<?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#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  <span class="p1">(<span class="default"><a href="cqc_lang.html#K12" title="CQC_LANG:func.12">All</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#K11" title="CQC_LANG:func.11">&lt;=&gt;</a> <font color="Maroon" title="c2">q</font></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#K12" title="CQC_LANG:func.12">All</a> <font color="Olive" title="b1">x</font>,<font color="Maroon" title="c1">p</font></span>)</span> <a href="cqc_lang.html#K11" title="CQC_LANG:func.11">&lt;=&gt;</a> <span class="p2">(<span class="default"><a href="cqc_lang.html#K12" title="CQC_LANG:func.12">All</a> <font color="Olive" title="b1">x</font>,<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="Red">::  thesis: </font></span></a><span class="hide"> <span class="p1">(<span class="default"><a href="cqc_lang.html#K12" title="CQC_LANG:func.12">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#K11" title="CQC_LANG:func.11">&lt;=&gt;</a> <font color="Maroon" title="c2">q</font></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#K12" title="CQC_LANG:func.12">All</a> <font color="Maroon" title="c3">x</font>,<font color="Maroon" title="c1">p</font></span>)</span> <a href="cqc_lang.html#K11" title="CQC_LANG:func.11">&lt;=&gt;</a> <span class="p2">(<span class="default"><a href="cqc_lang.html#K12" title="CQC_LANG:func.12">All</a> <font color="Maroon" title="c3">x</font>,<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="E1:52"/><span class="lab"><font color="Green" title="E38">A1</font></span>: 
<span class="p1">(<span class="default"><a href="cqc_lang.html#K12" title="CQC_LANG:func.12">All</a> <font color="Maroon" title="c3">x</font>,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon" title="c1">p</font> <a href="cqc_lang.html#K9" title="CQC_LANG:func.9">=&gt;</a> <font color="Maroon" title="c2">q</font></span>)</span> <a href="cqc_lang.html#K8" title="CQC_LANG:func.8">'&amp;'</a> <span class="p3">(<span class="default"><font color="Maroon" title="c2">q</font> <a href="cqc_lang.html#K9" title="CQC_LANG:func.9">=&gt;</a> <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"><font color="Maroon" title="c1">p</font> <a href="cqc_lang.html#K9" title="CQC_LANG:func.9">=&gt;</a> <font color="Maroon" title="c2">q</font></span>)</span> <a href="cqc_lang.html#K8" title="CQC_LANG:func.8">'&amp;'</a> <span class="p2">(<span class="default"><font color="Maroon" title="c2">q</font> <a href="cqc_lang.html#K9" title="CQC_LANG:func.9">=&gt;</a> <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="cqc_the1.html#T105" title="CQC_THE1:th.105">CQC_THE1:105</a></span>;<br/>
<a NAME="E2:52"/>
<span class="p1">(<span class="default"><font color="Maroon" title="c1">p</font> <a href="cqc_lang.html#K11" title="CQC_LANG:func.11">&lt;=&gt;</a> <font color="Maroon" title="c2">q</font></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#K11" title="CQC_LANG:func.11">&lt;=&gt;</a> <font color="Maroon" title="c2">q</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="lukasi_1.html#T44" title="LUKASI_1:th.44">LUKASI_1:44</a></span>;<br/>
<a NAME="E3:52"/><span class="kw">then </span>
<span class="p1">(<span class="default"><font color="Maroon" title="c1">p</font> <a href="cqc_lang.html#K11" title="CQC_LANG:func.11">&lt;=&gt;</a> <font color="Maroon" title="c2">q</font></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"><font color="Maroon" title="c1">p</font> <a href="cqc_lang.html#K9" title="CQC_LANG:func.9">=&gt;</a> <font color="Maroon" title="c2">q</font></span>)</span> <a href="cqc_lang.html#K8" title="CQC_LANG:func.8">'&amp;'</a> <span class="p2">(<span class="default"><font color="Maroon" title="c2">q</font> <a href="cqc_lang.html#K9" title="CQC_LANG:func.9">=&gt;</a> <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="qc_lang2.html#D4" title="QC_LANG2:def.4">QC_LANG2:def 4</a></span>;<br/>
<a NAME="E4:52"/><span class="kw">then </span>
