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<b>let </b><font color="Maroon" title="c1">G</font>, <font color="Maroon" title="c2">H</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> ;<br/>



<b>assume </b><a NAME="E1:57"/><i><font color="Green" title="E37">A1</font></i>: 
( <font color="Maroon" title="c1">G</font> <a href="qc_lang2.html#R2" title="QC_LANG2:pred.2">is_subformula_of</a> <font color="Maroon" title="c2">H</font> &amp; <font color="Maroon" title="c2">H</font> <a href="qc_lang2.html#R2" title="QC_LANG2:pred.2">is_subformula_of</a> <font color="Maroon" title="c1">G</font> )
 ;<br/>

<b>assume </b><a NAME="E2:57"/>
<font color="Maroon" title="c1">G</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c2">H</font>
 ;<br/>

<a NAME="E3:57"/><b>then </b>
( <font color="Maroon" title="c1">G</font> <a href="qc_lang2.html#R3" title="QC_LANG2:pred.3">is_proper_subformula_of</a> <font color="Maroon" title="c2">H</font> &amp; <font color="Maroon" title="c2">H</font> <a href="qc_lang2.html#R3" title="QC_LANG2:pred.3">is_proper_subformula_of</a> <font color="Maroon" title="c1">G</font> )
 
<b>by </b><i><a class="txt" href="qc_lang2.html#E1:57"><i><font color="Green" title="E37">A1</font></i></a>, <a class="ref" href="qc_lang2.html#D22" target="_self" title="QC_LANG2:def.22">Def22</a></i>;<br/>
<a NAME="E4:57"/><b>then </b>
(  <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <span class="p1">(<span class="default"><a href="qc_lang1.html#K10" title="QC_LANG1:func.10">@</a> <font color="Maroon" title="c1">G</font></span>)</span> <a href="xxreal_0.html#NR3" title="XXREAL_0:NR.3">&lt;</a>  <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <span class="p1">(<span class="default"><a href="qc_lang1.html#K10" title="QC_LANG1:func.10">@</a> <font color="Maroon" title="c2">H</font></span>)</span> &amp;  <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <span class="p1">(<span class="default"><a href="qc_lang1.html#K10" title="QC_LANG1:func.10">@</a> <font color="Maroon" title="c2">H</font></span>)</span> <a href="xxreal_0.html#NR3" title="XXREAL_0:NR.3">&lt;</a>  <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <span class="p1">(<span class="default"><a href="qc_lang1.html#K10" title="QC_LANG1:func.10">@</a> <font color="Maroon" title="c1">G</font></span>)</span> )
 
<b>by </b><i><a class="ref" href="qc_lang2.html#T74" target="_self" title="QC_LANG2:th.74">Th74</a></i>;<br/>
<b>hence </b><a NAME="E5:57"/>
contradiction
 ;<br/>


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