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<div><span class="kw">theorem </span><span class="lab"><font color="Green" title="E61">Th54</font></span>: <a NAME="T54"><span class="comment"><font color="firebrick">:: MESFUNC5:54</font></span><br/></a><div class="add"> for <font color="Olive" title="b1">L</font> being   <a href="mesfunc5.html#NM1" title="MESFUNC5:NM.1">ExtREAL_sequence</a>  st (  for <font color="Olive" title="b2">n</font>, <font color="Olive" title="b3">m</font> being   <a href="ordinal1.html#NM6" title="ORDINAL1:NM.6">Nat</a>  st <font color="Olive" title="b2">n</font> <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> <font color="Olive" title="b3">m</font> holds <br/><font color="Olive" title="b1">L</font> <a href="nat_1.html#K8" title="NAT_1:func.8">.</a> <font color="Olive" title="b2">n</font> <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> <font color="Olive" title="b1">L</font> <a href="nat_1.html#K8" title="NAT_1:func.8">.</a> <font color="Olive" title="b3">m</font> ) holds <br/>( <font color="Olive" title="b1">L</font> is  <a href="mesfunc5.html#V10" title="MESFUNC5:attr.10">convergent</a>  &amp;  <a href="mesfunc5.html#K2" title="MESFUNC5:func.2">lim</a> <font color="Olive" title="b1">L</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="supinf_2.html#K15" title="SUPINF_2:func.15">rng</a> <font color="Olive" title="b1">L</font></span>)</span> )</div></div>
