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<div><span class="kw">theorem </span><span class="lab"><font color="Green" title="E6">Th10</font></span>: <a NAME="T9"><span class="comment"><font color="firebrick">:: NDIFF13:9</font></span><br/></a><div class="add"> for <font color="Olive" title="b1">S</font>, <font color="Olive" title="b2">T</font> being   <a href="normsp_1.html#NM1" title="NORMSP_1:NM.1">RealNormSpace</a><br/>  for <font color="Olive" title="b3">f</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">T</font><br/>  for <font color="Olive" title="b4">X</font>, <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>  st <font color="Olive" title="b5">Z</font> is  <a href="nfcont_1.html#V3" title="NFCONT_1:attr.3">open</a>  &amp; <font color="Olive" title="b5">Z</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Olive" title="b4">X</font> holds <br/> for <font color="Olive" title="b6">i</font> being   <a href="ordinal1.html#NM6" title="ORDINAL1:NM.6">Nat</a>  st <font color="Olive" title="b3">f</font> <a href="ndiff_6.html#R1" title="NDIFF_6:pred.1">is_differentiable_on</a> <font color="Olive" title="b6">i</font>,<font color="Olive" title="b4">X</font> &amp;  <a href="ndiff_6.html#K6" title="NDIFF_6:func.6">diff</a> (<font color="Olive" title="b3">f</font>,<font color="Olive" title="b6">i</font>,<font color="Olive" title="b4">X</font>) <a href="nfcont_1.html#R3" title="NFCONT_1:pred.3">is_continuous_on</a> <font color="Olive" title="b4">X</font> holds <br/>( <font color="Olive" title="b3">f</font> <a href="ndiff_6.html#R1" title="NDIFF_6:pred.1">is_differentiable_on</a> <font color="Olive" title="b6">i</font>,<font color="Olive" title="b5">Z</font> &amp;  <a href="ndiff_6.html#K6" title="NDIFF_6:func.6">diff</a> (<font color="Olive" title="b3">f</font>,<font color="Olive" title="b6">i</font>,<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>
