<?xml version="1.0"?>
<div class="add">

<b>let </b><font color="Maroon">AFV</font> be  non <a href="struct_0.html#V3">empty</a>  <a href="analoaf.html#L1">AffinStruct</a> ;<br/>

<b>assume </b><a NAME="E1:4_1_1"/><i><font color="Green">E22</font></i>: 
<font color="Maroon">AFV</font> is <a href="tdgroup.html#V2">AffVect-like</a>
 ;<br/>

<a NAME="E2:4_1_1"/>
<font color="Maroon">AFV</font> is <a href="afvect0.html#V1" target="_self">WeakAffVect-like</a>
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="4_1_1_1"><b>proof </b></a><div class="add">

<a NAME="E1:4_1_1_1"/>
( ( for <font color="Olive">a</font>, <font color="Olive">b</font>, <font color="Olive">c</font> being  <a href="struct_0.html#NM1">Element</a> of <font color="Maroon">AFV</font>  st <font color="Olive">a</font>,<font color="Olive">b</font> <a href="analoaf.html#R2">//</a> <font color="Olive">c</font>,<font color="Olive">c</font> holds <br/><font color="Olive">a</font> <a href="hidden.html#R1">=</a> <font color="Olive">b</font> ) &amp; ( for <font color="Olive">a</font>, <font color="Olive">b</font>, <font color="Olive">c</font>, <font color="Olive">d</font>, <font color="Olive">p</font>, <font color="Olive">q</font> being  <a href="struct_0.html#NM1">Element</a> of <font color="Maroon">AFV</font>  st <font color="Olive">a</font>,<font color="Olive">b</font> <a href="analoaf.html#R2">//</a> <font color="Olive">p</font>,<font color="Olive">q</font> &amp; <font color="Olive">c</font>,<font color="Olive">d</font> <a href="analoaf.html#R2">//</a> <font color="Olive">p</font>,<font color="Olive">q</font> holds <br/><font color="Olive">a</font>,<font color="Olive">b</font> <a href="analoaf.html#R2">//</a> <font color="Olive">c</font>,<font color="Olive">d</font> ) &amp; ( for <font color="Olive">a</font>, <font color="Olive">b</font>, <font color="Olive">c</font> being  <a href="struct_0.html#NM1">Element</a> of <font color="Maroon">AFV</font>  ex <font color="Olive">d</font> being  <a href="struct_0.html#NM1">Element</a> of <font color="Maroon">AFV</font> st <font color="Olive">a</font>,<font color="Olive">b</font> <a href="analoaf.html#R2">//</a> <font color="Olive">c</font>,<font color="Olive">d</font> ) &amp; ( for <font color="Olive">a</font>, <font color="Olive">b</font>, <font color="Olive">c</font>, <font color="Olive">a'</font>, <font color="Olive">b'</font>, <font color="Olive">c'</font> being  <a href="struct_0.html#NM1">Element</a> of <font color="Maroon">AFV</font>  st <font color="Olive">a</font>,<font color="Olive">b</font> <a href="analoaf.html#R2">//</a> <font color="Olive">a'</font>,<font color="Olive">b'</font> &amp; <font color="Olive">a</font>,<font color="Olive">c</font> <a href="analoaf.html#R2">//</a> <font color="Olive">a'</font>,<font color="Olive">c'</font> holds <br/><font color="Olive">b</font>,<font color="Olive">c</font> <a href="analoaf.html#R2">//</a> <font color="Olive">b'</font>,<font color="Olive">c'</font> ) &amp; ( for <font color="Olive">a</font>, <font color="Olive">c</font> being  <a href="struct_0.html#NM1">Element</a> of <font color="Maroon">AFV</font>  ex <font color="Olive">b</font> being  <a href="struct_0.html#NM1">Element</a> of <font color="Maroon">AFV</font> st <font color="Olive">a</font>,<font color="Olive">b</font> <a href="analoaf.html#R2">//</a> <font color="Olive">b</font>,<font color="Olive">c</font> ) &amp; ( for <font color="Olive">a</font>, <font color="Olive">b</font>, <font color="Olive">c</font>, <font color="Olive">d</font> being  <a href="struct_0.html#NM1">Element</a> of <font color="Maroon">AFV</font>  st <font color="Olive">a</font>,<font color="Olive">b</font> <a href="analoaf.html#R2">//</a> <font color="Olive">c</font>,<font color="Olive">d</font> holds <br/><font color="Olive">a</font>,<font color="Olive">c</font> <a href="analoaf.html#R2">//</a> <font color="Olive">b</font>,<font color="Olive">d</font> ) )
 
<b>by </b><i>, <a class="ref" href="tdgroup.html#D8">TDGROUP:def 8</a></i>;<br/>
<b>hence </b><a NAME="E2:4_1_1_1"/>
<font color="Maroon">AFV</font> is <a href="afvect0.html#V1" target="_self">WeakAffVect-like</a>
 <b>by </b><i/>;<br/>


</div><b>end;</b></div>
<b>hence </b><a NAME="E3:4_1_1"/>
<font color="Maroon">AFV</font> is <a href="afvect0.html#V1" target="_self">WeakAffVect-like</a>
 ;<br/>


</div>
