<?xml version="1.0"?>
<div class="add">

<span class="kw">let </span><font color="Maroon" title="c1">p</font>, <font color="Maroon" title="c2">q</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> being   <a href="qc_lang1.html#NM3" title="QC_LANG1:NM.3">bound_QC-variable</a> holds  <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="Olive" title="b1">x</font>,<font color="Maroon" title="c1">p</font>)</span>)</span> <a href="cqc_lang.html#K8" title="CQC_LANG:func.8">=&gt;</a> <font color="Maroon" title="c2">q</font></span>)</span> <a href="cqc_lang.html#K8" title="CQC_LANG:func.8">=&gt;</a> <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>,<span class="p2">(<span class="default"><font color="Maroon" title="c1">p</font> <a href="cqc_lang.html#K8" title="CQC_LANG:func.8">=&gt;</a> <font color="Maroon" title="c2">q</font></span>)</span>)</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="c3">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="firebrick">::  thesis: </font></span></a><span class="hide"> <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="c3">x</font>,<font color="Maroon" title="c1">p</font>)</span>)</span> <a href="cqc_lang.html#K8" title="CQC_LANG:func.8">=&gt;</a> <font color="Maroon" title="c2">q</font></span>)</span> <a href="cqc_lang.html#K8" title="CQC_LANG:func.8">=&gt;</a> <span class="p1">(<span class="default"><a href="cqc_lang.html#K12" title="CQC_LANG:func.12">Ex</a> (<font color="Maroon" title="c3">x</font>,<span class="p2">(<span class="default"><font color="Maroon" title="c1">p</font> <a href="cqc_lang.html#K8" title="CQC_LANG:func.8">=&gt;</a> <font color="Maroon" title="c2">q</font></span>)</span>)</span>)</span> is  <a href="cqc_the1.html#V2" title="CQC_THE1:attr.2">valid</a> </span><br/>





<a NAME="E1:94"/>
<span class="p1">(<span class="default"><a href="cqc_lang.html#K11" title="CQC_LANG:func.11">All</a> (<font color="Maroon" title="c3">x</font>,<span class="p2">(<span class="default"><font color="Maroon" title="c1">p</font> <a href="cqc_lang.html#K7" title="CQC_LANG:func.7">'&amp;'</a> <span class="p3">(<span class="default"><a href="cqc_lang.html#K6" title="CQC_LANG:func.6">'not'</a> <font color="Maroon" title="c2">q</font></span>)</span></span>)</span>)</span>)</span> <a href="cqc_lang.html#K8" title="CQC_LANG:func.8">=&gt;</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="c3">x</font>,<font color="Maroon" title="c1">p</font>)</span>)</span> <a href="cqc_lang.html#K7" title="CQC_LANG:func.7">'&amp;'</a> <span class="p2">(<span class="default"><a href="cqc_lang.html#K6" title="CQC_LANG:func.6">'not'</a> <font color="Maroon" title="c2">q</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="cqc_the2.html#T65" target="_self" title="CQC_THE2:th.65">Th69</a></span>;<br/>
<a NAME="E2:94"/><span class="kw">then </span>
<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"><span class="p3">(<span class="default"><a href="cqc_lang.html#K11" title="CQC_LANG:func.11">All</a> (<font color="Maroon" title="c3">x</font>,<font color="Maroon" title="c1">p</font>)</span>)</span> <a href="cqc_lang.html#K7" title="CQC_LANG:func.7">'&amp;'</a> <span class="p3">(<span class="default"><a href="cqc_lang.html#K6" title="CQC_LANG:func.6">'not'</a> <font color="Maroon" title="c2">q</font></span>)</span></span>)</span></span>)</span> <a href="cqc_lang.html#K8" title="CQC_LANG:func.8">=&gt;</a> <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="c3">x</font>,<span class="p3">(<span class="default"><font color="Maroon" title="c1">p</font> <a href="cqc_lang.html#K7" title="CQC_LANG:func.7">'&amp;'</a> <span class="p4">(<span class="default"><a href="cqc_lang.html#K6" title="CQC_LANG:func.6">'not'</a> <font color="Maroon" title="c2">q</font></span>)</span></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#T52" title="LUKASI_1:th.52">LUKASI_1:52</a></span>;<br/>
