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<b>consider </b><font color="Maroon" title="c2">B</font> being    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of <span class="p1"><a href="zfmisc_1.html#K2" title="ZFMISC_1:func.2">[:</a><span class="default"><a href="substut1.html#K16" title="SUBSTUT1:func.16">QC-Sub-WFF</a> ,<a href="qc_lang1.html#K2" title="QC_LANG1:func.2">bound_QC-variables</a> </span><a href="zfmisc_1.html#K2" title="ZFMISC_1:func.2">:]</a></span>, <font color="Maroon" title="c3">SQ</font> being    <a href="substut1.html#M1" title="SUBSTUT1:mode.1">second_Q_comp</a> of <font color="Maroon" title="c2">B</font><b> such that </b><br/><a NAME="E2:42_1_1"/><i><font color="Green" title="E30">A2</font></i>: 
( <font color="Maroon" title="c1">S</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="substut1.html#K24" title="SUBSTUT1:func.24">Sub_All</a> <font color="Maroon" title="c2">B</font>,<font color="Maroon" title="c3">SQ</font> &amp; <font color="Maroon" title="c2">B</font> <a href="substut1.html#K22" title="SUBSTUT1:func.22">`1</a>  <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="substut1.html#K31" title="SUBSTUT1:func.31">Sub_the_scope_of</a> <font color="Maroon" title="c1">S</font> &amp; <font color="Maroon" title="c2">B</font> is <a href="substut1.html#V3" title="SUBSTUT1:attr.3">quantifiable</a> )
 <b>by </b><i><a class="txt" href="sublemma.html#E1:42"><i><font color="Green" title="E29">A1</font></i></a>, <a class="ref" href="substut1.html#D34" title="SUBSTUT1:def.34">SUBSTUT1:def 34</a></i>;<br/>
<a NAME="E3:42_1_1"/>
<font color="Maroon" title="c1">S</font> <a href="sublemma.html#K2" title="SUBLEMMA:func.2">`1</a>  <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"><font color="Maroon" title="c2">B</font> <a href="substut1.html#K23" title="SUBSTUT1:func.23">`2</a> </span>)</span>,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c2">B</font> <a href="substut1.html#K22" title="SUBSTUT1:func.22">`1</a> </span>)</span> <a href="substut1.html#K18" title="SUBSTUT1:func.18">`1</a> </span>)</span>
 
<b>by </b><i><a class="txt" href="sublemma.html#E2:42_1_1"><i><font color="Green" title="E30">A2</font></i></a>, <a class="ref" href="sublemma.html#T27" target="_self" title="SUBLEMMA:th.27">Th27</a></i>;<br/>
<a NAME="E4:42_1_1"/><b>then </b>
<span class="p1">(<span class="default"><font color="Maroon" title="c2">B</font> <a href="substut1.html#K22" title="SUBSTUT1:func.22">`1</a> </span>)</span> <a href="substut1.html#K18" title="SUBSTUT1:func.18">`1</a>  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="ref" href="cqc_lang.html#T23" title="CQC_LANG:th.23">CQC_LANG:23</a></i>;<br/>
<b>then consider </b><font color="Maroon" title="c4">S1</font> being    <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> <b> such that </b><br/><a NAME="E6:42_1_1"/><i><font color="Green" title="E31">A3</font></i>: 
( <font color="Maroon" title="c4">S1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c2">B</font> <a href="substut1.html#K22" title="SUBSTUT1:func.22">`1</a>  &amp; <font color="Maroon" title="c4">S1</font> <a href="substut1.html#K18" title="SUBSTUT1:func.18">`1</a>  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>  )
 ;<br/>
<a NAME="E7:42_1_1"/>
<font color="Maroon" title="c2">B</font> <a href="substut1.html#K22" title="SUBSTUT1:func.22">`1</a>  <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="substut1.html#K38" title="SUBSTUT1:func.38">CQC-Sub-WFF</a> 
 
<b>by </b><i><a class="txt" href="sublemma.html#E6:42_1_1"><i><font color="Green" title="E31">A3</font></i></a>, <a class="ref" href="substut1.html#D39" title="SUBSTUT1:def.39">SUBSTUT1:def 39</a></i>;<br/>
<b>hence </b><a NAME="E8:42_1_1"/>
 <a href="substut1.html#K31" title="SUBSTUT1:func.31">Sub_the_scope_of</a> <font color="Maroon" title="c1">S</font> is    <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> 
 <b>by </b><i><a class="txt" href="sublemma.html#E2:42_1_1"><i><font color="Green" title="E30">A2</font></i></a></i>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> verum</span><br/>


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