<?xml version="1.0"?>
<div><span class="kw">theorem </span><a NAME="T22"><span class="comment"><font color="firebrick">:: FDIFF_3:22</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">x0</font> being   <a href="xreal_0.html#NM1" title="XREAL_0:NM.1">Real</a>  st <font color="Olive" title="b1">f</font> <a href="fdiff_1.html#R1" title="FDIFF_1:pred.1">is_differentiable_in</a> <font color="Olive" title="b2">x0</font> holds <br/>( <font color="Olive" title="b1">f</font> <a href="fdiff_3.html#R3" title="FDIFF_3:pred.3">is_right_differentiable_in</a> <font color="Olive" title="b2">x0</font> &amp; <font color="Olive" title="b1">f</font> <a href="fdiff_3.html#R4" title="FDIFF_3:pred.4">is_left_differentiable_in</a> <font color="Olive" title="b2">x0</font> &amp;  <a href="fdiff_1.html#K1" title="FDIFF_1:func.1">diff</a> (<font color="Olive" title="b1">f</font>,<font color="Olive" title="b2">x0</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="b2">x0</font>) &amp;  <a href="fdiff_1.html#K1" title="FDIFF_1:func.1">diff</a> (<font color="Olive" title="b1">f</font>,<font color="Olive" title="b2">x0</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="b2">x0</font>) )</div></div>
