<?xml version="1.0"?>
<div class="add">

<span class="kw">let </span><font color="Maroon" title="c17">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="c17">n</font> <a href="number07.html#R6" title="NUMBER07:pred.6">satisfies_Sierpinski_problem_89</a>  &amp; <font color="Maroon" title="c17">n</font> <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> 201 implies <font color="Maroon" title="c17">n</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <span class="p1"><a href="enumset1.html#K3" title="ENUMSET1:func.3">{</a><span class="default">33,85,93,141,201</span><a href="enumset1.html#K3" title="ENUMSET1:func.3">}</a></span> )</span><br/>

<span class="kw">assume </span><span class="kw">that </span><br/><a NAME="E1:97"/><span class="lab"><font color="Green" title="E81">A1</font></span>: 
<font color="Maroon" title="c17">n</font> <a href="number07.html#R6" title="NUMBER07:pred.6">satisfies_Sierpinski_problem_89</a> 
 <span class="kw">and </span><br/><a NAME="E2:97"/><span class="lab"><font color="Green" title="E82">A2</font></span>: 
<font color="Maroon" title="c17">n</font> <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> 201
 <span class="kw">and </span><br/><a NAME="E3:97"/><span class="lab"><font color="Green" title="E83">A3</font></span>: 
 not <font color="Maroon" title="c17">n</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <span class="p1"><a href="enumset1.html#K3" title="ENUMSET1:func.3">{</a><span class="default">33,85,93,141,201</span><a href="enumset1.html#K3" title="ENUMSET1:func.3">}</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"> contradiction</span><br/>

<a NAME="E4:97"/>
( 4 <a href="xxreal_0.html#NR3" title="XXREAL_0:NR.3">&lt;</a> 6 &amp; 6 <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> <font color="Maroon" title="c17">n</font> )
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:97"><span class="lab"><font color="Green" title="E81">A1</font></span></a>, <a class="ref" href="number07.html#T65" target="_self" onmouseover="rs('number07/T65')" onmouseout="rh()">Th65</a></span>;<br/>
<a NAME="E5:97"/><span class="kw">then </span><span class="lab"><font color="Green" title="E84">A4</font></span>: 
4 <a href="xxreal_0.html#NR3" title="XXREAL_0:NR.3">&lt;</a> <font color="Maroon" title="c17">n</font>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="xxreal_0.html#T2" onmouseover="rs('xxreal_0/T2')" onmouseout="rh()">XXREAL_0:2</a></span>;<br/>
<span class="kw">set </span><font color="Maroon" title="c18">a</font> = <font color="Maroon" title="c17">n</font> <a href="nat_d.html#K3" title="NAT_D:func.3">div</a> 4;<br/>
<span class="kw">set </span><font color="Maroon" title="c19">b</font> = <font color="Maroon" title="c17">n</font> <a href="nat_d.html#K4" title="NAT_D:func.4">mod</a> 4;<br/>
<a NAME="E6:97"/><span class="lab"><font color="Green" title="E85">A5</font></span>: 
<font color="Maroon" title="c17">n</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c17">n</font> <a href="nat_d.html#K3" title="NAT_D:func.3">div</a> 4</span>)</span> <a href="xcmplx_0.html#K3" title="XCMPLX_0:func.3">*</a> 4</span>)</span> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> <span class="p1">(<span class="default"><font color="Maroon" title="c17">n</font> <a href="nat_d.html#K4" title="NAT_D:func.4">mod</a> 4</span>)</span>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="int_1.html#T59" onmouseover="rs('int_1/T59')" onmouseout="rh()">INT_1:59</a></span>;<br/>
<a NAME="E7:97"/><span class="lab"><font color="Green" title="E86">A6</font></span>: 
<font color="Maroon" title="c17">n</font> <a href="nat_d.html#K4" title="NAT_D:func.4">mod</a> 4 <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 1
 
<div><a class="txt" onmouseover="tooltip.show('hs2',this)" onmouseout="tooltip.hide()" onclick="hs2(this)" href="javascript:()" title="97_1"><span class="kw">proof </span></a><div class="add">

<a NAME="E1:97_1"/>
<font color="Maroon" title="c17">n</font> <a href="nat_d.html#K4" title="NAT_D:func.4">mod</a> 4 <a href="xxreal_0.html#NR3" title="XXREAL_0:NR.3">&lt;</a> 3 <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> 1
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="nat_d.html#T1" onmouseover="rs('nat_d/T1')" onmouseout="rh()">NAT_D:1</a></span>;<br/>
<a NAME="E2:97_1"/><span class="kw">then </span>
<font color="Maroon" title="c17">n</font> <a href="nat_d.html#K4" title="NAT_D:func.4">mod</a> 4 <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> 3
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="nat_1.html#T13" onmouseover="rs('nat_1/T13')" onmouseout="rh()">NAT_1:13</a></span>;<br/>
<a NAME="E3:97_1"/><span class="kw">then </span>
 not  not <font color="Maroon" title="c17">n</font> <a href="nat_d.html#K4" title="NAT_D:func.4">mod</a> 4 <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="c17">n</font> <a href="nat_d.html#K4" title="NAT_D:func.4">mod</a> 4 <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 3
 
;<br/>
<div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="97_1_1"><span class="kw">per </span></a><a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="kw">cases </span></a><span class="hide"><a NAME="E1:97_1_1"/><span class="kw">then </span>
( <font color="Maroon" title="c17">n</font> <a href="nat_d.html#K4" title="NAT_D:func.4">mod</a> 4 <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="numbers.html#K5" title="NUMBERS:func.5">0</a>  or <font color="Maroon" title="c17">n</font> <a href="nat_d.html#K4" title="NAT_D:func.4">mod</a> 4 <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 1 or <font color="Maroon" title="c17">n</font> <a href="nat_d.html#K4" title="NAT_D:func.4">mod</a> 4 <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 2 or <font color="Maroon" title="c17">n</font> <a href="nat_d.html#K4" title="NAT_D:func.4">mod</a> 4 <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 3 )
 </span>;<br/><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="97_1_1_1"><span class="kw">suppose </span></a><a NAME="E1:97_1_1_1"/>
<font color="Maroon" title="c17">n</font> <a href="nat_d.html#K4" title="NAT_D:func.4">mod</a> 4 <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="numbers.html#K5" title="NUMBERS:func.5">0</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="c17">n</font> <a href="nat_d.html#K4" title="NAT_D:func.4">mod</a> 4 <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 1</span><br/><div class="add"><a NAME="E2:97_1_1_1"/><span class="kw">then </span>
<font color="Maroon" title="c17">n</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 4 <a href="xcmplx_0.html#K3" title="XCMPLX_0:func.3">*</a> <span class="p1">(<span class="default"><font color="Maroon" title="c17">n</font> <a href="nat_d.html#K3" title="NAT_D:func.3">div</a> 4</span>)</span>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E6:97"><span class="lab"><font color="Green" title="E85">A5</font></span></a></span>;<br/><a NAME="E3:97_1_1_1"/><span class="kw">then </span>
( 4 <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c17">n</font> &amp; 4 <a href="nat_d.html#R1" title="NAT_D:pred.1">divides</a> <font color="Maroon" title="c17">n</font> )
