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<div><span class="kw">theorem </span><a NAME="T71"><span class="comment"><font color="firebrick">:: ASYMPT_1:71</font></span><br/></a><div class="add"> for <font color="Olive" title="b1">f</font>, <font color="Olive" title="b2">g</font> being   <a href="seq_1.html#NM1" title="SEQ_1:NM.1">Real_Sequence</a><br/>  for <font color="Olive" title="b3">N</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>   st (  for <font color="Olive" title="b4">n</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>   st <font color="Olive" title="b4">n</font> <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> <font color="Olive" title="b3">N</font> holds <br/><font color="Olive" title="b1">f</font> <a href="nat_1.html#K8" title="NAT_1:func.8">.</a> <font color="Olive" title="b4">n</font> <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> <font color="Olive" title="b2">g</font> <a href="nat_1.html#K8" title="NAT_1:func.8">.</a> <font color="Olive" title="b4">n</font> ) holds <br/> <a href="series_1.html#K6" title="SERIES_1:func.6">Sum</a> (<font color="Olive" title="b1">f</font>,<font color="Olive" title="b3">N</font>) <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a>  <a href="series_1.html#K6" title="SERIES_1:func.6">Sum</a> (<font color="Olive" title="b2">g</font>,<font color="Olive" title="b3">N</font>) <span class="kw">by</span> <span class="lab"><a class="txt" href="asympt_1.html#E23"><span class="lab"><font color="Green" title="E18">Lm13</font></span></a></span>;<br/></div></div>
