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<b>let </b><font color="Maroon">c<sub>1</sub></font> be   <a href="finseq_1.html#NM4">FinSubsequence</a>;<br/>

<b>consider </b><font color="Maroon">c<sub>2</sub></font> being   <a href="nat_1.html#NM1">Nat</a><b> such that </b><br/><a NAME="E2:5_1_1"/><i><font color="Green">E5</font></i>: 
 <a href="relat_1.html#K1">dom</a> <font color="Maroon">c<sub>1</sub></font> <a href="tarski.html#R1">c=</a>  <a href="finseq_1.html#K2">Seg</a> <font color="Maroon">c<sub>2</sub></font>
 <b>by </b><i><a class="ref" href="finseq_1.html#D12">FINSEQ_1:def 12</a></i>;<br/>
<a NAME="E3:5_1_1"/>
 <a href="relat_1.html#K1">dom</a> <font color="Maroon">c<sub>1</sub></font> is <a href="finset_1.html#V1">finite</a>
 
<b>by </b><i><a class="txt" href="pnproc_1.html#E2:5_1_1"><i><font color="Green">E5</font></i></a>, <a class="ref" href="finset_1.html#T13">FINSET_1:13</a></i>;<br/>
<b>hence </b><a NAME="E4:5_1_1"/>
<font color="Maroon">c<sub>1</sub></font> is <a href="finset_1.html#V1">finite</a>
 <b>by </b><i><a class="ref" href="finset_1.html#T29">FINSET_1:29</a></i>;<br/>


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