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<b>let </b><font color="Maroon">GF</font> be  non <a href="struct_0.html#V3">empty</a> <a href="rlvect_1.html#V3">Abelian</a> <a href="rlvect_1.html#V4">add-associative</a> <a href="rlvect_1.html#V5">right_zeroed</a> <a href="rlvect_1.html#V6">right_complementable</a> <a href="group_1.html#V4">associative</a> <a href="vectsp_1.html#V7">distributive</a> <a href="vectsp_1.html#V8">left_unital</a>  <a href="vectsp_1.html#L3">doubleLoopStr</a> ;<br/><b>let </b><font color="Maroon">V</font> be  non <a href="struct_0.html#V3">empty</a> <a href="rlvect_1.html#V3">Abelian</a> <a href="rlvect_1.html#V4">add-associative</a> <a href="rlvect_1.html#V5">right_zeroed</a> <a href="rlvect_1.html#V6">right_complementable</a> <a href="vectsp_1.html#V12">VectSp-like</a>  <a href="vectsp_1.html#L4">VectSpStr</a> of <font color="Maroon">GF</font>;<br/><b>let </b><font color="Maroon">A</font> be   <a href="struct_0.html#NM2">Subset</a> of <font color="Maroon">V</font>;<br/><b>let </b><font color="Maroon">L1</font> be    <a href="vectsp_6.html#M1" target="_self">Linear_Combination</a> of <font color="Maroon">V</font>;<br/><b>let </b><font color="Maroon">L2</font> be    <a href="vectsp_6.html#M1" target="_self">Linear_Combination</a> of <font color="Maroon">V</font>;<br/>









<b>assume </b><b>that </b><br/><a NAME="E1:51"/><i><font color="Green">E47</font></i>: 
<font color="Maroon">L1</font> is    <a href="vectsp_6.html#M2" target="_self">Linear_Combination</a> of <font color="Maroon">A</font>
 <b>and </b><br/><a NAME="E2:51"/><i><font color="Green">E55</font></i>: 
<font color="Maroon">L2</font> is    <a href="vectsp_6.html#M2" target="_self">Linear_Combination</a> of <font color="Maroon">A</font>
 ;<br/>

<a NAME="E3:51"/><i><font color="Green">E59</font></i>: 
 <a href="vectsp_6.html#K7" target="_self">-</a> <font color="Maroon">L2</font> is    <a href="vectsp_6.html#M2" target="_self">Linear_Combination</a> of <font color="Maroon">A</font>
 
<b>by </b><i>, </i>;<br/>
<b>thus </b><a NAME="E4:51"/>
<font color="Maroon">L1</font> <a href="vectsp_6.html#K8" target="_self">-</a> <font color="Maroon">L2</font> is    <a href="vectsp_6.html#M2" target="_self">Linear_Combination</a> of <font color="Maroon">A</font>
 <b>by </b><i>, , </i>;<br/>


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