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<div><span class="kw">theorem </span><span class="lab"><font color="Green" title="E8">Th8</font></span>: <a NAME="T9"><span class="comment"><font color="firebrick">:: ANPROJ_8:9</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> holds <br/> ( <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>  iff ( <font color="Olive" title="b2">u</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b3">v</font> or <font color="Olive" title="b2">u</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b4">w</font> or <font color="Olive" title="b3">v</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b4">w</font> or <span class="p1"><a href="domain_1.html#K8" title="DOMAIN_1:func.8">{</a><span class="default"><font color="Olive" title="b2">u</font>,<font color="Olive" title="b3">v</font>,<font color="Olive" title="b4">w</font></span><a href="domain_1.html#K8" title="DOMAIN_1:func.8">}</a></span> is  <a href="rlvect_3.html#NV2" title="RLVECT_3:NV.2">linearly-dependent</a>  ) )</div></div>