 <a href="cqc_lang.html#K12" title="CQC_LANG:func.12">All</a> <font color="Maroon" title="c3">x</font>,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c1">p</font> <a href="cqc_lang.html#K11" title="CQC_LANG:func.11">&lt;=&gt;</a> <font color="Maroon" title="c2">q</font></span>)</span> <a href="cqc_lang.html#K9" title="CQC_LANG:func.9">=&gt;</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon" title="c1">p</font> <a href="cqc_lang.html#K9" title="CQC_LANG:func.9">=&gt;</a> <font color="Maroon" title="c2">q</font></span>)</span> <a href="cqc_lang.html#K8" title="CQC_LANG:func.8">'&amp;'</a> <span class="p3">(<span class="default"><font color="Maroon" title="c2">q</font> <a href="cqc_lang.html#K9" title="CQC_LANG:func.9">=&gt;</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="cqc_the2.html#T26" target="_self" title="CQC_THE2:th.26">Th26</a></span>;<br/>
<a NAME="E5:52"/><span class="kw">then </span><span class="lab"><font color="Green" title="E39">A2</font></span>: 
<span class="p1">(<span class="default"><a href="cqc_lang.html#K12" title="CQC_LANG:func.12">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#K11" title="CQC_LANG:func.11">&lt;=&gt;</a> <font color="Maroon" title="c2">q</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#K12" title="CQC_LANG:func.12">All</a> <font color="Maroon" title="c3">x</font>,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon" title="c1">p</font> <a href="cqc_lang.html#K9" title="CQC_LANG:func.9">=&gt;</a> <font color="Maroon" title="c2">q</font></span>)</span> <a href="cqc_lang.html#K8" title="CQC_LANG:func.8">'&amp;'</a> <span class="p3">(<span class="default"><font color="Maroon" title="c2">q</font> <a href="cqc_lang.html#K9" title="CQC_LANG:func.9">=&gt;</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="cqc_the2.html#T35" target="_self" title="CQC_THE2:th.35">Th35</a></span>;<br/>
<a NAME="E6:52"/>
( <span class="p1">(<span class="default"><a href="cqc_lang.html#K12" title="CQC_LANG:func.12">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#K9" title="CQC_LANG:func.9">=&gt;</a> <font color="Maroon" title="c2">q</font></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#K12" title="CQC_LANG:func.12">All</a> <font color="Maroon" title="c3">x</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#K12" title="CQC_LANG:func.12">All</a> <font color="Maroon" title="c3">x</font>,<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>  &amp; <span class="p1">(<span class="default"><a href="cqc_lang.html#K12" title="CQC_LANG:func.12">All</a> <font color="Maroon" title="c3">x</font>,<span class="p2">(<span class="default"><font color="Maroon" title="c2">q</font> <a href="cqc_lang.html#K9" title="CQC_LANG:func.9">=&gt;</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"><span class="p2">(<span class="default"><a href="cqc_lang.html#K12" title="CQC_LANG:func.12">All</a> <font color="Maroon" title="c3">x</font>,<font color="Maroon" title="c2">q</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#K12" title="CQC_LANG:func.12">All</a> <font color="Maroon" title="c3">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="cqc_the2.html#T34" target="_self" title="CQC_THE2:th.34">Th34</a></span>;<br/>
<a NAME="E7:52"/><span class="kw">then </span>
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="cqc_lang.html#K12" title="CQC_LANG:func.12">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#K9" title="CQC_LANG:func.9">=&gt;</a> <font color="Maroon" title="c2">q</font></span>)</span></span>)</span> <a href="cqc_lang.html#K8" title="CQC_LANG:func.8">'&amp;'</a> <span class="p2">(<span class="default"><a href="cqc_lang.html#K12" title="CQC_LANG:func.12">All</a> <font color="Maroon" title="c3">x</font>,<span class="p3">(<span class="default"><font color="Maroon" title="c2">q</font> <a href="cqc_lang.html#K9" title="CQC_LANG:func.9">=&gt;</a> <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"><span class="p3">(<span class="default"><a href="cqc_lang.html#K12" title="CQC_LANG:func.12">All</a> <font color="Maroon" title="c3">x</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="p3">(<span