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

<b>let </b><font color="Maroon">p</font> be    <a href="subset_1.html#M1">Element</a> of  <a href="qc_lang1.html#K8">QC-WFF</a> ;<br/>

<b>thus </b><a NAME="E1:16"/>
( <font color="Maroon">p</font> is    <a href="subset_1.html#M2">Element</a> of  <a href="cqc_lang.html#K7" target="_self">CQC-WFF</a>  implies (  <a href="qc_lang3.html#K6">Fixed</a> <font color="Maroon">p</font> <a href="hidden.html#R1">=</a>  <a href="xboole_0.html#K1">{}</a>  &amp;  <a href="qc_lang3.html#K5">Free</a> <font color="Maroon">p</font> <a href="hidden.html#R1">=</a>  <a href="xboole_0.html#K1">{}</a>  ) )
 <div><a class="txt" onclick="hs2(this)" href="javascript:()" title="16_1"><b>proof </b></a><div class="add">

<b>assume </b><a NAME="E1:16_1"/>
<font color="Maroon">p</font> is    <a href="subset_1.html#M2">Element</a> of  <a href="cqc_lang.html#K7" target="_self">CQC-WFF</a> 
 ;<br/>

<a NAME="E2:16_1"/><b>then </b>
<font color="Maroon">p</font> <a href="hidden.html#R2">in</a>  <a href="cqc_lang.html#K7" target="_self">CQC-WFF</a> 
 
;<br/>
<a NAME="E3:16_1"/><b>then </b>
 ex <font color="Olive">s</font> being  <a href="qc_lang1.html#NM8">QC-formula</a> st <br/>( <font color="Olive">s</font> <a href="hidden.html#R1">=</a> <font color="Maroon">p</font> &amp;  <a href="qc_lang3.html#K6">Fixed</a> <font color="Olive">s</font> <a href="hidden.html#R1">=</a>  <a href="xboole_0.html#K1">{}</a>  &amp;  <a href="qc_lang3.html#K5">Free</a> <font color="Olive">s</font> <a href="hidden.html#R1">=</a>  <a href="xboole_0.html#K1">{}</a>  )
 
;<br/>
<b>hence </b><a NAME="E4:16_1"/>
(  <a href="qc_lang3.html#K6">Fixed</a> <font color="Maroon">p</font> <a href="hidden.html#R1">=</a>  <a href="xboole_0.html#K1">{}</a>  &amp;  <a href="qc_lang3.html#K5">Free</a> <font color="Maroon">p</font> <a href="hidden.html#R1">=</a>  <a href="xboole_0.html#K1">{}</a>  )
 ;<br/>


</div><b>end;</b></div>

<b>assume </b><a NAME="E2:16"/>
(  <a href="qc_lang3.html#K6">Fixed</a> <font color="Maroon">p</font> <a href="hidden.html#R1">=</a>  <a href="xboole_0.html#K1">{}</a>  &amp;  <a href="qc_lang3.html#K5">Free</a> <font color="Maroon">p</font> <a href="hidden.html#R1">=</a>  <a href="xboole_0.html#K1">{}</a>  )
 ;<br/>

<a NAME="E3:16"/><b>then </b>
<font color="Maroon">p</font> <a href="hidden.html#R2">in</a>  <a href="cqc_lang.html#K7" target="_self">CQC-WFF</a> 
 
;<br/>
<b>hence </b><a NAME="E4:16"/>
<font color="Maroon">p</font> is    <a href="subset_1.html#M2">Element</a> of  <a href="cqc_lang.html#K7" target="_self">CQC-WFF</a> 
 ;<br/>


</div>
