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<b>let </b><font color="Maroon" title="c1">R</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">R</font> is <a href="rlvect_1.html#V4" title="RLVECT_1:attr.4">right_zeroed</a> &amp; <font color="Maroon" title="c1">R</font> is <a href="algstr_0.html#V13" title="ALGSTR_0:attr.13">right_complementable</a> &amp; <font color="Maroon" title="c1">R</font> is <a href="rlvect_1.html#V3" title="RLVECT_1:attr.3">add-associative</a> implies <font color="Maroon" title="c1">R</font> is <a href="algstr_0.html#V6" title="ALGSTR_0:attr.6">right_add-cancelable</a> )</span><br/>

<b>assume </b><a NAME="E1:2_1_1"/>
( <font color="Maroon" title="c1">R</font> is <a href="rlvect_1.html#V4" title="RLVECT_1:attr.4">right_zeroed</a> &amp; <font color="Maroon" title="c1">R</font> is <a href="algstr_0.html#V13" title="ALGSTR_0:attr.13">right_complementable</a> &amp; <font color="Maroon" title="c1">R</font> is <a href="rlvect_1.html#V3" title="RLVECT_1:attr.3">add-associative</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">R</font> is <a href="algstr_0.html#V6" title="ALGSTR_0:attr.6">right_add-cancelable</a></span><br/>

<b>then reconsider </b><font color="Maroon" title="c2">R</font> = <font color="Maroon" title="c1">R</font> as  non <a href="struct_0.html#V2" title="STRUCT_0:attr.2">empty</a> <a href="algstr_0.html#V13" title="ALGSTR_0:attr.13">right_complementable</a> <a href="rlvect_1.html#V3" title="RLVECT_1:attr.3">add-associative</a> <a href="rlvect_1.html#V4" title="RLVECT_1:attr.4">right_zeroed</a>  <a href="algstr_0.html#L2" title="ALGSTR_0:struct.2">addLoopStr</a>  ;<br/>
<a NAME="E3:2_1_1"/>
<font color="Maroon" title="c2">R</font> is <a href="algstr_0.html#V6" title="ALGSTR_0:attr.6">right_add-cancelable</a>
 
;<br/>
<b>hence </b><a NAME="E4:2_1_1"/>
<font color="Maroon" title="c1">R</font> is <a href="algstr_0.html#V6" title="ALGSTR_0:attr.6">right_add-cancelable</a>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> verum</span><br/>


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