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<b>let </b><font color="Maroon">c<sub>1</sub></font>, <font color="Maroon">c<sub>2</sub></font> be   <a href="ami_1.html#NM4">State</a> of <a href="scmpds_2.html#K1">SCMPDS</a> ;<br/>

<b>set </b><font color="Maroon">c<sub>3</sub></font> = <span class="p1"><a href="tarski.html#K1">{</a><span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K2">IC</a> <a href="scmpds_2.html#K1">SCMPDS</a> </span>)</span></span><a href="tarski.html#K1">}</a></span>;<br/>
<b>set </b><font color="Maroon">c<sub>4</sub></font> =  <a href="ami_2.html#K2">SCM-Data-Loc</a> ;<br/>
<b>set </b><font color="Maroon">c<sub>5</sub></font> = the <a href="ami_1.html#U2">Instruction-Locations</a> of <a href="scmpds_2.html#K1">SCMPDS</a> ;<br/>
<a NAME="E1:25"/><i><font color="Green">E15</font></i>: 
<span class="p1">(<span class="default"><span class="p2"><a href="tarski.html#K1">{</a><span class="default"><span class="p3">(<span class="default"><a href="ami_1.html#K2">IC</a> <a href="scmpds_2.html#K1">SCMPDS</a> </span>)</span></span><a href="tarski.html#K1">}</a></span> <a href="xboole_0.html#K2">\/</a> <a href="ami_2.html#K2">SCM-Data-Loc</a> </span>)</span> <a href="xboole_0.html#K2">\/</a> the <a href="ami_1.html#U2">Instruction-Locations</a> of <a href="scmpds_2.html#K1">SCMPDS</a>  <a href="hidden.html#R1">=</a> <a href="ami_2.html#K2">SCM-Data-Loc</a>  <a href="xboole_0.html#K2">\/</a> <span class="p1">(<span class="default"><span class="p2"><a href="tarski.html#K1">{</a><span class="default"><span class="p3">(<span class="default"><a href="ami_1.html#K2">IC</a> <a href="scmpds_2.html#K1">SCMPDS</a> </span>)</span></span><a href="tarski.html#K1">}</a></span> <a href="xboole_0.html#K2">\/</a> the <a href="ami_1.html#U2">Instruction-Locations</a> of <a href="scmpds_2.html#K1">SCMPDS</a> </span>)</span>
 
<b>by </b><i><a class="ref" href="xboole_1.html#T4">XBOOLE_1:4</a></i>;<br/>
<a NAME="E2:25"/>
 <a href="relat_1.html#K1">dom</a> <font color="Maroon">c<sub>1</sub></font> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><span class="p2"><a href="tarski.html#K1">{</a><span class="default"><span class="p3">(<span class="default"><a href="ami_1.html#K2">IC</a> <a href="scmpds_2.html#K1">SCMPDS</a> </span>)</span></span><a href="tarski.html#K1">}</a></span> <a href="xboole_0.html#K2">\/</a> <a href="ami_2.html#K2">SCM-Data-Loc</a> </span>)</span> <a href="xboole_0.html#K2">\/</a> the <a href="ami_1.html#U2">Instruction-Locations</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>, <a class="ref" href="scmpds_3.html#T5">SCMPDS_3:5</a></i>;<br/>
<a NAME="E3:25"/><b>then </b><i><font color="Green">E16</font></i>: 
 <a href="ami_2.html#K2">SCM-Data-Loc</a>  <a href="tarski.html#R1">c=</a>  <a href="relat_1.html#K1">dom</a> <font color="Maroon">c<sub>1</sub></font>
 
<b>by </b><i><a class="txt" href="scmpds_4.html#E1:25"><i><font color="Green">E15</font></i></a>, <a class="ref" href="xboole_1.html#T7">XBOOLE_1:7</a></i>;<br/>
<a NAME="E4:25"/>
 <a href="relat_1.html#K1">dom</a> <font color="Maroon">c<sub>2</sub></font> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><span class="p2"><a href="tarski.html#K1">{</a><span class="default"><span class="p3">(<span class="default"><a href="ami_1.html#K2">IC</a> <a href="scmpds_2.html#K1">SCMPDS</a> </span>)</span></span><a href="tarski.html#K1">}</a></span> <a href="xboole_0.html#K2">\/</a> <a href="ami_2.html#K2">SCM-Data-Loc</a> </span>)</span> <a href="xboole_0.html#K2">\/</a> the <a href="ami_1.html#U2">Instruction-Locations</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>, <a class="ref" href="scmpds_3.html#T5">SCMPDS_3:5</a></i>;<br/>
<a NAME="E5:25"/><b>then </b><i><font color="Green">E17</font></i>: 
 <a href="ami_2.html#K2">SCM-Data-Loc</a>  <a href="tarski.html#R1">c=</a>  <a href="relat_1.html#K1">dom</a> <font color="Maroon">c<sub>2</sub></font>
 