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E5:97"><span class="lab"><font color="Green" title="E84">A4</font></span></a></span>;<br/><span class="kw">hence </span><a NAME="E4:97_1_1_1"/>
<font color="Maroon" title="c17">n</font> <a href="nat_d.html#K4" title="NAT_D:func.4">mod</a> 4 <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 1
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:97"><span class="lab"><font color="Green" title="E81">A1</font></span></a>, <a class="ref" href="number07.html#T63" target="_self" onmouseover="rs('number07/T63')" onmouseout="rh()">Th63</a>, <a class="ref" href="xprimes0.html#T4" onmouseover="rs('xprimes0/T4')" onmouseout="rh()">XPRIMES0:4</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/></div><span class="kw">end;</span></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="97_1_1_2"><span class="kw">suppose </span></a><a NAME="E1:97_1_1_2"/>
<font color="Maroon" title="c17">n</font> <a href="nat_d.html#K4" title="NAT_D:func.4">mod</a> 4 <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 1
 ; <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="c17">n</font> <a href="nat_d.html#K4" title="NAT_D:func.4">mod</a> 4 <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 1</span><br/><div class="add"><span class="kw">hence </span><a NAME="E2:97_1_1_2"/>
<font color="Maroon" title="c17">n</font> <a href="nat_d.html#K4" title="NAT_D:func.4">mod</a> 4 <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 1
 ; <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/></div><span class="kw">end;</span></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="97_1_1_3"><span class="kw">suppose </span></a><a NAME="E1:97_1_1_3"/>
<font color="Maroon" title="c17">n</font> <a href="nat_d.html#K4" title="NAT_D:func.4">mod</a> 4 <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 2
 ; <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="c17">n</font> <a href="nat_d.html#K4" title="NAT_D:func.4">mod</a> 4 <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 1</span><br/><div class="add"><a NAME="E2:97_1_1_3"/><span class="kw">then </span>
<font color="Maroon" title="c17">n</font> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> 2 <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 4 <a href="xcmplx_0.html#K3" title="XCMPLX_0:func.3">*</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c17">n</font> <a href="nat_d.html#K3" title="NAT_D:func.3">div</a> 4</span>)</span> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> 1</span>)</span>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E6:97"><span class="lab"><font color="Green" title="E85">A5</font></span></a></span>;<br/><a NAME="E3:97_1_1_3"/><span class="kw">then </span>
( 4 <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c17">n</font> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> 2 &amp; 4 <a href="nat_d.html#R1" title="NAT_D:pred.1">divides</a> <font color="Maroon" title="c17">n</font> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> 2 )
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E5:97"><span class="lab"><font color="Green" title="E84">A4</font></span></a></span>;<br/><span class="kw">hence </span><a NAME="E4:97_1_1_3"/>
<font color="Maroon" title="c17">n</font> <a href="nat_d.html#K4" title="NAT_D:func.4">mod</a> 4 <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 1
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:97"><span class="lab"><font color="Green" title="E81">A1</font></span></a>, <a class="ref" href="number07.html#T63" target="_self" onmouseover="rs('number07/T63')" onmouseout="rh()">Th63</a>, <a class="ref" href="xprimes0.html#T4" onmouseover="rs('xprimes0/T4')" onmouseout="rh()">XPRIMES0:4</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/></div><span class="kw">end;</span></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="97_1_1_4"><span class="kw">suppose </span></a><a NAME="E1:97_1_1_4"/>
<font color="Maroon" title="c17">n</font> <a href="nat_d.html#K4" title="NAT_D:func.4">mod</a> 4 <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 3
 ; <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="c17">n</font> <a href="nat_d.html#K4" title="NAT_D:func.4">mod</a> 4 <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 1</span><br/><div class="add"><a NAME="E2:97_1_1_4"/><span class="kw">then </span>
<font color="Maroon" title="c17">n</font> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> 1 <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 4 <a href="xcmplx_0.html#K3" title="XCMPLX_0:func.3">*</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c17">n</font> <a href="nat_d.html#K3" title="NAT_D:func.3">div</a> 4</span>)</span> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> 1</span>)</span>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E6:97"><span class="lab"><font color="Green" title="E85">A5</font></span></a></span>;<br/><a NAME="E3:97_1_1_4"/><span class="kw">then </span>
( 4 <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c17">n</font> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> 1 &amp; 4 <a href="nat_d.html#R1" title="NAT_D:pred.1">divides</a> <font color="Maroon" title="c17">n</font> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> 1 )
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E5:97"><span class="lab"><font color="Green" title="E84">A4</font></span></a>, <a class="ref" href="nat_1.html#T11" onmouseover="rs('nat_1/T11')" onmouseout="rh()">NAT_1:11</a></span>;<br/><span class="kw">hence </span><a NAME="E4:97_1_1_4"/>
<font color="Maroon" title="c17">n</font> <a href="nat_d.html#K4" title="NAT_D:func.4">mod</a> 4 <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 1
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:97"><span class="lab"><font color="Green" title="E81">A1</font></span></a>, <a class="ref" href="number07.html#T63" target="_self" onmouseover="rs('number07/T63')" onmouseout="rh()">Th63</a>, <a class="ref" href="xprimes0.html#T4" onmouseover="rs('xprimes0/T4')" onmouseout="rh()">XPRIMES0:4</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/></div><span class="kw">end;</span></div></div><span class="kw">end;</span></div>

</div><span class="kw">end;</span></div>
<a NAME="E8:97"/><span class="lab"><font color="Green" title="E87">A7</font></span>: 
<font color="Maroon" title="c17">n</font> <a href="nat_d.html#K3" title="NAT_D:func.3">div</a> 4 <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a>  <a href="numbers.html#K5" title="NUMBERS:func.5">0</a> 
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E5:97"><span class="lab"><font color="Green" title="E84">A4</font></span></a>, <a class="txt" href="#E6:97"><span class="lab"><font color="Green" title="E85">A5</font></span></a>, <a class="txt" href="#E7:97"><span class="lab"><font color="Green" title="E86">A6</font></span></a></span>;<br/>
<a NAME="E9:97"/>
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c17">n</font> <a href="nat_d.html#K3" title="NAT_D:func.3">div</a> 4</span>)</span> <a href="xcmplx_0.html#K3" title="XCMPLX_0:func.3">*</a> 4</span>)</span> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> 1 <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> <span class="p1">(<span class="default">50 <a href="xcmplx_0.html#K3" title="XCMPLX_0:func.3">*</a> 4</span>)</span> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> 1
