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<b>let </b><font color="Maroon">B1</font> be    <a href="subset_1.html#M1">Element</a> of <span class="p1"><a href="zfmisc_1.html#K2">[:</a><span class="default"><a href="substut1.html#K16" target="_self">QC-Sub-WFF</a> ,<a href="qc_lang1.html#K2">bound_QC-variables</a> </span><a href="zfmisc_1.html#K2">:]</a></span>, <font color="Maroon">B2</font> be    <a href="subset_1.html#M1">Element</a> of <span class="p1"><a href="zfmisc_1.html#K2">[:</a><span class="default"><a href="substut1.html#K16" target="_self">QC-Sub-WFF</a> ,<a href="qc_lang1.html#K2">bound_QC-variables</a> </span><a href="zfmisc_1.html#K2">:]</a></span>;<br/><b>let </b><font color="Maroon">SQ1</font> be    <a href="substut1.html#M1" target="_self">second_Q_comp</a> of <font color="Maroon">B1</font>;<br/><b>let </b><font color="Maroon">SQ2</font> be    <a href="substut1.html#M1" target="_self">second_Q_comp</a> of <font color="Maroon">B2</font>;<br/>





<b>assume </b><a NAME="E1:65"/><i><font color="Green">E40</font></i>: 
( <font color="Maroon">B1</font> is <a href="substut1.html#V3" target="_self">quantifiable</a> &amp; <font color="Maroon">B2</font> is <a href="substut1.html#V3" target="_self">quantifiable</a> &amp;  <a href="substut1.html#K24" target="_self">Sub_All</a> <font color="Maroon">B1</font>,<font color="Maroon">SQ1</font> <a href="hidden.html#R1">=</a>  <a href="substut1.html#K24" target="_self">Sub_All</a> <font color="Maroon">B2</font>,<font color="Maroon">SQ2</font> )
 ;<br/>

<a NAME="E2:65"/><i><font color="Green">E43</font></i>: 
(  <a href="substut1.html#K24" target="_self">Sub_All</a> <font color="Maroon">B1</font>,<font color="Maroon">SQ1</font> <a href="hidden.html#R1">=</a> <span class="p1"><a href="domain_1.html#K1">[</a><span class="default"><span class="p2">(<span class="default"><a href="qc_lang1.html#K14">All</a> <span class="p3">(<span class="default"><font color="Maroon">B1</font> <a href="substut1.html#K23" target="_self">`2</a> </span>)</span>,<span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">B1</font> <a href="substut1.html#K22" target="_self">`1</a> </span>)</span> <a href="substut1.html#K18" target="_self">`1</a> </span>)</span></span>)</span>,<font color="Maroon">SQ1</font></span><a href="domain_1.html#K1">]</a></span> &amp;  <a href="substut1.html#K24" target="_self">Sub_All</a> <font color="Maroon">B2</font>,<font color="Maroon">SQ2</font> <a href="hidden.html#R1">=</a> <span class="p1"><a href="domain_1.html#K1">[</a><span class="default"><span class="p2">(<span class="default"><a href="qc_lang1.html#K14">All</a> <span class="p3">(<span class="default"><font color="Maroon">B2</font> <a href="substut1.html#K23" target="_self">`2</a> </span>)</span>,<span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">B2</font> <a href="substut1.html#K22" target="_self">`1</a> </span>)</span> <a href="substut1.html#K18" target="_self">`1</a> </span>)</span></span>)</span>,<font color="Maroon">SQ2</font></span><a href="domain_1.html#K1">]</a></span> )
 
<b>by </b><i>, </i>;<br/>
<a NAME="E3:65"/><b>then </b>
(  <a href="qc_lang1.html#K14">All</a> <span class="p1">(<span class="default"><font color="Maroon">B1</font> <a href="substut1.html#K23" target="_self">`2</a> </span>)</span>,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">B1</font> <a href="substut1.html#K22" target="_self">`1</a> </span>)</span> <a href="substut1.html#K18" target="_self">`1</a> </span>)</span> <a href="hidden.html#R1">=</a>  <a href="qc_lang1.html#K14">All</a> <span class="p1">(<span class="default"><font color="Maroon">B2</font> <a href="substut1.html#K23" target="_self">`2</a> </span>)</span>,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">B2</font> <a href="substut1.html#K22" target="_self">`1</a> </span>)</span> <a href="substut1.html#K18" target="_self">`1</a> </span>)</span> &amp; <font color="Maroon">SQ1</font> <a href="hidden.html#R1">=</a> <font color="Maroon">SQ2</font> )
 
<b>by </b><i>, <a class="ref" href="zfmisc_1.html#T33">ZFMISC_1:33</a></i>;<br/>
<a NAME="E4:65"/><b>then </b><i><font color="Green">E45</font></i>: 
( <font color="Maroon">B1</font> <a href="substut1.html#K23" target="_self">`2</a>  <a href="hidden.html#R1">=</a> <font color="Maroon">B2</font> <a href="substut1.html#K23" target="_self">`2</a>  &amp; <span class="p1">(<span class="default"><font color="Maroon">B1</font> <a href="substut1.html#K22" target="_self">`1</a> </span>)</span> <a href="substut1.html#K18" target="_self">`1</a>  <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><font color="Maroon">B2</font> <a href="substut1.html#K22" target="_self">`1</a> </span>)</span> <a href="substut1.html#K18" target="_self">`1</a>  )
 
