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

<b>let </b><font color="Maroon">T</font> be  non <a href="struct_0.html#V3">empty</a>  <a href="struct_0.html#L1">1-sorted</a> ;<br/><b>let </b><font color="Maroon">S1</font> be   <a href="normsp_1.html#NM2">sequence</a> of <font color="Maroon">T</font>;<br/><b>let </b><font color="Maroon">S2</font> be    <a href="bhsp_3.html#M1">subsequence</a> of <font color="Maroon">S1</font>;<br/><b>let </b><font color="Maroon">S3</font> be    <a href="bhsp_3.html#M1">subsequence</a> of <font color="Maroon">S2</font>;<br/>







<b>consider </b><font color="Maroon">NS2</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="E2:15"/><i><font color="Green">E27</font></i>: 
<font color="Maroon">S3</font> <a href="funct_2.html#R2">=</a> <font color="Maroon">S2</font> <a href="frechet2.html#K2" target="_self">*</a> <font color="Maroon">NS2</font>
 <b>by </b><i><a class="ref" href="bhsp_3.html#D4">BHSP_3:def 4</a></i>;<br/>
<b>consider </b><font color="Maroon">NS1</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="E4:15"/><i><font color="Green">E31</font></i>: 
<font color="Maroon">S2</font> <a href="funct_2.html#R2">=</a> <font color="Maroon">S1</font> <a href="frechet2.html#K2" target="_self">*</a> <font color="Maroon">NS1</font>
 <b>by </b><i><a class="ref" href="bhsp_3.html#D4">BHSP_3:def 4</a></i>;<br/>
<a NAME="E5:15"/>
<font color="Maroon">S3</font> <a href="funct_2.html#R2">=</a> <font color="Maroon">S1</font> <a href="frechet2.html#K2" target="_self">*</a> <span class="p1">(<span class="default"><font color="Maroon">NS1</font> <a href="seqm_3.html#K4">*</a> <font color="Maroon">NS2</font></span>)</span>
 
<b>by </b><i>, , <a class="ref" href="relat_1.html#T55">RELAT_1:55</a></i>;<br/>
<b>hence </b><a NAME="E6:15"/>
<font color="Maroon">S3</font> is    <a href="bhsp_3.html#M1">subsequence</a> of <font color="Maroon">S1</font>
 ;<br/>


</div>
