<?xml version="1.0"?>
<div>:: <span class="kw">deftheorem </span>   defines <a href="fdiff_12.html#R1" title="FDIFF_12:pred.1">is_differentiable_on_interval</a> <a onclick="hs(this)" href="javascript:()">FDIFF_12:def 1 : <br/></a><span> 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">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> 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="b2">I</font> iff ( <font color="Olive" title="b2">I</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a>  <a href="relset_1.html#K1" title="RELSET_1:func.1">dom</a> <font color="Olive" title="b1">f</font> &amp;  <a href="supinf_2.html#K4" title="SUPINF_2:func.4">inf</a> <font color="Olive" title="b2">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="b2">I</font> &amp; (  <a href="supinf_2.html#K4" title="SUPINF_2:func.4">inf</a> <font color="Olive" title="b2">I</font> <a href="tarski.html#R2" title="TARSKI:pred.2">in</a> <font color="Olive" title="b2">I</font> implies <font color="Olive" title="b1">f</font> <a href="fdiff_3.html#R3" title="FDIFF_3:pred.3">is_right_differentiable_in</a>  <a href="seq_4.html#K3" title="SEQ_4:func.3">lower_bound</a> <font color="Olive" title="b2">I</font> ) &amp; (  <a href="supinf_2.html#K5" title="SUPINF_2:func.5">sup</a> <font color="Olive" title="b2">I</font> <a href="tarski.html#R2" title="TARSKI:pred.2">in</a> <font color="Olive" title="b2">I</font> implies <font color="Olive" title="b1">f</font> <a href="fdiff_3.html#R4" title="FDIFF_3:pred.4">is_left_differentiable_in</a>  <a href="seq_4.html#K2" title="SEQ_4:func.2">upper_bound</a> <font color="Olive" title="b2">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> <span class="p1"><a href="measure5.html#K1" title="MEASURE5:func.1">].</a><span class="default"><span class="p2">(<span class="default"><a href="supinf_2.html#K4" title="SUPINF_2:func.4">inf</a> <font color="Olive" title="b2">I</font></span>)</span>,<span class="p2">(<span class="default"><a href="supinf_2.html#K5" title="SUPINF_2:func.5">sup</a> <font color="Olive" title="b2">I</font></span>)</span></span><a href="measure5.html#K1" title="MEASURE5:func.1">.[</a></span> ) );<br/></span></div>
