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<b>let </b><font color="Maroon" title="c1">p</font> be    <a href="subset_1.html#M2" title="SUBSET_1:mode.2">Element</a> of  <a href="cqc_lang.html#K4" title="CQC_LANG:func.4">CQC-WFF</a> ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> for <font color="Olive" title="b1">A</font> being 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/> for <font color="Olive" title="b2">J</font> being   <a href="valuat_1.html#M1" title="VALUAT_1:mode.1">interpretation</a> of <font color="Olive" title="b1">A</font> holds <br/> (  <a href="valuat_1.html#K8" title="VALUAT_1:func.8">Valid</a> <a href="cqc_lang.html#K6" title="CQC_LANG:func.6">VERUM</a> ,<font color="Olive" title="b2">J</font> <a href="funct_2.html#R2" title="FUNCT_2:pred.2">=</a> <span class="p1">(<span class="default"><a href="valuat_1.html#K2" title="VALUAT_1:func.2">Valuations_in</a> <font color="Olive" title="b1">A</font></span>)</span> <a href="margrel1.html#K1" title="MARGREL1:func.1">--&gt;</a> <a href="margrel1.html#K8" title="MARGREL1:func.8">TRUE</a>  &amp; ( for <font color="Olive" title="b3">k</font> being   <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/> for <font color="Olive" title="b4">ll</font> being  <a href="cqc_lang.html#NM2" title="CQC_LANG:NM.2">CQC-variable_list</a> of <font color="Olive" title="b3">k</font><br/> for <font color="Olive" title="b5">P</font> being  <a href="qc_lang1.html#NM6" title="QC_LANG1:NM.6">QC-pred_symbol</a> of <font color="Olive" title="b3">k</font> holds   <a href="valuat_1.html#K8" title="VALUAT_1:func.8">Valid</a> <span class="p1">(<span class="default"><font color="Olive" title="b5">P</font> <a href="cqc_lang.html#K5" title="CQC_LANG:func.5">!</a> <font color="Olive" title="b4">ll</font></span>)</span>,<font color="Olive" title="b2">J</font> <a href="funct_2.html#R2" title="FUNCT_2:pred.2">=</a> <font color="Olive" title="b4">ll</font> <a href="valuat_1.html#K5" title="VALUAT_1:func.5">'in'</a> <span class="p1">(<span class="default"><font color="Olive" title="b2">J</font> <a href="valuat_1.html#K7" title="VALUAT_1:func.7">.</a> <font color="Olive" title="b5">P</font></span>)</span> ) &amp; ( for <font color="Olive" title="b3">p</font> being   <a href="subset_1.html#M2" title="SUBSET_1:mode.2">Element</a> of  <a href="cqc_lang.html#K4" title="CQC_LANG:func.4">CQC-WFF</a>  holds   <a href="valuat_1.html#K8" title="VALUAT_1:func.8">Valid</a> <span class="p1">(<span class="default"><a href="cqc_lang.html#K7" title="CQC_LANG:func.7">'not'</a> <font color="Olive" title="b3">p</font></span>)</span>,<font color="Olive" title="b2">J</font> <a href="funct_2.html#R2" title="FUNCT_2:pred.2">=</a>  <a href="margrel1.html#K15" title="MARGREL1:func.15">'not'</a> <span class="p1">(<span class="default"><a href="valuat_1.html#K8" title="VALUAT_1:func.8">Valid</a> <font color="Olive" title="b3">p</font>,<font color="Olive" title="b2">J</font></span>)</span> ) &amp; ( for <font color="Olive" title="b3">q</font> being   <a href="subset_1.html#M2" title="SUBSET_1:mode.2">Element</a> of  <a href="cqc_lang.html#K4" title="CQC_LANG:func.4">CQC-WFF</a>  holds   <a href="valuat_1.html#K8" title="VALUAT_1:func.8">Valid</a> <span class="p1">(<span class="default"><font color="Maroon" title="c1">p</font> <a href="cqc_lang.html#K8" title="CQC_LANG:func.8">'&amp;'</a> <font color="Olive" title="b3">q</font></span>)</span>,<font color="Olive" title="b2">J</font> <a href="funct_2.html#R2" title="FUNCT_2:pred.2">=</a> <span class="p1">(<span class="default"><a href="valuat_1.html#K8" title="VALUAT_1:func.8">Valid</a> <font color="Maroon" title="c1">p</font>,<font color="Olive" title="b2">J</font></span>)</span> <a href="margrel1.html#K16" title="MARGREL1:func.16">'&amp;'</a> <span class="p1">(<span class="default"><a href="valuat_1.html#K8" title="VALUAT_1:func.8">Valid</a> <font color="Olive" title="b3">q</font>,<font color="Olive" title="b2">J</font></span>)</span> ) &amp; ( for <font color="Olive" title="b3">x</font> being  <a href="qc_lang1.html#NM3" title="QC_LANG1:NM.3">bound_QC-variable</a> holds   <a href="valuat_1.html#K8" title="VALUAT_1:func.8">Valid</a> <span class="p1">(<span class="default"><a href="cqc_lang.html#K12" title="CQC_LANG:func.12">All</a> <font color="Olive" title="b3">x</font>,<font color="Maroon" title="c1">p</font></span>)</span>,<font color="Olive" title="b2">J</font> <a href="funct_2.html#R2" title="FUNCT_2:pred.2">=</a>  <a href="valuat_1.html#K3" title="VALUAT_1:func.3">FOR_ALL</a> <font color="Olive" title="b3">x</font>,<span class="p1">(<span class="default"><a href="valuat_1.html#K8" title="VALUAT_1:func.8">Valid</a> <font color="Maroon" title="c1">p</font>,<font color="Olive" title="b2">J</font></span>)</span> ) )</span><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> ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> for <font color="Olive" title="b1">J</font> being   <a href="valuat_1.html#M1" title="VALUAT_1:mode.1">interpretation</a> of <font color="Maroon" title="c2">A</font> holds <br/> (  <a href="valuat_1.html#K8" title="VALUAT_1:func.8">Valid</a> <a href="cqc_lang.html#K6" title="CQC_LANG:func.6">VERUM</a> ,<font