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

<b>let </b><font color="Maroon" title="c2">n</font> be  <a href="ordinal1.html#V7" title="ORDINAL1:attr.7">natural</a>  <a href="ordinal1.html#NM1" title="ORDINAL1:NM.1">number</a> ;<br/>

<b>assume </b><a NAME="E1:61"/><i><font color="Green" title="E43">A1</font></i>: 
0 <a href="xxreal_0.html#NR3" title="XXREAL_0:NR.3">&lt;</a> <font color="Maroon" title="c2">n</font>
 ;<br/>

<b>set </b><font color="Maroon" title="c3">M</font> =  <a href="int_3.html#K9" title="INT_3:func.9">INT.Ring</a> <font color="Maroon" title="c2">n</font>;<br/>
<b>let </b><font color="Maroon" title="c4">e</font>, <font color="Maroon" title="c5">h</font> be   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <span class="p1">(<span class="default"><a href="int_3.html#K9" title="INT_3:func.9">INT.Ring</a> <font color="Maroon" title="c2">n</font></span>)</span>;<br/>

<b>assume </b><a NAME="E2:61"/><i><font color="Green" title="E44">A2</font></i>: 
<font color="Maroon" title="c4">e</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 1
 ;<br/>

<b>reconsider </b><font color="Maroon" title="c6">a</font> = <font color="Maroon" title="c5">h</font>, <font color="Maroon" title="c7">b</font> = <font color="Maroon" title="c4">e</font> as    <a href="subset_1.html#M2" title="SUBSET_1:mode.2">Element</a> of  <a href="gr_cy_1.html#K1" title="GR_CY_1:func.1">Segm</a> <font color="Maroon" title="c2">n</font> ;<br/>
<b>reconsider </b><font color="Maroon" title="c8">a1</font> = <font color="Maroon" title="c6">a</font> as    <a href="subset_1.html#M2" title="SUBSET_1:mode.2">Element</a> of  <a href="numbers.html#K5" title="NUMBERS:func.5">NAT</a>  ;<br/>
<a NAME="E5:61"/><i><font color="Green" title="E45">A3</font></i>: 
<font color="Maroon" title="c8">a1</font> <a href="xxreal_0.html#NR3" title="XXREAL_0:NR.3">&lt;</a> <font color="Maroon" title="c2">n</font>
 
<b>by </b><i><a class="txt" href="int_3.html#E1:61"><i><font color="Green" title="E43">A1</font></i></a>, <a class="ref" href="gr_cy_1.html#T10" title="GR_CY_1:th.10">GR_CY_1:10</a></i>;<br/>
<b>thus </b><font color="Maroon" title="c5">h</font> <a href="group_1.html#K1" title="GROUP_1:func.1">*</a> <font color="Maroon" title="c4">e</font> = 
<span class="p1">(<span class="default"><font color="Maroon" title="c6">a</font> <a href="nat_1.html#K2" title="NAT_1:func.2">*</a> 1</span>)</span> <a href="nat_d.html#K4" title="NAT_D:func.4">mod</a> <font color="Maroon" title="c2">n</font>
<b>by </b><i><a class="txt" href="int_3.html#E2:61"><i><font color="Green" title="E44">A2</font></i></a>, <a class="txt" href="int_3.html#E1:61"><i><font color="Green" title="E43">A1</font></i></a>, <a class="ref" href="int_3.html#D11" target="_self" title="INT_3:def.11">Def11</a></i>
<br/>.= 
<font color="Maroon" title="c5">h</font>
<b>by </b><i><a class="txt" href="int_3.html#E5:61"><i><font color="Green" title="E45">A3</font></i></a>, <a class="ref" href="nat_d.html#T24" title="NAT_D:th.24">NAT_D:24</a></i>
;<br/>

<b>thus </b><font color="Maroon" title="c4">e</font> <a href="group_1.html#K1" title="GROUP_1:func.1">*</a> <font color="Maroon" title="c5">h</font> = 
<span class="p1">(<span class="default"><font color="Maroon" title="c6">a</font> <a href="nat_1.html#K2" title="NAT_1:func.2">*</a> 1</span>)</span> <a href="nat_d.html#K4" title="NAT_D:func.4">mod</a> <font color="Maroon" title="c2">n</font>
<b>by </b><i><a class="txt" href="int_3.html#E2:61"><i><font color="Green" title="E44">A2</font></i></a>, <a class="txt" href="int_3.html#E1:61"><i><font color="Green" title="E43">A1</font></i></a>, <a class="ref" href="int_3.html#D11" target="_self" title="INT_3:def.11">Def11</a></i>
<br/>.= 
<font color="Maroon" title="c5">h</font>
<b>by </b><i><a class="txt" href="int_3.html#E5:61"><i><font color="Green" title="E45">A3</font></i></a>, <a class="ref" href="nat_d.html#T24" title="NAT_D:th.24">NAT_D:24</a></i>
;<br/>


</div>
