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<b>let </b><font color="Maroon" title="c1">X</font>, <font color="Maroon" title="c2">Y</font> be   <a href="subset_1.html#NM2" title="SUBSET_1:NM.2">Subset</a> of <a href="cqc_lang.html#K7" title="CQC_LANG:func.7">CQC-WFF</a> ;<br/>



<div><i><font color="Green" title="E21">A1</font></i>: <a class="txt" onclick="hs2(this)" href="javascript:()" title="22_1"><b>now </b></a><div class="add"><b>assume </b><a NAME="E1:22_1"/>
<font color="Maroon" title="c1">X</font> <a href="cqc_the3.html#R4" title="CQC_THE3:pred.4">|-|</a> <font color="Maroon" title="c2">Y</font>
 ;<br/><a NAME="E2:22_1"/><b>then </b>
( <font color="Maroon" title="c1">X</font> <a href="cqc_the3.html#R2" title="CQC_THE3:pred.2">|-</a> <font color="Maroon" title="c2">Y</font> &amp; <font color="Maroon" title="c2">Y</font> <a href="cqc_the3.html#R2" title="CQC_THE3:pred.2">|-</a> <font color="Maroon" title="c1">X</font> )
 <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="E3:22_1"/><b>then </b>
( <font color="Maroon" title="c2">Y</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a>  <a href="cqc_the1.html#K1" title="CQC_THE1:func.1">Cn</a> <font color="Maroon" title="c1">X</font> &amp; <font color="Maroon" title="c1">X</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a>  <a href="cqc_the1.html#K1" title="CQC_THE1:func.1">Cn</a> <font color="Maroon" title="c2">Y</font> )
 <b>by </b><i><a class="ref" href="cqc_the3.html#T7" target="_self" title="CQC_THE3:th.7">Th7</a></i>;<br/><a NAME="E4:22_1"/><b>then </b>
(  <a href="cqc_the1.html#K1" title="CQC_THE1:func.1">Cn</a> <font color="Maroon" title="c2">Y</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a>  <a href="cqc_the1.html#K1" title="CQC_THE1:func.1">Cn</a> <font color="Maroon" title="c1">X</font> &amp;  <a href="cqc_the1.html#K1" title="CQC_THE1:func.1">Cn</a> <font color="Maroon" title="c1">X</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a>  <a href="cqc_the1.html#K1" title="CQC_THE1:func.1">Cn</a> <font color="Maroon" title="c2">Y</font> )
 <b>by </b><i><a class="ref" href="cqc_the3.html#T2" target="_self" title="CQC_THE3:th.2">Th2</a></i>;<br/><b>hence </b><a NAME="E5:22_1"/>
 <a href="cqc_the1.html#K1" title="CQC_THE1:func.1">Cn</a> <font color="Maroon" title="c1">X</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="cqc_the1.html#K1" title="CQC_THE1:func.1">Cn</a> <font color="Maroon" title="c2">Y</font>
 <b>by </b><i><a class="ref" href="xboole_0.html#D10" title="XBOOLE_0:def.10">XBOOLE_0:def 10</a></i>;<br/></div><b>end;</b></div>
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="22_2"><b>now </b></a><div class="add"><b>assume </b><a NAME="E1:22_2"/><i><font color="Green" title="E22">A2</font></i>: 
 <a href="cqc_the1.html#K1" title="CQC_THE1:func.1">Cn</a> <font color="Maroon" title="c1">X</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="cqc_the1.html#K1" title="CQC_THE1:func.1">Cn</a> <font color="Maroon" title="c2">Y</font>
 ;<br/><a NAME="E2:22_2"/>
( <font color="Maroon" title="c2">Y</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a>  <a href="cqc_the1.html#K1" title="CQC_THE1:func.1">Cn</a> <font color="Maroon" title="c2">Y</font> &amp; <font color="Maroon" title="c1">X</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a>  <a href="cqc_the1.html#K1" title="CQC_THE1:func.1">Cn</a> <font color="Maroon" title="c1">X</font> )
 <b>by </b><i><a class="ref" href="cqc_the1.html#T38" title="CQC_THE1:th.38">CQC_THE1:38</a></i>;<br/><a NAME="E3:22_2"/><b>then </b>
( <font color="Maroon" title="c1">X</font> <a href="cqc_the3.html#R2" title="CQC_THE3:pred.2">|-</a> <font color="Maroon" title="c2">Y</font> &amp; <font color="Maroon" title="c2">Y</font> <a href="cqc_the3.html#R2" title="CQC_THE3:pred.2">|-</a> <font color="Maroon" title="c1">X</font> )
 <b>by </b><i><a class="txt" href="cqc_the3.html#E1:22_2"><i><font color="Green" title="E22">A2</font></i></a>, <a class="ref" href="cqc_the3.html#T7" target="_self" title="CQC_THE3:th.7">Th7</a></i>;<br/><b>hence </b><a NAME="E4:22_2"/>
<font color="Maroon" title="c1">X</font> <a href="cqc_the3.html#R4" title="CQC_THE3:pred.4">|-|</a> <font color="Maroon" title="c2">Y</font>
 <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>
<b>hence </b><a NAME="E3:22"/>
( <font color="Maroon" title="c1">X</font> <a href="cqc_the3.html#R4" title="CQC_THE3:pred.4">|-|</a> <font color="Maroon" title="c2">Y</font> iff  <a href="cqc_the1.html#K1" title="CQC_THE1:func.1">Cn</a> <font color="Maroon" title="c1">X</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="cqc_the1.html#K1" title="CQC_THE1:func.1">Cn</a> <font color="Maroon" title="c2">Y</font> )
 <b>by </b><i><a class="txt" href="cqc_the3.html#E1:22"><i><font color="Green" title="E21">A1</font></i></a></i>;<br/>


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