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<div><span class="kw">theorem </span><a NAME="T19"><span class="comment"><font color="firebrick">:: PDIFF_6:19</font></span><br/></a><div class="add"> for <font color="Olive" title="b1">m</font>, <font color="Olive" title="b2">n</font> being   non  <a href="ordinal1.html#V8" title="ORDINAL1:attr.8">zero</a>  <a href="ordinal1.html#NM6" title="ORDINAL1:NM.6">Nat</a><br/>  for <font color="Olive" title="b3">f</font> being   <a href="partfun1.html#NM1" title="PARTFUN1:NM.1">PartFunc</a> of <span class="p1">(<span class="default"><a href="euclid.html#K1" title="EUCLID:func.1">REAL</a> <font color="Olive" title="b1">m</font></span>)</span>,<span class="p1">(<span class="default"><a href="euclid.html#K1" title="EUCLID:func.1">REAL</a> <font color="Olive" title="b2">n</font></span>)</span><br/>  for <font color="Olive" title="b4">x</font> being    <a href="finseq_2.html#M2" title="FINSEQ_2:mode.2">Element</a> of  <a href="euclid.html#K1" title="EUCLID:func.1">REAL</a> <font color="Olive" title="b1">m</font>  st <font color="Olive" title="b3">f</font> <a href="pdiff_1.html#R1" title="PDIFF_1:pred.1">is_differentiable_in</a> <font color="Olive" title="b4">x</font> holds <br/> <a href="pdiff_1.html#K8" title="PDIFF_1:func.8">diff</a> (<font color="Olive" title="b3">f</font>,<font color="Olive" title="b4">x</font>) is   <a href="pdiff_6.html#NM1" title="PDIFF_6:NM.1">LinearOperator</a> of <font color="Olive" title="b1">m</font>,<font color="Olive" title="b2">n</font></div></div>
