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<div>:: <span class="kw">deftheorem </span><span class="lab"><font color="Green" title="E13">Def2</font></span>   defines <a href="fdiff_12.html#K1" title="FDIFF_12:func.1">`\</a> <a onclick="hs(this)" href="javascript:()">FDIFF_12:def 2 : <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="xxreal_2.html#V6" title="XXREAL_2:attr.6">interval</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>  st <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> holds <br/> for <font color="Olive">b<sub>3</sub></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> holds <br/> ( <font color="Olive">b<sub>3</sub></font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b1">f</font> <a href="fdiff_12.html#K1" title="FDIFF_12:func.1">`\</a> <font color="Olive" title="b2">I</font> iff (  <a href="relset_1.html#K1" title="RELSET_1:func.1">dom</a> <font color="Olive">b<sub>3</sub></font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b2">I</font> &amp; (  for <font color="Olive" title="b4">x</font> being   <a href="xreal_0.html#NM1" title="XREAL_0:NM.1">Real</a>  st <font color="Olive" title="b4">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Olive" title="b2">I</font> holds <br/>( ( <font color="Olive" title="b4">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="supinf_2.html#K4" title="SUPINF_2:func.4">inf</a> <font color="Olive" title="b2">I</font> implies <font color="Olive">b<sub>3</sub></font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Olive" title="b4">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="fdiff_3.html#K2" title="FDIFF_3:func.2">Rdiff</a> (<font color="Olive" title="b1">f</font>,<font color="Olive" title="b4">x</font>) ) &amp; ( <font color="Olive" title="b4">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="supinf_2.html#K5" title="SUPINF_2:func.5">sup</a> <font color="Olive" title="b2">I</font> implies <font color="Olive">b<sub>3</sub></font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Olive" title="b4">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="fdiff_3.html#K1" title="FDIFF_3:func.1">Ldiff</a> (<font color="Olive" title="b1">f</font>,<font color="Olive" title="b4">x</font>) ) &amp; ( <font color="Olive" title="b4">x</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a>  <a href="supinf_2.html#K4" title="SUPINF_2:func.4">inf</a> <font color="Olive" title="b2">I</font> &amp; <font color="Olive" title="b4">x</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a>  <a href="supinf_2.html#K5" title="SUPINF_2:func.5">sup</a> <font color="Olive" title="b2">I</font> implies <font color="Olive">b<sub>3</sub></font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Olive" title="b4">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="fdiff_1.html#K1" title="FDIFF_1:func.1">diff</a> (<font color="Olive" title="b1">f</font>,<font color="Olive" title="b4">x</font>) ) ) ) ) );<br/></span></div>
