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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="E10">A1</font></i>: <a class="txt" onclick="hs2(this)" href="javascript:()" title="9_1"><b>now </b></a><div class="add"><b>assume </b><a NAME="E1:9_1"/><i><font color="Green" title="E11">A2</font></i>: 
<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>
 ;<br/><div><a class="txt" onclick="hs2(this)" href="javascript:()" title="9_1_1"><b>now </b></a><div class="add"><b>let </b><font color="Maroon" title="c3">p</font> be    <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a> ;<br/><b>assume </b><a NAME="E1:9_1_1"/><i><font color="Green" title="E12">A3</font></i>: 
<font color="Maroon" title="c3">p</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c2">Y</font>
 ;<br/><b>then reconsider </b><font color="Maroon" title="c4">p'</font> = <font color="Maroon" title="c3">p</font> as    <a href="subset_1.html#M2" title="SUBSET_1:mode.2">Element</a> of  <a href="cqc_lang.html#K7" title="CQC_LANG:func.7">CQC-WFF</a>  ;<br/><a NAME="E3:9_1_1"/>
<font color="Maroon" title="c1">X</font> <a href="cqc_the1.html#R3" title="CQC_THE1:pred.3">|-</a> <font color="Maroon" title="c4">p'</font>
 <b>by </b><i><a class="txt" href="cqc_the3.html#E1:9_1"><i><font color="Green" title="E11">A2</font></i></a>, <a class="txt" href="cqc_the3.html#E1:9_1_1"><i><font color="Green" title="E12">A3</font></i></a>, <a class="ref" href="cqc_the3.html#D2" target="_self" title="CQC_THE3:def.2">Def2</a></i>;<br/><b>hence </b><a NAME="E4:9_1_1"/>
<font color="Maroon" title="c3">p</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</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#D9" title="CQC_THE1:def.9">CQC_THE1:def 9</a></i>;<br/></div><b>end;</b></div><b>hence </b><a NAME="E3:9_1"/>
<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>
 <b>by </b><i><a class="ref" href="tarski.html#D3" title="TARSKI:def.3">TARSKI:def 3</a></i>;<br/></div><b>end;</b></div>
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="9_2"><b>now </b></a><div class="add"><b>assume </b><a NAME="E1:9_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="c1">X</font>
 ;<br/><a NAME="E2:9_2"/><b>then </b>
for <font color="Olive" title="b1">p</font> being   <a href="subset_1.html#M2" title="SUBSET_1:mode.2">Element</a> of  <a href="cqc_lang.html#K7" title="CQC_LANG:func.7">CQC-WFF</a>   st <font color="Olive" title="b1">p</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c2">Y</font> holds <br/><font color="Maroon" title="c1">X</font> <a href="cqc_the1.html#R3" title="CQC_THE1:pred.3">|-</a> <font color="Olive" title="b1">p</font>
 <b>by </b><i><a class="ref" href="cqc_the1.html#D9" title="CQC_THE1:def.9">CQC_THE1:def 9</a></i>;<br/><b>hence </b><a NAME="E3:9_2"/>
<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>
 <b>by </b><i><a class="ref" href="cqc_the3.html#D2" target="_self" title="CQC_THE3:def.2">Def2</a></i>;<br/></div><b>end;</b></div>
<b>hence </b><a NAME="E3:9"/>
( <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> iff <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> )
 <b>by </b><i><a class="txt" href="cqc_the3.html#E1:9"><i><font color="Green" title="E10">A1</font></i></a></i>;<br/>


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