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<b>let </b><font color="Maroon">c<sub>1</sub></font> be   <a href="seq_1.html#NM1">Real_Sequence</a>;<br/>

<b>assume </b><a NAME="E1:23"/><i><font color="Green">E21</font></i>: 
( <font color="Maroon">c<sub>1</sub></font> is <a href="seq_2.html#V2">bounded_below</a> &amp; <font color="Maroon">c<sub>1</sub></font> is <a href="partfun3.html#V4">nonnegative</a> )
 ;<br/>

<a NAME="E2:23"/>
for <font color="Olive">b<sub>1</sub></font> being  <a href="nat_1.html#NM1">Nat</a> holds <font color="Maroon">c<sub>1</sub></font> <a href="seq_1.html#K2">.</a> <font color="Olive">b<sub>1</sub></font> <a href="xxreal_0.html#NR2" target="_self">&gt;=</a> 0
 
<b>by </b><i><a class="txt" href="rinfsup1.html#E1:23"><i><font color="Green">E21</font></i></a>, <a class="ref" href="rinfsup1.html#D3" target="_self">Def3</a></i>;<br/>
<b>hence </b><a NAME="E3:23"/>
 <a href="rinfsup1.html#K2" target="_self">inf</a> <font color="Maroon">c<sub>1</sub></font> <a href="xxreal_0.html#NR2" target="_self">&gt;=</a> 0
 <b>by </b><i><a class="ref" href="rinfsup1.html#T10" target="_self">Th10</a></i>;<br/>


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