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

<b>set </b><font color="Maroon" title="c1">M</font> =  <a href="algstr_0.html#K3" title="ALGSTR_0:func.3">Trivial-addLoopStr</a> ;<br/>
<b>thus </b><a NAME="E1:35_1_1"/>
 <a href="algstr_0.html#K3" title="ALGSTR_0:func.3">Trivial-addLoopStr</a>  is <a href="algstr_0.html#V13" title="ALGSTR_0:attr.13">right_complementable</a>
  <i><font color="Red">:: according to </font></i><a class="ref" href="algstr_0.html#D17" target="_self" title="ALGSTR_0:def.17">ALGSTR_0:def 17</a><div><a class="txt" onclick="hs2(this)" href="javascript:()" title="35_1_1_1"><b>proof </b></a><div class="add">

<b>let </b><font color="Maroon" title="c2">x</font> be   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <a href="algstr_0.html#K3" title="ALGSTR_0:func.3">Trivial-addLoopStr</a> ; <i><font color="Red">:: according to </font></i><a class="ref" href="algstr_0.html#D16" target="_self" title="ALGSTR_0:def.16">ALGSTR_0:def 16</a><br/>

<b>take </b>
<font color="Maroon" title="c2">x</font>
; <i><font color="Red">:: according to </font></i><a class="ref" href="algstr_0.html#D11" target="_self" title="ALGSTR_0:def.11">ALGSTR_0:def 11</a><br/>

<b>thus </b><a NAME="E1:35_1_1_1"/>
<font color="Maroon" title="c2">x</font> <a href="algstr_0.html#K1" title="ALGSTR_0:func.1">+</a> <font color="Maroon" title="c2">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="struct_0.html#K4" title="STRUCT_0:func.4">0.</a> <a href="algstr_0.html#K3" title="ALGSTR_0:func.3">Trivial-addLoopStr</a> 
 <b>by </b><i><a class="ref" href="struct_0.html#D10" title="STRUCT_0:def.10">STRUCT_0:def 10</a></i>;<br/>


</div><b>end;</b></div>

<b>let </b><font color="Maroon" title="c2">x</font> be   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <a href="algstr_0.html#K3" title="ALGSTR_0:func.3">Trivial-addLoopStr</a> ; <i><font color="Red">:: according to </font></i><a class="ref" href="algstr_0.html#D15" target="_self" title="ALGSTR_0:def.15">ALGSTR_0:def 15</a><br/>

<b>take </b>
<font color="Maroon" title="c2">x</font>
; <i><font color="Red">:: according to </font></i><a class="ref" href="algstr_0.html#D10" target="_self" title="ALGSTR_0:def.10">ALGSTR_0:def 10</a><br/>

<b>thus </b><a NAME="E2:35_1_1"/>
<font color="Maroon" title="c2">x</font> <a href="algstr_0.html#K1" title="ALGSTR_0:func.1">+</a> <font color="Maroon" title="c2">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="struct_0.html#K4" title="STRUCT_0:func.4">0.</a> <a href="algstr_0.html#K3" title="ALGSTR_0:func.3">Trivial-addLoopStr</a> 
 <b>by </b><i><a class="ref" href="struct_0.html#D10" title="STRUCT_0:def.10">STRUCT_0:def 10</a></i>;<br/>


</div>
