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<div><span class="kw">theorem </span><span class="lab"><font color="Green" title="E21">Th21</font></span>: <a NAME="T21"><span class="comment"><font color="firebrick">:: PDIFF_5:21</font></span><br/></a><div class="add"> for <font color="Olive" title="b1">u</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> 3<br/>  for <font color="Olive" title="b2">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> 3</span>)</span>,<a href="numbers.html#K1" title="NUMBERS:func.1">REAL</a> holds <br/> ( <font color="Olive" title="b2">f</font> <a href="pdiff_5.html#R3" title="PDIFF_5:pred.3">is_hpartial_differentiable`13_in</a> <font color="Olive" title="b1">u</font> iff  <a href="pdiff_3.html#K1" title="PDIFF_3:func.1">pdiff1</a> (<font color="Olive" title="b2">f</font>,1) <a href="pdiff_1.html#R3" title="PDIFF_1:pred.3">is_partial_differentiable_in</a> <font color="Olive" title="b1">u</font>,3 ) <span class="kw">by</span> <span class="lab"><a class="ref" href="pdiff_4.html#T15" onmouseover="rs('pdiff_4/T15')" onmouseout="rh()">PDIFF_4:15</a></span>;<br/></div></div>
