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

<b>let </b><font color="Maroon">AS</font> be   <a href="diraf.html#NM1">AffinSpace</a>;<br/><b>let </b><font color="Maroon">p</font> be   <a href="struct_0.html#NM1">Element</a> of <font color="Maroon">AS</font>;<br/><b>let </b><font color="Maroon">a</font> be   <a href="struct_0.html#NM1">Element</a> of <font color="Maroon">AS</font>;<br/><b>let </b><font color="Maroon">a'</font> be   <a href="struct_0.html#NM1">Element</a> of <font color="Maroon">AS</font>;<br/><b>let </b><font color="Maroon">b</font> be   <a href="struct_0.html#NM1">Element</a> of <font color="Maroon">AS</font>;<br/>









<b>assume </b><b>that </b><br/><a NAME="E1:1"/><i><font color="Green">E34</font></i>: 
(  <a href="aff_1.html#R1">LIN</a> <font color="Maroon">p</font>,<font color="Maroon">a</font>,<font color="Maroon">a'</font> or  <a href="aff_1.html#R1">LIN</a> <font color="Maroon">p</font>,<font color="Maroon">a'</font>,<font color="Maroon">a</font> )
 <b>and </b><br/><a NAME="E2:1"/><i><font color="Green">E35</font></i>: 
<font color="Maroon">p</font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <font color="Maroon">a</font>
 ;<br/>

<a NAME="E3:1"/>
<font color="Maroon">a</font>,<font color="Maroon">p</font> <a href="analoaf.html#R2">//</a> <font color="Maroon">p</font>,<font color="Maroon">a'</font>
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="1_1"><b>proof </b></a><div class="add">

<a NAME="E1:1_1"/>
 <a href="aff_1.html#R1">LIN</a> <font color="Maroon">p</font>,<font color="Maroon">a</font>,<font color="Maroon">a'</font>
 
<b>by </b><i>, <a class="ref" href="aff_1.html#T15">AFF_1:15</a></i>;<br/>
<a NAME="E2:1_1"/><b>then </b>
<font color="Maroon">p</font>,<font color="Maroon">a</font> <a href="analoaf.html#R2">//</a> <font color="Maroon">p</font>,<font color="Maroon">a'</font>
 
<b>by </b><i><a class="ref" href="aff_1.html#D1">AFF_1:def 1</a></i>;<br/>
<b>hence </b><a NAME="E3:1_1"/>
<font color="Maroon">a</font>,<font color="Maroon">p</font> <a href="analoaf.html#R2">//</a> <font color="Maroon">p</font>,<font color="Maroon">a'</font>
 <b>by </b><i><a class="ref" href="aff_1.html#T13">AFF_1:13</a></i>;<br/>


</div><b>end;</b></div>
<b>then consider </b><font color="Maroon">b'</font> being   <a href="struct_0.html#NM1">Element</a> of <font color="Maroon">AS</font><b> such that </b><br/><a NAME="E5:1"/><i><font color="Green">E36</font></i>: 
<font color="Maroon">b</font>,<font color="Maroon">p</font> <a href="analoaf.html#R2">//</a> <font color="Maroon">p</font>,<font color="Maroon">b'</font>
 <b>and </b><br/><a NAME="E6:1"/><i><font color="Green">E37</font></i>: 
<font color="Maroon">b</font>,<font color="Maroon">a</font> <a href="analoaf.html#R2">//</a> <font color="Maroon">a'</font>,<font color="Maroon">b'</font>
 <b>by </b><i>, <a class="ref" href="diraf.html#T47">DIRAF:47</a></i>;<br/>
<a NAME="E7:1"/>
<font color="Maroon">p</font>,<font color="Maroon">b</font> <a href="analoaf.html#R2">//</a> <font color="Maroon">p</font>,<font color="Maroon">b'</font>
 
<b>by </b><i>, <a class="ref" href="aff_1.html#T13">AFF_1:13</a></i>;<br/>
<a NAME="E8:1"/><b>then </b>
(  <a href="aff_1.html#R1">LIN</a> <font color="Maroon">p</font>,<font color="Maroon">b</font>,<font color="Maroon">b'</font> &amp; <font color="Maroon">a</font>,<font color="Maroon">b</font> <a href="analoaf.html#R2">//</a> <font color="Maroon">a'</font>,<font color="Maroon">b'</font> )
 
<b>by </b><i>, <a class="ref" href="aff_1.html#T13">AFF_1:13</a>, <a class="ref" href="aff_1.html#D1">AFF_1:def 1</a></i>;<br/>
<b>hence </b><a NAME="E9:1"/>
 ex <font color="Olive">b'</font> being  <a href="struct_0.html#NM1">Element</a> of <font color="Maroon">AS</font> st <br/>(  <a href="aff_1.html#R1">LIN</a> <font color="Maroon">p</font>,<font color="Maroon">b</font>,<font color="Olive">b'</font> &amp; <font color="Maroon">a</font>,<font color="Maroon">b</font> <a href="analoaf.html#R2">//</a> <font color="Maroon">a'</font>,<font color="Olive">b'</font> )
 ;<br/>


</div>
