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<b>let </b><font color="Maroon">V</font> be  non <a href="struct_0.html#V3">empty</a> <a href="rlvect_1.html#V4" target="_self">add-associative</a> <a href="rlvect_1.html#V5" target="_self">right_zeroed</a> <a href="rlvect_1.html#V6" target="_self">right_complementable</a>  <a href="rlvect_1.html#L1" target="_self">LoopStr</a> ;<br/><b>let </b><font color="Maroon">v</font> be   <a href="struct_0.html#NM1">Element</a> of <font color="Maroon">V</font>, <font color="Maroon">w</font> be   <a href="struct_0.html#NM1">Element</a> of <font color="Maroon">V</font>;<br/>



<b>assume </b><a NAME="E1:18"/><i><font color="Green">E30</font></i>: 
<font color="Maroon">v</font> <a href="rlvect_1.html#K2" target="_self">+</a> <font color="Maroon">w</font> <a href="hidden.html#R1">=</a>  <a href="rlvect_1.html#K1" target="_self">0.</a> <font color="Maroon">V</font>
 ;<br/>

<b>consider </b><font color="Maroon">u</font> being   <a href="struct_0.html#NM1">Element</a> of <font color="Maroon">V</font><b> such that </b><br/><a NAME="E3:18"/><i><font color="Green">E32</font></i>: 
<font color="Maroon">w</font> <a href="rlvect_1.html#K2" target="_self">+</a> <font color="Maroon">u</font> <a href="hidden.html#R1">=</a>  <a href="rlvect_1.html#K1" target="_self">0.</a> <font color="Maroon">V</font>
 <b>by </b><i/>;<br/>
<font color="Maroon">w</font> <a href="rlvect_1.html#K2" target="_self">+</a> <font color="Maroon">v</font> = 
<font color="Maroon">w</font> <a href="rlvect_1.html#K2" target="_self">+</a> <span class="p1">(<span class="default"><font color="Maroon">v</font> <a href="rlvect_1.html#K2" target="_self">+</a> <span class="p2">(<span class="default"><font color="Maroon">w</font> <a href="rlvect_1.html#K2" target="_self">+</a> <font color="Maroon">u</font></span>)</span></span>)</span>
<b>by </b><i>, </i>
<br/>.= 
<font color="Maroon">w</font> <a href="rlvect_1.html#K2" target="_self">+</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">v</font> <a href="rlvect_1.html#K2" target="_self">+</a> <font color="Maroon">w</font></span>)</span> <a href="rlvect_1.html#K2" target="_self">+</a> <font color="Maroon">u</font></span>)</span>
<b>by </b><i/>
<br/>.= 
<span class="p1">(<span class="default"><font color="Maroon">w</font> <a href="rlvect_1.html#K2" target="_self">+</a> <span class="p2">(<span class="default"><font color="Maroon">v</font> <a href="rlvect_1.html#K2" target="_self">+</a> <font color="Maroon">w</font></span>)</span></span>)</span> <a href="rlvect_1.html#K2" target="_self">+</a> <font color="Maroon">u</font>
<b>by </b><i/>
<br/>.= 
<font color="Maroon">w</font> <a href="rlvect_1.html#K2" target="_self">+</a> <font color="Maroon">u</font>
<b>by </b><i>, </i>
;<br/>
<b>hence </b><a NAME="E5:18"/>
<font color="Maroon">w</font> <a href="rlvect_1.html#K2" target="_self">+</a> <font color="Maroon">v</font> <a href="hidden.html#R1">=</a>  <a href="rlvect_1.html#K1" target="_self">0.</a> <font color="Maroon">V</font>
 <b>by </b><i/>;<br/>


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