<?xml version="1.0"?>
<div class="add">

<span class="kw">let </span><font color="Maroon" title="c1">p</font> be    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of  <a href="qc_lang1.html#K8" title="QC_LANG1:func.8">QC-WFF</a> ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> for <font color="Olive" title="b1">V</font> being non  <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a>  <a href="subset_1.html#NM2" title="SUBSET_1:NM.2">Subset</a> of <a href="qc_lang1.html#K1" title="QC_LANG1:func.1">QC-variables</a>   st <font color="Maroon" title="c1">p</font> is  <a href="qc_lang2.html#V4" title="QC_LANG2:attr.4">existential</a>  holds <br/> <a href="qc_lang3.html#K4" title="QC_LANG3:func.4">Vars</a> <font color="Maroon" title="c1">p</font>,<font color="Olive" title="b1">V</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="qc_lang3.html#K4" title="QC_LANG3:func.4">Vars</a> <span class="p1">(<span class="default"><a href="qc_lang1.html#K17" title="QC_LANG1:func.17">the_argument_of</a> <span class="p2">(<span class="default"><a href="qc_lang1.html#K21" title="QC_LANG1:func.21">the_scope_of</a> <span class="p3">(<span class="default"><a href="qc_lang1.html#K17" title="QC_LANG1:func.17">the_argument_of</a> <font color="Maroon" title="c1">p</font></span>)</span></span>)</span></span>)</span>,<font color="Olive" title="b1">V</font></span><br/><span class="kw">let </span><font color="Maroon" title="c2">V</font> be  non  <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a>  <a href="subset_1.html#NM2" title="SUBSET_1:NM.2">Subset</a> of <a href="qc_lang1.html#K1" title="QC_LANG1:func.1">QC-variables</a> ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> ( <font color="Maroon" title="c1">p</font> is  <a href="qc_lang2.html#V4" title="QC_LANG2:attr.4">existential</a>  implies  <a href="qc_lang3.html#K4" title="QC_LANG3:func.4">Vars</a> <font color="Maroon" title="c1">p</font>,<font color="Maroon" title="c2">V</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="qc_lang3.html#K4" title="QC_LANG3:func.4">Vars</a> <span class="p1">(<span class="default"><a href="qc_lang1.html#K17" title="QC_LANG1:func.17">the_argument_of</a> <span class="p2">(<span class="default"><a href="qc_lang1.html#K21" title="QC_LANG1:func.21">the_scope_of</a> <span class="p3">(<span class="default"><a href="qc_lang1.html#K17" title="QC_LANG1:func.17">the_argument_of</a> <font color="Maroon" title="c1">p</font></span>)</span></span>)</span></span>)</span>,<font color="Maroon" title="c2">V</font> )</span><br/>



<span class="kw">set </span><font color="Maroon" title="c3">p1</font> =  <a href="qc_lang1.html#K17" title="QC_LANG1:func.17">the_argument_of</a> <span class="p1">(<span class="default"><a href="qc_lang1.html#K21" title="QC_LANG1:func.21">the_scope_of</a> <span class="p2">(<span class="default"><a href="qc_lang1.html#K17" title="QC_LANG1:func.17">the_argument_of</a> <font color="Maroon" title="c1">p</font></span>)</span></span>)</span>;<br/>
<span class="kw">set </span><font color="Maroon" title="c4">x</font> =  <a href="qc_lang1.html#K20" title="QC_LANG1:func.20">bound_in</a> <span class="p1">(<span class="default"><a href="qc_lang1.html#K17" title="QC_LANG1:func.17">the_argument_of</a> <font color="Maroon" title="c1">p</font></span>)</span>;<br/>
<span class="kw">assume </span><a NAME="E1:68"/>
<font color="Maroon" title="c1">p</font> is  <a href="qc_lang2.html#V4" title="QC_LANG2:attr.4">existential</a> 
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide">  <a href="qc_lang3.html#K4" title="QC_LANG3:func.4">Vars</a> <font color="Maroon" title="c1">p</font>,<font color="Maroon" title="c2">V</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="qc_lang3.html#K4" title="QC_LANG3:func.4">Vars</a> <span class="p1">(<span class="default"><a href="qc_lang1.html#K17" title="QC_LANG1:func.17">the_argument_of</a> <span class="p2">(<span class="default"><a href="qc_lang1.html#K21" title="QC_LANG1:func.21">the_scope_of</a> <span class="p3">(<span class="default"><a href="qc_lang1.html#K17" title="QC_LANG1:func.17">the_argument_of</a> <font color="Maroon" title="c1">p</font></span>)</span></span>)</span></span>)</span>,<font color="Maroon" title="c2">V</font></span><br/>

