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<b>let </b><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:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> for <font color="Olive" title="b1">h</font> being  <a href="qc_lang1.html#NM8" title="QC_LANG1:NM.8">QC-formula</a><br/> for <font color="Olive" title="b2">x</font>, <font color="Olive" title="b3">y</font> being  <a href="qc_lang1.html#NM3" title="QC_LANG1:NM.3">bound_QC-variable</a>  st <font color="Maroon" title="c1">p</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b1">h</font> <a href="cqc_lang.html#K14" title="CQC_LANG:func.14">.</a> <font color="Olive" title="b2">x</font> &amp; <font color="Maroon" title="c2">q</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b1">h</font> <a href="cqc_lang.html#K14" title="CQC_LANG:func.14">.</a> <font color="Olive" title="b3">y</font> &amp; not <font color="Olive" title="b3">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> <font color="Olive" title="b1">h</font> holds <br/> <a href="cqc_the1.html#NR5" title="CQC_THE1:NR.5">|-</a> <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="b3">y</font>,<font color="Maroon" title="c2">q</font></span>)</span></span><br/><b>let </b><font color="Maroon" title="c3">h</font> be   <a href="qc_lang1.html#NM8" title="QC_LANG1:NM.8">QC-formula</a>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></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="Maroon" title="c1">p</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c3">h</font> <a href="cqc_lang.html#K14" title="CQC_LANG:func.14">.</a> <font color="Olive" title="b1">x</font> &amp; <font color="Maroon" title="c2">q</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c3">h</font> <a href="cqc_lang.html#K14" title="CQC_LANG:func.14">.</a> <font color="Olive" title="b2">y</font> &amp; not <font color="Olive" title="b2">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> <font color="Maroon" title="c3">h</font> holds <br/> <a href="cqc_the1.html#NR5" title="CQC_THE1:NR.5">|-</a> <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="b2">y</font>,<font color="Maroon" title="c2">q</font></span>)</span></span><br/><b>let </b><font color="Maroon" title="c4">x</font>, <font color="Maroon" title="c5">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:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> ( <font color="Maroon" title="c1">p</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c3">h</font> <a href="cqc_lang.html#K14" title="CQC_LANG:func.14">.</a> <font color="Maroon" title="c4">x</font> &amp; <font color="Maroon" title="c2">q</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c3">h</font> <a href="cqc_lang.html#K14" title="CQC_LANG:func.14">.</a> <font color="Maroon" title="c5">y</font> &amp; not <font color="Maroon" title="c5">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> <font color="Maroon" title="c3">h</font> implies  <a href="cqc_the1.html#NR5" title="CQC_THE1:NR.5">|-</a> <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="c5">y</font>,<font color="Maroon" title="c2">q</font></span>)</span> )</span><br/>









<b>assume </b><a NAME="E1:38"/><i><font color="Green" title="E32">A1</font></i>: 
( <font color="Maroon" title="c1">p</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c3">h</font> <a href="cqc_lang.html#K14" title="CQC_LANG:func.14">.</a> <font color="Maroon" title="c4">x</font> &amp; <font color="Maroon" title="c2">q</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c3">h</font> <a href="cqc_lang.html#K14" title="CQC_LANG:func.14">.</a> <font color="Maroon" title="c5">y</font> &amp; not <font color="Maroon" title="c5">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> <font color="Maroon" title="c3">h</font> )
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide">  <a href="cqc_the1.html#NR5" title="CQC_THE1:NR.5">|-</a> <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="c5">y</font>,<font color="Maroon" title="c2">q</font></span>)</span></span><br/>

<a NAME="E2:38"/><i><font color="Green" title="E33">A2</font></i>: 
 <a href="cqc_the1.html#NR5" title="CQC_THE1:NR.5">|-</a> <font color="Maroon" title="c2">q</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="c5">y</font>,<font color="Maroon" title="c2">q</font></span>)</span>
 