color="Olive" title="b1">J</font> <a href="funct_2.html#R2" title="FUNCT_2:pred.2">=</a> <span class="p1">(<span class="default"><a href="valuat_1.html#K2" title="VALUAT_1:func.2">Valuations_in</a> <font color="Maroon" title="c2">A</font></span>)</span> <a href="margrel1.html#K1" title="MARGREL1:func.1">--&gt;</a> <a href="margrel1.html#K8" title="MARGREL1:func.8">TRUE</a>  &amp; ( for <font color="Olive" title="b2">k</font> being   <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/> for <font color="Olive" title="b3">ll</font> being  <a href="cqc_lang.html#NM2" title="CQC_LANG:NM.2">CQC-variable_list</a> of <font color="Olive" title="b2">k</font><br/> for <font color="Olive" title="b4">P</font> being  <a href="qc_lang1.html#NM6" title="QC_LANG1:NM.6">QC-pred_symbol</a> of <font color="Olive" title="b2">k</font> holds   <a href="valuat_1.html#K8" title="VALUAT_1:func.8">Valid</a> <span class="p1">(<span class="default"><font color="Olive" title="b4">P</font> <a href="cqc_lang.html#K5" title="CQC_LANG:func.5">!</a> <font color="Olive" title="b3">ll</font></span>)</span>,<font color="Olive" title="b1">J</font> <a href="funct_2.html#R2" title="FUNCT_2:pred.2">=</a> <font color="Olive" title="b3">ll</font> <a href="valuat_1.html#K5" title="VALUAT_1:func.5">'in'</a> <span class="p1">(<span class="default"><font color="Olive" title="b1">J</font> <a href="valuat_1.html#K7" title="VALUAT_1:func.7">.</a> <font color="Olive" title="b4">P</font></span>)</span> ) &amp; ( for <font color="Olive" title="b2">p</font> being   <a href="subset_1.html#M2" title="SUBSET_1:mode.2">Element</a> of  <a href="cqc_lang.html#K4" title="CQC_LANG:func.4">CQC-WFF</a>  holds   <a href="valuat_1.html#K8" title="VALUAT_1:func.8">Valid</a> <span class="p1">(<span class="default"><a href="cqc_lang.html#K7" title="CQC_LANG:func.7">'not'</a> <font color="Olive" title="b2">p</font></span>)</span>,<font color="Olive" title="b1">J</font> <a href="funct_2.html#R2" title="FUNCT_2:pred.2">=</a>  <a href="margrel1.html#K15" title="MARGREL1:func.15">'not'</a> <span class="p1">(<span class="default"><a href="valuat_1.html#K8" title="VALUAT_1:func.8">Valid</a> <font color="Olive" title="b2">p</font>,<font color="Olive" title="b1">J</font></span>)</span> ) &amp; ( for <font color="Olive" title="b2">q</font> being   <a href="subset_1.html#M2" title="SUBSET_1:mode.2">Element</a> of  <a href="cqc_lang.html#K4" title="CQC_LANG:func.4">CQC-WFF</a>  holds   <a href="valuat_1.html#K8" title="VALUAT_1:func.8">Valid</a> <span class="p1">(<span class="default"><font color="Maroon" title="c1">p</font> <a href="cqc_lang.html#K8" title="CQC_LANG:func.8">'&amp;'</a> <font color="Olive" title="b2">q</font></span>)</span>,<font color="Olive" title="b1">J</font> <a href="funct_2.html#R2" title="FUNCT_2:pred.2">=</a> <span class="p1">(<span class="default"><a href="valuat_1.html#K8" title="VALUAT_1:func.8">Valid</a> <font color="Maroon" title="c1">p</font>,<font color="Olive" title="b1">J</font></span>)</span> <a href="margrel1.html#K16" title="MARGREL1:func.16">'&amp;'</a> <span class="p1">(<span class="default"><a href="valuat_1.html#K8" title="VALUAT_1:func.8">Valid</a> <font color="Olive" title="b2">q</font>,<font color="Olive" title="b1">J</font></span>)</span> ) &amp; ( for <font color="Olive" title="b2">x</font> being  <a href="qc_lang1.html#NM3" title="QC_LANG1:NM.3">bound_QC-variable</a> holds   <a href="valuat_1.html#K8" title="VALUAT_1:func.8">Valid</a> <span class="p1">(<span class="default"><a href="cqc_lang.html#K12" title="CQC_LANG:func.12">All</a> <font color="Olive" title="b2">x</font>,<font color="Maroon" title="c1">p</font></span>)</span>,<font color="Olive" title="b1">J</font> <a href="funct_2.html#R2" title="FUNCT_2:pred.2">=</a>  <a href="valuat_1.html#K3" title="VALUAT_1:func.3">FOR_ALL</a> <font color="Olive" title="b2">x</font>,<span class="p1">(<span class="default"><a href="valuat_1.html#K8" title="VALUAT_1:func.8">Valid</a> <font color="Maroon" title="c1">p</font>,<font color="Olive" title="b1">J</font></span>)</span> ) )</span><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>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> (  <a href="valuat_1.html#K8" title="VALUAT_1:func.8">Valid</a> <a href="cqc_lang.html#K6" title="CQC_LANG:func.6">VERUM</a> ,<font color="Maroon" title="c3">J</font> <a href="funct_2.html#R2" title="FUNCT_2:pred.2">=</a> <span class="p1">(<span class="default"><a href="valuat_1.html#K2" title="VALUAT_1:func.2">Valuations_in</a> <font color="Maroon" title="c2">A</font></span>)</span> <a href="margrel1.html#K1" title="MARGREL1:func.1">--&gt;</a> <a href="margrel1.html#K8" title="MARGREL1:func.8">TRUE</a>  &amp; ( for <font color="Olive" title="b1">k</font> being   <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/> for <font color="Olive" title="b2">ll</font> being  <a href="cqc_lang.html#NM2" title="CQC_LANG:NM.2">CQC-variable_list</a> of <font color="Olive" title="b1">k</font><br/> for <font color="Olive" title="b3">P</font> being  <a href="qc_lang1.html#NM6" title="QC_LANG1:NM.6">QC-pred_symbol</a> of <font color="Olive" title="b1">k</font> holds   <a href="valuat_1.html#K8" title="VALUAT_1:func.8">Valid</a> <span class="p1">(<span class="default"><font color="Olive" title="b3">P</font> <a href="cqc_lang.html#K5" title="CQC_LANG:func.5">!