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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">W1</font> be    <a href="vectsp_4.html#M1" target="_self">Subspace</a> of <font color="Maroon">V</font>;<br/><b>let </b><font color="Maroon">W2</font> be    <a href="vectsp_4.html#M1" target="_self">Subspace</a> of <font color="Maroon">V</font>;<br/>







<a NAME="E1:42"/>
(  <a href="vectsp_4.html#K1" target="_self">(0).</a> <font color="Maroon">W1</font> <a href="hidden.html#R1">=</a>  <a href="vectsp_4.html#K1" target="_self">(0).</a> <font color="Maroon">V</font> &amp;  <a href="vectsp_4.html#K1" target="_self">(0).</a> <font color="Maroon">W2</font> <a href="hidden.html#R1">=</a>  <a href="vectsp_4.html#K1" target="_self">(0).</a> <font color="Maroon">V</font> )
 
<b>by </b><i><a class="ref" href="vectsp_4.html#T5" target="_self">Th5</a></i>;<br/>
<b>hence </b><a NAME="E2:42"/>
 <a href="vectsp_4.html#K1" target="_self">(0).</a> <font color="Maroon">W1</font> <a href="hidden.html#R1">=</a>  <a href="vectsp_4.html#K1" target="_self">(0).</a> <font color="Maroon">W2</font>
 ;<br/>


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