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<span class="kw">let </span><font color="Maroon" title="c1">Al</font> be    <a href="qc_lang1.html#M1" title="QC_LANG1:mode.1">QC-alphabet</a> ; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> <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#K5" title="CQC_LANG:func.5">VERUM</a> <font color="Maroon" title="c1">Al</font></span>)</span></span><a href="domain_1.html#K6" title="DOMAIN_1:func.6">}</a></span> is  <a href="henmodel.html#V1" title="HENMODEL:attr.1">Consistent</a> </span><br/>

<span class="kw">set </span><font color="Maroon" title="c2">A</font> =  the   non  <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a>   <a href="hidden.html#M2" title="HIDDEN:mode.2">set</a> ;<br/>
<span class="kw">set </span><font color="Maroon" title="c3">J</font> =  the    <a href="valuat_1.html#M1" title="VALUAT_1:mode.1">interpretation</a> of <font color="Maroon" title="c1">Al</font>, the   non  <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a>   <a href="hidden.html#M2" title="HIDDEN:mode.2">set</a> ;<br/>
<span class="kw">set </span><font color="Maroon" title="c4">v</font> =  the    <a href="funct_2.html#M2" title="FUNCT_2:mode.2">Element</a> of  <a href="valuat_1.html#K2" title="VALUAT_1:func.2">Valuations_in</a> (<font color="Maroon" title="c1">Al</font>, the   non  <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a>   <a href="hidden.html#M2" title="HIDDEN:mode.2">set</a> );<br/>
<a NAME="E1:19"/>
 the    <a href="valuat_1.html#M1" title="VALUAT_1:mode.1">interpretation</a> of <font color="Maroon" title="c1">Al</font>, the   non  <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a>   <a href="hidden.html#M2" title="HIDDEN:mode.2">set</a> , the    <a href="funct_2.html#M2" title="FUNCT_2:mode.2">Element</a> of  <a href="valuat_1.html#K2" title="VALUAT_1:func.2">Valuations_in</a> (<font color="Maroon" title="c1">Al</font>, the   non  <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a>   <a href="hidden.html#M2" title="HIDDEN:mode.2">set</a> ) <a href="valuat_1.html#R1" title="VALUAT_1:pred.1">|=</a>  <a href="cqc_lang.html#K5" title="CQC_LANG:func.5">VERUM</a> <font color="Maroon" title="c1">Al</font>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="valuat_1.html#T32" onmouseover="rs('valuat_1/T32')" onmouseout="rh()">VALUAT_1:32</a></span>;<br/>
<a NAME="E2:19"/><span class="kw">then </span>
 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#K3" title="CQC_LANG:func.3">CQC-WFF</a> <font color="Maroon" title="c1">Al</font>  st <font color="Olive" title="b1">p</font> <a href="tarski.html#R2" title="TARSKI:pred.2">in</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#K5" title="CQC_LANG:func.5">VERUM</a> <font color="Maroon" title="c1">Al</font></span>)</span></span><a href="domain_1.html#K6" title="DOMAIN_1:func.6">}</a></span> holds <br/> the    <a href="valuat_1.html#M1" title="VALUAT_1:mode.1">interpretation</a> of <font color="Maroon" title="c1">Al</font>, the   non  <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a>   <a href="hidden.html#M2" title="HIDDEN:mode.2">set</a> , the    <a href="funct_2.html#M2" title="FUNCT_2:mode.2">Element</a> of  <a href="valuat_1.html#K2" title="VALUAT_1:func.2">Valuations_in</a> (<font color="Maroon" title="c1">Al</font>, the   non  <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a>   <a href="hidden.html#M2" title="HIDDEN:mode.2">set</a> ) <a href="valuat_1.html#R1" title="VALUAT_1:pred.1">|=</a> <font color="Olive" title="b1">p</font>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="tarski.html#D1" onmouseover="rs('tarski/D1')" onmouseout="rh()">TARSKI:def 1</a></span>;<br/>
<a NAME="E3:19"/><span class="kw">then </span>
 the    <a href="valuat_1.html#M1" title="VALUAT_1:mode.1">interpretation</a> of <font color="Maroon" title="c1">Al</font>, the   non  <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a>   <a href="hidden.html#M2" title="HIDDEN:mode.2">set</a> , the    <a href="funct_2.html#M2" title="FUNCT_2:mode.2">Element</a> of  <a href="valuat_1.html#K2" title="VALUAT_1:func.2">Valuations_in</a> (<font color="Maroon" title="c1">Al</font>, the   non  <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a>   <a href="hidden.html#M2" title="HIDDEN:mode.2">set</a> ) <a href="calcul_1.html#R6" title="CALCUL_1:pred.6">|=</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#K5" title="CQC_LANG:func.5">VERUM</a> <font color="Maroon" title="c1">Al</font></span>)</span></span><a href="domain_1.html#K6" title="DOMAIN_1:func.6">}</a></span>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="calcul_1.html#D11" onmouseover="rs('calcul_1/D11')" onmouseout="rh()">CALCUL_1:def 11</a></span>;<br/>
<span class="kw">hence </span><a NAME="E4:19"/>
<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#K5" title="CQC_LANG:func.5">VERUM</a> <font color="Maroon" title="c1">Al</font></span>)</span></span><a href="domain_1.html#K6" title="DOMAIN_1:func.6">}</a></span> is  <a href="henmodel.html#V1" title="HENMODEL:attr.1">Consistent</a> 
 <span class="kw">by</span> <span class="lab"><a class="ref" href="henmodel.html#T12" target="_self" onmouseover="rs('henmodel/T12')" onmouseout="rh()">Th12</a></span>; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" 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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