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<b>let </b><font color="Maroon" title="c1">L</font> be  non <a href="struct_0.html#V2" title="STRUCT_0:attr.2">empty</a>  <a href="algstr_0.html#L2" title="ALGSTR_0:struct.2">addLoopStr</a> ;<br/>

<b>assume </b><a NAME="E1:95_2_1"/><i><font color="Green" title="E44">A2</font></i>: 
( <font color="Maroon" title="c1">L</font> is <a href="rlvect_1.html#V2" title="RLVECT_1:attr.2">Abelian</a> &amp; <font color="Maroon" title="c1">L</font> is <a href="algstr_0.html#V13" title="ALGSTR_0:attr.13">right_complementable</a> )
 ;<br/>

<b>let </b><font color="Maroon" title="c2">a</font> be   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c1">L</font>; <i><font color="Red">:: according to </font></i><a class="ref" href="algstr_0.html#D15" title="ALGSTR_0:def.15">ALGSTR_0:def 15</a><br/>

<a NAME="E2:95_2_1"/>
<font color="Maroon" title="c2">a</font> is <a href="algstr_0.html#V10" title="ALGSTR_0:attr.10">right_complementable</a>
 
<b>by </b><i><a class="txt" href="rlvect_1.html#E1:95_2_1"><i><font color="Green" title="E44">A2</font></i></a>, <a class="ref" href="algstr_0.html#D16" title="ALGSTR_0:def.16">ALGSTR_0:def 16</a></i>;<br/>
<b>then consider </b><font color="Maroon" title="c3">w</font> being   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c1">L</font><b> such that </b><br/><a NAME="E4:95_2_1"/><i><font color="Green" title="E45">A3</font></i>: 
<font color="Maroon" title="c2">a</font> <a href="algstr_0.html#K1" title="ALGSTR_0:func.1">+</a> <font color="Maroon" title="c3">w</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="struct_0.html#K4" title="STRUCT_0:func.4">0.</a> <font color="Maroon" title="c1">L</font>
 <b>by </b><i><a class="ref" href="algstr_0.html#D11" title="ALGSTR_0:def.11">ALGSTR_0:def 11</a></i>;<br/>
<b>take </b>
<font color="Maroon" title="c3">w</font>
; <i><font color="Red">:: according to </font></i><a class="ref" href="algstr_0.html#D10" title="ALGSTR_0:def.10">ALGSTR_0:def 10</a><br/>

<b>thus </b><a NAME="E5:95_2_1"/>
<font color="Maroon" title="c3">w</font> <a href="algstr_0.html#K1" title="ALGSTR_0:func.1">+</a> <font color="Maroon" title="c2">a</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="struct_0.html#K4" title="STRUCT_0:func.4">0.</a> <font color="Maroon" title="c1">L</font>
 <b>by </b><i><a class="txt" href="rlvect_1.html#E1:95_2_1"><i><font color="Green" title="E44">A2</font></i></a>, <a class="txt" href="rlvect_1.html#E4:95_2_1"><i><font color="Green" title="E45">A3</font></i></a>, <a class="ref" href="rlvect_1.html#D5" target="_self" title="RLVECT_1:def.5">Def5</a></i>;<br/>


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