<?xml version="1.0"?>
<div class="add">

<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">u</font> be   <a href="struct_0.html#NM1">Element</a> of <font color="Maroon">V</font>;<br/><b>let </b><font color="Maroon">W</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">B</font> be    <a href="vectsp_4.html#M2" target="_self">Coset</a> of <font color="Maroon">W</font>;<br/><b>let </b><font color="Maroon">C</font> be    <a href="vectsp_4.html#M2" target="_self">Coset</a> of <font color="Maroon">W</font>;<br/>











<b>assume </b><a NAME="E1:86"/><i><font color="Green">E26</font></i>: 
( <font color="Maroon">u</font> <a href="hidden.html#R2">in</a> <font color="Maroon">B</font> &amp; <font color="Maroon">u</font> <a href="hidden.html#R2">in</a> <font color="Maroon">C</font> )
 ;<br/>

<a NAME="E2:86"/><i><font color="Green">E27</font></i>: 
 ex <font color="Olive">v1</font> being  <a href="struct_0.html#NM1">Element</a> of <font color="Maroon">V</font> st <font color="Maroon">B</font> <a href="hidden.html#R1">=</a> <font color="Olive">v1</font> <a href="vectsp_4.html#K3" target="_self">+</a> <font color="Maroon">W</font>
 
<b>by </b><i/>;<br/>
<a NAME="E3:86"/>
 ex <font color="Olive">v2</font> being  <a href="struct_0.html#NM1">Element</a> of <font color="Maroon">V</font> st <font color="Maroon">C</font> <a href="hidden.html#R1">=</a> <font color="Olive">v2</font> <a href="vectsp_4.html#K3" target="_self">+</a> <font color="Maroon">W</font>
 
<b>by </b><i/>;<br/>
<b>hence </b><a NAME="E4:86"/>
<font color="Maroon">B</font> <a href="hidden.html#R1">=</a> <font color="Maroon">C</font>
 <b>by </b><i>, , </i>;<br/>


</div>
