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<span class="kw">let </span><font color="Maroon" title="c1">CX</font> be   <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#K3" title="CQC_LANG:func.3">CQC-WFF</a>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  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">CX</font> is  <a href="finset_1.html#V1" title="FINSET_1:attr.1">finite</a>  implies  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#K3" title="CQC_LANG:func.3">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="c1">CX</font> )</span><br/>

<span class="kw">assume </span><a NAME="E1:39"/>
 <a href="goedelcp.html#K6" title="GOEDELCP:func.6">still_not-bound_in</a> <font color="Maroon" title="c1">CX</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="firebrick">::  thesis: </font></span></a><span class="hide">  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#K3" title="CQC_LANG:func.3">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="c1">CX</font></span><br/>

<span class="kw">then </span><span class="kw">consider </span><font color="Maroon" title="c2">CY</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#K3" title="CQC_LANG:func.3">CQC-WFF</a><span class="kw"> such that </span><br/><a NAME="E3:39"/><span class="lab"><font color="Green" title="E39">A1</font></span>: 
<font color="Maroon" title="c1">CX</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Maroon" title="c2">CY</font>
 <span class="kw">and </span><br/><a NAME="E4:39"/><span class="lab"><font color="Green" title="E40">A2</font></span>: 
<font color="Maroon" title="c2">CY</font> is  <a href="goedelcp.html#V2" title="GOEDELCP:attr.2">with_examples</a> 
 <span class="kw">by</span> <span class="lab"><a class="ref" href="goedelcp.html#T31" target="_self" title="GOEDELCP:th.31">Th31</a></span>;<br/>
<span class="kw">consider </span><font color="Maroon" title="c3">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#K3" title="CQC_LANG:func.3">CQC-WFF</a><span class="kw"> such that </span><br/><a NAME="E6:39"/><span class="lab"><font color="Green" title="E41">A3</font></span>: 
<font color="Maroon" title="c2">CY</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Maroon" title="c3">CZ</font>
 <span class="kw">and </span><br/><a NAME="E7:39"/><span class="lab"><font color="Green" title="E42">A4</font></span>: 
<font color="Maroon" title="c3">CZ</font> is  <a href="goedelcp.html#V1" title="GOEDELCP:attr.1">negation_faithful</a> 
 <span class="kw">and </span><br/><a NAME="E8:39"/><span class="lab"><font color="Green" title="E43">A5</font></span>: 
<font color="Maroon" title="c3">CZ</font> is  <a href="goedelcp.html#V2" title="GOEDELCP:attr.2">with_examples</a> 
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E4:39"><span class="lab"><font color="Green" title="E40">A2</font></span></a>, <a class="ref" href="goedelcp.html#T33" target="_self" title="GOEDELCP:th.33">Th33</a></span>;<br/>
<a NAME="E9:39"/><span class="lab"><font color="Green" title="E44">A6</font></span>: 
<font color="Maroon" title="c1">CX</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Maroon" title="c3">CZ</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E3:39"><span class="lab"><font color="Green" title="E39">A1</font></span></a>, <a class="txt" href="#E6:39"><span class="lab"><font color="Green" title="E41">A3</font></span></a>, <a class="ref" href="xboole_1.html#T1" title="XBOOLE_1:th.1">XBOOLE_1:1</a></span>;<br/>
<span class="kw">set </span><font color="Maroon" title="c4">JH1</font> =  the    <a href="henmodel.html#M1" title="HENMODEL:mode.1">Henkin_interpretation</a> of <font color="Maroon" title="c3">CZ</font>;<br/>
<div><span class="lab"><font color="Green" title="E45">A7</font></span>: <a class="txt" onclick="hs2(this)" href="javascript:()" title="39_1"><span class="kw">now </span></a><div class="add"><span class="kw">let </span><font color="Maroon" title="c5">p</font> be    <a href="subset_1.html#M2" title="SUBSET_1:mode.2">Element</a> of  <a href="cqc_lang.html#K3" title="CQC_LANG:func.3">CQC-WFF</a> ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> ( <font color="Maroon" title="c5">p</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c1">CX</font> implies  the    <a href="henmodel.html#M1" title="HENMODEL:mode.1">Henkin_interpretation</a> of <font color="Maroon" title="c3">CZ</font>, <a href="henmodel.html#K3" title="HENMODEL:func.3">valH</a>  <a href="valuat_1.html#R1" title="VALUAT_1:pred.1">|=</a> <font color="Maroon" title="c5">p</font> )</span><br/><span class="kw">assume </span><a NAME="E1:39_1"/>
<font color="Maroon" title="c5">p</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c1">CX</font>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide">  the    <a href="henmodel.html#M1" title="HENMODEL:mode.1">Henkin_interpretation</a> of <font color="Maroon" title="c3">CZ</font>, <a href="henmodel.html#K3" title="HENMODEL:func.3">valH</a>  <a href="valuat_1.html#R1" title="VALUAT_1:pred.1">|=</a> <font color="Maroon" title="c5">p</font></span><br/><a NAME="E2:39_1"/><span class="kw">then </span>
<font color="Maroon" title="c3">CZ</font> <a href="henmodel.html#R1" title="HENMODEL:pred.1">|-</a> <font color="Maroon" title="c5">p</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E9:39"><span class="lab"><font color="Green" title="E44">A6</font></span></a>, <a class="ref" href="goedelcp.html#T21" target="_self" title="GOEDELCP:th.21">Th21</a></span>;<br/><span class="kw">hence </span><a NAME="E3:39_1"/>
 the    <a href="henmodel.html#M1" title="HENMODEL:mode.1">Henkin_interpretation</a> of <font color="Maroon" title="c3">CZ</font>, <a href="henmodel.html#K3" title="HENMODEL:func.3">valH</a>  <a href="valuat_1.html#R1" title="VALUAT_1:pred.1">|=</a> <font color="Maroon" title="c5">p</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E7:39"><span class="lab"><font color="Green" title="E42">A4</font></span></a>, <a class="txt" href="#E8:39"><span class="lab"><font color="Green" title="E43">A5</font></span></a>, <a class="ref" href="goedelcp.html#T17" target="_self" title="GOEDELCP:th.17">Th17</a></span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> verum</span><br/></div><span class="kw">end;</span></div>
<span class="kw">take </span>
<font color="Maroon" title="c3">CZ</font>
; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide">  ex <font color="Olive" title="b1">JH1</font> being    <a href="henmodel.html#M1" title="HENMODEL:mode.1">Henkin_interpretation</a> of <font color="Maroon" title="c3">CZ</font> st <font color="Olive" title="b1">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="c1">CX</font></span><br/>

<span class="kw">take </span>
 the    <a href="henmodel.html#M1" title="HENMODEL:mode.1">Henkin_interpretation</a> of <font color="Maroon" title="c3">CZ</font>
; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide">  the    <a href="henmodel.html#M1" title="HENMODEL:mode.1">Henkin_interpretation</a> of <font color="Maroon" title="c3">CZ</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="c1">CX</font></span><br/>

<span class="kw">thus </span><a NAME="E11:39"/>
 the    <a href="henmodel.html#M1" title="HENMODEL:mode.1">Henkin_interpretation</a> of <font color="Maroon" title="c3">CZ</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="c1">CX</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E10:39"><span class="lab"><font color="Green" title="E45">A7</font></span></a>, <a class="ref" href="calcul_1.html#D11" title="CALCUL_1:def.11">CALCUL_1:def 11</a></span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> verum</span><br/>


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