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<div><span class="kw">theorem </span><span class="lab"><font color="Green" title="E16">Th12</font></span>: <a NAME="T12"><span class="comment"><font color="firebrick">:: ANPROJ_1:12</font></span><br/></a><div class="add"> for <font color="Olive" title="b1">V</font> being   <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>,<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>  holds <br/>(  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>  &amp;  not  <a href="anproj_1.html#R1" title="ANPROJ_1:pred.1">are_Prop</a> <font color="Olive" title="b2">u</font>,<font color="Olive" title="b3">v</font> &amp;  not  <a href="anproj_1.html#R1" title="ANPROJ_1:pred.1">are_Prop</a> <font color="Olive" title="b3">v</font>,<font color="Olive" title="b4">w</font> &amp;  not  <a href="anproj_1.html#R1" title="ANPROJ_1:pred.1">are_Prop</a> <font color="Olive" title="b4">w</font>,<font color="Olive" title="b2">u</font> ) <span class="kw">by</span> <span class="lab"><a class="ref" href="anproj_1.html#T10" target="_self" onmouseover="rs('anproj_1/T10')" onmouseout="rh()">Th10</a>, <a class="ref" href="anproj_1.html#T11" target="_self" onmouseover="rs('anproj_1/T11')" onmouseout="rh()">Th11</a></span>;<br/></div></div>
