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<b>let </b><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:()"><i><font color="Red">::  thesis: </font></i></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/>

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


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