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<div><span class="kw">theorem </span><a NAME="T95"><span class="comment"><font color="firebrick">:: DBLSEQ_3:95</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><br/>  for <font color="Olive" title="b2">r</font> being   <a href="xreal_0.html#NM1" title="XREAL_0:NM.1">Real</a>  st (  for <font color="Olive" title="b3">n</font>, <font color="Olive" title="b4">m</font> being   <a href="ordinal1.html#NM6" title="ORDINAL1:NM.6">Nat</a> holds  <font color="Olive" title="b1">f</font> <a href="dblseq_3.html#K6" title="DBLSEQ_3:func.6">.</a> (<font color="Olive" title="b3">n</font>,<font color="Olive" title="b4">m</font>) <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b2">r</font> ) holds <br/>( <font color="Olive" title="b1">f</font> is  <a href="dblseq_3.html#V1" title="DBLSEQ_3:attr.1">P-convergent_to_finite_number</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> <font color="Olive" title="b2">r</font> )</div></div>
