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

<b>let </b><font color="Maroon">x0</font> be   <a href="real_1.html#NM1">Real</a>;<br/><b>let </b><font color="Maroon">h</font> be  <a href="fdiff_1.html#V1">convergent_to_0</a> <a href="seq_1.html#NM1">Real_Sequence</a>;<br/><b>let </b><font color="Maroon">c</font> be  <a href="funct_1.html#V3">constant</a> <a href="seq_1.html#NM1">Real_Sequence</a>;<br/>





<b>assume </b><a NAME="E1:5"/><i><font color="Green">E41</font></i>: 
 <a href="relset_1.html#K5">rng</a> <font color="Maroon">c</font> <a href="hidden.html#R1">=</a> <span class="p1"><a href="tarski.html#K1">{</a><span class="default"><font color="Maroon">x0</font></span><a href="tarski.html#K1">}</a></span>
 ;<br/>

<b>thus </b><a NAME="E2:5"/><i><font color="Green">E42</font></i>: 
<font color="Maroon">c</font> is <a href="seq_2.html#V4">convergent</a>
 <b>by </b><i><a class="ref" href="seq_4.html#T39">SEQ_4:39</a></i>;<br/>

<a NAME="E3:5"/>
<font color="Maroon">x0</font> <a href="hidden.html#R2">in</a>  <a href="relset_1.html#K5">rng</a> <font color="Maroon">c</font>
 
<b>by </b><i>, <a class="ref" href="tarski.html#D1">TARSKI:def 1</a></i>;<br/>
<b>hence </b><a NAME="E4:5"/><i><font color="Green">E43</font></i>: 
 <a href="seq_2.html#K2">lim</a> <font color="Maroon">c</font> <a href="hidden.html#R1">=</a> <font color="Maroon">x0</font>
 <b>by </b><i><a class="ref" href="seq_4.html#T40">SEQ_4:40</a></i>;<br/>

<a NAME="E5:5"/><i><font color="Green">E46</font></i>: 
( <font color="Maroon">h</font> is <a href="seq_2.html#V4">convergent</a> &amp;  <a href="seq_2.html#K2">lim</a> <font color="Maroon">h</font> <a href="hidden.html#R1">=</a> 0 )
 
<b>by </b><i><a class="ref" href="fdiff_1.html#D1">FDIFF_1:def 1</a></i>;<br/>
<b>hence </b><a NAME="E6:5"/>
<font color="Maroon">h</font> <a href="seq_1.html#K9">+</a> <font color="Maroon">c</font> is <a href="seq_2.html#V4">convergent</a>
 <b>by </b><i>, <a class="ref" href="seq_2.html#T19">SEQ_2:19</a></i>;<br/>

<b>thus </b> <a href="seq_2.html#K2">lim</a> <span class="p1">(<span class="default"><font color="Maroon">h</font> <a href="seq_1.html#K9">+</a> <font color="Maroon">c</font></span>)</span> = 
0 <a href="real_1.html#K3">+</a> <font color="Maroon">x0</font>
<b>by </b><i>, , , <a class="ref" href="seq_2.html#T20">SEQ_2:20</a></i>
<br/>.= 
<font color="Maroon">x0</font>

;<br/>


</div>