<a NAME="E3:94"/><span class="kw">then </span><span class="lab"><font color="Green" title="E65">A1</font></span>: 
<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="c3">x</font>,<font color="Maroon" title="c1">p</font>)</span>)</span> <a href="cqc_lang.html#K8" title="CQC_LANG:func.8">=&gt;</a> <font color="Maroon" title="c2">q</font></span>)</span> <a href="cqc_lang.html#K8" title="CQC_LANG:func.8">=&gt;</a> <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="c3">x</font>,<span class="p3">(<span class="default"><font color="Maroon" title="c1">p</font> <a href="cqc_lang.html#K7" title="CQC_LANG:func.7">'&amp;'</a> <span class="p4">(<span class="default"><a href="cqc_lang.html#K6" title="CQC_LANG:func.6">'not'</a> <font color="Maroon" title="c2">q</font></span>)</span></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="qc_lang2.html#D2" title="QC_LANG2:def.2">QC_LANG2:def 2</a></span>;<br/>
<a NAME="E4:94"/>
(  <a href="cqc_lang.html#K11" title="CQC_LANG:func.11">All</a> (<font color="Maroon" title="c3">x</font>,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="cqc_lang.html#K6" title="CQC_LANG:func.6">'not'</a> <span class="p3">(<span class="default"><a href="cqc_lang.html#K6" title="CQC_LANG:func.6">'not'</a> <span class="p4">(<span class="default"><font color="Maroon" title="c1">p</font> <a href="cqc_lang.html#K7" title="CQC_LANG:func.7">'&amp;'</a> <span class="p5">(<span class="default"><a href="cqc_lang.html#K6" title="CQC_LANG:func.6">'not'</a> <font color="Maroon" title="c2">q</font></span>)</span></span>)</span></span>)</span></span>)</span> <a href="cqc_lang.html#K8" title="CQC_LANG:func.8">=&gt;</a> <span class="p2">(<span class="default"><font color="Maroon" title="c1">p</font> <a href="cqc_lang.html#K7" title="CQC_LANG:func.7">'&amp;'</a> <span class="p3">(<span class="default"><a href="cqc_lang.html#K6" title="CQC_LANG:func.6">'not'</a> <font color="Maroon" title="c2">q</font></span>)</span></span>)</span></span>)</span>) is  <a href="cqc_the1.html#V2" title="CQC_THE1:attr.2">valid</a>  &amp; <span class="p1">(<span class="default"><a href="cqc_lang.html#K11" title="CQC_LANG:func.11">All</a> (<font color="Maroon" title="c3">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> <span class="p4">(<span class="default"><a href="cqc_lang.html#K6" title="CQC_LANG:func.6">'not'</a> <span class="p5">(<span class="default"><font color="Maroon" title="c1">p</font> <a href="cqc_lang.html#K7" title="CQC_LANG:func.7">'&amp;'</a> <span class="p0">(<span class="default"><a href="cqc_lang.html#K6" title="CQC_LANG:func.6">'not'</a> <font color="Maroon" title="c2">q</font></span>)</span></span>)</span></span>)</span></span>)</span> <a href="cqc_lang.html#K8" title="CQC_LANG:func.8">=&gt;</a> <span class="p3">(<span class="default"><font color="Maroon" title="c1">p</font> <a href="cqc_lang.html#K7" title="CQC_LANG:func.7">'&amp;'</a> <span class="p4">(<span class="default"><a href="cqc_lang.html#K6" title="CQC_LANG:func.6">'not'</a> <font color="Maroon" title="c2">q</font></span>)</span></span>)</span></span>)</span>)</span>)</span> <a