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<div><span class="kw">theorem </span><a NAME="T7"><span class="comment"><font color="firebrick">:: NDIFF13:7</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">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="b5">k</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="b5">k</font>,<font color="Olive" title="b4">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="b5">k</font>,<font color="Olive" title="b4">Z</font>) <a href="nfcont_1.html#R3" title="NFCONT_1:pred.3">is_continuous_on</a> <font color="Olive" title="b4">Z</font> holds <br/>( <font color="Olive" title="b3">f</font> <a href="partfun1.html#K2" title="PARTFUN1:func.2">|</a> <font color="Olive" title="b4">Z</font> <a href="ndiff_6.html#R1" title="NDIFF_6:pred.1">is_differentiable_on</a> <font color="Olive" title="b5">k</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="b3">f</font> <a href="partfun1.html#K2" title="PARTFUN1:func.2">|</a> <font color="Olive" title="b4">Z</font></span>)</span>,<font color="Olive" title="b5">k</font>,<font color="Olive" title="b4">Z</font>) <a href="nfcont_1.html#R3" title="NFCONT_1:pred.3">is_continuous_on</a> <font color="Olive" title="b4">Z</font> ) <span class="kw">by</span> <span class="lab"><a class="ref" href="ndiff13.html#T6" target="_self" onmouseover="rs('ndiff13/T6')" onmouseout="rh()">Th7</a></span>;<br/></div></div>
