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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">x</font> be   <a href="qc_lang1.html#NM3">bound_QC-variable</a>;<br/><b>let </b><font color="Maroon">y</font> be   <a href="qc_lang1.html#NM3">bound_QC-variable</a>;<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/><b>let </b><font color="Maroon">s</font> be   <a href="qc_lang1.html#NM8">QC-formula</a>;<br/>













<b>assume </b><b>that </b><br/><a NAME="E1:62"/><i><font color="Green">E25</font></i>: 
( <font color="Maroon">p</font> <a href="hidden.html#R1">=</a> <font color="Maroon">s</font> <a href="cqc_lang.html#K17">.</a> <font color="Maroon">x</font> &amp; <font color="Maroon">q</font> <a href="hidden.html#R1">=</a> <font color="Maroon">s</font> <a href="cqc_lang.html#K17">.</a> <font color="Maroon">y</font> )
 <b>and </b><br/><a NAME="E2:62"/><i><font color="Green">E30</font></i>: 
not <font color="Maroon">x</font> <a href="hidden.html#R2">in</a>  <a href="qc_lang1.html#K23">still_not-bound_in</a> <font color="Maroon">s</font>
 <b>and </b><br/><a NAME="E3:62"/><i><font color="Green">E32</font></i>: 
<font color="Maroon">J</font> <a href="valuat_1.html#R2" target="_self">|=</a> <font color="Maroon">p</font>
 ;<br/>

<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="62_1"><b>now </b></a><div class="add"><b>assume </b><a NAME="E1:62_1"/><i><font color="Green">E33</font></i>: 
<font color="Maroon">x</font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <font color="Maroon">y</font>
 ;<br/><div><i><font color="Green">E36</font></i>: <a class="txt" onclick="hs2(this)" href="javascript:()" title="62_1_1"><b>now </b></a><div class="add"><b>let </b><font color="Maroon">u</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>consider </b><font color="Maroon">w</font> being    <a href="fraenkel.html#M2">Element</a> of  <a href="valuat_1.html#K2" target="_self">Valuations_in</a> <font color="Maroon">A</font><b> such that </b><br/><a NAME="E2:62_1_1"/><i><font color="Green">E37</font></i>: 
( ( for <font color="Olive">z</font> being  <a href="qc_lang1.html#NM3">bound_QC-variable</a>  st <font color="Olive">z</font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <font color="Maroon">x</font> holds <br/><font color="Maroon">w</font> <a href="funct_2.html#K3">.</a> <font color="Olive">z</font> <a href="hidden.html#R1">=</a> <font color="Maroon">u</font> <a href="funct_2.html#K3">.</a> <font color="Olive">z</font> ) &amp; <font color="Maroon">w</font> <a href="funct_2.html#K3">.</a> <font color="Maroon">x</font> <a href="hidden.html#R1">=</a> <font color="Maroon">u</font> <a href="funct_2.html#K3">.</a> <font color="Maroon">y</font> )
 <b>from </b><i><a class="ref" href="valuat_1.html#S1" target="_self">VALUAT_1:sch 1</a>();<br/></i><a NAME="E3:62_1_1"/>
<font color="Maroon">w</font> <a href="funct_2.html#K3">.</a> <font color="Maroon">x</font> <a href="hidden.html#R1">=</a> <font color="Maroon">w</font> <a href="funct_2.html#K3">.</a> <font color="Maroon">y</font>
 <b>by </b><i/>;<br/><a NAME="E4:62_1_1"/><b>then </b><i><font color="Green">E38</font></i>: 
<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">w</font> <a href="hidden.html#R1">=</a> <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">w</font>
 <b>by </b><i>, <a class="txt" href="valuat_1.html#E3:62"><i><font color="Green">E32</font></i></a></i>;<br/><a NAME="E5:62_1_1"/>
<font color="Maroon">J</font>,<font color="Maroon">w</font> <a href="valuat_1.html#R1" target="_self">|=</a> <font color="Maroon">p</font>
 <b>by </b><i>, </i>;<br/><a NAME="E6:62_1_1"/><b>then </b><i><font color="Green">E39</font></i>: 
<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">w</font> <a href="hidden.html#R1">=</a>  <a href="margrel1.html#K8">TRUE</a> 
 <b>by </b><i/>;<br/><a NAME="E7:62_1_1"/>
not <font color="Maroon">x</font> <a href="hidden.html#R2">in</a>  <a href="qc_lang1.html#K23">still_not-bound_in</a> <font color="Maroon">q</font>
 <b>by </b><i>, , <a class="ref" href="valuat_1.html#D4" target="_self">Def4</a>, <a class="txt" href="valuat_1.html#E1:62_1"><i><font color="Green">E33</font></i></a></i>;<br/><b>hence </b><a NAME="E8:62_1_1"/>
<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">u</font> <a href="hidden.html#R1">=</a>  <a href="margrel1.html#K8">TRUE</a> 
 <b>by </b><i>, , , </i>;<br/></div><b>end;</b></div><div><a class="txt" onclick="hs2(this)" href="javascript:()" title="62_1_2"><b>now </b></a><div class="add"><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/><a NAME="E1:62_1_2"/>
<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/><b>hence </b><a NAME="E2:62_1_2"/>
<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>hence </b><a NAME="E4:62_1"/>
<font color="Maroon">J</font> <a href="valuat_1.html#R2" target="_self">|=</a> <font color="Maroon">q</font>
 <b>by </b><i/>;<br/></div><b>end;</b></div>
<b>hence </b><a NAME="E5:62"/>
<font color="Maroon">J</font> <a href="valuat_1.html#R2" target="_self">|=</a> <font color="Maroon">q</font>
 <b>by </b><i>, </i>;<br/>


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