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<b>let </b><font color="Maroon">c<sub>1</sub></font> be   <a href="csspace.html#NM1">ComplexUnitarySpace</a>;<br/><b>let </b><font color="Maroon">c<sub>2</sub></font>, <font color="Maroon">c<sub>3</sub></font>, <font color="Maroon">c<sub>4</sub></font> be   <a href="normsp_1.html#NM2">sequence</a> of <font color="Maroon">c<sub>1</sub></font>;<br/>







<b>assume </b><b>that </b><br/><a NAME="E1:95"/><i><font color="Green">E48</font></i>: 
<font color="Maroon">c<sub>2</sub></font> is    <a href="bhsp_3.html#M1">subsequence</a> of <font color="Maroon">c<sub>3</sub></font>
 <b>and </b><br/><a NAME="E2:95"/><i><font color="Green">E49</font></i>: 
<font color="Maroon">c<sub>3</sub></font> is    <a href="bhsp_3.html#M1">subsequence</a> of <font color="Maroon">c<sub>4</sub></font>
 ;<br/>

<b>consider </b><font color="Maroon">c<sub>5</sub></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="E4:95"/><i><font color="Green">E50</font></i>: 
<font color="Maroon">c<sub>2</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>3</sub></font> <a href="clvect_2.html#K7" target="_self">*</a> <font color="Maroon">c<sub>5</sub></font>
 <b>by </b><i><a class="txt" href="clvect_2.html#E1:95"><i><font color="Green">E48</font></i></a>, <a class="ref" href="bhsp_3.html#D4">BHSP_3:def 4</a></i>;<br/>
<b>consider </b><font color="Maroon">c<sub>6</sub></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="E6:95"/><i><font color="Green">E51</font></i>: 
<font color="Maroon">c<sub>3</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>4</sub></font> <a href="clvect_2.html#K7" target="_self">*</a> <font color="Maroon">c<sub>6</sub></font>
 <b>by </b><i><a class="txt" href="clvect_2.html#E2:95"><i><font color="Green">E49</font></i></a>, <a class="ref" href="bhsp_3.html#D4">BHSP_3:def 4</a></i>;<br/>
<a NAME="E7:95"/>
ex <font color="Olive">b<sub>1</sub></font> being <a href="seqm_3.html#V1">increasing</a> <a href="seqm_3.html#NM1">Seq_of_Nat</a> st <font color="Maroon">c<sub>2</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>4</sub></font> <a href="clvect_2.html#K7" target="_self">*</a> <font color="Olive">b<sub>1</sub></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">c<sub>7</sub></font> = <font color="Maroon">c<sub>6</sub></font> <a href="seqm_3.html#K4">*</a> <font color="Maroon">c<sub>5</sub></font>;<br/>

<b>thus </b><a NAME="E1:95_1"/>
<font color="Maroon">c<sub>2</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>4</sub></font> <a href="clvect_2.html#K7" target="_self">*</a> <font color="Maroon">c<sub>7</sub></font>
 <b>by </b><i><a class="txt" href="clvect_2.html#E4:95"><i><font color="Green">E50</font></i></a>, <a class="txt" href="clvect_2.html#E6:95"><i><font color="Green">E51</font></i></a>, <a class="ref" href="relat_1.html#T55">RELAT_1:55</a></i>;<br/>


</div><b>end;</b></div>
<b>hence </b><a NAME="E8:95"/>
<font color="Maroon">c<sub>2</sub></font> is    <a href="bhsp_3.html#M1">subsequence</a> of <font color="Maroon">c<sub>4</sub></font>
 <b>by </b><i><a class="ref" href="bhsp_3.html#D4">BHSP_3:def 4</a></i>;<br/>


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