<b>by </b><i><a class="ref" href="cqc_the2.html#T18" target="_self" title="CQC_THE2:th.18">Th18</a></i>;<br/>
<i><font color="Green" title="E34">A3</font></i>: <span class="p1">(<span class="default"><font color="Maroon" title="c3">h</font> <a href="qc_lang2.html#K2" title="QC_LANG2:func.2">=&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="c5">y</font>,<font color="Maroon" title="c2">q</font></span>)</span></span>)</span> <a href="cqc_lang.html#K14" title="CQC_LANG:func.14">.</a> <font color="Maroon" title="c5">y</font> = 
<span class="p1">(<span class="default"><font color="Maroon" title="c3">h</font> <a href="cqc_lang.html#K14" title="CQC_LANG:func.14">.</a> <font color="Maroon" title="c5">y</font></span>)</span> <a href="qc_lang2.html#K2" title="QC_LANG2:func.2">=&gt;</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="cqc_lang.html#K13" title="CQC_LANG:func.13">Ex</a> <font color="Maroon" title="c5">y</font>,<font color="Maroon" title="c2">q</font></span>)</span> <a href="cqc_lang.html#K14" title="CQC_LANG:func.14">.</a> <font color="Maroon" title="c5">y</font></span>)</span>
<b>by </b><i><a class="ref" href="cqc_the2.html#T14" target="_self" title="CQC_THE2:th.14">Th14</a></i>
<br/>.= 
<font color="Maroon" title="c2">q</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="c5">y</font>,<font color="Maroon" title="c2">q</font></span>)</span>
<b>by </b><i><a class="txt" href="cqc_the2.html#E1:38"><i><font color="Green" title="E32">A1</font></i></a>, <a class="ref" href="cqc_lang.html#T40" title="CQC_LANG:th.40">CQC_LANG:40</a></i>
;<br/>
<i><font color="Green" title="E35">A4</font></i>: <span class="p1">(<span class="default"><font color="Maroon" title="c3">h</font> <a href="qc_lang2.html#K2" title="QC_LANG2:func.2">=&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="c5">y</font>,<font color="Maroon" title="c2">q</font></span>)</span></span>)</span> <a href="cqc_lang.html#K14" title="CQC_LANG:func.14">.</a> <font color="Maroon" title="c4">x</font> = 
<span class="p1">(<span class="default"><font color="Maroon" title="c3">h</font> <a href="cqc_lang.html#K14" title="CQC_LANG:func.14">.</a> <font color="Maroon" title="c4">x</font></span>)</span> <a href="qc_lang2.html#K2" title="QC_LANG2:func.2">=&gt;</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="cqc_lang.html#K13" title="CQC_LANG:func.13">Ex</a> <font color="Maroon" title="c5">y</font>,<font color="Maroon" title="c2">q</font></span>)</span> <a href="cqc_lang.html#K14" title="CQC_LANG:func.14">.</a> <font color="Maroon" title="c4">x</font></span>)</span>
<b>by </b><i><a class="ref" href="cqc_the2.html#T14" target="_self" title="CQC_THE2:th.14">Th14</a></i>
<br/>.= 
<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="c5">y</font>,<font color="Maroon" title="c2">q</font></span>)</span>
<b>by </b><i><a class="txt" href="cqc_the2.html#E1:38"><i><font color="Green" title="E32">A1</font></i></a>, <a class="ref" href="cqc_lang.html#T40" title="CQC_LANG:th.40">CQC_LANG:40</a></i>
;<br/>
<a NAME="E5:38"/>
( not <font color="Maroon" title="c5">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#K13" title="CQC_LANG:func.13">Ex</a> <font color="Maroon" title="c5">y</font>,<font color="Maroon" title="c2">q</font></span>)</span> &amp; not <font color="Maroon" title="c5">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> <font color="Maroon" title="c3">h</font> )
 
<b>by </b><i><a class="txt" href="cqc_the2.html#E1:38"><i><font color="Green" title="E32">A1</font></i></a>, <a class="ref" href="cqc_the2.html#T6" target="_self" title="CQC_THE2:th.6">Th6</a></i>;<br/>
<a NAME="E6:38"/><b>then </b>
not <font color="Maroon" title="c5">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"><font color="Maroon" title="c3">h</font> <a href="qc_lang2.html#K2" title="QC_LANG2:func.2">=&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="c5">y</font>,<font color="Maroon" title="c2">q</font></span>)</span></span>)</span>
 
<b>by </b><i><a class="ref" href="cqc_the2.html#T7" target="_self" title="CQC_THE2:th.7">Th7</a></i>;<br/>
<b>hence </b><a NAME="E7:38"/>
 <a href="cqc_the1.html#NR5" title="CQC_THE1:NR.5">|-</a> <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="c5">y</font>,<font color="Maroon" title="c2">q</font></span>)</span>
 <b>by </b><i><a class="txt" href="cqc_the2.html#E2:38"><i><font color="Green" title="E33">A2</font></i></a>, <a class="txt" href="cqc_the2.html#E3:38"><i><font color="Green" title="E34">A3</font></i></a>, <a class="txt" href="cqc_the2.html#E4:38"><i><font color="Green" title="E35">A4</font></i></a>, <a class="ref" href="cqc_the1.html#T107" title="CQC_THE1:th.107">CQC_THE1:107</a></i>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> verum</span><br/>


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