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

<b>let </b><font color="Maroon">c<sub>1</sub></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">c<sub>2</sub></font> be   <a href="struct_0.html#NM1">Element</a> of <font color="Maroon">c<sub>1</sub></font>;<br/>



<a NAME="E1:76"/><i><font color="Green">E42</font></i>: 
<font color="Maroon">c<sub>2</sub></font> <a href="rlvect_1.html#K2" target="_self">+</a> <span class="p1">(<span class="default"><a href="rlvect_1.html#K5" target="_self">-</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="hidden.html#R1">=</a>  <a href="rlvect_1.html#K1" target="_self">0.</a> <font color="Maroon">c<sub>1</sub></font>
 
<b>by </b><i><a class="ref" href="rlvect_1.html#D10" target="_self">Def10</a></i>;<br/>
<b>hence </b><a NAME="E2:76"/>
 <a href="rlvect_1.html#K9" target="_self">Sum</a> <span class="p1"><a href="rlvect_1.html#K7" target="_self">&lt;*</a><span class="default"><font color="Maroon">c<sub>2</sub></font>,<span class="p2">(<span class="default"><a href="rlvect_1.html#K5" target="_self">-</a> <font color="Maroon">c<sub>2</sub></font></span>)</span></span><a href="rlvect_1.html#K7" target="_self">*&gt;</a></span> <a href="hidden.html#R1">=</a>  <a href="rlvect_1.html#K1" target="_self">0.</a> <font color="Maroon">c<sub>1</sub></font>
 <b>by </b><i><a class="ref" href="rlvect_1.html#T62" target="_self">Th62</a></i>;<br/>

<a NAME="E3:76"/>
<span class="p1">(<span class="default"><a href="rlvect_1.html#K5" target="_self">-</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="rlvect_1.html#K2" target="_self">+</a> <font color="Maroon">c<sub>2</sub></font> <a href="hidden.html#R1">=</a>  <a href="rlvect_1.html#K1" target="_self">0.</a> <font color="Maroon">c<sub>1</sub></font>
 
<b>by </b><i><a class="txt" href="rlvect_1.html#E1:76"><i><font color="Green">E42</font></i></a>, <a class="txt" href="rlvect_1.html#E18"><i><font color="Green">Lemma8</font></i></a></i>;<br/>
<b>hence </b><a NAME="E4:76"/>
 <a href="rlvect_1.html#K9" target="_self">Sum</a> <span class="p1"><a href="rlvect_1.html#K7" target="_self">&lt;*</a><span class="default"><span class="p2">(<span class="default"><a href="rlvect_1.html#K5" target="_self">-</a> <font color="Maroon">c<sub>2</sub></font></span>)</span>,<font color="Maroon">c<sub>2</sub></font></span><a href="rlvect_1.html#K7" target="_self">*&gt;</a></span> <a href="hidden.html#R1">=</a>  <a href="rlvect_1.html#K1" target="_self">0.</a> <font color="Maroon">c<sub>1</sub></font>
 <b>by </b><i><a class="ref" href="rlvect_1.html#T62" target="_self">Th62</a></i>;<br/>


</div>