</a> <font color="Olive" title="b2">ll</font></span>)</span>,<font color="Maroon" title="c3">J</font> <a href="funct_2.html#R2" title="FUNCT_2:pred.2">=</a> <font color="Olive" title="b2">ll</font> <a href="valuat_1.html#K5" title="VALUAT_1:func.5">'in'</a> <span class="p1">(<span class="default"><font color="Maroon" title="c3">J</font> <a href="valuat_1.html#K7" title="VALUAT_1:func.7">.</a> <font color="Olive" title="b3">P</font></span>)</span> ) &amp; ( for <font color="Olive" title="b1">p</font> being   <a href="subset_1.html#M2" title="SUBSET_1:mode.2">Element</a> of  <a href="cqc_lang.html#K4" title="CQC_LANG:func.4">CQC-WFF</a>  holds   <a href="valuat_1.html#K8" title="VALUAT_1:func.8">Valid</a> <span class="p1">(<span class="default"><a href="cqc_lang.html#K7" title="CQC_LANG:func.7">'not'</a> <font color="Olive" title="b1">p</font></span>)</span>,<font color="Maroon" title="c3">J</font> <a href="funct_2.html#R2" title="FUNCT_2:pred.2">=</a>  <a href="margrel1.html#K15" title="MARGREL1:func.15">'not'</a> <span class="p1">(<span class="default"><a href="valuat_1.html#K8" title="VALUAT_1:func.8">Valid</a> <font color="Olive" title="b1">p</font>,<font color="Maroon" title="c3">J</font></span>)</span> ) &amp; ( for <font color="Olive" title="b1">q</font> being   <a href="subset_1.html#M2" title="SUBSET_1:mode.2">Element</a> of  <a href="cqc_lang.html#K4" title="CQC_LANG:func.4">CQC-WFF</a>  holds   <a href="valuat_1.html#K8" title="VALUAT_1:func.8">Valid</a> <span class="p1">(<span class="default"><font color="Maroon" title="c1">p</font> <a href="cqc_lang.html#K8" title="CQC_LANG:func.8">'&amp;'</a> <font color="Olive" title="b1">q</font></span>)</span>,<font color="Maroon" title="c3">J</font> <a href="funct_2.html#R2" title="FUNCT_2:pred.2">=</a> <span class="p1">(<span class="default"><a href="valuat_1.html#K8" title="VALUAT_1:func.8">Valid</a> <font color="Maroon" title="c1">p</font>,<font color="Maroon" title="c3">J</font></span>)</span> <a href="margrel1.html#K16" title="MARGREL1:func.16">'&amp;'</a> <span class="p1">(<span class="default"><a href="valuat_1.html#K8" title="VALUAT_1:func.8">Valid</a> <font color="Olive" title="b1">q</font>,<font color="Maroon" title="c3">J</font></span>)</span> ) &amp; ( for <font color="Olive" title="b1">x</font> being  <a href="qc_lang1.html#NM3" title="QC_LANG1:NM.3">bound_QC-variable</a> holds   <a href="valuat_1.html#K8" title="VALUAT_1:func.8">Valid</a> <span class="p1">(<span class="default"><a href="cqc_lang.html#K12" title="CQC_LANG:func.12">All</a> <font color="Olive" title="b1">x</font>,<font color="Maroon" title="c1">p</font></span>)</span>,<font color="Maroon" title="c3">J</font> <a href="funct_2.html#R2" title="FUNCT_2:pred.2">=</a>  <a href="valuat_1.html#K3" title="VALUAT_1:func.3">FOR_ALL</a> <font color="Olive" title="b1">x</font>,<span class="p1">(<span class="default"><a href="valuat_1.html#K8" title="VALUAT_1:func.8">Valid</a> <font color="Maroon" title="c1">p</font>,<font color="Maroon" title="c3">J</font></span>)</span> ) )</span><br/>





<b>set </b><font color="Maroon" title="c4">D</font> =  <a href="fraenkel.html#K1" title="FRAENKEL:func.1">Funcs</a> <span class="p1">(<span class="default"><a href="valuat_1.html#K2" title="VALUAT_1:func.2">Valuations_in</a> <font color="Maroon" title="c2">A</font></span>)</span>,<a href="margrel1.html#K6" title="MARGREL1:func.6">BOOLEAN</a> ;<br/>
<b>set </b><font color="Maroon" title="c5">V</font> = <span class="p1">(<span class="default"><a href="valuat_1.html#K2" title="VALUAT_1:func.2">Valuations_in</a> <font color="Maroon" title="c2">A</font></span>)</span> <a href="margrel1.html#K1" title="MARGREL1:func.1">--&gt;</a> <a href="margrel1.html#K8" title="MARGREL1:func.8">TRUE</a> ;<br/>
<b>deffunc </b><font color="Maroon">H<sub>1</sub></font>(   <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> ,  <a href="qc_lang1.html#NM6" title="QC_LANG1:NM.6">QC-pred_symbol</a> of $1,  <a href="cqc_lang.html#NM2" title="CQC_LANG:NM.2">CQC-variable_list</a> of $1) <b>-&gt; </b>   <a href="fraenkel.html#M2" title="FRAENKEL:mode.2">Element</a> of  <a href="fraenkel.html#K1" title="FRAENKEL:func.1">Funcs</a> <span class="p1">(<span class="default"><a href="valuat_1.html#K2" title="VALUAT_1:func.2">Valuations_in</a> <font color="Maroon" title="c2">A</font></span>)</span>,<a href="margrel1.html#K6" title="MARGREL1:func.6">BOOLEAN</a>  = $3 <a href="valuat_1.html#K5" title="VALUAT_1:func.5">'in'</a> <span class="p1">(<span class="default"><font color="Maroon" title="c3">J</font> <a href="valuat_1.html#K7" title="VALUAT_1:func.7">.</a> $2</span>)</span>;<br/>
