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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> ;<br/><b>let </b><font color="Maroon" title="c2">x</font>, <font color="Maroon" title="c3">y</font> be   <a href="qc_lang1.html#NM3" title="QC_LANG1:NM.3">bound_QC-variable</a>;<br/>





<a NAME="E1:73"/>
<font color="Maroon" title="c1">p</font> <a href="cqc_lang.html#K9" title="CQC_LANG:func.9">=&gt;</a> <span class="p1">(<span class="default"><a href="cqc_lang.html#K13" title="CQC_LANG:func.13">Ex</a> <font color="Maroon" title="c2">x</font>,<font color="Maroon" title="c1">p</font></span>)</span> is <a href="cqc_the1.html#V2" title="CQC_THE1:attr.2">valid</a>
 
<b>by </b><i><a class="ref" href="cqc_the2.html#T18" target="_self" title="CQC_THE2:th.18">Th18</a></i>;<br/>
<a NAME="E2:73"/><b>then </b><i><font color="Green" title="E51">A1</font></i>: 
 <a href="cqc_lang.html#K12" title="CQC_LANG:func.12">All</a> <font color="Maroon" title="c3">y</font>,<span class="p1">(<span class="default"><font color="Maroon" title="c1">p</font> <a href="cqc_lang.html#K9" title="CQC_LANG:func.9">=&gt;</a> <span class="p2">(<span class="default"><a href="cqc_lang.html#K13" title="CQC_LANG:func.13">Ex</a> <font color="Maroon" title="c2">x</font>,<font color="Maroon" title="c1">p</font></span>)</span></span>)</span> is <a href="cqc_the1.html#V2" title="CQC_THE1:attr.2">valid</a>
 
<b>by </b><i><a class="ref" href="cqc_the2.html#T26" target="_self" title="CQC_THE2:th.26">Th26</a></i>;<br/>
<a NAME="E3:73"/>
<span class="p1">(<span class="default"><a href="cqc_lang.html#K12" title="CQC_LANG:func.12">All</a> <font color="Maroon" title="c3">y</font>,<span class="p2">(<span class="default"><font color="Maroon" title="c1">p</font> <a href="cqc_lang.html#K9" title="CQC_LANG:func.9">=&gt;</a> <span class="p3">(<span class="default"><a href="cqc_lang.html#K13" title="CQC_LANG:func.13">Ex</a> <font color="Maroon" title="c2">x</font>,<font color="Maroon" title="c1">p</font></span>)</span></span>)</span></span>)</span> <a href="cqc_lang.html#K9" title="CQC_LANG:func.9">=&gt;</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="cqc_lang.html#K13" title="CQC_LANG:func.13">Ex</a> <font color="Maroon" title="c3">y</font>,<font color="Maroon" title="c1">p</font></span>)</span> <a href="cqc_lang.html#K9" title="CQC_LANG:func.9">=&gt;</a> <span class="p2">(<span class="default"><a href="cqc_lang.html#K13" title="CQC_LANG:func.13">Ex</a> <font color="Maroon" title="c3">y</font>,<span class="p3">(<span class="default"><a href="cqc_lang.html#K13" title="CQC_LANG:func.13">Ex</a> <font color="Maroon" title="c2">x</font>,<font color="Maroon" title="c1">p</font></span>)</span></span>)</span></span>)</span> is <a href="cqc_the1.html#V2" title="CQC_THE1:attr.2">valid</a>
 
<b>by </b><i><a class="ref" href="cqc_the2.html#T38" target="_self" title="CQC_THE2:th.38">Th38</a></i>;<br/>
<a NAME="E4:73"/><b>then </b><i><font color="Green" title="E52">A2</font></i>: 
<span class="p1">(<span class="default"><a href="cqc_lang.html#K13" title="CQC_LANG:func.13">Ex</a> <font color="Maroon" title="c3">y</font>,<font color="Maroon" title="c1">p</font></span>)</span> <a href="cqc_lang.html#K9" title="CQC_LANG:func.9">=&gt;</a> <span class="p1">(<span class="default"><a href="cqc_lang.html#K13" title="CQC_LANG:func.13">Ex</a> <font color="Maroon" title="c3">y</font>,<span class="p2">(<span class="default"><a href="cqc_lang.html#K13" title="CQC_LANG:func.13">Ex</a> <font color="Maroon" title="c2">x</font>,<font color="Maroon" title="c1">p</font></span>)</span></span>)</span> is <a href="cqc_the1.html#V2" title="CQC_THE1:attr.2">valid</a>
 
