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<b>let </b><font color="Maroon">c<sub>1</sub></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">c<sub>2</sub></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">c<sub>1</sub></font>;<br/><b>let </b><font color="Maroon">c<sub>3</sub></font> be    <a href="vectsp_6.html#M1" target="_self">Linear_Combination</a> of <font color="Maroon">c<sub>2</sub></font>;<br/>





<span class="p1">(<span class="default"><a href="vectsp_6.html#K4" target="_self">Sum</a> <font color="Maroon">c<sub>3</sub></font></span>)</span> <a href="rlvect_1.html#K4">+</a> <span class="p1">(<span class="default"><a href="vectsp_6.html#K4" target="_self">Sum</a> <span class="p2">(<span class="default"><a href="vectsp_6.html#K7" target="_self">-</a> <font color="Maroon">c<sub>3</sub></font></span>)</span></span>)</span> = 
 <a href="vectsp_6.html#K4" target="_self">Sum</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="vectsp_6.html#K5" target="_self">+</a> <span class="p2">(<span class="default"><a href="vectsp_6.html#K7" target="_self">-</a> <font color="Maroon">c<sub>3</sub></font></span>)</span></span>)</span>
<b>by </b><i><a class="ref" href="vectsp_6.html#T77" target="_self">Th77</a></i>
<br/>.= 
 <a href="vectsp_6.html#K4" target="_self">Sum</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="vectsp_6.html#K8" target="_self">-</a> <font color="Maroon">c<sub>3</sub></font></span>)</span>

<br/>.= 
 <a href="vectsp_6.html#K4" target="_self">Sum</a> <span class="p1">(<span class="default"><a href="vectsp_6.html#K2" target="_self">ZeroLC</a> <font color="Maroon">c<sub>2</sub></font></span>)</span>
<b>by </b><i><a class="ref" href="vectsp_6.html#T76" target="_self">Th76</a></i>
<br/>.= 
 <a href="rlvect_1.html#K1">0.</a> <font color="Maroon">c<sub>2</sub></font>
<b>by </b><i><a class="txt" href="vectsp_6.html#E47"><i><font color="Green">Lemma13</font></i></a></i>
;<br/>
<b>hence </b><a NAME="E2:55"/>
 <a href="vectsp_6.html#K4" target="_self">Sum</a> <span class="p1">(<span class="default"><a href="vectsp_6.html#K7" target="_self">-</a> <font color="Maroon">c<sub>3</sub></font></span>)</span> <a href="hidden.html#R1">=</a>  <a href="rlvect_1.html#K5">-</a> <span class="p1">(<span class="default"><a href="vectsp_6.html#K4" target="_self">Sum</a> <font color="Maroon">c<sub>3</sub></font></span>)</span>
 <b>by </b><i><a class="ref" href="vectsp_1.html#T63">VECTSP_1:63</a></i>;<br/>


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