<b>deffunc </b><font color="Maroon">H<sub>2</sub></font>(   <a href="fraenkel.html#M2" title="FRAENKEL:mode.2">Element</a> of  <a href="fraenkel.html#K1" title="FRAENKEL:func.1">Funcs</a> <span class="p1">(<span class="default"><a href="valuat_1.html#K2" title="VALUAT_1:func.2">Valuations_in</a> <font color="Maroon" title="c2">A</font></span>)</span>,<a href="margrel1.html#K6" title="MARGREL1:func.6">BOOLEAN</a> ) <b>-&gt; </b>   <a href="fraenkel.html#M2" title="FRAENKEL:mode.2">Element</a> of  <a href="fraenkel.html#K1" title="FRAENKEL:func.1">Funcs</a> <span class="p1">(<span class="default"><a href="valuat_1.html#K2" title="VALUAT_1:func.2">Valuations_in</a> <font color="Maroon" title="c2">A</font></span>)</span>,<a href="margrel1.html#K6" title="MARGREL1:func.6">BOOLEAN</a>  =  <a href="margrel1.html#K15" title="MARGREL1:func.15">'not'</a> $1;<br/>
<b>deffunc </b><font color="Maroon">H<sub>3</sub></font>(   <a href="fraenkel.html#M2" title="FRAENKEL:mode.2">Element</a> of  <a href="fraenkel.html#K1" title="FRAENKEL:func.1">Funcs</a> <span class="p1">(<span class="default"><a href="valuat_1.html#K2" title="VALUAT_1:func.2">Valuations_in</a> <font color="Maroon" title="c2">A</font></span>)</span>,<a href="margrel1.html#K6" title="MARGREL1:func.6">BOOLEAN</a> ,   <a href="fraenkel.html#M2" title="FRAENKEL:mode.2">Element</a> of  <a href="fraenkel.html#K1" title="FRAENKEL:func.1">Funcs</a> <span class="p1">(<span class="default"><a href="valuat_1.html#K2" title="VALUAT_1:func.2">Valuations_in</a> <font color="Maroon" title="c2">A</font></span>)</span>,<a href="margrel1.html#K6" title="MARGREL1:func.6">BOOLEAN</a> ) <b>-&gt; </b>   <a href="fraenkel.html#M2" title="FRAENKEL:mode.2">Element</a> of  <a href="fraenkel.html#K1" title="FRAENKEL:func.1">Funcs</a> <span class="p1">(<span class="default"><a href="valuat_1.html#K2" title="VALUAT_1:func.2">Valuations_in</a> <font color="Maroon" title="c2">A</font></span>)</span>,<a href="margrel1.html#K6" title="MARGREL1:func.6">BOOLEAN</a>  = $1 <a href="margrel1.html#K16" title="MARGREL1:func.16">'&amp;'</a> $2;<br/>
<b>deffunc </b><font color="Maroon">H<sub>4</sub></font>(  <a href="qc_lang1.html#NM3" title="QC_LANG1:NM.3">bound_QC-variable</a>,   <a href="fraenkel.html#M2" title="FRAENKEL:mode.2">Element</a> of  <a href="fraenkel.html#K1" title="FRAENKEL:func.1">Funcs</a> <span class="p1">(<span class="default"><a href="valuat_1.html#K2" title="VALUAT_1:func.2">Valuations_in</a> <font color="Maroon" title="c2">A</font></span>)</span>,<a href="margrel1.html#K6" title="MARGREL1:func.6">BOOLEAN</a> ) <b>-&gt; </b>   <a href="fraenkel.html#M2" title="FRAENKEL:mode.2">Element</a> of  <a href="fraenkel.html#K1" title="FRAENKEL:func.1">Funcs</a> <span class="p1">(<span class="default"><a href="valuat_1.html#K2" title="VALUAT_1:func.2">Valuations_in</a> <font color="Maroon" title="c2">A</font></span>)</span>,<a href="margrel1.html#K6" title="MARGREL1:func.6">BOOLEAN</a>  =  <a href="valuat_1.html#K3" title="VALUAT_1:func.3">FOR_ALL</a> $1,$2;<br/>
<b>deffunc </b><font color="Maroon">H<sub>5</sub></font>(   <a href="subset_1.html#M2" title="SUBSET_1:mode.2">Element</a> of  <a href="cqc_lang.html#K4" title="CQC_LANG:func.4">CQC-WFF</a> ) <b>-&gt; </b>   <a href="fraenkel.html#M2" title="FRAENKEL:mode.2">Element</a> of  <a href="fraenkel.html#K1" title="FRAENKEL:func.1">Funcs</a> <span class="p1">(<span class="default"><a href="valuat_1.html#K2" title="VALUAT_1:func.2">Valuations_in</a> <font color="Maroon" title="c2">A</font></span>)</span>,<a href="margrel1.html#K6" title="MARGREL1:func.6">BOOLEAN</a>  =  <a href="valuat_1.html#K8" title="VALUAT_1:func.8">Valid</a> $1,<font color="Maroon" title="c3">J</font>;<br/>
<a NAME="E1:15"/><i><font color="Green" title="E9">A1</font></i>: 
for <font color="Olive" title="b1">p</font> being   <a href="subset_1.html#M2" title="SUBSET_1:mode.2">Element</a> of  <a href="cqc_lang.html#K4" title="CQC_LANG:func.4">CQC-WFF</a> <br/> for <font color="Olive" title="b2">d</font> being   <a href="fraenkel.html#M2" title="FRAENKEL:mode.2">Element</a> of  <a href="fraenkel.html#K1" title="FRAENKEL:func.1">Funcs</a> <span class="p1">(<span class="default"><a href="valuat_1.html#K2" title="VALUAT_1:func.2">Valuations_in</a> <font color="Maroon" title="c2">A</font></span>)</span>,<a href="margrel1.html#K6" title="MARGREL1:func.6">BOOLEAN</a>  holds <br/> ( <font color="Olive" title="b2">d</font> <a href="funct_2.html#R2" title="FUNCT_2:pred.2">=</a> <font color="Maroon">H<sub>5</sub></font>(<font color="Olive" title="b1">p</font>) iff  ex <font color="Olive" title="b3">F</font> being  <a href="funct_2.html#NM1" title="FUNCT_2:NM.1">Function</a> of  <a href="cqc_lang.html#K4" title="CQC_LANG:func.4">CQC-WFF</a> , <a href="fraenkel.html#K1" title="FRAENKEL:func.1">Funcs</a> <span class="p1">(<span class="default"><a href="valuat_1.html#K2" title="VALUAT_1:func.2">Valuations_in</a> <font color="Maroon" title="c2">A</font></span>)</span>,<a href="margrel1.html#K6" title="MARGREL1:func.6">BOOLEAN</a>  st <br/>( <font color="Olive" title="b2">d</font> <a href="funct_2.html#R2" title="FUNCT_2:pred.2">=</a> <font color="Olive" title="b3">F</font> <a href="valuat_1.html#K6" title="VALUAT_1:func.6">.</a> <font color="Olive" title="b1">p</font> &amp; <font color="Olive" title="b3">F</font> <a href="valuat_1.html#K6" title="VALUAT_1:func.6">.