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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">a</font>, <font color="Olive" title="b2">b</font>, <font color="Olive" title="b3">c</font>, <font color="Olive" title="b4">d</font>, <font color="Olive" title="b5">p</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/> ( <font color="Olive" title="b1">a</font>,<font color="Olive" title="b2">b</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Olive" title="b3">c</font>,<font color="Olive" title="b4">d</font> iff  <a href="afvect0.html#K1" title="AFVECT0:func.1">PSym</a> <font color="Olive" title="b5">p</font>,<font color="Olive" title="b1">a</font>, <a href="afvect0.html#K1" title="AFVECT0:func.1">PSym</a> <font color="Olive" title="b5">p</font>,<font color="Olive" title="b2">b</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a>  <a href="afvect0.html#K1" title="AFVECT0:func.1">PSym</a> <font color="Olive" title="b5">p</font>,<font color="Olive" title="b3">c</font>, <a href="afvect0.html#K1" title="AFVECT0:func.1">PSym</a> <font color="Olive" title="b5">p</font>,<font color="Olive" title="b4">d</font> )</span><br/><span class="kw">let </span><font color="Maroon" title="c2">a</font>, <font color="Maroon" title="c3">b</font>, <font color="Maroon" title="c4">c</font>, <font color="Maroon" title="c5">d</font>, <font color="Maroon" title="c6">p</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="c2">a</font>,<font color="Maroon" title="c3">b</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c4">c</font>,<font color="Maroon" title="c5">d</font> iff  <a href="afvect0.html#K1" title="AFVECT0:func.1">PSym</a> <font color="Maroon" title="c6">p</font>,<font color="Maroon" title="c2">a</font>, <a href="afvect0.html#K1" title="AFVECT0:func.1">PSym</a> <font color="Maroon" title="c6">p</font>,<font color="Maroon" title="c3">b</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a>  <a href="afvect0.html#K1" title="AFVECT0:func.1">PSym</a> <font color="Maroon" title="c6">p</font>,<font color="Maroon" title="c4">c</font>, <a href="afvect0.html#K1" title="AFVECT0:func.1">PSym</a> <font color="Maroon" title="c6">p</font>,<font color="Maroon" title="c5">d</font> )</span><br/>











<div><span class="lab"><font color="Green" title="E26">A1</font></span>: <a class="txt" onclick="hs2(this)" href="javascript:()" title="46_1"><span class="kw">now </span></a><div class="add"><span class="kw">assume </span><a NAME="E1:46_1"/><span class="lab"><font color="Green" title="E27">A2</font></span>: 
 <a href="afvect0.html#K1" title="AFVECT0:func.1">PSym</a> <font color="Maroon" title="c6">p</font>,<font color="Maroon" title="c2">a</font>, <a href="afvect0.html#K1" title="AFVECT0:func.1">PSym</a> <font color="Maroon" title="c6">p</font>,<font color="Maroon" title="c3">b</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a>  <a href="afvect0.html#K1" title="AFVECT0:func.1">PSym</a> <font color="Maroon" title="c6">p</font>,<font color="Maroon" title="c4">c</font>, <a href="afvect0.html#K1" title="AFVECT0:func.1">PSym</a> <font color="Maroon" title="c6">p</font>,<font color="Maroon" title="c5">d</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="c2">a</font>,<font color="Maroon" title="c3">b</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c4">c</font>,<font color="Maroon" title="c5">d</font></span><br/><a NAME="E2:46_1"/>
<font color="Maroon" title="c5">d</font>,<font color="Maroon" title="c4">c</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a>  <a href="afvect0.html#K1" title="AFVECT0:func.1">PSym</a> <font color="Maroon" title="c6">p</font>,<font color="Maroon" title="c4">c</font>, <a href="afvect0.html#K1" title="AFVECT0:func.1">PSym</a> <font color="Maroon" title="c6">p</font>,<font color="Maroon" title="c5">d</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="E3:46_1"/><span class="kw">then </span>
