<?xml version="1.0"?>
<div><span class="kw">theorem </span><a NAME="T5"><span class="comment"><font color="firebrick">:: PDIFF_5:5</font></span><br/></a><div class="add"> for <font color="Olive" title="b1">x0</font>, <font color="Olive" title="b2">y0</font>, <font color="Olive" title="b3">z0</font> being   <a href="xreal_0.html#NM1" title="XREAL_0:NM.1">Real</a><br/>  for <font color="Olive" title="b4">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="b5">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>  st <font color="Olive" title="b4">u</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"><a href="finseq_1.html#K11" title="FINSEQ_1:func.11">&lt;*</a><span class="default"><font color="Olive" title="b1">x0</font>,<font color="Olive" title="b2">y0</font>,<font color="Olive" title="b3">z0</font></span><a href="finseq_1.html#K11" title="FINSEQ_1:func.11">*&gt;</a></span> &amp; <font color="Olive" title="b5">f</font> <a href="pdiff_5.html#R5" title="PDIFF_5:pred.5">is_hpartial_differentiable`22_in</a> <font color="Olive" title="b4">u</font> holds <br/> <a href="pdiff_2.html#K1" title="PDIFF_2:func.1">SVF1</a> (2,<span class="p1">(<span class="default"><a href="pdiff_3.html#K1" title="PDIFF_3:func.1">pdiff1</a> (<font color="Olive" title="b5">f</font>,2)</span>)</span>,<font color="Olive" title="b4">u</font>) <a href="fdiff_1.html#R1" title="FDIFF_1:pred.1">is_differentiable_in</a> <font color="Olive" title="b2">y0</font></div></div>
