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<span class="kw">let </span><font color="Maroon" title="c2">n</font> be   <a href="ordinal1.html#NM6" title="ORDINAL1:NM.6">Nat</a>; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> ( <font color="Maroon" title="c2">n</font> <a href="number08.html#R2" title="NUMBER08:pred.2">satisfies_Sierpinski_problem_86</a>  implies <font color="Maroon" title="c2">n</font> is  <a href="abian.html#V1" title="ABIAN:attr.1">even</a>  )</span><br/>

<span class="kw">assume </span><a NAME="E1:82"/><span class="lab"><font color="Green" title="E64">A1</font></span>: 
<font color="Maroon" title="c2">n</font> <a href="number08.html#R2" title="NUMBER08:pred.2">satisfies_Sierpinski_problem_86</a> 
 ; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> <font color="Maroon" title="c2">n</font> is  <a href="abian.html#V1" title="ABIAN:attr.1">even</a> </span><br/>

<span class="kw">assume </span><a NAME="E2:82"/>
<font color="Maroon" title="c2">n</font> is  <a href="abian.html#NV2" title="ABIAN:NV.2">odd</a> 
 ; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> contradiction</span><br/>

<a NAME="E3:82"/><span class="kw">then </span><span class="lab"><font color="Green" title="E65">A2</font></span>: 
( <font color="Maroon" title="c2">n</font> <a href="xcmplx_0.html#K6" title="XCMPLX_0:func.6">-</a> 1 is  <a href="abian.html#V1" title="ABIAN:attr.1">even</a>  &amp; <font color="Maroon" title="c2">n</font> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1 is  <a href="abian.html#V1" title="ABIAN:attr.1">even</a>  )
 
;<br/>
<a NAME="E4:82"/>
( <font color="Maroon" title="c2">n</font> <a href="xcmplx_0.html#K6" title="XCMPLX_0:func.6">-</a> 1 is  <a href="int_2.html#V1" title="INT_2:attr.1">prime</a>  or <font color="Maroon" title="c2">n</font> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1 is  <a href="int_2.html#V1" title="INT_2:attr.1">prime</a>  )
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:82"><span class="lab"><font color="Green" title="E64">A1</font></span></a>, <a class="ref" href="number08.html#T52" target="_self" onmouseover="rs('number08/T52')" onmouseout="rh()">Th52</a></span>;<br/>
<a NAME="E5:82"/><span class="kw">then </span>
( <font color="Maroon" title="c2">n</font> <a href="xcmplx_0.html#K6" title="XCMPLX_0:func.6">-</a> 1 <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 2 or <font color="Maroon" title="c2">n</font> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1 <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 2 )
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E3:82"><span class="lab"><font color="Green" title="E65">A2</font></span></a></span>;<br/>
<a NAME="E6:82"/><span class="kw">then </span>
( <font color="Maroon" title="c2">n</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 3 or <font color="Maroon" title="c2">n</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 1 )
 
;<br/>
<span class="kw">hence </span><a NAME="E7:82"/>
contradiction
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:82"><span class="lab"><font color="Green" title="E64">A1</font></span></a>, <a class="ref" href="number08.html#T50" target="_self" onmouseover="rs('number08/T50')" onmouseout="rh()">Th50</a></span>; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" 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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