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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>assume </b><a NAME="E1:13"/>
not <font color="Maroon">c<sub>1</sub></font> is <a href="henmodel.html#V1" target="_self">Consistent</a>
 ;<br/>

<b>then consider </b><font color="Maroon">c<sub>2</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="E3:13"/><i><font color="Green">E12</font></i>: 
( <font color="Maroon">c<sub>1</sub></font> <a href="henmodel.html#R1" target="_self">|-</a> <font color="Maroon">c<sub>2</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>2</sub></font> )
 <b>by </b><i><a class="ref" href="henmodel.html#D3" target="_self">Def3</a></i>;<br/>
<b>consider </b><font color="Maroon">c<sub>3</sub></font> being    <a href="finseq_1.html#M2">FinSequence</a> of  <a href="cqc_lang.html#K7">CQC-WFF</a> <b> such that </b><br/><a NAME="E5:13"/><i><font color="Green">E13</font></i>: 
(  <a href="relset_1.html#K5">rng</a> <font color="Maroon">c<sub>3</sub></font> <a href="tarski.html#R1">c=</a> <font color="Maroon">c<sub>1</sub></font> &amp;  <a href="calcul_1.html#R4">|-</a> <font color="Maroon">c<sub>3</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>2</sub></font></span><a href="finseq_1.html#K12">*&gt;</a></span> )
 <b>by </b><i><a class="txt" href="henmodel.html#E3:13"><i><font color="Green">E12</font></i></a>, <a class="ref" href="henmodel.html#D2" target="_self">Def2</a></i>;<br/>
<b>consider </b><font color="Maroon">c<sub>4</sub></font> being    <a href="finseq_1.html#M2">FinSequence</a> of  <a href="cqc_lang.html#K7">CQC-WFF</a> <b> such that </b><br/><a NAME="E7:13"/><i><font color="Green">E14</font></i>: 
(  <a href="relset_1.html#K5">rng</a> <font color="Maroon">c<sub>4</sub></font> <a href="tarski.html#R1">c=</a> <font color="Maroon">c<sub>1</sub></font> &amp;  <a href="calcul_1.html#R4">|-</a> <font color="Maroon">c<sub>4</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>2</sub></font></span>)</span></span><a href="finseq_1.html#K12">*&gt;</a></span> )
 <b>by </b><i><a class="txt" href="henmodel.html#E3:13"><i><font color="Green">E12</font></i></a>, <a class="ref" href="henmodel.html#D2" target="_self">Def2</a></i>;<br/>
<a NAME="E8:13"/><i><font color="Green">E15</font></i>: 
(  <a href="calcul_1.html#R4">|-</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="finseq_1.html#K8">^</a> <font color="Maroon">c<sub>4</sub></font></span>)</span> <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>2</sub></font></span><a href="finseq_1.html#K12">*&gt;</a></span> &amp;  <a href="calcul_1.html#R4">|-</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="finseq_1.html#K8">^</a> <font color="Maroon">c<sub>4</sub></font></span>)</span> <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>2</sub></font></span>)</span></span><a href="finseq_1.html#K12">*&gt;</a></span> )
 
<b>by </b><i><a class="txt" href="henmodel.html#E5:13"><i><font color="Green">E13</font></i></a>, <a class="txt" href="henmodel.html#E7:13"><i><font color="Green">E14</font></i></a>, <a class="ref" href="henmodel.html#T5" target="_self">Th5</a>, <a class="ref" href="calcul_2.html#T20">CALCUL_2:20</a></i>;<br/>
<b>reconsider </b><font color="Maroon">c<sub>5</sub></font> =  <a href="relset_1.html#K5">rng</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="finseq_1.html#K8">^</a> <font color="Maroon">c<sub>4</sub></font></span>)</span> as   <a href="subset_1.html#NM2">Subset</a> of <a href="cqc_lang.html#K7">CQC-WFF</a>  ;<br/>
<b>take </b>
<font color="Maroon">c<sub>5</sub></font>
;<br/>

<a NAME="E10:13"/>
<font color="Maroon">c<sub>5</sub></font> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><a href="relset_1.html#K5">rng</a> <font color="Maroon">c<sub>3</sub></font></span>)</span> <a href="subset_1.html#K4">\/</a> <span class="p1">(<span class="default"><a href="relset_1.html#K5">rng</a> <font color="Maroon">c<sub>4</sub></font></span>)</span>
 
<b>by </b><i><a class="ref" href="finseq_1.html#T44">FINSEQ_1:44</a></i>;<br/>
<b>hence </b><a NAME="E11:13"/>
<font color="Maroon">c<sub>5</sub></font> <a href="tarski.html#R1">c=</a> <font color="Maroon">c<sub>1</sub></font>
 <b>by </b><i><a class="txt" href="henmodel.html#E5:13"><i><font color="Green">E13</font></i></a>, <a class="txt" href="henmodel.html#E7:13"><i><font color="Green">E14</font></i></a>, <a class="ref" href="xboole_1.html#T8">XBOOLE_1:8</a></i>;<br/>

<a NAME="E12:13"/>
( <font color="Maroon">c<sub>5</sub></font> <a href="henmodel.html#R1" target="_self">|-</a> <font color="Maroon">c<sub>2</sub></font> &amp; <font color="Maroon">c<sub>5</sub></font> <a href="henmodel.html#R1" target="_self">|-</a>  <a href="cqc_lang.html#K10">'not'</a> <font color="Maroon">c<sub>2</sub></font> )
 
<b>by </b><i><a class="txt" href="henmodel.html#E8:13"><i><font color="Green">E15</font></i></a>, <a class="ref" href="henmodel.html#D2" target="_self">Def2</a></i>;<br/>
<b>hence </b><a NAME="E13:13"/>
( <font color="Maroon">c<sub>5</sub></font> is <a href="finset_1.html#V1">finite</a> &amp; not <font color="Maroon">c<sub>5</sub></font> is <a href="henmodel.html#V1" target="_self">Consistent</a> )
 <b>by </b><i><a class="ref" href="henmodel.html#D3" target="_self">Def3</a></i>;<br/>


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