</a> <a href="cqc_lang.html#K6" title="CQC_LANG:func.6">VERUM</a>  <a href="funct_2.html#R2" title="FUNCT_2:pred.2">=</a> <span class="p1">(<span class="default"><a href="valuat_1.html#K2" title="VALUAT_1:func.2">Valuations_in</a> <font color="Maroon" title="c2">A</font></span>)</span> <a href="margrel1.html#K1" title="MARGREL1:func.1">--&gt;</a> <a href="margrel1.html#K8" title="MARGREL1:func.8">TRUE</a>  &amp; ( for <font color="Olive" title="b4">p</font>, <font color="Olive" title="b5">q</font> being   <a href="subset_1.html#M2" title="SUBSET_1:mode.2">Element</a> of  <a href="cqc_lang.html#K4" title="CQC_LANG:func.4">CQC-WFF</a> <br/> for <font color="Olive" title="b6">x</font> being  <a href="qc_lang1.html#NM3" title="QC_LANG1:NM.3">bound_QC-variable</a><br/> for <font color="Olive" title="b7">k</font> being   <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/> for <font color="Olive" title="b8">ll</font> being  <a href="cqc_lang.html#NM2" title="CQC_LANG:NM.2">CQC-variable_list</a> of <font color="Olive" title="b7">k</font><br/> for <font color="Olive" title="b9">P</font> being  <a href="qc_lang1.html#NM6" title="QC_LANG1:NM.6">QC-pred_symbol</a> of <font color="Olive" title="b7">k</font> holds <br/> ( <font color="Olive" title="b3">F</font> <a href="valuat_1.html#K6" title="VALUAT_1:func.6">.</a> <span class="p1">(<span class="default"><font color="Olive" title="b9">P</font> <a href="cqc_lang.html#K5" title="CQC_LANG:func.5">!</a> <font color="Olive" title="b8">ll</font></span>)</span> <a href="funct_2.html#R2" title="FUNCT_2:pred.2">=</a> <font color="Maroon">H<sub>1</sub></font>(<font color="Olive" title="b7">k</font>,<font color="Olive" title="b9">P</font>,<font color="Olive" title="b8">ll</font>) &amp; <font color="Olive" title="b3">F</font> <a href="valuat_1.html#K6" title="VALUAT_1:func.6">.</a> <span class="p1">(<span class="default"><a href="cqc_lang.html#K7" title="CQC_LANG:func.7">'not'</a> <font color="Olive" title="b4">p</font></span>)</span> <a href="funct_2.html#R2" title="FUNCT_2:pred.2">=</a> <font color="Maroon">H<sub>2</sub></font>(<font color="Olive" title="b3">F</font> <a href="valuat_1.html#K6" title="VALUAT_1:func.6">.</a> <font color="Olive" title="b4">p</font>) &amp; <font color="Olive" title="b3">F</font> <a href="valuat_1.html#K6" title="VALUAT_1:func.6">.</a> <span class="p1">(<span class="default"><font color="Olive" title="b4">p</font> <a href="cqc_lang.html#K8" title="CQC_LANG:func.8">'&amp;'</a> <font color="Olive" title="b5">q</font></span>)</span> <a href="funct_2.html#R2" title="FUNCT_2:pred.2">=</a> <font color="Maroon">H<sub>3</sub></font>(<font color="Olive" title="b3">F</font> <a href="valuat_1.html#K6" title="VALUAT_1:func.6">.</a> <font color="Olive" title="b4">p</font>,<font color="Olive" title="b3">F</font> <a href="valuat_1.html#K6" title="VALUAT_1:func.6">.</a> <font color="Olive" title="b5">q</font>) &amp; <font color="Olive" title="b3">F</font> <a href="valuat_1.html#K6" title="VALUAT_1:func.6">.</a> <span class="p1">(<span class="default"><a href="cqc_lang.html#K12" title="CQC_LANG:func.12">All</a> <font color="Olive" title="b6">x</font>,<font color="Olive" title="b4">p</font></span>)</span> <a href="funct_2.html#R2" title="FUNCT_2:pred.2">=</a> <font color="Maroon">H<sub>4</sub></font>(<font color="Olive" title="b6">x</font>,<font color="Olive" title="b3">F</font> <a href="valuat_1.html#K6" title="VALUAT_1:func.6">.</a> <font color="Olive" title="b4">p</font>) ) ) ) )
 
<b>by </b><i><a class="ref" href="valuat_1.html#D11" target="_self" title="VALUAT_1:def.11">Def11</a></i>;<br/>
<b>thus </b><a NAME="E2:15"/>
<font color="Maroon">H<sub>5</sub></font>( <a href="cqc_lang.html#K6" title="CQC_LANG:func.6">VERUM</a> ) <a href="funct_2.html#R2" title="FUNCT_2:pred.2">=</a> <span class="p1">(<span class="default"><a href="valuat_1.html#K2" title="VALUAT_1:func.2">Valuations_in</a> <font color="Maroon" title="c2">A</font></span>)</span> <a href="margrel1.html#K1" title="MARGREL1:func.1">--&gt;</a> <a href="margrel1.html#K8" title="MARGREL1:func.8">TRUE</a> 
 <b>from </b><i><a class="ref" href="cqc_lang.html#S5" title="CQC_LANG:sch.5">CQC_LANG:sch 5</a>(<a class="txt" href="#E1:15"><i><font color="Green" title="E9">A1</font></i></a>);</i> <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> ( ( for <font color="Olive" title="b1">k</font> being   <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/> for <font color="Olive" title="b2">ll</font> being  <a href="cqc_lang.html#NM2" title="CQC_LANG:NM.2">CQC-variable_list</a> of <font color="Olive" title="b1">k</font><br/> for <font color="Olive" title="b3">P</font> being  <a href="qc_lang1.html#NM6" title="QC_LANG1:NM.6">QC-pred_symbol</a> of <font color="Olive" title="b1">k</font> holds   <a href="valuat_1.html#K8" title="VALUAT_1:func.8">Valid</a> <span class="p1">(<span class="default"><font color="Olive" title="b3">P</font> <a href="cqc_lang.html#K5" title="CQC_LANG:func.5">!</a> <font color="Olive" title="b2">ll</font></span>)</span>,<font color="Maroon" title="c3">J</font> <a href="funct_2.html#R2" title="FUNCT_2:pred.2">=</a> <font color="Olive" title="b2">ll</font> <a href="valuat_1.html#K5" title="VALUAT_1:func.5">'in'</a> <span class="p1">(<span class="default"><font color="Maroon" title="c3">J</font> <a href="valuat_1.html#K7" title="VALUAT_1:func.7">.