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

<b>let </b><font color="Maroon" title="c1">n</font> be    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of  <a href="numbers.html#K5" title="NUMBERS:func.5">NAT</a> ;<br/><b>let </b><font color="Maroon" title="c2">z1</font>, <font color="Maroon" title="c3">z2</font> be    <a href="finseq_2.html#M2" title="FINSEQ_2:mode.2">Element</a> of  <a href="complsp1.html#K8" title="COMPLSP1:func.8">COMPLEX</a> <font color="Maroon" title="c1">n</font>;<br/>





<b>thus </b><a NAME="E1:68"/>
( <span class="p1"><a href="complsp1.html#K16" title="COMPLSP1:func.16">|.</a><span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c2">z1</font> <a href="complsp1.html#K13" title="COMPLSP1:func.13">-</a> <font color="Maroon" title="c3">z2</font></span>)</span></span><a href="complsp1.html#K16" title="COMPLSP1:func.16">.|</a></span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 0 implies <font color="Maroon" title="c2">z1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c3">z2</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" title="COMPLSP1:func.16">|.</a><span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c2">z1</font> <a href="complsp1.html#K13" title="COMPLSP1:func.13">-</a> <font color="Maroon" title="c3">z2</font></span>)</span></span><a href="complsp1.html#K16" title="COMPLSP1:func.16">.|</a></span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 0
 ;<br/>

<a NAME="E2:68_1"/><b>then </b>
<font color="Maroon" title="c2">z1</font> <a href="complsp1.html#K13" title="COMPLSP1:func.13">-</a> <font color="Maroon" title="c3">z2</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="complsp1.html#K11" title="COMPLSP1:func.11">0c</a> <font color="Maroon" title="c1">n</font>
 
<b>by </b><i><a class="ref" href="complsp1.html#T64" target="_self" title="COMPLSP1:th.64">Th64</a></i>;<br/>
<b>hence </b><a NAME="E3:68_1"/>
<font color="Maroon" title="c2">z1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c3">z2</font>
 <b>by </b><i><a class="ref" href="complsp1.html#T44" target="_self" title="COMPLSP1:th.44">Th44</a></i>;<br/>


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

<b>assume </b><a NAME="E2:68"/>
<font color="Maroon" title="c2">z1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c3">z2</font>
 ;<br/>

<a NAME="E3:68"/><b>then </b>
<font color="Maroon" title="c2">z1</font> <a href="complsp1.html#K13" title="COMPLSP1:func.13">-</a> <font color="Maroon" title="c3">z2</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="complsp1.html#K11" title="COMPLSP1:func.11">0c</a> <font color="Maroon" title="c1">n</font>
 
<b>by </b><i><a class="ref" href="complsp1.html#T43" target="_self" title="COMPLSP1:th.43">Th43</a></i>;<br/>
<b>hence </b><a NAME="E4:68"/>
<span class="p1"><a href="complsp1.html#K16" title="COMPLSP1:func.16">|.</a><span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c2">z1</font> <a href="complsp1.html#K13" title="COMPLSP1:func.13">-</a> <font color="Maroon" title="c3">z2</font></span>)</span></span><a href="complsp1.html#K16" title="COMPLSP1:func.16">.|</a></span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 0
 <b>by </b><i><a class="ref" href="complsp1.html#T63" target="_self" title="COMPLSP1:th.63">Th63</a></i>;<br/>


</div>
