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<b>let </b><font color="Maroon" title="c1">B1</font>, <font color="Maroon" title="c2">B2</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">SQ1</font> being   <a href="substut1.html#M1" title="SUBSTUT1:mode.1">second_Q_comp</a> of <font color="Maroon" title="c1">B1</font><br/> for <font color="Olive" title="b2">SQ2</font> being   <a href="substut1.html#M1" title="SUBSTUT1:mode.1">second_Q_comp</a> of <font color="Maroon" title="c2">B2</font>  st <font color="Maroon" title="c1">B1</font> is <a href="substut1.html#V3" title="SUBSTUT1:attr.3">quantifiable</a> &amp; <font color="Maroon" title="c2">B2</font> is <a href="substut1.html#V3" title="SUBSTUT1:attr.3">quantifiable</a> &amp;  <a href="substut1.html#K24" title="SUBSTUT1:func.24">Sub_All</a> <font color="Maroon" title="c1">B1</font>,<font color="Olive" title="b1">SQ1</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">B2</font>,<font color="Olive" title="b2">SQ2</font> holds <br/><font color="Maroon" title="c1">B1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c2">B2</font></span><br/><b>let </b><font color="Maroon" title="c3">SQ1</font> be    <a href="substut1.html#M1" title="SUBSTUT1:mode.1">second_Q_comp</a> of <font color="Maroon" title="c1">B1</font>; <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">SQ2</font> being   <a href="substut1.html#M1" title="SUBSTUT1:mode.1">second_Q_comp</a> of <font color="Maroon" title="c2">B2</font>  st <font color="Maroon" title="c1">B1</font> is <a href="substut1.html#V3" title="SUBSTUT1:attr.3">quantifiable</a> &amp; <font color="Maroon" title="c2">B2</font> is <a href="substut1.html#V3" title="SUBSTUT1:attr.3">quantifiable</a> &amp;  <a href="substut1.html#K24" title="SUBSTUT1:func.24">Sub_All</a> <font color="Maroon" title="c1">B1</font>,<font color="Maroon" title="c3">SQ1</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">B2</font>,<font color="Olive" title="b1">SQ2</font> holds <br/><font color="Maroon" title="c1">B1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c2">B2</font></span><br/><b>let </b><font color="Maroon" title="c4">SQ2</font> be    <a href="substut1.html#M1" title="SUBSTUT1:mode.1">second_Q_comp</a> of <font color="Maroon" title="c2">B2</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">B1</font> is <a href="substut1.html#V3" title="SUBSTUT1:attr.3">quantifiable</a> &amp; <font color="Maroon" title="c2">B2</font> is <a href="substut1.html#V3" title="SUBSTUT1:attr.3">quantifiable</a> &amp;  <a href="substut1.html#K24" title="SUBSTUT1:func.24">Sub_All</a> <font color="Maroon" title="c1">B1</font>,<font color="Maroon" title="c3">SQ1</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">B2</font>,<font color="Maroon" title="c4">SQ2</font> implies <font color="Maroon" title="c1">B1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c2">B2</font> )</span><br/>





<b>assume </b><a NAME="E1:65"/><i><font color="Green" title="E38">A1</font></i>: 
( <font color="Maroon" title="c1">B1</font> is <a href="substut1.html#V3" title="SUBSTUT1:attr.3">quantifiable</a> &amp; <font color="Maroon" title="c2">B2</font> is <a href="substut1.html#V3" title="SUBSTUT1:attr.3">quantifiable</a> &amp;  <a href="substut1.html#K24" title="SUBSTUT1:func.24">Sub_All</a> <font color="Maroon" title="c1">B1</font>,<font color="Maroon" title="c3">SQ1</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">B2</font>,<font color="Maroon" title="c4">SQ2</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">B1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c2">B2</font></span><br/>

