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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">a</font>, <font color="Olive" title="b2">b</font>, <font color="Olive" title="b3">c</font>, <font color="Olive" title="b4">b'</font> being  <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c1">AFV</font>  st  <a href="afvect0.html#R2" title="AFVECT0:pred.2">Mid</a> <font color="Olive" title="b1">a</font>,<font color="Olive" title="b2">b</font>,<font color="Olive" title="b3">c</font> &amp;  <a href="afvect0.html#R1" title="AFVECT0:pred.1">MDist</a> <font color="Olive" title="b2">b</font>,<font color="Olive" title="b4">b'</font> holds <br/> <a href="afvect0.html#R2" title="AFVECT0:pred.2">Mid</a> <font color="Olive" title="b1">a</font>,<font color="Olive" title="b4">b'</font>,<font color="Olive" title="b3">c</font></span><br/><b>let </b><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">b'</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#R2" title="AFVECT0:pred.2">Mid</a> <font color="Maroon" title="c2">a</font>,<font color="Maroon" title="c3">b</font>,<font color="Maroon" title="c4">c</font> &amp;  <a href="afvect0.html#R1" title="AFVECT0:pred.1">MDist</a> <font color="Maroon" title="c3">b</font>,<font color="Maroon" title="c5">b'</font> implies  <a href="afvect0.html#R2" title="AFVECT0:pred.2">Mid</a> <font color="Maroon" title="c2">a</font>,<font color="Maroon" title="c5">b'</font>,<font color="Maroon" title="c4">c</font> )</span><br/>









<b>assume </b><a NAME="E1:28"/>
(  <a href="afvect0.html#R2" title="AFVECT0:pred.2">Mid</a> <font color="Maroon" title="c2">a</font>,<font color="Maroon" title="c3">b</font>,<font color="Maroon" title="c4">c</font> &amp;  <a href="afvect0.html#R1" title="AFVECT0:pred.1">MDist</a> <font color="Maroon" title="c3">b</font>,<font color="Maroon" title="c5">b'</font> )
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide">  <a href="afvect0.html#R2" title="AFVECT0:pred.2">Mid</a> <font color="Maroon" title="c2">a</font>,<font color="Maroon" title="c5">b'</font>,<font color="Maroon" title="c4">c</font></span><br/>

<a NAME="E2:28"/><b>then </b><i><font color="Green" title="E18">A1</font></i>: 
( <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="c3">b</font>,<font color="Maroon" title="c4">c</font> &amp; <font color="Maroon" title="c3">b</font>,<font color="Maroon" title="c5">b'</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c5">b'</font>,<font color="Maroon" title="c3">b</font> )
 
<b>by </b><i><a class="ref" href="afvect0.html#D2" target="_self" title="AFVECT0:def.2">Def2</a>, <a class="ref" href="afvect0.html#D3" target="_self" title="AFVECT0:def.3">Def3</a></i>;<br/>
<b>consider </b><font color="Maroon" title="c6">d</font> being   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c1">AFV</font><b> such that </b><br/><a NAME="E4:28"/><i><font color="Green" title="E19">A2</font></i>: 
<font color="Maroon" title="c5">b'</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="c6">d</font>
 <b>by </b><i><a class="ref" href="afvect0.html#D1" target="_self" title="AFVECT0:def.1">Def1</a></i>;<br/>
<a NAME="E5:28"/>
<font color="Maroon" title="c4">c</font>,<font color="Maroon" title="c6">d</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c5">b'</font>,<font color="Maroon" title="c3">b</font>
 
<b>by </b><i><a class="txt" href="#E4:28"><i><font color="Green" title="E19">A2</font></i></a>, <a class="ref" href="afvect0.html#T4" target="_self" title="AFVECT0:th.4">Th4</a></i>;<br/>
<a NAME="E6:28"/><b>then </b><i><font color="Green" title="E20">A3</font></i>: 
<font color="Maroon" title="c3">b</font>,<font color="Maroon" title="c5">b'</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c4">c</font>,<font color="Maroon" title="c6">d</font>
 
<b>by </b><i><a class="txt" href="#E2:28"><i><font color="Green" title="E18">A1</font></i></a>, <a class="ref" href="afvect0.html#D1" target="_self" title="AFVECT0:def.1">Def1</a></i>;<br/>
<a NAME="E7:28"/>
<font color="Maroon" title="c3">b</font>,<font color="Maroon" title="c2">a</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c4">c</font>,<font color="Maroon" title="c3">b</font>
 
<b>by </b><i><a class="txt" href="#E2:28"><i><font color="Green" title="E18">A1</font></i></a>, <a class="ref" href="afvect0.html#T8" target="_self" title="AFVECT0:th.8">Th8</a></i>;<br/>
<a NAME="E8:28"/><b>then </b><i><font color="Green" title="E21">A4</font></i>: 
<font color="Maroon" title="c2">a</font>,<font color="Maroon" title="c5">b'</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c3">b</font>,<font color="Maroon" title="c6">d</font>
 
<b>by </b><i><a class="txt" href="#E6:28"><i><font color="Green" title="E20">A3</font></i></a>, <a class="ref" href="afvect0.html#D1" target="_self" title="AFVECT0:def.1">Def1</a></i>;<br/>
<a NAME="E9:28"/>
<font color="Maroon" title="c5">b'</font>,<font color="Maroon" title="c4">c</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c3">b</font>,<font color="Maroon" title="c6">d</font>
 
<b>by </b><i><a class="txt" href="#E4:28"><i><font color="Green" title="E19">A2</font></i></a>, <a class="ref" href="afvect0.html#D1" target="_self" title="AFVECT0:def.1">Def1</a></i>;<br/>
<a NAME="E10:28"/><b>then </b>
<font color="Maroon" title="c2">a</font>,<font color="Maroon" title="c5">b'</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c5">b'</font>,<font color="Maroon" title="c4">c</font>
 
<b>by </b><i><a class="txt" href="#E8:28"><i><font color="Green" title="E21">A4</font></i></a>, <a class="ref" href="afvect0.html#D1" target="_self" title="AFVECT0:def.1">Def1</a></i>;<br/>
<b>hence </b><a NAME="E11:28"/>
 <a href="afvect0.html#R2" title="AFVECT0:pred.2">Mid</a> <font color="Maroon" title="c2">a</font>,<font color="Maroon" title="c5">b'</font>,<font color="Maroon" title="c4">c</font>
 <b>by </b><i><a class="ref" href="afvect0.html#D3" target="_self" title="AFVECT0:def.3">Def3</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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