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<b>let </b><font color="Maroon">c<sub>1</sub></font>, <font color="Maroon">c<sub>2</sub></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><b>that </b><br/><a NAME="E1:60"/><i><font color="Green">E30</font></i>: 
<font color="Maroon">c<sub>1</sub></font> <a href="seq_1.html#K19">/"</a> <font color="Maroon">c<sub>2</sub></font> is <a href="seq_2.html#V4">convergent</a>
 <b>and </b><br/><a NAME="E2:60"/><i><font color="Green">E31</font></i>: 
 <a href="seq_2.html#K2">lim</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="seq_1.html#K19">/"</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="hidden.html#R1">=</a> 0
 ;<br/>

<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="60_1"><b>now </b></a><div class="add"><b>assume </b><a NAME="E1:60_1"/>
<font color="Maroon">c<sub>1</sub></font> <a href="hidden.html#R2">in</a>  <a href="asympt_0.html#K11" target="_self">Big_Theta</a> <font color="Maroon">c<sub>2</sub></font>
 ;<br/><a NAME="E2:60_1"/><b>then </b>
<font color="Maroon">c<sub>1</sub></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">c<sub>2</sub></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">c<sub>2</sub></font></span>)</span>
 ;<br/><a NAME="E3:60_1"/><b>then </b>
<font color="Maroon">c<sub>1</sub></font> <a href="hidden.html#R2">in</a>  <a href="asympt_0.html#K10" target="_self">Big_Omega</a> <font color="Maroon">c<sub>2</sub></font>
 <b>by </b><i><a class="ref" href="xboole_0.html#D3">XBOOLE_0:def 3</a></i>;<br/><a NAME="E4:60_1"/><b>then </b>
<font color="Maroon">c<sub>2</sub></font> <a href="hidden.html#R2">in</a>  <a href="asympt_0.html#K9" target="_self">Big_Oh</a> <font color="Maroon">c<sub>1</sub></font>
 <b>by </b><i><a class="ref" href="asympt_0.html#T19" target="_self">Th19</a></i>;<br/><b>hence </b><a NAME="E5:60_1"/>
contradiction
 <b>by </b><i><a class="txt" href="asympt_0.html#E1:60"><i><font color="Green">E30</font></i></a>, <a class="txt" href="asympt_0.html#E2:60"><i><font color="Green">E31</font></i></a>, <a class="ref" href="asympt_0.html#T16" target="_self">Th16</a></i>;<br/></div><b>end;</b></div>
<b>hence </b><a NAME="E4:60"/>
( <font color="Maroon">c<sub>1</sub></font> <a href="hidden.html#R2">in</a>  <a href="asympt_0.html#K9" target="_self">Big_Oh</a> <font color="Maroon">c<sub>2</sub></font> &amp; not <font color="Maroon">c<sub>1</sub></font> <a href="hidden.html#R2">in</a>  <a href="asympt_0.html#K11" target="_self">Big_Theta</a> <font color="Maroon">c<sub>2</sub></font> )
 <b>by </b><i><a class="txt" href="asympt_0.html#E1:60"><i><font color="Green">E30</font></i></a>, <a class="txt" href="asympt_0.html#E2:60"><i><font color="Green">E31</font></i></a>, <a class="ref" href="asympt_0.html#T16" target="_self">Th16</a></i>;<br/>


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