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<b>let </b><font color="Maroon" title="c1">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"> for <font color="Olive" title="b1">A</font> being 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/> for <font color="Olive" title="b2">J</font> being   <a href="valuat_1.html#M1" title="VALUAT_1:mode.1">interpretation</a> of <font color="Olive" title="b1">A</font><br/> for <font color="Olive" title="b3">v</font> being   <a href="fraenkel.html#M2" title="FRAENKEL:mode.2">Element</a> of  <a href="valuat_1.html#K2" title="VALUAT_1:func.2">Valuations_in</a> <font color="Olive" title="b1">A</font><br/> for <font color="Olive" title="b4">Sub</font> being  <a href="substut1.html#NM1" title="SUBSTUT1:NM.1">CQC_Substitution</a> holds <br/> ( <font color="Olive" title="b2">J</font>,<font color="Olive" title="b3">v</font> <a href="sublemma.html#R1" title="SUBLEMMA:pred.1">|=</a> <span class="p1"><a href="substut2.html#K2" title="SUBSTUT2:func.2">[</a><span class="default"><font color="Maroon" title="c1">p</font>,<font color="Olive" title="b4">Sub</font></span><a href="substut2.html#K2" title="SUBSTUT2:func.2">]</a></span> iff <font color="Olive" title="b2">J</font>,<font color="Olive" title="b3">v</font> <a href="valuat_1.html#R1" title="VALUAT_1:pred.1">|=</a> <font color="Maroon" title="c1">p</font> )</span><br/><b>let </b><font color="Maroon" title="c2">A</font> be  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 class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> for <font color="Olive" title="b1">J</font> being   <a href="valuat_1.html#M1" title="VALUAT_1:mode.1">interpretation</a> of <font color="Maroon" title="c2">A</font><br/> for <font color="Olive" title="b2">v</font> being   <a href="fraenkel.html#M2" title="FRAENKEL:mode.2">Element</a> of  <a href="valuat_1.html#K2" title="VALUAT_1:func.2">Valuations_in</a> <font color="Maroon" title="c2">A</font><br/> for <font color="Olive" title="b3">Sub</font> being  <a href="substut1.html#NM1" title="SUBSTUT1:NM.1">CQC_Substitution</a> holds <br/> ( <font color="Olive" title="b1">J</font>,<font color="Olive" title="b2">v</font> <a href="sublemma.html#R1" title="SUBLEMMA:pred.1">|=</a> <span class="p1"><a href="substut2.html#K2" title="SUBSTUT2:func.2">[</a><span class="default"><font color="Maroon" title="c1">p</font>,<font color="Olive" title="b3">Sub</font></span><a href="substut2.html#K2" title="SUBSTUT2:func.2">]</a></span> iff <font color="Olive" title="b1">J</font>,<font color="Olive" title="b2">v</font> <a href="valuat_1.html#R1" title="VALUAT_1:pred.1">|=</a> <font color="Maroon" title="c1">p</font> )</span><br/><b>let </b><font color="Maroon" title="c3">J</font> be    <a href="valuat_1.html#M1" title="VALUAT_1:mode.1">interpretation</a> of <font color="Maroon" title="c2">A</font>; <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">v</font> being   <a href="fraenkel.html#M2" title="FRAENKEL:mode.2">Element</a> of  <a href="valuat_1.html#K2" title="VALUAT_1:func.2">Valuations_in</a> <font color="Maroon" title="c2">A</font><br/> for <font color="Olive" title="b2">Sub</font> being  <a href="substut1.html#NM1" title="SUBSTUT1:NM.1">CQC_Substitution</a> holds <br/> ( <font color="Maroon" title="c3">J</font>,<font color="Olive" title="b1">v</font> <a href="sublemma.html#R1" title="SUBLEMMA:pred.1">|=</a> <span class="p1"><a href="substut2.html#K2" title="SUBSTUT2:func.2">[</a><span class="default"><font color="Maroon" title="c1">p</font>,<font color="Olive" title="b2">Sub</font></span><a href="substut2.html#K2" title="SUBSTUT2:func.2">]</a></span> iff <font color="Maroon" title="c3">J</font>,<font color="Olive" title="b1">v</font> <a href="valuat_1.html#R1" title="VALUAT_1:pred.1">|=</a> <font color="Maroon" title="c1">p</font> )</span><br/><b>let </b><font color="Maroon" title="c4">v</font> be    <a href="fraenkel.html#M2" title="FRAENKEL:mode.2">Element</a> of  <a href="valuat_1.html#K2" title="VALUAT_1:func.2">Valuations_in</a> <font color="Maroon" title="c2">A</font>; <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">Sub</font> being  <a href="substut1.html#NM1" title="SUBSTUT1:NM.1">CQC_Substitution</a> holds <br/> ( <font color="Maroon" title="c3">J</font>,<font color="Maroon" title="c4">v</font> <a href="sublemma.html#R1" title="SUBLEMMA:pred.1">|=</a> <span class="p1"><a href="substut2.html#K2" title="SUBSTUT2:func.2">[</a><span class="default"><font color="Maroon" title="c1">p</font>,<font color="Olive" title="b1">Sub</font></span><a href="substut2.html#K2" title="SUBSTUT2:func.2">]</a></span> iff <font color="Maroon" title="c3">J</font>,<font color="Maroon" title="c4">v</font> <a href="valuat_1.html#R1" title="VALUAT_1:pred.1">|=</a> <font color="Maroon" title="c1">p</font> )</span><br/><b>let </b><font color="Maroon" title="c5">Sub</font> be   <a href="substut1.html#NM1" title="SUBSTUT1:NM.1">CQC_Substitution</a>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> ( <font color="Maroon" title="c3">J</font>,<font color="Maroon" title="c4">v</font> <a href="sublemma.html#R1" title="SUBLEMMA:pred.1">|=</a> <span class="p1"><a href="substut2.html#K2" title="SUBSTUT2:func.2">[</a><span class="default"><font color="Maroon" title="c1">p</font>,<font color="Maroon" title="c5">Sub</font></span><a href="substut2.html#K2" title="SUBSTUT2:func.2">]</a></span> iff <font color="Maroon" title="c3">J</font>,<font color="Maroon" title="c4">v</font> <a href="valuat_1.html#R1" title="VALUAT_1:pred.1">|=</a> <font color="Maroon" title="c1">p</font> )</span><br/>