</a> <font color="Olive" title="b3">P</font></span>)</span> ) &amp; ( for <font color="Olive" title="b1">p</font> being   <a href="subset_1.html#M2" title="SUBSET_1:mode.2">Element</a> of  <a href="cqc_lang.html#K4" title="CQC_LANG:func.4">CQC-WFF</a>  holds   <a href="valuat_1.html#K8" title="VALUAT_1:func.8">Valid</a> <span class="p1">(<span class="default"><a href="cqc_lang.html#K7" title="CQC_LANG:func.7">'not'</a> <font color="Olive" title="b1">p</font></span>)</span>,<font color="Maroon" title="c3">J</font> <a href="funct_2.html#R2" title="FUNCT_2:pred.2">=</a>  <a href="margrel1.html#K15" title="MARGREL1:func.15">'not'</a> <span class="p1">(<span class="default"><a href="valuat_1.html#K8" title="VALUAT_1:func.8">Valid</a> <font color="Olive" title="b1">p</font>,<font color="Maroon" title="c3">J</font></span>)</span> ) &amp; ( for <font color="Olive" title="b1">q</font> being   <a href="subset_1.html#M2" title="SUBSET_1:mode.2">Element</a> of  <a href="cqc_lang.html#K4" title="CQC_LANG:func.4">CQC-WFF</a>  holds   <a href="valuat_1.html#K8" title="VALUAT_1:func.8">Valid</a> <span class="p1">(<span class="default"><font color="Maroon" title="c1">p</font> <a href="cqc_lang.html#K8" title="CQC_LANG:func.8">'&amp;'</a> <font color="Olive" title="b1">q</font></span>)</span>,<font color="Maroon" title="c3">J</font> <a href="funct_2.html#R2" title="FUNCT_2:pred.2">=</a> <span class="p1">(<span class="default"><a href="valuat_1.html#K8" title="VALUAT_1:func.8">Valid</a> <font color="Maroon" title="c1">p</font>,<font color="Maroon" title="c3">J</font></span>)</span> <a href="margrel1.html#K16" title="MARGREL1:func.16">'&amp;'</a> <span class="p1">(<span class="default"><a href="valuat_1.html#K8" title="VALUAT_1:func.8">Valid</a> <font color="Olive" title="b1">q</font>,<font color="Maroon" title="c3">J</font></span>)</span> ) &amp; ( for <font color="Olive" title="b1">x</font> being  <a href="qc_lang1.html#NM3" title="QC_LANG1:NM.3">bound_QC-variable</a> holds   <a href="valuat_1.html#K8" title="VALUAT_1:func.8">Valid</a> <span class="p1">(<span class="default"><a href="cqc_lang.html#K12" title="CQC_LANG:func.12">All</a> <font color="Olive" title="b1">x</font>,<font color="Maroon" title="c1">p</font></span>)</span>,<font color="Maroon" title="c3">J</font> <a href="funct_2.html#R2" title="FUNCT_2:pred.2">=</a>  <a href="valuat_1.html#K3" title="VALUAT_1:func.3">FOR_ALL</a> <font color="Olive" title="b1">x</font>,<span class="p1">(<span class="default"><a href="valuat_1.html#K8" title="VALUAT_1:func.8">Valid</a> <font color="Maroon" title="c1">p</font>,<font color="Maroon" title="c3">J</font></span>)</span> ) )</span><br/>

<div><b>hereby </b> <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> ( ( for <font color="Olive" title="b1">p</font> being   <a href="subset_1.html#M2" title="SUBSET_1:mode.2">Element</a> of  <a href="cqc_lang.html#K4" title="CQC_LANG:func.4">CQC-WFF</a>  holds   <a href="valuat_1.html#K8" title="VALUAT_1:func.8">Valid</a> <span class="p1">(<span class="default"><a href="cqc_lang.html#K7" title="CQC_LANG:func.7">'not'</a> <font color="Olive" title="b1">p</font></span>)</span>,<font color="Maroon" title="c3">J</font> <a href="funct_2.html#R2" title="FUNCT_2:pred.2">=</a>  <a href="margrel1.html#K15" title="MARGREL1:func.15">'not'</a> <span class="p1">(<span class="default"><a href="valuat_1.html#K8" title="VALUAT_1:func.8">Valid</a> <font color="Olive" title="b1">p</font>,<font color="Maroon" title="c3">J</font></span>)</span> ) &amp; ( for <font color="Olive" title="b1">q</font> being   <a href="subset_1.html#M2" title="SUBSET_1:mode.2">Element</a> of  <a href="cqc_lang.html#K4" title="CQC_LANG:func.4">CQC-WFF</a>  holds   <a href="valuat_1.html#K8" title="VALUAT_1:func.8">Valid</a> <span class="p1">(<span class="default"><font color="Maroon" title="c1">p</font> <a href="cqc_lang.html#K8" title="CQC_LANG:func.8">'&amp;'</a> <font color="Olive" title="b1">q</font></span>)</span>,<font color="Maroon" title="c3">J</font> <a href="funct_2.html#R2" title="FUNCT_2:pred.2">=</a> <span class="p1">(<span class="default"><a href="valuat_1.html#K8" title="VALUAT_1:func.8">Valid</a> <font color="Maroon" title="c1">p</font>,<font color="Maroon" title="c3">J</font></span>)</span> <a href="margrel1.html#K16" title="MARGREL1:func.16">'&amp;'</a> <span class="p1">(<span class="default"><a href="valuat_1.html#K8" title="VALUAT_1:func.8">Valid</a> <font color="Olive" title="b1">q</font>,<font color="Maroon" title="c3">J</font></span>)</span> ) &amp; ( for <font color="Olive" title="b1">x</font> being  <a href="qc_lang1.html#NM3" title="QC_LANG1:NM.3">bound_QC-variable</a> holds   <a href="valuat_1.html#K8" title="VALUAT_1:func.8">Valid</a> <span class="p1">(<span class="default"><a href="cqc_lang.html#K12" title="CQC_LANG:func.12">All</a> <font color="Olive" title="b1">x</font>,<font color="Maroon" title="c1">p</font></span>)</span>,<font color="Maroon" title="c3">J</font> <a href="funct_2.html#R2" title="FUNCT_2:pred.2">=</a>  <a href="valuat_1.html#K3" title="VALUAT_1:func.3">FOR_ALL</a> <font color="Olive" title="b1">x</font>,<span class="p1">(<span class="default"><a href="valuat_1.html#K8" title="VALUAT_1:func.8">Valid</a> <font color="Maroon" title="c1">p</font>,<font color="Maroon" title="c3">J</font></span>)</span> ) )</span>
