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<b>let </b><font color="Maroon" title="c1">GF</font> be   <a href="vectsp_1.html#NM2" title="VECTSP_1:NM.2">Field</a>;<br/><b>let </b><font color="Maroon" title="c2">V</font> be   <a href="vectsp_1.html#NM6" title="VECTSP_1:NM.6">VectSp</a> of <font color="Maroon" title="c1">GF</font>;<br/><b>let </b><font color="Maroon" title="c3">A</font>, <font color="Maroon" title="c4">B</font> be   <a href="struct_0.html#NM2" title="STRUCT_0:NM.2">Subset</a> of <font color="Maroon" title="c2">V</font>;<br/>







<b>assume </b><b>that </b><br/><a NAME="E1:3"/><i><font color="Green" title="E2">A1</font></i>: 
<font color="Maroon" title="c3">A</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Maroon" title="c4">B</font>
 <b>and </b><br/><a NAME="E2:3"/><i><font color="Green" title="E3">A2</font></i>: 
<font color="Maroon" title="c4">B</font> is <a href="vectsp_7.html#V1" title="VECTSP_7:attr.1">linearly-independent</a>
 ;<br/>

<b>let </b><font color="Maroon" title="c5">l</font> be    <a href="vectsp_6.html#M2" title="VECTSP_6:mode.2">Linear_Combination</a> of <font color="Maroon" title="c3">A</font>; <i><font color="Red">:: according to </font></i><a class="ref" href="vectsp_7.html#D1" target="_self" title="VECTSP_7:def.1">VECTSP_7:def 1</a><br/>

<b>assume </b><a NAME="E3:3"/><i><font color="Green" title="E4">A3</font></i>: 
 <a href="vectsp_6.html#K4" title="VECTSP_6:func.4">Sum</a> <font color="Maroon" title="c5">l</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="rlvect_1.html#K1" title="RLVECT_1:func.1">0.</a> <font color="Maroon" title="c2">V</font>
 ;<br/>

<b>reconsider </b><font color="Maroon" title="c6">L</font> = <font color="Maroon" title="c5">l</font> as    <a href="vectsp_6.html#M2" title="VECTSP_6:mode.2">Linear_Combination</a> of <font color="Maroon" title="c4">B</font> <b>by </b><i><a class="txt" href="vectsp_7.html#E1:3"><i><font color="Green" title="E2">A1</font></i></a>, <a class="ref" href="vectsp_6.html#T25" title="VECTSP_6:th.25">VECTSP_6:25</a></i>;<br/>
<a NAME="E5:3"/>
 <a href="vectsp_6.html#K1" title="VECTSP_6:func.1">Carrier</a> <font color="Maroon" title="c6">L</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a> 
 
<b>by </b><i><a class="txt" href="vectsp_7.html#E2:3"><i><font color="Green" title="E3">A2</font></i></a>, <a class="txt" href="vectsp_7.html#E3:3"><i><font color="Green" title="E4">A3</font></i></a>, <a class="ref" href="vectsp_7.html#D1" target="_self" title="VECTSP_7:def.1">Def1</a></i>;<br/>
<b>hence </b><a NAME="E6:3"/>
 <a href="vectsp_6.html#K1" title="VECTSP_6:func.1">Carrier</a> <font color="Maroon" title="c5">l</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a> 
 ;<br/>


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