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<b>let </b><font color="Maroon" title="c1">m</font>, <font color="Maroon" title="c2">p</font> be   <a href="nat_1.html#NM1" title="NAT_1:NM.1">Nat</a>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> (  not <font color="Maroon" title="c2">p</font> is <a href="int_2.html#V1" title="INT_2:attr.1">prime</a> or <font color="Maroon" title="c1">m</font>,<font color="Maroon" title="c2">p</font> <a href="int_2.html#R1" title="INT_2:pred.1">are_relative_prime</a>  or <font color="Maroon" title="c1">m</font> <a href="nat_d.html#K6" title="NAT_D:func.6">gcd</a> <font color="Maroon" title="c2">p</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c2">p</font> )</span><br/>



<b>assume </b><a NAME="E1:6"/><i><font color="Green" title="E6">A1</font></i>: 
<font color="Maroon" title="c2">p</font> is <a href="int_2.html#V1" title="INT_2:attr.1">prime</a>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> ( <font color="Maroon" title="c1">m</font>,<font color="Maroon" title="c2">p</font> <a href="int_2.html#R1" title="INT_2:pred.1">are_relative_prime</a>  or <font color="Maroon" title="c1">m</font> <a href="nat_d.html#K6" title="NAT_D:func.6">gcd</a> <font color="Maroon" title="c2">p</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c2">p</font> )</span><br/>

<a NAME="E2:6"/>
<font color="Maroon" title="c1">m</font> <a href="nat_d.html#K6" title="NAT_D:func.6">gcd</a> <font color="Maroon" title="c2">p</font> <a href="nat_d.html#R1" title="NAT_D:pred.1">divides</a> <font color="Maroon" title="c2">p</font>
 
<b>by </b><i><a class="ref" href="nat_d.html#D5" title="NAT_D:def.5">NAT_D:def 5</a></i>;<br/>
<a NAME="E3:6"/><b>then </b>
( <font color="Maroon" title="c1">m</font> <a href="nat_d.html#K6" title="NAT_D:func.6">gcd</a> <font color="Maroon" title="c2">p</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 1 or <font color="Maroon" title="c1">m</font> <a href="nat_d.html#K6" title="NAT_D:func.6">gcd</a> <font color="Maroon" title="c2">p</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c2">p</font> )
 
<b>by </b><i><a class="txt" href="#E1:6"><i><font color="Green" title="E6">A1</font></i></a>, <a class="ref" href="int_2.html#D5" title="INT_2:def.5">INT_2:def 5</a></i>;<br/>
<b>hence </b><a NAME="E4:6"/>
( <font color="Maroon" title="c1">m</font>,<font color="Maroon" title="c2">p</font> <a href="int_2.html#R1" title="INT_2:pred.1">are_relative_prime</a>  or <font color="Maroon" title="c1">m</font> <a href="nat_d.html#K6" title="NAT_D:func.6">gcd</a> <font color="Maroon" title="c2">p</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c2">p</font> )
 <b>by </b><i><a class="ref" href="int_2.html#D4" title="INT_2:def.4">INT_2:def 4</a></i>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> verum</span><br/>


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