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<b>let </b><font color="Maroon" title="c1">T</font> be  non <a href="struct_0.html#V2" title="STRUCT_0:attr.2">empty</a>  <a href="struct_0.html#L1" title="STRUCT_0:struct.1">1-sorted</a> ;<br/><b>let </b><font color="Maroon" title="c2">S1</font> be   <a href="struct_0.html#NM9" title="STRUCT_0:NM.9">sequence</a> of <font color="Maroon" title="c1">T</font>;<br/><b>let </b><font color="Maroon" title="c3">S2</font> be    <a href="bhsp_3.html#M1" title="BHSP_3:mode.1">subsequence</a> of <font color="Maroon" title="c2">S1</font>;<br/><b>let </b><font color="Maroon" title="c4">S3</font> be    <a href="bhsp_3.html#M1" title="BHSP_3:mode.1">subsequence</a> of <font color="Maroon" title="c3">S2</font>;<br/>







<b>consider </b><font color="Maroon" title="c5">NS2</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="E2:15"/><i><font color="Green" title="E15">A1</font></i>: 
<font color="Maroon" title="c4">S3</font> <a href="funct_2.html#R2" title="FUNCT_2:pred.2">=</a> <font color="Maroon" title="c3">S2</font> <a href="frechet2.html#K2" title="FRECHET2:func.2">*</a> <font color="Maroon" title="c5">NS2</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/>
<b>consider </b><font color="Maroon" title="c6">NS1</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="E4:15"/><i><font color="Green" title="E16">A2</font></i>: 
<font color="Maroon" title="c3">S2</font> <a href="funct_2.html#R2" title="FUNCT_2:pred.2">=</a> <font color="Maroon" title="c2">S1</font> <a href="frechet2.html#K2" title="FRECHET2:func.2">*</a> <font color="Maroon" title="c6">NS1</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/>
<a NAME="E5:15"/>
<font color="Maroon" title="c4">S3</font> <a href="funct_2.html#R2" title="FUNCT_2:pred.2">=</a> <font color="Maroon" title="c2">S1</font> <a href="frechet2.html#K2" title="FRECHET2:func.2">*</a> <span class="p1">(<span class="default"><font color="Maroon" title="c6">NS1</font> <a href="seqm_3.html#K4" title="SEQM_3:func.4">*</a> <font color="Maroon" title="c5">NS2</font></span>)</span>
 
<b>by </b><i><a class="txt" href="frechet2.html#E2:15"><i><font color="Green" title="E15">A1</font></i></a>, <a class="txt" href="frechet2.html#E4:15"><i><font color="Green" title="E16">A2</font></i></a>, <a class="ref" href="relat_1.html#T55" title="RELAT_1:th.55">RELAT_1:55</a></i>;<br/>
<b>hence </b><a NAME="E6:15"/>
<font color="Maroon" title="c4">S3</font> is    <a href="bhsp_3.html#M1" title="BHSP_3:mode.1">subsequence</a> of <font color="Maroon" title="c2">S1</font>
 ;<br/>


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