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

<b>set </b><font color="Maroon" title="c1">X</font> = <span class="p1">{<span class="default"> <font color="Olive" title="b1">S</font> where <font color="Olive" title="b1">S</font> is    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of  <a href="substut1.html#K16" title="SUBSTUT1:func.16">QC-Sub-WFF</a>  : <font color="Olive" title="b1">S</font> <a href="substut1.html#K18" title="SUBSTUT1:func.18">`1</a>  is    <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>  </span>}</span> ;<br/>
<a NAME="E1:87_1_1"/>
<span class="p1">{<span class="default"> <font color="Olive" title="b1">S</font> where <font color="Olive" title="b1">S</font> is    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of  <a href="substut1.html#K16" title="SUBSTUT1:func.16">QC-Sub-WFF</a>  : <font color="Olive" title="b1">S</font> <a href="substut1.html#K18" title="SUBSTUT1:func.18">`1</a>  is    <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>  </span>}</span>  <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a>  <a href="substut1.html#K16" title="SUBSTUT1:func.16">QC-Sub-WFF</a> 
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="87_1_1_1"><b>proof </b></a><div class="add">

<b>let </b><font color="Maroon" title="c2">a</font> be    <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a> ; <i><font color="Red">:: according to </font></i><a class="ref" href="tarski.html#D3" title="TARSKI:def.3">TARSKI:def 3</a> <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> (  not <font color="Maroon" title="c2">a</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <span class="p1">{<span class="default"> <font color="Olive" title="b1">S</font> where <font color="Olive" title="b1">S</font> is    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of  <a href="substut1.html#K16" title="SUBSTUT1:func.16">QC-Sub-WFF</a>  : <font color="Olive" title="b1">S</font> <a href="substut1.html#K18" title="SUBSTUT1:func.18">`1</a>  is    <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>  </span>}</span>  or <font color="Maroon" title="c2">a</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="substut1.html#K16" title="SUBSTUT1:func.16">QC-Sub-WFF</a>  )</span><br/>

<b>assume </b><a NAME="E1:87_1_1_1"/>
<font color="Maroon" title="c2">a</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <span class="p1">{<span class="default"> <font color="Olive" title="b1">S</font> where <font color="Olive" title="b1">S</font> is    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of  <a href="substut1.html#K16" title="SUBSTUT1:func.16">QC-Sub-WFF</a>  : <font color="Olive" title="b1">S</font> <a href="substut1.html#K18" title="SUBSTUT1:func.18">`1</a>  is    <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>  </span>}</span> 
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> <font color="Maroon" title="c2">a</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="substut1.html#K16" title="SUBSTUT1:func.16">QC-Sub-WFF</a> </span><br/>

<b>then consider </b><font color="Maroon" title="c3">S</font> being    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of  <a href="substut1.html#K16" title="SUBSTUT1:func.16">QC-Sub-WFF</a> <b> such that </b><br/><a NAME="E3:87_1_1_1"/><i><font color="Green" title="E52">A1</font></i>: 
( <font color="Maroon" title="c2">a</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c3">S</font> &amp; <font color="Maroon" title="c3">S</font> <a href="substut1.html#K18" title="SUBSTUT1:func.18">`1</a>  is    <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/>
<b>thus </b><a NAME="E4:87_1_1_1"/>
<font color="Maroon" title="c2">a</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="substut1.html#K16" title="SUBSTUT1:func.16">QC-Sub-WFF</a> 
 <b>by </b><i><a class="txt" href="#E3:87_1_1_1"><i><font color="Green" title="E52">A1</font></i></a></i>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> verum</span><br/>


</div><b>end;</b></div>
<b>hence </b><a NAME="E2:87_1_1"/>
<span class="p1">{<span class="default"> <font color="Olive" title="b1">S</font> where <font color="Olive" title="b1">S</font> is    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of  <a href="substut1.html#K16" title="SUBSTUT1:func.16">QC-Sub-WFF</a>  : <font color="Olive" title="b1">S</font> <a href="substut1.html#K18" title="SUBSTUT1:func.18">`1</a>  is    <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>  </span>}</span>  is   <a href="subset_1.html#NM2" title="SUBSET_1:NM.2">Subset</a> of <a href="substut1.html#K16" title="SUBSTUT1:func.16">QC-Sub-WFF</a> 
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> verum</span><br/>


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