href="cqc_lang.html#K8" title="CQC_LANG:func.8">=&gt;</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="c3">x</font>,<span class="p3">(<span class="default"><a href="cqc_lang.html#K6" title="CQC_LANG:func.6">'not'</a> <span class="p4">(<span class="default"><a href="cqc_lang.html#K6" title="CQC_LANG:func.6">'not'</a> <span class="p5">(<span class="default"><font color="Maroon" title="c1">p</font> <a href="cqc_lang.html#K7" title="CQC_LANG:func.7">'&amp;'</a> <span class="p0">(<span class="default"><a href="cqc_lang.html#K6" title="CQC_LANG:func.6">'not'</a> <font color="Maroon" title="c2">q</font></span>)</span></span>)</span></span>)</span></span>)</span>)</span>)</span> <a href="cqc_lang.html#K8" title="CQC_LANG:func.8">=&gt;</a> <span class="p2">(<span class="default"><a href="cqc_lang.html#K11" title="CQC_LANG:func.11">All</a> (<font color="Maroon" title="c3">x</font>,<span class="p3">(<span class="default"><font color="Maroon" title="c1">p</font> <a href="cqc_lang.html#K7" title="CQC_LANG:func.7">'&amp;'</a> <span class="p4">(<span class="default"><a href="cqc_lang.html#K6" title="CQC_LANG:func.6">'not'</a> <font color="Maroon" title="c2">q</font></span>)</span></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="cqc_the2.html#T23" target="_self" title="CQC_THE2:th.23">Th26</a>, <a class="ref" href="cqc_the2.html#T30" target="_self" title="CQC_THE2:th.30">Th34</a></span>;<br/>
<a NAME="E5:94"/><span class="kw">then </span>
<span class="p1">(<span class="default"><a href="cqc_lang.html#K11" title="CQC_LANG:func.11">All</a> (<font color="Maroon" title="c3">x</font>,<span class="p2">(<span class="default"><a href="cqc_lang.html#K6" title="CQC_LANG:func.6">'not'</a> <span class="p3">(<span class="default"><a href="cqc_lang.html#K6" title="CQC_LANG:func.6">'not'</a> <span class="p4">(<span class="default"><font color="Maroon" title="c1">p</font> <a href="cqc_lang.html#K7" title="CQC_LANG:func.7">'&amp;'</a> <span class="p5">(<span class="default"><a href="cqc_lang.html#K6" title="CQC_LANG:func.6">'not'</a> <font color="Maroon" title="c2">q</font></span>)</span></span>)</span></span>)</span></span>)</span>)</span>)</span> <a href="cqc_lang.html#K8" title="CQC_LANG:func.8">=&gt;</a> <span class="p1">(<span class="default"><a href="cqc_lang.html#K11" title="CQC_LANG:func.11">All</a> (<font color="Maroon" title="c3">x</font>,<span class="p2">(<span class="default"><font color="Maroon" title="c1">p</font> <a href="cqc_lang.html#K7" title="CQC_LANG:func.7">'&amp;'</a> <span class="p3">(<span class="default"><a href="cqc_lang.html#K6" title="CQC_LANG:func.6">'not'</a> <font color="Maroon" title="c2">q</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="cqc_the1.html#T65" title="CQC_THE1:th.65">CQC_THE1:65</a></span>;<br/>
<a NAME="E6:94"/><span class="kw">then </span>
<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="c3">x</font>,<span class="p3">(<span class="default"><font color="Maroon" title="c1">p</font> <a href="cqc_lang.html#K7" title="CQC_LANG:func.7">'&amp;'</a> <span class="p4">(<span class="default"><a href="cqc_lang.html#K6" title="CQC_LANG:func.6">'not'</a> <font color="Maroon" title="c2">q</font></span>)</span></span>)</span>)</span>)</span></span>)</span> <a href="cqc_lang.html#K8" title="CQC_LANG:func.8">=&gt;</a> <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="c3">x</font>,<span class="p3">(<span class="default"><a href="cqc_lang.html#K6" title="CQC_LANG:func.6">'not'</a> <span class="p4">(<span class="default"><a href="cqc_lang.html#K6" title="CQC_LANG:func.6">'not'</a> <span class="p5">(<span class="default"><font color="Maroon" title="c1">p</font> <a href="cqc_lang.html#K7" title="CQC_LANG:func.7">'&amp;'</a> <span class="p0">(<span class="default"><a href="cqc_lang.html#K6" title="CQC_LANG:func.6">'not'</a> <font color="Maroon" title="c2">q</font></span>)</span></span>)</span></span>)</span></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#T52" title="LUKASI_1:th.52">LUKASI_1:52</a></span>;<br/>
