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<span class="kw">let </span><font color="Maroon" title="c4">x</font>, <font color="Maroon" title="c5">y</font> be   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c1">R</font>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> ( <font color="Maroon" title="c4">x</font>,<font color="Maroon" title="c5">y</font> <a href="gcd_1.html#R6" title="GCD_1:pred.6">are_co-prime</a>  implies <font color="Maroon" title="c5">y</font>,<font color="Maroon" title="c4">x</font> <a href="gcd_1.html#R6" title="GCD_1:pred.6">are_co-prime</a>  )</span><br/>

<span class="kw">given </span><font color="Maroon" title="c6">Amp</font> being    <a href="gcd_1.html#M2" title="GCD_1:mode.2">AmpleSet</a> of <font color="Maroon" title="c1">R</font><span class="kw"> such that </span><a NAME="E2:73_1_1"/><span class="lab"><font color="Green" title="E54">A1</font></span>: 
 <a href="gcd_1.html#K5" title="GCD_1:func.5">gcd</a> <font color="Maroon" title="c4">x</font>,<font color="Maroon" title="c5">y</font>,<font color="Maroon" title="c6">Amp</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="struct_0.html#K5" title="STRUCT_0:func.5">1.</a> <font color="Maroon" title="c1">R</font>
 ; <span class="comment"><font color="Red">:: according to </font></span><a class="ref" href="gcd_1.html#D14" target="_self" title="GCD_1:def.14">GCD_1:def 14</a> <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> <font color="Maroon" title="c5">y</font>,<font color="Maroon" title="c4">x</font> <a href="gcd_1.html#R6" title="GCD_1:pred.6">are_co-prime</a> </span><br/>

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 <a href="gcd_1.html#K5" title="GCD_1:func.5">gcd</a> <font color="Maroon" title="c5">y</font>,<font color="Maroon" title="c4">x</font>,<font color="Maroon" title="c6">Amp</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="struct_0.html#K5" title="STRUCT_0:func.5">1.</a> <font color="Maroon" title="c1">R</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:73_1_1"><span class="lab"><font color="Green" title="E54">A1</font></span></a>, <a class="ref" href="gcd_1.html#T30" target="_self" title="GCD_1:th.30">Th30</a></span>;<br/>
<span class="kw">hence </span><a NAME="E4:73_1_1"/>
<font color="Maroon" title="c5">y</font>,<font color="Maroon" title="c4">x</font> <a href="gcd_1.html#R6" title="GCD_1:pred.6">are_co-prime</a> 
 <span class="kw">by</span> <span class="lab"><a class="ref" href="gcd_1.html#D14" target="_self" title="GCD_1:def.14">Def14</a></span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> verum</span><br/>


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