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

<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>;<br/>

<b>assume </b><b>that </b><br/><a NAME="E1:35"/><i><font color="Green" title="E30">A1</font></i>: 
<font color="Maroon" title="c1">seq</font> is <a href="seq_2.html#V4" title="SEQ_2:attr.4">convergent</a>
 <b>and </b><br/><a NAME="E2:35"/><i><font color="Green" title="E31">A2</font></i>: 
 <a href="seq_2.html#K2" title="SEQ_2:func.2">lim</a> <font color="Maroon" title="c1">seq</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> 0
 ;<br/>

<b>let </b><font color="Maroon" title="c2">seq1</font> be   <a href="seq_1.html#NM1" title="SEQ_1:NM.1">Real_Sequence</a>;<br/>

<b>assume </b><b>that </b><br/><a NAME="E3:35"/><i><font color="Green" title="E32">A3</font></i>: 
<font color="Maroon" title="c2">seq1</font> is    <a href="seqm_3.html#M1" title="SEQM_3:mode.1">subsequence</a> of <font color="Maroon" title="c1">seq</font>
 <b>and </b><br/><a NAME="E4:35"/><i><font color="Green" title="E33">A4</font></i>: 
<font color="Maroon" title="c2">seq1</font> <a href="seq_1.html#NR1" title="SEQ_1:NR.1">is_not_0</a> 
 ;<br/>

<a NAME="E5:35"/><i><font color="Green" title="E34">A5</font></i>: 
<font color="Maroon" title="c2">seq1</font> is <a href="seq_2.html#V4" title="SEQ_2:attr.4">convergent</a>
 
<b>by </b><i><a class="txt" href="seq_4.html#E1:35"><i><font color="Green" title="E30">A1</font></i></a>, <a class="txt" href="seq_4.html#E3:35"><i><font color="Green" title="E32">A3</font></i></a>, <a class="ref" href="seq_4.html#T29" target="_self" title="SEQ_4:th.29">Th29</a></i>;<br/>
<a NAME="E6:35"/>
 <a href="seq_2.html#K2" title="SEQ_2:func.2">lim</a> <font color="Maroon" title="c2">seq1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="seq_2.html#K2" title="SEQ_2:func.2">lim</a> <font color="Maroon" title="c1">seq</font>
 
<b>by </b><i><a class="txt" href="seq_4.html#E1:35"><i><font color="Green" title="E30">A1</font></i></a>, <a class="txt" href="seq_4.html#E3:35"><i><font color="Green" title="E32">A3</font></i></a>, <a class="ref" href="seq_4.html#T30" target="_self" title="SEQ_4:th.30">Th30</a></i>;<br/>
<b>hence </b><a NAME="E7:35"/>
 <a href="seq_2.html#K2" title="SEQ_2:func.2">lim</a> <span class="p1">(<span class="default"><font color="Maroon" title="c2">seq1</font> <a href="seq_1.html#K18" title="SEQ_1:func.18">"</a> </span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="seq_2.html#K2" title="SEQ_2:func.2">lim</a> <font color="Maroon" title="c1">seq</font></span>)</span> <a href="real_1.html#K2" title="REAL_1:func.2">"</a> 
 <b>by </b><i><a class="txt" href="seq_4.html#E2:35"><i><font color="Green" title="E31">A2</font></i></a>, <a class="txt" href="seq_4.html#E4:35"><i><font color="Green" title="E33">A4</font></i></a>, <a class="txt" href="seq_4.html#E5:35"><i><font color="Green" title="E34">A5</font></i></a>, <a class="ref" href="seq_2.html#T36" title="SEQ_2:th.36">SEQ_2:36</a></i>;<br/>


</div>
