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<b>let </b><font color="Maroon" title="c1">S</font> be   <a href="normsp_1.html#NM1" title="NORMSP_1:NM.1">RealNormSpace</a>;<br/><b>let </b><font color="Maroon" title="c2">seq</font>, <font color="Maroon" title="c3">seq1</font> be   <a href="struct_0.html#NM9" title="STRUCT_0:NM.9">sequence</a> of <font color="Maroon" title="c1">S</font>;<br/>





<b>assume </b><b>that </b><br/><a NAME="E1:22"/><i><font color="Green" title="E19">A1</font></i>: 
<font color="Maroon" title="c2">seq</font> is <a href="funct_1.html#V3" title="FUNCT_1:attr.3">constant</a>
 <b>and </b><br/><a NAME="E2:22"/><i><font color="Green" title="E20">A2</font></i>: 
<font color="Maroon" title="c3">seq1</font> is    <a href="bhsp_3.html#M1" title="BHSP_3:mode.1">subsequence</a> of <font color="Maroon" title="c2">seq</font>
 ;<br/>

<b>consider </b><font color="Maroon" title="c4">Nseq</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="E4:22"/><i><font color="Green" title="E21">A3</font></i>: 
<font color="Maroon" title="c3">seq1</font> <a href="funct_2.html#R2" title="FUNCT_2:pred.2">=</a> <font color="Maroon" title="c2">seq</font> <a href="lopban_3.html#K4" title="LOPBAN_3:func.4">*</a> <font color="Maroon" title="c4">Nseq</font>
 <b>by </b><i><a class="txt" href="ndiff_1.html#E2:22"><i><font color="Green" title="E20">A2</font></i></a>, <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="c5">r</font> being   <a href="pre_topc.html#NM2" title="PRE_TOPC:NM.2">Point</a> of <font color="Maroon" title="c1">S</font><b> such that </b><br/><a NAME="E6:22"/><i><font color="Green" title="E22">A4</font></i>: 
for <font color="Olive" title="b1">n</font> being   <a href="subset_1.html#M2" title="SUBSET_1:mode.2">Element</a> of  <a href="numbers.html#K5" title="NUMBERS:func.5">NAT</a>  holds  <font color="Maroon" title="c2">seq</font> <a href="normsp_1.html#K2" title="NORMSP_1:func.2">.</a> <font color="Olive" title="b1">n</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c5">r</font>
 <b>by </b><i><a class="txt" href="ndiff_1.html#E1:22"><i><font color="Green" title="E19">A1</font></i></a>, <a class="ref" href="lopban_3.html#D5" title="LOPBAN_3:def.5">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" title="c6">n</font> be    <a href="subset_1.html#M2" title="SUBSET_1:mode.2">Element</a> of  <a href="numbers.html#K5" title="NUMBERS:func.5">NAT</a> ;<br/><b>thus </b><font color="Maroon" title="c3">seq1</font> <a href="normsp_1.html#K2" title="NORMSP_1:func.2">.</a> <font color="Maroon" title="c6">n</font> = 
<font color="Maroon" title="c2">seq</font> <a href="normsp_1.html#K2" title="NORMSP_1:func.2">.</a> <span class="p1">(<span class="default"><font color="Maroon" title="c4">Nseq</font> <a href="seqm_3.html#K2" title="SEQM_3:func.2">.</a> <font color="Maroon" title="c6">n</font></span>)</span>
<b>by </b><i><a class="txt" href="ndiff_1.html#E4:22"><i><font color="Green" title="E21">A3</font></i></a>, <a class="ref" href="lopban_3.html#T7" title="LOPBAN_3:th.7">LOPBAN_3:7</a></i>
<br/>.= 
<font color="Maroon" title="c5">r</font>
<b>by </b><i><a class="txt" href="ndiff_1.html#E6:22"><i><font color="Green" title="E22">A4</font></i></a></i>
;<br/></div><b>end;</b></div>
<b>hence </b><a NAME="E8:22"/>
<font color="Maroon" title="c3">seq1</font> is <a href="funct_1.html#V3" title="FUNCT_1:attr.3">constant</a>
 <b>by </b><i><a class="ref" href="lopban_3.html#D5" title="LOPBAN_3:def.5">LOPBAN_3:def 5</a></i>;<br/>


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