<div class="add"><b>let </b><font color="Maroon" title="c6">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> ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> for <font color="Olive" title="b1">ll</font> being  <a href="cqc_lang.html#NM2" title="CQC_LANG:NM.2">CQC-variable_list</a> of <font color="Maroon" title="c6">k</font><br/> for <font color="Olive" title="b2">P</font> being  <a href="qc_lang1.html#NM6" title="QC_LANG1:NM.6">QC-pred_symbol</a> of <font color="Maroon" title="c6">k</font> holds  <font color="Maroon">H<sub>5</sub></font>(<font color="Olive" title="b2">P</font> <a href="cqc_lang.html#K5" title="CQC_LANG:func.5">!</a> <font color="Olive" title="b1">ll</font>) <a href="funct_2.html#R2" title="FUNCT_2:pred.2">=</a> <font color="Maroon">H<sub>1</sub></font>(<font color="Maroon" title="c6">k</font>,<font color="Olive" title="b2">P</font>,<font color="Olive" title="b1">ll</font>)</span><br/><b>let </b><font color="Maroon" title="c7">ll</font> be   <a href="cqc_lang.html#NM2" title="CQC_LANG:NM.2">CQC-variable_list</a> of <font color="Maroon" title="c6">k</font>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> for <font color="Olive" title="b1">P</font> being  <a href="qc_lang1.html#NM6" title="QC_LANG1:NM.6">QC-pred_symbol</a> of <font color="Maroon" title="c6">k</font> holds  <font color="Maroon">H<sub>5</sub></font>(<font color="Olive" title="b1">P</font> <a href="cqc_lang.html#K5" title="CQC_LANG:func.5">!</a> <font color="Maroon" title="c7">ll</font>) <a href="funct_2.html#R2" title="FUNCT_2:pred.2">=</a> <font color="Maroon">H<sub>1</sub></font>(<font color="Maroon" title="c6">k</font>,<font color="Olive" title="b1">P</font>,<font color="Maroon" title="c7">ll</font>)</span><br/><b>let </b><font color="Maroon" title="c8">P</font> be   <a href="qc_lang1.html#NM6" title="QC_LANG1:NM.6">QC-pred_symbol</a> of <font color="Maroon" title="c6">k</font>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> <font color="Maroon">H<sub>5</sub></font>(<font color="Maroon" title="c8">P</font> <a href="cqc_lang.html#K5" title="CQC_LANG:func.5">!</a> <font color="Maroon" title="c7">ll</font>) <a href="funct_2.html#R2" title="FUNCT_2:pred.2">=</a> <font color="Maroon">H<sub>1</sub></font>(<font color="Maroon" title="c6">k</font>,<font color="Maroon" title="c8">P</font>,<font color="Maroon" title="c7">ll</font>)</span><br/><b>thus </b><a NAME="E1:15_1"/>
<font color="Maroon">H<sub>5</sub></font>(<font color="Maroon" title="c8">P</font> <a href="cqc_lang.html#K5" title="CQC_LANG:func.5">!</a> <font color="Maroon" title="c7">ll</font>) <a href="funct_2.html#R2" title="FUNCT_2:pred.2">=</a> <font color="Maroon">H<sub>1</sub></font>(<font color="Maroon" title="c6">k</font>,<font color="Maroon" title="c8">P</font>,<font color="Maroon" title="c7">ll</font>)
 <b>from </b><i><a class="ref" href="cqc_lang.html#S6" title="CQC_LANG:sch.6">CQC_LANG:sch 6</a>(<a class="txt" href="#E1:15"><i><font color="Green" title="E9">A1</font></i></a>);</i> <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> verum</span><br/></div>
<b>end;</b></div>

<div><b>hereby </b> <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> ( ( for <font color="Olive" title="b1">q</font> being   <a href="subset_1.html#M2" title="SUBSET_1:mode.2">Element</a> of  <a href="cqc_lang.html#K4" title="CQC_LANG:func.4">CQC-WFF</a>  holds   <a href="valuat_1.html#K8" title="VALUAT_1:func.8">Valid</a> <span class="p1">(<span class="default"><font color="Maroon" title="c1">p</font> <a href="cqc_lang.html#K8" title="CQC_LANG:func.8">'&amp;'</a> <font color="Olive" title="b1">q</font></span>)</span>,<font color="Maroon" title="c3">J</font> <a href="funct_2.html#R2" title="FUNCT_2:pred.2">=</a> <span class="p1">(<span class="default"><a href="valuat_1.html#K8" title="VALUAT_1:func.8">Valid</a> <font color="Maroon" title="c1">p</font>,<font color="Maroon" title="c3">J</font></span>)</span> <a href="margrel1.html#K16" title="MARGREL1:func.16">'&amp;'</a> <span class="p1">(<span class="default"><a href="valuat_1.html#K8" title="VALUAT_1:func.8">Valid</a> <font color="Olive" title="b1">q</font>,<font color="Maroon" title="c3">J</font></span>)</span> ) &amp; ( for <font color="Olive" title="b1">x</font> being  <a href="qc_lang1.html#NM3" title="QC_LANG1:NM.3">bound_QC-variable</a> holds   <a href="valuat_1.html#K8" title="VALUAT_1:func.8">Valid</a> <span class="p1">(<span class="default"><a href="cqc_lang.html#K12" title="CQC_LANG:func.12">All</a> <font color="Olive" title="b1">x</font>,<font color="Maroon" title="c1">p</font></span>)</span>,<font color="Maroon" title="c3">J</font> <a href="funct_2.html#R2" title="FUNCT_2:pred.2">=</a>  <a href="valuat_1.html#K3" title="VALUAT_1:func.3">FOR_ALL</a> <font color="Olive" title="b1">x</font>,<span class="p1">(<span class="default"><a href="valuat_1.html#K8" title="VALUAT_1:func.8">Valid</a> <font color="Maroon" title="c1">p</font>,<font color="Maroon" title="c3">J</font></span>)</span> ) )</span>
