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<span class="kw">let </span><font color="Maroon" title="c1">AFV</font> be   <a href="afvect0.html#NM1" title="AFVECT0:NM.1">WeakAffVect</a>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> for <font color="Olive" title="b1">o</font> being  <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c1">AFV</font> holds <br/> (  <a href="afvect0.html#K5" title="AFVECT0:func.5">GroupVect</a> <font color="Maroon" title="c1">AFV</font>,<font color="Olive" title="b1">o</font> is  <a href="rlvect_1.html#V2" title="RLVECT_1:attr.2">Abelian</a>  &amp;  <a href="afvect0.html#K5" title="AFVECT0:func.5">GroupVect</a> <font color="Maroon" title="c1">AFV</font>,<font color="Olive" title="b1">o</font> is  <a href="rlvect_1.html#V3" title="RLVECT_1:attr.3">add-associative</a>  &amp;  <a href="afvect0.html#K5" title="AFVECT0:func.5">GroupVect</a> <font color="Maroon" title="c1">AFV</font>,<font color="Olive" title="b1">o</font> is  <a href="rlvect_1.html#V4" title="RLVECT_1:attr.4">right_zeroed</a>  )</span><br/><span class="kw">let </span><font color="Maroon" title="c2">o</font> be   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c1">AFV</font>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> (  <a href="afvect0.html#K5" title="AFVECT0:func.5">GroupVect</a> <font color="Maroon" title="c1">AFV</font>,<font color="Maroon" title="c2">o</font> is  <a href="rlvect_1.html#V2" title="RLVECT_1:attr.2">Abelian</a>  &amp;  <a href="afvect0.html#K5" title="AFVECT0:func.5">GroupVect</a> <font color="Maroon" title="c1">AFV</font>,<font color="Maroon" title="c2">o</font> is  <a href="rlvect_1.html#V3" title="RLVECT_1:attr.3">add-associative</a>  &amp;  <a href="afvect0.html#K5" title="AFVECT0:func.5">GroupVect</a> <font color="Maroon" title="c1">AFV</font>,<font color="Maroon" title="c2">o</font> is  <a href="rlvect_1.html#V4" title="RLVECT_1:attr.4">right_zeroed</a>  )</span><br/>



<span class="kw">thus </span><a NAME="E1:72"/>
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 <span class="p1">(<span class="default"><a href="afvect0.html#K5" title="AFVECT0:func.5">GroupVect</a> <font color="Maroon" title="c1">AFV</font>,<font color="Maroon" title="c2">o</font></span>)</span> holds  <font color="Olive" title="b1">a</font> <a href="algstr_0.html#K1" title="ALGSTR_0:func.1">+</a> <font color="Olive" title="b2">b</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b2">b</font> <a href="algstr_0.html#K1" title="ALGSTR_0:func.1">+</a> <font color="Olive" title="b1">a</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="afvect0.html#E68"><span class="lab"><font color="Green" title="E34">Lm2</font></span></a></span>; <span class="comment"><font color="Red">:: according to </font></span><a class="ref" href="rlvect_1.html#D5" title="RLVECT_1:def.5">RLVECT_1:def 5</a> <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> (  <a href="afvect0.html#K5" title="AFVECT0:func.5">GroupVect</a> <font color="Maroon" title="c1">AFV</font>,<font color="Maroon" title="c2">o</font> is  <a href="rlvect_1.html#V3" title="RLVECT_1:attr.3">add-associative</a>  &amp;  <a href="afvect0.html#K5" title="AFVECT0:func.5">GroupVect</a> <font color="Maroon" title="c1">AFV</font>,<font color="Maroon" title="c2">o</font> is  <a href="rlvect_1.html#V4" title="RLVECT_1:attr.4">right_zeroed</a>  )</span><br/>

<span class="kw">thus </span><a NAME="E2:72"/>
for <font color="Olive" title="b1">a</font>, <font color="Olive" title="b2">b</font>, <font color="Olive" title="b3">c</font> being  <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <span class="p1">(<span class="default"><a href="afvect0.html#K5" title="AFVECT0:func.5">GroupVect</a> <font color="Maroon" title="c1">AFV</font>,<font color="Maroon" title="c2">o</font></span>)</span> holds  <span class="p1">(<span class="default"><font color="Olive" title="b1">a</font> <a href="algstr_0.html#K1" title="ALGSTR_0:func.1">+</a> <font color="Olive" title="b2">b</font></span>)</span> <a href="algstr_0.html#K1" title="ALGSTR_0:func.1">+</a> <font color="Olive" title="b3">c</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b1">a</font> <a href="algstr_0.html#K1" title="ALGSTR_0:func.1">+</a> <span class="p1">(<span class="default"><font color="Olive" title="b2">b</font> <a href="algstr_0.html#K1" title="ALGSTR_0:func.1">+</a> <font color="Olive" title="b3">c</font></span>)</span>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="afvect0.html#E69"><span class="lab"><font color="Green" title="E35">Lm3</font></span></a></span>; <span class="comment"><font color="Red">:: according to </font></span><a class="ref" href="rlvect_1.html#D6" title="RLVECT_1:def.6">RLVECT_1:def 6</a> <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide">  <a href="afvect0.html#K5" title="AFVECT0:func.5">GroupVect</a> <font color="Maroon" title="c1">AFV</font>,<font color="Maroon" title="c2">o</font> is  <a href="rlvect_1.html#V4" title="RLVECT_1:attr.4">right_zeroed</a> </span><br/>

<span class="kw">thus </span><a NAME="E3:72"/>
for <font color="Olive" title="b1">a</font> being  <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <span class="p1">(<span class="default"><a href="afvect0.html#K5" title="AFVECT0:func.5">GroupVect</a> <font color="Maroon" title="c1">AFV</font>,<font color="Maroon" title="c2">o</font></span>)</span> holds  <font color="Olive" title="b1">a</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> <span class="p2">(<span class="default"><a href="afvect0.html#K5" title="AFVECT0:func.5">GroupVect</a> <font color="Maroon" title="c1">AFV</font>,<font color="Maroon" title="c2">o</font></span>)</span></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b1">a</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="afvect0.html#E70"><span class="lab"><font color="Green" title="E36">Lm4</font></span></a></span>; <span class="comment"><font color="Red">:: according to </font></span><a class="ref" href="rlvect_1.html#D7" title="RLVECT_1:def.7">RLVECT_1:def 7</a> <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> verum</span><br/>


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