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

<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> ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> ( <font color="Maroon" title="c1">L</font> is <a href="algstr_1.html#V4" title="ALGSTR_1:attr.4">Loop-like</a> implies <font color="Maroon" title="c1">L</font> is <a href="algstr_1.html#V2" title="ALGSTR_1:attr.2">add-left-invertible</a> )</span><br/>

<b>assume </b><a NAME="E1:20_1_1"/>
<font color="Maroon" title="c1">L</font> is <a href="algstr_1.html#V4" title="ALGSTR_1:attr.4">Loop-like</a>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> <font color="Maroon" title="c1">L</font> is <a href="algstr_1.html#V2" title="ALGSTR_1:attr.2">add-left-invertible</a></span><br/>

<b>hence </b><a NAME="E2:20_1_1"/>
for <font color="Olive" title="b1">a</font>, <font color="Olive" title="b2">b</font> being  <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c1">L</font>  ex <font color="Olive" title="b3">x</font> being  <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c1">L</font> st <font color="Olive" title="b3">x</font> <a href="algstr_0.html#K1" title="ALGSTR_0:func.1">+</a> <font color="Olive" title="b1">a</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b2">b</font>
 <b>by </b><i><a class="ref" href="algstr_1.html#T7" target="_self" title="ALGSTR_1:th.7">Th7</a></i>; <i><font color="Red">:: according to </font></i><a class="ref" href="algstr_1.html#D8" target="_self" title="ALGSTR_1:def.8">ALGSTR_1:def 8</a> <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> verum</span><br/>


</div>
