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

<span class="kw">let </span><font color="Maroon" title="c1">MS</font> be   <a href="analmetr.html#NM2" title="ANALMETR:NM.2">OrtAfPl</a>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> ( <font color="Maroon" title="c1">MS</font> is  <a href="euclmetr.html#V2" title="EUCLMETR:attr.2">Pappian</a>  iff <font color="Maroon" title="c1">MS</font> is  <a href="conmetr.html#V2" title="CONMETR:attr.2">satisfying_PAP</a>  )</span><br/>

<span class="kw">set </span><font color="Maroon" title="c2">AS</font> =  <a href="analmetr.html#K3" title="ANALMETR:func.3">Af</a> <font color="Maroon" title="c1">MS</font>;<br/>
<div><span class="lab"><font color="Green" title="E18">A1</font></span>: <a class="txt" onclick="hs2(this)" href="javascript:()" title="18_1"><span class="kw">now </span></a><div class="add"><span class="kw">assume </span><a NAME="E1:18_1"/>
<font color="Maroon" title="c1">MS</font> is  <a href="conmetr.html#V2" title="CONMETR:attr.2">satisfying_PAP</a> 
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> <font color="Maroon" title="c1">MS</font> is  <a href="euclmetr.html#V2" title="EUCLMETR:attr.2">Pappian</a> </span><br/><a NAME="E2:18_1"/><span class="kw">then </span>
 <a href="analmetr.html#K3" title="ANALMETR:func.3">Af</a> <font color="Maroon" title="c1">MS</font> is  <a href="aff_2.html#V2" title="AFF_2:attr.2">Pappian</a> 
 <span class="kw">by</span> <span class="lab"><a class="txt" href="euclmetr.html#E17"><span class="lab"><font color="Green" title="E16">Lm1</font></span></a></span>;<br/><span class="kw">hence </span><a NAME="E3:18_1"/>
<font color="Maroon" title="c1">MS</font> is  <a href="euclmetr.html#V2" title="EUCLMETR:attr.2">Pappian</a> 
 <span class="kw">by</span> <span class="lab"><a class="ref" href="euclmetr.html#D2" target="_self" title="EUCLMETR:def.2">Def2</a></span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> verum</span><br/></div><span class="kw">end;</span></div>
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="18_2"><span class="kw">now </span></a><div class="add"><span class="kw">assume </span><a NAME="E1:18_2"/>
<font color="Maroon" title="c1">MS</font> is  <a href="euclmetr.html#V2" title="EUCLMETR:attr.2">Pappian</a> 
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> <font color="Maroon" title="c1">MS</font> is  <a href="conmetr.html#V2" title="CONMETR:attr.2">satisfying_PAP</a> </span><br/><a NAME="E2:18_2"/><span class="kw">then </span>
 <a href="analmetr.html#K3" title="ANALMETR:func.3">Af</a> <font color="Maroon" title="c1">MS</font> is  <a href="aff_2.html#V2" title="AFF_2:attr.2">Pappian</a> 
 <span class="kw">by</span> <span class="lab"><a class="ref" href="euclmetr.html#D2" target="_self" title="EUCLMETR:def.2">Def2</a></span>;<br/><span class="kw">hence </span><a NAME="E3:18_2"/>
<font color="Maroon" title="c1">MS</font> is  <a href="conmetr.html#V2" title="CONMETR:attr.2">satisfying_PAP</a> 
 <span class="kw">by</span> <span class="lab"><a class="txt" href="euclmetr.html#E17"><span class="lab"><font color="Green" title="E16">Lm1</font></span></a></span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> verum</span><br/></div><span class="kw">end;</span></div>
<span class="kw">hence </span><a NAME="E3:18"/>
( <font color="Maroon" title="c1">MS</font> is  <a href="euclmetr.html#V2" title="EUCLMETR:attr.2">Pappian</a>  iff <font color="Maroon" title="c1">MS</font> is  <a href="conmetr.html#V2" title="CONMETR:attr.2">satisfying_PAP</a>  )
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:18"><span class="lab"><font color="Green" title="E18">A1</font></span></a></span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> verum</span><br/>


</div>
