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<b>let </b><font color="Maroon" title="c1">A</font> be  non <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a>  <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a> ;<br/><b>let </b><font color="Maroon" title="c2">v</font> be    <a href="fraenkel.html#M2" title="FRAENKEL:mode.2">Element</a> of  <a href="valuat_1.html#K2" title="VALUAT_1:func.2">Valuations_in</a> <font color="Maroon" title="c1">A</font>;<br/><b>let </b><font color="Maroon" title="c3">S</font> be    <a href="subset_1.html#M2" title="SUBSET_1:mode.2">Element</a> of  <a href="substut1.html#K38" title="SUBSTUT1:func.38">CQC-Sub-WFF</a> ;<br/>





<a NAME="E1:26"/>
 <a href="sublemma.html#K6" title="SUBLEMMA:func.6">Sub_not</a> <font color="Maroon" title="c3">S</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"><a href="domain_1.html#K1" title="DOMAIN_1:func.1">[</a><span class="default"><span class="p2">(<span class="default"><a href="cqc_lang.html#K10" title="CQC_LANG:func.10">'not'</a> <span class="p3">(<span class="default"><font color="Maroon" title="c3">S</font> <a href="sublemma.html#K2" title="SUBLEMMA:func.2">`1</a> </span>)</span></span>)</span>,<span class="p2">(<span class="default"><font color="Maroon" title="c3">S</font> <a href="substut1.html#K19" title="SUBSTUT1:func.19">`2</a> </span>)</span></span><a href="domain_1.html#K1" title="DOMAIN_1:func.1">]</a></span>
 
<b>by </b><i><a class="ref" href="substut1.html#D20" title="SUBSTUT1:def.20">SUBSTUT1:def 20</a></i>;<br/>
<a NAME="E2:26"/><b>then </b>
<span class="p1">(<span class="default"><a href="substut1.html#K2" title="SUBSTUT1:func.2">@</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="sublemma.html#K6" title="SUBLEMMA:func.6">Sub_not</a> <font color="Maroon" title="c3">S</font></span>)</span> <a href="substut1.html#K19" title="SUBSTUT1:func.19">`2</a> </span>)</span></span>)</span> <a href="relset_1.html#K7" title="RELSET_1:func.7">*</a> <font color="Maroon" title="c2">v</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="substut1.html#K2" title="SUBSTUT1:func.2">@</a> <span class="p2">(<span class="default"><font color="Maroon" title="c3">S</font> <a href="substut1.html#K19" title="SUBSTUT1:func.19">`2</a> </span>)</span></span>)</span> <a href="relset_1.html#K7" title="RELSET_1:func.7">*</a> <font color="Maroon" title="c2">v</font>
 
<b>by </b><i><a class="ref" href="mcart_1.html#T7" title="MCART_1:th.7">MCART_1:7</a></i>;<br/>
<a NAME="E3:26"/><b>then </b>
 <a href="sublemma.html#K3" title="SUBLEMMA:func.3">Val_S</a> <font color="Maroon" title="c2">v</font>,<span class="p1">(<span class="default"><a href="sublemma.html#K6" title="SUBLEMMA:func.6">Sub_not</a> <font color="Maroon" title="c3">S</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="substut1.html#K2" title="SUBSTUT1:func.2">@</a> <span class="p2">(<span class="default"><font color="Maroon" title="c3">S</font> <a href="substut1.html#K19" title="SUBSTUT1:func.19">`2</a> </span>)</span></span>)</span> <a href="relset_1.html#K7" title="RELSET_1:func.7">*</a> <font color="Maroon" title="c2">v</font>
 
;<br/>
<b>hence </b><a NAME="E4:26"/>
 <a href="sublemma.html#K3" title="SUBLEMMA:func.3">Val_S</a> <font color="Maroon" title="c2">v</font>,<font color="Maroon" title="c3">S</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="sublemma.html#K3" title="SUBLEMMA:func.3">Val_S</a> <font color="Maroon" title="c2">v</font>,<span class="p1">(<span class="default"><a href="sublemma.html#K6" title="SUBLEMMA:func.6">Sub_not</a> <font color="Maroon" title="c3">S</font></span>)</span>
 ;<br/>


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