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

<b>let </b><font color="Maroon">X</font> be   <a href="subset_1.html#NM2">Subset</a> of <a href="cqc_lang.html#K7">CQC-WFF</a> ;<br/><b>let </b><font color="Maroon">Y</font> be   <a href="subset_1.html#NM2">Subset</a> of <a href="cqc_lang.html#K7">CQC-WFF</a> ;<br/>



<div><i><font color="Green">E39</font></i>: <a class="txt" onclick="hs2(this)" href="javascript:()" title="20_1"><b>now </b></a><div class="add"><b>assume </b><a NAME="E1:20_1"/><i><font color="Green">E42</font></i>: 
<font color="Maroon">X</font> <a href="cqc_the3.html#R4" target="_self">|-|</a> <font color="Maroon">Y</font>
 ;<br/><div><a class="txt" onclick="hs2(this)" href="javascript:()" title="20_1_1"><b>now </b></a><div class="add"><b>let </b><font color="Maroon">p</font> be    <a href="subset_1.html#M2">Element</a> of  <a href="cqc_lang.html#K7">CQC-WFF</a> ;<br/><b>assume </b><a NAME="E1:20_1_1"/>
<font color="Maroon">p</font> <a href="hidden.html#R2">in</a> <font color="Maroon">Y</font>
 ;<br/><a NAME="E2:20_1_1"/><b>then </b>
<font color="Maroon">Y</font> <a href="cqc_the1.html#R3">|-</a> <font color="Maroon">p</font>
 <b>by </b><i/>;<br/><b>hence </b><a NAME="E3:20_1_1"/>
<font color="Maroon">X</font> <a href="cqc_the1.html#R3">|-</a> <font color="Maroon">p</font>
 <b>by </b><i>, </i>;<br/></div><b>end;</b></div><b>hence </b><a NAME="E3:20_1"/>
<font color="Maroon">X</font> <a href="cqc_the3.html#R2" target="_self">|-</a> <font color="Maroon">Y</font>
 <b>by </b><i/>;<br/><div><a class="txt" onclick="hs2(this)" href="javascript:()" title="20_1_2"><b>now </b></a><div class="add"><b>let </b><font color="Maroon">p</font> be    <a href="subset_1.html#M2">Element</a> of  <a href="cqc_lang.html#K7">CQC-WFF</a> ;<br/><b>assume </b><a NAME="E1:20_1_2"/>
<font color="Maroon">p</font> <a href="hidden.html#R2">in</a> <font color="Maroon">X</font>
 ;<br/><a NAME="E2:20_1_2"/><b>then </b>
<font color="Maroon">X</font> <a href="cqc_the1.html#R3">|-</a> <font color="Maroon">p</font>
 <b>by </b><i/>;<br/><b>hence </b><a NAME="E3:20_1_2"/>
<font color="Maroon">Y</font> <a href="cqc_the1.html#R3">|-</a> <font color="Maroon">p</font>
 <b>by </b><i>, </i>;<br/></div><b>end;</b></div><b>hence </b><a NAME="E5:20_1"/>
<font color="Maroon">Y</font> <a href="cqc_the3.html#R2" target="_self">|-</a> <font color="Maroon">X</font>
 <b>by </b><i/>;<br/></div><b>end;</b></div>
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="20_2"><b>now </b></a><div class="add"><b>assume </b><b>that </b><br/><a NAME="E1:20_2"/><i><font color="Green">E43</font></i>: 
<font color="Maroon">X</font> <a href="cqc_the3.html#R2" target="_self">|-</a> <font color="Maroon">Y</font>
 <b>and </b><br/><a NAME="E2:20_2"/><i><font color="Green">E60</font></i>: 
<font color="Maroon">Y</font> <a href="cqc_the3.html#R2" target="_self">|-</a> <font color="Maroon">X</font>
