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

<b>let </b><font color="Maroon" title="c1">X</font> be   <a href="diraf.html#NM2" title="DIRAF:NM.2">AffinPlane</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">X</font> is <a href="aff_2.html#V1" title="AFF_2:attr.1">satisfying_PPAP</a> iff <font color="Maroon" title="c1">X</font> is <a href="conmetr1.html#V4" title="CONMETR1:attr.4">satisfying_indirect_Scherungssatz</a> )</span><br/>

<a NAME="E1:17"/><i><font color="Green" title="E15">A1</font></i>: 
( <font color="Maroon" title="c1">X</font> is <a href="aff_2.html#V1" title="AFF_2:attr.1">satisfying_PPAP</a> implies <font color="Maroon" title="c1">X</font> is <a href="conmetr1.html#V4" title="CONMETR1:attr.4">satisfying_indirect_Scherungssatz</a> )
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="17_1"><b>proof </b></a><div class="add">

<b>assume </b><a NAME="E1:17_1"/>
<font color="Maroon" title="c1">X</font> is <a href="aff_2.html#V1" title="AFF_2:attr.1">satisfying_PPAP</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">X</font> is <a href="conmetr1.html#V4" title="CONMETR1:attr.4">satisfying_indirect_Scherungssatz</a></span><br/>

<a NAME="E2:17_1"/><b>then </b>
( <font color="Maroon" title="c1">X</font> is <a href="aff_2.html#V2" title="AFF_2:attr.2">Pappian</a> &amp; <font color="Maroon" title="c1">X</font> is <a href="aff_2.html#V13" title="AFF_2:attr.13">satisfying_pap</a> )
 
<b>by </b><i><a class="ref" href="aff_2.html#T24" title="AFF_2:th.24">AFF_2:24</a></i>;<br/>
<a NAME="E3:17_1"/><b>then </b>
( <font color="Maroon" title="c1">X</font> is <a href="conmetr1.html#V6" title="CONMETR1:attr.6">satisfying_major_indirect_Scherungssatz</a> &amp; <font color="Maroon" title="c1">X</font> is <a href="conmetr1.html#V5" title="CONMETR1:attr.5">satisfying_minor_indirect_Scherungssatz</a> )
 
<b>by </b><i><a class="ref" href="conmetr1.html#T9" target="_self" title="CONMETR1:th.9">Th9</a>, <a class="ref" href="conmetr1.html#T10" target="_self" title="CONMETR1:th.10">Th10</a></i>;<br/>
<b>hence </b><a NAME="E4:17_1"/>
<font color="Maroon" title="c1">X</font> is <a href="conmetr1.html#V4" title="CONMETR1:attr.4">satisfying_indirect_Scherungssatz</a>
 <b>by </b><i><a class="ref" href="conmetr1.html#T1" target="_self" title="CONMETR1:th.1">Th1</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>
<a NAME="E2:17"/>
( <font color="Maroon" title="c1">X</font> is <a href="conmetr1.html#V4" title="CONMETR1:attr.4">satisfying_indirect_Scherungssatz</a> implies <font color="Maroon" title="c1">X</font> is <a href="aff_2.html#V1" title="AFF_2:attr.1">satisfying_PPAP</a> )
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="17_2"><b>proof </b></a><div class="add">

<b>assume </b><a NAME="E1:17_2"/>
<font color="Maroon" title="c1">X</font> is <a href="conmetr1.html#V4" title="CONMETR1:attr.4">satisfying_indirect_Scherungssatz</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">X</font> is <a href="aff_2.html#V1" title="AFF_2:attr.1">satisfying_PPAP</a></span><br/>

<a NAME="E2:17_2"/><b>then </b>
( <font color="Maroon" title="c1">X</font> is <a href="conmetr1.html#V5" title="CONMETR1:attr.5">satisfying_minor_indirect_Scherungssatz</a> &amp; <font color="Maroon" title="c1">X</font> is <a href="conmetr1.html#V6" title="CONMETR1:attr.6">satisfying_major_indirect_Scherungssatz</a> )
 
<b>by </b><i><a class="ref" href="conmetr1.html#T1" target="_self" title="CONMETR1:th.1">Th1</a></i>;<br/>
<a NAME="E3:17_2"/><b>then </b>
( <font color="Maroon" title="c1">X</font> is <a href="aff_2.html#V2" title="AFF_2:attr.2">Pappian</a> &amp; <font color="Maroon" title="c1">X</font> is <a href="aff_2.html#V13" title="AFF_2:attr.13">satisfying_pap</a> )
 
<b>by </b><i><a class="ref" href="conmetr1.html#T9" target="_self" title="CONMETR1:th.9">Th9</a>, <a class="ref" href="conmetr1.html#T10" target="_self" title="CONMETR1:th.10">Th10</a></i>;<br/>
<b>hence </b><a NAME="E4:17_2"/>
<font color="Maroon" title="c1">X</font> is <a href="aff_2.html#V1" title="AFF_2:attr.1">satisfying_PPAP</a>
 <b>by </b><i><a class="ref" href="aff_2.html#T24" title="AFF_2:th.24">AFF_2:24</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="E3:17"/>
( <font color="Maroon" title="c1">X</font> is <a href="aff_2.html#V1" title="AFF_2:attr.1">satisfying_PPAP</a> iff <font color="Maroon" title="c1">X</font> is <a href="conmetr1.html#V4" title="CONMETR1:attr.4">satisfying_indirect_Scherungssatz</a> )
 <b>by </b><i><a class="txt" href="#E1:17"><i><font color="Green" title="E15">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/>


</div>