<b>by </b><i><a class="txt" href="scmpds_4.html#E1:25"><i><font color="Green">E15</font></i></a>, <a class="ref" href="xboole_1.html#T7">XBOOLE_1:7</a></i>;<br/>
<div><i><font color="Green">E18</font></i>: <a class="txt" onclick="hs2(this)" href="javascript:()" title="25_1"><b>now </b></a><div class="add"><b>assume </b><a NAME="E1:25_1"/><i><font color="Green">E19</font></i>: 
for <font color="Olive">b<sub>1</sub></font> being   <a href="scmpds_2.html#M1">Int_position</a>  holds <font color="Maroon">c<sub>1</sub></font> <a href="scmpds_2.html#K2">.</a> <font color="Olive">b<sub>1</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>2</sub></font> <a href="scmpds_2.html#K2">.</a> <font color="Olive">b<sub>1</sub></font>
 ;<br/><div><b>hereby </b>
<div class="add"><b>let </b><font color="Maroon">c<sub>6</sub></font> be    <a href="hidden.html#M1">set</a> ;<br/><b>assume </b><a NAME="E1:25_1_1"/>
<font color="Maroon">c<sub>6</sub></font> <a href="hidden.html#R2">in</a>  <a href="ami_2.html#K2">SCM-Data-Loc</a> 
 ;<br/><a NAME="E2:25_1_1"/><b>then </b>
<font color="Maroon">c<sub>6</sub></font> is    <a href="scmpds_2.html#M1">Int_position</a> 
 <b>by </b><i><a class="ref" href="scmpds_2.html#T9">SCMPDS_2:9</a></i>;<br/><b>hence </b><a NAME="E3:25_1_1"/>
<font color="Maroon">c<sub>1</sub></font> <a href="funct_1.html#K1">.</a> <font color="Maroon">c<sub>6</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>2</sub></font> <a href="funct_1.html#K1">.</a> <font color="Maroon">c<sub>6</sub></font>
 <b>by </b><i><a class="txt" href="scmpds_4.html#E1:25_1"><i><font color="Green">E19</font></i></a></i>;<br/></div>
<b>end;</b></div></div><b>end;</b></div>
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="25_2"><b>now </b></a><div class="add"><b>assume </b><a NAME="E1:25_2"/><i><font color="Green">E19</font></i>: 
for <font color="Olive">b<sub>1</sub></font> being   <a href="hidden.html#M1">set</a>  st <font color="Olive">b<sub>1</sub></font> <a href="hidden.html#R2">in</a>  <a href="ami_2.html#K2">SCM-Data-Loc</a>  holds <br/><font color="Maroon">c<sub>1</sub></font> <a href="funct_1.html#K1">.</a> <font color="Olive">b<sub>1</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>2</sub></font> <a href="funct_1.html#K1">.</a> <font color="Olive">b<sub>1</sub></font>
 ;<br/><div><b>hereby </b>
<div class="add"><b>let </b><font color="Maroon">c<sub>6</sub></font> be    <a href="scmpds_2.html#M1">Int_position</a> ;<br/><a NAME="E1:25_2_1"/>
<font color="Maroon">c<sub>6</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="scmpds_2.html#D2">SCMPDS_2:def 2</a></i>;<br/><b>hence </b><a NAME="E2:25_2_1"/>
<font color="Maroon">c<sub>1</sub></font> <a href="scmpds_2.html#K2">.</a> <font color="Maroon">c<sub>6</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>2</sub></font> <a href="scmpds_2.html#K2">.</a> <font color="Maroon">c<sub>6</sub></font>
 <b>by </b><i><a class="txt" href="scmpds_4.html#E1:25_2"><i><font color="Green">E19</font></i></a></i>;<br/></div>
<b>end;</b></div></div><b>end;</b></div>
<b>hence </b><a NAME="E8:25"/>
( ( for <font color="Olive">b<sub>1</sub></font> being   <a href="scmpds_2.html#M1">Int_position</a>  holds <font color="Maroon">c<sub>1</sub></font> <a href="scmpds_2.html#K2">.</a> <font color="Olive">b<sub>1</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>2</sub></font> <a href="scmpds_2.html#K2">.</a> <font color="Olive">b<sub>1</sub></font> ) iff <font color="Maroon">c<sub>1</sub></font> <a href="relat_1.html#K7">|</a> <a href="ami_2.html#K2">SCM-Data-Loc</a>  <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>2</sub></font> <a href="relat_1.html#K7">|</a> <a href="ami_2.html#K2">SCM-Data-Loc</a>  )
 <b>by </b><i><a class="txt" href="scmpds_4.html#E3:25"><i><font color="Green">E16</font></i></a>, <a class="txt" href="scmpds_4.html#E5:25"><i><font color="Green">E17</font></i></a>, <a class="txt" href="scmpds_4.html#E6:25"><i><font color="Green">E18</font></i></a>, <a class="ref" href="scmfsa6a.html#T9">SCMFSA6A:9</a></i>;<br/>


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