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<b>let </b><font color="Maroon" title="c1">V</font> be  <a href="rusub_4.html#V1" title="RUSUB_4:attr.1">finite-dimensional</a> <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">  <a href="rusub_4.html#K1" title="RUSUB_4:func.1">dim</a> <font color="Maroon" title="c1">V</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="rusub_4.html#K1" title="RUSUB_4:func.1">dim</a> <span class="p1">(<span class="default"><a href="rusub_1.html#K2" title="RUSUB_1:func.2">(Omega).</a> <font color="Maroon" title="c1">V</font></span>)</span></span><br/>

<b>consider </b><font color="Maroon" title="c2">I</font> being  <a href="finset_1.html#V1" title="FINSET_1:attr.1">finite</a> <a href="struct_0.html#NM2" title="STRUCT_0:NM.2">Subset</a> of <font color="Maroon" title="c1">V</font><b> such that </b><br/><a NAME="E2:18"/><i><font color="Green" title="E14">A1</font></i>: 
<font color="Maroon" title="c2">I</font> is    <a href="rusub_3.html#M1" title="RUSUB_3:mode.1">Basis</a> of <font color="Maroon" title="c1">V</font>
 <b>by </b><i><a class="ref" href="rusub_4.html#D1" target="_self" title="RUSUB_4:def.1">Def1</a></i>;<br/>
<a NAME="E3:18"/><i><font color="Green" title="E15">A2</font></i>: 
 <a href="card_1.html#K5" title="CARD_1:func.5">card</a> <font color="Maroon" title="c2">I</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="rusub_4.html#K1" title="RUSUB_4:func.1">dim</a> <font color="Maroon" title="c1">V</font>
 
<b>by </b><i><a class="txt" href="#E2:18"><i><font color="Green" title="E14">A1</font></i></a>, <a class="ref" href="rusub_4.html#D3" target="_self" title="RUSUB_4:def.3">Def3</a></i>;<br/>
<a NAME="E4:18"/><i><font color="Green" title="E16">A3</font></i>: 
<font color="Maroon" title="c2">I</font> is <a href="rlvect_3.html#V1" title="RLVECT_3:attr.1">linearly-independent</a>
 
<b>by </b><i><a class="txt" href="#E2:18"><i><font color="Green" title="E14">A1</font></i></a>, <a class="ref" href="rusub_3.html#D2" title="RUSUB_3:def.2">RUSUB_3:def 2</a></i>;<br/>
 <a href="rusub_1.html#K2" title="RUSUB_1:func.2">(Omega).</a> <font color="Maroon" title="c1">V</font> = 
 <a href="bhsp_1.html#G1" title="BHSP_1:aggr.1">UNITSTR</a>(# the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c1">V</font>,the <a href="struct_0.html#U2" title="STRUCT_0:sel.2">U2</a> of <font color="Maroon" title="c1">V</font>,the <a href="algstr_0.html#U1" title="ALGSTR_0:sel.1">addF</a> of <font color="Maroon" title="c1">V</font>,the <a href="rlvect_1.html#U1" title="RLVECT_1:sel.1">Mult</a> of <font color="Maroon" title="c1">V</font>,the <a href="bhsp_1.html#U1" title="BHSP_1:sel.1">scalar</a> of <font color="Maroon" title="c1">V</font> #)
<b>by </b><i><a class="ref" href="rusub_1.html#D3" title="RUSUB_1:def.3">RUSUB_1:def 3</a></i>
<br/>.= 
 <a href="rusub_3.html#K1" title="RUSUB_3:func.1">Lin</a> <font color="Maroon" title="c2">I</font>
<b>by </b><i><a class="txt" href="#E2:18"><i><font color="Green" title="E14">A1</font></i></a>, <a class="ref" href="rusub_3.html#D2" title="RUSUB_3:def.2">RUSUB_3:def 2</a></i>
;<br/>
<b>hence </b><a NAME="E6:18"/>
 <a href="rusub_4.html#K1" title="RUSUB_4:func.1">dim</a> <font color="Maroon" title="c1">V</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="rusub_4.html#K1" title="RUSUB_4:func.1">dim</a> <span class="p1">(<span class="default"><a href="rusub_1.html#K2" title="RUSUB_1:func.2">(Omega).</a> <font color="Maroon" title="c1">V</font></span>)</span>
 <b>by </b><i><a class="txt" href="#E3:18"><i><font color="Green" title="E15">A2</font></i></a>, <a class="txt" href="#E4:18"><i><font color="Green" title="E16">A3</font></i></a>, <a class="ref" href="rusub_4.html#T9" target="_self" title="RUSUB_4:th.9">Th9</a></i>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> verum</span><br/>


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