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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="E1:24"/>
( <font color="Maroon">c<sub>1</sub></font> is <a href="seq_2.html#V1">bounded_above</a> &amp; <font color="Maroon">c<sub>1</sub></font> is <a href="partfun3.html#V4">nonnegative</a> )
 ;<br/>

<a NAME="E2:24"/><b>then </b>
( <font color="Maroon">c<sub>1</sub></font> <a href="seq_1.html#K2">.</a> 0 <a href="xxreal_0.html#R1">&lt;=</a>  <a href="rinfsup1.html#K1" target="_self">sup</a> <font color="Maroon">c<sub>1</sub></font> &amp; <font color="Maroon">c<sub>1</sub></font> <a href="seq_1.html#K2">.</a> 0 <a href="xxreal_0.html#NR2" target="_self">&gt;=</a> 0 )
 
<b>by </b><i><a class="ref" href="rinfsup1.html#T7" target="_self">Th7</a>, <a class="ref" href="rinfsup1.html#D3" target="_self">Def3</a></i>;<br/>
<b>hence </b><a NAME="E3:24"/>
 <a href="rinfsup1.html#K1" target="_self">sup</a> <font color="Maroon">c<sub>1</sub></font> <a href="xxreal_0.html#NR2" target="_self">&gt;=</a> 0
 ;<br/>


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