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:97"><span class="lab"><font color="Green" title="E82">A2</font></span></a>, <a class="txt" href="#E6:97"><span class="lab"><font color="Green" title="E85">A5</font></span></a>, <a class="txt" href="#E7:97"><span class="lab"><font color="Green" title="E86">A6</font></span></a></span>;<br/>
<a NAME="E10:97"/><span class="kw">then </span>
<span class="p1">(<span class="default"><font color="Maroon" title="c17">n</font> <a href="nat_d.html#K3" title="NAT_D:func.3">div</a> 4</span>)</span> <a href="xcmplx_0.html#K3" title="XCMPLX_0:func.3">*</a> 4 <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> 50 <a href="xcmplx_0.html#K3" title="XCMPLX_0:func.3">*</a> 4
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="xreal_1.html#T6" onmouseover="rs('xreal_1/T6')" onmouseout="rh()">XREAL_1:6</a></span>;<br/>
<a NAME="E11:97"/><span class="kw">then </span>
( 1 <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> <font color="Maroon" title="c17">n</font> <a href="nat_d.html#K3" title="NAT_D:func.3">div</a> 4 &amp; <font color="Maroon" title="c17">n</font> <a href="nat_d.html#K3" title="NAT_D:func.3">div</a> 4 <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> 50 )
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="xreal_1.html#T68" onmouseover="rs('xreal_1/T68')" onmouseout="rh()">XREAL_1:68</a>, <a class="txt" href="#E8:97"><span class="lab"><font color="Green" title="E87">A7</font></span></a>, <a class="ref" href="nat_1.html#T14" onmouseover="rs('nat_1/T14')" onmouseout="rh()">NAT_1:14</a></span>;<br/>
<a NAME="E12:97"/><span class="kw">then </span>
 not  not <font color="Maroon" title="c17">n</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default">1 <a href="xcmplx_0.html#K3" title="XCMPLX_0:func.3">*</a> 4</span>)</span> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> 1 &amp;  ...  &amp;  not <font color="Maroon" title="c17">n</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default">50 <a href="xcmplx_0.html#K3" title="XCMPLX_0:func.3">*</a> 4</span>)</span> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> 1
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E6:97"><span class="lab"><font color="Green" title="E85">A5</font></span></a>, <a class="txt" href="#E7:97"><span class="lab"><font color="Green" title="E86">A6</font></span></a></span>;<br/>
<div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="97_2"><span class="kw">per </span></a><a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="kw">cases </span></a><span class="hide"><a NAME="E1:97_2"/><span class="kw">then </span>
( <font color="Maroon" title="c17">n</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 5 or <font color="Maroon" title="c17">n</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 9 or <font color="Maroon" title="c17">n</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 13 or <font color="Maroon" title="c17">n</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 17 or <font color="Maroon" title="c17">n</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 21 or <font color="Maroon" title="c17">n</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 25 or <font color="Maroon" title="c17">n</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 29 or <font color="Maroon" title="c17">n</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 37 or <font color="Maroon" title="c17">n</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 41 or <font color="Maroon" title="c17">n</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 45 or <font color="Maroon" title="c17">n</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 49 or <font color="Maroon" title="c17">n</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 53 or <font color="Maroon" title="c17">n</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 57 or <font color="Maroon" title="c17">n</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 61 or <font color="Maroon" title="c17">n</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 65 or <font color="Maroon" title="c17">n</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 69 or <font color="Maroon" title="c17">n</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 73 or <font color="Maroon" title="c17">n</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 77 or <font color="Maroon" title="c17">n</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 81 or <font color="Maroon" title="c17">n</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 89 or <font color="Maroon" title="c17">n</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 97 or <font color="Maroon" title="c17">n</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 101 or <font color="Maroon" title="c17">n</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 105 or <font color="Maroon" title="c17">n</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 109 or <font color="Maroon" title="c17">n</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 113 or <font color="Maroon" title="c17">n</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 117 or <font color="Maroon" title="c17">n</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 121 or <font color="Maroon" title="c17">n</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 125 or <font color="Maroon" title="c17">n</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 129 or <font color="Maroon" title="c17">n</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 133 or <font color="Maroon" title="c17">n</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 137 or <font color="Maroon" title="c17">n</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 145 or <font color="Maroon" title="c17">n</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 149 or <font color="Maroon" title="c17">n</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 153 or <font color="Maroon" title="c17">n</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 157 or <font color="Maroon" title="c17">n</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 161 or <font color="Maroon" title="c17">n</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 165 or <font color="Maroon" title="c17">n</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 169 or <font color="Maroon" title="c17">n</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 173 or <font color="Maroon" title="c17">n</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 177 or <font color="Maroon" title="c17">n</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 181 or <font color="Maroon" title="c17">n</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 185 or <font color="Maroon" title="c17">n</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 189 or <font color="Maroon" title="c17">n</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 193 or <font color="Maroon" title="c17">n</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 197 )
