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<span class="kw">consider </span><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><span class="kw"> such that </span><br/><a NAME="E2:43_1_1"/><span class="lab"><font color="Green" title="E30">A2</font></span>: 
<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>
 <span class="kw">and </span><br/><a NAME="E3:43_1_1"/><span class="lab"><font color="Green" title="E31">A3</font></span>: 
<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>
 <span class="kw">and </span><br/><a NAME="E4:43_1_1"/><span class="lab"><font color="Green" title="E32">A4</font></span>: 
<font color="Maroon" title="c2">B</font> is  <a href="substut1.html#V3" title="SUBSTUT1:attr.3">quantifiable</a> 
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:43"><span class="lab"><font color="Green" title="E29">A1</font></span></a>, <a class="ref" href="substut1.html#D34" title="SUBSTUT1:def.34">SUBSTUT1:def 34</a></span>;<br/>
<a NAME="E5:43_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>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:43_1_1"><span class="lab"><font color="Green" title="E30">A2</font></span></a>, <a class="txt" href="#E4:43_1_1"><span class="lab"><font color="Green" title="E32">A4</font></span></a>, <a class="ref" href="sublemma.html#T27" target="_self" title="SUBLEMMA:th.27">Th27</a></span>;<br/>
<a NAME="E6:43_1_1"/><span class="kw">then </span>
<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> 
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="cqc_lang.html#T23" title="CQC_LANG:th.23">CQC_LANG:23</a></span>;<br/>
<a NAME="E7:43_1_1"/><span class="kw">then </span>
<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> 
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="substut1.html#D39" title="SUBSTUT1:def.39">SUBSTUT1:def 39</a></span>;<br/>
<span class="kw">hence </span><a NAME="E8:43_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> 
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E3:43_1_1"><span class="lab"><font color="Green" title="E31">A3</font></span></a></span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> verum</span><br/>


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