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<div class="add">

<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> holds <br/> ( <span class="p1">(<span class="default"><a href="cqc_lang.html#K11" title="CQC_LANG:func.11">All</a> (<font color="Olive" title="b1">x</font>,<span class="p2">(<span class="default"><a href="cqc_lang.html#K11" title="CQC_LANG:func.11">All</a> (<font color="Olive" title="b2">y</font>,<font color="Maroon" title="c1">p</font>)</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="Olive" title="b2">y</font>,<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>)</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="qc_lang2.html#K6" title="QC_LANG2:func.6">All</a> (<font color="Olive" title="b1">x</font>,<font color="Olive" title="b2">y</font>,<font color="Maroon" title="c1">p</font>)</span>)</span> <a href="qc_lang2.html#K2" title="QC_LANG2:func.2">=&gt;</a> <span class="p1">(<span class="default"><a href="qc_lang2.html#K6" title="QC_LANG2:func.6">All</a> (<font color="Olive" title="b2">y</font>,<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>, <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"> ( <span class="p1">(<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="p2">(<span class="default"><a href="cqc_lang.html#K11" title="CQC_LANG:func.11">All</a> (<font color="Maroon" title="c3">y</font>,<font color="Maroon" title="c1">p</font>)</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">y</font>,<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>,<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>  &amp; <span class="p1">(<span class="default"><a href="qc_lang2.html#K6" title="QC_LANG2:func.6">All</a> (<font color="Maroon" title="c2">x</font>,<font color="Maroon" title="c3">y</font>,<font color="Maroon" title="c1">p</font>)</span>)</span> <a href="qc_lang2.html#K2" title="QC_LANG2:func.2">=&gt;</a> <span class="p1">(<span class="default"><a href="qc_lang2.html#K6" title="QC_LANG2:func.6">All</a> (<font color="Maroon" title="c3">y</font>,<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="E1:71"/>
 not <font color="Maroon" title="c3">y</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#K11" title="CQC_LANG:func.11">All</a> (<font color="Maroon" title="c3">y</font>,<font color="Maroon" title="c1">p</font>)</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="E2:71"/><span class="kw">then </span><span class="lab"><font color="Green" title="E51">A1</font></span>: 
 not <font color="Maroon" title="c3">y</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#K11" title="CQC_LANG:func.11">All</a> (<font color="Maroon" title="c2">x</font>,<span class="p2">(<span class="default"><a href="cqc_lang.html#K11" title="CQC_LANG:func.11">All</a> (<font color="Maroon" title="c3">y</font>,<font color="Maroon" title="c1">p</font>)</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="E3:71"/>
(  <a href="cqc_lang.html#K11" title="CQC_LANG:func.11">All</a> (<font color="Maroon" title="c2">x</font>,<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">y</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="c1">p</font></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="c2">x</font>,<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">y</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="c1">p</font></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="c2">x</font>,<span class="p3">(<span class="default"><a href="cqc_lang.html#K11" title="CQC_LANG:func.11">All</a> (<font color="Maroon" title="c3">y</font>,<font color="Maroon" title="c1">p</font>)</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="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="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>, <a class="ref" href="cqc_the1.html#T66" title="CQC_THE1:th.66">CQC_THE1:66</a></span>;<br/>
<a NAME="E4:71"/><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="c2">x</font>,<span class="p2">(<span class="default"><a href="cqc_lang.html#K11" title="CQC_LANG:func.11">All</a> (<font color="Maroon" title="c3">y</font>,<font color="Maroon" title="c1">p</font>)</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="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="cqc_the1.html#T65" title="CQC_THE1:th.65">CQC_THE1:65</a></span>;<br/>
<span class="kw">hence </span><a NAME="E5:71"/>
<span class="p1">(<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="p2">(<span class="default"><a href="cqc_lang.html#K11" title="CQC_LANG:func.11">All</a> (<font color="Maroon" title="c3">y</font>,<font color="Maroon" title="c1">p</font>)</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">y</font>,<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>,<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="#E2:71"><span class="lab"><font color="Green" title="E51">A1</font></span></a>, <a class="ref" href="cqc_the1.html#T67" title="CQC_THE1:th.67">CQC_THE1:67</a></span>; <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="qc_lang2.html#K6" title="QC_LANG2:func.6">All</a> (<font color="Maroon" title="c2">x</font>,<font color="Maroon" title="c3">y</font>,<font color="Maroon" title="c1">p</font>)</span>)</span> <a href="qc_lang2.html#K2" title="QC_LANG2:func.2">=&gt;</a> <span class="p1">(<span class="default"><a href="qc_lang2.html#K6" title="QC_LANG2:func.6">All</a> (<font color="Maroon" title="c3">y</font>,<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="E6:71"/><span class="kw">then </span>
<span class="p1">(<span class="default"><a href="qc_lang2.html#K6" title="QC_LANG2:func.6">All</a> (<font color="Maroon" title="c2">x</font>,<font color="Maroon" title="c3">y</font>,<font color="Maroon" title="c1">p</font>)</span>)</span> <a href="qc_lang2.html#K2" title="QC_LANG2:func.2">=&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">y</font>,<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>,<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#T14" title="QC_LANG2:th.14">QC_LANG2:14</a></span>;<br/>
<span class="kw">hence </span><a NAME="E7:71"/>
<span class="p1">(<span class="default"><a href="qc_lang2.html#K6" title="QC_LANG2:func.6">All</a> (<font color="Maroon" title="c2">x</font>,<font color="Maroon" title="c3">y</font>,<font color="Maroon" title="c1">p</font>)</span>)</span> <a href="qc_lang2.html#K2" title="QC_LANG2:func.2">=&gt;</a> <span class="p1">(<span class="default"><a href="qc_lang2.html#K6" title="QC_LANG2:func.6">All</a> (<font color="Maroon" title="c3">y</font>,<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#T14" title="QC_LANG2:th.14">QC_LANG2:14</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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