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<div><span class="kw">theorem </span><a NAME="T41"><span class="comment"><font color="firebrick">:: PDIFF_9:41</font></span><br/></a><div class="add"> for <font color="Olive" title="b1">i</font> being    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of  <a href="numbers.html#NK1" title="NUMBERS:NK.1">NAT</a> <br/>  for <font color="Olive" title="b2">f</font>, <font color="Olive" title="b3">g</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">i</font></span>)</span>,<a href="numbers.html#K1" title="NUMBERS:func.1">REAL</a><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">i</font>  st <font color="Olive" title="b2">f</font> <a href="nfcont_4.html#R2" title="NFCONT_4:pred.2">is_continuous_in</a> <font color="Olive" title="b4">x</font> &amp; <font color="Olive" title="b3">g</font> <a href="nfcont_4.html#R2" title="NFCONT_4:pred.2">is_continuous_in</a> <font color="Olive" title="b4">x</font> holds <br/><font color="Olive" title="b2">f</font> <a href="valued_1.html#K20" title="VALUED_1:func.20">(#)</a> <font color="Olive" title="b3">g</font> <a href="nfcont_4.html#R2" title="NFCONT_4:pred.2">is_continuous_in</a> <font color="Olive" title="b4">x</font></div></div>
