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<div><span class="kw">theorem </span><a NAME="T39"><span class="comment"><font color="firebrick">:: NDIFF13:39</font></span><br/></a><div class="add"> for <font color="Olive" title="b1">S</font>, <font color="Olive" title="b2">E</font>, <font color="Olive" title="b3">F</font>, <font color="Olive" title="b4">G</font> being   <a href="normsp_1.html#NM1" title="NORMSP_1:NM.1">RealNormSpace</a><br/>  for <font color="Olive" title="b5">Z</font> being   <a href="struct_0.html#NM2" title="STRUCT_0:NM.2">Subset</a> of <font color="Olive" title="b1">S</font><br/>  for <font color="Olive" title="b6">B</font> being   <a href="lopban_9.html#V1" title="LOPBAN_9:attr.1">Lipschitzian</a>  <a href="lopban_8.html#NM2" title="LOPBAN_8:NM.2">BilinearOperator</a> of <font color="Olive" title="b2">E</font>,<font color="Olive" title="b3">F</font>,<font color="Olive" title="b4">G</font><br/>  for <font color="Olive" title="b7">W</font> being   <a href="struct_0.html#NM12" title="STRUCT_0:NM.12">PartFunc</a> of <font color="Olive" title="b1">S</font>,<font color="Olive" title="b4">G</font><br/>  for <font color="Olive" title="b8">w</font> being   <a href="struct_0.html#NM12" title="STRUCT_0:NM.12">PartFunc</a> of <font color="Olive" title="b1">S</font>,<span class="p1"><a href="prvect_3.html#K9" title="PRVECT_3:func.9">[:</a><span class="default"><font color="Olive" title="b2">E</font>,<font color="Olive" title="b3">F</font></span><a href="prvect_3.html#K9" title="PRVECT_3:func.9">:]</a></span><br/>  for <font color="Olive" title="b9">u</font> being   <a href="struct_0.html#NM12" title="STRUCT_0:NM.12">PartFunc</a> of <font color="Olive" title="b1">S</font>,<font color="Olive" title="b2">E</font><br/>  for <font color="Olive" title="b10">v</font> being   <a href="struct_0.html#NM12" title="STRUCT_0:NM.12">PartFunc</a> of <font color="Olive" title="b1">S</font>,<font color="Olive" title="b3">F</font>  st <font color="Olive" title="b9">u</font> <a href="ndiff_1.html#R2" title="NDIFF_1:pred.2">is_differentiable_on</a> <font color="Olive" title="b5">Z</font> &amp; <font color="Olive" title="b9">u</font> <a href="ndiff_1.html#K4" title="NDIFF_1:func.4">`|</a> <font color="Olive" title="b5">Z</font> <a href="nfcont_1.html#R3" title="NFCONT_1:pred.3">is_continuous_on</a> <font color="Olive" title="b5">Z</font> &amp; <font color="Olive" title="b10">v</font> <a href="ndiff_1.html#R2" title="NDIFF_1:pred.2">is_differentiable_on</a> <font color="Olive" title="b5">Z</font> &amp; <font color="Olive" title="b10">v</font> <a href="ndiff_1.html#K4" title="NDIFF_1:func.4">`|</a> <font color="Olive" title="b5">Z</font> <a href="nfcont_1.html#R3" title="NFCONT_1:pred.3">is_continuous_on</a> <font color="Olive" title="b5">Z</font> &amp; <font color="Olive" title="b7">W</font> <a href="relset_1.html#R2" title="RELSET_1:pred.2">=</a> <font color="Olive" title="b6">B</font> <a href="partfun1.html#K1" title="PARTFUN1:func.1">*</a> <font color="Olive" title="b8">w</font> &amp; <font color="Olive" title="b8">w</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"><a href="funct_3.html#K13" title="FUNCT_3:func.13">&lt;:</a><span class="default"><font color="Olive" title="b9">u</font>,<font color="Olive" title="b10">v</font></span><a href="funct_3.html#K13" title="FUNCT_3:func.13">:&gt;</a></span> holds <br/>( <font color="Olive" title="b7">W</font> <a href="ndiff_1.html#R2" title="NDIFF_1:pred.2">is_differentiable_on</a> <font color="Olive" title="b5">Z</font> &amp; <font color="Olive" title="b7">W</font> <a href="ndiff_1.html#K4" title="NDIFF_1:func.4">`|</a> <font color="Olive" title="b5">Z</font> <a href="nfcont_1.html#R3" title="NFCONT_1:pred.3">is_continuous_on</a> <font color="Olive" title="b5">Z</font> )</div></div>
