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<div>:: <span class="kw">deftheorem </span><span class="lab"><font color="Green" title="E7">Def8</font></span>   defines <a href="lopban_9.html#V1" title="LOPBAN_9:attr.1">Lipschitzian</a> <a onclick="hs(this)" href="javascript:()">LOPBAN_9:def 3 : <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">IT</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">IT</font> is  <a href="lopban_9.html#V1" title="LOPBAN_9:attr.1">Lipschitzian</a>  iff  ex <font color="Olive" title="b5">K</font> being   <a href="xreal_0.html#NM1" title="XREAL_0:NM.1">Real</a> st <br/>(  <a href="numbers.html#K5" title="NUMBERS:func.5">0</a>  <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> <font color="Olive" title="b5">K</font> &amp; (  for <font color="Olive" title="b6">x</font> being   <a href="rlvect_1.html#NM1" title="RLVECT_1:NM.1">VECTOR</a> of <font color="Olive" title="b1">X</font><br/>  for <font color="Olive" title="b7">y</font> being   <a href="rlvect_1.html#NM1" title="RLVECT_1:NM.1">VECTOR</a> of <font color="Olive" title="b2">Y</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">IT</font> <a href="lopban_8.html#K2" title="LOPBAN_8:func.2">.</a> (<font color="Olive" title="b6">x</font>,<font color="Olive" title="b7">y</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> <span class="p1">(<span class="default"><font color="Olive" title="b5">K</font> <a href="xcmplx_0.html#K3" title="XCMPLX_0:func.3">*</a> <span class="p2"><a href="normsp_0.html#K2" title="NORMSP_0:func.2">||.</a><span class="default"><font color="Olive" title="b6">x</font></span><a href="normsp_0.html#K2" title="NORMSP_0:func.2">.||</a></span></span>)</span> <a href="xcmplx_0.html#K3" title="XCMPLX_0:func.3">*</a> <span class="p1"><a href="normsp_0.html#K2" title="NORMSP_0:func.2">||.</a><span class="default"><font color="Olive" title="b7">y</font></span><a href="normsp_0.html#K2" title="NORMSP_0:func.2">.||</a></span> ) ) );<br/></span></div>