 </span><span class="kw">by</span> <span class="lab"><a class="txt" href="#E3:97"><span class="lab"><font color="Green" title="E83">A3</font></span></a>, <a class="ref" href="enumset1.html#D3" onmouseover="rs('enumset1/D3')" onmouseout="rh()">ENUMSET1:def 3</a></span>;<br/><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="97_2_1"><span class="kw">suppose </span></a><a NAME="E1:97_2_1"/>
<font color="Maroon" title="c17">n</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 5
 ; <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/><div class="add"><span class="kw">hence </span><a NAME="E2:97_2_1"/>
contradiction
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:97"><span class="lab"><font color="Green" title="E81">A1</font></span></a>, <a class="ref" href="number07.html#T61" target="_self" onmouseover="rs('number07/T61')" onmouseout="rh()">Th61</a>, <a class="ref" href="xprimes1.html#T5" onmouseover="rs('xprimes1/T5')" onmouseout="rh()">XPRIMES1:5</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/></div><span class="kw">end;</span></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="97_2_2"><span class="kw">suppose </span></a><a NAME="E1:97_2_2"/>
<font color="Maroon" title="c17">n</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 9
 ; <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/><div class="add"><span class="kw">hence </span><a NAME="E2:97_2_2"/>
contradiction
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:97"><span class="lab"><font color="Green" title="E81">A1</font></span></a>, <a class="ref" href="number07.html#T61" target="_self" onmouseover="rs('number07/T61')" onmouseout="rh()">Th61</a>, <a class="ref" href="xprimes1.html#T11" onmouseover="rs('xprimes1/T11')" onmouseout="rh()">XPRIMES1:11</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/></div><span class="kw">end;</span></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="97_2_3"><span class="kw">suppose </span></a><a NAME="E1:97_2_3"/>
<font color="Maroon" title="c17">n</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 13
 ; <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/><div class="add"><span class="kw">hence </span><a NAME="E2:97_2_3"/>
contradiction
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:97"><span class="lab"><font color="Green" title="E81">A1</font></span></a>, <a class="ref" href="number07.html#T61" target="_self" onmouseover="rs('number07/T61')" onmouseout="rh()">Th61</a>, <a class="ref" href="xprimes1.html#T13" onmouseover="rs('xprimes1/T13')" onmouseout="rh()">XPRIMES1:13</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/></div><span class="kw">end;</span></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="97_2_4"><span class="kw">suppose </span></a><a NAME="E1:97_2_4"/>
<font color="Maroon" title="c17">n</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 17
 ; <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/><div class="add"><span class="kw">hence </span><a NAME="E2:97_2_4"/>
contradiction
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:97"><span class="lab"><font color="Green" title="E81">A1</font></span></a>, <a class="ref" href="number07.html#T61" target="_self" onmouseover="rs('number07/T61')" onmouseout="rh()">Th61</a>, <a class="ref" href="xprimes1.html#T17" onmouseover="rs('xprimes1/T17')" onmouseout="rh()">XPRIMES1:17</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/></div><span class="kw">end;</span></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="97_2_5"><span class="kw">suppose </span></a><a NAME="E1:97_2_5"/>
<font color="Maroon" title="c17">n</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 21
 ; <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/><div class="add"><span class="kw">hence </span><a NAME="E2:97_2_5"/>
contradiction
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:97"><span class="lab"><font color="Green" title="E81">A1</font></span></a>, <a class="ref" href="number07.html#T61" target="_self" onmouseover="rs('number07/T61')" onmouseout="rh()">Th61</a>, <a class="ref" href="xprimes1.html#T23" onmouseover="rs('xprimes1/T23')" onmouseout="rh()">XPRIMES1:23</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/></div><span class="kw">end;</span></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="97_2_6"><span class="kw">suppose </span></a><a NAME="E1:97_2_6"/><span class="lab"><font color="Green" title="E88">A</font></span>: 
<font color="Maroon" title="c17">n</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 25
 ; <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/><div class="add"><a NAME="E2:97_2_6"/>
25 <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 5 <a href="xcmplx_0.html#K3" title="XCMPLX_0:func.3">*</a> 5
 ;<br/><span class="kw">hence </span><a NAME="E3:97_2_6"/>
contradiction
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:97"><span class="lab"><font color="Green" title="E81">A1</font></span></a>, <a class="txt" href="#E1:97_2_6"><span class="lab"><font color="Green" title="E88">A</font></span></a>, <a class="ref" href="number07.html#T64" target="_self" onmouseover="rs('number07/T64')" onmouseout="rh()">Th64</a>, <a class="ref" href="xprimes1.html#T5" onmouseover="rs('xprimes1/T5')" onmouseout="rh()">XPRIMES1:5</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/></div><span class="kw">end;</span></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="97_2_7"><span class="kw">suppose </span></a><a NAME="E1:97_2_7"/>
<font color="Maroon" title="c17">n</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 29
 ; <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/><div class="add"><span class="kw">hence </span><a NAME="E2:97_2_7"/>
contradiction
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:97"><span class="lab"><font color="Green" title="E81">A1</font></span></a>, <a class="ref" href="number07.html#T61" target="_self" onmouseover="rs('number07/T61')" onmouseout="rh()">Th61</a>, <a class="ref" href="xprimes1.html#T29" onmouseover="rs('xprimes1/T29')" onmouseout="rh()">XPRIMES1:29</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/></div><span class="kw">end;</span></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="97_2_8"><span class="kw">suppose </span></a><a NAME="E1:97_2_8"/>
<font color="Maroon" title="c17">n</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 37
 ; <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/><div class="add"><span class="kw">hence </span><a NAME="E2:97_2_8"/>
contradiction
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:97"><span class="lab"><font color="Green" title="E81">A1</font></span></a>, <a class="ref" href="number07.html#T61" target="_self" onmouseover="rs('number07/T61')" onmouseout="rh()">Th61</a>, <a class="ref" href="xprimes1.html#T37" onmouseover="rs('xprimes1/T37')" onmouseout="rh()">XPRIMES1:37</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/></div><span class="kw">end;</span></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="97_2_9"><span class="kw">suppose </span></a><a NAME="E1:97_2_9"/>
<font color="Maroon" title="c17">n</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 41
