<?xml version="1.0"?>
<div class="add">

<b>let </b><font color="Maroon">c<sub>1</sub></font> be   <a href="bhsp_1.html#NM1">RealUnitarySpace</a>;<br/><b>let </b><font color="Maroon">c<sub>2</sub></font>, <font color="Maroon">c<sub>3</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="E1:37"/><i><font color="Green">E15</font></i>: 
<font color="Maroon">c<sub>2</sub></font> is <a href="funct_1.html#V3">constant</a>
 <b>and </b><br/><a NAME="E2:37"/><i><font color="Green">E16</font></i>: 
<font color="Maroon">c<sub>3</sub></font> is    <a href="bhsp_3.html#M1" target="_self">subsequence</a> of <font color="Maroon">c<sub>2</sub></font>
 ;<br/>

<b>consider </b><font color="Maroon">c<sub>4</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="E4:37"/><i><font color="Green">E17</font></i>: 
<font color="Maroon">c<sub>3</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>2</sub></font> <a href="bhsp_3.html#K1" target="_self">*</a> <font color="Maroon">c<sub>4</sub></font>
 <b>by </b><i><a class="txt" href="bhsp_3.html#E2:37"><i><font color="Green">E16</font></i></a>, <a class="ref" href="bhsp_3.html#D4" target="_self">Def4</a></i>;<br/>
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="37_1"><b>now </b></a><div class="add"><b>let </b><font color="Maroon">c<sub>5</sub></font> be   <a href="nat_1.html#NM1">Nat</a>;<br/><b>thus </b><font color="Maroon">c<sub>3</sub></font> <a href="normsp_1.html#K2">.</a> <font color="Maroon">c<sub>5</sub></font> = 
<font color="Maroon">c<sub>2</sub></font> <a href="normsp_1.html#K2">.</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>4</sub></font> <a href="seqm_3.html#K2">.</a> <font color="Maroon">c<sub>5</sub></font></span>)</span>
<b>by </b><i><a class="txt" href="bhsp_3.html#E4:37"><i><font color="Green">E17</font></i></a>, <a class="ref" href="bhsp_3.html#T26" target="_self">Th26</a></i>
<br/>.= 
<font color="Maroon">c<sub>2</sub></font> <a href="normsp_1.html#K2">.</a> <font color="Maroon">c<sub>5</sub></font>
<b>by </b><i><a class="txt" href="bhsp_3.html#E1:37"><i><font color="Green">E15</font></i></a>, <a class="ref" href="bhsp_1.html#T70">BHSP_1:70</a></i>
;<br/></div><b>end;</b></div>
<b>hence </b><a NAME="E6:37"/>
<font color="Maroon">c<sub>2</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>3</sub></font>
 <b>by </b><i><a class="ref" href="funct_2.html#T113">FUNCT_2:113</a></i>;<br/>


</div>
