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<b>let </b><font color="Maroon">F</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   <a href="vectsp_1.html#NM6">VectSp</a> of <font color="Maroon">F</font>;<br/><b>let </b><font color="Maroon">W</font> be    <a href="vectsp_4.html#M1">Subspace</a> of <font color="Maroon">V</font>;<br/>





<a NAME="E1:38"/><i><font color="Green">E29</font></i>: 
 <a href="rlvect_1.html#K1">0.</a> <font color="Maroon">V</font> <a href="hidden.html#R1">=</a>  <a href="rlvect_1.html#K1">0.</a> <font color="Maroon">W</font>
 
<b>by </b><i><a class="ref" href="vectsp_4.html#T19">VECTSP_4:19</a></i>;<br/>
<a NAME="E2:38"/><i><font color="Green">E35</font></i>: 
 <a href="rlvect_1.html#K1">0.</a> <font color="Maroon">W</font> <a href="rlvect_1.html#R1">in</a> <font color="Maroon">W</font>
 
<b>by </b><i><a class="ref" href="rlvect_1.html#D1">RLVECT_1:def 1</a></i>;<br/>
<b>thus </b><a NAME="E3:38"/>
 <a href="vectsp10.html#K4" target="_self">zeroCoset</a> <font color="Maroon">V</font>,<font color="Maroon">W</font> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><a href="rlvect_1.html#K1">0.</a> <font color="Maroon">V</font></span>)</span> <a href="vectsp_4.html#K3">+</a> <font color="Maroon">W</font>
 <b>by </b><i>, , <a class="ref" href="vectsp_4.html#T64">VECTSP_4:64</a></i>;<br/>

<b>thus </b><a NAME="E4:38"/>
 <a href="rlvect_1.html#K1">0.</a> <span class="p1">(<span class="default"><a href="vectsp10.html#K6" target="_self">VectQuot</a> <font color="Maroon">V</font>,<font color="Maroon">W</font></span>)</span> <a href="hidden.html#R1">=</a>  <a href="vectsp10.html#K4" target="_self">zeroCoset</a> <font color="Maroon">V</font>,<font color="Maroon">W</font>
 <b>by </b><i/>;<br/>


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