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

<b>let </b><font color="Maroon" title="c1">S</font> be   <a href="analoaf.html#NM1" title="ANALOAF:NM.1">OAffinSpace</a>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> for <font color="Olive" title="b1">x</font>, <font color="Olive" title="b2">y</font>, <font color="Olive" title="b3">z</font>, <font color="Olive" title="b4">t</font> being  <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c1">S</font>  st <font color="Olive" title="b1">x</font>,<font color="Olive" title="b2">y</font> <a href="diraf.html#R2" title="DIRAF:pred.2">'||'</a> <font color="Olive" title="b3">z</font>,<font color="Olive" title="b4">t</font> holds <br/>( <font color="Olive" title="b1">x</font>,<font color="Olive" title="b2">y</font> <a href="diraf.html#R2" title="DIRAF:pred.2">'||'</a> <font color="Olive" title="b4">t</font>,<font color="Olive" title="b3">z</font> &amp; <font color="Olive" title="b2">y</font>,<font color="Olive" title="b1">x</font> <a href="diraf.html#R2" title="DIRAF:pred.2">'||'</a> <font color="Olive" title="b3">z</font>,<font color="Olive" title="b4">t</font> &amp; <font color="Olive" title="b2">y</font>,<font color="Olive" title="b1">x</font> <a href="diraf.html#R2" title="DIRAF:pred.2">'||'</a> <font color="Olive" title="b4">t</font>,<font color="Olive" title="b3">z</font> &amp; <font color="Olive" title="b3">z</font>,<font color="Olive" title="b4">t</font> <a href="diraf.html#R2" title="DIRAF:pred.2">'||'</a> <font color="Olive" title="b1">x</font>,<font color="Olive" title="b2">y</font> &amp; <font color="Olive" title="b3">z</font>,<font color="Olive" title="b4">t</font> <a href="diraf.html#R2" title="DIRAF:pred.2">'||'</a> <font color="Olive" title="b2">y</font>,<font color="Olive" title="b1">x</font> &amp; <font color="Olive" title="b4">t</font>,<font color="Olive" title="b3">z</font> <a href="diraf.html#R2" title="DIRAF:pred.2">'||'</a> <font color="Olive" title="b1">x</font>,<font color="Olive" title="b2">y</font> &amp; <font color="Olive" title="b4">t</font>,<font color="Olive" title="b3">z</font> <a href="diraf.html#R2" title="DIRAF:pred.2">'||'</a> <font color="Olive" title="b2">y</font>,<font color="Olive" title="b1">x</font> )</span><br/><b>let </b><font color="Maroon" title="c2">x</font>, <font color="Maroon" title="c3">y</font>, <font color="Maroon" title="c4">z</font>, <font color="Maroon" title="c5">t</font> be   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c1">S</font>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> ( <font color="Maroon" title="c2">x</font>,<font color="Maroon" title="c3">y</font> <a href="diraf.html#R2" title="DIRAF:pred.2">'||'</a> <font color="Maroon" title="c4">z</font>,<font color="Maroon" title="c5">t</font> implies ( <font color="Maroon" title="c2">x</font>,<font color="Maroon" title="c3">y</font> <a href="diraf.html#R2" title="DIRAF:pred.2">'||'</a> <font color="Maroon" title="c5">t</font>,<font color="Maroon" title="c4">z</font> &amp; <font color="Maroon" title="c3">y</font>,<font color="Maroon" title="c2">x</font> <a href="diraf.html#R2" title="DIRAF:pred.2">'||'</a> <font color="Maroon" title="c4">z</font>,<font color="Maroon" title="c5">t</font> &amp; <font color="Maroon" title="c3">y</font>,<font color="Maroon" title="c2">x</font> <a href="diraf.html#R2" title="DIRAF:pred.2">'||'</a> <font color="Maroon" title="c5">t</font>,<font color="Maroon" title="c4">z</font> &amp; <font color="Maroon" title="c4">z</font>,<font color="Maroon" title="c5">t</font> <a href="diraf.html#R2" title="DIRAF:pred.2">'||'</a> <font color="Maroon" title="c2">x</font>,<font color="Maroon" title="c3">y</font> &amp; <font color="Maroon" title="c4">z</font>,<font color="Maroon" title="c5">t</font> <a href="diraf.html#R2" title="DIRAF:pred.2">'||'</a> <font color="Maroon" title="c3">y</font>,<font color="Maroon" title="c2">x</font> &amp; <font color="Maroon" title="c5">t</font>,<font color="Maroon" title="c4">z</font> <a href="diraf.html#R2" title="DIRAF:pred.2">'||'</a> <font color="Maroon" title="c2">x</font>,<font color="Maroon" title="c3">y</font> &amp; <font color="Maroon" title="c5">t</font>,<font color="Maroon" title="c4">z</font> <a href="diraf.html#R2" title="DIRAF:pred.2">'||'</a> <font color="Maroon" title="c3">y</font>,<font color="Maroon" title="c2">x</font> ) )</span><br/>









