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<span class="kw">let </span><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> ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> ( not <font color="Maroon" title="c1">X</font> is  <a href="henmodel.html#V1" title="HENMODEL:attr.1">Consistent</a>  implies  ex <font color="Olive" title="b1">Y</font> being  <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>  st <br/>( <font color="Olive" title="b1">Y</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Maroon" title="c1">X</font> &amp; <font color="Olive" title="b1">Y</font> is  <a href="finset_1.html#V1" title="FINSET_1:attr.1">finite</a>  &amp; not <font color="Olive" title="b1">Y</font> is  <a href="henmodel.html#V1" title="HENMODEL:attr.1">Consistent</a>  ) )</span><br/>

<span class="kw">assume </span><a NAME="E1:12"/>
not <font color="Maroon" title="c1">X</font> is  <a href="henmodel.html#V1" title="HENMODEL:attr.1">Consistent</a> 
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide">  ex <font color="Olive" title="b1">Y</font> being  <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>  st <br/>( <font color="Olive" title="b1">Y</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Maroon" title="c1">X</font> &amp; <font color="Olive" title="b1">Y</font> is  <a href="finset_1.html#V1" title="FINSET_1:attr.1">finite</a>  &amp; not <font color="Olive" title="b1">Y</font> is  <a href="henmodel.html#V1" title="HENMODEL:attr.1">Consistent</a>  )</span><br/>

<span class="kw">then </span><span class="kw">consider </span><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> <span class="kw"> such that </span><br/><a NAME="E3:12"/><span class="lab"><font color="Green" title="E11">A1</font></span>: 
<font color="Maroon" title="c1">X</font> <a href="henmodel.html#R1" title="HENMODEL:pred.1">|-</a> <font color="Maroon" title="c2">p</font>
 <span class="kw">and </span><br/><a NAME="E4:12"/><span class="lab"><font color="Green" title="E12">A2</font></span>: 
<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>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="henmodel.html#D3" target="_self" title="HENMODEL:def.3">Def3</a></span>;<br/>
<span class="kw">consider </span><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> <span class="kw"> such that </span><br/><a NAME="E6:12"/><span class="lab"><font color="Green" title="E13">A3</font></span>: 
 <a href="relset_1.html#K2" title="RELSET_1:func.2">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>
 <span class="kw">and </span><br/><a NAME="E7:12"/><span class="lab"><font color="Green" title="E14">A4</font></span>: 
 <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>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E3:12"><span class="lab"><font color="Green" title="E11">A1</font></span></a>, <a class="ref" href="henmodel.html#D2" target="_self" title="HENMODEL:def.2">Def2</a></span>;<br/>
<span class="kw">consider </span><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> <span class="kw"> such that </span><br/><a NAME="E9:12"/><span class="lab"><font color="Green" title="E15">A5</font></span>: 
 <a href="relset_1.html#K2" title="RELSET_1:func.2">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>
 <span class="kw">and </span><br/><a NAME="E10:12"/><span class="lab"><font color="Green" title="E16">A6</font></span>: 
 <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>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E4:12"><span class="lab"><font color="Green" title="E12">A2</font></span></a>, <a class="ref" href="henmodel.html#D2" target="_self" title="HENMODEL:def.2">Def2</a></span>;<br/>
<span class="kw">reconsider </span><font color="Maroon" title="c5">Y</font> =  <a href="relset_1.html#K2" title="RELSET_1:func.2">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/>
<span class="kw">take </span>
<font color="Maroon" title="c5">Y</font>
; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> ( <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> &amp; <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>  )</span><br/>

<a NAME="E12:12"/>
<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#K2" title="RELSET_1:func.2">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#K2" title="RELSET_1:func.2">rng</a> <font color="Maroon" title="c4">f2</font></span>)</span>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="finseq_1.html#T44" title="FINSEQ_1:th.44">FINSEQ_1:44</a></span>;<br/>
<span class="kw">hence </span><a NAME="E13:12"/>
<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>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E6:12"><span class="lab"><font color="Green" title="E13">A3</font></span></a>, <a class="txt" href="#E9:12"><span class="lab"><font color="Green" title="E15">A5</font></span></a>, <a class="ref" href="xboole_1.html#T8" title="XBOOLE_1:th.8">XBOOLE_1:8</a></span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> ( <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>  )</span><br/>

<a NAME="E14:12"/>
 <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>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E10:12"><span class="lab"><font color="Green" title="E16">A6</font></span></a>, <a class="ref" href="calcul_2.html#T20" title="CALCUL_2:th.20">CALCUL_2:20</a></span>;<br/>
<a NAME="E15:12"/><span class="kw">then </span><span class="lab"><font color="Green" title="E17">A7</font></span>: 
<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>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="henmodel.html#D2" target="_self" title="HENMODEL:def.2">Def2</a></span>;<br/>
<a NAME="E16:12"/>
 <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>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E7:12"><span class="lab"><font color="Green" title="E14">A4</font></span></a>, <a class="ref" href="henmodel.html#T5" target="_self" title="HENMODEL:th.5">Th5</a></span>;<br/>
<a NAME="E17:12"/><span class="kw">then </span>
<font color="Maroon" title="c5">Y</font> <a href="henmodel.html#R1" title="HENMODEL:pred.1">|-</a> <font color="Maroon" title="c2">p</font>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="henmodel.html#D2" target="_self" title="HENMODEL:def.2">Def2</a></span>;<br/>
<span class="kw">hence </span><a NAME="E18:12"/>
( <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>  )
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E15:12"><span class="lab"><font color="Green" title="E17">A7</font></span></a>, <a class="ref" href="henmodel.html#D3" target="_self" title="HENMODEL:def.3">Def3</a></span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> verum</span><br/>


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