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<b>let </b><font color="Maroon">c<sub>2</sub></font> be   <a href="partfun1.html#NM1">PartFunc</a> of  <a href="numbers.html#K1">REAL</a> , <a href="numbers.html#K1">REAL</a> ;<br/>

<b>given </b><font color="Maroon">c<sub>3</sub></font> being   <a href="real_1.html#NM1">Real</a><b> such that </b><a NAME="E1:91"/><i><font color="Green">E49</font></i>: 
( <font color="Maroon">c<sub>2</sub></font> <a href="rfunct_2.html#R2">is_decreasing_on</a>  <a href="limfunc1.html#K4" target="_self">right_open_halfline</a> <font color="Maroon">c<sub>3</sub></font> &amp; not <font color="Maroon">c<sub>2</sub></font> <a href="rfunct_1.html#R2">is_bounded_below_on</a>  <a href="limfunc1.html#K4" target="_self">right_open_halfline</a> <font color="Maroon">c<sub>3</sub></font> )
 ;<br/>

<b>assume </b><a NAME="E2:91"/><i><font color="Green">E50</font></i>: 
for <font color="Olive">b<sub>1</sub></font> being  <a href="real_1.html#NM1">Real</a>ex <font color="Olive">b<sub>2</sub></font> being  <a href="real_1.html#NM1">Real</a> st <br/>( <font color="Olive">b<sub>1</sub></font> <a href="xxreal_0.html#NR3" target="_self">&lt;</a> <font color="Olive">b<sub>2</sub></font> &amp; <font color="Olive">b<sub>2</sub></font> <a href="hidden.html#R2">in</a>  <a href="relset_1.html#K4">dom</a> <font color="Maroon">c<sub>2</sub></font> )
 ;<br/>

<a NAME="E3:91"/>
<font color="Maroon">c<sub>2</sub></font> <a href="rfunct_2.html#R4">is_non_increasing_on</a>  <a href="limfunc1.html#K4" target="_self">right_open_halfline</a> <font color="Maroon">c<sub>3</sub></font>
 
<b>by </b><i><a class="txt" href="limfunc1.html#E1:91"><i><font color="Green">E49</font></i></a>, <a class="ref" href="rfunct_2.html#T56">RFUNCT_2:56</a></i>;<br/>
<b>hence </b><a NAME="E4:91"/>
<font color="Maroon">c<sub>2</sub></font> is <a href="limfunc1.html#V5" target="_self">divergent_in+infty_to-infty</a>
 <b>by </b><i><a class="txt" href="limfunc1.html#E1:91"><i><font color="Green">E49</font></i></a>, <a class="txt" href="limfunc1.html#E2:91"><i><font color="Green">E50</font></i></a>, <a class="ref" href="limfunc1.html#T97" target="_self">Th97</a></i>;<br/>


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