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<div class="add">

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

<b>assume </b><b>that </b><br/><a NAME="E1:9"/><i><font color="Green">E28</font></i>: 
<font color="Maroon">rseq</font> is <a href="seq_2.html#V3">bounded</a>
 <b>and </b><br/><a NAME="E2:9"/><i><font color="Green">E30</font></i>: 
 <a href="pscomp_1.html#K2">sup</a> <span class="p1">(<span class="default"><a href="relset_1.html#K5">rng</a> <span class="p2">(<span class="default"><a href="seq_1.html#K22">abs</a> <font color="Maroon">rseq</font></span>)</span></span>)</span> <a href="hidden.html#R1">=</a> 0
 ;<br/>

<b>let </b><font color="Maroon">n</font> be    <a href="subset_1.html#M2">Element</a> of  <a href="numbers.html#K5">NAT</a> ;<br/>

<a NAME="E3:9"/><i><font color="Green">E31</font></i>: 
 <a href="seq_1.html#K22">abs</a> <font color="Maroon">rseq</font> is <a href="seq_2.html#V3">bounded</a>
 
<b>by </b><i>, <a class="ref" href="seqm_3.html#T70">SEQM_3:70</a></i>;<br/>
<a NAME="E4:9"/>
0 <a href="xxreal_0.html#R1">&lt;=</a> <span class="p1">(<span class="default"><a href="seq_1.html#K22">abs</a> <font color="Maroon">rseq</font></span>)</span> <a href="seq_1.html#K2">.</a> <font color="Maroon">n</font>
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="9_1"><b>proof </b></a><div class="add">

<a NAME="E1:9_1"/>
0 <a href="xxreal_0.html#R1">&lt;=</a>  <a href="complex1.html#K18">abs</a> <span class="p1">(<span class="default"><font color="Maroon">rseq</font> <a href="seq_1.html#K2">.</a> <font color="Maroon">n</font></span>)</span>
 
<b>by </b><i><a class="ref" href="complex1.html#T132">COMPLEX1:132</a></i>;<br/>
<b>hence </b><a NAME="E2:9_1"/>
0 <a href="xxreal_0.html#R1">&lt;=</a> <span class="p1">(<span class="default"><a href="seq_1.html#K22">abs</a> <font color="Maroon">rseq</font></span>)</span> <a href="seq_1.html#K2">.</a> <font color="Maroon">n</font>
 <b>by </b><i><a class="ref" href="seq_1.html#T16">SEQ_1:16</a></i>;<br/>


</div><b>end;</b></div>
<a NAME="E5:9"/><b>then </b>
<span class="p1">(<span class="default"><a href="seq_1.html#K22">abs</a> <font color="Maroon">rseq</font></span>)</span> <a href="seq_1.html#K2">.</a> <font color="Maroon">n</font> <a href="hidden.html#R1">=</a> 0
 
<b>by </b><i>, , </i>;<br/>
<a NAME="E6:9"/><b>then </b>
 <a href="complex1.html#K18">abs</a> <span class="p1">(<span class="default"><font color="Maroon">rseq</font> <a href="seq_1.html#K2">.</a> <font color="Maroon">n</font></span>)</span> <a href="hidden.html#R1">=</a> 0
 
<b>by </b><i><a class="ref" href="seq_1.html#T16">SEQ_1:16</a></i>;<br/>
<b>hence </b><a NAME="E7:9"/>
<font color="Maroon">rseq</font> <a href="seq_1.html#K2">.</a> <font color="Maroon">n</font> <a href="hidden.html#R1">=</a> 0
 <b>by </b><i><a class="ref" href="absvalue.html#T7">ABSVALUE:7</a></i>;<br/>


</div>
