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<div><span class="kw">theorem </span><a NAME="T40"><span class="comment"><font color="firebrick">:: ASYMPT_1:40</font></span><br/></a><div class="add"> for <font color="Olive" title="b1">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 <font color="Olive" title="b1">F</font> <a href="funct_2.html#R2" title="FUNCT_2:pred.2">=</a> <span class="p1">(<span class="default"><a href="asympt_1.html#K3" title="ASYMPT_1:func.3">seq_n^</a> 1</span>)</span> <a href="valued_1.html#K47" title="VALUED_1:func.47">-</a> <span class="p1">(<span class="default"><a href="seq_1.html#K1" title="SEQ_1:func.1">seq_const</a> 1</span>)</span> holds <br/><span class="p1">(<span class="default"><a href="asympt_0.html#K8" title="ASYMPT_0:func.8">Big_Theta</a> <font color="Olive" title="b1">F</font></span>)</span> <a href="asympt_0.html#K13" title="ASYMPT_0:func.13">+</a> <span class="p1">(<span class="default"><a href="asympt_0.html#K8" title="ASYMPT_0:func.8">Big_Theta</a> <span class="p2">(<span class="default"><a href="asympt_1.html#K3" title="ASYMPT_1:func.3">seq_n^</a> 1</span>)</span></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="asympt_0.html#K8" title="ASYMPT_0:func.8">Big_Theta</a> <span class="p1">(<span class="default"><a href="asympt_1.html#K3" title="ASYMPT_1:func.3">seq_n^</a> 1</span>)</span></div></div>
