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<span class="kw">let </span><font color="Maroon" title="c1">a</font>, <font color="Maroon" title="c2">b</font> be    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of  <a href="numbers.html#K5" title="NUMBERS:func.5">NAT</a> ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> (  not <font color="Maroon" title="c1">a</font>,<font color="Maroon" title="c2">b</font> <a href="int_2.html#R1" title="INT_2:pred.1">are_relative_prime</a>  or  not <font color="Maroon" title="c1">a</font> is  <a href="abian.html#V1" title="ABIAN:attr.1">even</a>  or  not <font color="Maroon" title="c2">b</font> is  <a href="abian.html#V1" title="ABIAN:attr.1">even</a>  )</span><br/>



<span class="kw">assume </span><a NAME="E1:23"/><span class="lab"><font color="Green" title="E13">A1</font></span>: 
<font color="Maroon" title="c1">a</font>,<font color="Maroon" title="c2">b</font> <a href="int_2.html#R1" title="INT_2:pred.1">are_relative_prime</a> 
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> (  not <font color="Maroon" title="c1">a</font> is  <a href="abian.html#V1" title="ABIAN:attr.1">even</a>  or  not <font color="Maroon" title="c2">b</font> is  <a href="abian.html#V1" title="ABIAN:attr.1">even</a>  )</span><br/>

<span class="kw">assume </span><a NAME="E2:23"/>
<font color="Maroon" title="c1">a</font> is  <a href="abian.html#V1" title="ABIAN:attr.1">even</a> 
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> not <font color="Maroon" title="c2">b</font> is  <a href="abian.html#V1" title="ABIAN:attr.1">even</a> </span><br/>

<a NAME="E3:23"/><span class="kw">then </span><span class="lab"><font color="Green" title="E14">A2</font></span>: 
2 <a href="nat_d.html#R1" title="NAT_D:pred.1">divides</a> <font color="Maroon" title="c1">a</font>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="pepin.html#T22" title="PEPIN:th.22">PEPIN:22</a></span>;<br/>
<span class="kw">assume </span><a NAME="E4:23"/>
<font color="Maroon" title="c2">b</font> is  <a href="abian.html#V1" title="ABIAN:attr.1">even</a> 
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> contradiction</span><br/>

<a NAME="E5:23"/><span class="kw">then </span>
2 <a href="nat_d.html#R1" title="NAT_D:pred.1">divides</a> <font color="Maroon" title="c2">b</font>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="pepin.html#T22" title="PEPIN:th.22">PEPIN:22</a></span>;<br/>
<span class="kw">hence </span><a NAME="E6:23"/>
contradiction
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:23"><span class="lab"><font color="Green" title="E13">A1</font></span></a>, <a class="txt" href="#E3:23"><span class="lab"><font color="Green" title="E14">A2</font></span></a>, <a class="ref" href="pythtrip.html#D1" target="_self" title="PYTHTRIP:def.1">Def1</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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