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

<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   <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="algstr_0.html#V13" title="ALGSTR_0:attr.13">right_complementable</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="algstr_0.html#V13" title="ALGSTR_0:attr.13">right_complementable</a> </span><br/><span class="kw">let </span><font color="Maroon" title="c3">s</font> be   <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>; <span class="comment"><font color="Red">:: according to </font></span><a class="ref" href="algstr_0.html#D16" title="ALGSTR_0:def.16">ALGSTR_0:def 16</a> <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> <font color="Maroon" title="c3">s</font> is  <a href="algstr_0.html#V10" title="ALGSTR_0:attr.10">right_complementable</a> </span><br/>





<span class="kw">reconsider </span><font color="Maroon" title="c4">s9</font> = <font color="Maroon" title="c3">s</font> as   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c1">AFV</font> ;<br/>
<span class="kw">reconsider </span><font color="Maroon" title="c5">t</font> = <span class="p1">(<span class="default"><a href="afvect0.html#K4" title="AFVECT0:func.4">Pcom</a> <font color="Maroon" title="c2">o</font></span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c4">s9</font> as   <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> ;<br/>
<span class="kw">take </span>
<font color="Maroon" title="c5">t</font>
; <span class="comment"><font color="Red">:: according to </font></span><a class="ref" href="algstr_0.html#D11" title="ALGSTR_0:def.11">ALGSTR_0:def 11</a> <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> <font color="Maroon" title="c3">s</font> <a href="algstr_0.html#K1" title="ALGSTR_0:func.1">+</a> <font color="Maroon" title="c5">t</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="struct_0.html#K4" title="STRUCT_0:func.4">0.</a> <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></span><br/>

<a NAME="E3:73"/>
 <a href="afvect0.html#NK3" title="AFVECT0:NK.3">Pcom</a> <font color="Maroon" title="c2">o</font>,<font color="Maroon" title="c2">o</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c2">o</font>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="afvect0.html#T35" target="_self" title="AFVECT0:th.35">Th35</a></span>;<br/>
<a NAME="E4:73"/><span class="kw">then </span>
<font color="Maroon" title="c2">o</font>,<font color="Maroon" title="c4">s9</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a>  <a href="afvect0.html#NK3" title="AFVECT0:NK.3">Pcom</a> <font color="Maroon" title="c2">o</font>,<font color="Maroon" title="c4">s9</font>,<font color="Maroon" title="c2">o</font>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="afvect0.html#T39" target="_self" title="AFVECT0:th.39">Th39</a></span>;<br/>
<a NAME="E5:73"/><span class="kw">then </span><span class="lab"><font color="Green" title="E39">A1</font></span>: 
 <a href="afvect0.html#K2" title="AFVECT0:func.2">Padd</a> <font color="Maroon" title="c2">o</font>,<font color="Maroon" title="c4">s9</font>,<span class="p1">(<span class="default"><a href="afvect0.html#NK3" title="AFVECT0:NK.3">Pcom</a> <font color="Maroon" title="c2">o</font>,<font color="Maroon" title="c4">s9</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c2">o</font>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="afvect0.html#D5" target="_self" title="AFVECT0:def.5">Def5</a></span>;<br/>
<span class="kw">thus </span><font color="Maroon" title="c3">s</font> <a href="algstr_0.html#K1" title="ALGSTR_0:func.1">+</a> <font color="Maroon" title="c5">t</font> = 
<span class="p1">(<span class="default"><a href="afvect0.html#K3" title="AFVECT0:func.3">Padd</a> <font color="Maroon" title="c2">o</font></span>)</span> <a href="binop_1.html#K4" title="BINOP_1:func.4">.</a> <font color="Maroon" title="c4">s9</font>,<span class="p1">(<span class="default"><a href="afvect0.html#NK3" title="AFVECT0:NK.3">Pcom</a> <font color="Maroon" title="c2">o</font>,<font color="Maroon" title="c4">s9</font></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="ref" href="afvect0.html#D8" target="_self" title="AFVECT0:def.8">Def8</a></span>
<br/>.= 
 <a href="struct_0.html#K4" title="STRUCT_0:func.4">0.</a> <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>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E5:73"><span class="lab"><font color="Green" title="E39">A1</font></span></a>, <a class="ref" href="afvect0.html#D7" target="_self" title="AFVECT0:def.7">Def7</a></span>
; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> verum</span><br/>


</div>