 ; <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/><div class="add"><span class="kw">hence </span><a NAME="E2:97_2_9"/>
contradiction
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:97"><span class="lab"><font color="Green" title="E81">A1</font></span></a>, <a class="ref" href="number07.html#T61" target="_self" onmouseover="rs('number07/T61')" onmouseout="rh()">Th61</a>, <a class="ref" href="xprimes1.html#T41" onmouseover="rs('xprimes1/T41')" onmouseout="rh()">XPRIMES1:41</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/></div><span class="kw">end;</span></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="97_2_10"><span class="kw">suppose </span></a><a NAME="E1:97_2_10"/>
<font color="Maroon" title="c17">n</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 45
 ; <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/><div class="add"><span class="kw">hence </span><a NAME="E2:97_2_10"/>
contradiction
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:97"><span class="lab"><font color="Green" title="E81">A1</font></span></a>, <a class="ref" href="number07.html#T61" target="_self" onmouseover="rs('number07/T61')" onmouseout="rh()">Th61</a>, <a class="ref" href="xprimes1.html#T47" onmouseover="rs('xprimes1/T47')" onmouseout="rh()">XPRIMES1:47</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/></div><span class="kw">end;</span></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="97_2_11"><span class="kw">suppose </span></a><a NAME="E1:97_2_11"/><span class="lab"><font color="Green" title="E88">A</font></span>: 
<font color="Maroon" title="c17">n</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 49
 ; <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/><div class="add"><a NAME="E2:97_2_11"/>
49 <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 7 <a href="xcmplx_0.html#K3" title="XCMPLX_0:func.3">*</a> 7
 ;<br/><span class="kw">hence </span><a NAME="E3:97_2_11"/>
contradiction
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:97"><span class="lab"><font color="Green" title="E81">A1</font></span></a>, <a class="txt" href="#E1:97_2_11"><span class="lab"><font color="Green" title="E88">A</font></span></a>, <a class="ref" href="number07.html#T64" target="_self" onmouseover="rs('number07/T64')" onmouseout="rh()">Th64</a>, <a class="ref" href="xprimes1.html#T7" onmouseover="rs('xprimes1/T7')" onmouseout="rh()">XPRIMES1:7</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/></div><span class="kw">end;</span></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="97_2_12"><span class="kw">suppose </span></a><a NAME="E1:97_2_12"/>
<font color="Maroon" title="c17">n</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 53
 ; <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/><div class="add"><span class="kw">hence </span><a NAME="E2:97_2_12"/>
contradiction
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:97"><span class="lab"><font color="Green" title="E81">A1</font></span></a>, <a class="ref" href="number07.html#T61" target="_self" onmouseover="rs('number07/T61')" onmouseout="rh()">Th61</a>, <a class="ref" href="xprimes1.html#T53" onmouseover="rs('xprimes1/T53')" onmouseout="rh()">XPRIMES1:53</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/></div><span class="kw">end;</span></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="97_2_13"><span class="kw">suppose </span></a><a NAME="E1:97_2_13"/>
<font color="Maroon" title="c17">n</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 57
 ; <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/><div class="add"><span class="kw">hence </span><a NAME="E2:97_2_13"/>
contradiction
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:97"><span class="lab"><font color="Green" title="E81">A1</font></span></a>, <a class="ref" href="number07.html#T61" target="_self" onmouseover="rs('number07/T61')" onmouseout="rh()">Th61</a>, <a class="ref" href="xprimes1.html#T59" onmouseover="rs('xprimes1/T59')" onmouseout="rh()">XPRIMES1:59</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/></div><span class="kw">end;</span></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="97_2_14"><span class="kw">suppose </span></a><a NAME="E1:97_2_14"/>
<font color="Maroon" title="c17">n</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 61
 ; <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/><div class="add"><span class="kw">hence </span><a NAME="E2:97_2_14"/>
contradiction
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:97"><span class="lab"><font color="Green" title="E81">A1</font></span></a>, <a class="ref" href="number07.html#T61" target="_self" onmouseover="rs('number07/T61')" onmouseout="rh()">Th61</a>, <a class="ref" href="xprimes1.html#T61" onmouseover="rs('xprimes1/T61')" onmouseout="rh()">XPRIMES1:61</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/></div><span class="kw">end;</span></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="97_2_15"><span class="kw">suppose </span></a><a NAME="E1:97_2_15"/>
<font color="Maroon" title="c17">n</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 65
 ; <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/><div class="add"><span class="kw">hence </span><a NAME="E2:97_2_15"/>
contradiction
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:97"><span class="lab"><font color="Green" title="E81">A1</font></span></a>, <a class="ref" href="number07.html#T61" target="_self" onmouseover="rs('number07/T61')" onmouseout="rh()">Th61</a>, <a class="ref" href="xprimes1.html#T67" onmouseover="rs('xprimes1/T67')" onmouseout="rh()">XPRIMES1:67</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/></div><span class="kw">end;</span></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="97_2_16"><span class="kw">suppose </span></a><a NAME="E1:97_2_16"/>
<font color="Maroon" title="c17">n</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 69
 ; <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/><div class="add"><span class="kw">hence </span><a NAME="E2:97_2_16"/>
contradiction
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:97"><span class="lab"><font color="Green" title="E81">A1</font></span></a>, <a class="ref" href="number07.html#T61" target="_self" onmouseover="rs('number07/T61')" onmouseout="rh()">Th61</a>, <a class="ref" href="xprimes1.html#T71" onmouseover="rs('xprimes1/T71')" onmouseout="rh()">XPRIMES1:71</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/></div><span class="kw">end;</span></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="97_2_17"><span class="kw">suppose </span></a><a NAME="E1:97_2_17"/>
<font color="Maroon" title="c17">n</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 73
 ; <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/><div class="add"><span class="kw">hence </span><a NAME="E2:97_2_17"/>
contradiction
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:97"><span class="lab"><font color="Green" title="E81">A1</font></span></a>, <a class="ref" href="number07.html#T61" target="_self" onmouseover="rs('number07/T61')" onmouseout="rh()">Th61</a>, <a class="ref" href="xprimes1.html#T73" onmouseover="rs('xprimes1/T73')" onmouseout="rh()">XPRIMES1:73</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/></div><span class="kw">end;</span></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="97_2_18"><span class="kw">suppose </span></a><a NAME="E1:97_2_18"/>
