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<b>let </b><font color="Maroon" title="c1">AS</font> be   <a href="diraf.html#NM1" title="DIRAF:NM.1">AffinSpace</a>;<br/><b>let </b><font color="Maroon" title="c2">K</font>, <font color="Maroon" title="c3">M</font>, <font color="Maroon" title="c4">N</font> be   <a href="struct_0.html#NM2" title="STRUCT_0:NM.2">Subset</a> of <font color="Maroon" title="c1">AS</font>;<br/>







<b>assume </b><a NAME="E1:58"/>
<font color="Maroon" title="c2">K</font>,<font color="Maroon" title="c3">M</font>,<font color="Maroon" title="c4">N</font> <a href="aff_4.html#R2" title="AFF_4:pred.2">is_coplanar</a> 
 ;<br/>

<a NAME="E2:58"/><b>then </b>
 ex <font color="Olive" title="b1">X</font> being  <a href="struct_0.html#NM2" title="STRUCT_0:NM.2">Subset</a> of <font color="Maroon" title="c1">AS</font> st <br/>( <font color="Maroon" title="c2">K</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Olive" title="b1">X</font> &amp; <font color="Maroon" title="c3">M</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Olive" title="b1">X</font> &amp; <font color="Maroon" title="c4">N</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Olive" title="b1">X</font> &amp; <font color="Olive" title="b1">X</font> <a href="aff_4.html#NR1" title="AFF_4:NR.1">is_plane</a>  )
 
<b>by </b><i><a class="ref" href="aff_4.html#D5" target="_self" title="AFF_4:def.5">Def5</a></i>;<br/>
<b>hence </b><a NAME="E3:58"/>
( <font color="Maroon" title="c2">K</font>,<font color="Maroon" title="c4">N</font>,<font color="Maroon" title="c3">M</font> <a href="aff_4.html#R2" title="AFF_4:pred.2">is_coplanar</a>  &amp; <font color="Maroon" title="c3">M</font>,<font color="Maroon" title="c2">K</font>,<font color="Maroon" title="c4">N</font> <a href="aff_4.html#R2" title="AFF_4:pred.2">is_coplanar</a>  &amp; <font color="Maroon" title="c3">M</font>,<font color="Maroon" title="c4">N</font>,<font color="Maroon" title="c2">K</font> <a href="aff_4.html#R2" title="AFF_4:pred.2">is_coplanar</a>  &amp; <font color="Maroon" title="c4">N</font>,<font color="Maroon" title="c2">K</font>,<font color="Maroon" title="c3">M</font> <a href="aff_4.html#R2" title="AFF_4:pred.2">is_coplanar</a>  &amp; <font color="Maroon" title="c4">N</font>,<font color="Maroon" title="c3">M</font>,<font color="Maroon" title="c2">K</font> <a href="aff_4.html#R2" title="AFF_4:pred.2">is_coplanar</a>  )
 <b>by </b><i><a class="ref" href="aff_4.html#D5" target="_self" title="AFF_4:def.5">Def5</a></i>;<br/>


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