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<div><span class="kw">theorem </span><a NAME="T13"><span class="comment"><font color="firebrick">:: LOPBAN_9:13</font></span><br/></a><div class="add"> for <font color="Olive" title="b1">X</font>, <font color="Olive" title="b2">Y</font>, <font color="Olive" title="b3">Z</font> being   <a href="normsp_1.html#NM1" title="NORMSP_1:NM.1">RealNormSpace</a><br/>  for <font color="Olive" title="b4">g</font> being   <a href="lopban_8.html#NM2" title="LOPBAN_8:NM.2">BilinearOperator</a> of <font color="Olive" title="b1">X</font>,<font color="Olive" title="b2">Y</font>,<font color="Olive" title="b3">Z</font> holds <br/> ( <font color="Olive" title="b4">g</font> is  <a href="lopban_9.html#V1" title="LOPBAN_9:attr.1">Lipschitzian</a>  iff  <a href="lopban_9.html#K8" title="LOPBAN_9:func.8">PreNorms</a> <font color="Olive" title="b4">g</font> is  <a href="xxreal_2.html#V4" title="XXREAL_2:attr.4">bounded_above</a>  )</div></div>