<b>assume </b><a NAME="E1:29"/>
<font color="Maroon" title="c2">x</font>,<font color="Maroon" title="c3">y</font> <a href="diraf.html#R2" title="DIRAF:pred.2">'||'</a> <font color="Maroon" title="c4">z</font>,<font color="Maroon" title="c5">t</font>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> ( <font color="Maroon" title="c2">x</font>,<font color="Maroon" title="c3">y</font> <a href="diraf.html#R2" title="DIRAF:pred.2">'||'</a> <font color="Maroon" title="c5">t</font>,<font color="Maroon" title="c4">z</font> &amp; <font color="Maroon" title="c3">y</font>,<font color="Maroon" title="c2">x</font> <a href="diraf.html#R2" title="DIRAF:pred.2">'||'</a> <font color="Maroon" title="c4">z</font>,<font color="Maroon" title="c5">t</font> &amp; <font color="Maroon" title="c3">y</font>,<font color="Maroon" title="c2">x</font> <a href="diraf.html#R2" title="DIRAF:pred.2">'||'</a> <font color="Maroon" title="c5">t</font>,<font color="Maroon" title="c4">z</font> &amp; <font color="Maroon" title="c4">z</font>,<font color="Maroon" title="c5">t</font> <a href="diraf.html#R2" title="DIRAF:pred.2">'||'</a> <font color="Maroon" title="c2">x</font>,<font color="Maroon" title="c3">y</font> &amp; <font color="Maroon" title="c4">z</font>,<font color="Maroon" title="c5">t</font> <a href="diraf.html#R2" title="DIRAF:pred.2">'||'</a> <font color="Maroon" title="c3">y</font>,<font color="Maroon" title="c2">x</font> &amp; <font color="Maroon" title="c5">t</font>,<font color="Maroon" title="c4">z</font> <a href="diraf.html#R2" title="DIRAF:pred.2">'||'</a> <font color="Maroon" title="c2">x</font>,<font color="Maroon" title="c3">y</font> &amp; <font color="Maroon" title="c5">t</font>,<font color="Maroon" title="c4">z</font> <a href="diraf.html#R2" title="DIRAF:pred.2">'||'</a> <font color="Maroon" title="c3">y</font>,<font color="Maroon" title="c2">x</font> )</span><br/>

<a NAME="E2:29"/><b>then </b><i><font color="Green" title="E19">A1</font></i>: 
( <font color="Maroon" title="c2">x</font>,<font color="Maroon" title="c3">y</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c4">z</font>,<font color="Maroon" title="c5">t</font> or <font color="Maroon" title="c2">x</font>,<font color="Maroon" title="c3">y</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c5">t</font>,<font color="Maroon" title="c4">z</font> )
 
