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<div><span class="kw">theorem </span><a NAME="T39"><span class="comment"><font color="firebrick">:: FDIFF_12:39</font></span><br/></a><div class="add"> for <font color="Olive" title="b1">f</font> being   <a href="partfun1.html#NM1" title="PARTFUN1:NM.1">PartFunc</a> of <a href="numbers.html#K1" title="NUMBERS:func.1">REAL</a>,<a href="numbers.html#K1" title="NUMBERS:func.1">REAL</a><br/>  for <font color="Olive" title="b2">Z</font> being   <a href="rcomp_1.html#V3" title="RCOMP_1:attr.3">open</a>  <a href="subset_1.html#NM2" title="SUBSET_1:NM.2">Subset</a> of <a href="numbers.html#K1" title="NUMBERS:func.1">REAL</a><br/>  for <font color="Olive" title="b3">I</font> being   non  <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a>  <a href="measure5.html#NM1" title="MEASURE5:NM.1">Interval</a>  st <font color="Olive" title="b3">I</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Olive" title="b2">Z</font> &amp;  <a href="supinf_2.html#K4" title="SUPINF_2:func.4">inf</a> <font color="Olive" title="b3">I</font> <a href="xxreal_0.html#NR3" title="XXREAL_0:NR.3">&lt;</a>  <a href="supinf_2.html#K5" title="SUPINF_2:func.5">sup</a> <font color="Olive" title="b3">I</font> &amp; <font color="Olive" title="b1">f</font> <a href="fdiff_1.html#R2" title="FDIFF_1:pred.2">is_differentiable_on</a> <font color="Olive" title="b2">Z</font> holds <br/><font color="Olive" title="b1">f</font> <a href="fdiff_12.html#R1" title="FDIFF_12:pred.1">is_differentiable_on_interval</a> <font color="Olive" title="b3">I</font></div></div>
