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

<a NAME="E1:24"/><i><font color="Green">E23</font></i>: 
for <font color="Olive">b<sub>1</sub></font>, <font color="Olive">b<sub>2</sub></font> being  <a href="struct_0.html#NM1">Element</a> of <a href="gr_cy_1.html#K3" target="_self">INT.Group</a> <br/>for <font color="Olive">b<sub>3</sub></font>, <font color="Olive">b<sub>4</sub></font> being  <a href="int_1.html#NM1">Integer</a> st <font color="Olive">b<sub>1</sub></font> <a href="hidden.html#R1">=</a> <font color="Olive">b<sub>3</sub></font> &amp; <font color="Olive">b<sub>2</sub></font> <a href="hidden.html#R1">=</a> <font color="Olive">b<sub>4</sub></font> holds <br/><font color="Olive">b<sub>1</sub></font> <a href="group_1.html#K1">*</a> <font color="Olive">b<sub>2</sub></font> <a href="hidden.html#R1">=</a> <font color="Olive">b<sub>3</sub></font> <a href="xcmplx_0.html#K2">+</a> <font color="Olive">b<sub>4</sub></font>
 
<b>by </b><i><a class="ref" href="gr_cy_1.html#T14" target="_self">Th14</a></i>;<br/>
<b>reconsider </b><font color="Maroon">c<sub>1</sub></font> = 0 as    <a href="subset_1.html#M1">Element</a> of  <a href="numbers.html#K4">INT</a>  <b>by </b><i><a class="ref" href="int_1.html#D2">INT_1:def 2</a></i>;<br/>
<b>reconsider </b><font color="Maroon">c<sub>2</sub></font> = <font color="Maroon">c<sub>1</sub></font> as   <a href="struct_0.html#NM1">Element</a> of <a href="gr_cy_1.html#K3" target="_self">INT.Group</a>  ;<br/>
<a NAME="E4:24"/>
for <font color="Olive">b<sub>1</sub></font> being  <a href="struct_0.html#NM1">Element</a> of <a href="gr_cy_1.html#K3" target="_self">INT.Group</a>  holds <br/>( <font color="Olive">b<sub>1</sub></font> <a href="group_1.html#K1">*</a> <font color="Maroon">c<sub>2</sub></font> <a href="hidden.html#R1">=</a> <font color="Olive">b<sub>1</sub></font> &amp; <font color="Maroon">c<sub>2</sub></font> <a href="group_1.html#K1">*</a> <font color="Olive">b<sub>1</sub></font> <a href="hidden.html#R1">=</a> <font color="Olive">b<sub>1</sub></font> )
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="24_1"><b>proof </b></a><div class="add">

<b>let </b><font color="Maroon">c<sub>3</sub></font> be   <a href="struct_0.html#NM1">Element</a> of <a href="gr_cy_1.html#K3" target="_self">INT.Group</a> ;<br/>

<b>reconsider </b><font color="Maroon">c<sub>4</sub></font> = <font color="Maroon">c<sub>3</sub></font> as   <a href="int_1.html#NM1">Integer</a> <b>by </b><i><a class="ref" href="int_1.html#D2">INT_1:def 2</a></i>;<br/>
<i><font color="Green">E24</font></i>: <font color="Maroon">c<sub>3</sub></font> <a href="group_1.html#K1">*</a> <font color="Maroon">c<sub>2</sub></font> = 
<font color="Maroon">c<sub>4</sub></font> <a href="xcmplx_0.html#K2">+</a> 0
<b>by </b><i><a class="txt" href="gr_cy_1.html#E1:24"><i><font color="Green">E23</font></i></a></i>
<br/>.= 
<font color="Maroon">c<sub>3</sub></font>

;<br/>
<font color="Maroon">c<sub>2</sub></font> <a href="group_1.html#K1">*</a> <font color="Maroon">c<sub>3</sub></font> = 
0 <a href="xcmplx_0.html#K2">+</a> <font color="Maroon">c<sub>4</sub></font>
<b>by </b><i><a class="txt" href="gr_cy_1.html#E1:24"><i><font color="Green">E23</font></i></a></i>
<br/>.= 
<font color="Maroon">c<sub>3</sub></font>

;<br/>
<b>hence </b><a NAME="E4:24_1"/>
( <font color="Maroon">c<sub>3</sub></font> <a href="group_1.html#K1">*</a> <font color="Maroon">c<sub>2</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>3</sub></font> &amp; <font color="Maroon">c<sub>2</sub></font> <a href="group_1.html#K1">*</a> <font color="Maroon">c<sub>3</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>3</sub></font> )
 <b>by </b><i><a class="txt" href="gr_cy_1.html#E2:24_1"><i><font color="Green">E24</font></i></a></i>;<br/>


</div><b>end;</b></div>
<b>hence </b><a NAME="E5:24"/>
 <a href="group_1.html#K2">1.</a> <a href="gr_cy_1.html#K3" target="_self">INT.Group</a>  <a href="hidden.html#R1">=</a> 0
 <b>by </b><i><a class="ref" href="group_1.html#T10">GROUP_1:10</a></i>;<br/>


</div>
