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<span class="kw">let </span><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:()"><span class="comment"><font color="Red">::  thesis: </font></span></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  <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="Olive" title="b1">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> </span><br/><span class="kw">let </span><font color="Maroon" title="c2">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:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> <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> </span><br/>



<a NAME="E1:34"/>
<span class="p1">(<span class="default"><a href="cqc_lang.html#K12" title="CQC_LANG:func.12">All</a> <font color="Maroon" title="c2">x</font>,<span class="p2">(<span class="default"><a href="cqc_lang.html#K7" title="CQC_LANG:func.7">'not'</a> <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#K7" title="CQC_LANG:func.7">'not'</a> <font color="Maroon" title="c1">p</font></span>)</span> is  <a href="cqc_the1.html#V2" title="CQC_THE1:attr.2">valid</a> 
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="cqc_the1.html#T105" title="CQC_THE1:th.105">CQC_THE1:105</a></span>;<br/>
<a NAME="E2:34"/><span class="kw">then </span>
<span class="p1">(<span class="default"><a href="cqc_lang.html#K7" title="CQC_LANG:func.7">'not'</a> <span class="p2">(<span class="default"><a href="cqc_lang.html#K7" title="CQC_LANG:func.7">'not'</a> <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#K7" title="CQC_LANG:func.7">'not'</a> <span class="p2">(<span class="default"><a href="cqc_lang.html#K12" title="CQC_LANG:func.12">All</a> <font color="Maroon" title="c2">x</font>,<span class="p3">(<span class="default"><a href="cqc_lang.html#K7" title="CQC_LANG:func.7">'not'</a> <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> 
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="lukasi_1.html#T63" title="LUKASI_1:th.63">LUKASI_1:63</a></span>;<br/>
<a NAME="E3:34"/><span class="kw">then </span><span class="lab"><font color="Green" title="E28">A1</font></span>: 
<span class="p1">(<span class="default"><a href="cqc_lang.html#K7" title="CQC_LANG:func.7">'not'</a> <span class="p2">(<span class="default"><a href="cqc_lang.html#K7" title="CQC_LANG:func.7">'not'</a> <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="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> 
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="qc_lang2.html#D5" title="QC_LANG2:def.5">QC_LANG2:def 5</a></span>;<br/>
<a NAME="E4:34"/>
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="cqc_lang.html#K7" title="CQC_LANG:func.7">'not'</a> <span class="p3">(<span class="default"><a href="cqc_lang.html#K7" title="CQC_LANG:func.7">'not'</a> <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="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> <a href="cqc_lang.html#K9" title="CQC_LANG:func.9">=&gt;</a> <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> 
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="lukasi_1.html#T67" title="LUKASI_1:th.67">LUKASI_1:67</a></span>;<br/>
<span class="kw">hence </span><a NAME="E5:34"/>
<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> 
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E3:34"><span class="lab"><font color="Green" title="E28">A1</font></span></a>, <a class="ref" href="cqc_the1.html#T104" title="CQC_THE1:th.104">CQC_THE1:104</a></span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> verum</span><br/>


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