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<div>:: <span class="kw">deftheorem </span>   defines <a href="lopban_9.html#K8" title="LOPBAN_9:func.8">PreNorms</a> <a onclick="hs(this)" href="javascript:()">LOPBAN_9:def 7 : <br/></a><span> 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">u</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   <a href="lopban_9.html#K8" title="LOPBAN_9:func.8">PreNorms</a> <font color="Olive" title="b4">u</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"> { <span class="default"> <span class="p2"><a href="normsp_0.html#K2" title="NORMSP_0:func.2">||.</a><span class="default"><span class="p3">(<span class="default"><font color="Olive" title="b4">u</font> <a href="lopban_8.html#K2" title="LOPBAN_8:func.2">.</a> (<font color="Olive" title="b5">t</font>,<font color="Olive" title="b6">s</font>)</span>)</span></span><a href="normsp_0.html#K2" title="NORMSP_0:func.2">.||</a></span> where <font color="Olive" title="b5">t</font> is   <a href="rlvect_1.html#NM1" title="RLVECT_1:NM.1">VECTOR</a> of <font color="Olive" title="b1">X</font>, <font color="Olive" title="b6">s</font> is   <a href="rlvect_1.html#NM1" title="RLVECT_1:NM.1">VECTOR</a> of <font color="Olive" title="b2">Y</font> : ( <span class="p1"><a href="normsp_0.html#K2" title="NORMSP_0:func.2">||.</a><span class="default"><font color="Olive" title="b5">t</font></span><a href="normsp_0.html#K2" title="NORMSP_0:func.2">.||</a></span> <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> 1 &amp; <span class="p1"><a href="normsp_0.html#K2" title="NORMSP_0:func.2">||.</a><span class="default"><font color="Olive" title="b6">s</font></span><a href="normsp_0.html#K2" title="NORMSP_0:func.2">.||</a></span> <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> 1 ) </span> } </span> ;<br/></span></div>
