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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="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>  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_lang2.html#K4" title="QC_LANG2:func.4">&lt;=&gt;</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="Red">::  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_lang2.html#K4" title="QC_LANG2:func.4">&lt;=&gt;</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/>





<a NAME="E1:67"/><span class="lab"><font color="Green" title="E33">A1</font></span>: 
 <a href="qc_lang2.html#K14" title="QC_LANG2:func.14">the_right_side_of</a> <span class="p1">(<span class="default"><font color="Maroon" title="c1">p</font> <a href="qc_lang2.html#K4" title="QC_LANG2:func.4">&lt;=&gt;</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_lang2.html#T47" title="QC_LANG2:th.47">QC_LANG2:47</a></span>;<br/>
<a NAME="E2:67"/>
( <font color="Maroon" title="c1">p</font> <a href="qc_lang2.html#K4" title="QC_LANG2:func.4">&lt;=&gt;</a> <font color="Maroon" title="c2">q</font> is  <a href="qc_lang2.html#V3" title="QC_LANG2:attr.3">biconditional</a>  &amp;  <a href="qc_lang2.html#K13" title="QC_LANG2:func.13">the_left_side_of</a> <span class="p1">(<span class="default"><font color="Maroon" title="c1">p</font> <a href="qc_lang2.html#K4" title="QC_LANG2:func.4">&lt;=&gt;</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> )
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="qc_lang2.html#T47" title="QC_LANG2:th.47">QC_LANG2:47</a>, <a class="ref" href="qc_lang2.html#D12" title="QC_LANG2:def.12">QC_LANG2:def 12</a></span>;<br/>
<span class="kw">hence </span><a NAME="E3:67"/>
 <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_lang2.html#K4" title="QC_LANG2:func.4">&lt;=&gt;</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="#E1:67"><span class="lab"><font color="Green" title="E33">A1</font></span></a>, <a class="ref" href="qc_lang3.html#T60" target="_self" title="QC_LANG3:th.60">Th60</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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