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<b>let </b><font color="Maroon" title="c1">X</font> be   <a href="csspace.html#NM1" title="CSSPACE:NM.1">ComplexUnitarySpace</a>;<br/><b>let </b><font color="Maroon" title="c2">seq1</font>, <font color="Maroon" title="c3">seq2</font>, <font color="Maroon" title="c4">seq3</font> be   <a href="normsp_1.html#NM2" title="NORMSP_1:NM.2">sequence</a> of <font color="Maroon" title="c1">X</font>;<br/>







<b>assume </b><b>that </b><br/><a NAME="E1:95"/><i><font color="Green" title="E48">A1</font></i>: 
<font color="Maroon" title="c2">seq1</font> is    <a href="bhsp_3.html#M1" title="BHSP_3:mode.1">subsequence</a> of <font color="Maroon" title="c3">seq2</font>
 <b>and </b><br/><a NAME="E2:95"/><i><font color="Green" title="E49">A2</font></i>: 
<font color="Maroon" title="c3">seq2</font> is    <a href="bhsp_3.html#M1" title="BHSP_3:mode.1">subsequence</a> of <font color="Maroon" title="c4">seq3</font>
 ;<br/>

<b>consider </b><font color="Maroon" title="c5">Nseq1</font> being  <a href="seqm_3.html#V1" title="SEQM_3:attr.1">increasing</a> <a href="seqm_3.html#NM1" title="SEQM_3:NM.1">Seq_of_Nat</a><b> such that </b><br/><a NAME="E4:95"/><i><font color="Green" title="E50">A3</font></i>: 
<font color="Maroon" title="c2">seq1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c3">seq2</font> <a href="clvect_2.html#K7" title="CLVECT_2:func.7">*</a> <font color="Maroon" title="c5">Nseq1</font>
 <b>by </b><i><a class="txt" href="clvect_2.html#E1:95"><i><font color="Green" title="E48">A1</font></i></a>, <a class="ref" href="bhsp_3.html#D4" title="BHSP_3:def.4">BHSP_3:def 4</a></i>;<br/>
<b>consider </b><font color="Maroon" title="c6">Nseq2</font> being  <a href="seqm_3.html#V1" title="SEQM_3:attr.1">increasing</a> <a href="seqm_3.html#NM1" title="SEQM_3:NM.1">Seq_of_Nat</a><b> such that </b><br/><a NAME="E6:95"/><i><font color="Green" title="E51">A4</font></i>: 
<font color="Maroon" title="c3">seq2</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c4">seq3</font> <a href="clvect_2.html#K7" title="CLVECT_2:func.7">*</a> <font color="Maroon" title="c6">Nseq2</font>
 <b>by </b><i><a class="txt" href="clvect_2.html#E2:95"><i><font color="Green" title="E49">A2</font></i></a>, <a class="ref" href="bhsp_3.html#D4" title="BHSP_3:def.4">BHSP_3:def 4</a></i>;<br/>
<a NAME="E7:95"/>
 ex <font color="Olive" title="b1">Nseq</font> being <a href="seqm_3.html#V1" title="SEQM_3:attr.1">increasing</a> <a href="seqm_3.html#NM1" title="SEQM_3:NM.1">Seq_of_Nat</a> st <font color="Maroon" title="c2">seq1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c4">seq3</font> <a href="clvect_2.html#K7" title="CLVECT_2:func.7">*</a> <font color="Olive" title="b1">Nseq</font>
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="95_1"><b>proof </b></a><div class="add">

<b>take </b><font color="Maroon" title="c7">Nseq</font> = <font color="Maroon" title="c6">Nseq2</font> <a href="seqm_3.html#K4" title="SEQM_3:func.4">*</a> <font color="Maroon" title="c5">Nseq1</font>;<br/>

<b>thus </b><a NAME="E1:95_1"/>
<font color="Maroon" title="c2">seq1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c4">seq3</font> <a href="clvect_2.html#K7" title="CLVECT_2:func.7">*</a> <font color="Maroon" title="c7">Nseq</font>
 <b>by </b><i><a class="txt" href="clvect_2.html#E4:95"><i><font color="Green" title="E50">A3</font></i></a>, <a class="txt" href="clvect_2.html#E6:95"><i><font color="Green" title="E51">A4</font></i></a>, <a class="ref" href="relat_1.html#T55" title="RELAT_1:th.55">RELAT_1:55</a></i>;<br/>


</div><b>end;</b></div>
<b>hence </b><a NAME="E8:95"/>
<font color="Maroon" title="c2">seq1</font> is    <a href="bhsp_3.html#M1" title="BHSP_3:mode.1">subsequence</a> of <font color="Maroon" title="c4">seq3</font>
 <b>by </b><i><a class="ref" href="bhsp_3.html#D4" title="BHSP_3:def.4">BHSP_3:def 4</a></i>;<br/>


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