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<div><span class="kw">theorem </span><a NAME="T42"><span class="comment"><font color="firebrick">:: ASYMPT_1:42</font></span><br/></a><div class="add"> for <font color="Olive" title="b1">c</font> being   non  <a href="xxreal_0.html#V3" title="XXREAL_0:attr.3">negative</a>  <a href="xreal_0.html#NM1" title="XREAL_0:NM.1">Real</a><br/>  for <font color="Olive" title="b2">x</font>, <font color="Olive" title="b3">f</font> being   <a href="asympt_0.html#V2" title="ASYMPT_0:attr.2">eventually-nonnegative</a>  <a href="seq_1.html#NM1" title="SEQ_1:NM.1">Real_Sequence</a>  st  ex <font color="Olive" title="b4">e</font> being   <a href="xreal_0.html#NM1" title="XREAL_0:NM.1">Real</a> ex <font color="Olive" title="b5">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 <br/>( <font color="Olive" title="b4">e</font> <a href="xxreal_0.html#NR4" title="XXREAL_0:NR.4">&gt;</a>  <a href="numbers.html#K5" title="NUMBERS:func.5">0</a>  &amp; (  for <font color="Olive" title="b6">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="b6">n</font> <a href="xxreal_0.html#NR2" title="XXREAL_0:NR.2">&gt;=</a> <font color="Olive" title="b5">N</font> holds <br/><font color="Olive" title="b3">f</font> <a href="nat_1.html#K8" title="NAT_1:func.8">.</a> <font color="Olive" title="b6">n</font> <a href="xxreal_0.html#NR2" title="XXREAL_0:NR.2">&gt;=</a> <font color="Olive" title="b4">e</font> ) ) &amp; <font color="Olive" title="b2">x</font> <a href="tarski.html#R2" title="TARSKI:pred.2">in</a>  <a href="asympt_0.html#K6" title="ASYMPT_0:func.6">Big_Oh</a> <span class="p1">(<span class="default"><font color="Olive" title="b1">c</font> <a href="asympt_0.html#K3" title="ASYMPT_0:func.3">+</a> <font color="Olive" title="b3">f</font></span>)</span> holds <br/><font color="Olive" title="b2">x</font> <a href="tarski.html#R2" title="TARSKI:pred.2">in</a>  <a href="asympt_0.html#K6" title="ASYMPT_0:func.6">Big_Oh</a> <font color="Olive" title="b3">f</font></div></div>