class="default"><a href="cqc_lang.html#K12" title="CQC_LANG:func.12">All</a> <font color="Maroon" title="c3">x</font>,<font color="Maroon" title="c2">q</font></span>)</span></span>)</span> <a href="cqc_lang.html#K8" title="CQC_LANG:func.8">'&amp;'</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="cqc_lang.html#K12" title="CQC_LANG:func.12">All</a> <font color="Maroon" title="c3">x</font>,<font color="Maroon" title="c2">q</font></span>)</span> <a href="cqc_lang.html#K9" title="CQC_LANG:func.9">=&gt;</a> <span class="p3">(<span class="default"><a href="cqc_lang.html#K12" title="CQC_LANG:func.12">All</a> <font color="Maroon" title="c3">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> 
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="cqc_the2.html#E9"><span class="lab"><font color="Green" title="E9">Lm5</font></span></a></span>;<br/>
<a NAME="E8:52"/><span class="kw">then </span><span class="lab"><font color="Green" title="E40">A3</font></span>: 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="cqc_lang.html#K12" title="CQC_LANG:func.12">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#K9" title="CQC_LANG:func.9">=&gt;</a> <font color="Maroon" title="c2">q</font></span>)</span></span>)</span> <a href="cqc_lang.html#K8" title="CQC_LANG:func.8">'&amp;'</a> <span class="p2">(<span class="default"><a href="cqc_lang.html#K12" title="CQC_LANG:func.12">All</a> <font color="Maroon" title="c3">x</font>,<span class="p3">(<span class="default"><font color="Maroon" title="c2">q</font> <a href="cqc_lang.html#K9" title="CQC_LANG:func.9">=&gt;</a> <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#K12" title="CQC_LANG:func.12">All</a> <font color="Maroon" title="c3">x</font>,<font color="Maroon" title="c1">p</font></span>)</span> <a href="cqc_lang.html#K11" title="CQC_LANG:func.11">&lt;=&gt;</a> <span class="p2">(<span class="default"><a href="cqc_lang.html#K12" title="CQC_LANG:func.12">All</a> <font color="Maroon" title="c3">x</font>,<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#D4" title="QC_LANG2:def.4">QC_LANG2:def 4</a></span>;<br/>
<a NAME="E9:52"/><span class="lab"><font color="Green" title="E41">A4</font></span>: 
not <font color="Maroon" title="c3">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#K12" title="CQC_LANG:func.12">All</a> <font color="Maroon" title="c3">x</font>,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon" title="c1">p</font> <a href="cqc_lang.html#K9" title="CQC_LANG:func.9">=&gt;</a> <font color="Maroon" title="c2">q</font></span>)</span> <a href="cqc_lang.html#K8" title="CQC_LANG:func.8">'&amp;'</a> <span class="p3">(<span class="default"><font color="Maroon" title="c2">q</font> <a href="cqc_lang.html#K9" title="CQC_LANG:func.9">=&gt;</a> <font color="Maroon" title="c1">p</font></span>)</span></span>)</span></span>)</span>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="cqc_the2.html#T5" target="_self" title="CQC_THE2:th.5">Th5</a></span>;<br/>
<a NAME="E10:52"/>
<span class="p1">(<span class="default"><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> <font color="Maroon" title="c2">q</font></span>)</span> <a href="cqc_lang.html#K8" title="CQC_LANG:func.8">'&amp;'</a> <span class="p2">(<span class="default"><font color="Maroon" title="c2">q</font> <a href="cqc_lang.html#K9" title="CQC_LANG:func.9">=&gt;</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"><font color="Maroon" title="c2">q</font> <a href="cqc_lang.html#K9" title="CQC_LANG:func.9">=&gt;</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="txt" href="cqc_the2.html#E5"><span class="lab"><font color="Green" title="E5">Lm1</font></span></a></span>;<br/>
<a NAME="E11:52"/><span class="kw">then </span>
