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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"> 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#K4" title="CQC_LANG:func.4">CQC-WFF</a>   st  <a href="goedelcp.html#K6" title="GOEDELCP:func.6">still_not-bound_in</a> <font color="Maroon" title="c1">X</font> is  <a href="finset_1.html#V1" title="FINSET_1:attr.1">finite</a>  &amp; <font color="Maroon" title="c1">X</font> <a href="calcul_1.html#R7" title="CALCUL_1:pred.7">|=</a> <font color="Olive" title="b1">p</font> holds <br/><font color="Maroon" title="c1">X</font> <a href="henmodel.html#R1" title="HENMODEL:pred.1">|-</a> <font color="Olive" title="b1">p</font></span><br/><span class="kw">let </span><font color="Maroon" title="c2">p</font> be    <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> ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> (  <a href="goedelcp.html#K6" title="GOEDELCP:func.6">still_not-bound_in</a> <font color="Maroon" title="c1">X</font> is  <a href="finset_1.html#V1" title="FINSET_1:attr.1">finite</a>  &amp; <font color="Maroon" title="c1">X</font> <a href="calcul_1.html#R7" title="CALCUL_1:pred.7">|=</a> <font color="Maroon" title="c2">p</font> implies <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><br/>



<span class="kw">assume </span><a NAME="E1:43"/><span class="lab"><font color="Green" title="E42">A1</font></span>: 
 <a href="goedelcp.html#K6" title="GOEDELCP:func.6">still_not-bound_in</a> <font color="Maroon" title="c1">X</font> is  <a href="finset_1.html#V1" title="FINSET_1:attr.1">finite</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> <a href="calcul_1.html#R7" title="CALCUL_1:pred.7">|=</a> <font color="Maroon" title="c2">p</font> or <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><br/>

<span class="kw">assume </span><a NAME="E2:43"/><span class="lab"><font color="Green" title="E43">A2</font></span>: 
<font color="Maroon" title="c1">X</font> <a href="calcul_1.html#R7" title="CALCUL_1:pred.7">|=</a> <font color="Maroon" title="c2">p</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="c1">X</font> <a href="henmodel.html#R1" title="HENMODEL:pred.1">|-</a> <font color="Maroon" title="c2">p</font></span><br/>

<span class="kw">assume </span><a NAME="E3:43"/><span class="lab"><font color="Green" title="E44">A3</font></span>: 
not <font color="Maroon" title="c1">X</font> <a href="henmodel.html#R1" title="HENMODEL:pred.1">|-</a> <font color="Maroon" title="c2">p</font>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> contradiction</span><br/>

<span class="kw">reconsider </span><font color="Maroon" title="c3">Y</font> = <font color="Maroon" title="c1">X</font> <a href="subset_1.html#K4" title="SUBSET_1:func.4">\/</a> <span class="p1"><a href="domain_1.html#K6" title="DOMAIN_1:func.6">{</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="domain_1.html#K6" title="DOMAIN_1:func.6">}</a></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/>
<a NAME="E5:43"/><span class="lab"><font color="Green" title="E45">A4</font></span>: 
 <a href="goedelcp.html#K6" title="GOEDELCP:func.6">still_not-bound_in</a> <font color="Maroon" title="c3">Y</font> is  <a href="finset_1.html#V1" title="FINSET_1:attr.1">finite</a> 
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:43"><span class="lab"><font color="Green" title="E42">A1</font></span></a>, <a class="ref" href="goedelcp.html#T36" target="_self" title="GOEDELCP:th.36">Th36</a></span>;<br/>
<a NAME="E6:43"/>
<font color="Maroon" title="c3">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="#E3:43"><span class="lab"><font color="Green" title="E44">A3</font></span></a>, <a class="ref" href="henmodel.html#T9" title="HENMODEL:th.9">HENMODEL:9</a></span>;<br/>
<a NAME="E7:43"/><span class="kw">then </span>
 ex <font color="Olive" title="b1">CZ</font> being  <a href="henmodel.html#V1" title="HENMODEL:attr.1">Consistent</a>  <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>  ex <font color="Olive" title="b2">JH1</font> being   <a href="henmodel.html#M1" title="HENMODEL:mode.1">Henkin_interpretation</a> of <font color="Olive" title="b1">CZ</font> st <font color="Olive" title="b2">JH1</font>, <a href="henmodel.html#K3" title="HENMODEL:func.3">valH</a>  <a href="calcul_1.html#R6" title="CALCUL_1:pred.6">|=</a> <font color="Maroon" title="c3">Y</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E5:43"><span class="lab"><font color="Green" title="E45">A4</font></span></a>, <a class="ref" href="goedelcp.html#T34" target="_self" title="GOEDELCP:th.34">Th34</a></span>;<br/>
<span class="kw">hence </span><a NAME="E8:43"/>
contradiction
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:43"><span class="lab"><font color="Green" title="E43">A2</font></span></a>, <a class="ref" href="goedelcp.html#T37" target="_self" title="GOEDELCP:th.37">Th37</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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