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<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>consider </b><font color="Maroon">c<sub>2</sub></font> being  <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> such that </b><br/><a NAME="E2:19"/><i><font color="Green">E15</font></i>: 
<font color="Maroon">c<sub>2</sub></font> is    <a href="rusub_3.html#M1">Basis</a> of <font color="Maroon">c<sub>1</sub></font>
 <b>by </b><i><a class="ref" href="rusub_4.html#D2" target="_self">Def2</a></i>;<br/>
<a NAME="E3:19"/><i><font color="Green">E16</font></i>: 
 <a href="card_1.html#K1">Card</a> <font color="Maroon">c<sub>2</sub></font> <a href="hidden.html#R1">=</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#E2:19"><i><font color="Green">E15</font></i></a>, <a class="ref" href="rusub_4.html#D3" target="_self">Def3</a></i>;<br/>
<a NAME="E4:19"/><i><font color="Green">E17</font></i>: 
<font color="Maroon">c<sub>2</sub></font> is <a href="rlvect_3.html#V1">linearly-independent</a>
 
<b>by </b><i><a class="txt" href="rusub_4.html#E2:19"><i><font color="Green">E15</font></i></a>, <a class="ref" href="rusub_3.html#D2">RUSUB_3:def 2</a></i>;<br/>
 <a href="rusub_1.html#K2">(Omega).</a> <font color="Maroon">c<sub>1</sub></font> = 
 <a href="bhsp_1.html#G1">UNITSTR</a>(# the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">c<sub>1</sub></font>,the <a href="struct_0.html#U2">Zero</a> of <font color="Maroon">c<sub>1</sub></font>,the <a href="rlvect_1.html#U1">add</a> of <font color="Maroon">c<sub>1</sub></font>,the <a href="rlvect_1.html#U2">Mult</a> of <font color="Maroon">c<sub>1</sub></font>,the <a href="bhsp_1.html#U1">scalar</a> of <font color="Maroon">c<sub>1</sub></font> #)
<b>by </b><i><a class="ref" href="rusub_1.html#D3">RUSUB_1:def 3</a></i>
<br/>.= 
 <a href="rusub_3.html#K1">Lin</a> <font color="Maroon">c<sub>2</sub></font>
<b>by </b><i><a class="txt" href="rusub_4.html#E2:19"><i><font color="Green">E15</font></i></a>, <a class="ref" href="rusub_3.html#D2">RUSUB_3:def 2</a></i>
;<br/>
<b>hence </b><a NAME="E6:19"/>
 <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="rusub_4.html#K1" target="_self">dim</a> <span class="p1">(<span class="default"><a href="rusub_1.html#K2">(Omega).</a> <font color="Maroon">c<sub>1</sub></font></span>)</span>
 <b>by </b><i><a class="txt" href="rusub_4.html#E3:19"><i><font color="Green">E16</font></i></a>, <a class="txt" href="rusub_4.html#E4:19"><i><font color="Green">E17</font></i></a>, <a class="ref" href="rusub_4.html#T9" target="_self">Th9</a></i>;<br/>


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