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<b>let </b><font color="Maroon">f</font> be  <a href="asympt_0.html#V2" target="_self">eventually-nonnegative</a> <a href="seq_1.html#NM1">Real_Sequence</a>, <font color="Maroon">g</font> be  <a href="asympt_0.html#V2" target="_self">eventually-nonnegative</a> <a href="seq_1.html#NM1">Real_Sequence</a>;<br/>

<b>assume </b><a NAME="E1:55"/>
<font color="Maroon">f</font> <a href="hidden.html#R2">in</a>  <a href="asympt_0.html#K11" target="_self">Big_Theta</a> <font color="Maroon">g</font>
 ;<br/>

<a NAME="E2:55"/><b>then </b>
<font color="Maroon">f</font> <a href="hidden.html#R2">in</a> <span class="p1">(<span class="default"><a href="asympt_0.html#K9" target="_self">Big_Oh</a> <font color="Maroon">g</font></span>)</span> <a href="xboole_0.html#K3">/\</a> <span class="p1">(<span class="default"><a href="asympt_0.html#K10" target="_self">Big_Omega</a> <font color="Maroon">g</font></span>)</span>
 
;<br/>
<a NAME="E3:55"/><b>then </b>
( <font color="Maroon">f</font> <a href="hidden.html#R2">in</a>  <a href="asympt_0.html#K9" target="_self">Big_Oh</a> <font color="Maroon">g</font> &amp; <font color="Maroon">f</font> <a href="hidden.html#R2">in</a>  <a href="asympt_0.html#K10" target="_self">Big_Omega</a> <font color="Maroon">g</font> )
 
<b>by </b><i><a class="ref" href="xboole_0.html#D3">XBOOLE_0:def 3</a></i>;<br/>
<a NAME="E4:55"/><b>then </b>
( <font color="Maroon">g</font> <a href="hidden.html#R2">in</a>  <a href="asympt_0.html#K10" target="_self">Big_Omega</a> <font color="Maroon">f</font> &amp; <font color="Maroon">g</font> <a href="hidden.html#R2">in</a>  <a href="asympt_0.html#K9" target="_self">Big_Oh</a> <font color="Maroon">f</font> )
 
<b>by </b><i/>;<br/>
<a NAME="E5:55"/><b>then </b>
<font color="Maroon">g</font> <a href="hidden.html#R2">in</a> <span class="p1">(<span class="default"><a href="asympt_0.html#K9" target="_self">Big_Oh</a> <font color="Maroon">f</font></span>)</span> <a href="xboole_0.html#K3">/\</a> <span class="p1">(<span class="default"><a href="asympt_0.html#K10" target="_self">Big_Omega</a> <font color="Maroon">f</font></span>)</span>
 
<b>by </b><i><a class="ref" href="xboole_0.html#D3">XBOOLE_0:def 3</a></i>;<br/>
<b>hence </b><a NAME="E6:55"/>
<font color="Maroon">g</font> <a href="hidden.html#R2">in</a>  <a href="asympt_0.html#K11" target="_self">Big_Theta</a> <font color="Maroon">f</font>
 ;<br/>


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