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

<b>reconsider </b><font color="Maroon" title="c1">e</font> = 0 as    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of  <a href="numbers.html#K4" title="NUMBERS:func.4">INT</a>  <b>by </b><i><a class="ref" href="int_1.html#D2" title="INT_1:def.2">INT_1:def 2</a></i>;<br/>
<b>reconsider </b><font color="Maroon" title="c2">e</font> = <font color="Maroon" title="c1">e</font> as   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <a href="gr_cy_1.html#K3" title="GR_CY_1:func.3">INT.Group</a>  ;<br/>
<a NAME="E3:27"/>
for <font color="Olive" title="b1">h</font> being  <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <a href="gr_cy_1.html#K3" title="GR_CY_1:func.3">INT.Group</a>  holds <br/> ( <font color="Olive" title="b1">h</font> <a href="group_1.html#K1" title="GROUP_1:func.1">*</a> <font color="Maroon" title="c2">e</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b1">h</font> &amp; <font color="Maroon" title="c2">e</font> <a href="group_1.html#K1" title="GROUP_1:func.1">*</a> <font color="Olive" title="b1">h</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b1">h</font> )
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="27_1"><b>proof </b></a><div class="add">

<b>let </b><font color="Maroon" title="c3">h</font> be   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <a href="gr_cy_1.html#K3" title="GR_CY_1:func.3">INT.Group</a> ;<br/>

<b>reconsider </b><font color="Maroon" title="c4">A</font> = <font color="Maroon" title="c3">h</font> as   <a href="int_1.html#NM1" title="INT_1:NM.1">Integer</a> ;<br/>
<b>thus </b><a NAME="E2:27_1"/>
( <font color="Maroon" title="c3">h</font> <a href="group_1.html#K1" title="GROUP_1:func.1">*</a> <font color="Maroon" title="c2">e</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c3">h</font> &amp; <font color="Maroon" title="c2">e</font> <a href="group_1.html#K1" title="GROUP_1:func.1">*</a> <font color="Maroon" title="c3">h</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c3">h</font> )
 ;<br/>


</div><b>end;</b></div>
<b>hence </b><a NAME="E4:27"/>
 <a href="group_1.html#K2" title="GROUP_1:func.2">1.</a> <a href="gr_cy_1.html#K3" title="GR_CY_1:func.3">INT.Group</a>  <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 0
 <b>by </b><i><a class="ref" href="group_1.html#T10" title="GROUP_1:th.10">GROUP_1:10</a></i>;<br/>


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