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<div><span class="kw">theorem </span><span class="lab"><font color="Green" title="E22">Th24</font></span>: <a NAME="T16"><span class="comment"><font color="firebrick">:: DUALSP04:16</font></span><br/></a><div class="add"> for <font color="Olive" title="b1">X</font> being   <a href="bhsp_1.html#NM1" title="BHSP_1:NM.1">RealUnitarySpace</a><br/>  for <font color="Olive" title="b2">f</font> being   <a href="bhsp_6.html#V2" title="BHSP_6:attr.2">Lipschitzian</a>  <a href="hahnban.html#NM3" title="HAHNBAN:NM.3">linear-Functional</a> of <font color="Olive" title="b1">X</font> holds  <span class="p1">(<span class="default"><a href="dualsp04.html#K6" title="DUALSP04:func.6">BoundedLinearFunctionalsNorm</a> <font color="Olive" title="b1">X</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Olive" title="b2">f</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="seq_4.html#K2" title="SEQ_4:func.2">upper_bound</a> <span class="p1">(<span class="default"><a href="dualsp04.html#K5" title="DUALSP04:func.5">PreNorms</a> <font color="Olive" title="b2">f</font></span>)</span></div></div>
