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<b>let </b><font color="Maroon" title="c1">K</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">K</font>;<br/><b>let </b><font color="Maroon" title="c3">a</font> be   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c1">K</font>;<br/><b>let </b><font color="Maroon" title="c4">KL1</font>, <font color="Maroon" title="c5">KL2</font> be    <a href="vectsp_6.html#M1" title="VECTSP_6:mode.1">Linear_Combination</a> of <font color="Maroon" title="c2">V</font>;<br/><b>let </b><font color="Maroon" title="c6">X</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="E1:14"/><i><font color="Green" title="E10">A1</font></i>: 
<font color="Maroon" title="c6">X</font> is <a href="vectsp_7.html#V1" title="VECTSP_7:attr.1">linearly-independent</a>
 <b>and </b><br/><a NAME="E2:14"/><i><font color="Green" title="E11">A2</font></i>: 
 <a href="vectsp_6.html#K1" title="VECTSP_6:func.1">Carrier</a> <font color="Maroon" title="c4">KL1</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Maroon" title="c6">X</font>
 <b>and </b><br/><a NAME="E3:14"/><i><font color="Green" title="E12">A3</font></i>: 
 <a href="vectsp_6.html#K1" title="VECTSP_6:func.1">Carrier</a> <font color="Maroon" title="c5">KL2</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Maroon" title="c6">X</font>
 <b>and </b><br/><a NAME="E4:14"/><i><font color="Green" title="E13">A4</font></i>: 
<font color="Maroon" title="c3">a</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a>  <a href="rlvect_1.html#K1" title="RLVECT_1:func.1">0.</a> <font color="Maroon" title="c1">K</font>
 <b>and </b><br/><a NAME="E5:14"/><i><font color="Green" title="E14">A5</font></i>: 
 <a href="vectsp_6.html#K4" title="VECTSP_6:func.4">Sum</a> <font color="Maroon" title="c4">KL1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c3">a</font> <a href="vectsp_1.html#K6" title="VECTSP_1:func.6">*</a> <span class="p1">(<span class="default"><a href="vectsp_6.html#K4" title="VECTSP_6:func.4">Sum</a> <font color="Maroon" title="c5">KL2</font></span>)</span>
 ;<br/>

<a NAME="E6:14"/><i><font color="Green" title="E15">A6</font></i>: 
 <a href="vectsp_6.html#K1" title="VECTSP_6:func.1">Carrier</a> <span class="p1">(<span class="default"><font color="Maroon" title="c3">a</font> <a href="vectsp_6.html#K6" title="VECTSP_6:func.6">*</a> <font color="Maroon" title="c5">KL2</font></span>)</span> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Maroon" title="c6">X</font>
 
<b>by </b><i><a class="txt" href="matrlin.html#E3:14"><i><font color="Green" title="E12">A3</font></i></a>, <a class="txt" href="matrlin.html#E4:14"><i><font color="Green" title="E13">A4</font></i></a>, <a class="ref" href="vectsp_6.html#T59" title="VECTSP_6:th.59">VECTSP_6:59</a></i>;<br/>
<a NAME="E7:14"/>
 <a href="vectsp_6.html#K4" title="VECTSP_6:func.4">Sum</a> <font color="Maroon" title="c4">KL1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="vectsp_6.html#K4" title="VECTSP_6:func.4">Sum</a> <span class="p1">(<span class="default"><font color="Maroon" title="c3">a</font> <a href="vectsp_6.html#K6" title="VECTSP_6:func.6">*</a> <font color="Maroon" title="c5">KL2</font></span>)</span>
 
<b>by </b><i><a class="txt" href="matrlin.html#E5:14"><i><font color="Green" title="E14">A5</font></i></a>, <a class="ref" href="vectsp_6.html#T78" title="VECTSP_6:th.78">VECTSP_6:78</a></i>;<br/>
<b>hence </b><a NAME="E8:14"/>
<font color="Maroon" title="c4">KL1</font> <a href="vectsp_6.html#R1" title="VECTSP_6:pred.1">=</a> <font color="Maroon" title="c3">a</font> <a href="vectsp_6.html#K6" title="VECTSP_6:func.6">*</a> <font color="Maroon" title="c5">KL2</font>
 <b>by </b><i><a class="txt" href="matrlin.html#E1:14"><i><font color="Green" title="E10">A1</font></i></a>, <a class="txt" href="matrlin.html#E2:14"><i><font color="Green" title="E11">A2</font></i></a>, <a class="txt" href="matrlin.html#E6:14"><i><font color="Green" title="E15">A6</font></i></a>, <a class="ref" href="matrlin.html#T9" target="_self" title="MATRLIN:th.9">Th9</a></i>;<br/>


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