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<span class="kw">let </span><font color="Maroon" title="c1">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:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide">  for <font color="Olive" title="b1">v</font> being    <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">A</font><br/>  for <font color="Olive" title="b2">p</font>, <font color="Olive" title="b3">q</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> <br/>  for <font color="Olive" title="b4">J</font> being    <a href="valuat_1.html#M1" title="VALUAT_1:mode.1">interpretation</a> of <font color="Maroon" title="c1">A</font> holds <br/> ( <font color="Olive" title="b4">J</font>,<font color="Olive" title="b1">v</font> <a href="valuat_1.html#R1" title="VALUAT_1:pred.1">|=</a> <font color="Olive" title="b2">p</font> <a href="cqc_lang.html#K7" title="CQC_LANG:func.7">'&amp;'</a> <font color="Olive" title="b3">q</font> iff ( <font color="Olive" title="b4">J</font>,<font color="Olive" title="b1">v</font> <a href="valuat_1.html#R1" title="VALUAT_1:pred.1">|=</a> <font color="Olive" title="b2">p</font> &amp; <font color="Olive" title="b4">J</font>,<font color="Olive" title="b1">v</font> <a href="valuat_1.html#R1" title="VALUAT_1:pred.1">|=</a> <font color="Olive" title="b3">q</font> ) )</span><br/><span class="kw">let </span><font color="Maroon" title="c2">v</font> be    <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">A</font>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide">  for <font color="Olive" title="b1">p</font>, <font color="Olive" title="b2">q</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> <br/>  for <font color="Olive" title="b3">J</font> being    <a href="valuat_1.html#M1" title="VALUAT_1:mode.1">interpretation</a> of <font color="Maroon" title="c1">A</font> holds <br/> ( <font color="Olive" title="b3">J</font>,<font color="Maroon" title="c2">v</font> <a href="valuat_1.html#R1" title="VALUAT_1:pred.1">|=</a> <font color="Olive" title="b1">p</font> <a href="cqc_lang.html#K7" title="CQC_LANG:func.7">'&amp;'</a> <font color="Olive" title="b2">q</font> iff ( <font color="Olive" title="b3">J</font>,<font color="Maroon" title="c2">v</font> <a href="valuat_1.html#R1" title="VALUAT_1:pred.1">|=</a> <font color="Olive" title="b1">p</font> &amp; <font color="Olive" title="b3">J</font>,<font color="Maroon" title="c2">v</font> <a href="valuat_1.html#R1" title="VALUAT_1:pred.1">|=</a> <font color="Olive" title="b2">q</font> ) )</span><br/><span class="kw">let </span><font color="Maroon" title="c3">p</font>, <font color="Maroon" title="c4">q</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">  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="c1">A</font> holds <br/> ( <font color="Olive" title="b1">J</font>,<font color="Maroon" title="c2">v</font> <a href="valuat_1.html#R1" title="VALUAT_1:pred.1">|=</a> <font color="Maroon" title="c3">p</font> <a href="cqc_lang.html#K7" title="CQC_LANG:func.7">'&amp;'</a> <font color="Maroon" title="c4">q</font> iff ( <font color="Olive" title="b1">J</font>,<font color="Maroon" title="c2">v</font> <a href="valuat_1.html#R1" title="VALUAT_1:pred.1">|=</a> <font color="Maroon" title="c3">p</font> &amp; <font color="Olive" title="b1">J</font>,<font color="Maroon" title="c2">v</font> <a href="valuat_1.html#R1" title="VALUAT_1:pred.1">|=</a> <font color="Maroon" title="c4">q</font> ) )</span><br/><span class="kw">let </span><font color="Maroon" title="c5">J</font> be    <a href="valuat_1.html#M1" title="VALUAT_1:mode.1">interpretation</a> of <font color="Maroon" title="c1">A</font>; <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">J</font>,<font