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

<b>consider </b><font color="Maroon">V</font> being   <a href="bhsp_1.html#NM1">RealUnitarySpace</a>;<br/>
<b>take </b>
 <a href="rusub_1.html#K1">(0).</a> <font color="Maroon">V</font>
;<br/>

<b>thus </b><a NAME="E2:6_1_1"/>
 <a href="rusub_1.html#K1">(0).</a> <font color="Maroon">V</font> is <a href="bhsp_1.html#V1">strict</a>
 ;<br/>

<b>take </b><font color="Maroon">A</font> =  <a href="subset_1.html#K1">{}</a> the <a href="struct_0.html#U1">carrier</a> of <span class="p1">(<span class="default"><a href="rusub_1.html#K1">(0).</a> <font color="Maroon">V</font></span>)</span>; <i><font color="Red">:: according to </font></i><a class="ref" href="rusub_4.html#D1" target="_self">RUSUB_4:def 1</a><br/>

<a NAME="E3:6_1_1"/><i><font color="Green">E26</font></i>: 
<font color="Maroon">A</font> is <a href="rlvect_3.html#V1">linearly-independent</a>
 
<b>by </b><i><a class="ref" href="rlvect_3.html#T8">RLVECT_3:8</a></i>;<br/>
<a NAME="E4:6_1_1"/>
 <a href="rusub_3.html#K1">Lin</a> <font color="Maroon">A</font> <a href="hidden.html#R1">=</a>  <a href="rusub_1.html#K1">(0).</a> <span class="p1">(<span class="default"><a href="rusub_1.html#K1">(0).</a> <font color="Maroon">V</font></span>)</span>
 
<b>by </b><i><a class="ref" href="rusub_3.html#T3">RUSUB_3:3</a></i>;<br/>
<a NAME="E5:6_1_1"/><b>then </b>
 <a href="rusub_3.html#K1">Lin</a> <font color="Maroon">A</font> <a href="hidden.html#R1">=</a>  <a href="bhsp_1.html#G1">UNITSTR</a>(# the <a href="struct_0.html#U1">carrier</a> of <span class="p1">(<span class="default"><a href="rusub_1.html#K1">(0).</a> <font color="Maroon">V</font></span>)</span>,the <a href="struct_0.html#U2">Zero</a> of <span class="p1">(<span class="default"><a href="rusub_1.html#K1">(0).</a> <font color="Maroon">V</font></span>)</span>,the <a href="rlvect_1.html#U1">add</a> of <span class="p1">(<span class="default"><a href="rusub_1.html#K1">(0).</a> <font color="Maroon">V</font></span>)</span>,the <a href="rlvect_1.html#U2">Mult</a> of <span class="p1">(<span class="default"><a href="rusub_1.html#K1">(0).</a> <font color="Maroon">V</font></span>)</span>,the <a href="bhsp_1.html#U1">scalar</a> of <span class="p1">(<span class="default"><a href="rusub_1.html#K1">(0).</a> <font color="Maroon">V</font></span>)</span> #)
 
<b>by </b><i><a class="ref" href="rusub_1.html#T30">RUSUB_1:30</a></i>;<br/>
<b>hence </b><a NAME="E6:6_1_1"/>
<font color="Maroon">A</font> is    <a href="rusub_3.html#M1">Basis</a> of  <a href="rusub_1.html#K1">(0).</a> <font color="Maroon">V</font>
 <b>by </b><i>, <a class="ref" href="rusub_3.html#D2">RUSUB_3:def 2</a></i>;<br/>


</div>
