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<b>let </b><font color="Maroon" title="c1">k</font> be    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of  <a href="numbers.html#K5" title="NUMBERS:func.5">NAT</a> ;<br/><b>let </b><font color="Maroon" title="c2">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="c3">J</font> be    <a href="valuat_1.html#M1" title="VALUAT_1:mode.1">interpretation</a> of <font color="Maroon" title="c2">A</font>;<br/><b>let </b><font color="Maroon" title="c4">P</font> be   <a href="qc_lang1.html#NM6" title="QC_LANG1:NM.6">QC-pred_symbol</a> of <font color="Maroon" title="c1">k</font>;<br/><b>let </b><font color="Maroon" title="c5">ll</font> be   <a href="cqc_lang.html#NM2" title="CQC_LANG:NM.2">CQC-variable_list</a> of <font color="Maroon" title="c1">k</font>;<br/><b>let </b><font color="Maroon" title="c6">v</font>, <font color="Maroon" title="c7">w</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="c2">A</font>;<br/>













<b>assume </b><a NAME="E1:77"/><i><font color="Green" title="E60">A1</font></i>: 
<font color="Maroon" title="c6">v</font> <a href="relset_1.html#K8" title="RELSET_1:func.8">|</a> <span class="p1">(<span class="default"><a href="qc_lang1.html#K23" title="QC_LANG1:func.23">still_not-bound_in</a> <span class="p2">(<span class="default"><font color="Maroon" title="c4">P</font> <a href="cqc_lang.html#K5" title="CQC_LANG:func.5">!</a> <font color="Maroon" title="c5">ll</font></span>)</span></span>)</span> <a href="relset_1.html#R2" title="RELSET_1:pred.2">=</a> <font color="Maroon" title="c7">w</font> <a href="relset_1.html#K8" title="RELSET_1:func.8">|</a> <span class="p1">(<span class="default"><a href="qc_lang1.html#K23" title="QC_LANG1:func.23">still_not-bound_in</a> <span class="p2">(<span class="default"><font color="Maroon" title="c4">P</font> <a href="cqc_lang.html#K5" title="CQC_LANG:func.5">!</a> <font color="Maroon" title="c5">ll</font></span>)</span></span>)</span>
 ;<br/>

<a NAME="E2:77"/><i><font color="Green" title="E61">A2</font></i>: 
 <a href="qc_lang1.html#K23" title="QC_LANG1:func.23">still_not-bound_in</a> <span class="p1">(<span class="default"><font color="Maroon" title="c4">P</font> <a href="cqc_lang.html#K5" title="CQC_LANG:func.5">!</a> <font color="Maroon" title="c5">ll</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="qc_lang1.html#K22" title="QC_LANG1:func.22">still_not-bound_in</a> <font color="Maroon" title="c5">ll</font>
 
<b>by </b><i><a class="ref" href="qc_lang3.html#T9" title="QC_LANG3:th.9">QC_LANG3:9</a></i>;<br/>
<a NAME="E3:77"/><i><font color="Green" title="E62">A3</font></i>: 
( <span class="p1">(<span class="default"><a href="valuat_1.html#K8" title="VALUAT_1:func.8">Valid</a> <span class="p2">(<span class="default"><font color="Maroon" title="c4">P</font> <a href="cqc_lang.html#K5" title="CQC_LANG:func.5">!</a> <font color="Maroon" title="c5">ll</font></span>)</span>,<font color="Maroon" title="c3">J</font></span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c6">v</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="margrel1.html#K8" title="MARGREL1:func.8">TRUE</a>  iff <font color="Maroon" title="c6">v</font> <a href="valuat_1.html#K4" title="VALUAT_1:func.4">*'</a> <font color="Maroon" title="c5">ll</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c3">J</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c4">P</font> )
 
<b>by </b><i><a class="ref" href="valuat_1.html#T16" title="VALUAT_1:th.16">VALUAT_1:16</a></i>;<br/>
<a NAME="E4:77"/><i><font color="Green" title="E63">A4</font></i>: 
( <font color="Maroon" title="c5">ll</font> <a href="relset_1.html#K7" title="RELSET_1:func.7">*</a> <span class="p1">(<span class="default"><font color="Maroon" title="c7">w</font> <a href="relset_1.html#K8" title="RELSET_1:func.8">|</a> <span class="p2">(<span class="default"><a href="qc_lang1.html#K22" title="QC_LANG1:func.22">still_not-bound_in</a> <font color="Maroon" title="c5">ll</font></span>)</span></span>)</span> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c3">J</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c4">P</font> iff <font color="Maroon" title="c7">w</font> <a href="valuat_1.html#K4" title="VALUAT_1:func.4">*'</a> <font color="Maroon" title="c5">ll</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c3">J</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c4">P</font> )
 
<b>by </b><i><a class="ref" href="sublemma.html#T60" target="_self" title="SUBLEMMA:th.60">Th60</a></i>;<br/>
<a NAME="E5:77"/>
( <font color="Maroon" title="c7">w</font> <a href="valuat_1.html#K4" title="VALUAT_1:func.4">*'</a> <font color="Maroon" title="c5">ll</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c3">J</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c4">P</font> iff <span class="p1">(<span class="default"><a href="valuat_1.html#K8" title="VALUAT_1:func.8">Valid</a> <span class="p2">(<span class="default"><font color="Maroon" title="c4">P</font> <a href="cqc_lang.html#K5" title="CQC_LANG:func.5">!</a> <font color="Maroon" title="c5">ll</font></span>)</span>,<font color="Maroon" title="c3">J</font></span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c7">w</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#T16" title="VALUAT_1:th.16">VALUAT_1:16</a></i>;<br/>
<b>hence </b><a NAME="E6:77"/>
( <font color="Maroon" title="c3">J</font>,<font color="Maroon" title="c6">v</font> <a href="valuat_1.html#R1" title="VALUAT_1:pred.1">|=</a> <font color="Maroon" title="c4">P</font> <a href="cqc_lang.html#K5" title="CQC_LANG:func.5">!</a> <font color="Maroon" title="c5">ll</font> iff <font color="Maroon" title="c3">J</font>,<font color="Maroon" title="c7">w</font> <a href="valuat_1.html#R1" title="VALUAT_1:pred.1">|=</a> <font color="Maroon" title="c4">P</font> <a href="cqc_lang.html#K5" title="CQC_LANG:func.5">!</a> <font color="Maroon" title="c5">ll</font> )
 <b>by </b><i><a class="txt" href="sublemma.html#E1:77"><i><font color="Green" title="E60">A1</font></i></a>, <a class="txt" href="sublemma.html#E2:77"><i><font color="Green" title="E61">A2</font></i></a>, <a class="txt" href="sublemma.html#E3:77"><i><font color="Green" title="E62">A3</font></i></a>, <a class="txt" href="sublemma.html#E4:77"><i><font color="Green" title="E63">A4</font></i></a>, <a class="ref" href="sublemma.html#T60" target="_self" title="SUBLEMMA:th.60">Th60</a>, <a class="ref" href="valuat_1.html#D12" title="VALUAT_1:def.12">VALUAT_1:def 12</a></i>;<br/>


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