<?xml version="1.0"?>
<div><span class="kw">theorem </span><span class="lab"><font color="Green" title="E13">Th12</font></span>: <a NAME="T12"><span class="comment"><font color="firebrick">:: RUSUB_4:12</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> holds <br/> (  <a href="rusub_4.html#K1" title="RUSUB_4:func.1">dim</a> <font color="Olive" title="b1">V</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="numbers.html#K5" title="NUMBERS:func.5">0</a>  iff  <a href="rusub_1.html#K2" title="RUSUB_1:func.2">(Omega).</a> <font color="Olive" title="b1">V</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="rusub_1.html#K1" title="RUSUB_1:func.1">(0).</a> <font color="Olive" title="b1">V</font> )</div></div>
