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

<b>let </b><font color="Maroon" title="c1">V</font> be  <a href="rlvect_5.html#V1" title="RLVECT_5:attr.1">finite-dimensional</a> <a href="rlvect_1.html#NM2" title="RLVECT_1:NM.2">RealLinearSpace</a>;<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="E2:37"/><i><font color="Green" title="E33">A1</font></i>: 
<font color="Maroon" title="c2">I</font> is    <a href="rlvect_3.html#M1" title="RLVECT_3:mode.1">Basis</a> of <font color="Maroon" title="c1">V</font>
 <b>by </b><i><a class="ref" href="rlvect_5.html#D1" target="_self" title="RLVECT_5:def.1">Def1</a></i>;<br/>
<a NAME="E3:37"/><i><font color="Green" title="E34">A2</font></i>: 
 <a href="card_1.html#K1" title="CARD_1:func.1">Card</a> <font color="Maroon" title="c2">I</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="rlvect_5.html#K1" title="RLVECT_5:func.1">dim</a> <font color="Maroon" title="c1">V</font>
 
<b>by </b><i><a class="txt" href="rlvect_5.html#E2:37"><i><font color="Green" title="E33">A1</font></i></a>, <a class="ref" href="rlvect_5.html#D3" target="_self" title="RLVECT_5:def.3">Def3</a></i>;<br/>
<a NAME="E4:37"/><i><font color="Green" title="E35">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="rlvect_5.html#E2:37"><i><font color="Green" title="E33">A1</font></i></a>, <a class="ref" href="rlvect_3.html#D3" title="RLVECT_3:def.3">RLVECT_3:def 3</a></i>;<br/>
 <a href="rlsub_1.html#K2" title="RLSUB_1:func.2">(Omega).</a> <font color="Maroon" title="c1">V</font> = 
 <a href="rlvect_1.html#G2" title="RLVECT_1:aggr.2">RLSStruct</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">Zero</a> of <font color="Maroon" title="c1">V</font>,the <a href="rlvect_1.html#U1" title="RLVECT_1:sel.1">add</a> of <font color="Maroon" title="c1">V</font>,the <a href="rlvect_1.html#U2" title="RLVECT_1:sel.2">Mult</a> of <font color="Maroon" title="c1">V</font> #)
<b>by </b><i><a class="ref" href="rlsub_1.html#D4" title="RLSUB_1:def.4">RLSUB_1:def 4</a></i>
<br/>.= 
 <a href="rlvect_3.html#K1" title="RLVECT_3:func.1">Lin</a> <font color="Maroon" title="c2">I</font>
<b>by </b><i><a class="txt" href="rlvect_5.html#E2:37"><i><font color="Green" title="E33">A1</font></i></a>, <a class="ref" href="rlvect_3.html#D3" title="RLVECT_3:def.3">RLVECT_3:def 3</a></i>
;<br/>
<b>hence </b><a NAME="E6:37"/>
 <a href="rlvect_5.html#K1" title="RLVECT_5:func.1">dim</a> <font color="Maroon" title="c1">V</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="rlvect_5.html#K1" title="RLVECT_5:func.1">dim</a> <span class="p1">(<span class="default"><a href="rlsub_1.html#K2" title="RLSUB_1:func.2">(Omega).</a> <font color="Maroon" title="c1">V</font></span>)</span>
 <b>by </b><i><a class="txt" href="rlvect_5.html#E3:37"><i><font color="Green" title="E34">A2</font></i></a>, <a class="txt" href="rlvect_5.html#E4:37"><i><font color="Green" title="E35">A3</font></i></a>, <a class="ref" href="rlvect_5.html#T30" target="_self" title="RLVECT_5:th.30">Th30</a></i>;<br/>


</div>
