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<b>let </b><font color="Maroon">c<sub>2</sub></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">E43</font></i>: 
0 <a href="xxreal_0.html#NR3" target="_self">&lt;</a> <font color="Maroon">c<sub>2</sub></font>
 ;<br/>

<b>set </b><font color="Maroon">c<sub>3</sub></font> =  <a href="int_3.html#K9" target="_self">INT.Ring</a> <font color="Maroon">c<sub>2</sub></font>;<br/>
<b>let </b><font color="Maroon">c<sub>4</sub></font>, <font color="Maroon">c<sub>5</sub></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">c<sub>2</sub></font></span>)</span>;<br/>

<b>assume </b><a NAME="E2:61"/><i><font color="Green">E44</font></i>: 
<font color="Maroon">c<sub>4</sub></font> <a href="hidden.html#R1">=</a> 1
 ;<br/>

<b>reconsider </b><font color="Maroon">c<sub>6</sub></font> = <font color="Maroon">c<sub>5</sub></font>, <font color="Maroon">c<sub>7</sub></font> = <font color="Maroon">c<sub>4</sub></font> as    <a href="subset_1.html#M2">Element</a> of  <a href="gr_cy_1.html#K1">Segm</a> <font color="Maroon">c<sub>2</sub></font> ;<br/>
<b>reconsider </b><font color="Maroon">c<sub>8</sub></font> = <font color="Maroon">c<sub>6</sub></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">E45</font></i>: 
<font color="Maroon">c<sub>8</sub></font> <a href="xxreal_0.html#NR3" target="_self">&lt;</a> <font color="Maroon">c<sub>2</sub></font>
 
<b>by </b><i><a class="txt" href="int_3.html#E1:61"><i><font color="Green">E43</font></i></a>, <a class="ref" href="gr_cy_1.html#T10">GR_CY_1:10</a></i>;<br/>
<b>thus </b><font color="Maroon">c<sub>5</sub></font> <a href="group_1.html#K1">*</a> <font color="Maroon">c<sub>4</sub></font> = 
<span class="p1">(<span class="default"><a href="int_3.html#K7" target="_self">multint</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="binop_1.html#K2">.</a> <font color="Maroon">c<sub>6</sub></font>,<font color="Maroon">c<sub>7</sub></font>

<br/>.= 
<span class="p1">(<span class="default"><font color="Maroon">c<sub>6</sub></font> <a href="nat_1.html#K2">*</a> 1</span>)</span> <a href="nat_1.html#K4">mod</a> <font color="Maroon">c<sub>2</sub></font>
<b>by </b><i><a class="txt" href="int_3.html#E2:61"><i><font color="Green">E44</font></i></a>, <a class="txt" href="int_3.html#E1:61"><i><font color="Green">E43</font></i></a>, <a class="ref" href="int_3.html#D11" target="_self">Def11</a></i>
<br/>.= 
<font color="Maroon">c<sub>5</sub></font>
<b>by </b><i><a class="txt" href="int_3.html#E5:61"><i><font color="Green">E45</font></i></a>, <a class="ref" href="nat_1.html#T76">NAT_1:76</a></i>
;<br/>

<b>thus </b><font color="Maroon">c<sub>4</sub></font> <a href="group_1.html#K1">*</a> <font color="Maroon">c<sub>5</sub></font> = 
<span class="p1">(<span class="default"><a href="int_3.html#K7" target="_self">multint</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="binop_1.html#K2">.</a> <font color="Maroon">c<sub>7</sub></font>,<font color="Maroon">c<sub>6</sub></font>

<br/>.= 
<span class="p1">(<span class="default"><font color="Maroon">c<sub>6</sub></font> <a href="nat_1.html#K2">*</a> 1</span>)</span> <a href="nat_1.html#K4">mod</a> <font color="Maroon">c<sub>2</sub></font>
<b>by </b><i><a class="txt" href="int_3.html#E2:61"><i><font color="Green">E44</font></i></a>, <a class="txt" href="int_3.html#E1:61"><i><font color="Green">E43</font></i></a>, <a class="ref" href="int_3.html#D11" target="_self">Def11</a></i>
<br/>.= 
<font color="Maroon">c<sub>5</sub></font>
<b>by </b><i><a class="txt" href="int_3.html#E5:61"><i><font color="Green">E45</font></i></a>, <a class="ref" href="nat_1.html#T76">NAT_1:76</a></i>
;<br/>


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