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<b>let </b><font color="Maroon">c<sub>3</sub></font>, <font color="Maroon">c<sub>4</sub></font> be    <a href="ami_1.html#M1">FinPartState</a> of  <a href="scmpds_2.html#K1">SCMPDS</a> ;<br/>

<b>assume </b><a NAME="E1:2"/><i><font color="Green">E2</font></i>: 
<font color="Maroon">c<sub>3</sub></font> <a href="tarski.html#R1">c=</a> <font color="Maroon">c<sub>4</sub></font>
 ;<br/>

<a NAME="E2:2"/><b>then </b><i><font color="Green">E3</font></i>: 
 <a href="relat_1.html#K1">dom</a> <font color="Maroon">c<sub>3</sub></font> <a href="tarski.html#R1">c=</a>  <a href="relat_1.html#K1">dom</a> <font color="Maroon">c<sub>4</sub></font>
 
<b>by </b><i><a class="ref" href="grfunc_1.html#T8">GRFUNC_1:8</a></i>;<br/>
<a NAME="E3:2"/><i><font color="Green">E4</font></i>: 
(  <a href="ami_5.html#K6">ProgramPart</a> <font color="Maroon">c<sub>3</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>3</sub></font> <a href="relat_1.html#K7">|</a> the <a href="ami_1.html#U2">Instruction-Locations</a> of <a href="scmpds_2.html#K1">SCMPDS</a>  &amp;  <a href="ami_5.html#K6">ProgramPart</a> <font color="Maroon">c<sub>4</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>4</sub></font> <a href="relat_1.html#K7">|</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_5.html#D6">AMI_5:def 6</a></i>;<br/>
<a NAME="E4:2"/><b>then </b><i><font color="Green">E5</font></i>: 
(  <a href="relat_1.html#K1">dom</a> <span class="p1">(<span class="default"><a href="ami_5.html#K6">ProgramPart</a> <font color="Maroon">c<sub>3</sub></font></span>)</span> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><a href="relat_1.html#K1">dom</a> <font color="Maroon">c<sub>3</sub></font></span>)</span> <a href="xboole_0.html#K3">/\</a> the <a href="ami_1.html#U2">Instruction-Locations</a> of <a href="scmpds_2.html#K1">SCMPDS</a>  &amp;  <a href="relat_1.html#K1">dom</a> <span class="p1">(<span class="default"><a href="ami_5.html#K6">ProgramPart</a> <font color="Maroon">c<sub>4</sub></font></span>)</span> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><a href="relat_1.html#K1">dom</a> <font color="Maroon">c<sub>4</sub></font></span>)</span> <a href="xboole_0.html#K3">/\</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="relat_1.html#T90">RELAT_1:90</a></i>;<br/>
<a NAME="E5:2"/><b>then </b><i><font color="Green">E6</font></i>: 
 <a href="relat_1.html#K1">dom</a> <span class="p1">(<span class="default"><a href="ami_5.html#K6">ProgramPart</a> <font color="Maroon">c<sub>3</sub></font></span>)</span> <a href="tarski.html#R1">c=</a>  <a href="relat_1.html#K1">dom</a> <span class="p1">(<span class="default"><a href="ami_5.html#K6">ProgramPart</a> <font color="Maroon">c<sub>4</sub></font></span>)</span>
 
<b>by </b><i><a class="txt" href="scmpds_7.html#E2:2"><i><font color="Green">E3</font></i></a>, <a class="ref" href="xboole_1.html#T26">XBOOLE_1:26</a></i>;<br/>
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="2_1"><b>now </b></a><div class="add"><b>let </b><font color="Maroon">c<sub>5</sub></font> be    <a href="hidden.html#M1">set</a> ;<br/><b>assume </b><a NAME="E1:2_1"/><i><font color="Green">E7</font></i>: 
<font color="Maroon">c<sub>5</sub></font> <a href="hidden.html#R2">in</a>  <a href="relat_1.html#K1">dom</a> <span class="p1">(<span class="default"><a href="ami_5.html#K6">ProgramPart</a> <font color="Maroon">c<sub>3</sub></font></span>)</span>
 ;<br/><a NAME="E2:2_1"/><b>then </b><i><font color="Green">E8</font></i>: 
<font color="Maroon">c<sub>5</sub></font> <a href="hidden.html#R2">in</a>  <a href="relat_1.html#K1">dom</a> <font color="Maroon">c<sub>3</sub></font>
 <b>by </b><i><a class="txt" href="scmpds_7.html#E4:2"><i><font color="Green">E5</font></i></a>, <a class="ref" href="xboole_0.html#D3">XBOOLE_0:def 3</a></i>;<br/><b>thus </b><span class="p1">(<span class="default"><a href="ami_5.html#K6">ProgramPart</a> <font color="Maroon">c<sub>3</sub></font></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">c<sub>5</sub></font> = 
<font color="Maroon">c<sub>3</sub></font> <a href="funct_1.html#K1">.</a> <font color="Maroon">c<sub>5</sub></font>
<b>by </b><i><a class="txt" href="scmpds_7.html#E3:2"><i><font color="Green">E4</font></i></a>, <a class="txt" href="scmpds_7.html#E1:2_1"><i><font color="Green">E7</font></i></a>, <a class="ref" href="funct_1.html#T68">FUNCT_1:68</a></i>
<br/>.= 
<font color="Maroon">c<sub>4</sub></font> <a href="funct_1.html#K1">.</a> <font color="Maroon">c<sub>5</sub></font>
<b>by </b><i><a class="txt" href="scmpds_7.html#E1:2"><i><font color="Green">E2</font></i></a>, <a class="txt" href="scmpds_7.html#E2:2_1"><i><font color="Green">E8</font></i></a>, <a class="ref" href="grfunc_1.html#T8">GRFUNC_1:8</a></i>
<br/>.= 
<span class="p1">(<span class="default"><a href="ami_5.html#K6">ProgramPart</a> <font color="Maroon">c<sub>4</sub></font></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">c<sub>5</sub></font>
<b>by </b><i><a class="txt" href="scmpds_7.html#E3:2"><i><font color="Green">E4</font></i></a>, <a class="txt" href="scmpds_7.html#E5:2"><i><font color="Green">E6</font></i></a>, <a class="txt" href="scmpds_7.html#E1:2_1"><i><font color="Green">E7</font></i></a>, <a class="ref" href="funct_1.html#T68">FUNCT_1:68</a></i>
;<br/></div><b>end;</b></div>
<b>hence </b><a NAME="E7:2"/>
 <a href="ami_5.html#K6">ProgramPart</a> <font color="Maroon">c<sub>3</sub></font> <a href="tarski.html#R1">c=</a>  <a href="ami_5.html#K6">ProgramPart</a> <font color="Maroon">c<sub>4</sub></font>
 <b>by </b><i><a class="txt" href="scmpds_7.html#E5:2"><i><font color="Green">E6</font></i></a>, <a class="ref" href="grfunc_1.html#T8">GRFUNC_1:8</a></i>;<br/>


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