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

<b>let </b><font color="Maroon">c<sub>1</sub></font> be  <a href="rusub_4.html#V1" target="_self">finite-dimensional</a> <a href="bhsp_1.html#NM1">RealUnitarySpace</a>;<br/><b>let </b><font color="Maroon">c<sub>2</sub></font> be    <a href="rusub_1.html#M1">Subspace</a> of <font color="Maroon">c<sub>1</sub></font>;<br/>



<b>reconsider </b><font color="Maroon">c<sub>3</sub></font> = <font color="Maroon">c<sub>1</sub></font> as   <a href="bhsp_1.html#NM1">RealUnitarySpace</a> ;<br/>
<b>consider </b><font color="Maroon">c<sub>4</sub></font> being    <a href="rusub_3.html#M1">Basis</a> of <font color="Maroon">c<sub>3</sub></font>;<br/>
<a NAME="E3:17"/><i><font color="Green">E13</font></i>: 
 <a href="rusub_3.html#K1">Lin</a> <font color="Maroon">c<sub>4</sub></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 <font color="Maroon">c<sub>3</sub></font>,the <a href="struct_0.html#U2">Zero</a> of <font color="Maroon">c<sub>3</sub></font>,the <a href="rlvect_1.html#U1">add</a> of <font color="Maroon">c<sub>3</sub></font>,the <a href="rlvect_1.html#U2">Mult</a> of <font color="Maroon">c<sub>3</sub></font>,the <a href="bhsp_1.html#U1">scalar</a> of <font color="Maroon">c<sub>3</sub></font> #)
 
<b>by </b><i><a class="ref" href="rusub_3.html#D2">RUSUB_3:def 2</a></i>;<br/>
<b>reconsider </b><font color="Maroon">c<sub>5</sub></font> = <font color="Maroon">c<sub>4</sub></font> as  <a href="finset_1.html#V1">finite</a> <a href="struct_0.html#NM2">Subset</a> of <font color="Maroon">c<sub>1</sub></font> <b>by </b><i><a class="ref" href="rusub_4.html#T3" target="_self">Th3</a></i>;<br/>
<a NAME="E5:17"/><i><font color="Green">E14</font></i>: 
 <a href="rusub_4.html#K1" target="_self">dim</a> <font color="Maroon">c<sub>1</sub></font> <a href="hidden.html#R1">=</a>  <a href="card_1.html#K1">Card</a> <font color="Maroon">c<sub>5</sub></font>
 
<b>by </b><i><a class="ref" href="rusub_4.html#D3" target="_self">Def3</a></i>;<br/>
<b>consider </b><font color="Maroon">c<sub>6</sub></font> being    <a href="rusub_3.html#M1">Basis</a> of <font color="Maroon">c<sub>2</sub></font>;<br/>
<b>reconsider </b><font color="Maroon">c<sub>7</sub></font> = <font color="Maroon">c<sub>6</sub></font> as   <a href="struct_0.html#NM2">Subset</a> of <font color="Maroon">c<sub>2</sub></font> ;<br/>
<a NAME="E8:17"/>
<font color="Maroon">c<sub>7</sub></font> is <a href="rlvect_3.html#V1">linearly-independent</a>
 
<b>by </b><i><a class="ref" href="rusub_3.html#D2">RUSUB_3:def 2</a></i>;<br/>
<b>then reconsider </b><font color="Maroon">c<sub>8</sub></font> = <font color="Maroon">c<sub>7</sub></font> as  <a href="rlvect_3.html#V1">linearly-independent</a> <a href="struct_0.html#NM2">Subset</a> of <font color="Maroon">c<sub>1</sub></font> <b>by </b><i><a class="ref" href="rusub_3.html#T22">RUSUB_3:22</a></i>;<br/>
<b>reconsider </b><font color="Maroon">c<sub>9</sub></font> = <font color="Maroon">c<sub>8</sub></font> as  <a href="finset_1.html#V1">finite</a> <a href="struct_0.html#NM2">Subset</a> of <font color="Maroon">c<sub>1</sub></font> <b>by </b><i><a class="ref" href="rusub_4.html#T3" target="_self">Th3</a></i>;<br/>
<a NAME="E11:17"/>
 <a href="card_1.html#K4">card</a> <font color="Maroon">c<sub>9</sub></font> <a href="xxreal_0.html#R1">&lt;=</a>  <a href="card_1.html#K4">card</a> <font color="Maroon">c<sub>5</sub></font>
 
<b>by </b><i><a class="txt" href="rusub_4.html#E3:17"><i><font color="Green">E13</font></i></a>, <a class="ref" href="rusub_4.html#T2" target="_self">Th2</a></i>;<br/>
<b>hence </b><a NAME="E12:17"/>
 <a href="rusub_4.html#K1" target="_self">dim</a> <font color="Maroon">c<sub>2</sub></font> <a href="xxreal_0.html#R1">&lt;=</a>  <a href="rusub_4.html#K1" target="_self">dim</a> <font color="Maroon">c<sub>1</sub></font>
 <b>by </b><i><a class="txt" href="rusub_4.html#E5:17"><i><font color="Green">E14</font></i></a>, <a class="ref" href="rusub_4.html#D3" target="_self">Def3</a></i>;<br/>


</div>
