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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">L</font> be    <a href="vectsp_6.html#M1" target="_self">Linear_Combination</a> of <font color="Maroon">V</font>;<br/>





<b>assume </b><a NAME="E1:23"/>
 <a href="vectsp_6.html#K1" target="_self">Carrier</a> <font color="Maroon">L</font> <a href="hidden.html#R1">=</a>  <a href="xboole_0.html#K1">{}</a> 
 ;<br/>

<a NAME="E2:23"/><b>then </b>
<font color="Maroon">L</font> <a href="funct_2.html#R2">=</a>  <a href="vectsp_6.html#K2" target="_self">ZeroLC</a> <font color="Maroon">V</font>
 
<b>by </b><i/>;<br/>
<b>hence </b><a NAME="E3:23"/>
 <a href="vectsp_6.html#K4" target="_self">Sum</a> <font color="Maroon">L</font> <a href="hidden.html#R1">=</a>  <a href="rlvect_1.html#K1">0.</a> <font color="Maroon">V</font>
 <b>by </b><i/>;<br/>


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