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<b>let </b><font color="Maroon">A</font> be  non <a href="xboole_0.html#V1">empty</a>  <a href="hidden.html#M1">set</a> ;<br/><b>let </b><font color="Maroon">v</font> be    <a href="fraenkel.html#M2">Element</a> of  <a href="valuat_1.html#K2">Valuations_in</a> <font color="Maroon">A</font>;<br/><b>let </b><font color="Maroon">S</font> be    <a href="subset_1.html#M2">Element</a> of  <a href="substut1.html#K38">CQC-Sub-WFF</a> ;<br/>





<a NAME="E1:26"/>
 <a href="sublemma.html#K6" target="_self">Sub_not</a> <font color="Maroon">S</font> <a href="hidden.html#R1">=</a> <span class="p1"><a href="domain_1.html#K1">[</a><span class="default"><span class="p2">(<span class="default"><a href="cqc_lang.html#K10">'not'</a> <span class="p3">(<span class="default"><font color="Maroon">S</font> <a href="sublemma.html#K2" target="_self">`1</a> </span>)</span></span>)</span>,<span class="p2">(<span class="default"><font color="Maroon">S</font> <a href="substut1.html#K19">`2</a> </span>)</span></span><a href="domain_1.html#K1">]</a></span>
 
<b>by </b><i><a class="ref" href="substut1.html#D20">SUBSTUT1:def 20</a></i>;<br/>
<a NAME="E2:26"/><b>then </b>
<span class="p1">(<span class="default"><a href="substut1.html#K2">@</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="sublemma.html#K6" target="_self">Sub_not</a> <font color="Maroon">S</font></span>)</span> <a href="substut1.html#K19">`2</a> </span>)</span></span>)</span> <a href="relset_1.html#K7">*</a> <font color="Maroon">v</font> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><a href="substut1.html#K2">@</a> <span class="p2">(<span class="default"><font color="Maroon">S</font> <a href="substut1.html#K19">`2</a> </span>)</span></span>)</span> <a href="relset_1.html#K7">*</a> <font color="Maroon">v</font>
 
<b>by </b><i><a class="ref" href="mcart_1.html#T7">MCART_1:7</a></i>;<br/>
<a NAME="E3:26"/><b>then </b>
 <a href="sublemma.html#K3" target="_self">Val_S</a> <font color="Maroon">v</font>,<span class="p1">(<span class="default"><a href="sublemma.html#K6" target="_self">Sub_not</a> <font color="Maroon">S</font></span>)</span> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><a href="substut1.html#K2">@</a> <span class="p2">(<span class="default"><font color="Maroon">S</font> <a href="substut1.html#K19">`2</a> </span>)</span></span>)</span> <a href="relset_1.html#K7">*</a> <font color="Maroon">v</font>
 
;<br/>
<b>hence </b><a NAME="E4:26"/>
 <a href="sublemma.html#K3" target="_self">Val_S</a> <font color="Maroon">v</font>,<font color="Maroon">S</font> <a href="hidden.html#R1">=</a>  <a href="sublemma.html#K3" target="_self">Val_S</a> <font color="Maroon">v</font>,<span class="p1">(<span class="default"><a href="sublemma.html#K6" target="_self">Sub_not</a> <font color="Maroon">S</font></span>)</span>
 ;<br/>


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