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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">x</font> be   <a href="qc_lang1.html#NM3" title="QC_LANG1:NM.3">bound_QC-variable</a>;<br/><b>let </b><font color="Maroon" title="c3">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="c4">p</font> be    <a href="subset_1.html#M2" title="SUBSET_1:mode.2">Element</a> of  <a href="cqc_lang.html#K7" title="CQC_LANG:func.7">CQC-WFF</a> ;<br/><b>let </b><font color="Maroon" title="c5">J</font> be    <a href="valuat_1.html#M1" title="VALUAT_1:mode.1">interpretation</a> of <font color="Maroon" title="c1">A</font>;<br/>









<div><b>hereby </b>
<div class="add"><b>assume </b><a NAME="E1:34_1"/>
<font color="Maroon" title="c5">J</font>,<font color="Maroon" title="c3">v</font> <a href="valuat_1.html#R1" title="VALUAT_1:pred.1">|=</a>  <a href="cqc_lang.html#K15" title="CQC_LANG:func.15">All</a> <font color="Maroon" title="c2">x</font>,<font color="Maroon" title="c4">p</font>
 ;<br/><a NAME="E2:34_1"/><b>then </b>
<span class="p1">(<span class="default"><a href="valuat_1.html#K7" title="VALUAT_1:func.7">FOR_ALL</a> <font color="Maroon" title="c2">x</font>,<span class="p2">(<span class="default"><a href="valuat_1.html#K12" title="VALUAT_1:func.12">Valid</a> <font color="Maroon" title="c4">p</font>,<font color="Maroon" title="c5">J</font></span>)</span></span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c3">v</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="margrel1.html#K8" title="MARGREL1:func.8">TRUE</a> 
 <b>by </b><i><a class="ref" href="valuat_1.html#T30" target="_self" title="VALUAT_1:th.30">Th30</a></i>;<br/><b>hence </b><a NAME="E3:34_1"/>
for <font color="Olive" title="b1">v1</font> being   <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>  st ( for <font color="Olive" title="b2">y</font> being  <a href="qc_lang1.html#NM3" title="QC_LANG1:NM.3">bound_QC-variable</a>  st <font color="Maroon" title="c2">x</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Olive" title="b2">y</font> holds <br/><font color="Olive" title="b1">v1</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Olive" title="b2">y</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c3">v</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Olive" title="b2">y</font> ) holds <br/><span class="p1">(<span class="default"><a href="valuat_1.html#K12" title="VALUAT_1:func.12">Valid</a> <font color="Maroon" title="c4">p</font>,<font color="Maroon" title="c5">J</font></span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Olive" title="b1">v1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="margrel1.html#K8" title="MARGREL1:func.8">TRUE</a> 
 <b>by </b><i><a class="ref" href="valuat_1.html#T8" target="_self" title="VALUAT_1:th.8">Th8</a></i>;<br/></div>
<b>end;</b></div>

<b>assume </b><a NAME="E2:34"/>
for <font color="Olive" title="b1">v1</font> being   <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>  st ( for <font color="Olive" title="b2">y</font> being  <a href="qc_lang1.html#NM3" title="QC_LANG1:NM.3">bound_QC-variable</a>  st <font color="Maroon" title="c2">x</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Olive" title="b2">y</font> holds <br/><font color="Olive" title="b1">v1</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Olive" title="b2">y</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c3">v</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Olive" title="b2">y</font> ) holds <br/><span class="p1">(<span class="default"><a href="valuat_1.html#K12" title="VALUAT_1:func.12">Valid</a> <font color="Maroon" title="c4">p</font>,<font color="Maroon" title="c5">J</font></span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Olive" title="b1">v1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="margrel1.html#K8" title="MARGREL1:func.8">TRUE</a> 
 ;<br/>

<a NAME="E3:34"/><b>then </b>
<span class="p1">(<span class="default"><a href="valuat_1.html#K7" title="VALUAT_1:func.7">FOR_ALL</a> <font color="Maroon" title="c2">x</font>,<span class="p2">(<span class="default"><a href="valuat_1.html#K12" title="VALUAT_1:func.12">Valid</a> <font color="Maroon" title="c4">p</font>,<font color="Maroon" title="c5">J</font></span>)</span></span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c3">v</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="margrel1.html#K8" title="MARGREL1:func.8">TRUE</a> 
 
<b>by </b><i><a class="ref" href="valuat_1.html#T8" target="_self" title="VALUAT_1:th.8">Th8</a></i>;<br/>
<b>hence </b><a NAME="E4:34"/>
<font color="Maroon" title="c5">J</font>,<font color="Maroon" title="c3">v</font> <a href="valuat_1.html#R1" title="VALUAT_1:pred.1">|=</a>  <a href="cqc_lang.html#K15" title="CQC_LANG:func.15">All</a> <font color="Maroon" title="c2">x</font>,<font color="Maroon" title="c4">p</font>
 <b>by </b><i><a class="ref" href="valuat_1.html#T30" target="_self" title="VALUAT_1:th.30">Th30</a></i>;<br/>


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