<?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">q</font>, <font color="Olive" title="b2">p</font>, <font color="Olive" title="b3">a</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#K1" title="AFVECT0:func.1">PSym</a> <font color="Olive" title="b1">q</font>,<span class="p1">(<span class="default"><a href="afvect0.html#K1" title="AFVECT0:func.1">PSym</a> <font color="Olive" title="b2">p</font>,<span class="p2">(<span class="default"><a href="afvect0.html#K1" title="AFVECT0:func.1">PSym</a> <font color="Olive" title="b1">q</font>,<font color="Olive" title="b3">a</font></span>)</span></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="afvect0.html#K1" title="AFVECT0:func.1">PSym</a> <span class="p1">(<span class="default"><a href="afvect0.html#K1" title="AFVECT0:func.1">PSym</a> <font color="Olive" title="b1">q</font>,<font color="Olive" title="b2">p</font></span>)</span>,<font color="Olive" title="b3">a</font></span><br/><span class="kw">let </span><font color="Maroon" title="c2">q</font>, <font color="Maroon" title="c3">p</font>, <font color="Maroon" title="c4">a</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#K1" title="AFVECT0:func.1">PSym</a> <font color="Maroon" title="c2">q</font>,<span class="p1">(<span class="default"><a href="afvect0.html#K1" title="AFVECT0:func.1">PSym</a> <font color="Maroon" title="c3">p</font>,<span class="p2">(<span class="default"><a href="afvect0.html#K1" title="AFVECT0:func.1">PSym</a> <font color="Maroon" title="c2">q</font>,<font color="Maroon" title="c4">a</font></span>)</span></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="afvect0.html#K1" title="AFVECT0:func.1">PSym</a> <span class="p1">(<span class="default"><a href="afvect0.html#K1" title="AFVECT0:func.1">PSym</a> <font color="Maroon" title="c2">q</font>,<font color="Maroon" title="c3">p</font></span>)</span>,<font color="Maroon" title="c4">a</font></span><br/>







<a NAME="E1:50"/>
 <a href="afvect0.html#R2" title="AFVECT0:pred.2">Mid</a>  <a href="afvect0.html#K1" title="AFVECT0:func.1">PSym</a> <font color="Maroon" title="c2">q</font>,<font color="Maroon" title="c4">a</font>,<font color="Maroon" title="c3">p</font>, <a href="afvect0.html#K1" title="AFVECT0:func.1">PSym</a> <font color="Maroon" title="c3">p</font>,<span class="p1">(<span class="default"><a href="afvect0.html#K1" title="AFVECT0:func.1">PSym</a> <font color="Maroon" title="c2">q</font>,<font color="Maroon" title="c4">a</font></span>)</span>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="afvect0.html#D4" target="_self" title="AFVECT0:def.4">Def4</a></span>;<br/>
<a NAME="E2:50"/><span class="kw">then </span>
 <a href="afvect0.html#R2" title="AFVECT0:pred.2">Mid</a>  <a href="afvect0.html#K1" title="AFVECT0:func.1">PSym</a> <font color="Maroon" title="c2">q</font>,<span class="p1">(<span class="default"><a href="afvect0.html#K1" title="AFVECT0:func.1">PSym</a> <font color="Maroon" title="c2">q</font>,<font color="Maroon" title="c4">a</font></span>)</span>, <a href="afvect0.html#K1" title="AFVECT0:func.1">PSym</a> <font color="Maroon" title="c2">q</font>,<font color="Maroon" title="c3">p</font>, <a href="afvect0.html#K1" title="AFVECT0:func.1">PSym</a> <font color="Maroon" title="c2">q</font>,<span class="p1">(<span class="default"><a href="afvect0.html#K1" title="AFVECT0:func.1">PSym</a> <font color="Maroon" title="c3">p</font>,<span class="p2">(<span class="default"><a href="afvect0.html#K1" title="AFVECT0:func.1">PSym</a> <font color="Maroon" title="c2">q</font>,<font color="Maroon" title="c4">a</font></span>)</span></span>)</span>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="afvect0.html#T42" target="_self" title="AFVECT0:th.42">Th42</a></span>;<br/>
<a NAME="E3:50"/><span class="kw">then </span>
 <a href="afvect0.html#K1" title="AFVECT0:func.1">PSym</a> <font color="Maroon" title="c2">q</font>,<span class="p1">(<span class="default"><a href="afvect0.html#K1" title="AFVECT0:func.1">PSym</a> <font color="Maroon" title="c3">p</font>,<span class="p2">(<span class="default"><a href="afvect0.html#K1" title="AFVECT0:func.1">PSym</a> <font color="Maroon" title="c2">q</font>,<font color="Maroon" title="c4">a</font></span>)</span></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="afvect0.html#K1" title="AFVECT0:func.1">PSym</a> <span class="p1">(<span class="default"><a href="afvect0.html#K1" title="AFVECT0:func.1">PSym</a> <font color="Maroon" title="c2">q</font>,<font color="Maroon" title="c3">p</font></span>)</span>,<span class="p1">(<span class="default"><a href="afvect0.html#K1" title="AFVECT0:func.1">PSym</a> <font color="Maroon" title="c2">q</font>,<span class="p2">(<span class="default"><a href="afvect0.html#K1" title="AFVECT0:func.1">PSym</a> <font color="Maroon" title="c2">q</font>,<font color="Maroon" title="c4">a</font></span>)</span></span>)</span>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="afvect0.html#D4" target="_self" title="AFVECT0:def.4">Def4</a></span>;<br/>
<span class="kw">hence </span><a NAME="E4:50"/>
 <a href="afvect0.html#K1" title="AFVECT0:func.1">PSym</a> <font color="Maroon" title="c2">q</font>,<span class="p1">(<span class="default"><a href="afvect0.html#K1" title="AFVECT0:func.1">PSym</a> <font color="Maroon" title="c3">p</font>,<span class="p2">(<span class="default"><a href="afvect0.html#K1" title="AFVECT0:func.1">PSym</a> <font color="Maroon" title="c2">q</font>,<font color="Maroon" title="c4">a</font></span>)</span></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="afvect0.html#K1" title="AFVECT0:func.1">PSym</a> <span class="p1">(<span class="default"><a href="afvect0.html#K1" title="AFVECT0:func.1">PSym</a> <font color="Maroon" title="c2">q</font>,<font color="Maroon" title="c3">p</font></span>)</span>,<font color="Maroon" title="c4">a</font>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="afvect0.html#T36" target="_self" title="AFVECT0:th.36">Th36</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>