<b>by </b><i><a class="ref" href="qc_lang2.html#T6">QC_LANG2:6</a></i>;<br/>
<a NAME="E5:65"/><i><font color="Green">E46</font></i>: 
<span class="p1">(<span class="default"><font color="Maroon">B1</font> <a href="substut1.html#K22" target="_self">`1</a> </span>)</span> <a href="substut1.html#K19" target="_self">`2</a>  <a href="hidden.html#R1">=</a> <a href="substut1.html#K15" target="_self">QSub</a>  <a href="funct_1.html#K1">.</a> <span class="p1"><a href="domain_1.html#K1">[</a><span class="default"><span class="p2">(<span class="default"><a href="qc_lang1.html#K14">All</a> <span class="p3">(<span class="default"><font color="Maroon">B1</font> <a href="substut1.html#K23" target="_self">`2</a> </span>)</span>,<span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">B1</font> <a href="substut1.html#K22" target="_self">`1</a> </span>)</span> <a href="substut1.html#K18" target="_self">`1</a> </span>)</span></span>)</span>,<font color="Maroon">SQ1</font></span><a href="domain_1.html#K1">]</a></span>
 
<b>by </b><i>, </i>;<br/>
<a NAME="E6:65"/><i><font color="Green">E47</font></i>: 
( <font color="Maroon">B1</font> <a href="substut1.html#K22" target="_self">`1</a>  <a href="hidden.html#R1">=</a> <span class="p1"><a href="domain_1.html#K1">[</a><span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">B1</font> <a href="substut1.html#K22" target="_self">`1</a> </span>)</span> <a href="substut1.html#K18" target="_self">`1</a> </span>)</span>,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">B1</font> <a href="substut1.html#K22" target="_self">`1</a> </span>)</span> <a href="substut1.html#K19" target="_self">`2</a> </span>)</span></span><a href="domain_1.html#K1">]</a></span> &amp; <font color="Maroon">B2</font> <a href="substut1.html#K22" target="_self">`1</a>  <a href="hidden.html#R1">=</a> <span class="p1"><a href="domain_1.html#K1">[</a><span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">B2</font> <a href="substut1.html#K22" target="_self">`1</a> </span>)</span> <a href="substut1.html#K18" target="_self">`1</a> </span>)</span>,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">B2</font> <a href="substut1.html#K22" target="_self">`1</a> </span>)</span> <a href="substut1.html#K19" target="_self">`2</a> </span>)</span></span><a href="domain_1.html#K1">]</a></span> )
 
<b>by </b><i/>;<br/>
<a NAME="E7:65"/>
(  ex <font color="Olive">a</font>, <font color="Olive">b</font> being   <a href="hidden.html#M1">set</a>  st <br/>( <font color="Olive">a</font> <a href="hidden.html#R2">in</a>  <a href="substut1.html#K16" target="_self">QC-Sub-WFF</a>  &amp; <font color="Olive">b</font> <a href="hidden.html#R2">in</a>  <a href="qc_lang1.html#K2">bound_QC-variables</a>  &amp; <font color="Maroon">B1</font> <a href="hidden.html#R1">=</a> <span class="p1"><a href="tarski.html#K4">[</a><span class="default"><font color="Olive">a</font>,<font color="Olive">b</font></span><a href="tarski.html#K4">]</a></span> ) &amp;  ex <font color="Olive">a</font>, <font color="Olive">b</font> being   <a href="hidden.html#M1">set</a>  st <br/>( <font color="Olive">a</font> <a href="hidden.html#R2">in</a>  <a href="substut1.html#K16" target="_self">QC-Sub-WFF</a>  &amp; <font color="Olive">b</font> <a href="hidden.html#R2">in</a>  <a href="qc_lang1.html#K2">bound_QC-variables</a>  &amp; <font color="Maroon">B2</font> <a href="hidden.html#R1">=</a> <span class="p1"><a href="tarski.html#K4">[</a><span class="default"><font color="Olive">a</font>,<font color="Olive">b</font></span><a href="tarski.html#K4">]</a></span> ) )
 
<b>by </b><i><a class="ref" href="zfmisc_1.html#D2">ZFMISC_1:def 2</a></i>;<br/>
<a NAME="E8:65"/><b>then </b>
( <font color="Maroon">B1</font> <a href="hidden.html#R1">=</a> <span class="p1"><a href="substut1.html#K25" target="_self">[</a><span class="default"><span class="p2">(<span class="default"><font color="Maroon">B1</font> <a href="substut1.html#K22" target="_self">`1</a> </span>)</span>,<span class="p2">(<span class="default"><font color="Maroon">B1</font> <a href="substut1.html#K23" target="_self">`2</a> </span>)</span></span><a href="substut1.html#K25" target="_self">]</a></span> &amp; <font color="Maroon">B2</font> <a href="hidden.html#R1">=</a> <span class="p1"><a href="substut1.html#K25" target="_self">[</a><span class="default"><span class="p2">(<span class="default"><font color="Maroon">B2</font> <a href="substut1.html#K22" target="_self">`1</a> </span>)</span>,<span class="p2">(<span class="default"><font color="Maroon">B2</font> <a href="substut1.html#K23" target="_self">`2</a> </span>)</span></span><a href="substut1.html#K25" target="_self">]</a></span> )
 
<b>by </b><i><a class="ref" href="mcart_1.html#T8">MCART_1:8</a></i>;<br/>
<b>hence </b><a NAME="E9:65"/>
<font color="Maroon">B1</font> <a href="hidden.html#R1">=</a> <font color="Maroon">B2</font>
 <b>by </b><i>, <a class="ref" href="substut1.html#D3" target="_self">Def3</a>, <a class="txt" href="substut1.html#E1:65"><i><font color="Green">E40</font></i></a>, , , </i>;<br/>


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