.= 
<font color="Maroon" title="c7">d1</font>
<b>by </b><i><a class="ref" href="finseq_1.html#T61" title="FINSEQ_1:th.61">FINSEQ_1:61</a></i>
;<br/><b>hence </b><a NAME="E13:33_1"/>
<font color="Maroon" title="c4">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="ami_2.html#K4" title="AMI_2:func.4">SCM-Data-Loc</a> 
 <b>by </b><i><a class="ref" href="scmring2.html#T1" title="SCMRING2:th.1">SCMRING2:1</a></i>;<br/></div>
<b>end;</b></div>

<b>let </b><font color="Maroon" title="c4">x</font> be    <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a> ; <i><font color="Red">:: according to </font></i><a class="ref" href="tarski.html#D3" title="TARSKI:def.3">TARSKI:def 3</a><br/>

<b>assume </b><a NAME="E5:33"/>
<font color="Maroon" title="c4">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="ami_2.html#K4" title="AMI_2:func.4">SCM-Data-Loc</a> 
 ;<br/>

<b>then reconsider </b><font color="Maroon" title="c5">x</font> = <font color="Maroon" title="c4">x</font> as    <a href="scmring2.html#M1" title="SCMRING2:mode.1">Data-Location</a> of <font color="Maroon" title="c1">R</font> <b>by </b><i><a class="ref" href="scmring2.html#T1" title="SCMRING2:th.1">SCMRING2:1</a></i>;<br/>
<b>consider </b><font color="Maroon" title="c6">d1</font> being    <a href="scmring2.html#M1" title="SCMRING2:mode.1">Data-Location</a> of <font color="Maroon" title="c1">R</font>;<br/>
<a NAME="E8:33"/>
 <a href="ami_1.html#K20" title="AMI_1:func.20">InsCode</a> <span class="p1">(<span class="default"><a href="scmring2.html#K5" title="SCMRING2:func.5">AddTo</a> <font color="Maroon" title="c5">x</font>,<font color="Maroon" title="c6">d1</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 2
 
<b>by </b><i><a class="ref" href="mcart_1.html#D1" title="MCART_1:def.1">MCART_1:def 1</a></i>;<br/>
<a NAME="E9:33"/><b>then </b>
 <a href="amistd_2.html#K3" title="AMISTD_2:func.3">AddressPart</a> <span class="p1">(<span class="default"><a href="scmring2.html#K5" title="SCMRING2:func.5">AddTo</a> <font color="Maroon" title="c5">x</font>,<font color="Maroon" title="c6">d1</font></span>)</span> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="amistd_2.html#K4" title="AMISTD_2:func.4">AddressParts</a> <span class="p1">(<span class="default"><a href="ami_1.html#K20" title="AMI_1:func.20">InsCode</a> <span class="p2">(<span class="default"><a href="scmring2.html#K5" title="SCMRING2:func.5">AddTo</a> <font color="Maroon" title="c2">a</font>,<font color="Maroon" title="c3">b</font></span>)</span></span>)</span>
 
<b>by </b><i><a class="txt" href="scmring3.html#E1:33"><i><font color="Green" title="E37">A1</font></i></a></i>;<br/>
<a NAME="E10:33"/><b>then </b><i><font color="Green" title="E39">A8</font></i>: 
<span class="p1">(<span class="default"><a href="amistd_2.html#K3" title="AMISTD_2:func.3">AddressPart</a> <span class="p2">(<span class="default"><a href="scmring2.html#K5" title="SCMRING2:func.5">AddTo</a> <font color="Maroon" title="c5">x</font>,<font color="Maroon" title="c6">d1</font></span>)</span></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> 1 <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="card_3.html#K5" title="CARD_3:func.5">pi</a> <span class="p1">(<span class="default"><a href="amistd_2.html#K4" title="AMISTD_2:func.4">AddressParts</a> <span class="p2">(<span class="default"><a href="ami_1.html#K20" title="AMI_1:func.20">InsCode</a> <span class="p3">(<span class="default"><a href="scmring2.html#K5" title="SCMRING2:func.5">AddTo</a> <font color="Maroon" title="c2">a</font>,<font color="Maroon" title="c3">b</font></span>)</span></span>)</span></span>)</span>,1
 
<b>by </b><i><a class="ref" href="card_3.html#D6" title="CARD_3:def.6">CARD_3:def 6</a></i>;<br/>
<span class="p1">(<span class="default"><a href="amistd_2.html#K3" title="AMISTD_2:func.3">AddressPart</a> <span class="p2">(<span class="default"><a href="scmring2.html#K5" title="SCMRING2:func.5">AddTo</a> <font color="Maroon" title="c5">x</font>,<font color="Maroon" title="c6">d1</font></span>)</span></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> 1 = 
<span class="p1"><a href="finseq_1.html#K10" title="FINSEQ_1:func.10">&lt;*</a><span class="default"><font color="Maroon" title="c5">x</font>,<font color="Maroon" title="c6">d1</font></span><a href="finseq_1.html#K10" title="FINSEQ_1:func.10">*&gt;</a></span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> 1
<b>by </b><i><a class="ref" href="mcart_1.html#D2" title="MCART_1:def.2">MCART_1:def 2</a></i>
<br/>.= 
<font color="Maroon" title="c5">x</font>
<b>by </b><i><a class="ref" href="finseq_1.html#T61" title="FINSEQ_1:th.61">FINSEQ_1:61</a></i>
;<br/>
<b>hence </b><a NAME="E12:33"/>
<font color="Maroon" title="c4">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <span class="p1">(<span class="default"><a href="card_3.html#K10" title="CARD_3:func.10">product"</a> <span class="p2">(<span class="default"><a href="amistd_2.html#K4" title="AMISTD_2:func.4">AddressParts</a> <span class="p3">(<span class="default"><a href="ami_1.html#K20" title="AMI_1:func.20">InsCode</a> <span class="p4">(<span class="default"><a href="scmring2.html#K5" title="SCMRING2:func.5">AddTo</a> <font color="Maroon" title="c2">a</font>,<font color="Maroon" title="c3">b</font></span>)</span></span>)</span></span>)</span></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> 1
 <b>by </b><i><a class="txt" href="scmring3.html#E3:33"><i><font color="Green" title="E38">A2</font></i></a>, <a class="txt" href="scmring3.html#E10:33"><i><font color="Green" title="E39">A8</font></i></a>, <a class="ref" href="card_3.html#D13" title="CARD_3:def.13">CARD_3:def 13</a></i>;<br/>


</div>
