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

<b>let </b><font color="Maroon">X</font> be   <a href="diraf.html#NM2">AffinPlane</a>;<br/>

<a NAME="E1:23"/><i><font color="Green">E45</font></i>: 
( <font color="Maroon">X</font> <a href="aff_2.html#NR1" target="_self">satisfies_PPAP</a>  implies <font color="Maroon">X</font> <a href="conmetr1.html#NR4" target="_self">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">X</font> <a href="aff_2.html#NR1" target="_self">satisfies_PPAP</a> 
 ;<br/>

<a NAME="E2:23_1"/><b>then </b>
( <font color="Maroon">X</font> <a href="aff_2.html#NR2" target="_self">satisfies_PAP</a>  &amp; <font color="Maroon">X</font> <a href="aff_2.html#NR13" target="_self">satisfies_pap</a>  )
 
<b>by </b><i><a class="ref" href="aff_2.html#T24">AFF_2:24</a></i>;<br/>
<a NAME="E3:23_1"/><b>then </b>
( <font color="Maroon">X</font> <a href="conmetr1.html#NR6" target="_self">satisfies_major_SCH*</a>  &amp; <font color="Maroon">X</font> <a href="conmetr1.html#NR5" target="_self">satisfies_minor_SCH*</a>  )
 
<b>by </b><i>, </i>;<br/>
<b>hence </b><a NAME="E4:23_1"/>
<font color="Maroon">X</font> <a href="conmetr1.html#NR4" target="_self">satisfies_SCH*</a> 
 <b>by </b><i/>;<br/>


</div><b>end;</b></div>
<a NAME="E2:23"/>
( <font color="Maroon">X</font> <a href="conmetr1.html#NR4" target="_self">satisfies_SCH*</a>  implies <font color="Maroon">X</font> <a href="aff_2.html#NR1" target="_self">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">X</font> <a href="conmetr1.html#NR4" target="_self">satisfies_SCH*</a> 
 ;<br/>

<a NAME="E2:23_2"/><b>then </b>
( <font color="Maroon">X</font> <a href="conmetr1.html#NR5" target="_self">satisfies_minor_SCH*</a>  &amp; <font color="Maroon">X</font> <a href="conmetr1.html#NR6" target="_self">satisfies_major_SCH*</a>  )
 
<b>by </b><i/>;<br/>
<a NAME="E3:23_2"/><b>then </b>
( <font color="Maroon">X</font> <a href="aff_2.html#NR2" target="_self">satisfies_PAP</a>  &amp; <font color="Maroon">X</font> <a href="aff_2.html#NR13" target="_self">satisfies_pap</a>  )
 
<b>by </b><i>, </i>;<br/>
<b>hence </b><a NAME="E4:23_2"/>
<font color="Maroon">X</font> <a href="aff_2.html#NR1" target="_self">satisfies_PPAP</a> 
 <b>by </b><i><a class="ref" href="aff_2.html#T24">AFF_2:24</a></i>;<br/>


</div><b>end;</b></div>
<b>hence </b><a NAME="E3:23"/>
( <font color="Maroon">X</font> <a href="aff_2.html#NR1" target="_self">satisfies_PPAP</a>  iff <font color="Maroon">X</font> <a href="conmetr1.html#NR4" target="_self">satisfies_SCH*</a>  )
 <b>by </b><i/>;<br/>


</div>
