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<div>:: <span class="kw">deftheorem </span>   defines <a href="lopban10.html#K16" title="LOPBAN10:func.16">PreNorms</a> <a onclick="hs(this)" href="javascript:()">LOPBAN10:def 14 : <br/></a><span> for <font color="Olive" title="b1">X</font> being   <a href="prvect_2.html#NM3" title="PRVECT_2:NM.3">RealNormSpace-Sequence</a><br/>  for <font color="Olive" title="b2">Y</font> being   <a href="normsp_1.html#NM1" title="NORMSP_1:NM.1">RealNormSpace</a><br/>  for <font color="Olive" title="b3">u</font> being   <a href="lopban10.html#NM2" title="LOPBAN10:NM.2">MultilinearOperator</a> of <font color="Olive" title="b1">X</font>,<font color="Olive" title="b2">Y</font> holds   <a href="lopban10.html#K16" title="LOPBAN10:func.16">PreNorms</a> <font color="Olive" title="b3">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="b3">u</font> <a href="lopban10.html#K9" title="LOPBAN10:func.9">.</a> <font color="Olive" title="b4">t</font></span>)</span></span><a href="normsp_0.html#K2" title="NORMSP_0:func.2">.||</a></span> where <font color="Olive" title="b4">t</font> is   <a href="rlvect_1.html#NM1" title="RLVECT_1:NM.1">VECTOR</a> of <span class="p1">(<span class="default"><a href="prvect_2.html#K10" title="PRVECT_2:func.10">product</a> <font color="Olive" title="b1">X</font></span>)</span> :  for <font color="Olive" title="b5">i</font> being    <a href="subset_1.html#M2" title="SUBSET_1:mode.2">Element</a> of  <a href="finseq_1.html#K4" title="FINSEQ_1:func.4">dom</a> <font color="Olive" title="b1">X</font> holds  <span class="p1"><a href="normsp_0.html#K2" title="NORMSP_0:func.2">||.</a><span class="default"><span class="p2">(<span class="default"><font color="Olive" title="b4">t</font> <a href="lopban10.html#K10" title="LOPBAN10:func.10">.</a> <font color="Olive" title="b5">i</font></span>)</span></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>
