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<div><span class="kw">theorem </span><a NAME="T14"><span class="comment"><font color="firebrick">:: FDIFF_12:14</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>, <font color="Olive" title="b3">r</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_3.html#R4" title="FDIFF_3:pred.4">is_left_differentiable_in</a> <font color="Olive" title="b2">x0</font> &amp;  <a href="xtuple_0.html#K10" title="XTUPLE_0:func.10">rng</a> <font color="Olive" title="b1">f</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"><a href="seq_4.html#K1" title="SEQ_4:func.1">{</a><span class="default"><font color="Olive" title="b3">r</font></span><a href="seq_4.html#K1" title="SEQ_4:func.1">}</a></span> holds <br/> <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>) <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="numbers.html#K5" title="NUMBERS:func.5">0</a> </div></div>
