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<b>let </b><font color="Maroon" title="c1">f</font> be   <a href="finseq_1.html#NM4" title="FINSEQ_1:NM.4">FinSubsequence</a>;<br/>

<b>assume </b><a NAME="E1:123"/>
<font color="Maroon" title="c1">f</font> is   <a href="finseq_1.html#NM1" title="FINSEQ_1:NM.1">FinSequence</a>
 ;<br/>

<b>then reconsider </b><font color="Maroon" title="c2">ss'</font> = <font color="Maroon" title="c1">f</font> as   <a href="finseq_1.html#NM1" title="FINSEQ_1:NM.1">FinSequence</a> ;<br/>
<b>consider </b><font color="Maroon" title="c3">k</font> being    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of  <a href="numbers.html#K5" title="NUMBERS:func.5">NAT</a> <b> such that </b><br/><a NAME="E4:123"/><i><font color="Green" title="E76">A1</font></i>: 
 <a href="finseq_1.html#K4" title="FINSEQ_1:func.4">dom</a> <font color="Maroon" title="c2">ss'</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="finseq_1.html#K2" title="FINSEQ_1:func.2">Seg</a> <font color="Maroon" title="c3">k</font>
 <b>by </b><i><a class="ref" href="finseq_1.html#D2" title="FINSEQ_1:def.2">FINSEQ_1:def 2</a></i>;<br/>
<a NAME="E5:123"/><i><font color="Green" title="E77">A2</font></i>: 
 <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Maroon" title="c2">ss'</font> <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> <font color="Maroon" title="c3">k</font>
 
<b>by </b><i><a class="txt" href="finseq_3.html#E4:123"><i><font color="Green" title="E76">A1</font></i></a>, <a class="ref" href="finseq_1.html#D3" title="FINSEQ_1:def.3">FINSEQ_1:def 3</a></i>;<br/>
 <a href="finseq_1.html#K15" title="FINSEQ_1:func.15">Seq</a> <font color="Maroon" title="c1">f</font> = 
<font color="Maroon" title="c1">f</font> <a href="funct_1.html#NK3" title="FUNCT_1:NK.3">*</a> <span class="p1">(<span class="default"><a href="finseq_1.html#K14" title="FINSEQ_1:func.14">Sgm</a> <span class="p2">(<span class="default"><a href="finseq_1.html#K2" title="FINSEQ_1:func.2">Seg</a> <font color="Maroon" title="c3">k</font></span>)</span></span>)</span>
<b>by </b><i><a class="txt" href="finseq_3.html#E4:123"><i><font color="Green" title="E76">A1</font></i></a>, <a class="ref" href="finseq_1.html#D14" title="FINSEQ_1:def.14">FINSEQ_1:def 14</a></i>
<br/>.= 
<font color="Maroon" title="c1">f</font> <a href="funct_1.html#NK3" title="FUNCT_1:NK.3">*</a> <span class="p1">(<span class="default"><a href="finseq_2.html#K1" title="FINSEQ_2:func.1">idseq</a> <font color="Maroon" title="c3">k</font></span>)</span>
<b>by </b><i><a class="ref" href="finseq_3.html#T54" target="_self" title="FINSEQ_3:th.54">Th54</a></i>
<br/>.= 
<font color="Maroon" title="c1">f</font>
<b>by </b><i><a class="txt" href="finseq_3.html#E5:123"><i><font color="Green" title="E77">A2</font></i></a>, <a class="ref" href="finseq_2.html#T64" title="FINSEQ_2:th.64">FINSEQ_2:64</a></i>
;<br/>
<b>hence </b><a NAME="E7:123"/>
 <a href="finseq_1.html#K15" title="FINSEQ_1:func.15">Seq</a> <font color="Maroon" title="c1">f</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c1">f</font>
 ;<br/>


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