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<div><span class="kw">theorem </span><a NAME="T25"><span class="comment"><font color="firebrick">:: PASCH:25</font></span><br/></a><div class="add"> for <font color="Olive" title="b1">OAS</font> being   <a href="analoaf.html#NM1" title="ANALOAF:NM.1">OAffinSpace</a><br/>  for <font color="Olive" title="b2">a</font>, <font color="Olive" title="b3">b</font>, <font color="Olive" title="b4">c</font>, <font color="Olive" title="b5">d</font> being   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Olive" title="b1">OAS</font>  st <font color="Olive" title="b2">a</font>,<font color="Olive" title="b3">b</font> <a href="diraf.html#R2" title="DIRAF:pred.2">'||'</a> <font color="Olive" title="b4">c</font>,<font color="Olive" title="b5">d</font> &amp; <font color="Olive" title="b2">a</font>,<font color="Olive" title="b4">c</font> <a href="diraf.html#R2" title="DIRAF:pred.2">'||'</a> <font color="Olive" title="b3">b</font>,<font color="Olive" title="b5">d</font> &amp;  not <font color="Olive" title="b2">a</font>,<font color="Olive" title="b3">b</font>,<font color="Olive" title="b4">c</font> <a href="diraf.html#R3" title="DIRAF:pred.3">are_collinear</a>  holds <br/> ex <font color="Olive" title="b6">x</font> being   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Olive" title="b1">OAS</font> st <br/>( <font color="Olive" title="b6">x</font>,<font color="Olive" title="b2">a</font>,<font color="Olive" title="b5">d</font> <a href="diraf.html#R3" title="DIRAF:pred.3">are_collinear</a>  &amp; <font color="Olive" title="b6">x</font>,<font color="Olive" title="b3">b</font>,<font color="Olive" title="b4">c</font> <a href="diraf.html#R3" title="DIRAF:pred.3">are_collinear</a>  )</div></div>
