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<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> 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>,<font color="Olive" title="b3">z</font> <a href="diraf.html#NR4" title="DIRAF:NR.4">is_collinear</a>  holds <br/>( <font color="Olive" title="b1">x</font>,<font color="Olive" title="b3">z</font>,<font color="Olive" title="b2">y</font> <a href="diraf.html#NR4" title="DIRAF:NR.4">is_collinear</a>  &amp; <font color="Olive" title="b2">y</font>,<font color="Olive" title="b1">x</font>,<font color="Olive" title="b3">z</font> <a href="diraf.html#NR4" title="DIRAF:NR.4">is_collinear</a>  )</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> 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>,<font color="Maroon" title="c4">z</font> <a href="diraf.html#NR4" title="DIRAF:NR.4">is_collinear</a>  implies ( <font color="Maroon" title="c2">x</font>,<font color="Maroon" title="c4">z</font>,<font color="Maroon" title="c3">y</font> <a href="diraf.html#NR4" title="DIRAF:NR.4">is_collinear</a>  &amp; <font color="Maroon" title="c3">y</font>,<font color="Maroon" title="c2">x</font>,<font color="Maroon" title="c4">z</font> <a href="diraf.html#NR4" title="DIRAF:NR.4">is_collinear</a>  ) )</span><br/>







<b>assume </b><a NAME="E1:39"/>
<font color="Maroon" title="c2">x</font>,<font color="Maroon" title="c3">y</font>,<font color="Maroon" title="c4">z</font> <a href="diraf.html#NR4" title="DIRAF:NR.4">is_collinear</a> 
 ; <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="c4">z</font>,<font color="Maroon" title="c3">y</font> <a href="diraf.html#NR4" title="DIRAF:NR.4">is_collinear</a>  &amp; <font color="Maroon" title="c3">y</font>,<font color="Maroon" title="c2">x</font>,<font color="Maroon" title="c4">z</font> <a href="diraf.html#NR4" title="DIRAF:NR.4">is_collinear</a>  )</span><br/>

<a NAME="E2:39"/><b>then </b>
<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="c4">z</font>
 
<b>by </b><i><a class="ref" href="diraf.html#D5" target="_self" title="DIRAF:def.5">Def5</a></i>;<br/>
<a NAME="E3:39"/><b>then </b>
( <font color="Maroon" title="c2">x</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="c3">y</font>,<font color="Maroon" title="c2">x</font> <a href="diraf.html#R2" title="DIRAF:pred.2">'||'</a> <font color="Maroon" title="c3">y</font>,<font color="Maroon" title="c4">z</font> )
 
<b>by </b><i><a class="ref" href="diraf.html#T26" target="_self" title="DIRAF:th.26">Th26</a>, <a class="ref" href="diraf.html#T27" target="_self" title="DIRAF:th.27">Th27</a></i>;<br/>
<b>hence </b><a NAME="E4:39"/>
( <font color="Maroon" title="c2">x</font>,<font color="Maroon" title="c4">z</font>,<font color="Maroon" title="c3">y</font> <a href="diraf.html#NR4" title="DIRAF:NR.4">is_collinear</a>  &amp; <font color="Maroon" title="c3">y</font>,<font color="Maroon" title="c2">x</font>,<font color="Maroon" title="c4">z</font> <a href="diraf.html#NR4" title="DIRAF:NR.4">is_collinear</a>  )
 <b>by </b><i><a class="ref" href="diraf.html#D5" target="_self" title="DIRAF:def.5">Def5</a></i>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> verum</span><br/>


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