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

<b>let </b><font color="Maroon" title="c2">seq1</font>, <font color="Maroon" title="c3">seq2</font> be   <a href="comseq_1.html#NM1" title="COMSEQ_1:NM.1">Complex_Sequence</a>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> ( <font color="Maroon" title="c2">seq1</font> is <a href="comseq_2.html#V2" title="COMSEQ_2:attr.2">convergent</a> &amp; <font color="Maroon" title="c3">seq2</font> is <a href="comseq_2.html#V2" title="COMSEQ_2:attr.2">convergent</a> &amp;  <a href="comseq_2.html#K2" title="COMSEQ_2:func.2">lim</a> <span class="p1">(<span class="default"><font color="Maroon" title="c2">seq1</font> <a href="valued_1.html#K46" title="VALUED_1:func.46">-</a> <font color="Maroon" title="c3">seq2</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="complex1.html#K5" title="COMPLEX1:func.5">0c</a>  implies  <a href="comseq_2.html#K2" title="COMSEQ_2:func.2">lim</a> <font color="Maroon" title="c2">seq1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="comseq_2.html#K2" title="COMSEQ_2:func.2">lim</a> <font color="Maroon" title="c3">seq2</font> )</span><br/>



<b>assume </b><a NAME="E1:12"/><i><font color="Green" title="E5">A1</font></i>: 
( <font color="Maroon" title="c2">seq1</font> is <a href="comseq_2.html#V2" title="COMSEQ_2:attr.2">convergent</a> &amp; <font color="Maroon" title="c3">seq2</font> is <a href="comseq_2.html#V2" title="COMSEQ_2:attr.2">convergent</a> &amp;  <a href="comseq_2.html#K2" title="COMSEQ_2:func.2">lim</a> <span class="p1">(<span class="default"><font color="Maroon" title="c2">seq1</font> <a href="valued_1.html#K46" title="VALUED_1:func.46">-</a> <font color="Maroon" title="c3">seq2</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="complex1.html#K5" title="COMPLEX1:func.5">0c</a>  )
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide">  <a href="comseq_2.html#K2" title="COMSEQ_2:func.2">lim</a> <font color="Maroon" title="c2">seq1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="comseq_2.html#K2" title="COMSEQ_2:func.2">lim</a> <font color="Maroon" title="c3">seq2</font></span><br/>

<a NAME="E2:12"/><b>then </b>
 <a href="comseq_2.html#K2" title="COMSEQ_2:func.2">lim</a> <span class="p1">(<span class="default"><font color="Maroon" title="c2">seq1</font> <a href="valued_1.html#K46" title="VALUED_1:func.46">-</a> <font color="Maroon" title="c3">seq2</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="comseq_2.html#K2" title="COMSEQ_2:func.2">lim</a> <font color="Maroon" title="c2">seq1</font></span>)</span> <a href="complex1.html#K11" title="COMPLEX1:func.11">-</a> <span class="p1">(<span class="default"><a href="comseq_2.html#K2" title="COMSEQ_2:func.2">lim</a> <font color="Maroon" title="c3">seq2</font></span>)</span>
 
<b>by </b><i><a class="ref" href="comseq_2.html#T26" title="COMSEQ_2:th.26">COMSEQ_2:26</a></i>;<br/>
<b>hence </b><a NAME="E3:12"/>
 <a href="comseq_2.html#K2" title="COMSEQ_2:func.2">lim</a> <font color="Maroon" title="c2">seq1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="comseq_2.html#K2" title="COMSEQ_2:func.2">lim</a> <font color="Maroon" title="c3">seq2</font>
 <b>by </b><i><a class="txt" href="comseq_3.html#E1:12"><i><font color="Green" title="E5">A1</font></i></a></i>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> verum</span><br/>


</div>
