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<b>let </b><font color="Maroon">c<sub>1</sub></font>, <font color="Maroon">c<sub>2</sub></font> be    <a href="subset_1.html#M1">Element</a> of  <a href="qc_lang1.html#K8">QC-WFF</a> ;<br/>



<b>assume </b><a NAME="E1:28"/><i><font color="Green">E25</font></i>: 
( <font color="Maroon">c<sub>1</sub></font> <a href="qc_lang2.html#R2">is_subformula_of</a> <font color="Maroon">c<sub>2</sub></font> &amp;  <a href="finseq_1.html#K3">len</a> <span class="p1">(<span class="default"><a href="qc_lang1.html#K10">@</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="hidden.html#R1">=</a>  <a href="finseq_1.html#K3">len</a> <span class="p1">(<span class="default"><a href="qc_lang1.html#K10">@</a> <font color="Maroon">c<sub>2</sub></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">c<sub>1</sub></font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <font color="Maroon">c<sub>2</sub></font>
 ;<br/><a NAME="E2:28_1"/><b>then </b>
<font color="Maroon">c<sub>1</sub></font> <a href="qc_lang2.html#R3">is_proper_subformula_of</a> <font color="Maroon">c<sub>2</sub></font>
 <b>by </b><i><a class="txt" href="qc_lang4.html#E1:28"><i><font color="Green">E25</font></i></a>, <a class="ref" href="qc_lang2.html#D22">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">E25</font></i></a>, <a class="ref" href="qc_lang2.html#T74">QC_LANG2:74</a></i>;<br/></div><b>end;</b></div>
<b>hence </b><a NAME="E3:28"/>
<font color="Maroon">c<sub>1</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>2</sub></font>
 ;<br/>


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