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<b>let </b><font color="Maroon" title="c1">f</font>, <font color="Maroon" title="c2">g</font> be  <a href="asympt_0.html#V4" title="ASYMPT_0:attr.4">eventually-positive</a> <a href="seq_1.html#NM1" title="SEQ_1:NM.1">Real_Sequence</a>;<br/>

<b>assume </b><a NAME="E1:39"/><i><font color="Green" title="E23">A1</font></i>: 
( <font color="Maroon" title="c1">f</font> <a href="seq_1.html#K19" title="SEQ_1:func.19">/"</a> <font color="Maroon" title="c2">g</font> is <a href="seq_2.html#V4" title="SEQ_2:attr.4">convergent</a> &amp;  <a href="seq_2.html#K2" title="SEQ_2:func.2">lim</a> <span class="p1">(<span class="default"><font color="Maroon" title="c1">f</font> <a href="seq_1.html#K19" title="SEQ_1:func.19">/"</a> <font color="Maroon" title="c2">g</font></span>)</span> <a href="xxreal_0.html#NR4" title="XXREAL_0:NR.4">&gt;</a> 0 )
 ;<br/>

<a NAME="E2:39"/><b>then </b><i><font color="Green" title="E24">A2</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>
 
<b>by </b><i><a class="txt" href="asympt_0.html#E29"><i><font color="Green" title="E21">Lm3</font></i></a></i>;<br/>
<a NAME="E3:39"/><i><font color="Green" title="E25">A3</font></i>: 
( <font color="Maroon" title="c2">g</font> <a href="seq_1.html#K19" title="SEQ_1:func.19">/"</a> <font color="Maroon" title="c1">f</font> is <a href="seq_2.html#V4" title="SEQ_2:attr.4">convergent</a> &amp;  <a href="seq_2.html#K2" title="SEQ_2:func.2">lim</a> <span class="p1">(<span class="default"><font color="Maroon" title="c2">g</font> <a href="seq_1.html#K19" title="SEQ_1:func.19">/"</a> <font color="Maroon" title="c1">f</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="seq_2.html#K2" title="SEQ_2:func.2">lim</a> <span class="p2">(<span class="default"><font color="Maroon" title="c1">f</font> <a href="seq_1.html#K19" title="SEQ_1:func.19">/"</a> <font color="Maroon" title="c2">g</font></span>)</span></span>)</span> <a href="real_1.html#K2" title="REAL_1:func.2">"</a>  )
 
<b>by </b><i><a class="txt" href="asympt_0.html#E1:39"><i><font color="Green" title="E23">A1</font></i></a>, <a class="ref" href="asympt_0.html#T2" target="_self" title="ASYMPT_0:th.2">Th2</a></i>;<br/>
<a NAME="E4:39"/>
<span class="p1">(<span class="default"><a href="seq_2.html#K2" title="SEQ_2:func.2">lim</a> <span class="p2">(<span class="default"><font color="Maroon" title="c1">f</font> <a href="seq_1.html#K19" title="SEQ_1:func.19">/"</a> <font color="Maroon" title="c2">g</font></span>)</span></span>)</span> <a href="real_1.html#K2" title="REAL_1:func.2">"</a>  <a href="xxreal_0.html#NR4" title="XXREAL_0:NR.4">&gt;</a> 0
 
<b>by </b><i><a class="txt" href="asympt_0.html#E1:39"><i><font color="Green" title="E23">A1</font></i></a>, <a class="ref" href="xreal_1.html#T124" title="XREAL_1:th.124">XREAL_1:124</a></i>;<br/>
<a NAME="E5:39"/><b>then </b>
<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="c1">f</font>
 
<b>by </b><i><a class="txt" href="asympt_0.html#E3:39"><i><font color="Green" title="E25">A3</font></i></a>, <a class="txt" href="asympt_0.html#E29"><i><font color="Green" title="E21">Lm3</font></i></a></i>;<br/>
<b>hence </b><a NAME="E6:39"/>
 <a href="asympt_0.html#K9" title="ASYMPT_0:func.9">Big_Oh</a> <font color="Maroon" title="c1">f</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="asympt_0.html#K9" title="ASYMPT_0:func.9">Big_Oh</a> <font color="Maroon" title="c2">g</font>
 <b>by </b><i><a class="txt" href="asympt_0.html#E2:39"><i><font color="Green" title="E24">A2</font></i></a>, <a class="txt" href="asympt_0.html#E26"><i><font color="Green" title="E20">Lm2</font></i></a></i>;<br/>


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