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

<b>let </b><font color="Maroon">X</font> be   <a href="bhsp_1.html#NM1">RealUnitarySpace</a>;<br/><b>let </b><font color="Maroon">Y</font> be    <a href="bhsp_5.html#M2">OrthonormalFamily</a> of <font color="Maroon">X</font>;<br/><b>let </b><font color="Maroon">Z</font> be   <a href="struct_0.html#NM2">Subset</a> of <font color="Maroon">X</font>;<br/>





<b>assume </b><a NAME="E1:8"/><i><font color="Green">E38</font></i>: 
<font color="Maroon">Z</font> is   <a href="subset_1.html#NM2">Subset</a> of <font color="Maroon">Y</font>
 ;<br/>

<a NAME="E2:8"/>
( <font color="Maroon">Y</font> is    <a href="bhsp_5.html#M1">OrthogonalFamily</a> of <font color="Maroon">X</font> &amp; ( for <font color="Olive">x</font> being  <a href="pre_topc.html#NM2">Point</a> of <font color="Maroon">X</font>  st <font color="Olive">x</font> <a href="hidden.html#R2">in</a> <font color="Maroon">Y</font> holds <br/><font color="Olive">x</font> <a href="bhsp_1.html#K2">.|.</a> <font color="Olive">x</font> <a href="hidden.html#R1">=</a> 1 ) )
 
<b>by </b><i><a class="ref" href="bhsp_5.html#D9">BHSP_5:def 9</a></i>;<br/>
<a NAME="E3:8"/><b>then </b><i><font color="Green">E39</font></i>: 
<font color="Maroon">Z</font> is    <a href="bhsp_5.html#M1">OrthogonalFamily</a> of <font color="Maroon">X</font>
 
<b>by </b><i>, </i>;<br/>
<a NAME="E4:8"/>
for <font color="Olive">x</font> being  <a href="pre_topc.html#NM2">Point</a> of <font color="Maroon">X</font>  st <font color="Olive">x</font> <a href="hidden.html#R2">in</a> <font color="Maroon">Z</font> holds <br/><font color="Olive">x</font> <a href="bhsp_1.html#K2">.|.</a> <font color="Olive">x</font> <a href="hidden.html#R1">=</a> 1
 
<b>by </b><i>, <a class="ref" href="bhsp_5.html#D9">BHSP_5:def 9</a></i>;<br/>
<b>hence </b><a NAME="E5:8"/>
<font color="Maroon">Z</font> is    <a href="bhsp_5.html#M2">OrthonormalFamily</a> of <font color="Maroon">X</font>
 <b>by </b><i>, <a class="ref" href="bhsp_5.html#D9">BHSP_5:def 9</a></i>;<br/>


</div>
