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<b>let </b><font color="Maroon">X</font> be   <a href="bhsp_1.html#NM1">RealUnitarySpace</a>;<br/><b>let </b><font color="Maroon">seq1</font> be   <a href="normsp_1.html#NM2">sequence</a> of <font color="Maroon">X</font>;<br/><b>let </b><font color="Maroon">seq2</font> be   <a href="normsp_1.html#NM2">sequence</a> of <font color="Maroon">X</font>;<br/><b>let </b><font color="Maroon">seq3</font> be   <a href="normsp_1.html#NM2">sequence</a> of <font color="Maroon">X</font>;<br/>







<b>assume </b><b>that </b><br/><a NAME="E1:35"/><i><font color="Green">E50</font></i>: 
<font color="Maroon">seq1</font> is    <a href="bhsp_3.html#M1" target="_self">subsequence</a> of <font color="Maroon">seq2</font>
 <b>and </b><br/><a NAME="E2:35"/><i><font color="Green">E51</font></i>: 
<font color="Maroon">seq2</font> is    <a href="bhsp_3.html#M1" target="_self">subsequence</a> of <font color="Maroon">seq3</font>
 ;<br/>

<b>consider </b><font color="Maroon">Nseq1</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="E4:35"/><i><font color="Green">E52</font></i>: 
<font color="Maroon">seq1</font> <a href="hidden.html#R1">=</a> <font color="Maroon">seq2</font> <a href="bhsp_3.html#K1" target="_self">*</a> <font color="Maroon">Nseq1</font>
 <b>by </b><i>, </i>;<br/>
<b>consider </b><font color="Maroon">Nseq2</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="E6:35"/><i><font color="Green">E53</font></i>: 
<font color="Maroon">seq2</font> <a href="hidden.html#R1">=</a> <font color="Maroon">seq3</font> <a href="bhsp_3.html#K1" target="_self">*</a> <font color="Maroon">Nseq2</font>
 <b>by </b><i>, </i>;<br/>
<b>take </b><font color="Maroon">Nseq</font> = <font color="Maroon">Nseq2</font> <a href="seqm_3.html#K4">*</a> <font color="Maroon">Nseq1</font>; <i><font color="Red">:: according to </font></i><a class="ref" href="bhsp_3.html#D4" target="_self">BHSP_3:def 4</a><br/>

<b>thus </b><a NAME="E7:35"/>
<font color="Maroon">seq1</font> <a href="hidden.html#R1">=</a> <font color="Maroon">seq3</font> <a href="bhsp_3.html#K1" target="_self">*</a> <font color="Maroon">Nseq</font>
 <b>by </b><i>, , <a class="ref" href="relat_1.html#T55">RELAT_1:55</a></i>;<br/>


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