color="Maroon" title="c2">v</font> <a href="valuat_1.html#R1" title="VALUAT_1:pred.1">|=</a> <font color="Maroon" title="c3">p</font> <a href="cqc_lang.html#K7" title="CQC_LANG:func.7">'&amp;'</a> <font color="Maroon" title="c4">q</font> iff ( <font color="Maroon" title="c5">J</font>,<font color="Maroon" title="c2">v</font> <a href="valuat_1.html#R1" title="VALUAT_1:pred.1">|=</a> <font color="Maroon" title="c3">p</font> &amp; <font color="Maroon" title="c5">J</font>,<font color="Maroon" title="c2">v</font> <a href="valuat_1.html#R1" title="VALUAT_1:pred.1">|=</a> <font color="Maroon" title="c4">q</font> ) )</span><br/>









<div><span class="lab"><font color="Green" title="E16">A1</font></span>: <a class="txt" onclick="hs2(this)" href="javascript:()" title="26_1"><span class="kw">now </span></a><div class="add"><span class="kw">assume </span><a NAME="E1:26_1"/>
( <font color="Maroon" title="c5">J</font>,<font color="Maroon" title="c2">v</font> <a href="valuat_1.html#R1" title="VALUAT_1:pred.1">|=</a> <font color="Maroon" title="c3">p</font> &amp; <font color="Maroon" title="c5">J</font>,<font color="Maroon" title="c2">v</font> <a href="valuat_1.html#R1" title="VALUAT_1:pred.1">|=</a> <font color="Maroon" title="c4">q</font> )
 ; <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">J</font>,<font color="Maroon" title="c2">v</font> <a href="valuat_1.html#R1" title="VALUAT_1:pred.1">|=</a> <font color="Maroon" title="c3">p</font> <a href="cqc_lang.html#K7" title="CQC_LANG:func.7">'&amp;'</a> <font color="Maroon" title="c4">q</font></span><br/><a NAME="E2:26_1"/><span class="kw">then </span>
( <span class="p1">(<span class="default"><a href="valuat_1.html#K8" title="VALUAT_1:func.8">Valid</a> (<font color="Maroon" title="c3">p</font>,<font color="Maroon" title="c5">J</font>)</span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c2">v</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="margrel1.html#K8" title="MARGREL1:func.8">TRUE</a>  &amp; <span class="p1">(<span class="default"><a href="valuat_1.html#K8" title="VALUAT_1:func.8">Valid</a> (<font color="Maroon" title="c4">q</font>,<font color="Maroon" title="c5">J</font>)</span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c2">v</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="margrel1.html#K8" title="MARGREL1:func.8">TRUE</a>  )
 <span class="kw">by</span> <span class="lab"><a class="ref" href="valuat_1.html#D7" target="_self" title="VALUAT_1:def.7">Def12</a></span>;<br/><a NAME="E3:26_1"/><span class="kw">then </span>
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="valuat_1.html#K8" title="VALUAT_1:func.8">Valid</a> (<font color="Maroon" title="c3">p</font>,<font color="Maroon" title="c5">J</font>)</span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c2">v</font></span>)</span> <a href="margrel1.html#K10" title="MARGREL1:func.10">'&amp;'</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="valuat_1.html#K8" title="VALUAT_1:func.8">Valid</a> (<font color="Maroon" title="c4">q</font>,<font color="Maroon" title="c5">J</font>)</span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c2">v</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="margrel1.html#K8" title="MARGREL1:func.8">TRUE</a> 
 ;<br/><a NAME="E4:26_1"/><span class="kw">then </span>
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="valuat_1.html#K8" title="VALUAT_1:func.8">Valid</a> (<font color="Maroon" title="c3">p</font>,<font color="Maroon" title="c5">J</font>)</span>)</span> <a href="margrel1.html#K16" title="MARGREL1:func.16">'&amp;'</a> <span class="p2">(<span class="default"><a href="valuat_1.html#K8" title="VALUAT_1:func.8">Valid</a> (<font color="Maroon" title="c4">q</font>,<font color="Maroon" title="c5">J</font>)</span>)</span></span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c2">v</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="margrel1.html#K8" title="MARGREL1:func.8">TRUE</a> 
