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<b>let </b><font color="Maroon" title="c2">f</font> be   <a href="partfun1.html#NM1" title="PARTFUN1:NM.1">PartFunc</a> of  <a href="numbers.html#K1" title="NUMBERS:func.1">REAL</a> , <a href="numbers.html#K1" title="NUMBERS:func.1">REAL</a> ;<br/>

<b>given </b><font color="Maroon" title="c3">r</font> being   <a href="real_1.html#NM1" title="REAL_1:NM.1">Real</a><b> such that </b><a NAME="E2:82"/><i><font color="Green" title="E49">A1</font></i>: 
( <font color="Maroon" title="c2">f</font> <a href="rfunct_2.html#R1" title="RFUNCT_2:pred.1">is_increasing_on</a>  <a href="limfunc1.html#K4" title="LIMFUNC1:func.4">right_open_halfline</a> <font color="Maroon" title="c3">r</font> &amp; not <font color="Maroon" title="c2">f</font> <a href="rfunct_1.html#R1" title="RFUNCT_1:pred.1">is_bounded_above_on</a>  <a href="limfunc1.html#K4" title="LIMFUNC1:func.4">right_open_halfline</a> <font color="Maroon" title="c3">r</font> )
 ;<br/>

<b>assume </b><a NAME="E3:82"/><i><font color="Green" title="E50">A2</font></i>: 
for <font color="Olive" title="b1">r</font> being  <a href="real_1.html#NM1" title="REAL_1:NM.1">Real</a>  ex <font color="Olive" title="b2">g</font> being  <a href="real_1.html#NM1" title="REAL_1:NM.1">Real</a> st <br/>( <font color="Olive" title="b1">r</font> <a href="xxreal_0.html#NR3" title="XXREAL_0:NR.3">&lt;</a> <font color="Olive" title="b2">g</font> &amp; <font color="Olive" title="b2">g</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="relset_1.html#K4" title="RELSET_1:func.4">dom</a> <font color="Maroon" title="c2">f</font> )
 ;<br/>

<a NAME="E4:82"/>
<font color="Maroon" title="c2">f</font> <a href="rfunct_2.html#R3" title="RFUNCT_2:pred.3">is_non_decreasing_on</a>  <a href="limfunc1.html#K4" title="LIMFUNC1:func.4">right_open_halfline</a> <font color="Maroon" title="c3">r</font>
 
<b>by </b><i><a class="txt" href="limfunc1.html#E2:82"><i><font color="Green" title="E49">A1</font></i></a>, <a class="ref" href="rfunct_2.html#T55" title="RFUNCT_2:th.55">RFUNCT_2:55</a></i>;<br/>
<b>hence </b><a NAME="E5:82"/>
<font color="Maroon" title="c2">f</font> is <a href="limfunc1.html#V4" title="LIMFUNC1:attr.4">divergent_in+infty_to+infty</a>
 <b>by </b><i><a class="txt" href="limfunc1.html#E2:82"><i><font color="Green" title="E49">A1</font></i></a>, <a class="txt" href="limfunc1.html#E3:82"><i><font color="Green" title="E50">A2</font></i></a>, <a class="ref" href="limfunc1.html#T95" target="_self" title="LIMFUNC1:th.95">Th95</a></i>;<br/>


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