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<b>let </b><font color="Maroon" title="c1">B</font> be    <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>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> for <font color="Olive" title="b1">SQ</font> being   <a href="substut1.html#M1" title="SUBSTUT1:mode.1">second_Q_comp</a> of <font color="Maroon" title="c1">B</font>  st <font color="Maroon" title="c1">B</font> is <a href="substut1.html#V3" title="SUBSTUT1:attr.3">quantifiable</a> holds <br/>( <span class="p1">(<span class="default"><a href="substut1.html#K24" title="SUBSTUT1:func.24">Sub_All</a> <font color="Maroon" title="c1">B</font>,<font color="Olive" title="b1">SQ</font></span>)</span> <a href="substut1.html#K18" title="SUBSTUT1:func.18">`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="c1">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="c1">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> &amp; <span class="p1">(<span class="default"><a href="substut1.html#K24" title="SUBSTUT1:func.24">Sub_All</a> <font color="Maroon" title="c1">B</font>,<font color="Olive" title="b1">SQ</font></span>)</span> <a href="substut1.html#K19" title="SUBSTUT1:func.19">`2</a>  <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b1">SQ</font> )</span><br/><b>let </b><font color="Maroon" title="c2">SQ</font> be    <a href="substut1.html#M1" title="SUBSTUT1:mode.1">second_Q_comp</a> of <font color="Maroon" title="c1">B</font>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> ( <font color="Maroon" title="c1">B</font> is <a href="substut1.html#V3" title="SUBSTUT1:attr.3">quantifiable</a> implies ( <span class="p1">(<span class="default"><a href="substut1.html#K24" title="SUBSTUT1:func.24">Sub_All</a> <font color="Maroon" title="c1">B</font>,<font color="Maroon" title="c2">SQ</font></span>)</span> <a href="substut1.html#K18" title="SUBSTUT1:func.18">`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="c1">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="c1">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> &amp; <span class="p1">(<span class="default"><a href="substut1.html#K24" title="SUBSTUT1:func.24">Sub_All</a> <font color="Maroon" title="c1">B</font>,<font color="Maroon" title="c2">SQ</font></span>)</span> <a href="substut1.html#K19" title="SUBSTUT1:func.19">`2</a>  <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c2">SQ</font> ) )</span><br/>



<b>assume </b><a NAME="E1:35"/>
<font color="Maroon" title="c1">B</font> is <a href="substut1.html#V3" title="SUBSTUT1:attr.3">quantifiable</a>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> ( <span class="p1">(<span class="default"><a href="substut1.html#K24" title="SUBSTUT1:func.24">Sub_All</a> <font color="Maroon" title="c1">B</font>,<font color="Maroon" title="c2">SQ</font></span>)</span> <a href="substut1.html#K18" title="SUBSTUT1:func.18">`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="c1">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="c1">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> &amp; <span class="p1">(<span class="default"><a href="substut1.html#K24" title="SUBSTUT1:func.24">Sub_All</a> <font color="Maroon" title="c1">B</font>,<font color="Maroon" title="c2">SQ</font></span>)</span> <a href="substut1.html#K19" title="SUBSTUT1:func.19">`2</a>  <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c2">SQ</font> )</span><br/>

<a NAME="E2:35"/><b>then </b>
 <a href="substut1.html#K24" title="SUBSTUT1:func.24">Sub_All</a> <font color="Maroon" title="c1">B</font>,<font color="Maroon" title="c2">SQ</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"><a href="domain_1.html#K1" title="DOMAIN_1:func.1">[</a><span class="default"><span class="p2">(<span class="default"><a href="qc_lang1.html#K14" title="QC_LANG1:func.14">All</a> <span class="p3">(<span class="default"><font color="Maroon" title="c1">B</font> <a href="substut1.html#K23" title="SUBSTUT1:func.23">`2</a> </span>)</span>,<span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon" title="c1">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>)</span>,<font color="Maroon" title="c2">SQ</font></span><a href="domain_1.html#K1" title="DOMAIN_1:func.1">]</a></span>
 
<b>by </b><i><a class="ref" href="substut1.html#D24" title="SUBSTUT1:def.24">SUBSTUT1:def 24</a></i>;<br/>
<b>hence </b><a NAME="E3:35"/>
( <span class="p1">(<span class="default"><a href="substut1.html#K24" title="SUBSTUT1:func.24">Sub_All</a> <font color="Maroon" title="c1">B</font>,<font color="Maroon" title="c2">SQ</font></span>)</span> <a href="substut1.html#K18" title="SUBSTUT1:func.18">`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="c1">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="c1">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> &amp; <span class="p1">(<span class="default"><a href="substut1.html#K24" title="SUBSTUT1:func.24">Sub_All</a> <font color="Maroon" title="c1">B</font>,<font color="Maroon" title="c2">SQ</font></span>)</span> <a href="substut1.html#K19" title="SUBSTUT1:func.19">`2</a>  <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c2">SQ</font> )
 <b>by </b><i><a class="ref" href="mcart_1.html#T7" title="MCART_1:th.7">MCART_1:7</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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