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<b>let </b><font color="Maroon" title="c1">X</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> ;<br/>

<b>assume </b><a NAME="E1:12"/>
not <font color="Maroon" title="c1">X</font> is <a href="henmodel.html#V1" title="HENMODEL:attr.1">Consistent</a>
 ;<br/>

<b>then consider </b><font color="Maroon" title="c2">p</font> being    <a href="subset_1.html#M2" title="SUBSET_1:mode.2">Element</a> of  <a href="cqc_lang.html#K4" title="CQC_LANG:func.4">CQC-WFF</a> <b> such that </b><br/><a NAME="E3:12"/><i><font color="Green" title="E11">A1</font></i>: 
( <font color="Maroon" title="c1">X</font> <a href="henmodel.html#R1" title="HENMODEL:pred.1">|-</a> <font color="Maroon" title="c2">p</font> &amp; <font color="Maroon" title="c1">X</font> <a href="henmodel.html#R1" title="HENMODEL:pred.1">|-</a>  <a href="cqc_lang.html#K7" title="CQC_LANG:func.7">'not'</a> <font color="Maroon" title="c2">p</font> )
 <b>by </b><i><a class="ref" href="henmodel.html#D3" target="_self" title="HENMODEL:def.3">Def3</a></i>;<br/>
<b>consider </b><font color="Maroon" title="c3">f1</font> being    <a href="finseq_1.html#M2" title="FINSEQ_1:mode.2">FinSequence</a> of  <a href="cqc_lang.html#K4" title="CQC_LANG:func.4">CQC-WFF</a> <b> such that </b><br/><a NAME="E5:12"/><i><font color="Green" title="E12">A2</font></i>: 
(  <a href="relset_1.html#K5" title="RELSET_1:func.5">rng</a> <font color="Maroon" title="c3">f1</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Maroon" title="c1">X</font> &amp;  <a href="calcul_1.html#R4" title="CALCUL_1:pred.4">|-</a> <font color="Maroon" title="c3">f1</font> <a href="finseq_1.html#K8" title="FINSEQ_1:func.8">^</a> <span class="p1"><a href="finseq_1.html#K12" title="FINSEQ_1:func.12">&lt;*</a><span class="default"><font color="Maroon" title="c2">p</font></span><a href="finseq_1.html#K12" title="FINSEQ_1:func.12">*&gt;</a></span> )
 <b>by </b><i><a class="txt" href="henmodel.html#E3:12"><i><font color="Green" title="E11">A1</font></i></a>, <a class="ref" href="henmodel.html#D2" target="_self" title="HENMODEL:def.2">Def2</a></i>;<br/>
<b>consider </b><font color="Maroon" title="c4">f2</font> being    <a href="finseq_1.html#M2" title="FINSEQ_1:mode.2">FinSequence</a> of  <a href="cqc_lang.html#K4" title="CQC_LANG:func.4">CQC-WFF</a> <b> such that </b><br/><a NAME="E7:12"/><i><font color="Green" title="E13">A3</font></i>: 
(  <a href="relset_1.html#K5" title="RELSET_1:func.5">rng</a> <font color="Maroon" title="c4">f2</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Maroon" title="c1">X</font> &amp;  <a href="calcul_1.html#R4" title="CALCUL_1:pred.4">|-</a> <font color="Maroon" title="c4">f2</font> <a href="finseq_1.html#K8" title="FINSEQ_1:func.8">^</a> <span class="p1"><a href="finseq_1.html#K12" title="FINSEQ_1:func.12">&lt;*</a><span class="default"><span class="p2">(<span class="default"><a href="cqc_lang.html#K7" title="CQC_LANG:func.7">'not'</a> <font color="Maroon" title="c2">p</font></span>)</span></span><a href="finseq_1.html#K12" title="FINSEQ_1:func.12">*&gt;</a></span> )
 <b>by </b><i><a class="txt" href="henmodel.html#E3:12"><i><font color="Green" title="E11">A1</font></i></a>, <a class="ref" href="henmodel.html#D2" target="_self" title="HENMODEL:def.2">Def2</a></i>;<br/>
<a NAME="E8:12"/><i><font color="Green" title="E14">A4</font></i>: 
(  <a href="calcul_1.html#R4" title="CALCUL_1:pred.4">|-</a> <span class="p1">(<span class="default"><font color="Maroon" title="c3">f1</font> <a href="finseq_1.html#K8" title="FINSEQ_1:func.8">^</a> <font color="Maroon" title="c4">f2</font></span>)</span> <a href="finseq_1.html#K8" title="FINSEQ_1:func.8">^</a> <span class="p1"><a href="finseq_1.html#K12" title="FINSEQ_1:func.12">&lt;*</a><span class="default"><font color="Maroon" title="c2">p</font></span><a href="finseq_1.html#K12" title="FINSEQ_1:func.12">*&gt;</a></span> &amp;  <a href="calcul_1.html#R4" title="CALCUL_1:pred.4">|-</a> <span class="p1">(<span class="default"><font color="Maroon" title="c3">f1</font> <a href="finseq_1.html#K8" title="FINSEQ_1:func.8">^</a> <font color="Maroon" title="c4">f2</font></span>)</span> <a href="finseq_1.html#K8" title="FINSEQ_1:func.8">^</a> <span class="p1"><a href="finseq_1.html#K12" title="FINSEQ_1:func.12">&lt;*</a><span class="default"><span class="p2">(<span class="default"><a href="cqc_lang.html#K7" title="CQC_LANG:func.7">'not'</a> <font color="Maroon" title="c2">p</font></span>)</span></span><a href="finseq_1.html#K12" title="FINSEQ_1:func.12">*&gt;</a></span> )
 