 <span class="kw">by</span> <span class="lab"><a class="ref" href="margrel1.html#D20" title="MARGREL1:def.20">MARGREL1:def 20</a></span>;<br/><a NAME="E5:26_1"/><span class="kw">then </span>
<span class="p1">(<span class="default"><a href="valuat_1.html#K8" title="VALUAT_1:func.8">Valid</a> (<span class="p2">(<span class="default"><font color="Maroon" title="c3">p</font> <a href="cqc_lang.html#K7" title="CQC_LANG:func.7">'&amp;'</a> <font color="Maroon" title="c4">q</font></span>)</span>,<font color="Maroon" title="c5">J</font>)</span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c2">v</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="margrel1.html#K8" title="MARGREL1:func.8">TRUE</a> 
 <span class="kw">by</span> <span class="lab"><a class="txt" href="valuat_1.html#E10"><span class="lab"><font color="Green" title="E8">Lm1</font></span></a></span>;<br/><span class="kw">hence </span><a NAME="E6:26_1"/>
<font color="Maroon" title="c5">J</font>,<font color="Maroon" title="c2">v</font> <a href="valuat_1.html#R1" title="VALUAT_1:pred.1">|=</a> <font color="Maroon" title="c3">p</font> <a href="cqc_lang.html#K7" title="CQC_LANG:func.7">'&amp;'</a> <font color="Maroon" title="c4">q</font>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="valuat_1.html#D7" target="_self" title="VALUAT_1:def.7">Def12</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>
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="26_2"><span class="kw">now </span></a><div class="add"><span class="kw">assume </span><a NAME="E1:26_2"/>
<font color="Maroon" title="c5">J</font>,<font color="Maroon" title="c2">v</font> <a href="valuat_1.html#R1" title="VALUAT_1:pred.1">|=</a> <font color="Maroon" title="c3">p</font> <a href="cqc_lang.html#K7" title="CQC_LANG:func.7">'&amp;'</a> <font color="Maroon" title="c4">q</font>
 ; <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">J</font>,<font color="Maroon" title="c2">v</font> <a href="valuat_1.html#R1" title="VALUAT_1:pred.1">|=</a> <font color="Maroon" title="c3">p</font> &amp; <font color="Maroon" title="c5">J</font>,<font color="Maroon" title="c2">v</font> <a href="valuat_1.html#R1" title="VALUAT_1:pred.1">|=</a> <font color="Maroon" title="c4">q</font> )</span><br/><a NAME="E2:26_2"/><span class="kw">then </span>
<span class="p1">(<span class="default"><a href="valuat_1.html#K8" title="VALUAT_1:func.8">Valid</a> (<span class="p2">(<span class="default"><font color="Maroon" title="c3">p</font> <a href="cqc_lang.html#K7" title="CQC_LANG:func.7">'&amp;'</a> <font color="Maroon" title="c4">q</font></span>)</span>,<font color="Maroon" title="c5">J</font>)</span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c2">v</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="margrel1.html#K8" title="MARGREL1:func.8">TRUE</a> 
 <span class="kw">by</span> <span class="lab"><a class="ref" href="valuat_1.html#D7" target="_self" title="VALUAT_1:def.7">Def12</a></span>;<br/><a NAME="E3:26_2"/><span class="kw">then </span>
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="valuat_1.html#K8" title="VALUAT_1:func.8">Valid</a> (<font color="Maroon" title="c3">p</font>,<font color="Maroon" title="c5">J</font>)</span>)</span> <a href="margrel1.html#K16" title="MARGREL1:func.16">'&amp;'</a> <span class="p2">(<span class="default"><a href="valuat_1.html#K8" title="VALUAT_1:func.8">Valid</a> (<font color="Maroon" title="c4">q</font>,<font color="Maroon" title="c5">J</font>)</span>)</span></span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c2">v</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="margrel1.html#K8" title="MARGREL1:func.8">TRUE</a> 
