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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#K3" title="CQC_LANG:func.3">CQC-WFF</a> ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide">  for <font color="Olive" title="b1">x</font>, <font color="Olive" title="b2">y</font> being   <a href="qc_lang1.html#NM3" title="QC_LANG1:NM.3">bound_QC-variable</a>  st <font color="Olive" title="b1">x</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Olive" title="b2">y</font> holds <br/><span class="p1">(<span class="default"><a href="cqc_lang.html#K12" title="CQC_LANG:func.12">Ex</a> (<font color="Olive" title="b1">x</font>,<font color="Maroon" title="c1">p</font>)</span>)</span> <a href="cqc_lang.html#K13" title="CQC_LANG:func.13">.</a> <font color="Olive" title="b2">y</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="qc_lang2.html#K5" title="QC_LANG2:func.5">Ex</a> (<font color="Olive" title="b1">x</font>,<span class="p1">(<span class="default"><font color="Maroon" title="c1">p</font> <a href="cqc_lang.html#K13" title="CQC_LANG:func.13">.</a> <font color="Olive" title="b2">y</font></span>)</span>)</span><br/><span class="kw">let </span><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>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> ( <font color="Maroon" title="c2">x</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c3">y</font> implies <span class="p1">(<span class="default"><a href="cqc_lang.html#K12" title="CQC_LANG:func.12">Ex</a> (<font color="Maroon" title="c2">x</font>,<font color="Maroon" title="c1">p</font>)</span>)</span> <a href="cqc_lang.html#K13" title="CQC_LANG:func.13">.</a> <font color="Maroon" title="c3">y</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="qc_lang2.html#K5" title="QC_LANG2:func.5">Ex</a> (<font color="Maroon" title="c2">x</font>,<span class="p1">(<span class="default"><font color="Maroon" title="c1">p</font> <a href="cqc_lang.html#K13" title="CQC_LANG:func.13">.</a> <font color="Maroon" title="c3">y</font></span>)</span>) )</span><br/>





<span class="kw">assume </span><a NAME="E1:30"/><span class="lab"><font color="Green" title="E27">A1</font></span>: 
<font color="Maroon" title="c2">x</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c3">y</font>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> <span class="p1">(<span class="default"><a href="cqc_lang.html#K12" title="CQC_LANG:func.12">Ex</a> (<font color="Maroon" title="c2">x</font>,<font color="Maroon" title="c1">p</font>)</span>)</span> <a href="cqc_lang.html#K13" title="CQC_LANG:func.13">.</a> <font color="Maroon" title="c3">y</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="qc_lang2.html#K5" title="QC_LANG2:func.5">Ex</a> (<font color="Maroon" title="c2">x</font>,<span class="p1">(<span class="default"><font color="Maroon" title="c1">p</font> <a href="cqc_lang.html#K13" title="CQC_LANG:func.13">.</a> <font color="Maroon" title="c3">y</font></span>)</span>)</span><br/>

<span class="kw">thus </span><span class="p1">(<span class="default"><a href="cqc_lang.html#K12" title="CQC_LANG:func.12">Ex</a> (<font color="Maroon" title="c2">x</font>,<font color="Maroon" title="c1">p</font>)</span>)</span> <a href="cqc_lang.html#K13" title="CQC_LANG:func.13">.</a> <font color="Maroon" title="c3">y</font> = 
<span class="p1">(<span class="default"><a href="cqc_lang.html#K6" title="CQC_LANG:func.6">'not'</a> <span class="p2">(<span class="default"><a href="cqc_lang.html#K11" title="CQC_LANG:func.11">All</a> (<font color="Maroon" title="c2">x</font>,<span class="p3">(<span class="default"><a href="cqc_lang.html#K6" title="CQC_LANG:func.6">'not'</a> <font color="Maroon" title="c1">p</font></span>)</span>)</span>)</span></span>)</span> <a href="cqc_lang.html#K13" title="CQC_LANG:func.13">.</a> <font color="Maroon" title="c3">y</font>
<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 href="qc_lang1.html#K12" title="QC_LANG1:func.12">'not'</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="cqc_lang.html#K11" title="CQC_LANG:func.11">All</a> (<font color="Maroon" title="c2">x</font>,<span class="p3">(<span class="default"><a href="cqc_lang.html#K6" title="CQC_LANG:func.6">'not'</a> <font color="Maroon" title="c1">p</font></span>)</span>)</span>)</span> <a href="cqc_lang.html#K13" title="CQC_LANG:func.13">.</a> <font color="Maroon" title="c3">y</font></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="ref" href="cqc_lang.html#T19" title="CQC_LANG:th.19">CQC_LANG:19</a></span>
<br/>.= 
 <a href="qc_lang1.html#K12" title="QC_LANG1:func.12">'not'</a> <span class="p1">(<span class="default"><a href="qc_lang1.html#K14" title="QC_LANG1:func.14">All</a> (<font color="Maroon" title="c2">x</font>,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="cqc_lang.html#K6" title="CQC_LANG:func.6">'not'</a> <font color="Maroon" title="c1">p</font></span>)</span> <a href="cqc_lang.html#K13" title="CQC_LANG:func.13">.</a> <font color="Maroon" title="c3">y</font></span>)</span>)</span>)</span>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:30"><span class="lab"><font color="Green" title="E27">A1</font></span></a>, <a class="ref" href="cqc_lang.html#T25" title="CQC_LANG:th.25">CQC_LANG:25</a></span>
<br/>.= 
 <a href="qc_lang1.html#K12" title="QC_LANG1:func.12">'not'</a> <span class="p1">(<span class="default"><a href="qc_lang1.html#K14" title="QC_LANG1:func.14">All</a> (<font color="Maroon" title="c2">x</font>,<span class="p2">(<span class="default"><a href="qc_lang1.html#K12" title="QC_LANG1:func.12">'not'</a> <span class="p3">(<span class="default"><font color="Maroon" title="c1">p</font> <a href="cqc_lang.html#K13" title="CQC_LANG:func.13">.</a> <font color="Maroon" title="c3">y</font></span>)</span></span>)</span>)</span>)</span>
<span class="kw">by</span> <span class="lab"><a class="ref" href="cqc_lang.html#T19" title="CQC_LANG:th.19">CQC_LANG:19</a></span>
<br/>.= 
 <a href="qc_lang2.html#K5" title="QC_LANG2:func.5">Ex</a> (<font color="Maroon" title="c2">x</font>,<span class="p1">(<span class="default"><font color="Maroon" title="c1">p</font> <a href="cqc_lang.html#K13" title="CQC_LANG:func.13">.</a> <font color="Maroon" title="c3">y</font></span>)</span>)
<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>
; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> verum</span><br/>


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