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

<b>let </b><font color="Maroon" title="c1">AS</font> be   <a href="diraf.html#NM1" title="DIRAF:NM.1">AffinSpace</a>;<br/><b>let </b><font color="Maroon" title="c2">a</font>, <font color="Maroon" title="c3">b</font> be   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c1">AS</font>;<br/><b>let </b><font color="Maroon" title="c4">A</font>, <font color="Maroon" title="c5">C</font> be   <a href="struct_0.html#NM2" title="STRUCT_0:NM.2">Subset</a> of <font color="Maroon" title="c1">AS</font>;<br/>









<b>assume </b><a NAME="E1:56"/><i><font color="Green" title="E49">A1</font></i>: 
( <font color="Maroon" title="c2">a</font>,<font color="Maroon" title="c3">b</font> <a href="aff_1.html#R2" title="AFF_1:pred.2">//</a> <font color="Maroon" title="c4">A</font> &amp; <font color="Maroon" title="c4">A</font> <a href="aff_1.html#R4" title="AFF_1:pred.4">//</a> <font color="Maroon" title="c5">C</font> )
 ;<br/>

<b>then consider </b><font color="Maroon" title="c6">p</font>, <font color="Maroon" title="c7">q</font>, <font color="Maroon" title="c8">c</font>, <font color="Maroon" title="c9">d</font> being   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c1">AS</font><b> such that </b><br/><a NAME="E3:56"/><i><font color="Green" title="E50">A2</font></i>: 
( <font color="Maroon" title="c6">p</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c7">q</font> &amp; <font color="Maroon" title="c8">c</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c9">d</font> &amp; <font color="Maroon" title="c6">p</font>,<font color="Maroon" title="c7">q</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c8">c</font>,<font color="Maroon" title="c9">d</font> &amp; <font color="Maroon" title="c4">A</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="aff_1.html#K2" title="AFF_1:func.2">Line</a> <font color="Maroon" title="c6">p</font>,<font color="Maroon" title="c7">q</font> &amp; <font color="Maroon" title="c5">C</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="aff_1.html#K2" title="AFF_1:func.2">Line</a> <font color="Maroon" title="c8">c</font>,<font color="Maroon" title="c9">d</font> )
 <b>by </b><i><a class="ref" href="aff_1.html#T51" target="_self" title="AFF_1:th.51">Th51</a></i>;<br/>
<a NAME="E4:56"/><i><font color="Green" title="E51">A3</font></i>: 
( <font color="Maroon" title="c6">p</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c4">A</font> &amp; <font color="Maroon" title="c7">q</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c4">A</font> )
 
<b>by </b><i><a class="txt" href="aff_1.html#E3:56"><i><font color="Green" title="E50">A2</font></i></a>, <a class="ref" href="aff_1.html#T26" target="_self" title="AFF_1:th.26">Th26</a></i>;<br/>
<a NAME="E5:56"/>
<font color="Maroon" title="c4">A</font> <a href="aff_1.html#NR2" title="AFF_1:NR.2">is_line</a> 
 
<b>by </b><i><a class="txt" href="aff_1.html#E1:56"><i><font color="Green" title="E49">A1</font></i></a>, <a class="ref" href="aff_1.html#T50" target="_self" title="AFF_1:th.50">Th50</a></i>;<br/>
<a NAME="E6:56"/><b>then </b>
<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="c6">p</font>,<font color="Maroon" title="c7">q</font>
 
<b>by </b><i><a class="txt" href="aff_1.html#E1:56"><i><font color="Green" title="E49">A1</font></i></a>, <a class="txt" href="aff_1.html#E3:56"><i><font color="Green" title="E50">A2</font></i></a>, <a class="txt" href="aff_1.html#E4:56"><i><font color="Green" title="E51">A3</font></i></a>, <a class="ref" href="aff_1.html#T41" target="_self" title="AFF_1:th.41">Th41</a></i>;<br/>
<a NAME="E7:56"/><b>then </b>
<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="c8">c</font>,<font color="Maroon" title="c9">d</font>
 
<b>by </b><i><a class="txt" href="aff_1.html#E3:56"><i><font color="Green" title="E50">A2</font></i></a>, <a class="ref" href="aff_1.html#T14" target="_self" title="AFF_1:th.14">Th14</a></i>;<br/>
<b>hence </b><a NAME="E8:56"/>
<font color="Maroon" title="c2">a</font>,<font color="Maroon" title="c3">b</font> <a href="aff_1.html#R2" title="AFF_1:pred.2">//</a> <font color="Maroon" title="c5">C</font>
 <b>by </b><i><a class="txt" href="aff_1.html#E3:56"><i><font color="Green" title="E50">A2</font></i></a>, <a class="ref" href="aff_1.html#D4" target="_self" title="AFF_1:def.4">Def4</a></i>;<br/>


</div>
