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<b>let </b><font color="Maroon" title="c1">x</font> be   <a href="qc_lang1.html#NM3" title="QC_LANG1:NM.3">bound_QC-variable</a>;<br/><b>let </b><font color="Maroon" title="c2">S</font> be    <a href="subset_1.html#M2" title="SUBSET_1:mode.2">Element</a> of  <a href="substut1.html#K38" title="SUBSTUT1:func.38">CQC-Sub-WFF</a> ;<br/><b>let </b><font color="Maroon" title="c3">xSQ</font> be    <a href="substut1.html#M1" title="SUBSTUT1:mode.1">second_Q_comp</a> of <span class="p1"><a href="sublemma.html#K8" title="SUBLEMMA:func.8">[</a><span class="default"><font color="Maroon" title="c2">S</font>,<font color="Maroon" title="c1">x</font></span><a href="sublemma.html#K8" title="SUBLEMMA:func.8">]</a></span>;<br/>





<b>assume </b><a NAME="E1:45"/><i><font color="Green" title="E35">A1</font></i>: 
<span class="p1"><a href="sublemma.html#K8" title="SUBLEMMA:func.8">[</a><span class="default"><font color="Maroon" title="c2">S</font>,<font color="Maroon" title="c1">x</font></span><a href="sublemma.html#K8" title="SUBLEMMA:func.8">]</a></span> is <a href="substut1.html#V3" title="SUBSTUT1:attr.3">quantifiable</a>
 ;<br/>

<a NAME="E2:45"/>
 <a href="sublemma.html#K11" title="SUBLEMMA:func.11">CQCSub_the_scope_of</a> <span class="p1">(<span class="default"><a href="sublemma.html#K10" title="SUBLEMMA:func.10">CQCSub_All</a> <span class="p2"><a href="sublemma.html#K8" title="SUBLEMMA:func.8">[</a><span class="default"><font color="Maroon" title="c2">S</font>,<font color="Maroon" title="c1">x</font></span><a href="sublemma.html#K8" title="SUBLEMMA:func.8">]</a></span>,<font color="Maroon" title="c3">xSQ</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"><a href="sublemma.html#K8" title="SUBLEMMA:func.8">[</a><span class="default"><font color="Maroon" title="c2">S</font>,<font color="Maroon" title="c1">x</font></span><a href="sublemma.html#K8" title="SUBLEMMA:func.8">]</a></span> <a href="sublemma.html#K9" title="SUBLEMMA:func.9">`1</a> 
 
<b>by </b><i><a class="txt" href="sublemma.html#E1:45"><i><font color="Green" title="E35">A1</font></i></a>, <a class="ref" href="sublemma.html#T30" target="_self" title="SUBLEMMA:th.30">Th30</a></i>;<br/>
<b>hence </b><a NAME="E3:45"/>
(  <a href="sublemma.html#K11" title="SUBLEMMA:func.11">CQCSub_the_scope_of</a> <span class="p1">(<span class="default"><a href="sublemma.html#K10" title="SUBLEMMA:func.10">CQCSub_All</a> <span class="p2"><a href="sublemma.html#K8" title="SUBLEMMA:func.8">[</a><span class="default"><font color="Maroon" title="c2">S</font>,<font color="Maroon" title="c1">x</font></span><a href="sublemma.html#K8" title="SUBLEMMA:func.8">]</a></span>,<font color="Maroon" title="c3">xSQ</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c2">S</font> &amp;  <a href="sublemma.html#K12" title="SUBLEMMA:func.12">CQCQuant</a> <span class="p1">(<span class="default"><a href="sublemma.html#K10" title="SUBLEMMA:func.10">CQCSub_All</a> <span class="p2"><a href="sublemma.html#K8" title="SUBLEMMA:func.8">[</a><span class="default"><font color="Maroon" title="c2">S</font>,<font color="Maroon" title="c1">x</font></span><a href="sublemma.html#K8" title="SUBLEMMA:func.8">]</a></span>,<font color="Maroon" title="c3">xSQ</font></span>)</span>,<span class="p1">(<span class="default"><a href="substut1.html#K39" title="SUBSTUT1:func.39">CQC_Sub</a> <span class="p2">(<span class="default"><a href="sublemma.html#K11" title="SUBLEMMA:func.11">CQCSub_the_scope_of</a> <span class="p3">(<span class="default"><a href="sublemma.html#K10" title="SUBLEMMA:func.10">CQCSub_All</a> <span class="p4"><a href="sublemma.html#K8" title="SUBLEMMA:func.8">[</a><span class="default"><font color="Maroon" title="c2">S</font>,<font color="Maroon" title="c1">x</font></span><a href="sublemma.html#K8" title="SUBLEMMA:func.8">]</a></span>,<font color="Maroon" title="c3">xSQ</font></span>)</span></span>)</span></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="sublemma.html#K12" title="SUBLEMMA:func.12">CQCQuant</a> <span class="p1">(<span class="default"><a href="sublemma.html#K10" title="SUBLEMMA:func.10">CQCSub_All</a> <span class="p2"><a href="sublemma.html#K8" title="SUBLEMMA:func.8">[</a><span class="default"><font color="Maroon" title="c2">S</font>,<font color="Maroon" title="c1">x</font></span><a href="sublemma.html#K8" title="SUBLEMMA:func.8">]</a></span>,<font color="Maroon" title="c3">xSQ</font></span>)</span>,<span class="p1">(<span class="default"><a href="substut1.html#K39" title="SUBSTUT1:func.39">CQC_Sub</a> <font color="Maroon" title="c2">S</font></span>)</span> )
 <b>by </b><i><a class="ref" href="mcart_1.html#T7" title="MCART_1:th.7">MCART_1:7</a></i>;<br/>


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