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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#M1" title="SUBSET_1:mode.1">Element</a> of  <a href="substut1.html#K16" title="SUBSTUT1:func.16">QC-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="substut1.html#K25" title="SUBSTUT1:func.25">[</a><span class="default"><font color="Maroon" title="c2">S</font>,<font color="Maroon" title="c1">x</font></span><a href="substut1.html#K25" title="SUBSTUT1:func.25">]</a></span>;<br/>





<b>set </b><font color="Maroon" title="c4">S'</font> =  <a href="substut1.html#K24" title="SUBSTUT1:func.24">Sub_All</a> <span class="p1"><a href="substut1.html#K25" title="SUBSTUT1:func.25">[</a><span class="default"><font color="Maroon" title="c2">S</font>,<font color="Maroon" title="c1">x</font></span><a href="substut1.html#K25" title="SUBSTUT1:func.25">]</a></span>,<font color="Maroon" title="c3">xSQ</font>;<br/>
<b>assume </b><a NAME="E1:95"/><i><font color="Green" title="E59">A1</font></i>: 
(  <a href="substut1.html#K37" title="SUBSTUT1:func.37">CQC_Sub</a> <font color="Maroon" title="c2">S</font> 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>  &amp; <span class="p1"><a href="substut1.html#K25" title="SUBSTUT1:func.25">[</a><span class="default"><font color="Maroon" title="c2">S</font>,<font color="Maroon" title="c1">x</font></span><a href="substut1.html#K25" title="SUBSTUT1:func.25">]</a></span> is <a href="substut1.html#V3" title="SUBSTUT1:attr.3">quantifiable</a> )
 ;<br/>

<a NAME="E2:95"/><b>then </b>
 <a href="substut1.html#K31" title="SUBSTUT1:func.31">Sub_the_scope_of</a> <span class="p1">(<span class="default"><a href="substut1.html#K24" title="SUBSTUT1:func.24">Sub_All</a> <span class="p2"><a href="substut1.html#K25" title="SUBSTUT1:func.25">[</a><span class="default"><font color="Maroon" title="c2">S</font>,<font color="Maroon" title="c1">x</font></span><a href="substut1.html#K25" title="SUBSTUT1:func.25">]</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="substut1.html#K25" title="SUBSTUT1:func.25">[</a><span class="default"><font color="Maroon" title="c2">S</font>,<font color="Maroon" title="c1">x</font></span><a href="substut1.html#K25" title="SUBSTUT1:func.25">]</a></span> <a href="substut1.html#K22" title="SUBSTUT1:func.22">`1</a> 
 
<b>by </b><i><a class="ref" href="substut1.html#T21" target="_self" title="SUBSTUT1:th.21">Th21</a></i>;<br/>
<a NAME="E3:95"/><b>then </b>
 <a href="substut1.html#K36" title="SUBSTUT1:func.36">Quant</a> <span class="p1">(<span class="default"><a href="substut1.html#K24" title="SUBSTUT1:func.24">Sub_All</a> <span class="p2"><a href="substut1.html#K25" title="SUBSTUT1:func.25">[</a><span class="default"><font color="Maroon" title="c2">S</font>,<font color="Maroon" title="c1">x</font></span><a href="substut1.html#K25" title="SUBSTUT1:func.25">]</a></span>,<font color="Maroon" title="c3">xSQ</font></span>)</span>,<span class="p1">(<span class="default"><a href="substut1.html#K37" title="SUBSTUT1:func.37">CQC_Sub</a> <span class="p2">(<span class="default"><a href="substut1.html#K31" title="SUBSTUT1:func.31">Sub_the_scope_of</a> <span class="p3">(<span class="default"><a href="substut1.html#K24" title="SUBSTUT1:func.24">Sub_All</a> <span class="p4"><a href="substut1.html#K25" title="SUBSTUT1:func.25">[</a><span class="default"><font color="Maroon" title="c2">S</font>,<font color="Maroon" title="c1">x</font></span><a href="substut1.html#K25" title="SUBSTUT1:func.25">]</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="qc_lang1.html#K14" title="QC_LANG1:func.14">All</a> <span class="p1">(<span class="default"><a href="substut1.html#K35" title="SUBSTUT1:func.35">S_Bound</a> <span class="p2">(<span class="default"><a href="substut1.html#K32" title="SUBSTUT1:func.32">@</a> <span class="p3">(<span class="default"><a href="substut1.html#K24" title="SUBSTUT1:func.24">Sub_All</a> <span class="p4"><a href="substut1.html#K25" title="SUBSTUT1:func.25">[</a><span class="default"><font color="Maroon" title="c2">S</font>,<font color="Maroon" title="c1">x</font></span><a href="substut1.html#K25" title="SUBSTUT1:func.25">]</a></span>,<font color="Maroon" title="c3">xSQ</font></span>)</span></span>)</span></span>)</span>,<span class="p1">(<span class="default"><a href="substut1.html#K37" title="SUBSTUT1:func.37">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/>
<a NAME="E4:95"/><b>then </b>
 <a href="substut1.html#K36" title="SUBSTUT1:func.36">Quant</a> <span class="p1">(<span class="default"><a href="substut1.html#K24" title="SUBSTUT1:func.24">Sub_All</a> <span class="p2"><a href="substut1.html#K25" title="SUBSTUT1:func.25">[</a><span class="default"><font color="Maroon" title="c2">S</font>,<font color="Maroon" title="c1">x</font></span><a href="substut1.html#K25" title="SUBSTUT1:func.25">]</a></span>,<font color="Maroon" title="c3">xSQ</font></span>)</span>,<span class="p1">(<span class="default"><a href="substut1.html#K37" title="SUBSTUT1:func.37">CQC_Sub</a> <span class="p2">(<span class="default"><a href="substut1.html#K31" title="SUBSTUT1:func.31">Sub_the_scope_of</a> <span class="p3">(<span class="default"><a href="substut1.html#K24" title="SUBSTUT1:func.24">Sub_All</a> <span class="p4"><a href="substut1.html#K25" title="SUBSTUT1:func.25">[</a><span class="default"><font color="Maroon" title="c2">S</font>,<font color="Maroon" title="c1">x</font></span><a href="substut1.html#K25" title="SUBSTUT1:func.25">]</a></span>,<font color="Maroon" title="c3">xSQ</font></span>)</span></span>)</span></span>)</span> 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> 
 
<b>by </b><i><a class="txt" href="substut1.html#E1:95"><i><font color="Green" title="E59">A1</font></i></a>, <a class="ref" href="cqc_lang.html#T23" title="CQC_LANG:th.23">CQC_LANG:23</a></i>;<br/>
<b>hence </b><a NAME="E5:95"/>
 <a href="substut1.html#K37" title="SUBSTUT1:func.37">CQC_Sub</a> <span class="p1">(<span class="default"><a href="substut1.html#K24" title="SUBSTUT1:func.24">Sub_All</a> <span class="p2"><a href="substut1.html#K25" title="SUBSTUT1:func.25">[</a><span class="default"><font color="Maroon" title="c2">S</font>,<font color="Maroon" title="c1">x</font></span><a href="substut1.html#K25" title="SUBSTUT1:func.25">]</a></span>,<font color="Maroon" title="c3">xSQ</font></span>)</span> 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> 
 <b>by </b><i><a class="txt" href="substut1.html#E1:95"><i><font color="Green" title="E59">A1</font></i></a>, <a class="ref" href="substut1.html#T14" target="_self" title="SUBSTUT1:th.14">Th14</a>, <a class="ref" href="substut1.html#T32" target="_self" title="SUBSTUT1:th.32">Th32</a></i>;<br/>


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