<font color="Maroon" title="c5">d</font>,<font color="Maroon" title="c4">c</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a>  <a href="afvect0.html#K1" title="AFVECT0:func.1">PSym</a> <font color="Maroon" title="c6">p</font>,<font color="Maroon" title="c2">a</font>, <a href="afvect0.html#K1" title="AFVECT0:func.1">PSym</a> <font color="Maroon" title="c6">p</font>,<font color="Maroon" title="c3">b</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:46_1"><span class="lab"><font color="Green" title="E27">A2</font></span></a>, <a class="ref" href="afvect0.html#D1" target="_self" title="AFVECT0:def.1">Def1</a></span>;<br/><a NAME="E4:46_1"/><span class="kw">then </span><span class="lab"><font color="Green" title="E28">A3</font></span>: 
<font color="Maroon" title="c4">c</font>,<font color="Maroon" title="c5">d</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a>  <a href="afvect0.html#K1" title="AFVECT0:func.1">PSym</a> <font color="Maroon" title="c6">p</font>,<font color="Maroon" title="c3">b</font>, <a href="afvect0.html#K1" title="AFVECT0:func.1">PSym</a> <font color="Maroon" title="c6">p</font>,<font color="Maroon" title="c2">a</font>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="afvect0.html#T8" target="_self" title="AFVECT0:th.8">Th8</a></span>;<br/><a NAME="E5:46_1"/>
<font color="Maroon" title="c2">a</font>,<font color="Maroon" title="c3">b</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a>  <a href="afvect0.html#K1" title="AFVECT0:func.1">PSym</a> <font color="Maroon" title="c6">p</font>,<font color="Maroon" title="c3">b</font>, <a href="afvect0.html#K1" title="AFVECT0:func.1">PSym</a> <font color="Maroon" title="c6">p</font>,<font color="Maroon" title="c2">a</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/><span class="kw">hence </span><a NAME="E6:46_1"/>
<font color="Maroon" title="c2">a</font>,<font color="Maroon" title="c3">b</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c4">c</font>,<font color="Maroon" title="c5">d</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E4:46_1"><span class="lab"><font color="Green" title="E28">A3</font></span></a>, <a class="ref" href="afvect0.html#D1" target="_self" title="AFVECT0:def.1">Def1</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><span class="kw">end;</span></div>
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="46_2"><span class="kw">now </span></a><div class="add"><a NAME="E1:46_2"/><span class="lab"><font color="Green" title="E27">A4</font></span>: 
 <a href="afvect0.html#K1" title="AFVECT0:func.1">PSym</a> <font color="Maroon" title="c6">p</font>,<font color="Maroon" title="c3">b</font>, <a href="afvect0.html#K1" title="AFVECT0:func.1">PSym</a> <font color="Maroon" title="c6">p</font>,<font color="Maroon" title="c2">a</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c2">a</font>,<font color="Maroon" title="c3">b</font>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="afvect0.html#T4" target="_self" title="AFVECT0:th.4">Th4</a>, <a class="ref" href="afvect0.html#T39" target="_self" title="AFVECT0:th.39">Th39</a></span>;<br/><span class="kw">assume </span><a NAME="E2:46_2"/><span class="lab"><font color="Green" title="E28">A5</font></span>: 
<font color="Maroon" title="c2">a</font>,<font color="Maroon" title="c3">b</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c4">c</font>,<font color="Maroon" title="c5">d</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="c6">p</font>,<font color="Maroon" title="c2">a</font>, <a href="afvect0.html#K1" title="AFVECT0:func.1">PSym</a> <font color="Maroon" title="c6">p</font>,<font color="Maroon" title="c3">b</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a>  <a href="afvect0.html#K1" title="AFVECT0:func.1">PSym</a> <font color="Maroon" title="c6">p</font>,<font color="Maroon" title="c4">c</font>, <a href="afvect0.html#K1" title="AFVECT0:func.1">PSym</a> <font color="Maroon" title="c6">p</font>,<font color="Maroon" title="c5">d</font></span><br/><a NAME="E3:46_2"/>
