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<div><span class="kw">theorem </span><span class="lab"><font color="Green" title="E19">Th25</font></span>: <a NAME="T24"><span class="comment"><font color="firebrick">:: NDIFF13:24</font></span><br/></a><div class="add"> for <font color="Olive" title="b1">E</font>, <font color="Olive" title="b2">F</font>, <font color="Olive" title="b3">G</font> being   <a href="normsp_1.html#NM1" title="NORMSP_1:NM.1">RealNormSpace</a><br/>  for <font color="Olive" title="b4">Z</font> being   <a href="struct_0.html#NM2" title="STRUCT_0:NM.2">Subset</a> of <font color="Olive" title="b1">E</font><br/>  for <font color="Olive" title="b5">u</font> being   <a href="struct_0.html#NM12" title="STRUCT_0:NM.12">PartFunc</a> of <font color="Olive" title="b1">E</font>,<font color="Olive" title="b2">F</font><br/>  for <font color="Olive" title="b6">L</font> being   <a href="lopban_1.html#V2" title="LOPBAN_1:attr.2">Lipschitzian</a>  <a href="lopban_1.html#NM1" title="LOPBAN_1:NM.1">LinearOperator</a> of <font color="Olive" title="b2">F</font>,<font color="Olive" title="b3">G</font><br/>  for <font color="Olive" title="b7">i</font> being   <a href="ordinal1.html#NM6" title="ORDINAL1:NM.6">Nat</a>  st <font color="Olive" title="b5">u</font> <a href="ndiff_6.html#R1" title="NDIFF_6:pred.1">is_differentiable_on</a> <font color="Olive" title="b7">i</font>,<font color="Olive" title="b4">Z</font> holds <br/>( <font color="Olive" title="b6">L</font> <a href="partfun1.html#K1" title="PARTFUN1:func.1">*</a> <font color="Olive" title="b5">u</font> <a href="ndiff_6.html#R1" title="NDIFF_6:pred.1">is_differentiable_on</a> <font color="Olive" title="b7">i</font>,<font color="Olive" title="b4">Z</font> &amp;  <a href="ndiff_6.html#K6" title="NDIFF_6:func.6">diff</a> (<span class="p1">(<span class="default"><font color="Olive" title="b6">L</font> <a href="partfun1.html#K1" title="PARTFUN1:func.1">*</a> <font color="Olive" title="b5">u</font></span>)</span>,<font color="Olive" title="b7">i</font>,<font color="Olive" title="b4">Z</font>) <a href="relset_1.html#R2" title="RELSET_1:pred.2">=</a> <span class="p1">(<span class="default"><a href="ndiff13.html#K2" title="NDIFF13:func.2">LTRN</a> (<font color="Olive" title="b7">i</font>,<font color="Olive" title="b6">L</font>,<font color="Olive" title="b1">E</font>)</span>)</span> <a href="partfun1.html#K1" title="PARTFUN1:func.1">*</a> <span class="p1">(<span class="default"><a href="ndiff_6.html#K6" title="NDIFF_6:func.6">diff</a> (<font color="Olive" title="b5">u</font>,<font color="Olive" title="b7">i</font>,<font color="Olive" title="b4">Z</font>)</span>)</span> )</div></div>