<font color="Maroon" title="c17">n</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 77
 ; <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/><div class="add"><span class="kw">hence </span><a NAME="E2:97_2_18"/>
contradiction
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:97"><span class="lab"><font color="Green" title="E81">A1</font></span></a>, <a class="ref" href="number07.html#T61" target="_self" onmouseover="rs('number07/T61')" onmouseout="rh()">Th61</a>, <a class="ref" href="xprimes1.html#T79" onmouseover="rs('xprimes1/T79')" onmouseout="rh()">XPRIMES1:79</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/></div><span class="kw">end;</span></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="97_2_19"><span class="kw">suppose </span></a><a NAME="E1:97_2_19"/>
<font color="Maroon" title="c17">n</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 81
 ; <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/><div class="add"><span class="kw">hence </span><a NAME="E2:97_2_19"/>
contradiction
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:97"><span class="lab"><font color="Green" title="E81">A1</font></span></a>, <a class="ref" href="number07.html#T61" target="_self" onmouseover="rs('number07/T61')" onmouseout="rh()">Th61</a>, <a class="ref" href="xprimes1.html#T83" onmouseover="rs('xprimes1/T83')" onmouseout="rh()">XPRIMES1:83</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/></div><span class="kw">end;</span></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="97_2_20"><span class="kw">suppose </span></a><a NAME="E1:97_2_20"/>
<font color="Maroon" title="c17">n</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 89
 ; <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/><div class="add"><span class="kw">hence </span><a NAME="E2:97_2_20"/>
contradiction
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:97"><span class="lab"><font color="Green" title="E81">A1</font></span></a>, <a class="ref" href="number07.html#T61" target="_self" onmouseover="rs('number07/T61')" onmouseout="rh()">Th61</a>, <a class="ref" href="xprimes1.html#T89" onmouseover="rs('xprimes1/T89')" onmouseout="rh()">XPRIMES1:89</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/></div><span class="kw">end;</span></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="97_2_21"><span class="kw">suppose </span></a><a NAME="E1:97_2_21"/>
<font color="Maroon" title="c17">n</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 97
 ; <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/><div class="add"><span class="kw">hence </span><a NAME="E2:97_2_21"/>
contradiction
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:97"><span class="lab"><font color="Green" title="E81">A1</font></span></a>, <a class="ref" href="number07.html#T61" target="_self" onmouseover="rs('number07/T61')" onmouseout="rh()">Th61</a>, <a class="ref" href="xprimes1.html#T97" onmouseover="rs('xprimes1/T97')" onmouseout="rh()">XPRIMES1:97</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/></div><span class="kw">end;</span></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="97_2_22"><span class="kw">suppose </span></a><a NAME="E1:97_2_22"/>
<font color="Maroon" title="c17">n</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 101
 ; <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/><div class="add"><span class="kw">hence </span><a NAME="E2:97_2_22"/>
contradiction
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:97"><span class="lab"><font color="Green" title="E81">A1</font></span></a>, <a class="ref" href="number07.html#T61" target="_self" onmouseover="rs('number07/T61')" onmouseout="rh()">Th61</a>, <a class="ref" href="xprimes1.html#T101" onmouseover="rs('xprimes1/T101')" onmouseout="rh()">XPRIMES1:101</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/></div><span class="kw">end;</span></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="97_2_23"><span class="kw">suppose </span></a><a NAME="E1:97_2_23"/>
<font color="Maroon" title="c17">n</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 105
 ; <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/><div class="add"><span class="kw">hence </span><a NAME="E2:97_2_23"/>
contradiction
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:97"><span class="lab"><font color="Green" title="E81">A1</font></span></a>, <a class="ref" href="number07.html#T61" target="_self" onmouseover="rs('number07/T61')" onmouseout="rh()">Th61</a>, <a class="ref" href="xprimes1.html#T107" onmouseover="rs('xprimes1/T107')" onmouseout="rh()">XPRIMES1:107</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/></div><span class="kw">end;</span></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="97_2_24"><span class="kw">suppose </span></a><a NAME="E1:97_2_24"/>
<font color="Maroon" title="c17">n</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 109
 ; <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/><div class="add"><span class="kw">hence </span><a NAME="E2:97_2_24"/>
contradiction
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:97"><span class="lab"><font color="Green" title="E81">A1</font></span></a>, <a class="ref" href="number07.html#T61" target="_self" onmouseover="rs('number07/T61')" onmouseout="rh()">Th61</a>, <a class="ref" href="xprimes1.html#T109" onmouseover="rs('xprimes1/T109')" onmouseout="rh()">XPRIMES1:109</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/></div><span class="kw">end;</span></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="97_2_25"><span class="kw">suppose </span></a><a NAME="E1:97_2_25"/>
<font color="Maroon" title="c17">n</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 113
 ; <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/><div class="add"><span class="kw">hence </span><a NAME="E2:97_2_25"/>
contradiction
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:97"><span class="lab"><font color="Green" title="E81">A1</font></span></a>, <a class="ref" href="number07.html#T61" target="_self" onmouseover="rs('number07/T61')" onmouseout="rh()">Th61</a>, <a class="ref" href="xprimes1.html#T113" onmouseover="rs('xprimes1/T113')" onmouseout="rh()">XPRIMES1:113</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/></div><span class="kw">end;</span></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="97_2_26"><span class="kw">suppose </span></a><a NAME="E1:97_2_26"/><span class="lab"><font color="Green" title="E88">A</font></span>: 
<font color="Maroon" title="c17">n</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 117
 ; <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/><div class="add"><a NAME="E2:97_2_26"/>
9 <a href="nat_d.html#R1" title="NAT_D:pred.1">divides</a> 9 <a href="xcmplx_0.html#K3" title="XCMPLX_0:func.3">*</a> 13
 ;<br/><span class="kw">hence </span><a NAME="E3:97_2_26"/>
contradiction
