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<b>let </b><font color="Maroon">f</font> be  <a href="asympt_0.html#V4" target="_self">eventually-positive</a> <a href="seq_1.html#NM1">Real_Sequence</a>, <font color="Maroon">g</font> be  <a href="asympt_0.html#V4" target="_self">eventually-positive</a> <a href="seq_1.html#NM1">Real_Sequence</a>;<br/>

<b>assume </b><a NAME="E1:39"/><i><font color="Green">E36</font></i>: 
( <font color="Maroon">f</font> <a href="seq_1.html#K19">/"</a> <font color="Maroon">g</font> is <a href="seq_2.html#V4">convergent</a> &amp;  <a href="seq_2.html#K2">lim</a> <span class="p1">(<span class="default"><font color="Maroon">f</font> <a href="seq_1.html#K19">/"</a> <font color="Maroon">g</font></span>)</span> <a href="xxreal_0.html#NR4" target="_self">&gt;</a> 0 )
 ;<br/>

<a NAME="E2:39"/><b>then </b><i><font color="Green">E40</font></i>: 
<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>
 
<b>by </b><i/>;<br/>
<a NAME="E3:39"/><i><font color="Green">E41</font></i>: 
( <font color="Maroon">g</font> <a href="seq_1.html#K19">/"</a> <font color="Maroon">f</font> is <a href="seq_2.html#V4">convergent</a> &amp;  <a href="seq_2.html#K2">lim</a> <span class="p1">(<span class="default"><font color="Maroon">g</font> <a href="seq_1.html#K19">/"</a> <font color="Maroon">f</font></span>)</span> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><a href="seq_2.html#K2">lim</a> <span class="p2">(<span class="default"><font color="Maroon">f</font> <a href="seq_1.html#K19">/"</a> <font color="Maroon">g</font></span>)</span></span>)</span> <a href="real_1.html#K2">"</a>  )
 
<b>by </b><i>, </i>;<br/>
<a NAME="E4:39"/>
<span class="p1">(<span class="default"><a href="seq_2.html#K2">lim</a> <span class="p2">(<span class="default"><font color="Maroon">f</font> <a href="seq_1.html#K19">/"</a> <font color="Maroon">g</font></span>)</span></span>)</span> <a href="real_1.html#K2">"</a>  <a href="xxreal_0.html#NR4" target="_self">&gt;</a> 0
 
<b>by </b><i>, <a class="ref" href="xreal_1.html#T124">XREAL_1:124</a></i>;<br/>
<a NAME="E5:39"/><b>then </b>
<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>, </i>;<br/>
<b>hence </b><a NAME="E6:39"/>
 <a href="asympt_0.html#K9" target="_self">Big_Oh</a> <font color="Maroon">f</font> <a href="hidden.html#R1">=</a>  <a href="asympt_0.html#K9" target="_self">Big_Oh</a> <font color="Maroon">g</font>
 <b>by </b><i>, </i>;<br/>


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