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<b>let </b><font color="Maroon">seq</font> be   <a href="comseq_1.html#NM1">Complex_Sequence</a>;<br/><b>let </b><font color="Maroon">seq1</font> be   <a href="comseq_1.html#NM1">Complex_Sequence</a>;<br/>



<b>assume </b><a NAME="E1:63"/>
<font color="Maroon">seq</font> is    <a href="comseq_3.html#M1" target="_self">subsequence</a> of <font color="Maroon">seq1</font>
 ;<br/>

<b>then consider </b><font color="Maroon">Nseq</font> being  <a href="seqm_3.html#V1">increasing</a> <a href="seqm_3.html#NM1">Seq_of_Nat</a><b> such that </b><br/><a NAME="E3:63"/><i><font color="Green">E35</font></i>: 
<font color="Maroon">seq</font> <a href="funct_2.html#R2">=</a> <font color="Maroon">seq1</font> <a href="comseq_3.html#K5" target="_self">*</a> <font color="Maroon">Nseq</font>
 <b>by </b><i/>;<br/>
<a NAME="E4:63"/>
 <a href="comseq_3.html#K3" target="_self">Re</a> <font color="Maroon">seq</font> <a href="funct_2.html#R2">=</a> <span class="p1">(<span class="default"><a href="comseq_3.html#K3" target="_self">Re</a> <font color="Maroon">seq1</font></span>)</span> <a href="seqm_3.html#K3">*</a> <font color="Maroon">Nseq</font>
 
<b>by </b><i><a class="ref" href="comseq_3.html#T3" target="_self">Th3</a>, </i>;<br/>
<b>hence </b><a NAME="E5:63"/>
 <a href="comseq_3.html#K3" target="_self">Re</a> <font color="Maroon">seq</font> is    <a href="seqm_3.html#M1">subsequence</a> of  <a href="comseq_3.html#K3" target="_self">Re</a> <font color="Maroon">seq1</font>
 <b>by </b><i><a class="ref" href="seqm_3.html#D10">SEQM_3:def 10</a></i>;<br/>

<a NAME="E6:63"/>
 <a href="comseq_3.html#K4" target="_self">Im</a> <font color="Maroon">seq</font> <a href="funct_2.html#R2">=</a> <span class="p1">(<span class="default"><a href="comseq_3.html#K4" target="_self">Im</a> <font color="Maroon">seq1</font></span>)</span> <a href="seqm_3.html#K3">*</a> <font color="Maroon">Nseq</font>
 
<b>by </b><i><a class="ref" href="comseq_3.html#T3" target="_self">Th3</a>, </i>;<br/>
<b>hence </b><a NAME="E7:63"/>
 <a href="comseq_3.html#K4" target="_self">Im</a> <font color="Maroon">seq</font> is    <a href="seqm_3.html#M1">subsequence</a> of  <a href="comseq_3.html#K4" target="_self">Im</a> <font color="Maroon">seq1</font>
 <b>by </b><i><a class="ref" href="seqm_3.html#D10">SEQM_3:def 10</a></i>;<br/>


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