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<b>let </b><font color="Maroon" title="c1">S</font> be   <a href="analoaf.html#NM2" title="ANALOAF:NM.2">OAffinPlane</a>;<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>;<br/>









<b>assume </b><a NAME="E1:54"/>
not <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>
 ;<br/>

<a NAME="E2:54"/><b>then </b>
( not <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> &amp; not <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>then consider </b><font color="Maroon" title="c6">u</font> being   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c1">S</font><b> such that </b><br/><a NAME="E4:54"/><i><font color="Green" title="E35">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="c2">x</font>,<font color="Maroon" title="c6">u</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="c6">u</font>,<font color="Maroon" title="c2">x</font> ) &amp; ( <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="c4">z</font>,<font color="Maroon" title="c6">u</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="c6">u</font>,<font color="Maroon" title="c4">z</font> ) )
 <b>by </b><i><a class="ref" href="analoaf.html#D6" title="ANALOAF:def.6">ANALOAF:def 6</a></i>;<br/>
<a NAME="E5:54"/>
( <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="c2">x</font>,<font color="Maroon" title="c6">u</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="c4">z</font>,<font color="Maroon" title="c6">u</font> )
 
<b>by </b><i><a class="txt" href="diraf.html#E4:54"><i><font color="Green" title="E35">A1</font></i></a>, <a class="ref" href="diraf.html#D4" target="_self" title="DIRAF:def.4">Def4</a></i>;<br/>
<b>hence </b><a NAME="E6:54"/>
 ex <font color="Olive" title="b1">u</font> being  <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c1">S</font> st <br/>( <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="c2">x</font>,<font color="Olive" title="b1">u</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="c4">z</font>,<font color="Olive" title="b1">u</font> )
 ;<br/>


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