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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="nat_1.html#NM1">Nat</a>;<br/><b>let </b><font color="Maroon">c<sub>3</sub></font> be  non <a href="xboole_0.html#V1">empty</a>  <a href="hidden.html#M1">set</a> ;<br/>





<b>consider </b><font color="Maroon">c<sub>4</sub></font> being    <a href="subset_1.html#M1">Element</a> of <font color="Maroon">c<sub>3</sub></font>;<br/>
<a NAME="E2:130"/>
( <font color="Maroon">c<sub>1</sub></font> <a href="finseq_2.html#K2" target="_self">|-&gt;</a> <font color="Maroon">c<sub>4</sub></font> is    <a href="finseq_1.html#M2">FinSequence</a> of <font color="Maroon">c<sub>3</sub></font> &amp;  <a href="finseq_1.html#K3">len</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="finseq_2.html#K2" target="_self">|-&gt;</a> <font color="Maroon">c<sub>4</sub></font></span>)</span> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>1</sub></font> )
 
<b>by </b><i><a class="ref" href="finseq_2.html#T69" target="_self">Th69</a>, <a class="ref" href="finseq_2.html#T77" target="_self">Th77</a></i>;<br/>
<b>then reconsider </b><font color="Maroon">c<sub>5</sub></font> = <font color="Maroon">c<sub>1</sub></font> <a href="finseq_2.html#K2" target="_self">|-&gt;</a> <font color="Maroon">c<sub>4</sub></font> as    <a href="finseq_2.html#M2" target="_self">Element</a> of <font color="Maroon">c<sub>1</sub></font> <a href="finseq_2.html#K4" target="_self">-tuples_on</a> <font color="Maroon">c<sub>3</sub></font> <b>by </b><i><a class="ref" href="finseq_2.html#T110" target="_self">Th110</a></i>;<br/>
<b>assume </b><a NAME="E4:130"/>
<font color="Maroon">c<sub>1</sub></font> <a href="finseq_2.html#K4" target="_self">-tuples_on</a> <font color="Maroon">c<sub>3</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>2</sub></font> <a href="finseq_2.html#K4" target="_self">-tuples_on</a> <font color="Maroon">c<sub>3</sub></font>
 ;<br/>

<a NAME="E5:130"/><b>then </b>
(  <a href="finseq_1.html#K3">len</a> <font color="Maroon">c<sub>5</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>1</sub></font> &amp;  <a href="finseq_1.html#K3">len</a> <font color="Maroon">c<sub>5</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>2</sub></font> )
 
<b>by </b><i><a class="ref" href="finseq_2.html#T109" target="_self">Th109</a></i>;<br/>
<b>hence </b><a NAME="E6:130"/>
<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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