 <a href="afvect0.html#K1" title="AFVECT0:func.1">PSym</a> <font color="Maroon" title="c6">p</font>,<font color="Maroon" title="c5">d</font>, <a href="afvect0.html#K1" title="AFVECT0:func.1">PSym</a> <font color="Maroon" title="c6">p</font>,<font color="Maroon" title="c4">c</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c4">c</font>,<font color="Maroon" title="c5">d</font>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="afvect0.html#T4" target="_self" title="AFVECT0:th.4">Th4</a>, <a class="ref" href="afvect0.html#T39" target="_self" title="AFVECT0:th.39">Th39</a></span>;<br/><a NAME="E4:46_2"/><span class="kw">then </span>
 <a href="afvect0.html#K1" title="AFVECT0:func.1">PSym</a> <font color="Maroon" title="c6">p</font>,<font color="Maroon" title="c5">d</font>, <a href="afvect0.html#K1" title="AFVECT0:func.1">PSym</a> <font color="Maroon" title="c6">p</font>,<font color="Maroon" title="c4">c</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c2">a</font>,<font color="Maroon" title="c3">b</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:46_2"><span class="lab"><font color="Green" title="E28">A5</font></span></a>, <a class="ref" href="afvect0.html#D1" target="_self" title="AFVECT0:def.1">Def1</a></span>;<br/><a NAME="E5:46_2"/><span class="kw">then </span>
 <a href="afvect0.html#K1" title="AFVECT0:func.1">PSym</a> <font color="Maroon" title="c6">p</font>,<font color="Maroon" title="c3">b</font>, <a href="afvect0.html#K1" title="AFVECT0:func.1">PSym</a> <font color="Maroon" title="c6">p</font>,<font color="Maroon" title="c2">a</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a>  <a href="afvect0.html#K1" title="AFVECT0:func.1">PSym</a> <font color="Maroon" title="c6">p</font>,<font color="Maroon" title="c5">d</font>, <a href="afvect0.html#K1" title="AFVECT0:func.1">PSym</a> <font color="Maroon" title="c6">p</font>,<font color="Maroon" title="c4">c</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:46_2"><span class="lab"><font color="Green" title="E27">A4</font></span></a>, <a class="ref" href="afvect0.html#D1" target="_self" title="AFVECT0:def.1">Def1</a></span>;<br/><span class="kw">hence </span><a NAME="E6:46_2"/>
 <a href="afvect0.html#K1" title="AFVECT0:func.1">PSym</a> <font color="Maroon" title="c6">p</font>,<font color="Maroon" title="c2">a</font>, <a href="afvect0.html#K1" title="AFVECT0:func.1">PSym</a> <font color="Maroon" title="c6">p</font>,<font color="Maroon" title="c3">b</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a>  <a href="afvect0.html#K1" title="AFVECT0:func.1">PSym</a> <font color="Maroon" title="c6">p</font>,<font color="Maroon" title="c4">c</font>, <a href="afvect0.html#K1" title="AFVECT0:func.1">PSym</a> <font color="Maroon" title="c6">p</font>,<font color="Maroon" title="c5">d</font>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="afvect0.html#T8" target="_self" title="AFVECT0:th.8">Th8</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><span class="kw">end;</span></div>
<span class="kw">hence </span><a NAME="E3:46"/>
( <font color="Maroon" title="c2">a</font>,<font color="Maroon" title="c3">b</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c4">c</font>,<font color="Maroon" title="c5">d</font> iff  <a href="afvect0.html#K1" title="AFVECT0:func.1">PSym</a> <font color="Maroon" title="c6">p</font>,<font color="Maroon" title="c2">a</font>, <a href="afvect0.html#K1" title="AFVECT0:func.1">PSym</a> <font color="Maroon" title="c6">p</font>,<font color="Maroon" title="c3">b</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a>  <a href="afvect0.html#K1" title="AFVECT0:func.1">PSym</a> <font color="Maroon" title="c6">p</font>,<font color="Maroon" title="c4">c</font>, <a href="afvect0.html#K1" title="AFVECT0:func.1">PSym</a> <font color="Maroon" title="c6">p</font>,<font color="Maroon" title="c5">d</font> )
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:46"><span class="lab"><font color="Green" title="E26">A1</font></span></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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