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

<b>let </b><font color="Maroon">MS</font> be   <a href="analmetr.html#NM2">OrtAfPl</a>;<br/>

<b>set </b><font color="Maroon">AS</font> =  <a href="analmetr.html#K3">Af</a> <font color="Maroon">MS</font>;<br/>
<div><i><font color="Green">E34</font></i>: <a class="txt" onclick="hs2(this)" href="javascript:()" title="20_1"><b>now </b></a><div class="add"><b>assume </b><a NAME="E1:20_1"/>
<font color="Maroon">MS</font> is <a href="euclmetr.html#V3" target="_self">Desarguesian</a>
 ;<br/><a NAME="E2:20_1"/><b>then </b>
 <a href="analmetr.html#K3">Af</a> <font color="Maroon">MS</font> <a href="papdesaf.html#NR2" target="_self">satisfies_DES'</a> 
 <b>by </b><i/>;<br/><b>hence </b><a NAME="E3:20_1"/>
 <a href="conaffm.html#NR1" target="_self">DES_holds_in</a> <font color="Maroon">MS</font>
 <b>by </b><i/>;<br/></div><b>end;</b></div>
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="20_2"><b>now </b></a><div class="add"><b>assume </b><a NAME="E1:20_2"/>
 <a href="conaffm.html#NR1" target="_self">DES_holds_in</a> <font color="Maroon">MS</font>
 ;<br/><a NAME="E2:20_2"/><b>then </b>
 <a href="analmetr.html#K3">Af</a> <font color="Maroon">MS</font> is <a href="aff_2.html#V4">Desarguesian</a>
 <b>by </b><i/>;<br/><b>hence </b><a NAME="E3:20_2"/>
<font color="Maroon">MS</font> is <a href="euclmetr.html#V3" target="_self">Desarguesian</a>
 <b>by </b><i/>;<br/></div><b>end;</b></div>
<b>hence </b><a NAME="E3:20"/>
( <font color="Maroon">MS</font> is <a href="euclmetr.html#V3" target="_self">Desarguesian</a> iff  <a href="conaffm.html#NR1" target="_self">DES_holds_in</a> <font color="Maroon">MS</font> )
 <b>by </b><i/>;<br/>


</div>
