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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/>



<div><i><font color="Green" title="E30">A1</font></i>: <a class="txt" onclick="hs2(this)" href="javascript:()" title="32_1"><b>now </b></a><div class="add"><b>assume </b><a NAME="E1:32_1"/>
<font color="Maroon" title="c1">p</font> <a href="cqc_the3.html#R5" title="CQC_THE3:pred.5">|-|</a> <font color="Maroon" title="c2">q</font>
 ;<br/><a NAME="E2:32_1"/><b>then </b>
( <font color="Maroon" title="c1">p</font> <a href="cqc_the3.html#R1" title="CQC_THE3:pred.1">|-</a> <font color="Maroon" title="c2">q</font> &amp; <font color="Maroon" title="c2">q</font> <a href="cqc_the3.html#R1" title="CQC_THE3:pred.1">|-</a> <font color="Maroon" title="c1">p</font> )
 <b>by </b><i><a class="ref" href="cqc_the3.html#D5" target="_self" title="CQC_THE3:def.5">Def5</a></i>;<br/><a NAME="E3:32_1"/><b>then </b>
( <span class="p1"><a href="domain_1.html#K6" title="DOMAIN_1:func.6">{</a><span class="default"><font color="Maroon" title="c1">p</font></span><a href="domain_1.html#K6" title="DOMAIN_1:func.6">}</a></span> <a href="cqc_the3.html#R2" title="CQC_THE3:pred.2">|-</a> <span class="p1"><a href="domain_1.html#K6" title="DOMAIN_1:func.6">{</a><span class="default"><font color="Maroon" title="c2">q</font></span><a href="domain_1.html#K6" title="DOMAIN_1:func.6">}</a></span> &amp; <span class="p1"><a href="domain_1.html#K6" title="DOMAIN_1:func.6">{</a><span class="default"><font color="Maroon" title="c2">q</font></span><a href="domain_1.html#K6" title="DOMAIN_1:func.6">}</a></span> <a href="cqc_the3.html#R2" title="CQC_THE3:pred.2">|-</a> <span class="p1"><a href="domain_1.html#K6" title="DOMAIN_1:func.6">{</a><span class="default"><font color="Maroon" title="c1">p</font></span><a href="domain_1.html#K6" title="DOMAIN_1:func.6">}</a></span> )
 <b>by </b><i><a class="ref" href="cqc_the3.html#T11" target="_self" title="CQC_THE3:th.11">Th11</a></i>;<br/><b>hence </b><a NAME="E4:32_1"/>
<span class="p1"><a href="domain_1.html#K6" title="DOMAIN_1:func.6">{</a><span class="default"><font color="Maroon" title="c1">p</font></span><a href="domain_1.html#K6" title="DOMAIN_1:func.6">}</a></span> <a href="cqc_the3.html#R4" title="CQC_THE3:pred.4">|-|</a> <span class="p1"><a href="domain_1.html#K6" title="DOMAIN_1:func.6">{</a><span class="default"><font color="Maroon" title="c2">q</font></span><a href="domain_1.html#K6" title="DOMAIN_1:func.6">}</a></span>
 <b>by </b><i><a class="ref" href="cqc_the3.html#T18" target="_self" title="CQC_THE3:th.18">Th18</a></i>;<br/></div><b>end;</b></div>
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="32_2"><b>now </b></a><div class="add"><b>assume </b><a NAME="E1:32_2"/>
<span class="p1"><a href="domain_1.html#K6" title="DOMAIN_1:func.6">{</a><span class="default"><font color="Maroon" title="c1">p</font></span><a href="domain_1.html#K6" title="DOMAIN_1:func.6">}</a></span> <a href="cqc_the3.html#R4" title="CQC_THE3:pred.4">|-|</a> <span class="p1"><a href="domain_1.html#K6" title="DOMAIN_1:func.6">{</a><span class="default"><font color="Maroon" title="c2">q</font></span><a href="domain_1.html#K6" title="DOMAIN_1:func.6">}</a></span>
 ;<br/><a NAME="E2:32_2"/><b>then </b>
( <span class="p1"><a href="domain_1.html#K6" title="DOMAIN_1:func.6">{</a><span class="default"><font color="Maroon" title="c1">p</font></span><a href="domain_1.html#K6" title="DOMAIN_1:func.6">}</a></span> <a href="cqc_the3.html#R2" title="CQC_THE3:pred.2">|-</a> <span class="p1"><a href="domain_1.html#K6" title="DOMAIN_1:func.6">{</a><span class="default"><font color="Maroon" title="c2">q</font></span><a href="domain_1.html#K6" title="DOMAIN_1:func.6">}</a></span> &amp; <span class="p1"><a href="domain_1.html#K6" title="DOMAIN_1:func.6">{</a><span class="default"><font color="Maroon" title="c2">q</font></span><a href="domain_1.html#K6" title="DOMAIN_1:func.6">}</a></span> <a href="cqc_the3.html#R2" title="CQC_THE3:pred.2">|-</a> <span class="p1"><a href="domain_1.html#K6" title="DOMAIN_1:func.6">{</a><span class="default"><font color="Maroon" title="c1">p</font></span><a href="domain_1.html#K6" title="DOMAIN_1:func.6">}</a></span> )
 <b>by </b><i><a class="ref" href="cqc_the3.html#T18" target="_self" title="CQC_THE3:th.18">Th18</a></i>;<br/><a NAME="E3:32_2"/><b>then </b>
( <font color="Maroon" title="c1">p</font> <a href="cqc_the3.html#R1" title="CQC_THE3:pred.1">|-</a> <font color="Maroon" title="c2">q</font> &amp; <font color="Maroon" title="c2">q</font> <a href="cqc_the3.html#R1" title="CQC_THE3:pred.1">|-</a> <font color="Maroon" title="c1">p</font> )
 <b>by </b><i><a class="ref" href="cqc_the3.html#T11" target="_self" title="CQC_THE3:th.11">Th11</a></i>;<br/><b>hence </b><a NAME="E4:32_2"/>
<font color="Maroon" title="c1">p</font> <a href="cqc_the3.html#R5" title="CQC_THE3:pred.5">|-|</a> <font color="Maroon" title="c2">q</font>
 <b>by </b><i><a class="ref" href="cqc_the3.html#D5" target="_self" title="CQC_THE3:def.5">Def5</a></i>;<br/></div><b>end;</b></div>
<b>hence </b><a NAME="E3:32"/>
( <font color="Maroon" title="c1">p</font> <a href="cqc_the3.html#R5" title="CQC_THE3:pred.5">|-|</a> <font color="Maroon" title="c2">q</font> iff <span class="p1"><a href="domain_1.html#K6" title="DOMAIN_1:func.6">{</a><span class="default"><font color="Maroon" title="c1">p</font></span><a href="domain_1.html#K6" title="DOMAIN_1:func.6">}</a></span> <a href="cqc_the3.html#R4" title="CQC_THE3:pred.4">|-|</a> <span class="p1"><a href="domain_1.html#K6" title="DOMAIN_1:func.6">{</a><span class="default"><font color="Maroon" title="c2">q</font></span><a href="domain_1.html#K6" title="DOMAIN_1:func.6">}</a></span> )
 <b>by </b><i><a class="txt" href="cqc_the3.html#E1:32"><i><font color="Green" title="E30">A1</font></i></a></i>;<br/>


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