<div class="add"><b>let </b><font color="Maroon" title="c6">p</font> be    <a href="subset_1.html#M2" title="SUBSET_1:mode.2">Element</a> of  <a href="cqc_lang.html#K4" title="CQC_LANG:func.4">CQC-WFF</a> ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> <font color="Maroon">H<sub>5</sub></font>( <a href="cqc_lang.html#K7" title="CQC_LANG:func.7">'not'</a> <font color="Maroon" title="c6">p</font>) <a href="funct_2.html#R2" title="FUNCT_2:pred.2">=</a> <font color="Maroon">H<sub>2</sub></font>(<font color="Maroon">H<sub>5</sub></font>(<font color="Maroon" title="c6">p</font>))</span><br/><b>thus </b><a NAME="E1:15_2"/>
<font color="Maroon">H<sub>5</sub></font>( <a href="cqc_lang.html#K7" title="CQC_LANG:func.7">'not'</a> <font color="Maroon" title="c6">p</font>) <a href="funct_2.html#R2" title="FUNCT_2:pred.2">=</a> <font color="Maroon">H<sub>2</sub></font>(<font color="Maroon">H<sub>5</sub></font>(<font color="Maroon" title="c6">p</font>))
 <b>from </b><i><a class="ref" href="cqc_lang.html#S7" title="CQC_LANG:sch.7">CQC_LANG:sch 7</a>(<a class="txt" href="#E1:15"><i><font color="Green" title="E9">A1</font></i></a>);</i> <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> verum</span><br/></div>
<b>end;</b></div>

<div><b>hereby </b> <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> for <font color="Olive" title="b1">x</font> being  <a href="qc_lang1.html#NM3" title="QC_LANG1:NM.3">bound_QC-variable</a> holds   <a href="valuat_1.html#K8" title="VALUAT_1:func.8">Valid</a> <span class="p1">(<span class="default"><a href="cqc_lang.html#K12" title="CQC_LANG:func.12">All</a> <font color="Olive" title="b1">x</font>,<font color="Maroon" title="c1">p</font></span>)</span>,<font color="Maroon" title="c3">J</font> <a href="funct_2.html#R2" title="FUNCT_2:pred.2">=</a>  <a href="valuat_1.html#K3" title="VALUAT_1:func.3">FOR_ALL</a> <font color="Olive" title="b1">x</font>,<span class="p1">(<span class="default"><a href="valuat_1.html#K8" title="VALUAT_1:func.8">Valid</a> <font color="Maroon" title="c1">p</font>,<font color="Maroon" title="c3">J</font></span>)</span></span>
<div class="add"><b>let </b><font color="Maroon" title="c6">q</font> be    <a href="subset_1.html#M2" title="SUBSET_1:mode.2">Element</a> of  <a href="cqc_lang.html#K4" title="CQC_LANG:func.4">CQC-WFF</a> ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> <font color="Maroon">H<sub>5</sub></font>(<font color="Maroon" title="c1">p</font> <a href="cqc_lang.html#K8" title="CQC_LANG:func.8">'&amp;'</a> <font color="Maroon" title="c6">q</font>) <a href="funct_2.html#R2" title="FUNCT_2:pred.2">=</a> <font color="Maroon">H<sub>3</sub></font>(<font color="Maroon">H<sub>5</sub></font>(<font color="Maroon" title="c1">p</font>),<font color="Maroon">H<sub>5</sub></font>(<font color="Maroon" title="c6">q</font>))</span><br/><b>thus </b><a NAME="E1:15_3"/>
<font color="Maroon">H<sub>5</sub></font>(<font color="Maroon" title="c1">p</font> <a href="cqc_lang.html#K8" title="CQC_LANG:func.8">'&amp;'</a> <font color="Maroon" title="c6">q</font>) <a href="funct_2.html#R2" title="FUNCT_2:pred.2">=</a> <font color="Maroon">H<sub>3</sub></font>(<font color="Maroon">H<sub>5</sub></font>(<font color="Maroon" title="c1">p</font>),<font color="Maroon">H<sub>5</sub></font>(<font color="Maroon" title="c6">q</font>))
 <b>from </b><i><a class="ref" href="cqc_lang.html#S8" title="CQC_LANG:sch.8">CQC_LANG:sch 8</a>(<a class="txt" href="#E1:15"><i><font color="Green" title="E9">A1</font></i></a>);</i> <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> verum</span><br/></div>
<b>end;</b></div>

<b>let </b><font color="Maroon" title="c6">x</font> be   <a href="qc_lang1.html#NM3" title="QC_LANG1:NM.3">bound_QC-variable</a>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide">  <a href="valuat_1.html#K8" title="VALUAT_1:func.8">Valid</a> <span class="p1">(<span class="default"><a href="cqc_lang.html#K12" title="CQC_LANG:func.12">All</a> <font color="Maroon" title="c6">x</font>,<font color="Maroon" title="c1">p</font></span>)</span>,<font color="Maroon" title="c3">J</font> <a href="funct_2.html#R2" title="FUNCT_2:pred.2">=</a>  <a href="valuat_1.html#K3" title="VALUAT_1:func.3">FOR_ALL</a> <font color="Maroon" title="c6">x</font>,<span class="p1">(<span class="default"><a href="valuat_1.html#K8" title="VALUAT_1:func.8">Valid</a> <font color="Maroon" title="c1">p</font>,<font color="Maroon" title="c3">J</font></span>)</span></span><br/>

<b>thus </b><a NAME="E6:15"/>
<font color="Maroon">H<sub>5</sub></font>( <a href="cqc_lang.html#K12" title="CQC_LANG:func.12">All</a> <font color="Maroon" title="c6">x</font>,<font color="Maroon" title="c1">p</font>) <a href="funct_2.html#R2" title="FUNCT_2:pred.2">=</a> <font color="Maroon">H<sub>4</sub></font>(<font color="Maroon" title="c6">x</font>,<font color="Maroon">H<sub>5</sub></font>(<font color="Maroon" title="c1">p</font>))
 <b>from </b><i><a class="ref" href="cqc_lang.html#S9" title="CQC_LANG:sch.9">CQC_LANG:sch 9</a>(<a class="txt" href="#E1:15"><i><font color="Green" title="E9">A1</font></i></a>);</i> <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> verum</span><br/>


</div>
