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<span class="kw">let </span><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:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></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="rinfsup1.html#NV1" title="RINFSUP1:NV.1">nonnegative</a>  implies  <a href="rinfsup1.html#K2" title="RINFSUP1:func.2">lower_bound</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/>

<span class="kw">assume </span><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="rinfsup1.html#NV1" title="RINFSUP1:NV.1">nonnegative</a>  )
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide">  <a href="rinfsup1.html#K2" title="RINFSUP1:func.2">lower_bound</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"/><span class="kw">then </span>
 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> 
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="rinfsup1.html#D3" target="_self" title="RINFSUP1:def.3">Def3</a></span>;<br/>
<span class="kw">hence </span><a NAME="E3:23"/>
 <a href="rinfsup1.html#K2" title="RINFSUP1:func.2">lower_bound</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 class="kw">by</span> <span class="lab"><a class="ref" href="rinfsup1.html#T10" target="_self" title="RINFSUP1:th.10">Th10</a></span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> verum</span><br/>


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