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<b>let </b><font color="Maroon">x</font> be   <a href="qc_lang1.html#NM3">bound_QC-variable</a>;<br/><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>let </b><font color="Maroon">xSQ</font> be    <a href="substut1.html#M1" target="_self">second_Q_comp</a> of <span class="p1"><a href="substut1.html#K25" target="_self">[</a><span class="default"><font color="Maroon">S</font>,<font color="Maroon">x</font></span><a href="substut1.html#K25" target="_self">]</a></span>;<br/>





<b>set </b><font color="Maroon">S'</font> =  <a href="substut1.html#K24" target="_self">Sub_All</a> <span class="p1"><a href="substut1.html#K25" target="_self">[</a><span class="default"><font color="Maroon">S</font>,<font color="Maroon">x</font></span><a href="substut1.html#K25" target="_self">]</a></span>,<font color="Maroon">xSQ</font>;<br/>
<b>assume </b><a NAME="E1:95"/><i><font color="Green">E40</font></i>: 
(  <a href="substut1.html#K37" target="_self">CQC_Sub</a> <font color="Maroon">S</font> is    <a href="subset_1.html#M2">Element</a> of  <a href="cqc_lang.html#K7">CQC-WFF</a>  &amp; <span class="p1"><a href="substut1.html#K25" target="_self">[</a><span class="default"><font color="Maroon">S</font>,<font color="Maroon">x</font></span><a href="substut1.html#K25" target="_self">]</a></span> is <a href="substut1.html#V3" target="_self">quantifiable</a> )
 ;<br/>

<a NAME="E2:95"/><b>then </b><i><font color="Green">E43</font></i>: 
 <a href="substut1.html#K24" target="_self">Sub_All</a> <span class="p1"><a href="substut1.html#K25" target="_self">[</a><span class="default"><font color="Maroon">S</font>,<font color="Maroon">x</font></span><a href="substut1.html#K25" target="_self">]</a></span>,<font color="Maroon">xSQ</font> is <a href="substut1.html#V7" target="_self">Sub_universal</a>
 
<b>by </b><i/>;<br/>
<a NAME="E3:95"/>
 <a href="substut1.html#K31" target="_self">Sub_the_scope_of</a> <span class="p1">(<span class="default"><a href="substut1.html#K24" target="_self">Sub_All</a> <span class="p2"><a href="substut1.html#K25" target="_self">[</a><span class="default"><font color="Maroon">S</font>,<font color="Maroon">x</font></span><a href="substut1.html#K25" target="_self">]</a></span>,<font color="Maroon">xSQ</font></span>)</span> <a href="hidden.html#R1">=</a> <span class="p1"><a href="substut1.html#K25" target="_self">[</a><span class="default"><font color="Maroon">S</font>,<font color="Maroon">x</font></span><a href="substut1.html#K25" target="_self">]</a></span> <a href="substut1.html#K22" target="_self">`1</a> 
 
<b>by </b><i><a class="ref" href="substut1.html#D8" target="_self">Def8</a>, </i>;<br/>
<a NAME="E4:95"/><b>then </b>
 <a href="substut1.html#K36" target="_self">Quant</a> <span class="p1">(<span class="default"><a href="substut1.html#K24" target="_self">Sub_All</a> <span class="p2"><a href="substut1.html#K25" target="_self">[</a><span class="default"><font color="Maroon">S</font>,<font color="Maroon">x</font></span><a href="substut1.html#K25" target="_self">]</a></span>,<font color="Maroon">xSQ</font></span>)</span>,<span class="p1">(<span class="default"><a href="substut1.html#K37" target="_self">CQC_Sub</a> <span class="p2">(<span class="default"><a href="substut1.html#K31" target="_self">Sub_the_scope_of</a> <span class="p3">(<span class="default"><a href="substut1.html#K24" target="_self">Sub_All</a> <span class="p4"><a href="substut1.html#K25" target="_self">[</a><span class="default"><font color="Maroon">S</font>,<font color="Maroon">x</font></span><a href="substut1.html#K25" target="_self">]</a></span>,<font color="Maroon">xSQ</font></span>)</span></span>)</span></span>)</span> <a href="hidden.html#R1">=</a>  <a href="qc_lang1.html#K14">All</a> <span class="p1">(<span class="default"><a href="substut1.html#K35" target="_self">S_Bound</a> <span class="p2">(<span class="default"><a href="substut1.html#K32" target="_self">@</a> <span class="p3">(<span class="default"><a href="substut1.html#K24" target="_self">Sub_All</a> <span class="p4"><a href="substut1.html#K25" target="_self">[</a><span class="default"><font color="Maroon">S</font>,<font color="Maroon">x</font></span><a href="substut1.html#K25" target="_self">]</a></span>,<font color="Maroon">xSQ</font></span>)</span></span>)</span></span>)</span>,<span class="p1">(<span class="default"><a href="substut1.html#K37" target="_self">CQC_Sub</a> <font color="Maroon">S</font></span>)</span>
 
<b>by </b><i><a class="ref" href="mcart_1.html#T7">MCART_1:7</a></i>;<br/>
<a NAME="E5:95"/><b>then </b>
 <a href="substut1.html#K36" target="_self">Quant</a> <span class="p1">(<span class="default"><a href="substut1.html#K24" target="_self">Sub_All</a> <span class="p2"><a href="substut1.html#K25" target="_self">[</a><span class="default"><font color="Maroon">S</font>,<font color="Maroon">x</font></span><a href="substut1.html#K25" target="_self">]</a></span>,<font color="Maroon">xSQ</font></span>)</span>,<span class="p1">(<span class="default"><a href="substut1.html#K37" target="_self">CQC_Sub</a> <span class="p2">(<span class="default"><a href="substut1.html#K31" target="_self">Sub_the_scope_of</a> <span class="p3">(<span class="default"><a href="substut1.html#K24" target="_self">Sub_All</a> <span class="p4"><a href="substut1.html#K25" target="_self">[</a><span class="default"><font color="Maroon">S</font>,<font color="Maroon">x</font></span><a href="substut1.html#K25" target="_self">]</a></span>,<font color="Maroon">xSQ</font></span>)</span></span>)</span></span>)</span> is    <a href="subset_1.html#M2">Element</a> of  <a href="cqc_lang.html#K7">CQC-WFF</a> 
 
<b>by </b><i><a class="ref" href="substut1.html#D8" target="_self">Def8</a>, <a class="ref" href="cqc_lang.html#T23">CQC_LANG:23</a></i>;<br/>
<b>hence </b><a NAME="E6:95"/>
 <a href="substut1.html#K37" target="_self">CQC_Sub</a> <span class="p1">(<span class="default"><a href="substut1.html#K24" target="_self">Sub_All</a> <span class="p2"><a href="substut1.html#K25" target="_self">[</a><span class="default"><font color="Maroon">S</font>,<font color="Maroon">x</font></span><a href="substut1.html#K25" target="_self">]</a></span>,<font color="Maroon">xSQ</font></span>)</span> is    <a href="subset_1.html#M2">Element</a> of  <a href="cqc_lang.html#K7">CQC-WFF</a> 
 <b>by </b><i>, </i>;<br/>


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