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

<span class="kw">let </span><font color="Maroon" title="c1">X</font> be   <a href="diraf.html#NM2" title="DIRAF:NM.2">AffinPlane</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">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"/><span class="lab"><font color="Green" title="E9">A1</font></span>: 
( <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" onmouseover="tooltip.show('hs2',this)" onmouseout="tooltip.hide()" onclick="hs2(this)" href="javascript:()" title="17_1"><span class="kw">proof </span></a><div class="add">

<span class="kw">assume </span><a NAME="E1:17_1"/><span class="lab"><font color="Green" title="E10">A2</font></span>: 
<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" 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">X</font> is  <a href="conmetr1.html#V4" title="CONMETR1:attr.4">satisfying_indirect_Scherungssatz</a> </span><br/>

<a NAME="E2:17_1"/><span class="kw">then </span>
<font color="Maroon" title="c1">X</font> is  <a href="aff_2.html#V13" title="AFF_2:attr.13">satisfying_pap</a> 
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="aff_2.html#T10" onmouseover="rs('aff_2/T10')" onmouseout="rh()">AFF_2:10</a></span>;<br/>
<a NAME="E3:17_1"/><span class="kw">then </span><span class="lab"><font color="Green" title="E11">A3</font></span>: 
<font color="Maroon" title="c1">X</font> is  <a href="conmetr1.html#V5" title="CONMETR1:attr.5">satisfying_minor_indirect_Scherungssatz</a> 
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="conmetr1.html#T9" target="_self" onmouseover="rs('conmetr1/T9')" onmouseout="rh()">Th9</a></span>;<br/>
<a NAME="E4:17_1"/>
<font color="Maroon" title="c1">X</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="#E1:17_1"><span class="lab"><font color="Green" title="E10">A2</font></span></a>, <a class="ref" href="aff_2.html#T10" onmouseover="rs('aff_2/T10')" onmouseout="rh()">AFF_2:10</a></span>;<br/>
<a NAME="E5:17_1"/><span class="kw">then </span>
<font color="Maroon" title="c1">X</font> is  <a href="conmetr1.html#V6" title="CONMETR1:attr.6">satisfying_major_indirect_Scherungssatz</a> 
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="conmetr1.html#T10" target="_self" onmouseover="rs('conmetr1/T10')" onmouseout="rh()">Th10</a></span>;<br/>
<span class="kw">hence </span><a NAME="E6:17_1"/>
<font color="Maroon" title="c1">X</font> is  <a href="conmetr1.html#V4" title="CONMETR1:attr.4">satisfying_indirect_Scherungssatz</a> 
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E3:17_1"><span class="lab"><font color="Green" title="E11">A3</font></span></a>, <a class="ref" href="conmetr1.html#T1" target="_self" onmouseover="rs('conmetr1/T1')" onmouseout="rh()">Th1</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/>


</div><span class="kw">end;</span></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" onmouseover="tooltip.show('hs2',this)" onmouseout="tooltip.hide()" onclick="hs2(this)" href="javascript:()" title="17_2"><span class="kw">proof </span></a><div class="add">

<span class="kw">assume </span><a NAME="E1:17_2"/><span class="lab"><font color="Green" title="E10">A4</font></span>: 
<font color="Maroon" title="c1">X</font> is  <a href="conmetr1.html#V4" title="CONMETR1:attr.4">satisfying_indirect_Scherungssatz</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">X</font> is  <a href="aff_2.html#V1" title="AFF_2:attr.1">satisfying_PPAP</a> </span><br/>

<a NAME="E2:17_2"/><span class="kw">then </span>
<font color="Maroon" title="c1">X</font> is  <a href="conmetr1.html#V6" title="CONMETR1:attr.6">satisfying_major_indirect_Scherungssatz</a> 
 
;<br/>
<a NAME="E3:17_2"/><span class="kw">then </span><span class="lab"><font color="Green" title="E11">A5</font></span>: 
<font color="Maroon" title="c1">X</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="conmetr1.html#T10" target="_self" onmouseover="rs('conmetr1/T10')" onmouseout="rh()">Th10</a></span>;<br/>
<a NAME="E4:17_2"/>
<font color="Maroon" title="c1">X</font> is  <a href="conmetr1.html#V5" title="CONMETR1:attr.5">satisfying_minor_indirect_Scherungssatz</a> 
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:17_2"><span class="lab"><font color="Green" title="E10">A4</font></span></a>, <a class="ref" href="conmetr1.html#T1" target="_self" onmouseover="rs('conmetr1/T1')" onmouseout="rh()">Th1</a></span>;<br/>
<a NAME="E5:17_2"/><span class="kw">then </span>
<font color="Maroon" title="c1">X</font> is  <a href="aff_2.html#V13" title="AFF_2:attr.13">satisfying_pap</a> 
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="conmetr1.html#T9" target="_self" onmouseover="rs('conmetr1/T9')" onmouseout="rh()">Th9</a></span>;<br/>
<span class="kw">hence </span><a NAME="E6:17_2"/>
<font color="Maroon" title="c1">X</font> is  <a href="aff_2.html#V1" title="AFF_2:attr.1">satisfying_PPAP</a> 
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E3:17_2"><span class="lab"><font color="Green" title="E11">A5</font></span></a>, <a class="ref" href="aff_2.html#T10" onmouseover="rs('aff_2/T10')" onmouseout="rh()">AFF_2:10</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/>


</div><span class="kw">end;</span></div>
<span class="kw">hence </span><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>  )
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:17"><span class="lab"><font color="Green" title="E9">A1</font></span></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/>


</div>
