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<b>let </b><font color="Maroon" title="c1">f</font>, <font color="Maroon" title="c2">g</font>, <font color="Maroon" title="c3">h</font> be  <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>;<br/>

<b>assume </b><b>that </b><br/><a NAME="E1:56"/><i><font color="Green" title="E30">A1</font></i>: 
<font color="Maroon" title="c1">f</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="asympt_0.html#K11" title="ASYMPT_0:func.11">Big_Theta</a> <font color="Maroon" title="c2">g</font>
 <b>and </b><br/><a NAME="E2:56"/><i><font color="Green" title="E31">A2</font></i>: 
<font color="Maroon" title="c2">g</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="asympt_0.html#K11" title="ASYMPT_0:func.11">Big_Theta</a> <font color="Maroon" title="c3">h</font>
 ;<br/>

<a NAME="E3:56"/>
<font color="Maroon" title="c1">f</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <span class="p1">(<span class="default"><a href="asympt_0.html#K9" title="ASYMPT_0:func.9">Big_Oh</a> <font color="Maroon" title="c2">g</font></span>)</span> <a href="xboole_0.html#K3" title="XBOOLE_0:func.3">/\</a> <span class="p1">(<span class="default"><a href="asympt_0.html#K10" title="ASYMPT_0:func.10">Big_Omega</a> <font color="Maroon" title="c2">g</font></span>)</span>
 
<b>by </b><i><a class="txt" href="asympt_0.html#E1:56"><i><font color="Green" title="E30">A1</font></i></a></i>;<br/>
<a NAME="E4:56"/><b>then </b><i><font color="Green" title="E32">A3</font></i>: 
( <font color="Maroon" title="c1">f</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="asympt_0.html#K9" title="ASYMPT_0:func.9">Big_Oh</a> <font color="Maroon" title="c2">g</font> &amp; <font color="Maroon" title="c1">f</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="asympt_0.html#K10" title="ASYMPT_0:func.10">Big_Omega</a> <font color="Maroon" title="c2">g</font> )
 
<b>by </b><i><a class="ref" href="xboole_0.html#D3" title="XBOOLE_0:def.3">XBOOLE_0:def 3</a></i>;<br/>
<a NAME="E5:56"/>
<font color="Maroon" title="c2">g</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <span class="p1">(<span class="default"><a href="asympt_0.html#K9" title="ASYMPT_0:func.9">Big_Oh</a> <font color="Maroon" title="c3">h</font></span>)</span> <a href="xboole_0.html#K3" title="XBOOLE_0:func.3">/\</a> <span class="p1">(<span class="default"><a href="asympt_0.html#K10" title="ASYMPT_0:func.10">Big_Omega</a> <font color="Maroon" title="c3">h</font></span>)</span>
 
<b>by </b><i><a class="txt" href="asympt_0.html#E2:56"><i><font color="Green" title="E31">A2</font></i></a></i>;<br/>
<a NAME="E6:56"/><b>then </b><i><font color="Green" title="E33">A4</font></i>: 
( <font color="Maroon" title="c2">g</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="asympt_0.html#K9" title="ASYMPT_0:func.9">Big_Oh</a> <font color="Maroon" title="c3">h</font> &amp; <font color="Maroon" title="c2">g</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="asympt_0.html#K10" title="ASYMPT_0:func.10">Big_Omega</a> <font color="Maroon" title="c3">h</font> )
 
<b>by </b><i><a class="ref" href="xboole_0.html#D3" title="XBOOLE_0:def.3">XBOOLE_0:def 3</a></i>;<br/>
<a NAME="E7:56"/><b>then </b><i><font color="Green" title="E34">A5</font></i>: 
<font color="Maroon" title="c1">f</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="asympt_0.html#K9" title="ASYMPT_0:func.9">Big_Oh</a> <font color="Maroon" title="c3">h</font>
 
<b>by </b><i><a class="txt" href="asympt_0.html#E4:56"><i><font color="Green" title="E32">A3</font></i></a>, <a class="ref" href="asympt_0.html#T12" target="_self" title="ASYMPT_0:th.12">Th12</a></i>;<br/>
<a NAME="E8:56"/>
<font color="Maroon" title="c1">f</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="asympt_0.html#K10" title="ASYMPT_0:func.10">Big_Omega</a> <font color="Maroon" title="c3">h</font>
 
<b>by </b><i><a class="txt" href="asympt_0.html#E4:56"><i><font color="Green" title="E32">A3</font></i></a>, <a class="txt" href="asympt_0.html#E6:56"><i><font color="Green" title="E33">A4</font></i></a>, <a class="ref" href="asympt_0.html#T21" target="_self" title="ASYMPT_0:th.21">Th21</a></i>;<br/>
<a NAME="E9:56"/><b>then </b>
<font color="Maroon" title="c1">f</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <span class="p1">(<span class="default"><a href="asympt_0.html#K9" title="ASYMPT_0:func.9">Big_Oh</a> <font color="Maroon" title="c3">h</font></span>)</span> <a href="xboole_0.html#K3" title="XBOOLE_0:func.3">/\</a> <span class="p1">(<span class="default"><a href="asympt_0.html#K10" title="ASYMPT_0:func.10">Big_Omega</a> <font color="Maroon" title="c3">h</font></span>)</span>
 
<b>by </b><i><a class="txt" href="asympt_0.html#E7:56"><i><font color="Green" title="E34">A5</font></i></a>, <a class="ref" href="xboole_0.html#D3" title="XBOOLE_0:def.3">XBOOLE_0:def 3</a></i>;<br/>
<b>hence </b><a NAME="E10:56"/>
<font color="Maroon" title="c1">f</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="asympt_0.html#K11" title="ASYMPT_0:func.11">Big_Theta</a> <font color="Maroon" title="c3">h</font>
 ;<br/>


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