<b>by </b><i><a class="txt" href="cqc_the2.html#E2:73"><i><font color="Green" title="E51">A1</font></i></a>, <a class="ref" href="cqc_the1.html#T104" title="CQC_THE1:th.104">CQC_THE1:104</a></i>;<br/>
<a NAME="E5:73"/>
not <font color="Maroon" title="c2">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="qc_lang1.html#K23" title="QC_LANG1:func.23">still_not-bound_in</a> <span class="p1">(<span class="default"><a href="cqc_lang.html#K13" title="CQC_LANG:func.13">Ex</a> <font color="Maroon" title="c2">x</font>,<font color="Maroon" title="c1">p</font></span>)</span>
 
<b>by </b><i><a class="ref" href="cqc_the2.html#T6" target="_self" title="CQC_THE2:th.6">Th6</a></i>;<br/>
<a NAME="E6:73"/><b>then </b>
not <font color="Maroon" title="c2">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="qc_lang1.html#K23" title="QC_LANG1:func.23">still_not-bound_in</a> <span class="p1">(<span class="default"><a href="cqc_lang.html#K13" title="CQC_LANG:func.13">Ex</a> <font color="Maroon" title="c3">y</font>,<span class="p2">(<span class="default"><a href="cqc_lang.html#K13" title="CQC_LANG:func.13">Ex</a> <font color="Maroon" title="c2">x</font>,<font color="Maroon" title="c1">p</font></span>)</span></span>)</span>
 
<b>by </b><i><a class="ref" href="cqc_the2.html#T6" target="_self" title="CQC_THE2:th.6">Th6</a></i>;<br/>
<b>hence </b><a NAME="E7:73"/>
<span class="p1">(<span class="default"><a href="cqc_lang.html#K13" title="CQC_LANG:func.13">Ex</a> <font color="Maroon" title="c2">x</font>,<span class="p2">(<span class="default"><a href="cqc_lang.html#K13" title="CQC_LANG:func.13">Ex</a> <font color="Maroon" title="c3">y</font>,<font color="Maroon" title="c1">p</font></span>)</span></span>)</span> <a href="cqc_lang.html#K9" title="CQC_LANG:func.9">=&gt;</a> <span class="p1">(<span class="default"><a href="cqc_lang.html#K13" title="CQC_LANG:func.13">Ex</a> <font color="Maroon" title="c3">y</font>,<span class="p2">(<span class="default"><a href="cqc_lang.html#K13" title="CQC_LANG:func.13">Ex</a> <font color="Maroon" title="c2">x</font>,<font color="Maroon" title="c1">p</font></span>)</span></span>)</span> is <a href="cqc_the1.html#V2" title="CQC_THE1:attr.2">valid</a>
 <b>by </b><i><a class="txt" href="cqc_the2.html#E4:73"><i><font color="Green" title="E52">A2</font></i></a>, <a class="ref" href="cqc_the2.html#T22" target="_self" title="CQC_THE2:th.22">Th22</a></i>;<br/>

<a NAME="E8:73"/><b>then </b>
<span class="p1">(<span class="default"><a href="qc_lang2.html#K7" title="QC_LANG2:func.7">Ex</a> <font color="Maroon" title="c2">x</font>,<font color="Maroon" title="c3">y</font>,<font color="Maroon" title="c1">p</font></span>)</span> <a href="qc_lang2.html#K2" title="QC_LANG2:func.2">=&gt;</a> <span class="p1">(<span class="default"><a href="cqc_lang.html#K13" title="CQC_LANG:func.13">Ex</a> <font color="Maroon" title="c3">y</font>,<span class="p2">(<span class="default"><a href="cqc_lang.html#K13" title="CQC_LANG:func.13">Ex</a> <font color="Maroon" title="c2">x</font>,<font color="Maroon" title="c1">p</font></span>)</span></span>)</span> is <a href="cqc_the1.html#V2" title="CQC_THE1:attr.2">valid</a>
 
<b>by </b><i><a class="ref" href="qc_lang2.html#T20" title="QC_LANG2:th.20">QC_LANG2:20</a></i>;<br/>
<b>hence </b><a NAME="E9:73"/>
<span class="p1">(<span class="default"><a href="qc_lang2.html#K7" title="QC_LANG2:func.7">Ex</a> <font color="Maroon" title="c2">x</font>,<font color="Maroon" title="c3">y</font>,<font color="Maroon" title="c1">p</font></span>)</span> <a href="qc_lang2.html#K2" title="QC_LANG2:func.2">=&gt;</a> <span class="p1">(<span class="default"><a href="qc_lang2.html#K7" title="QC_LANG2:func.7">Ex</a> <font color="Maroon" title="c3">y</font>,<font color="Maroon" title="c2">x</font>,<font color="Maroon" title="c1">p</font></span>)</span> is <a href="cqc_the1.html#V2" title="CQC_THE1:attr.2">valid</a>
 <b>by </b><i><a class="ref" href="qc_lang2.html#T20" title="QC_LANG2:th.20">QC_LANG2:20</a></i>;<br/>


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