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<b>let </b><font color="Maroon">s1</font> be   <a href="ami_1.html#NM4">State</a> of <a href="scmpds_2.html#K1" target="_self">SCMPDS</a> , <font color="Maroon">s2</font> be   <a href="ami_1.html#NM4">State</a> of <a href="scmpds_2.html#K1" target="_self">SCMPDS</a> ;<br/>

<b>assume </b><b>that </b><br/><a NAME="E1:66"/><i><font color="Green">E22</font></i>: 
 <a href="ami_1.html#K6">IC</a> <font color="Maroon">s1</font> <a href="hidden.html#R1">=</a>  <a href="ami_1.html#K6">IC</a> <font color="Maroon">s2</font>
 <b>and </b><br/><a NAME="E2:66"/><i><font color="Green">E23</font></i>: 
for <font color="Olive">a</font> being   <a href="scmpds_2.html#M1" target="_self">Int_position</a>  holds  <font color="Maroon">s1</font> <a href="scmpds_2.html#K2" target="_self">.</a> <font color="Olive">a</font> <a href="hidden.html#R1">=</a> <font color="Maroon">s2</font> <a href="scmpds_2.html#K2" target="_self">.</a> <font color="Olive">a</font>
 <b>and </b><br/><a NAME="E3:66"/><i><font color="Green">E25</font></i>: 
for <font color="Olive">i</font> being  <a href="ami_1.html#NM2">Instruction-Location</a> of <a href="scmpds_2.html#K1" target="_self">SCMPDS</a>  holds  <font color="Maroon">s1</font> <a href="ami_1.html#K13">.</a> <font color="Olive">i</font> <a href="hidden.html#R1">=</a> <font color="Maroon">s2</font> <a href="ami_1.html#K13">.</a> <font color="Olive">i</font>
 ;<br/>

<b>consider </b><font color="Maroon">g1</font> being   <a href="funct_1.html#NM1">Function</a><b> such that </b><br/><a NAME="E5:66"/><i><font color="Green">E26</font></i>: 
( <font color="Maroon">s1</font> <a href="hidden.html#R1">=</a> <font color="Maroon">g1</font> &amp;  <a href="relat_1.html#K1">dom</a> <font color="Maroon">g1</font> <a href="hidden.html#R1">=</a>  <a href="relat_1.html#K1">dom</a> <a href="scmpds_1.html#K2">SCMPDS-OK</a>  &amp; ( 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="relat_1.html#K1">dom</a> <a href="scmpds_1.html#K2">SCMPDS-OK</a>  holds <br/><font color="Maroon">g1</font> <a href="funct_1.html#K1">.</a> <font color="Olive">x</font> <a href="hidden.html#R2">in</a> <a href="scmpds_1.html#K2">SCMPDS-OK</a>  <a href="funct_1.html#K1">.</a> <font color="Olive">x</font> ) )
 <b>by </b><i><a class="ref" href="card_3.html#D5">CARD_3:def 5</a></i>;<br/>
<b>consider </b><font color="Maroon">g2</font> being   <a href="funct_1.html#NM1">Function</a><b> such that </b><br/><a NAME="E7:66"/><i><font color="Green">E61</font></i>: 
( <font color="Maroon">s2</font> <a href="hidden.html#R1">=</a> <font color="Maroon">g2</font> &amp;  <a href="relat_1.html#K1">dom</a> <font color="Maroon">g2</font> <a href="hidden.html#R1">=</a>  <a href="relat_1.html#K1">dom</a> <a href="scmpds_1.html#K2">SCMPDS-OK</a>  &amp; ( 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="relat_1.html#K1">dom</a> <a href="scmpds_1.html#K2">SCMPDS-OK</a>  holds <br/><font color="Maroon">g2</font> <a href="funct_1.html#K1">.</a> <font color="Olive">x</font> <a href="hidden.html#R2">in</a> <a href="scmpds_1.html#K2">SCMPDS-OK</a>  <a href="funct_1.html#K1">.</a> <font color="Olive">x</font> ) )
 <b>by </b><i><a class="ref" href="card_3.html#D5">CARD_3:def 5</a></i>;<br/>
<a NAME="E8:66"/><i><font color="Green">E62</font></i>: 
(  <a href="numbers.html#K5">NAT</a>  <a href="hidden.html#R1">=</a>  <a href="relat_1.html#K1">dom</a> <font color="Maroon">g1</font> &amp;  <a href="numbers.html#K5">NAT</a>  <a href="hidden.html#R1">=</a>  <a href="relat_1.html#K1">dom</a> <font color="Maroon">g2</font> )
 