<a NAME="E7:94"/><span class="kw">then </span>
<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="c3">x</font>,<font color="Maroon" title="c1">p</font>)</span>)</span> <a href="cqc_lang.html#K8" title="CQC_LANG:func.8">=&gt;</a> <font color="Maroon" title="c2">q</font></span>)</span> <a href="cqc_lang.html#K8" title="CQC_LANG:func.8">=&gt;</a> <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="c3">x</font>,<span class="p3">(<span class="default"><a href="cqc_lang.html#K6" title="CQC_LANG:func.6">'not'</a> <span class="p4">(<span class="default"><a href="cqc_lang.html#K6" title="CQC_LANG:func.6">'not'</a> <span class="p5">(<span class="default"><font color="Maroon" title="c1">p</font> <a href="cqc_lang.html#K7" title="CQC_LANG:func.7">'&amp;'</a> <span class="p0">(<span class="default"><a href="cqc_lang.html#K6" title="CQC_LANG:func.6">'not'</a> <font color="Maroon" title="c2">q</font></span>)</span></span>)</span></span>)</span></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="txt" href="#E3:94"><span class="lab"><font color="Green" title="E65">A1</font></span></a>, <a class="ref" href="lukasi_1.html#T42" title="LUKASI_1:th.42">LUKASI_1:42</a></span>;<br/>
<a NAME="E8:94"/><span class="kw">then </span>
<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="c3">x</font>,<font color="Maroon" title="c1">p</font>)</span>)</span> <a href="cqc_lang.html#K8" title="CQC_LANG:func.8">=&gt;</a> <font color="Maroon" title="c2">q</font></span>)</span> <a href="cqc_lang.html#K8" title="CQC_LANG:func.8">=&gt;</a> <span class="p1">(<span class="default"><a href="cqc_lang.html#K12" title="CQC_LANG:func.12">Ex</a> (<font color="Maroon" title="c3">x</font>,<span class="p2">(<span class="default"><a href="cqc_lang.html#K6" title="CQC_LANG:func.6">'not'</a> <span class="p3">(<span class="default"><font color="Maroon" title="c1">p</font> <a href="cqc_lang.html#K7" title="CQC_LANG:func.7">'&amp;'</a> <span class="p4">(<span class="default"><a href="cqc_lang.html#K6" title="CQC_LANG:func.6">'not'</a> <font color="Maroon" title="c2">q</font></span>)</span></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="qc_lang2.html#D5" title="QC_LANG2:def.5">QC_LANG2:def 5</a></span>;<br/>
<span class="kw">hence </span><a NAME="E9:94"/>
<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="c3">x</font>,<font color="Maroon" title="c1">p</font>)</span>)</span> <a href="cqc_lang.html#K8" title="CQC_LANG:func.8">=&gt;</a> <font color="Maroon" title="c2">q</font></span>)</span> <a href="cqc_lang.html#K8" title="CQC_LANG:func.8">=&gt;</a> <span class="p1">(<span class="default"><a href="cqc_lang.html#K12" title="CQC_LANG:func.12">Ex</a> (<font color="Maroon" title="c3">x</font>,<span class="p2">(<span class="default"><font color="Maroon" title="c1">p</font> <a href="cqc_lang.html#K8" title="CQC_LANG:func.8">=&gt;</a> <font color="Maroon" title="c2">q</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="qc_lang2.html#D2" title="QC_LANG2:def.2">QC_LANG2:def 2</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/>


</div>