<a NAME="E1:39"/>
( <font color="Maroon" title="c3">J</font>,<font color="Maroon" title="c4">v</font> <a href="sublemma.html#R1" title="SUBLEMMA:pred.1">|=</a> <span class="p1"><a href="substut2.html#K2" title="SUBSTUT2:func.2">[</a><span class="default"><font color="Maroon" title="c1">p</font>,<font color="Maroon" title="c5">Sub</font></span><a href="substut2.html#K2" title="SUBSTUT2:func.2">]</a></span> iff <font color="Maroon" title="c3">J</font>,<font color="Maroon" title="c4">v</font> <a href="valuat_1.html#R1" title="VALUAT_1:pred.1">|=</a> <span class="p1"><a href="substut2.html#K2" title="SUBSTUT2:func.2">[</a><span class="default"><font color="Maroon" title="c1">p</font>,<font color="Maroon" title="c5">Sub</font></span><a href="substut2.html#K2" title="SUBSTUT2:func.2">]</a></span> <a href="sublemma.html#K2" title="SUBLEMMA:func.2">`1</a>  )
 
<b>by </b><i><a class="ref" href="sublemma.html#D3" title="SUBLEMMA:def.3">SUBLEMMA:def 3</a></i>;<br/>
<b>hence </b><a NAME="E2:39"/>
( <font color="Maroon" title="c3">J</font>,<font color="Maroon" title="c4">v</font> <a href="sublemma.html#R1" title="SUBLEMMA:pred.1">|=</a> <span class="p1"><a href="substut2.html#K2" title="SUBSTUT2:func.2">[</a><span class="default"><font color="Maroon" title="c1">p</font>,<font color="Maroon" title="c5">Sub</font></span><a href="substut2.html#K2" title="SUBSTUT2:func.2">]</a></span> iff <font color="Maroon" title="c3">J</font>,<font color="Maroon" title="c4">v</font> <a href="valuat_1.html#R1" title="VALUAT_1:pred.1">|=</a> <font color="Maroon" title="c1">p</font> )
 <b>by </b><i><a class="ref" href="mcart_1.html#T7" title="MCART_1:th.7">MCART_1:7</a></i>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> verum</span><br/>


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