<b>by </b><i><a class="txt" href="scmpds_2.html#E3:66"><i><font color="Green">E25</font></i></a>, <a class="txt" href="scmpds_2.html#E5:66"><i><font color="Green">E26</font></i></a>, <a class="ref" href="funct_2.html#D1">FUNCT_2:def 1</a></i>;<br/>
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="66_1"><b>now </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="E1:66_1"/><i><font color="Green">E63</font></i>: 
<font color="Maroon">x</font> <a href="hidden.html#R2">in</a>  <a href="numbers.html#K5">NAT</a> 
 ;<br/><a NAME="E2:66_1"/><i><font color="Green">E64</font></i>: 
( <font color="Maroon">x</font> <a href="hidden.html#R2">in</a> <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" target="_self">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>  or <font color="Maroon">x</font> <a href="hidden.html#R2">in</a>  <a href="ami_2.html#K3">SCM-Instr-Loc</a>  )
 <b>by </b><i>, , <a class="ref" href="xboole_0.html#D2">XBOOLE_0:def 2</a></i>;<br/><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="66_1_1"><b>per </b></a><a class="txt" onclick="hs(this)" href="javascript:()"><b>cases </b></a><span class="hide"><a NAME="E1:66_1_1"/>
( <font color="Maroon">x</font> <a href="hidden.html#R2">in</a> <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" target="_self">SCMPDS</a> </span>)</span></span><a href="tarski.html#K1">}</a></span> or <font color="Maroon">x</font> <a href="hidden.html#R2">in</a>  <a href="ami_2.html#K2">SCM-Data-Loc</a>  or <font color="Maroon">x</font> <a href="hidden.html#R2">in</a>  <a href="ami_2.html#K3">SCM-Instr-Loc</a>  )
 </span><b>by </b><i><a class="ref" href="scmpds_2.html#T3" target="_self">Th3</a>, <a class="ref" href="xboole_0.html#D2">XBOOLE_0:def 2</a></i>;<br/><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="66_1_1_1"><b>suppose </b></a><a NAME="E1:66_1_1_1"/>
<font color="Maroon">x</font> <a href="hidden.html#R2">in</a> <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" target="_self">SCMPDS</a> </span>)</span></span><a href="tarski.html#K1">}</a></span>
 ;<br/><div class="add"><a NAME="E2:66_1_1_1"/><b>then </b><i><font color="Green">E65</font></i>: 
<font color="Maroon">x</font> <a href="hidden.html#R1">=</a>  <a href="ami_1.html#K2">IC</a> <a href="scmpds_2.html#K1" target="_self">SCMPDS</a> 
 <b>by </b><i><a class="ref" href="tarski.html#D1">TARSKI:def 1</a></i>;<br/><a NAME="E3:66_1_1_1"/>
<font color="Maroon">s1</font> <a href="funct_1.html#K1">.</a> <span class="p1">(<span class="default"><a href="ami_1.html#K2">IC</a> <a href="scmpds_2.html#K1" target="_self">SCMPDS</a> </span>)</span> <a href="hidden.html#R1">=</a> <font color="Maroon">s2</font> <a href="funct_1.html#K1">.</a> <span class="p1">(<span class="default"><a href="ami_1.html#K2">IC</a> <a href="scmpds_2.html#K1" target="_self">SCMPDS</a> </span>)</span>
 <b>by </b><i><a class="txt" href="scmpds_2.html#E1:66"><i><font color="Green">E22</font></i></a></i>;<br/><b>hence </b><a NAME="E4:66_1_1_1"/>
<font color="Maroon">g1</font> <a href="funct_1.html#K1">.</a> <font color="Maroon">x</font> <a href="hidden.html#R1">=</a> <font color="Maroon">g2</font> <a href="funct_1.html#K1">.</a> <font color="Maroon">x</font>
 <b>by </b><i><a class="txt" href="scmpds_2.html#E3:66"><i><font color="Green">E25</font></i></a>, <a class="txt" href="scmpds_2.html#E5:66"><i><font color="Green">E26</font></i></a>, </i>;<br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="66_1_1_2"><b>suppose </b></a><a NAME="E1:66_1_1_2"/>
<font color="Maroon">x</font> <a href="hidden.html#R2">in</a>  <a href="ami_2.html#K2">SCM-Data-Loc</a> 
 ;<br/><div class="add"><a NAME="E2:66_1_1_2"/><b>then </b>
<font color="Maroon">x</font> is    <a href="scmpds_2.html#M1" target="_self">Int_position</a> 
 <b>by </b><i/>;<br/><b>hence </b><a NAME="E3:66_1_1_2"/>
<font color="Maroon">g1</font> <a href="funct_1.html#K1">.</a> <font color="Maroon">x</font> <a href="hidden.html#R1">=</a> <font color="Maroon">g2</font> <a href="funct_1.html#K1">.</a> <font color="Maroon">x</font>
 <b>by </b><i><a class="txt" href="scmpds_2.html#E2:66"><i><font color="Green">E23</font></i></a>, <a class="txt" href="scmpds_2.html#E3:66"><i><font color="Green">E25</font></i></a>, <a class="txt" href="scmpds_2.html#E5:66"><i><font color="Green">E26</font></i></a></i>;<br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="66_1_1_3"><b>suppose </b></a><a NAME="E1:66_1_1_3"/>
<font color="Maroon">x</font> <a href="hidden.html#R2">in</a>  <a href="ami_2.html#K3">SCM-Instr-Loc</a> 
 ;<br/><div class="add"><b>hence </b><a NAME="E2:66_1_1_3"/>
<font color="Maroon">g1</font> <a href="funct_1.html#K1">.</a> <font color="Maroon">x</font> <a href="hidden.html#R1">=</a> <font color="Maroon">g2</font> <a href="funct_1.html#K1">.</a> <font color="Maroon">x</font>
 <b>by </b><i>, <a class="txt" href="scmpds_2.html#E3:66"><i><font color="Green">E25</font></i></a>, <a class="txt" href="scmpds_2.html#E5:66"><i><font color="Green">E26</font></i></a></i>;<br/></div><b>end;</b></div></div><b>end;</b></div></div><b>end;</b></div>
<b>hence </b><a NAME="E10:66"/>
<font color="Maroon">s1</font> <a href="hidden.html#R1">=</a> <font color="Maroon">s2</font>
 <b>by </b><i><a class="txt" href="scmpds_2.html#E3:66"><i><font color="Green">E25</font></i></a>, <a class="txt" href="scmpds_2.html#E5:66"><i><font color="Green">E26</font></i></a>, <a class="ref" href="scmpds_2.html#T2" target="_self">Th2</a>, <a class="ref" href="funct_1.html#T9">FUNCT_1:9</a></i>;<br/>


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