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<b>let </b><font color="Maroon" title="c1">seq</font> be   <a href="seq_1.html#NM1" title="SEQ_1:NM.1">Real_Sequence</a>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> ( <font color="Maroon" title="c1">seq</font> is <a href="seq_2.html#V2" title="SEQ_2:attr.2">bounded_below</a> &amp; <font color="Maroon" title="c1">seq</font> is <a href="partfun3.html#V4" title="PARTFUN3:attr.4">nonnegative</a> implies  <a href="rinfsup1.html#K2" title="RINFSUP1:func.2">inf</a> <font color="Maroon" title="c1">seq</font> <a href="xxreal_0.html#NR2" title="XXREAL_0:NR.2">&gt;=</a>  <a href="numbers.html#K6" title="NUMBERS:func.6">0</a>  )</span><br/>

<b>assume </b><a NAME="E1:23"/>
( <font color="Maroon" title="c1">seq</font> is <a href="seq_2.html#V2" title="SEQ_2:attr.2">bounded_below</a> &amp; <font color="Maroon" title="c1">seq</font> is <a href="partfun3.html#V4" title="PARTFUN3:attr.4">nonnegative</a> )
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide">  <a href="rinfsup1.html#K2" title="RINFSUP1:func.2">inf</a> <font color="Maroon" title="c1">seq</font> <a href="xxreal_0.html#NR2" title="XXREAL_0:NR.2">&gt;=</a>  <a href="numbers.html#K6" title="NUMBERS:func.6">0</a> </span><br/>

<a NAME="E2:23"/><b>then </b>
for <font color="Olive" title="b1">n</font> being   <a href="subset_1.html#M2" title="SUBSET_1:mode.2">Element</a> of  <a href="numbers.html#K5" title="NUMBERS:func.5">NAT</a>  holds  <font color="Maroon" title="c1">seq</font> <a href="seq_1.html#K1" title="SEQ_1:func.1">.</a> <font color="Olive" title="b1">n</font> <a href="xxreal_0.html#NR2" title="XXREAL_0:NR.2">&gt;=</a>  <a href="numbers.html#K6" title="NUMBERS:func.6">0</a> 
 
<b>by </b><i><a class="ref" href="rinfsup1.html#D3" target="_self" title="RINFSUP1:def.3">Def3</a></i>;<br/>
<b>hence </b><a NAME="E3:23"/>
 <a href="rinfsup1.html#K2" title="RINFSUP1:func.2">inf</a> <font color="Maroon" title="c1">seq</font> <a href="xxreal_0.html#NR2" title="XXREAL_0:NR.2">&gt;=</a>  <a href="numbers.html#K6" title="NUMBERS:func.6">0</a> 
 <b>by </b><i><a class="ref" href="rinfsup1.html#T10" target="_self" title="RINFSUP1:th.10">Th10</a></i>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> verum</span><br/>


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