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<span class="kw">let </span><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#K3" title="CQC_LANG:func.3">CQC-WFF</a>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></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><span class="lab"><font color="Green" title="E21">A1</font></span>: <a class="txt" onclick="hs2(this)" href="javascript:()" title="21_1"><span class="kw">now </span></a><div class="add"><span class="kw">assume </span><a NAME="E1:21_1"/><span class="lab"><font color="Green" title="E22">A2</font></span>: 
<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:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></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"/><span class="kw">then </span>
<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>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="cqc_the3.html#T18" target="_self" title="CQC_THE3:th.18">Th18</a></span>;<br/><a NAME="E3:21_1"/><span class="kw">then </span>
<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>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="cqc_the3.html#T7" target="_self" title="CQC_THE3:th.7">Th7</a></span>;<br/><a NAME="E4:21_1"/><span class="kw">then </span><span class="lab"><font color="Green" title="E23">A3</font></span>: 
 <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>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="cqc_the1.html#T15" title="CQC_THE1:th.15">CQC_THE1:15</a>, <a class="ref" href="cqc_the1.html#T16" title="CQC_THE1:th.16">CQC_THE1:16</a></span>;<br/><a NAME="E5:21_1"/>
<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>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:21_1"><span class="lab"><font color="Green" title="E22">A2</font></span></a>, <a class="ref" href="cqc_the3.html#T18" target="_self" title="CQC_THE3:th.18">Th18</a></span>;<br/><a NAME="E6:21_1"/><span class="kw">then </span>
<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>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="cqc_the3.html#T7" target="_self" title="CQC_THE3:th.7">Th7</a></span>;<br/><a NAME="E7:21_1"/><span class="kw">then </span>
 <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>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="cqc_the1.html#T15" title="CQC_THE1:th.15">CQC_THE1:15</a>, <a class="ref" href="cqc_the1.html#T16" title="CQC_THE1:th.16">CQC_THE1:16</a></span>;<br/><span class="kw">hence </span><a NAME="E8:21_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>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E4:21_1"><span class="lab"><font color="Green" title="E23">A3</font></span></a>, <a class="ref" href="xboole_0.html#D10" title="XBOOLE_0:def.10">XBOOLE_0:def 10</a></span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> verum</span><br/></div><span class="kw">end;</span></div>
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="21_2"><span class="kw">now </span></a><div class="add"><span class="kw">assume </span><a NAME="E1:21_2"/><span class="lab"><font color="Green" title="E22">A4</font></span>: 
 <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:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></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="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>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="cqc_the1.html#T17" title="CQC_THE1:th.17">CQC_THE1:17</a></span>;<br/><a NAME="E3:21_2"/><span class="kw">then </span><span class="lab"><font color="Green" title="E23">A5</font></span>: 
<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>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:21_2"><span class="lab"><font color="Green" title="E22">A4</font></span></a>, <a class="ref" href="cqc_the3.html#T7" target="_self" title="CQC_THE3:th.7">Th7</a></span>;<br/><a NAME="E4:21_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>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="cqc_the1.html#T17" title="CQC_THE1:th.17">CQC_THE1:17</a></span>;<br/><a NAME="E5:21_2"/><span class="kw">then </span>
<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>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:21_2"><span class="lab"><font color="Green" title="E22">A4</font></span></a>, <a class="ref" href="cqc_the3.html#T7" target="_self" title="CQC_THE3:th.7">Th7</a></span>;<br/><span class="kw">hence </span><a NAME="E6:21_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>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E3:21_2"><span class="lab"><font color="Green" title="E23">A5</font></span></a>, <a class="ref" href="cqc_the3.html#T18" target="_self" title="CQC_THE3:th.18">Th18</a></span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> verum</span><br/></div><span class="kw">end;</span></div>
<span class="kw">hence </span><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> )
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:21"><span class="lab"><font color="Green" title="E21">A1</font></span></a></span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> verum</span><br/>


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