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<b>let </b><font color="Maroon">x</font> be   <a href="struct_0.html#NM1">Element</a> of <font color="Maroon">R</font>, <font color="Maroon">y</font> be   <a href="struct_0.html#NM1">Element</a> of <font color="Maroon">R</font>;<br/>

<b>given </b><font color="Maroon">Amp</font> being    <a href="gcd_1.html#M2" target="_self">AmpleSet</a> of <font color="Maroon">R</font><b> such that </b><a NAME="E1:72_1_1"/><i><font color="Green">E20</font></i>: 
 <a href="gcd_1.html#K5" target="_self">gcd</a> <font color="Maroon">x</font>,<font color="Maroon">y</font>,<font color="Maroon">Amp</font> <a href="hidden.html#R1">=</a>  <a href="group_1.html#K2">1.</a> <font color="Maroon">R</font>
 ; <i><font color="Red">:: according to </font></i><a class="ref" href="gcd_1.html#D14" target="_self">GCD_1:def 14</a><br/>

<a NAME="E2:72_1_1"/>
 <a href="gcd_1.html#K5" target="_self">gcd</a> <font color="Maroon">y</font>,<font color="Maroon">x</font>,<font color="Maroon">Amp</font> <a href="hidden.html#R1">=</a>  <a href="group_1.html#K2">1.</a> <font color="Maroon">R</font>
 
<b>by </b><i>, <a class="ref" href="gcd_1.html#D4" target="_self">Def4</a></i>;<br/>
<b>hence </b><a NAME="E3:72_1_1"/>
<font color="Maroon">y</font>,<font color="Maroon">x</font> <a href="gcd_1.html#R6" target="_self">are_co-prime</a> 
 <b>by </b><i/>;<br/>


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