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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> <a href="xxreal_0.html#NR2" title="XXREAL_0:NR.2">&gt;=</a> 6 )</span><br/>

<span class="kw">given </span><font color="Maroon" title="c3">a</font>, <font color="Maroon" title="c4">b</font>, <font color="Maroon" title="c5">c</font> being   <a href="int_2.html#NM1" title="INT_2:NM.1">Prime</a><span class="kw"> such that </span><a NAME="E2:79"/><span class="lab"><font color="Green" title="E61">A1</font></span>: 
<font color="Maroon" title="c3">a</font>,<font color="Maroon" title="c4">b</font>,<font color="Maroon" title="c5">c</font> <a href="zfmisc_1.html#R1" title="ZFMISC_1:pred.1">are_mutually_distinct</a> 
 <span class="kw">and </span><br/><a NAME="E3:79"/><span class="lab"><font color="Green" title="E62">A2</font></span>: 
<span class="p1">(<span class="default"><font color="Maroon" title="c2">n</font> <a href="newton.html#K1" title="NEWTON:func.1">|^</a> 2</span>)</span> <a href="xcmplx_0.html#K6" title="XCMPLX_0:func.6">-</a> 1 <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><font color="Maroon" title="c3">a</font> <a href="xcmplx_0.html#K3" title="XCMPLX_0:func.3">*</a> <font color="Maroon" title="c4">b</font></span>)</span> <a href="xcmplx_0.html#K3" title="XCMPLX_0:func.3">*</a> <font color="Maroon" title="c5">c</font>
 ; <span class="comment"><font color="firebrick">:: according to </font></span><a class="ref" href="number08.html#D5" target="_self" onmouseover="rs('number08/D5')" onmouseout="rh()">NUMBER08:def 5</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="xxreal_0.html#NR2" title="XXREAL_0:NR.2">&gt;=</a> 6</span><br/>