 ;<br/><div><a class="txt" onclick="hs2(this)" href="javascript:()" title="20_2_1"><b>now </b></a><div class="add"><b>let </b><font color="Maroon">p</font> be    <a href="subset_1.html#M2">Element</a> of  <a href="cqc_lang.html#K7">CQC-WFF</a> ;<br/><div><i><font color="Green">E61</font></i>: <a class="txt" onclick="hs2(this)" href="javascript:()" title="20_2_1_1"><b>now </b></a><div class="add"><b>assume </b><a NAME="E1:20_2_1_1"/>
<font color="Maroon">X</font> <a href="cqc_the1.html#R3">|-</a> <font color="Maroon">p</font>
 ;<br/><a NAME="E2:20_2_1_1"/><b>then </b>
<font color="Maroon">X</font> <a href="cqc_the3.html#R2" target="_self">|-</a> <span class="p1"><a href="domain_1.html#K6">{</a><span class="default"><font color="Maroon">p</font></span><a href="domain_1.html#K6">}</a></span>
 <b>by </b><i/>;<br/><a NAME="E3:20_2_1_1"/><b>then </b>
<font color="Maroon">Y</font> <a href="cqc_the3.html#R2" target="_self">|-</a> <span class="p1"><a href="domain_1.html#K6">{</a><span class="default"><font color="Maroon">p</font></span><a href="domain_1.html#K6">}</a></span>
 <b>by </b><i>, </i>;<br/><b>hence </b><a NAME="E4:20_2_1_1"/>
<font color="Maroon">Y</font> <a href="cqc_the1.html#R3">|-</a> <font color="Maroon">p</font>
 <b>by </b><i/>;<br/></div><b>end;</b></div><div><a class="txt" onclick="hs2(this)" href="javascript:()" title="20_2_1_2"><b>now </b></a><div class="add"><b>assume </b><a NAME="E1:20_2_1_2"/>
<font color="Maroon">Y</font> <a href="cqc_the1.html#R3">|-</a> <font color="Maroon">p</font>
 ;<br/><a NAME="E2:20_2_1_2"/><b>then </b>
<font color="Maroon">Y</font> <a href="cqc_the3.html#R2" target="_self">|-</a> <span class="p1"><a href="domain_1.html#K6">{</a><span class="default"><font color="Maroon">p</font></span><a href="domain_1.html#K6">}</a></span>
 <b>by </b><i/>;<br/><a NAME="E3:20_2_1_2"/><b>then </b>
<font color="Maroon">X</font> <a href="cqc_the3.html#R2" target="_self">|-</a> <span class="p1"><a href="domain_1.html#K6">{</a><span class="default"><font color="Maroon">p</font></span><a href="domain_1.html#K6">}</a></span>
 <b>by </b><i>, </i>;<br/><b>hence </b><a NAME="E4:20_2_1_2"/>
<font color="Maroon">X</font> <a href="cqc_the1.html#R3">|-</a> <font color="Maroon">p</font>
 <b>by </b><i/>;<br/></div><b>end;</b></div><b>hence </b><a NAME="E3:20_2_1"/>
( <font color="Maroon">X</font> <a href="cqc_the1.html#R3">|-</a> <font color="Maroon">p</font> iff <font color="Maroon">Y</font> <a href="cqc_the1.html#R3">|-</a> <font color="Maroon">p</font> )
 <b>by </b><i/>;<br/></div><b>end;</b></div><b>hence </b><a NAME="E4:20_2"/>
<font color="Maroon">X</font> <a href="cqc_the3.html#R4" target="_self">|-|</a> <font color="Maroon">Y</font>
 <b>by </b><i/>;<br/></div><b>end;</b></div>
<b>hence </b><a NAME="E3:20"/>
( <font color="Maroon">X</font> <a href="cqc_the3.html#R4" target="_self">|-|</a> <font color="Maroon">Y</font> iff ( <font color="Maroon">X</font> <a href="cqc_the3.html#R2" target="_self">|-</a> <font color="Maroon">Y</font> &amp; <font color="Maroon">Y</font> <a href="cqc_the3.html#R2" target="_self">|-</a> <font color="Maroon">X</font> ) )
 <b>by </b><i/>;<br/>


</div>
