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<span class="kw">let </span><font color="Maroon" title="c1">p</font>, <font color="Maroon" title="c2">q</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="firebrick">::  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> holds   <a href="qc_lang3.html#K4" title="QC_LANG3:func.4">Vars</a> (<span class="p1">(<span class="default"><font color="Maroon" title="c1">p</font> <a href="qc_lang1.html#K13" title="QC_LANG1:func.13">'&amp;'</a> <font color="Maroon" title="c2">q</font></span>)</span>,<font color="Olive" title="b1">V</font>) <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><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>)</span>)</span> <a href="subset_1.html#K4" title="SUBSET_1:func.4">\/</a> <span class="p1">(<span class="default"><a href="qc_lang3.html#K4" title="QC_LANG3:func.4">Vars</a> (<font color="Maroon" title="c2">q</font>,<font color="Olive" title="b1">V</font>)</span>)</span></span><br/><span class="kw">let </span><font color="Maroon" title="c3">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="firebrick">::  thesis: </font></span></a><span class="hide">  <a href="qc_lang3.html#K4" title="QC_LANG3:func.4">Vars</a> (<span class="p1">(<span class="default"><font color="Maroon" title="c1">p</font> <a href="qc_lang1.html#K13" title="QC_LANG1:func.13">'&amp;'</a> <font color="Maroon" title="c2">q</font></span>)</span>,<font color="Maroon" title="c3">V</font>) <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="qc_lang3.html#K4" title="QC_LANG3:func.4">Vars</a> (<font color="Maroon" title="c1">p</font>,<font color="Maroon" title="c3">V</font>)</span>)</span> <a href="subset_1.html#K4" title="SUBSET_1:func.4">\/</a> <span class="p1">(<span class="default"><a href="qc_lang3.html#K4" title="QC_LANG3:func.4">Vars</a> (<font color="Maroon" title="c2">q</font>,<font color="Maroon" title="c3">V</font>)</span>)</span></span><br/>





<span class="kw">set </span><font color="Maroon" title="c4">pq</font> = <font color="Maroon" title="c1">p</font> <a href="qc_lang1.html#K13" title="QC_LANG1:func.13">'&amp;'</a> <font color="Maroon" title="c2">q</font>;<br/>
<a NAME="E1:49"/><span class="lab"><font color="Green" title="E28">A1</font></span>: 
<font color="Maroon" title="c1">p</font> <a href="qc_lang1.html#K13" title="QC_LANG1:func.13">'&amp;'</a> <font color="Maroon" title="c2">q</font> is  <a href="qc_lang1.html#V4" title="QC_LANG1:attr.4">conjunctive</a> 
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="qc_lang1.html#D18" title="QC_LANG1:def.18">QC_LANG1:def 18</a></span>;<br/>
<a NAME="E2:49"/><span class="kw">then </span>
(  <a href="qc_lang1.html#K18" title="QC_LANG1:func.18">the_left_argument_of</a> <span class="p1">(<span class="default"><font color="Maroon" title="c1">p</font> <a href="qc_lang1.html#K13" title="QC_LANG1:func.13">'&amp;'</a> <font color="Maroon" title="c2">q</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c1">p</font> &amp;  <a href="qc_lang1.html#K19" title="QC_LANG1:func.19">the_right_argument_of</a> <span class="p1">(<span class="default"><font color="Maroon" title="c1">p</font> <a href="qc_lang1.html#K13" title="QC_LANG1:func.13">'&amp;'</a> <font color="Maroon" title="c2">q</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c2">q</font> )
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="qc_lang1.html#D23" title="QC_LANG1:def.23">QC_LANG1:def 23</a>, <a class="ref" href="qc_lang1.html#D24" title="QC_LANG1:def.24">QC_LANG1:def 24</a></span>;<br/>
<span class="kw">hence </span><a NAME="E3:49"/>
 <a href="qc_lang3.html#K4" title="QC_LANG3:func.4">Vars</a> (<span class="p1">(<span class="default"><font color="Maroon" title="c1">p</font> <a href="qc_lang1.html#K13" title="QC_LANG1:func.13">'&amp;'</a> <font color="Maroon" title="c2">q</font></span>)</span>,<font color="Maroon" title="c3">V</font>) <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="qc_lang3.html#K4" title="QC_LANG3:func.4">Vars</a> (<font color="Maroon" title="c1">p</font>,<font color="Maroon" title="c3">V</font>)</span>)</span> <a href="subset_1.html#K4" title="SUBSET_1:func.4">\/</a> <span class="p1">(<span class="default"><a href="qc_lang3.html#K4" title="QC_LANG3:func.4">Vars</a> (<font color="Maroon" title="c2">q</font>,<font color="Maroon" title="c3">V</font>)</span>)</span>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:49"><span class="lab"><font color="Green" title="E28">A1</font></span></a>, <a class="txt" href="qc_lang3.html#E40"><span class="lab"><font color="Green" title="E22">Lm2</font></span></a></span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> verum</span><br/>


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