<a NAME="E2:68"/><span class="kw">then </span>
<font color="Maroon" title="c1">p</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="qc_lang2.html#K5" title="QC_LANG2:func.5">Ex</a> <span class="p1">(<span class="default"><a href="qc_lang1.html#K20" title="QC_LANG1:func.20">bound_in</a> <span class="p2">(<span class="default"><a href="qc_lang1.html#K17" title="QC_LANG1:func.17">the_argument_of</a> <font color="Maroon" title="c1">p</font></span>)</span></span>)</span>,<span class="p1">(<span class="default"><a href="qc_lang1.html#K17" title="QC_LANG1:func.17">the_argument_of</a> <span class="p2">(<span class="default"><a href="qc_lang1.html#K21" title="QC_LANG1:func.21">the_scope_of</a> <span class="p3">(<span class="default"><a href="qc_lang1.html#K17" title="QC_LANG1:func.17">the_argument_of</a> <font color="Maroon" title="c1">p</font></span>)</span></span>)</span></span>)</span>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="qc_lang2.html#T56" title="QC_LANG2:th.56">QC_LANG2:56</a></span>;<br/>
<a NAME="E3:68"/><span class="kw">then </span>
<font color="Maroon" title="c1">p</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="qc_lang1.html#K12" title="QC_LANG1:func.12">'not'</a> <span class="p1">(<span class="default"><a href="qc_lang1.html#K14" title="QC_LANG1:func.14">All</a> <span class="p2">(<span class="default"><a href="qc_lang1.html#K20" title="QC_LANG1:func.20">bound_in</a> <span class="p3">(<span class="default"><a href="qc_lang1.html#K17" title="QC_LANG1:func.17">the_argument_of</a> <font color="Maroon" title="c1">p</font></span>)</span></span>)</span>,<span class="p2">(<span class="default"><a href="qc_lang1.html#K12" title="QC_LANG1:func.12">'not'</a> <span class="p3">(<span class="default"><a href="qc_lang1.html#K17" title="QC_LANG1:func.17">the_argument_of</a> <span class="p4">(<span class="default"><a href="qc_lang1.html#K21" title="QC_LANG1:func.21">the_scope_of</a> <span class="p5">(<span class="default"><a href="qc_lang1.html#K17" title="QC_LANG1:func.17">the_argument_of</a> <font color="Maroon" title="c1">p</font></span>)</span></span>)</span></span>)</span></span>)</span></span>)</span>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="qc_lang2.html#D5" title="QC_LANG2:def.5">QC_LANG2:def 5</a></span>;<br/>
<span class="kw">then </span> <a href="qc_lang3.html#K4" title="QC_LANG3:func.4">Vars</a> <font color="Maroon" title="c1">p</font>,<font color="Maroon" title="c2">V</font> = 
 <a href="qc_lang3.html#K4" title="QC_LANG3:func.4">Vars</a> <span class="p1">(<span class="default"><a href="qc_lang1.html#K14" title="QC_LANG1:func.14">All</a> <span class="p2">(<span class="default"><a href="qc_lang1.html#K20" title="QC_LANG1:func.20">bound_in</a> <span class="p3">(<span class="default"><a href="qc_lang1.html#K17" title="QC_LANG1:func.17">the_argument_of</a> <font color="Maroon" title="c1">p</font></span>)</span></span>)</span>,<span class="p2">(<span class="default"><a href="qc_lang1.html#K12" title="QC_LANG1:func.12">'not'</a> <span class="p3">(<span class="default"><a href="qc_lang1.html#K17" title="QC_LANG1:func.17">the_argument_of</a> <span class="p4">(<span class="default"><a href="qc_lang1.html#K21" title="QC_LANG1:func.21">the_scope_of</a> <span class="p5">(<span class="default"><a href="qc_lang1.html#K17" title="QC_LANG1:func.17">the_argument_of</a> <font color="Maroon" title="c1">p</font></span>)</span></span>)</span></span>)</span></span>)</span></span>)</span>,<font color="Maroon" title="c2">V</font>
<span class="kw">by</span> <span class="lab"><a class="ref" href="qc_lang3.html#T50" target="_self" title="QC_LANG3:th.50">Th50</a></span>
<br/>.= 
 <a href="qc_lang3.html#K4" title="QC_LANG3:func.4">Vars</a> <span class="p1">(<span class="default"><a href="qc_lang1.html#K12" title="QC_LANG1:func.12">'not'</a> <span class="p2">(<span class="default"><a href="qc_lang1.html#K17" title="QC_LANG1:func.17">the_argument_of</a> <span class="p3">(<span class="default"><a href="qc_lang1.html#K21" title="QC_LANG1:func.21">the_scope_of</a> <span class="p4">(<span class="default"><a href="qc_lang1.html#K17" title="QC_LANG1:func.17">the_argument_of</a> <font color="Maroon" title="c1">p</font></span>)</span></span>)</span></span>)</span></span>)</span>,<font color="Maroon" title="c2">V</font>
<span class="kw">by</span> <span class="lab"><a class="ref" href="qc_lang3.html#T55" target="_self" title="QC_LANG3:th.55">Th55</a></span>
<br/>.= 
 <a href="qc_lang3.html#K4" title="QC_LANG3:func.4">Vars</a> <span class="p1">(<span class="default"><a href="qc_lang1.html#K17" title="QC_LANG1:func.17">the_argument_of</a> <span class="p2">(<span class="default"><a href="qc_lang1.html#K21" title="QC_LANG1:func.21">the_scope_of</a> <span class="p3">(<span class="default"><a href="qc_lang1.html#K17" title="QC_LANG1:func.17">the_argument_of</a> <font color="Maroon" title="c1">p</font></span>)</span></span>)</span></span>)</span>,<font color="Maroon" title="c2">V</font>
<span class="kw">by</span> <span class="lab"><a class="ref" href="qc_lang3.html#T50" target="_self" title="QC_LANG3:th.50">Th50</a></span>
;<br/>
<span class="kw">hence </span><a NAME="E5:68"/>
 <a href="qc_lang3.html#K4" title="QC_LANG3:func.4">Vars</a> <font color="Maroon" title="c1">p</font>,<font color="Maroon" title="c2">V</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="qc_lang3.html#K4" title="QC_LANG3:func.4">Vars</a> <span class="p1">(<span class="default"><a href="qc_lang1.html#K17" title="QC_LANG1:func.17">the_argument_of</a> <span class="p2">(<span class="default"><a href="qc_lang1.html#K21" title="QC_LANG1:func.21">the_scope_of</a> <span class="p3">(<span class="default"><a href="qc_lang1.html#K17" title="QC_LANG1:func.17">the_argument_of</a> <font color="Maroon" title="c1">p</font></span>)</span></span>)</span></span>)</span>,<font color="Maroon" title="c2">V</font>
 ; <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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