<?xml version="1.0"?>
<div class="add">

<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> ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></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/><b>let </b><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:()"><i><font color="Red">::  thesis: </font></i></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/>



<b>assume </b><a NAME="E1:43"/><i><font color="Green" title="E42">A1</font></i>: 
 <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:()"><i><font color="Red">::  thesis: </font></i></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/>

<b>assume </b><a NAME="E2:43"/><i><font color="Green" title="E43">A2</font></i>: 
<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:()"><i><font color="Red">::  thesis: </font></i></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/>

<b>assume </b><a NAME="E3:43"/><i><font color="Green" title="E44">A3</font></i>: 
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:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> contradiction</span><br/>

<b>reconsider </b><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"/><i><font color="Green" title="E45">A4</font></i>: 
 <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>
 
<b>by </b><i><a class="txt" href="goedelcp.html#E1:43"><i><font color="Green" title="E42">A1</font></i></a>, <a class="ref" href="goedelcp.html#T36" target="_self" title="GOEDELCP:th.36">Th36</a></i>;<br/>
<a NAME="E6:43"/>
<font color="Maroon" title="c3">Y</font> is <a href="henmodel.html#V1" title="HENMODEL:attr.1">Consistent</a>
 
<b>by </b><i><a class="txt" href="goedelcp.html#E3:43"><i><font color="Green" title="E44">A3</font></i></a>, <a class="ref" href="henmodel.html#T9" title="HENMODEL:th.9">HENMODEL:9</a></i>;<br/>
<b>then consider </b><font color="Maroon" title="c4">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> , <font color="Maroon" title="c5">JH1</font> being    <a href="henmodel.html#M1" title="HENMODEL:mode.1">Henkin_interpretation</a> of <font color="Maroon" title="c4">CZ</font><b> such that </b><br/><a NAME="E8:43"/><i><font color="Green" title="E46">A5</font></i>: 
<font color="Maroon" title="c5">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>
 <b>by </b><i><a class="txt" href="goedelcp.html#E5:43"><i><font color="Green" title="E45">A4</font></i></a>, <a class="ref" href="goedelcp.html#T34" target="_self" title="GOEDELCP:th.34">Th34</a></i>;<br/>
<b>thus </b><a NAME="E9:43"/>
contradiction
 <b>by </b><i><a class="txt" href="goedelcp.html#E2:43"><i><font color="Green" title="E43">A2</font></i></a>, <a class="txt" href="goedelcp.html#E8:43"><i><font color="Green" title="E46">A5</font></i></a>, <a class="ref" href="goedelcp.html#T37" target="_self" title="GOEDELCP:th.37">Th37</a></i>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> verum</span><br/>


</div>
