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<div><span class="kw">theorem </span><span class="lab"><font color="Green" title="E14">Th21</font></span>: <a NAME="T20"><span class="comment"><font color="firebrick">:: NDIFF13:20</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">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="b5">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="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>  st <font color="Olive" title="b4">u</font> <a href="ndiff_1.html#R2" title="NDIFF_1:pred.2">is_differentiable_on</a> <font color="Olive" title="b5">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="b4">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; (  for <font color="Olive" title="b7">x</font> being   <a href="pre_topc.html#NM2" title="PRE_TOPC:NM.2">Point</a> of <font color="Olive" title="b1">E</font>  st <font color="Olive" title="b7">x</font> <a href="tarski.html#R2" title="TARSKI:pred.2">in</a> <font color="Olive" title="b5">Z</font> holds <br/><span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Olive" title="b6">L</font> <a href="partfun1.html#K1" title="PARTFUN1:func.1">*</a> <font color="Olive" title="b4">u</font></span>)</span> <a href="ndiff_1.html#K4" title="NDIFF_1:func.4">`|</a> <font color="Olive" title="b5">Z</font></span>)</span> <a href="partfun1.html#K7" title="PARTFUN1:func.7">/.</a> <font color="Olive" title="b7">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b6">L</font> <a href="funct_1.html#NK3" title="FUNCT_1:NK.3">*</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Olive" title="b4">u</font> <a href="ndiff_1.html#K4" title="NDIFF_1:func.4">`|</a> <font color="Olive" title="b5">Z</font></span>)</span> <a href="partfun1.html#K7" title="PARTFUN1:func.7">/.</a> <font color="Olive" title="b7">x</font></span>)</span> ) )</div></div>
