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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>;<br/>



<b>thus </b> <a href="rlvect_1.html#K9" target="_self">Sum</a> <span class="p1"><a href="rlvect_1.html#K8" target="_self">&lt;*</a><span class="default"><span class="p2">(<span class="default"><a href="rlvect_1.html#K1" target="_self">0.</a> <font color="Maroon">V</font></span>)</span>,<span class="p2">(<span class="default"><a href="rlvect_1.html#K1" target="_self">0.</a> <font color="Maroon">V</font></span>)</span>,<font color="Maroon">v</font></span><a href="rlvect_1.html#K8" target="_self">*&gt;</a></span> = 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="rlvect_1.html#K1" target="_self">0.</a> <font color="Maroon">V</font></span>)</span> <a href="rlvect_1.html#K2" target="_self">+</a> <span class="p2">(<span class="default"><a href="rlvect_1.html#K1" target="_self">0.</a> <font color="Maroon">V</font></span>)</span></span>)</span> <a href="rlvect_1.html#K2" target="_self">+</a> <font color="Maroon">v</font>
<b>by </b><i/>
<br/>.= 
<span class="p1">(<span class="default"><a href="rlvect_1.html#K1" target="_self">0.</a> <font color="Maroon">V</font></span>)</span> <a href="rlvect_1.html#K2" target="_self">+</a> <font color="Maroon">v</font>
<b>by </b><i/>
<br/>.= 
<font color="Maroon">v</font>
<b>by </b><i/>
;<br/>

<b>thus </b> <a href="rlvect_1.html#K9" target="_self">Sum</a> <span class="p1"><a href="rlvect_1.html#K8" target="_self">&lt;*</a><span class="default"><span class="p2">(<span class="default"><a href="rlvect_1.html#K1" target="_self">0.</a> <font color="Maroon">V</font></span>)</span>,<font color="Maroon">v</font>,<span class="p2">(<span class="default"><a href="rlvect_1.html#K1" target="_self">0.</a> <font color="Maroon">V</font></span>)</span></span><a href="rlvect_1.html#K8" target="_self">*&gt;</a></span> = 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="rlvect_1.html#K1" target="_self">0.</a> <font color="Maroon">V</font></span>)</span> <a href="rlvect_1.html#K2" target="_self">+</a> <font color="Maroon">v</font></span>)</span> <a href="rlvect_1.html#K2" target="_self">+</a> <span class="p1">(<span class="default"><a href="rlvect_1.html#K1" target="_self">0.</a> <font color="Maroon">V</font></span>)</span>
<b>by </b><i/>
<br/>.= 
<span class="p1">(<span class="default"><a href="rlvect_1.html#K1" target="_self">0.</a> <font color="Maroon">V</font></span>)</span> <a href="rlvect_1.html#K2" target="_self">+</a> <font color="Maroon">v</font>
<b>by </b><i/>
<br/>.= 
<font color="Maroon">v</font>
<b>by </b><i/>
;<br/>

<b>thus </b> <a href="rlvect_1.html#K9" target="_self">Sum</a> <span class="p1"><a href="rlvect_1.html#K8" target="_self">&lt;*</a><span class="default"><font color="Maroon">v</font>,<span class="p2">(<span class="default"><a href="rlvect_1.html#K1" target="_self">0.</a> <font color="Maroon">V</font></span>)</span>,<span class="p2">(<span class="default"><a href="rlvect_1.html#K1" target="_self">0.</a> <font color="Maroon">V</font></span>)</span></span><a href="rlvect_1.html#K8" target="_self">*&gt;</a></span> = 
<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"><a href="rlvect_1.html#K1" target="_self">0.</a> <font color="Maroon">V</font></span>)</span></span>)</span> <a href="rlvect_1.html#K2" target="_self">+</a> <span class="p1">(<span class="default"><a href="rlvect_1.html#K1" target="_self">0.</a> <font color="Maroon">V</font></span>)</span>
<b>by </b><i/>
<br/>.= 
<font color="Maroon">v</font> <a href="rlvect_1.html#K2" target="_self">+</a> <span class="p1">(<span class="default"><a href="rlvect_1.html#K1" target="_self">0.</a> <font color="Maroon">V</font></span>)</span>
<b>by </b><i/>
<br/>.= 
<font color="Maroon">v</font>
<b>by </b><i/>
;<br/>


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