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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">V1</font> be   <a href="struct_0.html#NM2">Subset</a> of <font color="Maroon">V</font>;<br/>





<b>assume </b><a NAME="E1:77"/>
<font color="Maroon">V1</font> is    <a href="vectsp_4.html#M2" target="_self">Coset</a> of  <a href="vectsp_4.html#K1" target="_self">(0).</a> <font color="Maroon">V</font>
 ;<br/>

<b>then consider </b><font color="Maroon">v</font> being   <a href="struct_0.html#NM1">Element</a> of <font color="Maroon">V</font><b> such that </b><br/><a NAME="E3:77"/><i><font color="Green">E26</font></i>: 
<font color="Maroon">V1</font> <a href="hidden.html#R1">=</a> <font color="Maroon">v</font> <a href="vectsp_4.html#K3" target="_self">+</a> <span class="p1">(<span class="default"><a href="vectsp_4.html#K1" target="_self">(0).</a> <font color="Maroon">V</font></span>)</span>
 <b>by </b><i/>;<br/>
<b>take </b>
<font color="Maroon">v</font>
;<br/>

<b>thus </b><a NAME="E4:77"/>
<font color="Maroon">V1</font> <a href="hidden.html#R1">=</a> <span class="p1"><a href="domain_1.html#K6">{</a><span class="default"><font color="Maroon">v</font></span><a href="domain_1.html#K6">}</a></span>
 <b>by </b><i>, </i>;<br/>


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