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

<b>let </b><font color="Maroon" title="c1">F</font>, <font color="Maroon" title="c2">G</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="E1:28"/><i><font color="Green" title="E25">A1</font></i>: 
( <font color="Maroon" title="c1">F</font> <a href="qc_lang2.html#R2" title="QC_LANG2:pred.2">is_subformula_of</a> <font color="Maroon" title="c2">G</font> &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="c1">F</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</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">G</font></span>)</span> )
 ;<br/>

<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="28_1"><b>now </b></a><div class="add"><b>assume </b><a NAME="E1:28_1"/>
<font color="Maroon" title="c1">F</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c2">G</font>
 ;<br/><a NAME="E2:28_1"/><b>then </b>
<font color="Maroon" title="c1">F</font> <a href="qc_lang2.html#R3" title="QC_LANG2:pred.3">is_proper_subformula_of</a> <font color="Maroon" title="c2">G</font>
 <b>by </b><i><a class="txt" href="qc_lang4.html#E1:28"><i><font color="Green" title="E25">A1</font></i></a>, <a class="ref" href="qc_lang2.html#D22" title="QC_LANG2:def.22">QC_LANG2:def 22</a></i>;<br/><b>hence </b><a NAME="E3:28_1"/>
contradiction
 <b>by </b><i><a class="txt" href="qc_lang4.html#E1:28"><i><font color="Green" title="E25">A1</font></i></a>, <a class="ref" href="qc_lang2.html#T74" title="QC_LANG2:th.74">QC_LANG2:74</a></i>;<br/></div><b>end;</b></div>
<b>hence </b><a NAME="E3:28"/>
<font color="Maroon" title="c1">F</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c2">G</font>
 ;<br/>


</div>
