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<div><span class="kw">theorem </span><span class="lab"><font color="Green" title="E41">Th49</font></span>: <a NAME="T48"><span class="comment"><font color="firebrick">:: NDIFF13:48</font></span><br/></a><div class="add"> for <font color="Olive" title="b1">E</font>, <font color="Olive" title="b2">F</font> being   <a href="normsp_1.html#NM1" title="NORMSP_1:NM.1">RealNormSpace</a><br/>  for <font color="Olive" title="b3">Z</font> being   non  <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a>  <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="b4">L1</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">L0</font> being   <a href="pre_topc.html#NM2" title="PRE_TOPC:NM.2">Point</a> of <font color="Olive" title="b2">F</font>  st <font color="Olive" title="b3">Z</font> is  <a href="nfcont_1.html#V3" title="NFCONT_1:attr.3">open</a>  &amp; <font color="Olive" title="b4">L1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b3">Z</font> <a href="funcop_1.html#K8" title="FUNCOP_1:func.8">--&gt;</a> <font color="Olive" title="b5">L0</font> holds <br/> for <font color="Olive" title="b6">i</font> being   <a href="ordinal1.html#NM6" title="ORDINAL1:NM.6">Nat</a> holds <br/> (  ex <font color="Olive" title="b7">P</font> being   <a href="pre_topc.html#NM2" title="PRE_TOPC:NM.2">Point</a> of <span class="p1">(<span class="default"><a href="ndiff_6.html#K3" title="NDIFF_6:func.3">diff_SP</a> (<font color="Olive" title="b6">i</font>,<font color="Olive" title="b1">E</font>,<font color="Olive" title="b2">F</font>)</span>)</span> st  <a href="ndiff_6.html#K6" title="NDIFF_6:func.6">diff</a> (<font color="Olive" title="b4">L1</font>,<font color="Olive" title="b6">i</font>,<font color="Olive" title="b3">Z</font>) <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b3">Z</font> <a href="funcop_1.html#K8" title="FUNCOP_1:func.8">--&gt;</a> <font color="Olive" title="b7">P</font> &amp;  <a href="ndiff_6.html#K6" title="NDIFF_6:func.6">diff</a> (<font color="Olive" title="b4">L1</font>,<font color="Olive" title="b6">i</font>,<font color="Olive" title="b3">Z</font>) <a href="ndiff_1.html#R2" title="NDIFF_1:pred.2">is_differentiable_on</a> <font color="Olive" title="b3">Z</font> &amp; <span class="p1">(<span class="default"><a href="ndiff_6.html#K6" title="NDIFF_6:func.6">diff</a> (<font color="Olive" title="b4">L1</font>,<font color="Olive" title="b6">i</font>,<font color="Olive" title="b3">Z</font>)</span>)</span> <a href="ndiff_1.html#K4" title="NDIFF_1:func.4">`|</a> <font color="Olive" title="b3">Z</font> <a href="nfcont_1.html#R3" title="NFCONT_1:pred.3">is_continuous_on</a> <font color="Olive" title="b3">Z</font> )</div></div>
