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<span class="kw">let </span><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> ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide">  for <font color="Olive" title="b1">v</font> being    <a href="funct_2.html#M2" title="FUNCT_2: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/>  for <font color="Olive" title="b2">S</font> being    <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>  holds   <a href="sublemma.html#K3" title="SUBLEMMA:func.3">Val_S</a> (<font color="Olive" title="b1">v</font>,<font color="Olive" title="b2">S</font>) <a href="relset_1.html#R2" title="RELSET_1:pred.2">=</a>  <a href="sublemma.html#K3" title="SUBLEMMA:func.3">Val_S</a> (<font color="Olive" title="b1">v</font>,<span class="p1">(<span class="default"><a href="sublemma.html#K5" title="SUBLEMMA:func.5">Sub_not</a> <font color="Olive" title="b2">S</font></span>)</span>)</span><br/><span class="kw">let </span><font color="Maroon" title="c2">v</font> be    <a href="funct_2.html#M2" title="FUNCT_2: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>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide">  for <font color="Olive" title="b1">S</font> being    <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>  holds   <a href="sublemma.html#K3" title="SUBLEMMA:func.3">Val_S</a> (<font color="Maroon" title="c2">v</font>,<font color="Olive" title="b1">S</font>) <a href="relset_1.html#R2" title="RELSET_1:pred.2">=</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#K5" title="SUBLEMMA:func.5">Sub_not</a> <font color="Olive" title="b1">S</font></span>)</span>)</span><br/><span class="kw">let </span><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> ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide">  <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="relset_1.html#R2" title="RELSET_1:pred.2">=</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#K5" title="SUBLEMMA:func.5">Sub_not</a> <font color="Maroon" title="c3">S</font></span>)</span>)</span><br/>





<a NAME="E1:27"/>
 <a href="sublemma.html#K5" title="SUBLEMMA:func.5">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#K6" title="CQC_LANG:func.6">'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>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="substut1.html#D20" title="SUBSTUT1:def.20">SUBSTUT1:def 20</a></span>;<br/>
<span class="kw">hence </span><a NAME="E2:27"/>
 <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="relset_1.html#R2" title="RELSET_1:pred.2">=</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#K5" title="SUBLEMMA:func.5">Sub_not</a> <font color="Maroon" title="c3">S</font></span>)</span>)
 <span class="kw">by</span> <span class="lab"><a class="ref" href="mcart_1.html#T7" title="MCART_1:th.7">MCART_1:7</a></span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> verum</span><br/>


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