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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="firebrick">::  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">b9</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">b9</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">b9</font>,<font color="Olive" title="b3">c</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">b9</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="firebrick">::  thesis: </font></span></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">b9</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">b9</font>,<font color="Maroon" title="c4">c</font> )</span><br/>









<span class="kw">assume </span><span class="kw">that </span><br/><a NAME="E1:28"/><span class="lab"><font color="Green" title="E18">A1</font></span>: 
 <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>
 <span class="kw">and </span><br/><a NAME="E2:28"/><span class="lab"><font color="Green" title="E19">A2</font></span>: 
 <a href="afvect0.html#R1" title="AFVECT0:pred.1">MDist</a> <font color="Maroon" title="c3">b</font>,<font color="Maroon" title="c5">b9</font>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></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">b9</font>,<font color="Maroon" title="c4">c</font></span><br/>

<a NAME="E3:28"/><span class="lab"><font color="Green" title="E20">A3</font></span>: 
<font color="Maroon" title="c3">b</font>,<font color="Maroon" title="c5">b9</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c5">b9</font>,<font color="Maroon" title="c3">b</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:28"><span class="lab"><font color="Green" title="E19">A2</font></span></a>, <a class="ref" href="afvect0.html#D2" target="_self" title="AFVECT0:def.2">Def2</a></span>;<br/>
<a NAME="E4:28"/>
<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>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:28"><span class="lab"><font color="Green" title="E18">A1</font></span></a>, <a class="ref" href="afvect0.html#D3" target="_self" title="AFVECT0:def.3">Def3</a></span>;<br/>
<a NAME="E5:28"/><span class="kw">then </span><span class="lab"><font color="Green" title="E21">A4</font></span>: 
<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>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="afvect0.html#T7" target="_self" title="AFVECT0:th.7">Th8</a></span>;<br/>
<span class="kw">consider </span><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><span class="kw"> such that </span><br/><a NAME="E7:28"/><span class="lab"><font color="Green" title="E22">A5</font></span>: 
<font color="Maroon" title="c5">b9</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>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="afvect0.html#D1" target="_self" title="AFVECT0:def.1">Def1</a></span>;<br/>
<a NAME="E8:28"/>
<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">b9</font>,<font color="Maroon" title="c3">b</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E7:28"><span class="lab"><font color="Green" title="E22">A5</font></span></a>, <a class="ref" href="afvect0.html#T3" target="_self" title="AFVECT0:th.3">Th4</a></span>;<br/>
<a NAME="E9:28"/><span class="kw">then </span>
<font color="Maroon" title="c3">b</font>,<font color="Maroon" title="c5">b9</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>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E3:28"><span class="lab"><font color="Green" title="E20">A3</font></span></a>, <a class="ref" href="afvect0.html#D1" target="_self" title="AFVECT0:def.1">Def1</a></span>;<br/>
<a NAME="E10:28"/><span class="kw">then </span><span class="lab"><font color="Green" title="E23">A6</font></span>: 
<font color="Maroon" title="c2">a</font>,<font color="Maroon" title="c5">b9</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>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E5:28"><span class="lab"><font color="Green" title="E21">A4</font></span></a>, <a class="ref" href="afvect0.html#D1" target="_self" title="AFVECT0:def.1">Def1</a></span>;<br/>
<a NAME="E11:28"/>
<font color="Maroon" title="c5">b9</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>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E7:28"><span class="lab"><font color="Green" title="E22">A5</font></span></a>, <a class="ref" href="afvect0.html#D1" target="_self" title="AFVECT0:def.1">Def1</a></span>;<br/>
<a NAME="E12:28"/><span class="kw">then </span>
<font color="Maroon" title="c2">a</font>,<font color="Maroon" title="c5">b9</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c5">b9</font>,<font color="Maroon" title="c4">c</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E10:28"><span class="lab"><font color="Green" title="E23">A6</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="E13:28"/>
 <a href="afvect0.html#R2" title="AFVECT0:pred.2">Mid</a> <font color="Maroon" title="c2">a</font>,<font color="Maroon" title="c5">b9</font>,<font color="Maroon" title="c4">c</font>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="afvect0.html#D3" target="_self" title="AFVECT0:def.3">Def3</a></span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> verum</span><br/>


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