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<span class="kw">set </span><font color="Maroon" title="c1">A</font> =  the   non  <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a>   <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a> ;<br/>
<span class="kw">set </span><font color="Maroon" title="c2">J</font> =  the    <a href="valuat_1.html#M1" title="VALUAT_1:mode.1">interpretation</a> of  the   non  <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a>   <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a> ;<br/>
<span class="kw">set </span><font color="Maroon" title="c3">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>  the   non  <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a>   <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a> ;<br/>
<a NAME="E1:19"/>
 the    <a href="valuat_1.html#M1" title="VALUAT_1:mode.1">interpretation</a> of  the   non  <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a>   <a href="hidden.html#M1" title="HIDDEN:mode.1">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>  the   non  <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a>   <a href="hidden.html#M1" title="HIDDEN:mode.1">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> 
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="valuat_1.html#T32" title="VALUAT_1:th.32">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>   st <font color="Olive" title="b1">p</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <span class="p1"><a href="domain_1.html#K6" title="DOMAIN_1:func.6">{</a><span class="default"><a href="cqc_lang.html#K5" title="CQC_LANG:func.5">VERUM</a></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  the   non  <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a>   <a href="hidden.html#M1" title="HIDDEN:mode.1">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>  the   non  <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a>   <a href="hidden.html#M1" title="HIDDEN:mode.1">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" title="TARSKI:def.1">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  the   non  <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a>   <a href="hidden.html#M1" title="HIDDEN:mode.1">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>  the   non  <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a>   <a href="hidden.html#M1" title="HIDDEN:mode.1">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"><a href="cqc_lang.html#K5" title="CQC_LANG:func.5">VERUM</a></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" title="CALCUL_1:def.11">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"><a href="cqc_lang.html#K5" title="CQC_LANG:func.5">VERUM</a></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" title="HENMODEL:th.12">Th12</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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