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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="zf_lang.html#NM2">ZF-formula</a>;<br/>



<b>assume </b><a NAME="E1:85"/><i><font color="Green">E71</font></i>: 
( <font color="Maroon">c<sub>1</sub></font> <a href="zf_lang.html#R2" target="_self">is_subformula_of</a> <font color="Maroon">c<sub>2</sub></font> &amp; <font color="Maroon">c<sub>2</sub></font> <a href="zf_lang.html#R2" target="_self">is_subformula_of</a> <font color="Maroon">c<sub>1</sub></font> )
 ;<br/>

<b>assume </b><a NAME="E2:85"/>
<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="E3:85"/><b>then </b>
( <font color="Maroon">c<sub>1</sub></font> <a href="zf_lang.html#R3" target="_self">is_proper_subformula_of</a> <font color="Maroon">c<sub>2</sub></font> &amp; <font color="Maroon">c<sub>2</sub></font> <a href="zf_lang.html#R3" target="_self">is_proper_subformula_of</a> <font color="Maroon">c<sub>1</sub></font> )
 
<b>by </b><i><a class="txt" href="zf_lang.html#E1:85"><i><font color="Green">E71</font></i></a>, <a class="ref" href="zf_lang.html#D41" target="_self">Def41</a></i>;<br/>
<a NAME="E4:85"/><b>then </b>
(  <a href="finseq_1.html#K3">len</a> <font color="Maroon">c<sub>1</sub></font> <a href="xxreal_0.html#NR3" target="_self">&lt;</a>  <a href="finseq_1.html#K3">len</a> <font color="Maroon">c<sub>2</sub></font> &amp;  <a href="finseq_1.html#K3">len</a> <font color="Maroon">c<sub>2</sub></font> <a href="xxreal_0.html#NR3" target="_self">&lt;</a>  <a href="finseq_1.html#K3">len</a> <font color="Maroon">c<sub>1</sub></font> )
 
<b>by </b><i><a class="ref" href="zf_lang.html#T83" target="_self">Th83</a></i>;<br/>
<b>hence </b><a NAME="E5:85"/>
contradiction
 ;<br/>


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