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

<b>let </b><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> ;<br/><b>let </b><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#K7" title="CQC_LANG:func.7">CQC-WFF</a> ;<br/><b>let </b><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>;<br/>







<b>assume </b><b>that </b><br/><a NAME="E1:59"/><i><font color="Green" title="E40">A1</font></i>: 
<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>
 <b>and </b><br/><a NAME="E2:59"/><i><font color="Green" title="E41">A2</font></i>: 
<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#K12" title="CQC_LANG:func.12">=&gt;</a> <font color="Maroon" title="c3">q</font>
 ;<br/>

<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="59_1"><b>now </b></a><div class="add"><b>let </b><font color="Maroon" title="c5">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="c1">A</font>;<br/><a NAME="E1:59_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#K12" title="CQC_LANG:func.12">=&gt;</a> <font color="Maroon" title="c3">q</font> )
 <b>by </b><i><a class="txt" href="valuat_1.html#E1:59"><i><font color="Green" title="E40">A1</font></i></a>, <a class="txt" href="valuat_1.html#E2:59"><i><font color="Green" title="E41">A2</font></i></a>, <a class="ref" href="valuat_1.html#D13" target="_self" title="VALUAT_1:def.13">Def13</a></i>;<br/><b>hence </b><a NAME="E2:59_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>
 <b>by </b><i><a class="ref" href="valuat_1.html#T36" target="_self" title="VALUAT_1:th.36">Th36</a></i>;<br/></div><b>end;</b></div>
<b>hence </b><a NAME="E4:59"/>
<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>
 <b>by </b><i><a class="ref" href="valuat_1.html#D13" target="_self" title="VALUAT_1:def.13">Def13</a></i>;<br/>


</div>
