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

<b>let </b><font color="Maroon">c<sub>1</sub></font>, <font color="Maroon">c<sub>2</sub></font> be   <a href="struct_0.html#NM1">Element</a> of <a href="complfld.html#K1" target="_self">F_Complex</a> ;<br/>



<b>reconsider </b><font color="Maroon">c<sub>3</sub></font> = <font color="Maroon">c<sub>1</sub></font>, <font color="Maroon">c<sub>4</sub></font> = <font color="Maroon">c<sub>2</sub></font> as    <a href="subset_1.html#M1">Element</a> of  <a href="numbers.html#K2">COMPLEX</a>  <b>by </b><i><a class="ref" href="complfld.html#D1" target="_self">Def1</a></i>;<br/>
<b>thus </b><a NAME="E2:68"/>
( <span class="p1"><a href="complfld.html#K3" target="_self">|.</a><span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="rlvect_1.html#K6">-</a> <font color="Maroon">c<sub>2</sub></font></span>)</span></span><a href="complfld.html#K3" target="_self">.|</a></span> <a href="hidden.html#R1">=</a> 0 implies <font color="Maroon">c<sub>1</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>2</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"/><i><font color="Green">E14</font></i>: 
<span class="p1"><a href="complfld.html#K3" target="_self">|.</a><span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="rlvect_1.html#K6">-</a> <font color="Maroon">c<sub>2</sub></font></span>)</span></span><a href="complfld.html#K3" target="_self">.|</a></span> <a href="hidden.html#R1">=</a> 0
 ;<br/>

<a NAME="E2:68_1"/>
<font color="Maroon">c<sub>1</sub></font> <a href="rlvect_1.html#K6">-</a> <font color="Maroon">c<sub>2</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>3</sub></font> <a href="complex1.html#K11">-</a> <font color="Maroon">c<sub>4</sub></font>
 
<b>by </b><i><a class="ref" href="complfld.html#T5" target="_self">Th5</a></i>;<br/>
<a NAME="E3:68_1"/><b>then </b>
<span class="p1"><a href="complex1.html#K17">|.</a><span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="complex1.html#K11">-</a> <font color="Maroon">c<sub>4</sub></font></span>)</span></span><a href="complex1.html#K17">.|</a></span> <a href="hidden.html#R1">=</a> 0
 
<b>by </b><i><a class="txt" href="complfld.html#E1:68_1"><i><font color="Green">E14</font></i></a></i>;<br/>
<b>hence </b><a NAME="E4:68_1"/>
<font color="Maroon">c<sub>1</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>2</sub></font>
 <b>by </b><i><a class="ref" href="complex1.html#T147">COMPLEX1:147</a></i>;<br/>


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

<a NAME="E3:68"/>
<font color="Maroon">c<sub>3</sub></font> <a href="complex1.html#K11">-</a> <font color="Maroon">c<sub>4</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>1</sub></font> <a href="rlvect_1.html#K6">-</a> <font color="Maroon">c<sub>2</sub></font>
 
<b>by </b><i><a class="ref" href="complfld.html#T5" target="_self">Th5</a></i>;<br/>
<a NAME="E4:68"/><b>then </b><i><font color="Green">E14</font></i>: 
<span class="p1"><a href="complex1.html#K17">|.</a><span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="complex1.html#K11">-</a> <font color="Maroon">c<sub>4</sub></font></span>)</span></span><a href="complex1.html#K17">.|</a></span> <a href="hidden.html#R1">=</a> <span class="p1"><a href="complfld.html#K3" target="_self">|.</a><span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="rlvect_1.html#K6">-</a> <font color="Maroon">c<sub>2</sub></font></span>)</span></span><a href="complfld.html#K3" target="_self">.|</a></span>
 
;<br/>
<b>assume </b><a NAME="E5:68"/>
<font color="Maroon">c<sub>1</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>2</sub></font>
 ;<br/>

<b>hence </b><a NAME="E6:68"/>
<span class="p1"><a href="complfld.html#K3" target="_self">|.</a><span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="rlvect_1.html#K6">-</a> <font color="Maroon">c<sub>2</sub></font></span>)</span></span><a href="complfld.html#K3" target="_self">.|</a></span> <a href="hidden.html#R1">=</a> 0
 <b>by </b><i><a class="txt" href="complfld.html#E4:68"><i><font color="Green">E14</font></i></a>, <a class="ref" href="complex1.html#T147">COMPLEX1:147</a></i>;<br/>


</div>
