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<b>let </b><font color="Maroon">n</font> be  <a href="ordinal1.html#V7">natural</a>  <a href="ordinal1.html#NM1" target="_self">number</a> ;<br/>

<b>assume </b><a NAME="E1:61"/><i><font color="Green">E19</font></i>: 
0 <a href="xxreal_0.html#NR3" target="_self">&lt;</a> <font color="Maroon">n</font>
 ;<br/>

<b>set </b><font color="Maroon">M</font> =  <a href="int_3.html#K9" target="_self">INT.Ring</a> <font color="Maroon">n</font>;<br/>
<b>let </b><font color="Maroon">e</font> be   <a href="struct_0.html#NM1">Element</a> of <span class="p1">(<span class="default"><a href="int_3.html#K9" target="_self">INT.Ring</a> <font color="Maroon">n</font></span>)</span>, <font color="Maroon">h</font> be   <a href="struct_0.html#NM1">Element</a> of <span class="p1">(<span class="default"><a href="int_3.html#K9" target="_self">INT.Ring</a> <font color="Maroon">n</font></span>)</span>;<br/>

<b>assume </b><a NAME="E2:61"/><i><font color="Green">E22</font></i>: 
<font color="Maroon">e</font> <a href="hidden.html#R1">=</a> 1
 ;<br/>

<b>reconsider </b><font color="Maroon">a</font> = <font color="Maroon">h</font>, <font color="Maroon">b</font> = <font color="Maroon">e</font> as    <a href="subset_1.html#M2">Element</a> of  <a href="gr_cy_1.html#K1">Segm</a> <font color="Maroon">n</font> ;<br/>
<b>reconsider </b><font color="Maroon">a1</font> = <font color="Maroon">a</font> as    <a href="subset_1.html#M2">Element</a> of  <a href="numbers.html#K5">NAT</a>  ;<br/>
<a NAME="E5:61"/><i><font color="Green">E23</font></i>: 
<font color="Maroon">a1</font> <a href="xxreal_0.html#NR3" target="_self">&lt;</a> <font color="Maroon">n</font>
 
<b>by </b><i>, <a class="ref" href="gr_cy_1.html#T10">GR_CY_1:10</a></i>;<br/>
<b>thus </b><font color="Maroon">h</font> <a href="group_1.html#K1">*</a> <font color="Maroon">e</font> = 
<span class="p1">(<span class="default"><font color="Maroon">a</font> <a href="nat_1.html#K2">*</a> 1</span>)</span> <a href="nat_1.html#K6">mod</a> <font color="Maroon">n</font>
<b>by </b><i>, , </i>
<br/>.= 
<font color="Maroon">h</font>
<b>by </b><i>, <a class="ref" href="nat_1.html#T76">NAT_1:76</a></i>
;<br/>

<b>thus </b><font color="Maroon">e</font> <a href="group_1.html#K1">*</a> <font color="Maroon">h</font> = 
<span class="p1">(<span class="default"><font color="Maroon">a</font> <a href="nat_1.html#K2">*</a> 1</span>)</span> <a href="nat_1.html#K6">mod</a> <font color="Maroon">n</font>
<b>by </b><i>, , </i>
<br/>.= 
<font color="Maroon">h</font>
<b>by </b><i>, <a class="ref" href="nat_1.html#T76">NAT_1:76</a></i>
;<br/>


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