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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> ;<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>;<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>;<br/>









<b>assume </b><b>that </b><br/><a NAME="E1:73"/><i><font color="Green" title="E56">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>
 <b>and </b><br/><a NAME="E2:73"/><i><font color="Green" title="E57">A2</font></i>: 
<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>
 <b>and </b><br/><a NAME="E3:73"/><i><font color="Green" title="E58">A3</font></i>: 
not <font color="Maroon" title="c4">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> <font color="Maroon" title="c3">h</font>
 <b>and </b><br/><a NAME="E4:73"/><i><font color="Green" title="E59">A4</font></i>: 
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>
 ;<br/>

<div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="73_1"><b>per </b></a><a class="txt" onclick="hs(this)" href="javascript:()"><b>cases </b></a><span class="hide"><a NAME="E1:73_1"/>
( <font color="Maroon" title="c4">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c5">y</font> or <font color="Maroon" title="c4">x</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c5">y</font> )
 </span>;<br/><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="73_1_1"><b>suppose </b></a><a NAME="E1:73_1_1"/>
<font color="Maroon" title="c4">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c5">y</font>
 ;<br/><div class="add"><b>hence </b><a NAME="E2:73_1_1"/>
 <a href="cqc_lang.html#K12" title="CQC_LANG:func.12">All</a> <font color="Maroon" title="c4">x</font>,<font color="Maroon" title="c1">p</font> <a href="cqc_the3.html#R7" title="CQC_THE3:pred.7">&lt;==&gt;</a>  <a href="cqc_lang.html#K12" title="CQC_LANG:func.12">All</a> <font color="Maroon" title="c5">y</font>,<font color="Maroon" title="c2">q</font>
 <b>by </b><i><a class="txt" href="cqc_the3.html#E1:73"><i><font color="Green" title="E56">A1</font></i></a>, <a class="txt" href="cqc_the3.html#E2:73"><i><font color="Green" title="E57">A2</font></i></a></i>;<br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="73_1_2"><b>suppose </b></a><a NAME="E1:73_1_2"/><i><font color="Green" title="E60">A5</font></i>: 
<font color="Maroon" title="c4">x</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c5">y</font>
 ;<br/><div class="add"><a NAME="E2:73_1_2"/><b>then </b><i><font color="Green" title="E61">A6</font></i>: 
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="c1">p</font>
 <b>by </b><i><a class="txt" href="cqc_the3.html#E1:73"><i><font color="Green" title="E56">A1</font></i></a>, <a class="txt" href="cqc_the3.html#E4:73"><i><font color="Green" title="E59">A4</font></i></a>, <a class="ref" href="cqc_the3.html#T65" target="_self" title="CQC_THE3:th.65">Th65</a></i>;<br/><a NAME="E3:73_1_2"/>
not <font color="Maroon" title="c4">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> <font color="Maroon" title="c2">q</font>
 <b>by </b><i><a class="txt" href="cqc_the3.html#E2:73"><i><font color="Green" title="E57">A2</font></i></a>, <a class="txt" href="cqc_the3.html#E3:73"><i><font color="Green" title="E58">A3</font></i></a>, <a class="txt" href="cqc_the3.html#E1:73_1_2"><i><font color="Green" title="E60">A5</font></i></a>, <a class="ref" href="cqc_the3.html#T65" target="_self" title="CQC_THE3:th.65">Th65</a></i>;<br/><a NAME="E4:73_1_2"/><b>then </b>
(  <a href="cqc_the1.html#NR5" title="CQC_THE1:NR.5">|-</a> <span class="p1">(<span class="default"><a href="cqc_lang.html#K12" title="CQC_LANG:func.12">All</a> <font color="Maroon" title="c4">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="p1">(<span class="default"><a href="cqc_lang.html#K12" title="CQC_LANG:func.12">All</a> <font color="Maroon" title="c5">y</font>,<font color="Maroon" title="c2">q</font></span>)</span> &amp;  <a href="cqc_the1.html#NR5" title="CQC_THE1:NR.5">|-</a> <span class="p1">(<span class="default"><a href="cqc_lang.html#K12" title="CQC_LANG:func.12">All</a> <font color="Maroon" title="c5">y</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="p1">(<span class="default"><a href="cqc_lang.html#K12" title="CQC_LANG:func.12">All</a> <font color="Maroon" title="c4">x</font>,<font color="Maroon" title="c1">p</font></span>)</span> )
 <b>by </b><i><a class="txt" href="cqc_the3.html#E1:73"><i><font color="Green" title="E56">A1</font></i></a>, <a class="txt" href="cqc_the3.html#E2:73"><i><font color="Green" title="E57">A2</font></i></a>, <a class="txt" href="cqc_the3.html#E3:73"><i><font color="Green" title="E58">A3</font></i></a>, <a class="txt" href="cqc_the3.html#E4:73"><i><font color="Green" title="E59">A4</font></i></a>, <a class="txt" href="cqc_the3.html#E2:73_1_2"><i><font color="Green" title="E61">A6</font></i></a>, <a class="ref" href="cqc_the2.html#T30" title="CQC_THE2:th.30">CQC_THE2:30</a></i>;<br/><b>hence </b><a NAME="E5:73_1_2"/>
 <a href="cqc_lang.html#K12" title="CQC_LANG:func.12">All</a> <font color="Maroon" title="c4">x</font>,<font color="Maroon" title="c1">p</font> <a href="cqc_the3.html#R7" title="CQC_THE3:pred.7">&lt;==&gt;</a>  <a href="cqc_lang.html#K12" title="CQC_LANG:func.12">All</a> <font color="Maroon" title="c5">y</font>,<font color="Maroon" title="c2">q</font>
 <b>by </b><i><a class="ref" href="cqc_the3.html#T50" target="_self" title="CQC_THE3:th.50">Th50</a></i>;<br/></div><b>end;</b></div></div><b>end;</b></div>

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