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<b>let </b><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:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> for <font color="Olive" title="b1">p</font>, <font color="Olive" title="b2">a</font>, <font color="Olive" title="b3">q</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#K1" title="AFVECT0:func.1">PSym</a> <font color="Olive" title="b1">p</font>,<font color="Olive" title="b2">a</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="afvect0.html#K1" title="AFVECT0:func.1">PSym</a> <font color="Olive" title="b3">q</font>,<font color="Olive" title="b2">a</font> iff ( <font color="Olive" title="b1">p</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b3">q</font> or  <a href="afvect0.html#R1" title="AFVECT0:pred.1">MDist</a> <font color="Olive" title="b1">p</font>,<font color="Olive" title="b3">q</font> ) )</span><br/><b>let </b><font color="Maroon" title="c2">p</font>, <font color="Maroon" title="c3">a</font>, <font color="Maroon" title="c4">q</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:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> (  <a href="afvect0.html#K1" title="AFVECT0:func.1">PSym</a> <font color="Maroon" title="c2">p</font>,<font color="Maroon" title="c3">a</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="afvect0.html#K1" title="AFVECT0:func.1">PSym</a> <font color="Maroon" title="c4">q</font>,<font color="Maroon" title="c3">a</font> iff ( <font color="Maroon" title="c2">p</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c4">q</font> or  <a href="afvect0.html#R1" title="AFVECT0:pred.1">MDist</a> <font color="Maroon" title="c2">p</font>,<font color="Maroon" title="c4">q</font> ) )</span><br/>







<div><i><font color="Green" title="E28">A1</font></i>: <a class="txt" onclick="hs2(this)" href="javascript:()" title="42_1"><b>now </b></a><div class="add"><b>assume </b><a NAME="E1:42_1"/><i><font color="Green" title="E29">A2</font></i>: 
 <a href="afvect0.html#K1" title="AFVECT0:func.1">PSym</a> <font color="Maroon" title="c2">p</font>,<font color="Maroon" title="c3">a</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="afvect0.html#K1" title="AFVECT0:func.1">PSym</a> <font color="Maroon" title="c4">q</font>,<font color="Maroon" title="c3">a</font>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> ( <font color="Maroon" title="c2">p</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c4">q</font> or  <a href="afvect0.html#R1" title="AFVECT0:pred.1">MDist</a> <font color="Maroon" title="c2">p</font>,<font color="Maroon" title="c4">q</font> )</span><br/><a NAME="E2:42_1"/>
(  <a href="afvect0.html#R2" title="AFVECT0:pred.2">Mid</a> <font color="Maroon" title="c3">a</font>,<font color="Maroon" title="c2">p</font>, <a href="afvect0.html#K1" title="AFVECT0:func.1">PSym</a> <font color="Maroon" title="c2">p</font>,<font color="Maroon" title="c3">a</font> &amp;  <a href="afvect0.html#R2" title="AFVECT0:pred.2">Mid</a> <font color="Maroon" title="c3">a</font>,<font color="Maroon" title="c4">q</font>, <a href="afvect0.html#K1" title="AFVECT0:func.1">PSym</a> <font color="Maroon" title="c4">q</font>,<font color="Maroon" title="c3">a</font> )
 <b>by </b><i><a class="ref" href="afvect0.html#D4" target="_self" title="AFVECT0:def.4">Def4</a></i>;<br/><b>hence </b><a NAME="E3:42_1"/>
( <font color="Maroon" title="c2">p</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c4">q</font> or  <a href="afvect0.html#R1" title="AFVECT0:pred.1">MDist</a> <font color="Maroon" title="c2">p</font>,<font color="Maroon" title="c4">q</font> )
 <b>by </b><i><a class="txt" href="#E1:42_1"><i><font color="Green" title="E29">A2</font></i></a>, <a class="ref" href="afvect0.html#T25" target="_self" title="AFVECT0:th.25">Th25</a></i>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> verum</span><br/></div><b>end;</b></div>
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="42_2"><b>now </b></a><div class="add"><b>assume </b><a NAME="E1:42_2"/><i><font color="Green" title="E29">A3</font></i>: 
 <a href="afvect0.html#R1" title="AFVECT0:pred.1">MDist</a> <font color="Maroon" title="c2">p</font>,<font color="Maroon" title="c4">q</font>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide">  <a href="afvect0.html#K1" title="AFVECT0:func.1">PSym</a> <font color="Maroon" title="c2">p</font>,<font color="Maroon" title="c3">a</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="afvect0.html#K1" title="AFVECT0:func.1">PSym</a> <font color="Maroon" title="c4">q</font>,<font color="Maroon" title="c3">a</font></span><br/><a NAME="E2:42_2"/>
(  <a href="afvect0.html#R2" title="AFVECT0:pred.2">Mid</a> <font color="Maroon" title="c3">a</font>,<font color="Maroon" title="c2">p</font>, <a href="afvect0.html#K1" title="AFVECT0:func.1">PSym</a> <font color="Maroon" title="c2">p</font>,<font color="Maroon" title="c3">a</font> &amp;  <a href="afvect0.html#R2" title="AFVECT0:pred.2">Mid</a> <font color="Maroon" title="c3">a</font>,<font color="Maroon" title="c4">q</font>, <a href="afvect0.html#K1" title="AFVECT0:func.1">PSym</a> <font color="Maroon" title="c4">q</font>,<font color="Maroon" title="c3">a</font> )
 <b>by </b><i><a class="ref" href="afvect0.html#D4" target="_self" title="AFVECT0:def.4">Def4</a></i>;<br/><b>hence </b><a NAME="E3:42_2"/>
 <a href="afvect0.html#K1" title="AFVECT0:func.1">PSym</a> <font color="Maroon" title="c2">p</font>,<font color="Maroon" title="c3">a</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="afvect0.html#K1" title="AFVECT0:func.1">PSym</a> <font color="Maroon" title="c4">q</font>,<font color="Maroon" title="c3">a</font>
 <b>by </b><i><a class="txt" href="#E1:42_2"><i><font color="Green" title="E29">A3</font></i></a>, <a class="ref" href="afvect0.html#T29" target="_self" title="AFVECT0:th.29">Th29</a></i>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> verum</span><br/></div><b>end;</b></div>
<b>hence </b><a NAME="E3:42"/>
(  <a href="afvect0.html#K1" title="AFVECT0:func.1">PSym</a> <font color="Maroon" title="c2">p</font>,<font color="Maroon" title="c3">a</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="afvect0.html#K1" title="AFVECT0:func.1">PSym</a> <font color="Maroon" title="c4">q</font>,<font color="Maroon" title="c3">a</font> iff ( <font color="Maroon" title="c2">p</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c4">q</font> or  <a href="afvect0.html#R1" title="AFVECT0:pred.1">MDist</a> <font color="Maroon" title="c2">p</font>,<font color="Maroon" title="c4">q</font> ) )
 <b>by </b><i><a class="txt" href="#E1:42"><i><font color="Green" title="E28">A1</font></i></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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