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<b>let </b><font color="Maroon">X</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">p</font> be    <a href="subset_1.html#M2">Element</a> of  <a href="cqc_lang.html#K7">CQC-WFF</a> ;<br/>



<b>assume </b><a NAME="E1:43"/><i><font color="Green">E54</font></i>: 
 <a href="goedelcp.html#K6" target="_self">still_not-bound_in</a> <font color="Maroon">X</font> is <a href="finset_1.html#V1">finite</a>
 ;<br/>

<b>assume </b><a NAME="E2:43"/><i><font color="Green">E55</font></i>: 
<font color="Maroon">X</font> <a href="calcul_1.html#R7">|=</a> <font color="Maroon">p</font>
 ;<br/>

<b>assume </b><a NAME="E3:43"/><i><font color="Green">E56</font></i>: 
not <font color="Maroon">X</font> <a href="henmodel.html#R1">|-</a> <font color="Maroon">p</font>
 ;<br/>

<b>reconsider </b><font color="Maroon">Y</font> = <font color="Maroon">X</font> <a href="subset_1.html#K4">\/</a> <span class="p1"><a href="domain_1.html#K6">{</a><span class="default"><span class="p2">(<span class="default"><a href="cqc_lang.html#K10">'not'</a> <font color="Maroon">p</font></span>)</span></span><a href="domain_1.html#K6">}</a></span> as   <a href="subset_1.html#NM2">Subset</a> of <a href="cqc_lang.html#K7">CQC-WFF</a>  ;<br/>
<a NAME="E5:43"/><i><font color="Green">E57</font></i>: 
 <a href="goedelcp.html#K6" target="_self">still_not-bound_in</a> <font color="Maroon">Y</font> is <a href="finset_1.html#V1">finite</a>
 
<b>by </b><i>, </i>;<br/>
<a NAME="E6:43"/><i><font color="Green">E58</font></i>: 
for <font color="Olive">A</font> being non <a href="xboole_0.html#V1">empty</a>  <a href="hidden.html#M1">set</a> <br/> for <font color="Olive">J</font> being   <a href="valuat_1.html#M1">interpretation</a> of <font color="Olive">A</font><br/> for <font color="Olive">v</font> being   <a href="subset_1.html#M1">Element</a> of  <a href="valuat_1.html#K2">Valuations_in</a> <font color="Olive">A</font>  holds not <font color="Olive">J</font>,<font color="Olive">v</font> <a href="calcul_1.html#R6">|=</a> <font color="Maroon">Y</font>
 
<b>by </b><i>, </i>;<br/>
<a NAME="E7:43"/><i><font color="Green">E59</font></i>: 
<font color="Maroon">Y</font> is <a href="henmodel.html#V1">Consistent</a>
 
<b>by </b><i>, <a class="ref" href="henmodel.html#T9">HENMODEL:9</a></i>;<br/>
<b>consider </b><font color="Maroon">CZ</font> being  <a href="henmodel.html#V1">Consistent</a> <a href="subset_1.html#NM2">Subset</a> of <a href="cqc_lang.html#K7">CQC-WFF</a> , <font color="Maroon">JH1</font> being    <a href="henmodel.html#M1">Henkin_interpretation</a> of <font color="Maroon">CZ</font><b> such that </b><br/><a NAME="E9:43"/><i><font color="Green">E60</font></i>: 
<font color="Maroon">JH1</font>, <a href="henmodel.html#K4">valH</a>  <a href="calcul_1.html#R6">|=</a> <font color="Maroon">Y</font>
 <b>by </b><i>, <a class="ref" href="goedelcp.html#D2" target="_self">Def2</a>, </i>;<br/>
<b>thus </b><a NAME="E10:43"/>
contradiction
 <b>by </b><i><a class="ref" href="goedelcp.html#D1" target="_self">Def1</a>, <a class="ref" href="goedelcp.html#T1" target="_self">Th1</a></i>;<br/>


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