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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> ; <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="rlvect_1.html#V2" title="RLVECT_1:attr.2">Abelian</a> &amp; <font color="Maroon" title="c1">L</font> is <a href="rlvect_1.html#V4" title="RLVECT_1:attr.4">right_zeroed</a> implies <font color="Maroon" title="c1">L</font> is <a href="algstr_1.html#V1" title="ALGSTR_1:attr.1">left_zeroed</a> )</span><br/>

<b>assume </b><b>that </b><br/><a NAME="E1:79_1_1"/><i><font color="Green" title="E37">A1</font></i>: 
<font color="Maroon" title="c1">L</font> is <a href="rlvect_1.html#V2" title="RLVECT_1:attr.2">Abelian</a>
 <b>and </b><br/><a NAME="E2:79_1_1"/><i><font color="Green" title="E38">A2</font></i>: 
<font color="Maroon" title="c1">L</font> is <a href="rlvect_1.html#V4" title="RLVECT_1:attr.4">right_zeroed</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#V1" title="ALGSTR_1:attr.1">left_zeroed</a></span><br/>

<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 <font color="Maroon" title="c1">L</font>; <i><font color="Red">:: according to </font></i><a class="ref" href="algstr_1.html#D5" title="ALGSTR_1:def.5">ALGSTR_1:def 5</a> <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> <span class="p1">(<span class="default"><a href="struct_0.html#K4" title="STRUCT_0:func.4">0.</a> <font color="Maroon" title="c1">L</font></span>)</span> <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> <font color="Maroon" title="c2">x</font></span><br/>

<b>thus </b><span class="p1">(<span class="default"><a href="struct_0.html#K4" title="STRUCT_0:func.4">0.</a> <font color="Maroon" title="c1">L</font></span>)</span> <a href="algstr_0.html#K1" title="ALGSTR_0:func.1">+</a> <font color="Maroon" title="c2">x</font> = 
<font color="Maroon" title="c2">x</font> <a href="algstr_0.html#K1" title="ALGSTR_0:func.1">+</a> <span class="p1">(<span class="default"><a href="struct_0.html#K4" title="STRUCT_0:func.4">0.</a> <font color="Maroon" title="c1">L</font></span>)</span>
<b>by </b><i><a class="txt" href="#E1:79_1_1"><i><font color="Green" title="E37">A1</font></i></a>, <a class="ref" href="rlvect_1.html#D5" title="RLVECT_1:def.5">RLVECT_1:def 5</a></i>
<br/>.= 
<font color="Maroon" title="c2">x</font>
<b>by </b><i><a class="txt" href="#E2:79_1_1"><i><font color="Green" title="E38">A2</font></i></a>, <a class="ref" href="rlvect_1.html#D7" title="RLVECT_1:def.7">RLVECT_1:def 7</a></i>
; <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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