<?xml version="1.0"?>
<div class="add">

<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="E1:29"/>
<font color="Maroon">c<sub>1</sub></font> is <a href="seqm_3.html#V1" target="_self">increasing</a>
 ;<br/>

<a NAME="E2:29"/><b>then </b>
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#R1">&lt;=</a> <font color="Maroon">c<sub>1</sub></font> <a href="seq_1.html#K2">.</a> <span class="p1">(<span class="default"><font color="Olive">b<sub>1</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span>
 
<b>by </b><i><a class="txt" href="seqm_3.html#E10"><i><font color="Green">Lemma10</font></i></a></i>;<br/>
<b>hence </b><a NAME="E3:29"/>
<font color="Maroon">c<sub>1</sub></font> is <a href="seqm_3.html#V3" target="_self">non-decreasing</a>
 <b>by </b><i><a class="txt" href="seqm_3.html#E12"><i><font color="Green">Lemma12</font></i></a></i>;<br/>


</div>