<a NAME="E2:65"/><i><font color="Green" title="E39">A2</font></i>: 
(  <a href="substut1.html#K24" title="SUBSTUT1:func.24">Sub_All</a> <font color="Maroon" title="c1">B1</font>,<font color="Maroon" title="c3">SQ1</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">B1</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">B1</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="c3">SQ1</font></span><a href="domain_1.html#K1" title="DOMAIN_1:func.1">]</a></span> &amp;  <a href="substut1.html#K24" title="SUBSTUT1:func.24">Sub_All</a> <font color="Maroon" title="c2">B2</font>,<font color="Maroon" title="c4">SQ2</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="c2">B2</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="c2">B2</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="c4">SQ2</font></span><a href="domain_1.html#K1" title="DOMAIN_1:func.1">]</a></span> )
 
<b>by </b><i><a class="txt" href="substut1.html#E1:65"><i><font color="Green" title="E38">A1</font></i></a>, <a class="ref" href="substut1.html#D24" target="_self" title="SUBSTUT1:def.24">Def24</a></i>;<br/>
<a NAME="E3:65"/><b>then </b>
(  <a href="qc_lang1.html#K14" title="QC_LANG1:func.14">All</a> <span class="p1">(<span class="default"><font color="Maroon" title="c1">B1</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">B1</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> <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">B2</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">B2</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; <font color="Maroon" title="c3">SQ1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c4">SQ2</font> )
 
<b>by </b><i><a class="txt" href="substut1.html#E1:65"><i><font color="Green" title="E38">A1</font></i></a>, <a class="ref" href="zfmisc_1.html#T33" title="ZFMISC_1:th.33">ZFMISC_1:33</a></i>;<br/>
<a NAME="E4:65"/><b>then </b><i><font color="Green" title="E40">A3</font></i>: 
( <font color="Maroon" title="c1">B1</font> <a href="substut1.html#K23" title="SUBSTUT1:func.23">`2</a>  <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c2">B2</font> <a href="substut1.html#K23" title="SUBSTUT1:func.23">`2</a>  &amp; <span class="p1">(<span class="default"><font color="Maroon" title="c1">B1</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>  <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><font color="Maroon" title="c2">B2</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>  )
 
<b>by </b><i><a class="ref" href="qc_lang2.html#T6" title="QC_LANG2:th.6">QC_LANG2:6</a></i>;<br/>
<a NAME="E5:65"/><i><font color="Green" title="E41">A4</font></i>: 
<span class="p1">(<span class="default"><font color="Maroon" title="c1">B1</font> <a href="substut1.html#K22" title="SUBSTUT1:func.22">`1</a> </span>)</span> <a href="substut1.html#K19" title="SUBSTUT1:func.19">`2</a>  <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <a href="substut1.html#K15" title="SUBSTUT1:func.15">QSub</a>  <a href="funct_1.html#K1" title="FUNCT_1:func.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">B1</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">B1</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="c3">SQ1</font></span><a href="domain_1.html#K1" title="DOMAIN_1:func.1">]</a></span>
 
<b>by </b><i><a class="txt" href="substut1.html#E1:65"><i><font color="Green" title="E38">A1</font></i></a>, <a class="ref" href="substut1.html#D23" target="_self" title="SUBSTUT1:def.23">Def23</a></i>;<br/>
<a NAME="E6:65"/><i><font color="Green" title="E42">A5</font></i>: 
( <font color="Maroon" title="c1">B1</font> <a href="substut1.html#K22" title="SUBSTUT1:func.22">`1</a>  <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"><span class="p3">(<span class="default"><font color="Maroon" title="c1">B1</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="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon" title="c1">B1</font> <a href="substut1.html#K22" title="SUBSTUT1:func.22">`1</a> </span>)</span> <a href="substut1.html#K19" title="SUBSTUT1:func.19">`2</a> </span>)</span></span><a href="domain_1.html#K1" title="DOMAIN_1:func.1">]</a></span> &amp; <font color="Maroon" title="c2">B2</font> <a href="substut1.html#K22" title="SUBSTUT1:func.22">`1</a>  <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"><span class="p3">(<span class="default"><font color="Maroon" title="c2">B2</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="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon" title="c2">B2</font> <a href="substut1.html#K22" title="SUBSTUT1:func.22">`1</a> </span>)</span> <a href="substut1.html#K19" title="SUBSTUT1:func.19">`2</a> </span>)</span></span><a href="domain_1.html#K1" title="DOMAIN_1:func.1">]</a></span> )
 
