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<b>let </b><font color="Maroon">k</font> be    <a href="subset_1.html#M2">Element</a> of  <a href="numbers.html#K5">NAT</a> ;<br/><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">ll</font> be   <a href="cqc_lang.html#NM2">CQC-variable_list</a> of <font color="Maroon">k</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">J</font> be    <a href="valuat_1.html#M1" target="_self">interpretation</a> of <font color="Maroon">A</font>;<br/><b>let </b><font color="Maroon">P</font> be   <a href="qc_lang1.html#NM6">QC-pred_symbol</a> of <font color="Maroon">k</font>;<br/><b>let </b><font color="Maroon">r</font> be    <a href="subset_1.html#M1">Element</a> of  <a href="margrel1.html#K3">relations_on</a> <font color="Maroon">A</font>;<br/>















<b>assume </b><a NAME="E1:24"/><i><font color="Green">E25</font></i>: 
( <font color="Maroon">p</font> <a href="hidden.html#R1">=</a> <font color="Maroon">P</font> <a href="cqc_lang.html#K8">!</a> <font color="Maroon">ll</font> &amp; <font color="Maroon">r</font> <a href="margrel1.html#R1">=</a> <font color="Maroon">J</font> <a href="valuat_1.html#K11" target="_self">.</a> <font color="Maroon">P</font> )
 ;<br/>

<div><i><font color="Green">E30</font></i>: <a class="txt" onclick="hs2(this)" href="javascript:()" title="24_1"><b>now </b></a><div class="add"><b>assume </b><a NAME="E1:24_1"/>
not <font color="Maroon">v</font> <a href="valuat_1.html#K8" target="_self">*'</a> <font color="Maroon">ll</font> <a href="hidden.html#R2">in</a> <font color="Maroon">r</font>
 ;<br/><a NAME="E2:24_1"/><b>then </b>
<span class="p1">(<span class="default"><font color="Maroon">ll</font> <a href="valuat_1.html#K9" target="_self">'in'</a> <span class="p2">(<span class="default"><font color="Maroon">J</font> <a href="valuat_1.html#K11" target="_self">.</a> <font color="Maroon">P</font></span>)</span></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> 
 <b>by </b><i>, </i>;<br/><b>hence </b><a NAME="E3:24_1"/>
<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> 
 <b>by </b><i>, </i>;<br/></div><b>end;</b></div>
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="24_2"><b>now </b></a><div class="add"><b>assume </b><a NAME="E1:24_2"/>
<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> 
 ;<br/><a NAME="E2:24_2"/><b>then </b>
<span class="p1">(<span class="default"><font color="Maroon">ll</font> <a href="valuat_1.html#K9" target="_self">'in'</a> <span class="p2">(<span class="default"><font color="Maroon">J</font> <a href="valuat_1.html#K11" target="_self">.</a> <font color="Maroon">P</font></span>)</span></span>)</span> <a href="funct_2.html#K3">.</a> <font color="Maroon">v</font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a>  <a href="margrel1.html#K8">TRUE</a> 
 <b>by </b><i>, </i>;<br/><b>hence </b><a NAME="E3:24_2"/>
not <font color="Maroon">v</font> <a href="valuat_1.html#K8" target="_self">*'</a> <font color="Maroon">ll</font> <a href="hidden.html#R2">in</a> <font color="Maroon">r</font>
 <b>by </b><i>, </i>;<br/></div><b>end;</b></div>
<b>hence </b><a NAME="E4:24"/>
( not <font color="Maroon">v</font> <a href="valuat_1.html#K8" target="_self">*'</a> <font color="Maroon">ll</font> <a href="hidden.html#R2">in</a> <font color="Maroon">r</font> iff <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>  )
 <b>by </b><i/>;<br/>


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