<span class="p1">(<span class="default"><a href="cqc_lang.html#K12" title="CQC_LANG:func.12">All</a> <font color="Maroon" title="c3">x</font>,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon" title="c1">p</font> <a href="cqc_lang.html#K9" title="CQC_LANG:func.9">=&gt;</a> <font color="Maroon" title="c2">q</font></span>)</span> <a href="cqc_lang.html#K8" title="CQC_LANG:func.8">'&amp;'</a> <span class="p3">(<span class="default"><font color="Maroon" title="c2">q</font> <a href="cqc_lang.html#K9" title="CQC_LANG:func.9">=&gt;</a> <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"><font color="Maroon" title="c2">q</font> <a href="cqc_lang.html#K9" title="CQC_LANG:func.9">=&gt;</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="txt" href="#E1:52"><span class="lab"><font color="Green" title="E38">A1</font></span></a>, <a class="ref" href="lukasi_1.html#T43" title="LUKASI_1:th.43">LUKASI_1:43</a></span>;<br/>
<a NAME="E12:52"/><span class="kw">then </span><span class="lab"><font color="Green" title="E42">A5</font></span>: 
<span class="p1">(<span class="default"><a href="cqc_lang.html#K12" title="CQC_LANG:func.12">All</a> <font color="Maroon" title="c3">x</font>,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon" title="c1">p</font> <a href="cqc_lang.html#K9" title="CQC_LANG:func.9">=&gt;</a> <font color="Maroon" title="c2">q</font></span>)</span> <a href="cqc_lang.html#K8" title="CQC_LANG:func.8">'&amp;'</a> <span class="p3">(<span class="default"><font color="Maroon" title="c2">q</font> <a href="cqc_lang.html#K9" title="CQC_LANG:func.9">=&gt;</a> <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"><a href="cqc_lang.html#K12" title="CQC_LANG:func.12">All</a> <font color="Maroon" title="c3">x</font>,<span class="p2">(<span class="default"><font color="Maroon" title="c2">q</font> <a href="cqc_lang.html#K9" title="CQC_LANG:func.9">=&gt;</a> <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="txt" href="#E9:52"><span class="lab"><font color="Green" title="E41">A4</font></span></a>, <a class="ref" href="cqc_the1.html#T106" title="CQC_THE1:th.106">CQC_THE1:106</a></span>;<br/>
<a NAME="E13:52"/>
<span class="p1">(<span class="default"><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> <font color="Maroon" title="c2">q</font></span>)</span> <a href="cqc_lang.html#K8" title="CQC_LANG:func.8">'&amp;'</a> <span class="p2">(<span class="default"><font color="Maroon" title="c2">q</font> <a href="cqc_lang.html#K9" title="CQC_LANG:func.9">=&gt;</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"><font color="Maroon" title="c1">p</font> <a href="cqc_lang.html#K9" title="CQC_LANG:func.9">=&gt;</a> <font color="Maroon" title="c2">q</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="cqc_the2.html#E5"><span class="lab"><font color="Green" title="E5">Lm1</font></span></a></span>;<br/>
<a NAME="E14:52"/><span class="kw">then </span>
<span class="p1">(<span class="default"><a href="cqc_lang.html#K12" title="CQC_LANG:func.12">All</a> <font color="Maroon" title="c3">x</font>,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon" title="c1">p</font> <a href="cqc_lang.html#K9" title="CQC_LANG:func.9">=&gt;</a> <font color="Maroon" title="c2">q</font></span>)</span> <a href="cqc_lang.html#K8" title="CQC_LANG:func.8">'&amp;'</a> <span class="p3">(<span class="default"><font color="Maroon" title="c2">q</font> <a href="cqc_lang.html#K9" title="CQC_LANG:func.9">=&gt;</a> <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"><font color="Maroon" title="c1">p</font> <a href="cqc_lang.html#K9" title="CQC_LANG:func.9">=&gt;</a> <font color="Maroon" title="c2">q</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="#E1:52"><span class="lab"><font color="Green" title="E38">A1</font></span></a>, <a class="ref" href="lukasi_1.html#T43" title="LUKASI_1:th.43">LUKASI_1:43</a></span>;<br/>
<a NAME="E15:52"/><span class="kw">then </span>
<span class="p1">(<span class="default"><a href="cqc_lang.html#K12" title="CQC_LANG:func.12">All</a> <font color="Maroon" title="c3">x</font>,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon" title="c1">p</font> <a href="cqc_lang.html#K9" title="CQC_LANG:func.9">=&gt;</a> <font color="Maroon" title="c2">q</font></span>)</span> <a href="cqc_lang.html#K8" title="CQC_LANG:func.8">'&amp;'</a> <span class="p3">(<span class="default"><font color="Maroon" title="c2">q</font> <a href="cqc_lang.html#K9" title="CQC_LANG:func.9">=&gt;</a> <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"><a href="cqc_lang.html#K12" title="CQC_LANG:func.12">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#K9" title="CQC_LANG:func.9">=&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="txt" href="#E9:52"><span class="lab"><font color="Green" title="E41">A4</font></span></a>, <a class="ref" href="cqc_the1.html#T106" title="CQC_THE1:th.106">CQC_THE1:106</a></span>;<br/>
