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

<b>let </b><font color="Maroon">c<sub>1</sub></font> be   <a href="nat_1.html#NM1">Nat</a>;<br/><b>let </b><font color="Maroon">c<sub>2</sub></font>, <font color="Maroon">c<sub>3</sub></font> be    <a href="finseq_2.html#M2">Element</a> of  <a href="complsp1.html#K8" target="_self">COMPLEX</a> <font color="Maroon">c<sub>1</sub></font>;<br/>





<b>thus </b><a NAME="E1:68"/>
( <span class="p1"><a href="complsp1.html#K16" target="_self">|.</a><span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="complsp1.html#K13" target="_self">-</a> <font color="Maroon">c<sub>3</sub></font></span>)</span></span><a href="complsp1.html#K16" target="_self">.|</a></span> <a href="hidden.html#R1">=</a> 0 implies <font color="Maroon">c<sub>2</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>3</sub></font> )
 <div><a class="txt" onclick="hs2(this)" href="javascript:()" title="68_1"><b>proof </b></a><div class="add">

<b>assume </b><a NAME="E1:68_1"/>
<span class="p1"><a href="complsp1.html#K16" target="_self">|.</a><span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="complsp1.html#K13" target="_self">-</a> <font color="Maroon">c<sub>3</sub></font></span>)</span></span><a href="complsp1.html#K16" target="_self">.|</a></span> <a href="hidden.html#R1">=</a> 0
 ;<br/>

<a NAME="E2:68_1"/><b>then </b>
<font color="Maroon">c<sub>2</sub></font> <a href="complsp1.html#K13" target="_self">-</a> <font color="Maroon">c<sub>3</sub></font> <a href="hidden.html#R1">=</a>  <a href="complsp1.html#K11" target="_self">0c</a> <font color="Maroon">c<sub>1</sub></font>
 
<b>by </b><i><a class="ref" href="complsp1.html#T64" target="_self">Th64</a></i>;<br/>
<b>hence </b><a NAME="E3:68_1"/>
<font color="Maroon">c<sub>2</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>3</sub></font>
 <b>by </b><i><a class="ref" href="complsp1.html#T44" target="_self">Th44</a></i>;<br/>


</div><b>end;</b></div>

<b>assume </b><a NAME="E2:68"/>
<font color="Maroon">c<sub>2</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>3</sub></font>
 ;<br/>

<a NAME="E3:68"/><b>then </b>
<font color="Maroon">c<sub>2</sub></font> <a href="complsp1.html#K13" target="_self">-</a> <font color="Maroon">c<sub>3</sub></font> <a href="hidden.html#R1">=</a>  <a href="complsp1.html#K11" target="_self">0c</a> <font color="Maroon">c<sub>1</sub></font>
 
<b>by </b><i><a class="ref" href="complsp1.html#T43" target="_self">Th43</a></i>;<br/>
<b>hence </b><a NAME="E4:68"/>
<span class="p1"><a href="complsp1.html#K16" target="_self">|.</a><span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="complsp1.html#K13" target="_self">-</a> <font color="Maroon">c<sub>3</sub></font></span>)</span></span><a href="complsp1.html#K16" target="_self">.|</a></span> <a href="hidden.html#R1">=</a> 0
 <b>by </b><i><a class="ref" href="complsp1.html#T63" target="_self">Th63</a></i>;<br/>


</div>