<a NAME="E4:79"/>
( ( <font color="Maroon" title="c3">a</font> <a href="xxreal_0.html#NR2" title="XXREAL_0:NR.2">&gt;=</a> 2 &amp; <font color="Maroon" title="c4">b</font> <a href="xxreal_0.html#NR2" title="XXREAL_0:NR.2">&gt;=</a> 3 &amp; <font color="Maroon" title="c5">c</font> <a href="xxreal_0.html#NR2" title="XXREAL_0:NR.2">&gt;=</a> 5 ) or ( <font color="Maroon" title="c3">a</font> <a href="xxreal_0.html#NR2" title="XXREAL_0:NR.2">&gt;=</a> 2 &amp; <font color="Maroon" title="c4">b</font> <a href="xxreal_0.html#NR2" title="XXREAL_0:NR.2">&gt;=</a> 5 &amp; <font color="Maroon" title="c5">c</font> <a href="xxreal_0.html#NR2" title="XXREAL_0:NR.2">&gt;=</a> 3 ) or ( <font color="Maroon" title="c3">a</font> <a href="xxreal_0.html#NR2" title="XXREAL_0:NR.2">&gt;=</a> 3 &amp; <font color="Maroon" title="c4">b</font> <a href="xxreal_0.html#NR2" title="XXREAL_0:NR.2">&gt;=</a> 2 &amp; <font color="Maroon" title="c5">c</font> <a href="xxreal_0.html#NR2" title="XXREAL_0:NR.2">&gt;=</a> 5 ) or ( <font color="Maroon" title="c3">a</font> <a href="xxreal_0.html#NR2" title="XXREAL_0:NR.2">&gt;=</a> 3 &amp; <font color="Maroon" title="c4">b</font> <a href="xxreal_0.html#NR2" title="XXREAL_0:NR.2">&gt;=</a> 5 &amp; <font color="Maroon" title="c5">c</font> <a href="xxreal_0.html#NR2" title="XXREAL_0:NR.2">&gt;=</a> 2 ) or ( <font color="Maroon" title="c3">a</font> <a href="xxreal_0.html#NR2" title="XXREAL_0:NR.2">&gt;=</a> 5 &amp; <font color="Maroon" title="c4">b</font> <a href="xxreal_0.html#NR2" title="XXREAL_0:NR.2">&gt;=</a> 2 &amp; <font color="Maroon" title="c5">c</font> <a href="xxreal_0.html#NR2" title="XXREAL_0:NR.2">&gt;=</a> 3 ) or ( <font color="Maroon" title="c3">a</font> <a href="xxreal_0.html#NR2" title="XXREAL_0:NR.2">&gt;=</a> 5 &amp; <font color="Maroon" title="c4">b</font> <a href="xxreal_0.html#NR2" title="XXREAL_0:NR.2">&gt;=</a> 3 &amp; <font color="Maroon" title="c5">c</font> <a href="xxreal_0.html#NR2" title="XXREAL_0:NR.2">&gt;=</a> 2 ) )
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:79"><span class="lab"><font color="Green" title="E61">A1</font></span></a>, <a class="ref" href="number08.html#T49" target="_self" onmouseover="rs('number08/T49')" onmouseout="rh()">Th49</a></span>;<br/>
<a NAME="E5:79"/><span class="kw">then </span><span class="lab"><font color="Green" title="E63">A3</font></span>: 
( <span class="p1">(<span class="default"><font color="Maroon" title="c3">a</font> <a href="xcmplx_0.html#K3" title="XCMPLX_0:func.3">*</a> <font color="Maroon" title="c4">b</font></span>)</span> <a href="xcmplx_0.html#K3" title="XCMPLX_0:func.3">*</a> <font color="Maroon" title="c5">c</font> <a href="xxreal_0.html#NR2" title="XXREAL_0:NR.2">&gt;=</a> <span class="p1">(<span class="default">2 <a href="nat_1.html#K2" title="NAT_1:func.2">*</a> 3</span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">*</a> 5 or <span class="p1">(<span class="default"><font color="Maroon" title="c3">a</font> <a href="xcmplx_0.html#K3" title="XCMPLX_0:func.3">*</a> <font color="Maroon" title="c4">b</font></span>)</span> <a href="xcmplx_0.html#K3" title="XCMPLX_0:func.3">*</a> <font color="Maroon" title="c5">c</font> <a href="xxreal_0.html#NR2" title="XXREAL_0:NR.2">&gt;=</a> <span class="p1">(<span class="default">3 <a href="nat_1.html#K2" title="NAT_1:func.2">*</a> 5</span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">*</a> 2 or <span class="p1">(<span class="default"><font color="Maroon" title="c3">a</font> <a href="xcmplx_0.html#K3" title="XCMPLX_0:func.3">*</a> <font color="Maroon" title="c4">b</font></span>)</span> <a href="xcmplx_0.html#K3" title="XCMPLX_0:func.3">*</a> <font color="Maroon" title="c5">c</font> <a href="xxreal_0.html#NR2" title="XXREAL_0:NR.2">&gt;=</a> <span class="p1">(<span class="default">5 <a href="nat_1.html#K2" title="NAT_1:func.2">*</a> 2</span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">*</a> 3 )
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="number08.html#E69"><span class="lab"><font color="Green" title="E59">Lm15</font></span></a></span>;<br/>
<a NAME="E6:79"/><span class="lab"><font color="Green" title="E64">A4</font></span>: 
5 <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 6 <a href="xcmplx_0.html#K6" title="XCMPLX_0:func.6">-</a> 1
 
;<br/>
<a NAME="E7:79"/><span class="lab"><font color="Green" title="E65">A5</font></span>: 
<font color="Maroon" title="c2">n</font> <a href="newton.html#K1" title="NEWTON:func.1">|^</a> 2 <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c2">n</font> <a href="xcmplx_0.html#K3" title="XCMPLX_0:func.3">*</a> <font color="Maroon" title="c2">n</font>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="wsierp_1.html#T1" onmouseover="rs('wsierp_1/T1')" onmouseout="rh()">WSIERP_1:1</a></span>;<br/>
<span class="kw">assume </span><a NAME="E8:79"/>
<font color="Maroon" title="c2">n</font> <a href="xxreal_0.html#NR3" title="XXREAL_0:NR.3">&lt;</a> 6
 ; <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="E9:79"/><span class="kw">then </span>
 not  not <font color="Maroon" title="c2">n</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="numbers.html#K5" title="NUMBERS:func.5">0</a>  &amp;  ...  &amp;  not <font color="Maroon" title="c2">n</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 5
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E6:79"><span class="lab"><font color="Green" title="E64">A4</font></span></a>, <a class="ref" href="number02.html#T7" onmouseover="rs('number02/T7')" onmouseout="rh()">NUMBER02:7</a></span>;<br/>
<span class="kw">hence </span><a NAME="E10:79"/>
contradiction
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E3:79"><span class="lab"><font color="Green" title="E62">A2</font></span></a>, <a class="txt" href="#E5:79"><span class="lab"><font color="Green" title="E63">A3</font></span></a>, <a class="txt" href="#E7:79"><span class="lab"><font color="Green" title="E65">A5</font></span></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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