<b>by </b><i><a class="txt" href="henmodel.html#E5:12"><i><font color="Green" title="E12">A2</font></i></a>, <a class="txt" href="henmodel.html#E7:12"><i><font color="Green" title="E13">A3</font></i></a>, <a class="ref" href="henmodel.html#T5" target="_self" title="HENMODEL:th.5">Th5</a>, <a class="ref" href="calcul_2.html#T20" title="CALCUL_2:th.20">CALCUL_2:20</a></i>;<br/>
<b>reconsider </b><font color="Maroon" title="c5">Y</font> =  <a href="relset_1.html#K5" title="RELSET_1:func.5">rng</a> <span class="p1">(<span class="default"><font color="Maroon" title="c3">f1</font> <a href="finseq_1.html#K8" title="FINSEQ_1:func.8">^</a> <font color="Maroon" title="c4">f2</font></span>)</span> as   <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>  ;<br/>
<b>take </b>
<font color="Maroon" title="c5">Y</font>
;<br/>

<a NAME="E10:12"/>
<font color="Maroon" title="c5">Y</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="relset_1.html#K5" title="RELSET_1:func.5">rng</a> <font color="Maroon" title="c3">f1</font></span>)</span> <a href="subset_1.html#K4" title="SUBSET_1:func.4">\/</a> <span class="p1">(<span class="default"><a href="relset_1.html#K5" title="RELSET_1:func.5">rng</a> <font color="Maroon" title="c4">f2</font></span>)</span>
 
<b>by </b><i><a class="ref" href="finseq_1.html#T44" title="FINSEQ_1:th.44">FINSEQ_1:44</a></i>;<br/>
<b>hence </b><a NAME="E11:12"/>
<font color="Maroon" title="c5">Y</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Maroon" title="c1">X</font>
 <b>by </b><i><a class="txt" href="henmodel.html#E5:12"><i><font color="Green" title="E12">A2</font></i></a>, <a class="txt" href="henmodel.html#E7:12"><i><font color="Green" title="E13">A3</font></i></a>, <a class="ref" href="xboole_1.html#T8" title="XBOOLE_1:th.8">XBOOLE_1:8</a></i>;<br/>

<a NAME="E12:12"/>
( <font color="Maroon" title="c5">Y</font> <a href="henmodel.html#R1" title="HENMODEL:pred.1">|-</a> <font color="Maroon" title="c2">p</font> &amp; <font color="Maroon" title="c5">Y</font> <a href="henmodel.html#R1" title="HENMODEL:pred.1">|-</a>  <a href="cqc_lang.html#K7" title="CQC_LANG:func.7">'not'</a> <font color="Maroon" title="c2">p</font> )
 
<b>by </b><i><a class="txt" href="henmodel.html#E8:12"><i><font color="Green" title="E14">A4</font></i></a>, <a class="ref" href="henmodel.html#D2" target="_self" title="HENMODEL:def.2">Def2</a></i>;<br/>
<b>hence </b><a NAME="E13:12"/>
( <font color="Maroon" title="c5">Y</font> is <a href="finset_1.html#V1" title="FINSET_1:attr.1">finite</a> &amp; not <font color="Maroon" title="c5">Y</font> is <a href="henmodel.html#V1" title="HENMODEL:attr.1">Consistent</a> )
 <b>by </b><i><a class="ref" href="henmodel.html#D3" target="_self" title="HENMODEL:def.3">Def3</a></i>;<br/>


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