<b>by </b><i><a class="ref" href="diraf.html#D4" target="_self" title="DIRAF:def.4">Def4</a></i>;<br/>
<b>hence </b><a NAME="E3:29"/>
<font color="Maroon" title="c2">x</font>,<font color="Maroon" title="c3">y</font> <a href="diraf.html#R2" title="DIRAF:pred.2">'||'</a> <font color="Maroon" title="c5">t</font>,<font color="Maroon" title="c4">z</font>
 <b>by </b><i><a class="ref" href="diraf.html#D4" target="_self" title="DIRAF:def.4">Def4</a></i>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> ( <font color="Maroon" title="c3">y</font>,<font color="Maroon" title="c2">x</font> <a href="diraf.html#R2" title="DIRAF:pred.2">'||'</a> <font color="Maroon" title="c4">z</font>,<font color="Maroon" title="c5">t</font> &amp; <font color="Maroon" title="c3">y</font>,<font color="Maroon" title="c2">x</font> <a href="diraf.html#R2" title="DIRAF:pred.2">'||'</a> <font color="Maroon" title="c5">t</font>,<font color="Maroon" title="c4">z</font> &amp; <font color="Maroon" title="c4">z</font>,<font color="Maroon" title="c5">t</font> <a href="diraf.html#R2" title="DIRAF:pred.2">'||'</a> <font color="Maroon" title="c2">x</font>,<font color="Maroon" title="c3">y</font> &amp; <font color="Maroon" title="c4">z</font>,<font color="Maroon" title="c5">t</font> <a href="diraf.html#R2" title="DIRAF:pred.2">'||'</a> <font color="Maroon" title="c3">y</font>,<font color="Maroon" title="c2">x</font> &amp; <font color="Maroon" title="c5">t</font>,<font color="Maroon" title="c4">z</font> <a href="diraf.html#R2" title="DIRAF:pred.2">'||'</a> <font color="Maroon" title="c2">x</font>,<font color="Maroon" title="c3">y</font> &amp; <font color="Maroon" title="c5">t</font>,<font color="Maroon" title="c4">z</font> <a href="diraf.html#R2" title="DIRAF:pred.2">'||'</a> <font color="Maroon" title="c3">y</font>,<font color="Maroon" title="c2">x</font> )</span><br/>

<a NAME="E4:29"/>
( <font color="Maroon" title="c3">y</font>,<font color="Maroon" title="c2">x</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c5">t</font>,<font color="Maroon" title="c4">z</font> or <font color="Maroon" title="c3">y</font>,<font color="Maroon" title="c2">x</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c4">z</font>,<font color="Maroon" title="c5">t</font> )
 
<b>by </b><i><a class="txt" href="#E2:29"><i><font color="Green" title="E19">A1</font></i></a>, <a class="ref" href="analoaf.html#D5" title="ANALOAF:def.5">ANALOAF:def 5</a></i>;<br/>
<b>hence </b><a NAME="E5:29"/>
( <font color="Maroon" title="c3">y</font>,<font color="Maroon" title="c2">x</font> <a href="diraf.html#R2" title="DIRAF:pred.2">'||'</a> <font color="Maroon" title="c4">z</font>,<font color="Maroon" title="c5">t</font> &amp; <font color="Maroon" title="c3">y</font>,<font color="Maroon" title="c2">x</font> <a href="diraf.html#R2" title="DIRAF:pred.2">'||'</a> <font color="Maroon" title="c5">t</font>,<font color="Maroon" title="c4">z</font> )
 <b>by </b><i><a class="ref" href="diraf.html#D4" target="_self" title="DIRAF:def.4">Def4</a></i>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> ( <font color="Maroon" title="c4">z</font>,<font color="Maroon" title="c5">t</font> <a href="diraf.html#R2" title="DIRAF:pred.2">'||'</a> <font color="Maroon" title="c2">x</font>,<font color="Maroon" title="c3">y</font> &amp; <font color="Maroon" title="c4">z</font>,<font color="Maroon" title="c5">t</font> <a href="diraf.html#R2" title="DIRAF:pred.2">'||'</a> <font color="Maroon" title="c3">y</font>,<font color="Maroon" title="c2">x</font> &amp; <font color="Maroon" title="c5">t</font>,<font color="Maroon" title="c4">z</font> <a href="diraf.html#R2" title="DIRAF:pred.2">'||'</a> <font color="Maroon" title="c2">x</font>,<font color="Maroon" title="c3">y</font> &amp; <font color="Maroon" title="c5">t</font>,<font color="Maroon" title="c4">z</font> <a href="diraf.html#R2" title="DIRAF:pred.2">'||'</a> <font color="Maroon" title="c3">y</font>,<font color="Maroon" title="c2">x</font> )</span><br/>

