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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" target="_self">Valuations_in</a> <font color="Maroon">A</font>;<br/><b>let </b><font color="Maroon">p</font> be    <a href="subset_1.html#M2">Element</a> of  <a href="cqc_lang.html#K7">CQC-WFF</a> ;<br/><b>let </b><font color="Maroon">q</font> be    <a href="subset_1.html#M2">Element</a> of  <a href="cqc_lang.html#K7">CQC-WFF</a> ;<br/><b>let </b><font color="Maroon">J</font> be    <a href="valuat_1.html#M1" target="_self">interpretation</a> of <font color="Maroon">A</font>;<br/>









<div><b>hereby </b>
<div class="add"><b>assume </b><a NAME="E1:38_1"/>
<font color="Maroon">J</font>,<font color="Maroon">v</font> <a href="valuat_1.html#R1" target="_self">|=</a> <font color="Maroon">p</font> <a href="cqc_lang.html#K12">=&gt;</a> <font color="Maroon">q</font>
 ;<br/><a NAME="E2:38_1"/><b>then </b>
( <span class="p1">(<span class="default"><a href="valuat_1.html#K12" target="_self">Valid</a> <font color="Maroon">p</font>,<font color="Maroon">J</font></span>)</span> <a href="funct_2.html#K3">.</a> <font color="Maroon">v</font> <a href="hidden.html#R1">=</a>  <a href="margrel1.html#K7">FALSE</a>  or <span class="p1">(<span class="default"><a href="valuat_1.html#K12" target="_self">Valid</a> <font color="Maroon">q</font>,<font color="Maroon">J</font></span>)</span> <a href="funct_2.html#K3">.</a> <font color="Maroon">v</font> <a href="hidden.html#R1">=</a>  <a href="margrel1.html#K8">TRUE</a>  )
 <b>by </b><i><a class="ref" href="valuat_1.html#D2" target="_self">Def2</a></i>;<br/><b>hence </b><a NAME="E3:38_1"/>
( <font color="Maroon">J</font>,<font color="Maroon">v</font> <a href="valuat_1.html#R1" target="_self">|=</a> <font color="Maroon">p</font> implies <font color="Maroon">J</font>,<font color="Maroon">v</font> <a href="valuat_1.html#R1" target="_self">|=</a> <font color="Maroon">q</font> )
 <b>by </b><i/>;<br/></div>
<b>end;</b></div>

<b>assume </b><a NAME="E2:38"/>
( <font color="Maroon">J</font>,<font color="Maroon">v</font> <a href="valuat_1.html#R1" target="_self">|=</a> <font color="Maroon">p</font> implies <font color="Maroon">J</font>,<font color="Maroon">v</font> <a href="valuat_1.html#R1" target="_self">|=</a> <font color="Maroon">q</font> )
 ;<br/>

<a NAME="E3:38"/><b>then </b>
( <span class="p1">(<span class="default"><a href="valuat_1.html#K12" target="_self">Valid</a> <font color="Maroon">p</font>,<font color="Maroon">J</font></span>)</span> <a href="funct_2.html#K3">.</a> <font color="Maroon">v</font> <a href="hidden.html#R1">=</a>  <a href="margrel1.html#K8">TRUE</a>  implies <span class="p1">(<span class="default"><a href="valuat_1.html#K12" target="_self">Valid</a> <font color="Maroon">q</font>,<font color="Maroon">J</font></span>)</span> <a href="funct_2.html#K3">.</a> <font color="Maroon">v</font> <a href="hidden.html#R1">=</a>  <a href="margrel1.html#K8">TRUE</a>  )
 
<b>by </b><i/>;<br/>
<a NAME="E4:38"/><b>then </b>
( <span class="p1">(<span class="default"><a href="valuat_1.html#K12" target="_self">Valid</a> <font color="Maroon">p</font>,<font color="Maroon">J</font></span>)</span> <a href="funct_2.html#K3">.</a> <font color="Maroon">v</font> <a href="hidden.html#R1">=</a>  <a href="margrel1.html#K7">FALSE</a>  or <span class="p1">(<span class="default"><a href="valuat_1.html#K12" target="_self">Valid</a> <font color="Maroon">q</font>,<font color="Maroon">J</font></span>)</span> <a href="funct_2.html#K3">.</a> <font color="Maroon">v</font> <a href="hidden.html#R1">=</a>  <a href="margrel1.html#K8">TRUE</a>  )
 
<b>by </b><i><a class="ref" href="margrel1.html#T43">MARGREL1:43</a></i>;<br/>
<b>hence </b><a NAME="E5:38"/>
<font color="Maroon">J</font>,<font color="Maroon">v</font> <a href="valuat_1.html#R1" target="_self">|=</a> <font color="Maroon">p</font> <a href="cqc_lang.html#K12">=&gt;</a> <font color="Maroon">q</font>
 <b>by </b><i><a class="ref" href="valuat_1.html#D2" target="_self">Def2</a></i>;<br/>


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