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<b>let </b><font color="Maroon">L</font> be  non <a href="struct_0.html#V3">empty</a>  <a href="rlvect_1.html#L1">LoopStr</a> ;<br/>

<b>assume </b><b>that </b><br/><a NAME="E1:89_1_1"/><i><font color="Green">E48</font></i>: 
<font color="Maroon">L</font> is <a href="rlvect_1.html#V3">Abelian</a>
 <b>and </b><br/><a NAME="E2:89_1_1"/><i><font color="Green">E55</font></i>: 
<font color="Maroon">L</font> is <a href="rlvect_1.html#V5">right_zeroed</a>
 ;<br/>

<b>let </b><font color="Maroon">x</font> be   <a href="struct_0.html#NM1">Element</a> of <font color="Maroon">L</font>; <i><font color="Red">:: according to </font></i><a class="ref" href="algstr_1.html#D5">ALGSTR_1:def 5</a><br/>

<b>thus </b><span class="p1">(<span class="default"><a href="rlvect_1.html#K1">0.</a> <font color="Maroon">L</font></span>)</span> <a href="rlvect_1.html#K2">+</a> <font color="Maroon">x</font> = 
<font color="Maroon">x</font> <a href="rlvect_1.html#K2">+</a> <span class="p1">(<span class="default"><a href="rlvect_1.html#K1">0.</a> <font color="Maroon">L</font></span>)</span>
<b>by </b><i><a class="txt" href="fvsum_1.html#E17"><i><font color="Green">Lemma46</font></i></a>, <a class="ref" href="rlvect_1.html#D5">RLVECT_1:def 5</a></i>
<br/>.= 
<font color="Maroon">x</font>
<b>by </b><i><a class="ref" href="fvsum_1.html#T15" target="_self">Th15</a>, <a class="ref" href="rlvect_1.html#D7">RLVECT_1:def 7</a></i>
;<br/>


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