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

<b>consider </b><font color="Maroon">k</font> being    <a href="subset_1.html#M2">Element</a> of  <a href="numbers.html#K5">NAT</a> <b> such that </b><br/><a NAME="E2:31"/><i><font color="Green">E34</font></i>: 
 <a href="relat_1.html#K1">dom</a> <font color="Maroon">q</font> <a href="tarski.html#R1">c=</a>  <a href="finseq_1.html#K2">Seg</a> <font color="Maroon">k</font>
 <b>by </b><i><a class="ref" href="finseq_1.html#D12">FINSEQ_1:def 12</a></i>;<br/>
<b>reconsider </b><font color="Maroon">IK</font> =  <a href="relat_1.html#K6">id</a> <span class="p1">(<span class="default"><a href="finseq_1.html#K2">Seg</a> <font color="Maroon">k</font></span>)</span> as   <a href="funct_1.html#NM1">Function</a> ;<br/>
<b>set </b><font color="Maroon">IS</font> = <font color="Maroon">IK</font> <a href="funct_4.html#K1">+*</a> <font color="Maroon">q</font>;<br/>
 <a href="relat_1.html#K1">dom</a> <span class="p1">(<span class="default"><font color="Maroon">IK</font> <a href="funct_4.html#K1">+*</a> <font color="Maroon">q</font></span>)</span> = 
<span class="p1">(<span class="default"><a href="relat_1.html#K1">dom</a> <font color="Maroon">IK</font></span>)</span> <a href="xboole_0.html#K2">\/</a> <span class="p1">(<span class="default"><a href="relat_1.html#K1">dom</a> <font color="Maroon">q</font></span>)</span>
<b>by </b><i><a class="ref" href="funct_4.html#D1">FUNCT_4:def 1</a></i>
<br/>.= 
<span class="p1">(<span class="default"><a href="finseq_1.html#K2">Seg</a> <font color="Maroon">k</font></span>)</span> <a href="xboole_0.html#K2">\/</a> <span class="p1">(<span class="default"><a href="relat_1.html#K1">dom</a> <font color="Maroon">q</font></span>)</span>
<b>by </b><i><a class="ref" href="relat_1.html#T71">RELAT_1:71</a></i>
<br/>.= 
 <a href="finseq_1.html#K2">Seg</a> <font color="Maroon">k</font>
<b>by </b><i>, <a class="ref" href="xboole_1.html#T12">XBOOLE_1:12</a></i>
;<br/>
<b>then reconsider </b><font color="Maroon">IS</font> = <font color="Maroon">IK</font> <a href="funct_4.html#K1">+*</a> <font color="Maroon">q</font> as   <a href="finseq_1.html#NM1">FinSequence</a> <b>by </b><i><a class="ref" href="finseq_1.html#D2">FINSEQ_1:def 2</a></i>;<br/>
<a NAME="E6:31"/>
<font color="Maroon">q</font> <a href="tarski.html#R1">c=</a> <font color="Maroon">IS</font>
 
<b>by </b><i><a class="ref" href="funct_4.html#T26">FUNCT_4:26</a></i>;<br/>
<b>hence </b><a NAME="E7:31"/>
 ex <font color="Olive">p</font> being  <a href="finseq_1.html#NM1">FinSequence</a> st <font color="Maroon">q</font> <a href="tarski.html#R1">c=</a> <font color="Olive">p</font>
 ;<br/>


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