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<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" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> ( <font color="Maroon" title="c1">MS</font> is  <a href="euclmetr.html#V1" title="EUCLMETR:attr.1">Euclidean</a>  &amp; <font color="Maroon" title="c1">MS</font> is  <a href="euclmetr.html#V3" title="EUCLMETR:attr.3">Desarguesian</a>  implies <font color="Maroon" title="c1">MS</font> is  <a href="euclmetr.html#V2" title="EUCLMETR:attr.2">Pappian</a>  )</span><br/>

<span class="kw">assume </span><a NAME="E1:21"/>
( <font color="Maroon" title="c1">MS</font> is  <a href="euclmetr.html#V1" title="EUCLMETR:attr.1">Euclidean</a>  &amp; <font color="Maroon" title="c1">MS</font> is  <a href="euclmetr.html#V3" title="EUCLMETR:attr.3">Desarguesian</a>  )
 ; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  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="E2:21"/><span class="kw">then </span>
( <font color="Maroon" title="c1">MS</font> is  <a href="conaffm.html#V3" title="CONAFFM:attr.3">satisfying_3H</a>  &amp; <font color="Maroon" title="c1">MS</font> is  <a href="conaffm.html#V1" title="CONAFFM:attr.1">satisfying_DES</a>  )
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="euclmetr.html#T8" target="_self" onmouseover="rs('euclmetr/T8')" onmouseout="rh()">Th8</a>, <a class="ref" href="euclmetr.html#T11" target="_self" onmouseover="rs('euclmetr/T11')" onmouseout="rh()">Th11</a></span>;<br/>
<a NAME="E3:21"/><span class="kw">then </span>
<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="ref" href="conmetr.html#T13" onmouseover="rs('conmetr/T13')" onmouseout="rh()">CONMETR:13</a>, <a class="ref" href="conmetr.html#T15" onmouseover="rs('conmetr/T15')" onmouseout="rh()">CONMETR:15</a></span>;<br/>
<span class="kw">hence </span><a NAME="E4:21"/>
<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#T10" target="_self" onmouseover="rs('euclmetr/T10')" onmouseout="rh()">Th10</a></span>; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> verum</span><br/>


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