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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><br/> for <font color="Olive" title="b2">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="Olive" title="b1">o</font></span>)</span><br/> for <font color="Olive" title="b3">a9</font> being  <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c1">AFV</font>  st <font color="Olive" title="b2">a</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b3">a9</font> holds <br/> <a href="algstr_0.html#K4" title="ALGSTR_0:func.4">-</a> <font color="Olive" title="b2">a</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="afvect0.html#K4" title="AFVECT0:func.4">Pcom</a> <font color="Olive" title="b1">o</font></span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Olive" title="b3">a9</font></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"> 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><br/> for <font color="Olive" title="b2">a9</font> being  <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c1">AFV</font>  st <font color="Olive" title="b1">a</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b2">a9</font> holds <br/> <a href="algstr_0.html#K4" title="ALGSTR_0:func.4">-</a> <font color="Olive" title="b1">a</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <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="Olive" title="b2">a9</font></span><br/><span class="kw">let </span><font color="Maroon" title="c3">a</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>; <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">a9</font> being  <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c1">AFV</font>  st <font color="Maroon" title="c3">a</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b1">a9</font> holds <br/> <a href="algstr_0.html#K4" title="ALGSTR_0:func.4">-</a> <font color="Maroon" title="c3">a</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <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="Olive" title="b1">a9</font></span><br/><span class="kw">let </span><font color="Maroon" title="c4">a9</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"> ( <font color="Maroon" title="c3">a</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c4">a9</font> implies  <a href="algstr_0.html#K4" title="ALGSTR_0:func.4">-</a> <font color="Maroon" title="c3">a</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <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">a9</font> )</span><br/>







<span class="kw">assume </span><a NAME="E1:75"/><span class="lab"><font color="Green" title="E40">A1</font></span>: 
<font color="Maroon" title="c3">a</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c4">a9</font>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide">  <a href="algstr_0.html#K4" title="ALGSTR_0:func.4">-</a> <font color="Maroon" title="c3">a</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <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">a9</font></span><br/>

<span class="kw">reconsider </span><font color="Maroon" title="c5">aa</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">a9</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/>
<a NAME="E3:75"/>
(  <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> &amp; <font color="Maroon" title="c2">o</font>,<font color="Maroon" title="c4">a9</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">a9</font>, <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> )
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="afvect0.html#T35" target="_self" title="AFVECT0:th.35">Th35</a>, <a class="ref" href="afvect0.html#T39" target="_self" title="AFVECT0:th.39">Th39</a></span>;<br/>
<a NAME="E4:75"/><span class="kw">then </span><span class="lab"><font color="Green" title="E41">A2</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">a9</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">a9</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/>
<font color="Maroon" title="c3">a</font> <a href="rlvect_1.html#K3" title="RLVECT_1:func.3">+</a> <font color="Maroon" title="c5">aa</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#K1" title="BINOP_1:func.1">.</a> <font color="Maroon" title="c3">a</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">a9</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="#E1:75"><span class="lab"><font color="Green" title="E40">A1</font></span></a>, <a class="txt" href="#E4:75"><span class="lab"><font color="Green" title="E41">A2</font></span></a>, <a class="ref" href="afvect0.html#D7" target="_self" title="AFVECT0:def.7">Def7</a></span>
;<br/>
<span class="kw">hence </span><a NAME="E6:75"/>
 <a href="algstr_0.html#K4" title="ALGSTR_0:func.4">-</a> <font color="Maroon" title="c3">a</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <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">a9</font>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="rlvect_1.html#D13" title="RLVECT_1:def.13">RLVECT_1:def 13</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/>


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