<a NAME="E16:52"/><span class="kw">then </span>
<span class="p1">(<span class="default"><a href="cqc_lang.html#K12" title="CQC_LANG:func.12">All</a> <font color="Maroon" title="c3">x</font>,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon" title="c1">p</font> <a href="cqc_lang.html#K9" title="CQC_LANG:func.9">=&gt;</a> <font color="Maroon" title="c2">q</font></span>)</span> <a href="cqc_lang.html#K8" title="CQC_LANG:func.8">'&amp;'</a> <span class="p3">(<span class="default"><font color="Maroon" title="c2">q</font> <a href="cqc_lang.html#K9" title="CQC_LANG:func.9">=&gt;</a> <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#K12" title="CQC_LANG:func.12">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#K9" title="CQC_LANG:func.9">=&gt;</a> <font color="Maroon" title="c2">q</font></span>)</span></span>)</span> <a href="cqc_lang.html#K8" title="CQC_LANG:func.8">'&amp;'</a> <span class="p2">(<span class="default"><a href="cqc_lang.html#K12" title="CQC_LANG:func.12">All</a> <font color="Maroon" title="c3">x</font>,<span class="p3">(<span class="default"><font color="Maroon" title="c2">q</font> <a href="cqc_lang.html#K9" title="CQC_LANG:func.9">=&gt;</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="txt" href="#E12:52"><span class="lab"><font color="Green" title="E42">A5</font></span></a>, <a class="txt" href="cqc_the2.html#E7"><span class="lab"><font color="Green" title="E7">Lm3</font></span></a></span>;<br/>
<a NAME="E17:52"/><span class="kw">then </span>
<span class="p1">(<span class="default"><a href="cqc_lang.html#K12" title="CQC_LANG:func.12">All</a> <font color="Maroon" title="c3">x</font>,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon" title="c1">p</font> <a href="cqc_lang.html#K9" title="CQC_LANG:func.9">=&gt;</a> <font color="Maroon" title="c2">q</font></span>)</span> <a href="cqc_lang.html#K8" title="CQC_LANG:func.8">'&amp;'</a> <span class="p3">(<span class="default"><font color="Maroon" title="c2">q</font> <a href="cqc_lang.html#K9" title="CQC_LANG:func.9">=&gt;</a> <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#K12" title="CQC_LANG:func.12">All</a> <font color="Maroon" title="c3">x</font>,<font color="Maroon" title="c1">p</font></span>)</span> <a href="cqc_lang.html#K11" title="CQC_LANG:func.11">&lt;=&gt;</a> <span class="p2">(<span class="default"><a href="cqc_lang.html#K12" title="CQC_LANG:func.12">All</a> <font color="Maroon" title="c3">x</font>,<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="txt" href="#E8:52"><span class="lab"><font color="Green" title="E40">A3</font></span></a>, <a class="ref" href="lukasi_1.html#T43" title="LUKASI_1:th.43">LUKASI_1:43</a></span>;<br/>
<span class="kw">hence </span><a NAME="E18:52"/>
<span class="p1">(<span class="default"><a href="cqc_lang.html#K12" title="CQC_LANG:func.12">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#K11" title="CQC_LANG:func.11">&lt;=&gt;</a> <font color="Maroon" title="c2">q</font></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#K12" title="CQC_LANG:func.12">All</a> <font color="Maroon" title="c3">x</font>,<font color="Maroon" title="c1">p</font></span>)</span> <a href="cqc_lang.html#K11" title="CQC_LANG:func.11">&lt;=&gt;</a> <span class="p2">(<span class="default"><a href="cqc_lang.html#K12" title="CQC_LANG:func.12">All</a> <font color="Maroon" title="c3">x</font>,<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="txt" href="#E5:52"><span class="lab"><font color="Green" title="E39">A2</font></span></a>, <a class="ref" href="lukasi_1.html#T43" title="LUKASI_1:th.43">LUKASI_1:43</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/>


</div>
