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<b>let </b><font color="Maroon">c<sub>1</sub></font>, <font color="Maroon">c<sub>2</sub></font> be   <a href="nat_1.html#NM1">Nat</a>;<br/><b>let </b><font color="Maroon">c<sub>3</sub></font>, <font color="Maroon">c<sub>4</sub></font> be   <a href="int_1.html#NM1">Integer</a>;<br/>







<b>assume </b><a NAME="E1:21"/>
<font color="Maroon">c<sub>3</sub></font> <a href="int_2.html#K3">gcd</a> <font color="Maroon">c<sub>4</sub></font> <a href="hidden.html#R1">=</a> 1
 ;<br/>

<a NAME="E2:21"/><b>then </b><i><font color="Green">E22</font></i>: 
<font color="Maroon">c<sub>3</sub></font>,<font color="Maroon">c<sub>4</sub></font> <a href="int_2.html#R1">are_relative_prime</a> 
 
<b>by </b><i><a class="ref" href="int_2.html#D4">INT_2:def 4</a></i>;<br/>
<a NAME="E3:21"/><b>then </b><i><font color="Green">E23</font></i>: 
<font color="Maroon">c<sub>3</sub></font>,<font color="Maroon">c<sub>4</sub></font> <a href="newton.html#K2">|^</a> <font color="Maroon">c<sub>1</sub></font> <a href="int_2.html#R1">are_relative_prime</a> 
 
<b>by </b><i><a class="ref" href="wsierp_1.html#T15" target="_self">Th15</a></i>;<br/>
<a NAME="E4:21"/>
<font color="Maroon">c<sub>3</sub></font> <a href="newton.html#K2">|^</a> <font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>4</sub></font> <a href="newton.html#K2">|^</a> <font color="Maroon">c<sub>1</sub></font> <a href="int_2.html#R1">are_relative_prime</a> 
 
<b>by </b><i><a class="txt" href="wsierp_1.html#E2:21"><i><font color="Green">E22</font></i></a>, <a class="ref" href="wsierp_1.html#T16" target="_self">Th16</a></i>;<br/>
<b>hence </b><a NAME="E5:21"/>
( <font color="Maroon">c<sub>3</sub></font> <a href="int_2.html#K3">gcd</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>4</sub></font> <a href="newton.html#K2">|^</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="hidden.html#R1">=</a> 1 &amp; <span class="p1">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="newton.html#K2">|^</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="int_2.html#K3">gcd</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>4</sub></font> <a href="newton.html#K2">|^</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="hidden.html#R1">=</a> 1 )
 <b>by </b><i><a class="txt" href="wsierp_1.html#E3:21"><i><font color="Green">E23</font></i></a>, <a class="ref" href="int_2.html#D4">INT_2:def 4</a></i>;<br/>


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