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<div><span class="kw">theorem </span><a NAME="T68"><span class="comment"><font color="firebrick">:: PDIFF_5:68</font></span><br/></a><div class="add"> for <font color="Olive" title="b1">u0</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">f1</font>, <font color="Olive" title="b3">f2</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>  st <font color="Olive" title="b2">f1</font> <a href="pdiff_5.html#R2" title="PDIFF_5:pred.2">is_hpartial_differentiable`12_in</a> <font color="Olive" title="b1">u0</font> &amp; <font color="Olive" title="b3">f2</font> <a href="pdiff_5.html#R2" title="PDIFF_5:pred.2">is_hpartial_differentiable`12_in</a> <font color="Olive" title="b1">u0</font> holds <br/><span class="p1">(<span class="default"><a href="pdiff_3.html#K1" title="PDIFF_3:func.1">pdiff1</a> (<font color="Olive" title="b2">f1</font>,1)</span>)</span> <a href="valued_1.html#K20" title="VALUED_1:func.20">(#)</a> <span class="p1">(<span class="default"><a href="pdiff_3.html#K1" title="PDIFF_3:func.1">pdiff1</a> (<font color="Olive" title="b3">f2</font>,1)</span>)</span> <a href="pdiff_1.html#R3" title="PDIFF_1:pred.3">is_partial_differentiable_in</a> <font color="Olive" title="b1">u0</font>,2</div></div>