<b>by </b><i><a class="ref" href="substut1.html#T10" target="_self" title="SUBSTUT1:th.10">Th10</a></i>;<br/>
<a NAME="E7:65"/>
(  ex <font color="Olive" title="b1">a</font>, <font color="Olive" title="b2">b</font> being   <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a>  st <br/>( <font color="Olive" title="b1">a</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="substut1.html#K16" title="SUBSTUT1:func.16">QC-Sub-WFF</a>  &amp; <font color="Olive" title="b2">b</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="qc_lang1.html#K2" title="QC_LANG1:func.2">bound_QC-variables</a>  &amp; <font color="Maroon" title="c1">B1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"><a href="tarski.html#K4" title="TARSKI:func.4">[</a><span class="default"><font color="Olive" title="b1">a</font>,<font color="Olive" title="b2">b</font></span><a href="tarski.html#K4" title="TARSKI:func.4">]</a></span> ) &amp;  ex <font color="Olive" title="b1">a</font>, <font color="Olive" title="b2">b</font> being   <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a>  st <br/>( <font color="Olive" title="b1">a</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="substut1.html#K16" title="SUBSTUT1:func.16">QC-Sub-WFF</a>  &amp; <font color="Olive" title="b2">b</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="qc_lang1.html#K2" title="QC_LANG1:func.2">bound_QC-variables</a>  &amp; <font color="Maroon" title="c2">B2</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"><a href="tarski.html#K4" title="TARSKI:func.4">[</a><span class="default"><font color="Olive" title="b1">a</font>,<font color="Olive" title="b2">b</font></span><a href="tarski.html#K4" title="TARSKI:func.4">]</a></span> ) )
 
<b>by </b><i><a class="ref" href="zfmisc_1.html#D2" title="ZFMISC_1:def.2">ZFMISC_1:def 2</a></i>;<br/>
<a NAME="E8:65"/><b>then </b>
( <font color="Maroon" title="c1">B1</font> <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"><span class="p2">(<span class="default"><font color="Maroon" title="c1">B1</font> <a href="substut1.html#K22" title="SUBSTUT1:func.22">`1</a> </span>)</span>,<span class="p2">(<span class="default"><font color="Maroon" title="c1">B1</font> <a href="substut1.html#K23" title="SUBSTUT1:func.23">`2</a> </span>)</span></span><a href="substut1.html#K25" title="SUBSTUT1:func.25">]</a></span> &amp; <font color="Maroon" title="c2">B2</font> <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"><span class="p2">(<span class="default"><font color="Maroon" title="c2">B2</font> <a href="substut1.html#K22" title="SUBSTUT1:func.22">`1</a> </span>)</span>,<span class="p2">(<span class="default"><font color="Maroon" title="c2">B2</font> <a href="substut1.html#K23" title="SUBSTUT1:func.23">`2</a> </span>)</span></span><a href="substut1.html#K25" title="SUBSTUT1:func.25">]</a></span> )
 
<b>by </b><i><a class="ref" href="mcart_1.html#T8" title="MCART_1:th.8">MCART_1:8</a></i>;<br/>
<b>hence </b><a NAME="E9:65"/>
<font color="Maroon" title="c1">B1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c2">B2</font>
 <b>by </b><i><a class="txt" href="substut1.html#E1:65"><i><font color="Green" title="E38">A1</font></i></a>, <a class="txt" href="substut1.html#E2:65"><i><font color="Green" title="E39">A2</font></i></a>, <a class="txt" href="substut1.html#E4:65"><i><font color="Green" title="E40">A3</font></i></a>, <a class="txt" href="substut1.html#E5:65"><i><font color="Green" title="E41">A4</font></i></a>, <a class="txt" href="substut1.html#E6:65"><i><font color="Green" title="E42">A5</font></i></a>, <a class="ref" href="substut1.html#D23" target="_self" title="SUBSTUT1:def.23">Def23</a></i>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> verum</span><br/>


</div>
