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<span class="p1">(<span class="default">3 <a href="pepin.html#K2" title="PEPIN:func.2">^2</a></span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> <span class="p1">(<span class="default">4 <a href="pepin.html#K2" title="PEPIN:func.2">^2</a></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 5 <a href="pepin.html#K2" title="PEPIN:func.2">^2</a> 
 
;<br/>
<span class="kw">then </span><span class="kw">reconsider </span><font color="Maroon" title="c1">X</font> = <span class="p1"><a href="domain_1.html#K8" title="DOMAIN_1:func.8">{</a><span class="default">3,4,5</span><a href="domain_1.html#K8" title="DOMAIN_1:func.8">}</a></span> as    <a href="pythtrip.html#M1" title="PYTHTRIP:mode.1">Pythagorean_triple</a>  <span class="kw">by</span> <span class="lab"><a class="ref" href="pythtrip.html#D4" target="_self" title="PYTHTRIP:def.4">Def4</a></span>;<br/>
3 <a href="nat_d.html#K6" title="NAT_D:func.6">gcd</a> 4 = 
3 <a href="int_2.html#K3" title="INT_2:func.3">gcd</a> <span class="p1">(<span class="default">4 <a href="xcmplx_0.html#K6" title="XCMPLX_0:func.6">-</a> 3</span>)</span>
<span class="kw">by</span> <span class="lab"><a class="ref" href="prepower.html#T97" title="PREPOWER:th.97">PREPOWER:97</a></span>
<br/>.= 
1
<span class="kw">by</span> <span class="lab"><a class="ref" href="wsierp_1.html#T8" title="WSIERP_1:th.8">WSIERP_1:8</a></span>
;<br/>
<a NAME="E4:34"/><span class="kw">then </span><span class="lab"><font color="Green" title="E20">A1</font></span>: 
( 4 <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c1">X</font> &amp; 3,4 <a href="int_2.html#R1" title="INT_2:pred.1">are_relative_prime</a>  )
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="enumset1.html#D1" title="ENUMSET1:def.1">ENUMSET1:def 1</a>, <a class="ref" href="int_2.html#D3" title="INT_2:def.3">INT_2:def 3</a></span>;<br/>
<a NAME="E5:34"/>
(  not  <a href="numbers.html#K6" title="NUMBERS:func.6">0</a>  <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c1">X</font> &amp; 3 <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c1">X</font> )
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="enumset1.html#D1" title="ENUMSET1:def.1">ENUMSET1:def 1</a></span>;<br/>
<span class="kw">hence </span><a NAME="E6:34"/>
<span class="p1"><a href="domain_1.html#K8" title="DOMAIN_1:func.8">{</a><span class="default">3,4,5</span><a href="domain_1.html#K8" title="DOMAIN_1:func.8">}</a></span> is   non  <a href="pythtrip.html#V2" title="PYTHTRIP:attr.2">degenerate</a>   <a href="pythtrip.html#V3" title="PYTHTRIP:attr.3">simplified</a>   <a href="pythtrip.html#M1" title="PYTHTRIP:mode.1">Pythagorean_triple</a> 
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E4:34"><span class="lab"><font color="Green" title="E20">A1</font></span></a>, <a class="ref" href="pythtrip.html#D6" target="_self" title="PYTHTRIP:def.6">Def6</a>, <a class="ref" href="pythtrip.html#D8" target="_self" title="PYTHTRIP:def.8">Def8</a></span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> verum</span><br/>


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