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

<b>let </b><font color="Maroon" title="c1">X</font> be   <a href="bhsp_1.html#NM1" title="BHSP_1:NM.1">RealUnitarySpace</a>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> for <font color="Olive" title="b1">seq</font> being  <a href="struct_0.html#NM9" title="STRUCT_0:NM.9">sequence</a> of <font color="Maroon" title="c1">X</font><br/> for <font color="Olive" title="b2">k</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>   st <font color="Olive" title="b1">seq</font> is <a href="funct_1.html#V3" title="FUNCT_1:attr.3">constant</a> holds <br/><font color="Olive" title="b1">seq</font> <a href="bhsp_3.html#K2" title="BHSP_3:func.2">^\</a> <font color="Olive" title="b2">k</font> is <a href="funct_1.html#V3" title="FUNCT_1:attr.3">constant</a></span><br/><b>let </b><font color="Maroon" title="c2">seq</font> be   <a href="struct_0.html#NM9" title="STRUCT_0:NM.9">sequence</a> of <font color="Maroon" title="c1">X</font>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> for <font color="Olive" title="b1">k</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>   st <font color="Maroon" title="c2">seq</font> is <a href="funct_1.html#V3" title="FUNCT_1:attr.3">constant</a> holds <br/><font color="Maroon" title="c2">seq</font> <a href="bhsp_3.html#K2" title="BHSP_3:func.2">^\</a> <font color="Olive" title="b1">k</font> is <a href="funct_1.html#V3" title="FUNCT_1:attr.3">constant</a></span><br/><b>let </b><font color="Maroon" title="c3">k</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> ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> ( <font color="Maroon" title="c2">seq</font> is <a href="funct_1.html#V3" title="FUNCT_1:attr.3">constant</a> implies <font color="Maroon" title="c2">seq</font> <a href="bhsp_3.html#K2" title="BHSP_3:func.2">^\</a> <font color="Maroon" title="c3">k</font> is <a href="funct_1.html#V3" title="FUNCT_1:attr.3">constant</a> )</span><br/>





<b>assume </b><a NAME="E1:58"/><i><font color="Green" title="E23">A1</font></i>: 
<font color="Maroon" title="c2">seq</font> is <a href="funct_1.html#V3" title="FUNCT_1:attr.3">constant</a>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> <font color="Maroon" title="c2">seq</font> <a href="bhsp_3.html#K2" title="BHSP_3:func.2">^\</a> <font color="Maroon" title="c3">k</font> is <a href="funct_1.html#V3" title="FUNCT_1:attr.3">constant</a></span><br/>

<a NAME="E2:58"/>
<font color="Maroon" title="c2">seq</font> <a href="bhsp_3.html#K2" title="BHSP_3:func.2">^\</a> <font color="Maroon" title="c3">k</font> is    <a href="bhsp_3.html#M1" title="BHSP_3:mode.1">subsequence</a> of <font color="Maroon" title="c2">seq</font>
 
<b>by </b><i><a class="ref" href="bhsp_3.html#T43" target="_self" title="BHSP_3:th.43">Th43</a></i>;<br/>
<b>hence </b><a NAME="E3:58"/>
<font color="Maroon" title="c2">seq</font> <a href="bhsp_3.html#K2" title="BHSP_3:func.2">^\</a> <font color="Maroon" title="c3">k</font> is <a href="funct_1.html#V3" title="FUNCT_1:attr.3">constant</a>
 <b>by </b><i><a class="txt" href="bhsp_3.html#E1:58"><i><font color="Green" title="E23">A1</font></i></a>, <a class="ref" href="bhsp_3.html#T29" target="_self" title="BHSP_3:th.29">Th29</a></i>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> verum</span><br/>


</div>
