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<div><span class="kw">theorem </span><a NAME="T52"><span class="comment"><font color="firebrick">:: FDIFF_12:52</font></span><br/></a><div class="add"> for <font color="Olive" title="b1">f1</font>, <font color="Olive" title="b2">f2</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="b3">I</font>, <font color="Olive" title="b4">J</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="b1">f1</font> <a href="fdiff_12.html#R1" title="FDIFF_12:pred.1">is_differentiable_on_interval</a> <font color="Olive" title="b3">I</font> &amp; <font color="Olive" title="b2">f2</font> <a href="fdiff_12.html#R1" title="FDIFF_12:pred.1">is_differentiable_on_interval</a> <font color="Olive" title="b4">J</font> &amp; <font color="Olive" title="b1">f1</font> <a href="relat_1.html#K7" title="RELAT_1:func.7">.:</a> <font color="Olive" title="b3">I</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Olive" title="b4">J</font> holds <br/>( <font color="Olive" title="b2">f2</font> <a href="partfun1.html#K1" title="PARTFUN1:func.1">*</a> <font color="Olive" title="b1">f1</font> <a href="fdiff_12.html#R1" title="FDIFF_12:pred.1">is_differentiable_on_interval</a> <font color="Olive" title="b3">I</font> &amp; <span class="p1">(<span class="default"><font color="Olive" title="b2">f2</font> <a href="partfun1.html#K1" title="PARTFUN1:func.1">*</a> <font color="Olive" title="b1">f1</font></span>)</span> <a href="fdiff_12.html#K1" title="FDIFF_12:func.1">`\</a> <font color="Olive" title="b3">I</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Olive" title="b2">f2</font> <a href="fdiff_12.html#K1" title="FDIFF_12:func.1">`\</a> <font color="Olive" title="b4">J</font></span>)</span> <a href="partfun1.html#K1" title="PARTFUN1:func.1">*</a> <font color="Olive" title="b1">f1</font></span>)</span> <a href="valued_1.html#K20" title="VALUED_1:func.20">(#)</a> <span class="p1">(<span class="default"><font color="Olive" title="b1">f1</font> <a href="fdiff_12.html#K1" title="FDIFF_12:func.1">`\</a> <font color="Olive" title="b3">I</font></span>)</span> )</div></div>
