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<div><span class="kw">theorem </span><a NAME="T24"><span class="comment"><font color="firebrick">:: ANPROJ_1:24</font></span><br/></a><div class="add"> 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="hidden.html#M1" title="HIDDEN:mode.1">object</a> <br/>  for <font color="Olive" title="b4">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>  st <span class="p1"><a href="xtuple_0.html#K3" title="XTUPLE_0:func.3">[</a><span class="default"><font color="Olive" title="b1">x</font>,<font color="Olive" title="b2">y</font>,<font color="Olive" title="b3">z</font></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="b4">V</font></span>)</span> holds <br/> ex <font color="Olive" title="b5">p</font>, <font color="Olive" title="b6">q</font>, <font color="Olive" title="b7">r</font> being   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Olive" title="b4">V</font> st <br/>( <font color="Olive" title="b1">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="anproj_1.html#K2" title="ANPROJ_1:func.2">Dir</a> <font color="Olive" title="b5">p</font> &amp; <font color="Olive" title="b2">y</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="anproj_1.html#K2" title="ANPROJ_1:func.2">Dir</a> <font color="Olive" title="b6">q</font> &amp; <font color="Olive" title="b3">z</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="anproj_1.html#K2" title="ANPROJ_1:func.2">Dir</a> <font color="Olive" title="b7">r</font> &amp;  not <font color="Olive" title="b5">p</font> is  <a href="struct_0.html#V9" title="STRUCT_0:attr.9">zero</a>  &amp;  not <font color="Olive" title="b6">q</font> is  <a href="struct_0.html#V9" title="STRUCT_0:attr.9">zero</a>  &amp;  not <font color="Olive" title="b7">r</font> is  <a href="struct_0.html#V9" title="STRUCT_0:attr.9">zero</a>  &amp; <font color="Olive" title="b5">p</font>,<font color="Olive" title="b6">q</font>,<font color="Olive" title="b7">r</font> <a href="anproj_1.html#R2" title="ANPROJ_1:pred.2">are_LinDep</a>  ) <span class="kw">by</span> <span class="lab"><a class="ref" href="anproj_1.html#D6" target="_self" onmouseover="rs('anproj_1/D6')" onmouseout="rh()">Def6</a></span>;<br/></div></div>
