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<b>let </b><font color="Maroon" title="c1">G</font> be  non <a href="struct_0.html#V3" title="STRUCT_0:attr.3">empty</a> <a href="rlvect_1.html#V3" title="RLVECT_1:attr.3">Abelian</a> <a href="algstr_1.html#V2" title="ALGSTR_1:attr.2">add-left-cancelable</a> <a href="algstr_1.html#V5" title="ALGSTR_1:attr.5">add-right-invertible</a>  <a href="rlvect_1.html#L1" title="RLVECT_1:struct.1">LoopStr</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">G</font>;<br/>



<a NAME="E1:11"/>
<span class="p1">(<span class="default"><a href="algstr_2.html#K1" title="ALGSTR_2:func.1">-</a> <font color="Maroon" title="c2">a</font></span>)</span> <a href="rlvect_1.html#K4" title="RLVECT_1:func.4">+</a> <font color="Maroon" title="c2">a</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="rlvect_1.html#K1" title="RLVECT_1:func.1">0.</a> <font color="Maroon" title="c1">G</font>
 
<b>by </b><i><a class="ref" href="algstr_2.html#D7" target="_self" title="ALGSTR_2:def.7">Def7</a></i>;<br/>
<b>hence </b><a NAME="E2:11"/>
 <a href="algstr_2.html#K1" title="ALGSTR_2:func.1">-</a> <span class="p1">(<span class="default"><a href="algstr_2.html#K1" title="ALGSTR_2:func.1">-</a> <font color="Maroon" title="c2">a</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c2">a</font>
 <b>by </b><i><a class="ref" href="algstr_2.html#D7" target="_self" title="ALGSTR_2:def.7">Def7</a></i>;<br/>


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