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<div><span class="kw">theorem </span><a NAME="T19"><span class="comment"><font color="firebrick">:: RUSUB_4:19</font></span><br/></a><div class="add"> for <font color="Olive" title="b1">V</font> being   <a href="rusub_4.html#V1" title="RUSUB_4:attr.1">finite-dimensional</a>  <a href="bhsp_1.html#NM1" title="BHSP_1:NM.1">RealUnitarySpace</a><br/>  for <font color="Olive" title="b2">n</font> being    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of  <a href="numbers.html#NK1" title="NUMBERS:NK.1">NAT</a>   st <font color="Olive" title="b2">n</font> <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a>  <a href="rusub_4.html#K1" title="RUSUB_4:func.1">dim</a> <font color="Olive" title="b1">V</font> holds <br/> not <font color="Olive" title="b2">n</font> <a href="rusub_4.html#K2" title="RUSUB_4:func.2">Subspaces_of</a> <font color="Olive" title="b1">V</font> is  <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> </div></div>
