<?xml version="1.0"?>
<div class="add">

<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="Red">::  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#K4" title="CQC_LANG:func.4">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>  st <font color="Olive" title="b3">J</font> <a href="valuat_1.html#R2" title="VALUAT_1:pred.2">|=</a> <font color="Olive" title="b1">p</font> &amp; <font color="Olive" title="b3">J</font> <a href="valuat_1.html#R2" title="VALUAT_1:pred.2">|=</a> <font color="Olive" title="b1">p</font> <a href="cqc_lang.html#K9" title="CQC_LANG:func.9">=&gt;</a> <font color="Olive" title="b2">q</font> holds <br/><font color="Olive" title="b3">J</font> <a href="valuat_1.html#R2" title="VALUAT_1:pred.2">|=</a> <font color="Olive" title="b2">q</font></span><br/><span class="kw">let </span><font color="Maroon" title="c2">p</font>, <font color="Maroon" title="c3">q</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:()"><span class="comment"><font color="Red">::  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>  st <font color="Olive" title="b1">J</font> <a href="valuat_1.html#R2" title="VALUAT_1:pred.2">|=</a> <font color="Maroon" title="c2">p</font> &amp; <font color="Olive" title="b1">J</font> <a href="valuat_1.html#R2" title="VALUAT_1:pred.2">|=</a> <font color="Maroon" title="c2">p</font> <a href="cqc_lang.html#K9" title="CQC_LANG:func.9">=&gt;</a> <font color="Maroon" title="c3">q</font> holds <br/><font color="Olive" title="b1">J</font> <a href="valuat_1.html#R2" title="VALUAT_1:pred.2">|=</a> <font color="Maroon" title="c3">q</font></span><br/><span class="kw">let </span><font color="Maroon" title="c4">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="Red">::  thesis: </font></span></a><span class="hide"> ( <font color="Maroon" title="c4">J</font> <a href="valuat_1.html#R2" title="VALUAT_1:pred.2">|=</a> <font color="Maroon" title="c2">p</font> &amp; <font color="Maroon" title="c4">J</font> <a href="valuat_1.html#R2" title="VALUAT_1:pred.2">|=</a> <font color="Maroon" title="c2">p</font> <a href="cqc_lang.html#K9" title="CQC_LANG:func.9">=&gt;</a> <font color="Maroon" title="c3">q</font> implies <font color="Maroon" title="c4">J</font> <a href="valuat_1.html#R2" title="VALUAT_1:pred.2">|=</a> <font color="Maroon" title="c3">q</font> )</span><br/>







<span class="kw">assume </span><a NAME="E1:66"/><span class="lab"><font color="Green" title="E35">A1</font></span>: 
( <font color="Maroon" title="c4">J</font> <a href="valuat_1.html#R2" title="VALUAT_1:pred.2">|=</a> <font color="Maroon" title="c2">p</font> &amp; <font color="Maroon" title="c4">J</font> <a href="valuat_1.html#R2" title="VALUAT_1:pred.2">|=</a> <font color="Maroon" title="c2">p</font> <a href="cqc_lang.html#K9" title="CQC_LANG:func.9">=&gt;</a> <font color="Maroon" title="c3">q</font> )
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> <font color="Maroon" title="c4">J</font> <a href="valuat_1.html#R2" title="VALUAT_1:pred.2">|=</a> <font color="Maroon" title="c3">q</font></span><br/>

<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="66_1"><span class="kw">now </span></a><div class="add"><span class="kw">let </span><font color="Maroon" title="c5">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="Red">::  thesis: </font></span></a><span class="hide"> <font color="Maroon" title="c4">J</font>,<font color="Maroon" title="c5">v</font> <a href="valuat_1.html#R1" title="VALUAT_1:pred.1">|=</a> <font color="Maroon" title="c3">q</font></span><br/><a NAME="E1:66_1"/>
( <font color="Maroon" title="c4">J</font>,<font color="Maroon" title="c5">v</font> <a href="valuat_1.html#R1" title="VALUAT_1:pred.1">|=</a> <font color="Maroon" title="c2">p</font> &amp; <font color="Maroon" title="c4">J</font>,<font color="Maroon" title="c5">v</font> <a href="valuat_1.html#R1" title="VALUAT_1:pred.1">|=</a> <font color="Maroon" title="c2">p</font> <a href="cqc_lang.html#K9" title="CQC_LANG:func.9">=&gt;</a> <font color="Maroon" title="c3">q</font> )
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:66"><span class="lab"><font color="Green" title="E35">A1</font></span></a>, <a class="ref" href="valuat_1.html#D13" target="_self" title="VALUAT_1:def.13">Def13</a></span>;<br/><span class="kw">hence </span><a NAME="E2:66_1"/>
<font color="Maroon" title="c4">J</font>,<font color="Maroon" title="c5">v</font> <a href="valuat_1.html#R1" title="VALUAT_1:pred.1">|=</a> <font color="Maroon" title="c3">q</font>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="valuat_1.html#T36" target="_self" title="VALUAT_1:th.36">Th36</a></span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> verum</span><br/></div><span class="kw">end;</span></div>
<span class="kw">hence </span><a NAME="E3:66"/>
<font color="Maroon" title="c4">J</font> <a href="valuat_1.html#R2" title="VALUAT_1:pred.2">|=</a> <font color="Maroon" title="c3">q</font>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="valuat_1.html#D13" target="_self" title="VALUAT_1:def.13">Def13</a></span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> verum</span><br/>


</div>
