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<b>let </b><font color="Maroon">i</font> be   <a href="ami_1.html#NM3">Instruction</a> of <a href="scmpds_2.html#K1">SCMPDS</a> ;<br/><b>let </b><font color="Maroon">s</font> be   <a href="ami_1.html#NM4">State</a> of <a href="scmpds_2.html#K1">SCMPDS</a> ;<br/>



<a NAME="E1:7"/>
 <a href="relat_1.html#K1">dom</a> <span class="p1">(<span class="default"><a href="ami_1.html#K4">Exec</a> <font color="Maroon">i</font>,<font color="Maroon">s</font></span>)</span> <a href="hidden.html#R1">=</a> the <a href="struct_0.html#U1">carrier</a> of <a href="scmpds_2.html#K1">SCMPDS</a> 
 
<b>by </b><i><a class="ref" href="ami_3.html#T36">AMI_3:36</a></i>;<br/>
<a NAME="E2:7"/><b>then </b><i><font color="Green">E33</font></i>: 
 <a href="relat_1.html#K1">dom</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K4">Exec</a> <font color="Maroon">i</font>,<font color="Maroon">s</font></span>)</span> <a href="relat_1.html#K7">|</a> <a href="ami_2.html#K3">SCM-Instr-Loc</a> </span>)</span> <a href="hidden.html#R1">=</a>  <a href="ami_2.html#K3">SCM-Instr-Loc</a> 
 
<b>by </b><i><a class="ref" href="relat_1.html#T91">RELAT_1:91</a>, <a class="ref" href="scmpds_2.html#D1">SCMPDS_2:def 1</a></i>;<br/>
<a NAME="E3:7"/>
 <a href="relat_1.html#K1">dom</a> <font color="Maroon">s</font> <a href="hidden.html#R1">=</a> the <a href="struct_0.html#U1">carrier</a> of <a href="scmpds_2.html#K1">SCMPDS</a> 
 
<b>by </b><i><a class="ref" href="ami_3.html#T36">AMI_3:36</a></i>;<br/>
<a NAME="E4:7"/><b>then </b><i><font color="Green">E35</font></i>: 
 <a href="relat_1.html#K1">dom</a> <span class="p1">(<span class="default"><font color="Maroon">s</font> <a href="relat_1.html#K7">|</a> <a href="ami_2.html#K3">SCM-Instr-Loc</a> </span>)</span> <a href="hidden.html#R1">=</a>  <a href="ami_2.html#K3">SCM-Instr-Loc</a> 
 
<b>by </b><i><a class="ref" href="relat_1.html#T91">RELAT_1:91</a>, <a class="ref" href="scmpds_2.html#D1">SCMPDS_2:def 1</a></i>;<br/>
<a NAME="E5:7"/>
for <font color="Olive">x</font> being   <a href="hidden.html#M1">set</a>   st <font color="Olive">x</font> <a href="hidden.html#R2">in</a>  <a href="ami_2.html#K3">SCM-Instr-Loc</a>  holds <br/><span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K4">Exec</a> <font color="Maroon">i</font>,<font color="Maroon">s</font></span>)</span> <a href="relat_1.html#K7">|</a> <a href="ami_2.html#K3">SCM-Instr-Loc</a> </span>)</span> <a href="funct_1.html#K1">.</a> <font color="Olive">x</font> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><font color="Maroon">s</font> <a href="relat_1.html#K7">|</a> <a href="ami_2.html#K3">SCM-Instr-Loc</a> </span>)</span> <a href="funct_1.html#K1">.</a> <font color="Olive">x</font>
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="7_1"><b>proof </b></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="E1:7_1"/><i><font color="Green">E36</font></i>: 
<font color="Maroon">x</font> <a href="hidden.html#R2">in</a>  <a href="ami_2.html#K3">SCM-Instr-Loc</a> 
 ;<br/>

<b>then reconsider </b><font color="Maroon">l</font> = <font color="Maroon">x</font> as   <a href="ami_1.html#NM2">Instruction-Location</a> of <a href="scmpds_2.html#K1">SCMPDS</a>  <b>by </b><i><a class="ref" href="scmpds_2.html#D1">SCMPDS_2:def 1</a></i>;<br/>
<b>thus </b><span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K4">Exec</a> <font color="Maroon">i</font>,<font color="Maroon">s</font></span>)</span> <a href="relat_1.html#K7">|</a> <a href="ami_2.html#K3">SCM-Instr-Loc</a> </span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">x</font> = 
<span class="p1">(<span class="default"><a href="ami_1.html#K4">Exec</a> <font color="Maroon">i</font>,<font color="Maroon">s</font></span>)</span> <a href="ami_1.html#K13">.</a> <font color="Maroon">l</font>
<b>by </b><i>, <a class="ref" href="funct_1.html#T72">FUNCT_1:72</a></i>
<br/>.= 
<font color="Maroon">s</font> <a href="ami_1.html#K13">.</a> <font color="Maroon">l</font>
<b>by </b><i><a class="ref" href="ami_1.html#D13">AMI_1:def 13</a></i>
<br/>.= 
<span class="p1">(<span class="default"><font color="Maroon">s</font> <a href="relat_1.html#K7">|</a> <a href="ami_2.html#K3">SCM-Instr-Loc</a> </span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">x</font>
<b>by </b><i>, <a class="ref" href="funct_1.html#T72">FUNCT_1:72</a></i>
;<br/>


</div><b>end;</b></div>
<b>hence </b><a NAME="E6:7"/>
<span class="p1">(<span class="default"><a href="ami_1.html#K4">Exec</a> <font color="Maroon">i</font>,<font color="Maroon">s</font></span>)</span> <a href="relat_1.html#K7">|</a> <a href="ami_2.html#K3">SCM-Instr-Loc</a>  <a href="hidden.html#R1">=</a> <font color="Maroon">s</font> <a href="relat_1.html#K7">|</a> <a href="ami_2.html#K3">SCM-Instr-Loc</a> 
 <b>by </b><i>, , <a class="ref" href="funct_1.html#T9">FUNCT_1:9</a></i>;<br/>


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