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<b>let </b><font color="Maroon">c<sub>1</sub></font> be   <a href="subset_1.html#NM2">Subset</a> of <a href="cqc_lang.html#K7">CQC-WFF</a> ;<br/><b>let </b><font color="Maroon">c<sub>2</sub></font> be    <a href="finseq_1.html#M2">FinSequence</a> of  <a href="cqc_lang.html#K7">CQC-WFF</a> ;<br/>



<b>assume </b><a NAME="E1:10"/><i><font color="Green">E9</font></i>: 
( <font color="Maroon">c<sub>1</sub></font> is <a href="henmodel.html#V1" target="_self">Consistent</a> &amp;  <a href="relset_1.html#K5">rng</a> <font color="Maroon">c<sub>2</sub></font> <a href="tarski.html#R1">c=</a> <font color="Maroon">c<sub>1</sub></font> )
 ;<br/>

<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="10_1"><b>now </b></a><div class="add"><b>assume </b><a NAME="E1:10_1"/>
not <font color="Maroon">c<sub>2</sub></font> is <a href="henmodel.html#V2" target="_self">Consistent</a>
 ;<br/><b>then consider </b><font color="Maroon">c<sub>3</sub></font> being    <a href="subset_1.html#M2">Element</a> of  <a href="cqc_lang.html#K7">CQC-WFF</a> <b> such that </b><br/><a NAME="E3:10_1"/><i><font color="Green">E10</font></i>: 
(  <a href="calcul_1.html#R4">|-</a> <font color="Maroon">c<sub>2</sub></font> <a href="finseq_1.html#K8">^</a> <span class="p1"><a href="finseq_1.html#K12">&lt;*</a><span class="default"><font color="Maroon">c<sub>3</sub></font></span><a href="finseq_1.html#K12">*&gt;</a></span> &amp;  <a href="calcul_1.html#R4">|-</a> <font color="Maroon">c<sub>2</sub></font> <a href="finseq_1.html#K8">^</a> <span class="p1"><a href="finseq_1.html#K12">&lt;*</a><span class="default"><span class="p2">(<span class="default"><a href="cqc_lang.html#K10">'not'</a> <font color="Maroon">c<sub>3</sub></font></span>)</span></span><a href="finseq_1.html#K12">*&gt;</a></span> )
 <b>by </b><i><a class="ref" href="henmodel.html#D4" target="_self">Def4</a></i>;<br/><a NAME="E4:10_1"/>
( <font color="Maroon">c<sub>1</sub></font> <a href="henmodel.html#R1" target="_self">|-</a> <font color="Maroon">c<sub>3</sub></font> &amp; <font color="Maroon">c<sub>1</sub></font> <a href="henmodel.html#R1" target="_self">|-</a>  <a href="cqc_lang.html#K10">'not'</a> <font color="Maroon">c<sub>3</sub></font> )
 <b>by </b><i><a class="txt" href="henmodel.html#E1:10"><i><font color="Green">E9</font></i></a>, <a class="txt" href="henmodel.html#E3:10_1"><i><font color="Green">E10</font></i></a>, <a class="ref" href="henmodel.html#D2" target="_self">Def2</a></i>;<br/><b>hence </b><a NAME="E5:10_1"/>
contradiction
 <b>by </b><i><a class="txt" href="henmodel.html#E1:10"><i><font color="Green">E9</font></i></a>, <a class="ref" href="henmodel.html#D3" target="_self">Def3</a></i>;<br/></div><b>end;</b></div>
<b>hence </b><a NAME="E3:10"/>
<font color="Maroon">c<sub>2</sub></font> is <a href="henmodel.html#V2" target="_self">Consistent</a>
 ;<br/>


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