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<b>let </b><font color="Maroon">S</font> be    <a href="subset_1.html#M1">Element</a> of  <a href="substut1.html#K16" target="_self">QC-Sub-WFF</a> ;<br/>

<b>assume </b><a NAME="E1:70"/>
<font color="Maroon">S</font> is <a href="substut1.html#V7" target="_self">Sub_universal</a>
 ;<br/>

<b>then consider </b><font color="Maroon">B</font> being    <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">SQ</font> being    <a href="substut1.html#M1" target="_self">second_Q_comp</a> of <font color="Maroon">B</font><b> such that </b><br/><a NAME="E3:70"/><i><font color="Green">E40</font></i>: 
( <font color="Maroon">S</font> <a href="hidden.html#R1">=</a>  <a href="substut1.html#K24" target="_self">Sub_All</a> <font color="Maroon">B</font>,<font color="Maroon">SQ</font> &amp; <font color="Maroon">B</font> is <a href="substut1.html#V3" target="_self">quantifiable</a> )
 <b>by </b><i/>;<br/>
<a NAME="E4:70"/><i><font color="Green">E43</font></i>: 
<font color="Maroon">S</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">B</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">B</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">SQ</font></span><a href="domain_1.html#K1">]</a></span>
 
<b>by </b><i>, </i>;<br/>
<a NAME="E5:70"/><i><font color="Green">E45</font></i>: 
<span class="p1">(<span class="default"><a href="substut1.html#K31" target="_self">Sub_the_scope_of</a> <font color="Maroon">S</font></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">B</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>, </i>;<br/>
<a NAME="E6:70"/><i><font color="Green">E46</font></i>: 
<font color="Maroon">S</font> <a href="substut1.html#K18" target="_self">`1</a>  <a href="hidden.html#R1">=</a>  <a href="qc_lang1.html#K14">All</a> <span class="p1">(<span class="default"><font color="Maroon">B</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">B</font> <a href="substut1.html#K22" target="_self">`1</a> </span>)</span> <a href="substut1.html#K18" target="_self">`1</a> </span>)</span>
 
<b>by </b><i><a class="txt" href="substut1.html#E4:70"><i><font color="Green">E43</font></i></a>, <a class="ref" href="mcart_1.html#T7">MCART_1:7</a></i>;<br/>
<a NAME="E7:70"/>
 <a href="qc_lang1.html#K14">All</a> <span class="p1">(<span class="default"><font color="Maroon">B</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">B</font> <a href="substut1.html#K22" target="_self">`1</a> </span>)</span> <a href="substut1.html#K18" target="_self">`1</a> </span>)</span> is <a href="qc_lang1.html#V5">universal</a>
 
<b>by </b><i><a class="ref" href="qc_lang1.html#D20">QC_LANG1:def 20</a></i>;<br/>
<a NAME="E8:70"/><b>then </b>
 <a href="finseq_1.html#K3">len</a> <span class="p1">(<span class="default"><a href="qc_lang1.html#K10">@</a> <span class="p2">(<span class="default"><a href="qc_lang1.html#K21">the_scope_of</a> <span class="p3">(<span class="default"><a href="qc_lang1.html#K14">All</a> <span class="p4">(<span class="default"><font color="Maroon">B</font> <a href="substut1.html#K23" target="_self">`2</a> </span>)</span>,<span class="p4">(<span class="default"><span class="p5">(<span class="default"><font color="Maroon">B</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></span>)</span></span>)</span> <a href="xxreal_0.html#NR3" target="_self">&lt;</a>  <a href="finseq_1.html#K3">len</a> <span class="p1">(<span class="default"><a href="qc_lang1.html#K10">@</a> <span class="p2">(<span class="default"><font color="Maroon">S</font> <a href="substut1.html#K18" target="_self">`1</a> </span>)</span></span>)</span>
 
<b>by </b><i><a class="txt" href="substut1.html#E5:70"><i><font color="Green">E45</font></i></a>, <a class="ref" href="qc_lang1.html#T47">QC_LANG1:47</a></i>;<br/>
<b>hence </b><a NAME="E9:70"/>
 <a href="finseq_1.html#K3">len</a> <span class="p1">(<span class="default"><a href="qc_lang1.html#K10">@</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="substut1.html#K31" target="_self">Sub_the_scope_of</a> <font color="Maroon">S</font></span>)</span> <a href="substut1.html#K18" target="_self">`1</a> </span>)</span></span>)</span> <a href="xxreal_0.html#NR3" target="_self">&lt;</a>  <a href="finseq_1.html#K3">len</a> <span class="p1">(<span class="default"><a href="qc_lang1.html#K10">@</a> <span class="p2">(<span class="default"><font color="Maroon">S</font> <a href="substut1.html#K18" target="_self">`1</a> </span>)</span></span>)</span>
 <b>by </b><i>, <a class="ref" href="qc_lang2.html#T8">QC_LANG2:8</a></i>;<br/>


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