 <span class="kw">by</span> <span class="lab"><a class="txt" href="valuat_1.html#E10"><span class="lab"><font color="Green" title="E8">Lm1</font></span></a></span>;<br/><a NAME="E4:26_2"/><span class="kw">then </span>
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="valuat_1.html#K8" title="VALUAT_1:func.8">Valid</a> (<font color="Maroon" title="c3">p</font>,<font color="Maroon" title="c5">J</font>)</span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c2">v</font></span>)</span> <a href="margrel1.html#K10" title="MARGREL1:func.10">'&amp;'</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="valuat_1.html#K8" title="VALUAT_1:func.8">Valid</a> (<font color="Maroon" title="c4">q</font>,<font color="Maroon" title="c5">J</font>)</span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c2">v</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="margrel1.html#K8" title="MARGREL1:func.8">TRUE</a> 
 <span class="kw">by</span> <span class="lab"><a class="ref" href="margrel1.html#D20" title="MARGREL1:def.20">MARGREL1:def 20</a></span>;<br/><a NAME="E5:26_2"/><span class="kw">then </span>
( <span class="p1">(<span class="default"><a href="valuat_1.html#K8" title="VALUAT_1:func.8">Valid</a> (<font color="Maroon" title="c3">p</font>,<font color="Maroon" title="c5">J</font>)</span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c2">v</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="margrel1.html#K8" title="MARGREL1:func.8">TRUE</a>  &amp; <span class="p1">(<span class="default"><a href="valuat_1.html#K8" title="VALUAT_1:func.8">Valid</a> (<font color="Maroon" title="c4">q</font>,<font color="Maroon" title="c5">J</font>)</span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c2">v</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="margrel1.html#K8" title="MARGREL1:func.8">TRUE</a>  )
 <span class="kw">by</span> <span class="lab"><a class="ref" href="margrel1.html#T12" title="MARGREL1:th.12">MARGREL1:12</a></span>;<br/><span class="kw">hence </span><a NAME="E6:26_2"/>
( <font color="Maroon" title="c5">J</font>,<font color="Maroon" title="c2">v</font> <a href="valuat_1.html#R1" title="VALUAT_1:pred.1">|=</a> <font color="Maroon" title="c3">p</font> &amp; <font color="Maroon" title="c5">J</font>,<font color="Maroon" title="c2">v</font> <a href="valuat_1.html#R1" title="VALUAT_1:pred.1">|=</a> <font color="Maroon" title="c4">q</font> )
 <span class="kw">by</span> <span class="lab"><a class="ref" href="valuat_1.html#D7" target="_self" title="VALUAT_1:def.7">Def12</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">hence </span><a NAME="E3:26"/>
( <font color="Maroon" title="c5">J</font>,<font color="Maroon" title="c2">v</font> <a href="valuat_1.html#R1" title="VALUAT_1:pred.1">|=</a> <font color="Maroon" title="c3">p</font> <a href="cqc_lang.html#K7" title="CQC_LANG:func.7">'&amp;'</a> <font color="Maroon" title="c4">q</font> iff ( <font color="Maroon" title="c5">J</font>,<font color="Maroon" title="c2">v</font> <a href="valuat_1.html#R1" title="VALUAT_1:pred.1">|=</a> <font color="Maroon" title="c3">p</font> &amp; <font color="Maroon" title="c5">J</font>,<font color="Maroon" title="c2">v</font> <a href="valuat_1.html#R1" title="VALUAT_1:pred.1">|=</a> <font color="Maroon" title="c4">q</font> ) )
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:26"><span class="lab"><font color="Green" title="E16">A1</font></span></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>
