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<div><span class="kw">theorem </span><a NAME="T25"><span class="comment"><font color="firebrick">:: ANPROJ_1:25</font></span><br/></a><div class="add"> for <font color="Olive" title="b1">V</font> being   non  <a href="struct_0.html#V7" title="STRUCT_0:attr.7">trivial</a>  <a href="rlvect_1.html#NM2" title="RLVECT_1:NM.2">RealLinearSpace</a><br/>  for <font color="Olive" title="b2">u</font>, <font color="Olive" title="b3">v</font>, <font color="Olive" title="b4">w</font> being   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Olive" title="b1">V</font>  st  not <font color="Olive" title="b2">u</font> is  <a href="struct_0.html#V9" title="STRUCT_0:attr.9">zero</a>  &amp;  not <font color="Olive" title="b3">v</font> is  <a href="struct_0.html#V9" title="STRUCT_0:attr.9">zero</a>  &amp;  not <font color="Olive" title="b4">w</font> is  <a href="struct_0.html#V9" title="STRUCT_0:attr.9">zero</a>  holds <br/>( <span class="p1"><a href="xtuple_0.html#K3" title="XTUPLE_0:func.3">[</a><span class="default"><span class="p2">(<span class="default"><a href="anproj_1.html#K2" title="ANPROJ_1:func.2">Dir</a> <font color="Olive" title="b2">u</font></span>)</span>,<span class="p2">(<span class="default"><a href="anproj_1.html#K2" title="ANPROJ_1:func.2">Dir</a> <font color="Olive" title="b3">v</font></span>)</span>,<span class="p2">(<span class="default"><a href="anproj_1.html#K2" title="ANPROJ_1:func.2">Dir</a> <font color="Olive" title="b4">w</font></span>)</span></span><a href="xtuple_0.html#K3" title="XTUPLE_0:func.3">]</a></span> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  the <a href="collsp.html#U1" title="COLLSP:sel.1">Collinearity</a> of <span class="p1">(<span class="default"><a href="anproj_1.html#K5" title="ANPROJ_1:func.5">ProjectiveSpace</a> <font color="Olive" title="b1">V</font></span>)</span> iff <font color="Olive" title="b2">u</font>,<font color="Olive" title="b3">v</font>,<font color="Olive" title="b4">w</font> <a href="anproj_1.html#R2" title="ANPROJ_1:pred.2">are_LinDep</a>  )</div></div>
