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<div><span class="kw">theorem </span><span class="lab"><font color="Green" title="E64">Th96</font></span>: <a NAME="T96"><span class="comment"><font color="firebrick">:: DBLSEQ_3:96</font></span><br/></a><div class="add"> for <font color="Olive" title="b1">f</font> being   <a href="funct_2.html#NM1" title="FUNCT_2:NM.1">Function</a> of <span class="p1"><a href="zfmisc_1.html#K2" title="ZFMISC_1:func.2">[:</a><span class="default"><a href="numbers.html#NK1" title="NUMBERS:NK.1">NAT</a>,<a href="numbers.html#NK1" title="NUMBERS:NK.1">NAT</a></span><a href="zfmisc_1.html#K2" title="ZFMISC_1:func.2">:]</a></span>,<a href="numbers.html#K6" title="NUMBERS:func.6">ExtREAL</a>  st (  for <font color="Olive" title="b2">n1</font>, <font color="Olive" title="b3">m1</font>, <font color="Olive" title="b4">n2</font>, <font color="Olive" title="b5">m2</font> being   <a href="ordinal1.html#NM6" title="ORDINAL1:NM.6">Nat</a>  st <font color="Olive" title="b2">n1</font> <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> <font color="Olive" title="b4">n2</font> &amp; <font color="Olive" title="b3">m1</font> <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> <font color="Olive" title="b5">m2</font> holds <br/><font color="Olive" title="b1">f</font> <a href="dblseq_3.html#K6" title="DBLSEQ_3:func.6">.</a> (<font color="Olive" title="b2">n1</font>,<font color="Olive" title="b3">m1</font>) <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> <font color="Olive" title="b1">f</font> <a href="dblseq_3.html#K6" title="DBLSEQ_3:func.6">.</a> (<font color="Olive" title="b4">n2</font>,<font color="Olive" title="b5">m2</font>) ) holds <br/>( <font color="Olive" title="b1">f</font> is  <a href="dblseq_3.html#V12" title="DBLSEQ_3:attr.12">P-convergent</a>  &amp;  <a href="dblseq_3.html#K12" title="DBLSEQ_3:func.12">P-lim</a> <font color="Olive" title="b1">f</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="supinf_2.html#K8" title="SUPINF_2:func.8">sup</a> <span class="p1">(<span class="default"><a href="relset_1.html#K2" title="RELSET_1:func.2">rng</a> <font color="Olive" title="b1">f</font></span>)</span> )</div></div>