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:97"><span class="lab"><font color="Green" title="E81">A1</font></span></a>, <a class="txt" href="#E1:97_2_26"><span class="lab"><font color="Green" title="E88">A</font></span></a>, <a class="ref" href="number07.html#T63" target="_self" onmouseover="rs('number07/T63')" onmouseout="rh()">Th63</a>, <a class="ref" href="xprimes0.html#T9" onmouseover="rs('xprimes0/T9')" onmouseout="rh()">XPRIMES0:9</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/></div><span class="kw">end;</span></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="97_2_27"><span class="kw">suppose </span></a><a NAME="E1:97_2_27"/><span class="lab"><font color="Green" title="E88">A</font></span>: 
<font color="Maroon" title="c17">n</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 121
 ; <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/><div class="add"><a NAME="E2:97_2_27"/>
121 <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 11 <a href="xcmplx_0.html#K3" title="XCMPLX_0:func.3">*</a> 11
 ;<br/><span class="kw">hence </span><a NAME="E3:97_2_27"/>
contradiction
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:97"><span class="lab"><font color="Green" title="E81">A1</font></span></a>, <a class="txt" href="#E1:97_2_27"><span class="lab"><font color="Green" title="E88">A</font></span></a>, <a class="ref" href="number07.html#T64" target="_self" onmouseover="rs('number07/T64')" onmouseout="rh()">Th64</a>, <a class="ref" href="xprimes1.html#T11" onmouseover="rs('xprimes1/T11')" onmouseout="rh()">XPRIMES1:11</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/></div><span class="kw">end;</span></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="97_2_28"><span class="kw">suppose </span></a><a NAME="E1:97_2_28"/>
<font color="Maroon" title="c17">n</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 125
 ; <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/><div class="add"><span class="kw">hence </span><a NAME="E2:97_2_28"/>
contradiction
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:97"><span class="lab"><font color="Green" title="E81">A1</font></span></a>, <a class="ref" href="number07.html#T61" target="_self" onmouseover="rs('number07/T61')" onmouseout="rh()">Th61</a>, <a class="ref" href="xprimes1.html#T127" onmouseover="rs('xprimes1/T127')" onmouseout="rh()">XPRIMES1:127</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/></div><span class="kw">end;</span></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="97_2_29"><span class="kw">suppose </span></a><a NAME="E1:97_2_29"/>
<font color="Maroon" title="c17">n</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 129
 ; <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/><div class="add"><span class="kw">hence </span><a NAME="E2:97_2_29"/>
contradiction
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:97"><span class="lab"><font color="Green" title="E81">A1</font></span></a>, <a class="ref" href="number07.html#T61" target="_self" onmouseover="rs('number07/T61')" onmouseout="rh()">Th61</a>, <a class="ref" href="xprimes1.html#T131" onmouseover="rs('xprimes1/T131')" onmouseout="rh()">XPRIMES1:131</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/></div><span class="kw">end;</span></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="97_2_30"><span class="kw">suppose </span></a><a NAME="E1:97_2_30"/><span class="lab"><font color="Green" title="E88">A</font></span>: 
<font color="Maroon" title="c17">n</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 133
 ; <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/><div class="add"><a NAME="E2:97_2_30"/>
9 <a href="nat_d.html#R1" title="NAT_D:pred.1">divides</a> 9 <a href="xcmplx_0.html#K3" title="XCMPLX_0:func.3">*</a> 15
 ;<br/><span class="kw">hence </span><a NAME="E3:97_2_30"/>
contradiction
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:97"><span class="lab"><font color="Green" title="E81">A1</font></span></a>, <a class="txt" href="#E1:97_2_30"><span class="lab"><font color="Green" title="E88">A</font></span></a>, <a class="ref" href="number07.html#T63" target="_self" onmouseover="rs('number07/T63')" onmouseout="rh()">Th63</a>, <a class="ref" href="xprimes0.html#T9" onmouseover="rs('xprimes0/T9')" onmouseout="rh()">XPRIMES0:9</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/></div><span class="kw">end;</span></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="97_2_31"><span class="kw">suppose </span></a><a NAME="E1:97_2_31"/>
<font color="Maroon" title="c17">n</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 137
 ; <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/><div class="add"><span class="kw">hence </span><a NAME="E2:97_2_31"/>
contradiction
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:97"><span class="lab"><font color="Green" title="E81">A1</font></span></a>, <a class="ref" href="number07.html#T61" target="_self" onmouseover="rs('number07/T61')" onmouseout="rh()">Th61</a>, <a class="ref" href="xprimes1.html#T137" onmouseover="rs('xprimes1/T137')" onmouseout="rh()">XPRIMES1:137</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/></div><span class="kw">end;</span></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="97_2_32"><span class="kw">suppose </span></a><a NAME="E1:97_2_32"/><span class="lab"><font color="Green" title="E88">A</font></span>: 
<font color="Maroon" title="c17">n</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 145
 ; <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/><div class="add"><a NAME="E2:97_2_32"/>
21 <a href="nat_d.html#R1" title="NAT_D:pred.1">divides</a> 21 <a href="xcmplx_0.html#K3" title="XCMPLX_0:func.3">*</a> 7
 ;<br/><span class="kw">hence </span><a NAME="E3:97_2_32"/>
contradiction
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:97"><span class="lab"><font color="Green" title="E81">A1</font></span></a>, <a class="txt" href="#E1:97_2_32"><span class="lab"><font color="Green" title="E88">A</font></span></a>, <a class="ref" href="number07.html#T63" target="_self" onmouseover="rs('number07/T63')" onmouseout="rh()">Th63</a>, <a class="ref" href="xprimes0.html#T21" onmouseover="rs('xprimes0/T21')" onmouseout="rh()">XPRIMES0:21</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/></div><span class="kw">end;</span></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="97_2_33"><span class="kw">suppose </span></a><a NAME="E1:97_2_33"/>
<font color="Maroon" title="c17">n</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 149
 ; <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/><div class="add"><span class="kw">hence </span><a NAME="E2:97_2_33"/>
contradiction
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:97"><span class="lab"><font color="Green" title="E81">A1</font></span></a>, <a class="ref" href="number07.html#T61" target="_self" onmouseover="rs('number07/T61')" onmouseout="rh()">Th61</a>, <a class="ref" href="xprimes1.html#T149" onmouseover="rs('xprimes1/T149')" onmouseout="rh()">XPRIMES1:149</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/></div><span class="kw">end;</span></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="97_2_34"><span class="kw">suppose </span></a><a NAME="E1:97_2_34"/><span class="lab"><font color="Green" title="E88">A</font></span>: 
