<?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> <a href="aff_2.html#NR1" title="AFF_2:NR.1">satisfies_PPAP</a>  iff <font color="Maroon" title="c1">X</font> <a href="conmetr1.html#NR4" title="CONMETR1:NR.4">satisfies_SCH*</a>  )</span><br/>

<a NAME="E1:23"/><i><font color="Green" title="E15">A1</font></i>: 
( <font color="Maroon" title="c1">X</font> <a href="aff_2.html#NR1" title="AFF_2:NR.1">satisfies_PPAP</a>  implies <font color="Maroon" title="c1">X</font> <a href="conmetr1.html#NR4" title="CONMETR1:NR.4">satisfies_SCH*</a>  )
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="23_1"><b>proof </b></a><div class="add">

<b>assume </b><a NAME="E1:23_1"/>
<font color="Maroon" title="c1">X</font> <a href="aff_2.html#NR1" title="AFF_2:NR.1">satisfies_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> <a href="conmetr1.html#NR4" title="CONMETR1:NR.4">satisfies_SCH*</a> </span><br/>

<a NAME="E2:23_1"/><b>then </b>
( <font color="Maroon" title="c1">X</font> <a href="aff_2.html#NR2" title="AFF_2:NR.2">satisfies_PAP</a>  &amp; <font color="Maroon" title="c1">X</font> <a href="aff_2.html#NR13" title="AFF_2:NR.13">satisfies_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="E3:23_1"/><b>then </b>
( <font color="Maroon" title="c1">X</font> <a href="conmetr1.html#NR6" title="CONMETR1:NR.6">satisfies_major_SCH*</a>  &amp; <font color="Maroon" title="c1">X</font> <a href="conmetr1.html#NR5" title="CONMETR1:NR.5">satisfies_minor_SCH*</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="E4:23_1"/>
<font color="Maroon" title="c1">X</font> <a href="conmetr1.html#NR4" title="CONMETR1:NR.4">satisfies_SCH*</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="E2:23"/>
( <font color="Maroon" title="c1">X</font> <a href="conmetr1.html#NR4" title="CONMETR1:NR.4">satisfies_SCH*</a>  implies <font color="Maroon" title="c1">X</font> <a href="aff_2.html#NR1" title="AFF_2:NR.1">satisfies_PPAP</a>  )
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="23_2"><b>proof </b></a><div class="add">

<b>assume </b><a NAME="E1:23_2"/>
<font color="Maroon" title="c1">X</font> <a href="conmetr1.html#NR4" title="CONMETR1:NR.4">satisfies_SCH*</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> <a href="aff_2.html#NR1" title="AFF_2:NR.1">satisfies_PPAP</a> </span><br/>

<a NAME="E2:23_2"/><b>then </b>
( <font color="Maroon" title="c1">X</font> <a href="conmetr1.html#NR5" title="CONMETR1:NR.5">satisfies_minor_SCH*</a>  &amp; <font color="Maroon" title="c1">X</font> <a href="conmetr1.html#NR6" title="CONMETR1:NR.6">satisfies_major_SCH*</a>  )
 
<b>by </b><i><a class="ref" href="conmetr1.html#T1" target="_self" title="CONMETR1:th.1">Th1</a></i>;<br/>
<a NAME="E3:23_2"/><b>then </b>
( <font color="Maroon" title="c1">X</font> <a href="aff_2.html#NR2" title="AFF_2:NR.2">satisfies_PAP</a>  &amp; <font color="Maroon" title="c1">X</font> <a href="aff_2.html#NR13" title="AFF_2:NR.13">satisfies_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="E4:23_2"/>
<font color="Maroon" title="c1">X</font> <a href="aff_2.html#NR1" title="AFF_2:NR.1">satisfies_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="E3:23"/>
( <font color="Maroon" title="c1">X</font> <a href="aff_2.html#NR1" title="AFF_2:NR.1">satisfies_PPAP</a>  iff <font color="Maroon" title="c1">X</font> <a href="conmetr1.html#NR4" title="CONMETR1:NR.4">satisfies_SCH*</a>  )
 <b>by </b><i><a class="txt" href="conmetr1.html#E1:23"><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>
