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<b>let </b><font color="Maroon">seq</font> be   <a href="seq_1.html#NM1">Real_Sequence</a>;<br/><b>let </b><font color="Maroon">seq1</font> be   <a href="seq_1.html#NM1">Real_Sequence</a>;<br/><b>let </b><font color="Maroon">seq2</font> be   <a href="seq_1.html#NM1">Real_Sequence</a>;<br/>





<b>assume </b><b>that </b><br/><a NAME="E1:62"/><i><font color="Green">E31</font></i>: 
<font color="Maroon">seq</font> is    <a href="seqm_3.html#M1" target="_self">subsequence</a> of <font color="Maroon">seq1</font>
 <b>and </b><br/><a NAME="E2:62"/><i><font color="Green">E33</font></i>: 
<font color="Maroon">seq1</font> is    <a href="seqm_3.html#M1" target="_self">subsequence</a> of <font color="Maroon">seq2</font>
 ;<br/>

<b>consider </b><font color="Maroon">Nseq1</font> being  <a href="seqm_3.html#V1" target="_self">increasing</a> <a href="seqm_3.html#NM1">Seq_of_Nat</a><b> such that </b><br/><a NAME="E4:62"/><i><font color="Green">E34</font></i>: 
<font color="Maroon">seq</font> <a href="hidden.html#R1">=</a> <font color="Maroon">seq1</font> <a href="seqm_3.html#K3" target="_self">*</a> <font color="Maroon">Nseq1</font>
 <b>by </b><i>, <a class="txt" href="seqm_3.html#E6:62"><i><font color="Green">E37</font></i></a></i>;<br/>
<b>consider </b><font color="Maroon">Nseq2</font> being  <a href="seqm_3.html#V1" target="_self">increasing</a> <a href="seqm_3.html#NM1">Seq_of_Nat</a><b> such that </b><br/><a NAME="E6:62"/><i><font color="Green">E37</font></i>: 
<font color="Maroon">seq1</font> <a href="hidden.html#R1">=</a> <font color="Maroon">seq2</font> <a href="seqm_3.html#K3" target="_self">*</a> <font color="Maroon">Nseq2</font>
 <b>by </b><i><a class="txt" href="seqm_3.html#E5"><i><font color="Green">Lemma43</font></i></a>, <a class="txt" href="seqm_3.html#E6:62"><i><font color="Green">E37</font></i></a></i>;<br/>
<b>take </b><font color="Maroon">Nseq</font> = <font color="Maroon">Nseq2</font> <a href="seqm_3.html#K4" target="_self">*</a> <font color="Maroon">Nseq1</font>; <i><font color="Red">:: according to </font></i><a class="ref" href="seqm_3.html#D10" target="_self">SEQM_3:def 10</a><br/>

<b>thus </b><a NAME="E7:62"/>
<font color="Maroon">seq</font> <a href="hidden.html#R1">=</a> <font color="Maroon">seq2</font> <a href="seqm_3.html#K3" target="_self">*</a> <font color="Maroon">Nseq</font>
 <b>by </b><i><a class="ref" href="seqm_3.html#D1" target="_self">Def1</a>, <a class="ref" href="seqm_3.html#D2" target="_self">Def2</a>, <a class="ref" href="relat_1.html#T55">RELAT_1:55</a></i>;<br/>


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