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<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">h</font> be   <a href="qc_lang1.html#NM8">QC-formula</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>assume </b><a NAME="E1:41"/><i><font color="Green">E37</font></i>: 
( <font color="Maroon">p</font> <a href="hidden.html#R1">=</a> <font color="Maroon">h</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">h</font> <a href="cqc_lang.html#K17">.</a> <font color="Maroon">y</font> &amp; 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">h</font> )
 ;<br/>

<a NAME="E2:41"/><i><font color="Green">E56</font></i>: 
<span class="p1">(<span class="default"><a href="cqc_lang.html#K15">All</a> <font color="Maroon">x</font>,<font color="Maroon">p</font></span>)</span> <a href="cqc_lang.html#K12">=&gt;</a> <font color="Maroon">p</font> is <a href="cqc_the1.html#V2">valid</a>
 
<b>by </b><i><a class="ref" href="cqc_the1.html#T105">CQC_THE1:105</a></i>;<br/>
<i><font color="Green">E69</font></i>: <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="cqc_lang.html#K15">All</a> <font color="Maroon">x</font>,<font color="Maroon">p</font></span>)</span> <a href="qc_lang2.html#K2">=&gt;</a> <font color="Maroon">h</font></span>)</span> <a href="cqc_lang.html#K17">.</a> <font color="Maroon">x</font> = 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="cqc_lang.html#K15">All</a> <font color="Maroon">x</font>,<font color="Maroon">p</font></span>)</span> <a href="cqc_lang.html#K17">.</a> <font color="Maroon">x</font></span>)</span> <a href="qc_lang2.html#K2">=&gt;</a> <font color="Maroon">p</font>
<b>by </b><i>, </i>
<br/>.= 
<span class="p1">(<span class="default"><a href="cqc_lang.html#K15">All</a> <font color="Maroon">x</font>,<font color="Maroon">p</font></span>)</span> <a href="cqc_lang.html#K12">=&gt;</a> <font color="Maroon">p</font>
<b>by </b><i><a class="ref" href="cqc_lang.html#T40">CQC_LANG:40</a></i>
;<br/>
<i><font color="Green">E70</font></i>: <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="cqc_lang.html#K15">All</a> <font color="Maroon">x</font>,<font color="Maroon">p</font></span>)</span> <a href="qc_lang2.html#K2">=&gt;</a> <font color="Maroon">h</font></span>)</span> <a href="cqc_lang.html#K17">.</a> <font color="Maroon">y</font> = 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="cqc_lang.html#K15">All</a> <font color="Maroon">x</font>,<font color="Maroon">p</font></span>)</span> <a href="cqc_lang.html#K17">.</a> <font color="Maroon">y</font></span>)</span> <a href="qc_lang2.html#K2">=&gt;</a> <font color="Maroon">q</font>
<b>by </b><i>, </i>
<br/>.= 
<span class="p1">(<span class="default"><a href="cqc_lang.html#K15">All</a> <font color="Maroon">x</font>,<font color="Maroon">p</font></span>)</span> <a href="cqc_lang.html#K12">=&gt;</a> <font color="Maroon">q</font>
<b>by </b><i><a class="ref" href="cqc_lang.html#T40">CQC_LANG:40</a></i>
;<br/>
<a NAME="E5:41"/>
not <font color="Maroon">x</font> <a href="hidden.html#R2">in</a>  <a href="qc_lang1.html#K23">still_not-bound_in</a> <span class="p1">(<span class="default"><a href="cqc_lang.html#K15">All</a> <font color="Maroon">x</font>,<font color="Maroon">p</font></span>)</span>
 
<b>by </b><i/>;<br/>
<a NAME="E6:41"/><b>then </b>
not <font color="Maroon">x</font> <a href="hidden.html#R2">in</a>  <a href="qc_lang1.html#K23">still_not-bound_in</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="cqc_lang.html#K15">All</a> <font color="Maroon">x</font>,<font color="Maroon">p</font></span>)</span> <a href="qc_lang2.html#K2">=&gt;</a> <font color="Maroon">h</font></span>)</span>
 
<b>by </b><i>, </i>;<br/>
<b>hence </b><a NAME="E7:41"/>
<span class="p1">(<span class="default"><a href="cqc_lang.html#K15">All</a> <font color="Maroon">x</font>,<font color="Maroon">p</font></span>)</span> <a href="cqc_lang.html#K12">=&gt;</a> <font color="Maroon">q</font> is <a href="cqc_the1.html#V2">valid</a>
 <b>by </b><i><a class="ref" href="cqc_the2.html#T1" target="_self">Th1</a>, <a class="txt" href="cqc_the2.html#E1:41"><i><font color="Green">E37</font></i></a>, <a class="ref" href="cqc_the2.html#T2" target="_self">Th2</a>, <a class="ref" href="cqc_the1.html#T107">CQC_THE1:107</a></i>;<br/>


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