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<b>let </b><font color="Maroon">c<sub>1</sub></font> be   <a href="int_1.html#NM1">Integer</a>;<br/>

<b>assume </b><a NAME="E1:14"/><i><font color="Green">E11</font></i>: 
( <font color="Maroon">c<sub>1</sub></font> <a href="int_1.html#R2">divides</a> 1 or <font color="Maroon">c<sub>1</sub></font> <a href="int_1.html#R2">divides</a>  <a href="real_1.html#K1">-</a> 1 )
 ;<br/>

<a NAME="E2:14"/><i><font color="Green">E12</font></i>: 
(  not <font color="Maroon">c<sub>1</sub></font> <a href="int_1.html#R2">divides</a> 1 or <font color="Maroon">c<sub>1</sub></font> <a href="hidden.html#R1">=</a> 1 or <font color="Maroon">c<sub>1</sub></font> <a href="hidden.html#R1">=</a>  <a href="real_1.html#K1">-</a> 1 )
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="14_1"><b>proof </b></a><div class="add">

<b>assume </b><a NAME="E1:14_1"/>
<font color="Maroon">c<sub>1</sub></font> <a href="int_1.html#R2">divides</a> 1
 ;<br/>

<b>then consider </b><font color="Maroon">c<sub>2</sub></font> being   <a href="int_1.html#NM1">Integer</a><b> such that </b><br/><a NAME="E3:14_1"/><i><font color="Green">E13</font></i>: 
1 <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>1</sub></font> <a href="xcmplx_0.html#K3">*</a> <font color="Maroon">c<sub>2</sub></font>
 <b>by </b><i><a class="ref" href="int_1.html#D9">INT_1:def 9</a></i>;<br/>
<b>thus </b><a NAME="E4:14_1"/>
( <font color="Maroon">c<sub>1</sub></font> <a href="hidden.html#R1">=</a> 1 or <font color="Maroon">c<sub>1</sub></font> <a href="hidden.html#R1">=</a>  <a href="real_1.html#K1">-</a> 1 )
 <b>by </b><i><a class="txt" href="int_2.html#E3:14_1"><i><font color="Green">E13</font></i></a>, <a class="ref" href="int_1.html#T22">INT_1:22</a></i>;<br/>


</div><b>end;</b></div>
<a NAME="E3:14"/>
(  not <font color="Maroon">c<sub>1</sub></font> <a href="int_1.html#R2">divides</a>  <a href="real_1.html#K1">-</a> 1 or <font color="Maroon">c<sub>1</sub></font> <a href="hidden.html#R1">=</a> 1 or <font color="Maroon">c<sub>1</sub></font> <a href="hidden.html#R1">=</a>  <a href="real_1.html#K1">-</a> 1 )
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="14_2"><b>proof </b></a><div class="add">

<b>assume </b><a NAME="E1:14_2"/>
<font color="Maroon">c<sub>1</sub></font> <a href="int_1.html#R2">divides</a>  <a href="real_1.html#K1">-</a> 1
 ;<br/>

<a NAME="E2:14_2"/><b>then </b>
ex <font color="Olive">b<sub>1</sub></font> being  <a href="int_1.html#NM1">Integer</a> st  <a href="real_1.html#K1">-</a> 1 <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>1</sub></font> <a href="xcmplx_0.html#K3">*</a> <font color="Olive">b<sub>1</sub></font>
 
<b>by </b><i><a class="ref" href="int_1.html#D9">INT_1:def 9</a></i>;<br/>
<b>hence </b><a NAME="E3:14_2"/>
( <font color="Maroon">c<sub>1</sub></font> <a href="hidden.html#R1">=</a> 1 or <font color="Maroon">c<sub>1</sub></font> <a href="hidden.html#R1">=</a>  <a href="real_1.html#K1">-</a> 1 )
 <b>by </b><i><a class="ref" href="int_1.html#T23">INT_1:23</a></i>;<br/>


</div><b>end;</b></div>
<b>hence </b><a NAME="E4:14"/>
( <font color="Maroon">c<sub>1</sub></font> <a href="hidden.html#R1">=</a> 1 or <font color="Maroon">c<sub>1</sub></font> <a href="hidden.html#R1">=</a>  <a href="real_1.html#K1">-</a> 1 )
 <b>by </b><i><a class="txt" href="int_2.html#E1:14"><i><font color="Green">E11</font></i></a>, <a class="txt" href="int_2.html#E2:14"><i><font color="Green">E12</font></i></a></i>;<br/>


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