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<div><span class="kw">theorem </span><a NAME="T10"><span class="comment"><font color="firebrick">:: ASYMPT_1:10</font></span><br/></a><div class="add"> for <font color="Olive" title="b1">f</font> being   <a href="seq_1.html#NM1" title="SEQ_1:NM.1">Real_Sequence</a>  st (  for <font color="Olive" title="b2">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>  holds  <font color="Olive" title="b1">f</font> <a href="nat_1.html#K8" title="NAT_1:func.8">.</a> <font color="Olive" title="b2">n</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default">3 <a href="nat_1.html#K2" title="NAT_1:func.2">*</a> <span class="p3">(<span class="default">10 <a href="series_1.html#K5" title="SERIES_1:func.5">to_power</a> 6</span>)</span></span>)</span> <a href="xcmplx_0.html#K6" title="XCMPLX_0:func.6">-</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default">18 <a href="nat_1.html#K2" title="NAT_1:func.2">*</a> <span class="p4">(<span class="default">10 <a href="series_1.html#K5" title="SERIES_1:func.5">to_power</a> 3</span>)</span></span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">*</a> <font color="Olive" title="b2">n</font></span>)</span></span>)</span> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> <span class="p1">(<span class="default">27 <a href="xcmplx_0.html#K3" title="XCMPLX_0:func.3">*</a> <span class="p2">(<span class="default"><font color="Olive" title="b2">n</font> <a href="square_1.html#K1" title="SQUARE_1:func.1">^2</a></span>)</span></span>)</span> ) holds <br/><font color="Olive" title="b1">f</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"><a href="asympt_1.html#K3" title="ASYMPT_1:func.3">seq_n^</a> 2</span>)</span></div></div>
