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

<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="rlvect_1.html#L1">LoopStr</a> ;<br/><b>let </b><font color="Maroon">v1</font> be   <a href="struct_0.html#NM1">Element</a> of <font color="Maroon">V</font>, <font color="Maroon">v2</font> be   <a href="struct_0.html#NM1">Element</a> of <font color="Maroon">V</font>;<br/>



<b>assume </b><a NAME="E1:14"/>
<font color="Maroon">v1</font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <font color="Maroon">v2</font>
 ;<br/>

<a NAME="E2:14"/><b>then </b>
(  <a href="relat_1.html#K2">rng</a> <span class="p1"><a href="finseq_4.html#K2">&lt;*</a><span class="default"><font color="Maroon">v1</font>,<font color="Maroon">v2</font></span><a href="finseq_4.html#K2">*&gt;</a></span> <a href="hidden.html#R1">=</a> <span class="p1"><a href="domain_1.html#K7">{</a><span class="default"><font color="Maroon">v1</font>,<font color="Maroon">v2</font></span><a href="domain_1.html#K7">}</a></span> &amp; <span class="p1"><a href="finseq_4.html#K2">&lt;*</a><span class="default"><font color="Maroon">v1</font>,<font color="Maroon">v2</font></span><a href="finseq_4.html#K2">*&gt;</a></span> is <a href="funct_1.html#V2">one-to-one</a> &amp;  <a href="rlvect_1.html#K9">Sum</a> <span class="p1"><a href="finseq_4.html#K2">&lt;*</a><span class="default"><font color="Maroon">v1</font>,<font color="Maroon">v2</font></span><a href="finseq_4.html#K2">*&gt;</a></span> <a href="hidden.html#R1">=</a> <font color="Maroon">v1</font> <a href="rlvect_1.html#K4">+</a> <font color="Maroon">v2</font> )
 
<b>by </b><i><a class="ref" href="finseq_2.html#T147">FINSEQ_2:147</a>, <a class="ref" href="finseq_3.html#T103">FINSEQ_3:103</a>, <a class="ref" href="rlvect_1.html#T62">RLVECT_1:62</a></i>;<br/>
<b>hence </b><a NAME="E3:14"/>
 <a href="rlvect_2.html#K2" target="_self">Sum</a> <span class="p1"><a href="domain_1.html#K7">{</a><span class="default"><font color="Maroon">v1</font>,<font color="Maroon">v2</font></span><a href="domain_1.html#K7">}</a></span> <a href="hidden.html#R1">=</a> <font color="Maroon">v1</font> <a href="rlvect_1.html#K4">+</a> <font color="Maroon">v2</font>
 <b>by </b><i/>;<br/>


</div>
