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<b>let </b><font color="Maroon">S</font> be   <a href="normsp_1.html#NM1">RealNormSpace</a>;<br/><b>let </b><font color="Maroon">seq</font> be   <a href="normsp_1.html#NM2">sequence</a> of <font color="Maroon">S</font>;<br/><b>let </b><font color="Maroon">seq1</font> be   <a href="normsp_1.html#NM2">sequence</a> of <font color="Maroon">S</font>;<br/>





<b>assume </b><b>that </b><br/><a NAME="E1:22"/><i><font color="Green">E43</font></i>: 
<font color="Maroon">seq</font> is <a href="funct_1.html#V3">constant</a>
 <b>and </b><br/><a NAME="E2:22"/><i><font color="Green">E45</font></i>: 
<font color="Maroon">seq1</font> is    <a href="bhsp_3.html#M1">subsequence</a> of <font color="Maroon">seq</font>
 ;<br/>

<b>consider </b><font color="Maroon">Nseq</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="E4:22"/><i><font color="Green">E46</font></i>: 
<font color="Maroon">seq1</font> <a href="funct_2.html#R2">=</a> <font color="Maroon">seq</font> <a href="lopban_3.html#K5">*</a> <font color="Maroon">Nseq</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">r</font> being   <a href="pre_topc.html#NM2">Point</a> of <font color="Maroon">S</font><b> such that </b><br/><a NAME="E6:22"/><i><font color="Green">E47</font></i>: 
for <font color="Olive">n</font> being   <a href="subset_1.html#M2">Element</a> of  <a href="numbers.html#K5">NAT</a>  holds  <font color="Maroon">seq</font> <a href="normsp_1.html#K2">.</a> <font color="Olive">n</font> <a href="hidden.html#R1">=</a> <font color="Maroon">r</font>
 <b>by </b><i>, <a class="ref" href="lopban_3.html#D5">LOPBAN_3:def 5</a></i>;<br/>
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="22_1"><b>now </b></a><div class="add"><b>let </b><font color="Maroon">n</font> be    <a href="subset_1.html#M2">Element</a> of  <a href="numbers.html#K5">NAT</a> ;<br/><b>thus </b><font color="Maroon">seq1</font> <a href="normsp_1.html#K2">.</a> <font color="Maroon">n</font> = 
<font color="Maroon">seq</font> <a href="normsp_1.html#K2">.</a> <span class="p1">(<span class="default"><font color="Maroon">Nseq</font> <a href="seqm_3.html#K2">.</a> <font color="Maroon">n</font></span>)</span>
<b>by </b><i>, <a class="ref" href="lopban_3.html#T7">LOPBAN_3:7</a></i>
<br/>.= 
<font color="Maroon">r</font>
<b>by </b><i/>
;<br/></div><b>end;</b></div>
<b>hence </b><a NAME="E8:22"/>
<font color="Maroon">seq1</font> is <a href="funct_1.html#V3">constant</a>
 <b>by </b><i><a class="ref" href="lopban_3.html#D5">LOPBAN_3:def 5</a></i>;<br/>


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