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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#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"> ( <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> )</span><br/>



<div><i><font color="Green" title="E21">A1</font></i>: <a class="txt" onclick="hs2(this)" href="javascript:()" title="21_1"><b>now </b></a><div class="add"><b>assume </b><a NAME="E1:21_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>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide">  <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></span><br/><a NAME="E2:21_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="E3:21_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="E4:21_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_the1.html#T36" title="CQC_THE1:th.36">CQC_THE1:36</a>, <a class="ref" href="cqc_the1.html#T37" title="CQC_THE1:th.37">CQC_THE1:37</a></i>;<br/><b>hence </b><a NAME="E5:21_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>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> verum</span><br/></div><b>end;</b></div>
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="21_2"><b>now </b></a><div class="add"><b>assume </b><a NAME="E1:21_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>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> <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></span><br/><a NAME="E2:21_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="E3:21_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#E1:21_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="E4:21_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>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> verum</span><br/></div><b>end;</b></div>
<b>hence </b><a NAME="E3:21"/>
( <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#E1:21"><i><font color="Green" title="E21">A1</font></i></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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