<a NAME="E6:29"/>
( <font color="Maroon" title="c4">z</font>,<font color="Maroon" title="c5">t</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c2">x</font>,<font color="Maroon" title="c3">y</font> or <font color="Maroon" title="c4">z</font>,<font color="Maroon" title="c5">t</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c3">y</font>,<font color="Maroon" title="c2">x</font> )
 
<b>by </b><i><a class="txt" href="#E2:29"><i><font color="Green" title="E19">A1</font></i></a>, <a class="ref" href="diraf.html#T5" target="_self" title="DIRAF:th.5">Th5</a></i>;<br/>
<b>hence </b><a NAME="E7:29"/>
( <font color="Maroon" title="c4">z</font>,<font color="Maroon" title="c5">t</font> <a href="diraf.html#R2" title="DIRAF:pred.2">'||'</a> <font color="Maroon" title="c2">x</font>,<font color="Maroon" title="c3">y</font> &amp; <font color="Maroon" title="c4">z</font>,<font color="Maroon" title="c5">t</font> <a href="diraf.html#R2" title="DIRAF:pred.2">'||'</a> <font color="Maroon" title="c3">y</font>,<font color="Maroon" title="c2">x</font> )
 <b>by </b><i><a class="ref" href="diraf.html#D4" target="_self" title="DIRAF:def.4">Def4</a></i>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> ( <font color="Maroon" title="c5">t</font>,<font color="Maroon" title="c4">z</font> <a href="diraf.html#R2" title="DIRAF:pred.2">'||'</a> <font color="Maroon" title="c2">x</font>,<font color="Maroon" title="c3">y</font> &amp; <font color="Maroon" title="c5">t</font>,<font color="Maroon" title="c4">z</font> <a href="diraf.html#R2" title="DIRAF:pred.2">'||'</a> <font color="Maroon" title="c3">y</font>,<font color="Maroon" title="c2">x</font> )</span><br/>

<a NAME="E8:29"/>
( <font color="Maroon" title="c5">t</font>,<font color="Maroon" title="c4">z</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c3">y</font>,<font color="Maroon" title="c2">x</font> or <font color="Maroon" title="c5">t</font>,<font color="Maroon" title="c4">z</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c2">x</font>,<font color="Maroon" title="c3">y</font> )
 
<b>by </b><i><a class="txt" href="#E2:29"><i><font color="Green" title="E19">A1</font></i></a>, <a class="ref" href="diraf.html#T5" target="_self" title="DIRAF:th.5">Th5</a></i>;<br/>
<b>hence </b><a NAME="E9:29"/>
( <font color="Maroon" title="c5">t</font>,<font color="Maroon" title="c4">z</font> <a href="diraf.html#R2" title="DIRAF:pred.2">'||'</a> <font color="Maroon" title="c2">x</font>,<font color="Maroon" title="c3">y</font> &amp; <font color="Maroon" title="c5">t</font>,<font color="Maroon" title="c4">z</font> <a href="diraf.html#R2" title="DIRAF:pred.2">'||'</a> <font color="Maroon" title="c3">y</font>,<font color="Maroon" title="c2">x</font> )
 <b>by </b><i><a class="ref" href="diraf.html#D4" target="_self" title="DIRAF:def.4">Def4</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>
