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<b>let </b><font color="Maroon">GF</font> be   <a href="vectsp_1.html#NM2">Field</a>;<br/><b>let </b><font color="Maroon">V</font> be  <a href="matrlin.html#V2">finite-dimensional</a> <a href="vectsp_1.html#NM6">VectSp</a> of <font color="Maroon">GF</font>;<br/>



<b>consider </b><font color="Maroon">I</font> being  <a href="finset_1.html#V1">finite</a> <a href="struct_0.html#NM2">Subset</a> of <font color="Maroon">V</font><b> such that </b><br/><a NAME="E2:34"/><i><font color="Green">E32</font></i>: 
<font color="Maroon">I</font> is    <a href="vectsp_7.html#M1">Basis</a> of <font color="Maroon">V</font>
 <b>by </b><i/>;<br/>
<a NAME="E3:34"/><i><font color="Green">E40</font></i>: 
 <a href="card_1.html#K1">Card</a> <font color="Maroon">I</font> <a href="hidden.html#R1">=</a>  <a href="vectsp_9.html#K1" target="_self">dim</a> <font color="Maroon">V</font>
 
<b>by </b><i><a class="txt" href="vectsp_9.html#E5"><i><font color="Green">Lemma30</font></i></a>, </i>;<br/>
<a NAME="E4:34"/><i><font color="Green">E42</font></i>: 
<font color="Maroon">I</font> is <a href="vectsp_7.html#V1">linearly-independent</a>
 
<b>by </b><i><a class="txt" href="vectsp_9.html#E5"><i><font color="Green">Lemma30</font></i></a>, <a class="ref" href="vectsp_7.html#D3">VECTSP_7:def 3</a></i>;<br/>
 <a href="vectsp_4.html#K2">(Omega).</a> <font color="Maroon">V</font> = 
 <a href="vectsp_1.html#G4">VectSpStr</a>(# the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">V</font>,the <a href="rlvect_1.html#U1">add</a> of <font color="Maroon">V</font>,the <a href="struct_0.html#U2">Zero</a> of <font color="Maroon">V</font>,the <a href="vectsp_1.html#U2">lmult</a> of <font color="Maroon">V</font> #)
<b>by </b><i><a class="ref" href="vectsp_4.html#D4">VECTSP_4:def 4</a></i>
<br/>.= 
 <a href="vectsp_7.html#K1">Lin</a> <font color="Maroon">I</font>
<b>by </b><i><a class="txt" href="vectsp_9.html#E5"><i><font color="Green">Lemma30</font></i></a>, <a class="ref" href="vectsp_7.html#D3">VECTSP_7:def 3</a></i>
;<br/>
<b>hence </b><a NAME="E6:34"/>
 <a href="vectsp_9.html#K1" target="_self">dim</a> <font color="Maroon">V</font> <a href="hidden.html#R1">=</a>  <a href="vectsp_9.html#K1" target="_self">dim</a> <span class="p1">(<span class="default"><a href="vectsp_4.html#K2">(Omega).</a> <font color="Maroon">V</font></span>)</span>
 <b>by </b><i>, <a class="txt" href="vectsp_9.html#E2:34"><i><font color="Green">E32</font></i></a>, </i>;<br/>


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