<font color="Maroon" title="c17">n</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 153
 ; <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/><div class="add"><a NAME="E2:97_2_34"/>
14 <a href="nat_d.html#R1" title="NAT_D:pred.1">divides</a> 14 <a href="xcmplx_0.html#K3" title="XCMPLX_0:func.3">*</a> 11
 ;<br/><span class="kw">hence </span><a NAME="E3:97_2_34"/>
contradiction
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:97"><span class="lab"><font color="Green" title="E81">A1</font></span></a>, <a class="txt" href="#E1:97_2_34"><span class="lab"><font color="Green" title="E88">A</font></span></a>, <a class="ref" href="number07.html#T63" target="_self" onmouseover="rs('number07/T63')" onmouseout="rh()">Th63</a>, <a class="ref" href="xprimes0.html#T14" onmouseover="rs('xprimes0/T14')" onmouseout="rh()">XPRIMES0:14</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/></div><span class="kw">end;</span></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="97_2_35"><span class="kw">suppose </span></a><a NAME="E1:97_2_35"/>
<font color="Maroon" title="c17">n</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 157
 ; <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/><div class="add"><span class="kw">hence </span><a NAME="E2:97_2_35"/>
contradiction
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:97"><span class="lab"><font color="Green" title="E81">A1</font></span></a>, <a class="ref" href="number07.html#T61" target="_self" onmouseover="rs('number07/T61')" onmouseout="rh()">Th61</a>, <a class="ref" href="xprimes1.html#T157" onmouseover="rs('xprimes1/T157')" onmouseout="rh()">XPRIMES1:157</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/></div><span class="kw">end;</span></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="97_2_36"><span class="kw">suppose </span></a><a NAME="E1:97_2_36"/>
<font color="Maroon" title="c17">n</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 161
 ; <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/><div class="add"><span class="kw">hence </span><a NAME="E2:97_2_36"/>
contradiction
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:97"><span class="lab"><font color="Green" title="E81">A1</font></span></a>, <a class="ref" href="number07.html#T61" target="_self" onmouseover="rs('number07/T61')" onmouseout="rh()">Th61</a>, <a class="ref" href="xprimes1.html#T163" onmouseover="rs('xprimes1/T163')" onmouseout="rh()">XPRIMES1:163</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/></div><span class="kw">end;</span></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="97_2_37"><span class="kw">suppose </span></a><a NAME="E1:97_2_37"/>
<font color="Maroon" title="c17">n</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 165
 ; <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/><div class="add"><span class="kw">hence </span><a NAME="E2:97_2_37"/>
contradiction
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:97"><span class="lab"><font color="Green" title="E81">A1</font></span></a>, <a class="ref" href="number07.html#T61" target="_self" onmouseover="rs('number07/T61')" onmouseout="rh()">Th61</a>, <a class="ref" href="xprimes1.html#T167" onmouseover="rs('xprimes1/T167')" onmouseout="rh()">XPRIMES1:167</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/></div><span class="kw">end;</span></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="97_2_38"><span class="kw">suppose </span></a><a NAME="E1:97_2_38"/><span class="lab"><font color="Green" title="E88">A</font></span>: 
<font color="Maroon" title="c17">n</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 169
 ; <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/><div class="add"><a NAME="E2:97_2_38"/>
169 <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 13 <a href="xcmplx_0.html#K3" title="XCMPLX_0:func.3">*</a> 13
 ;<br/><span class="kw">hence </span><a NAME="E3:97_2_38"/>
contradiction
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:97"><span class="lab"><font color="Green" title="E81">A1</font></span></a>, <a class="txt" href="#E1:97_2_38"><span class="lab"><font color="Green" title="E88">A</font></span></a>, <a class="ref" href="number07.html#T64" target="_self" onmouseover="rs('number07/T64')" onmouseout="rh()">Th64</a>, <a class="ref" href="xprimes1.html#T13" onmouseover="rs('xprimes1/T13')" onmouseout="rh()">XPRIMES1:13</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/></div><span class="kw">end;</span></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="97_2_39"><span class="kw">suppose </span></a><a NAME="E1:97_2_39"/>
<font color="Maroon" title="c17">n</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 173
 ; <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/><div class="add"><span class="kw">hence </span><a NAME="E2:97_2_39"/>
contradiction
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:97"><span class="lab"><font color="Green" title="E81">A1</font></span></a>, <a class="ref" href="number07.html#T61" target="_self" onmouseover="rs('number07/T61')" onmouseout="rh()">Th61</a>, <a class="ref" href="xprimes1.html#T173" onmouseover="rs('xprimes1/T173')" onmouseout="rh()">XPRIMES1:173</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/></div><span class="kw">end;</span></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="97_2_40"><span class="kw">suppose </span></a><a NAME="E1:97_2_40"/>
<font color="Maroon" title="c17">n</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 177
 ; <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/><div class="add"><span class="kw">hence </span><a NAME="E2:97_2_40"/>
contradiction
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:97"><span class="lab"><font color="Green" title="E81">A1</font></span></a>, <a class="ref" href="number07.html#T61" target="_self" onmouseover="rs('number07/T61')" onmouseout="rh()">Th61</a>, <a class="ref" href="xprimes1.html#T179" onmouseover="rs('xprimes1/T179')" onmouseout="rh()">XPRIMES1:179</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/></div><span class="kw">end;</span></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="97_2_41"><span class="kw">suppose </span></a><a NAME="E1:97_2_41"/>
<font color="Maroon" title="c17">n</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 181
 ; <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/><div class="add"><span class="kw">hence </span><a NAME="E2:97_2_41"/>
contradiction
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:97"><span class="lab"><font color="Green" title="E81">A1</font></span></a>, <a class="ref" href="number07.html#T61" target="_self" onmouseover="rs('number07/T61')" onmouseout="rh()">Th61</a>, <a class="ref" href="xprimes1.html#T181" onmouseover="rs('xprimes1/T181')" onmouseout="rh()">XPRIMES1:181</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/></div><span class="kw">end;</span></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="97_2_42"><span class="kw">suppose </span></a><a NAME="E1:97_2_42"/><span class="lab"><font color="Green" title="E88">A</font></span>: 
<font color="Maroon" title="c17">n</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 185
 ; <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/><div class="add"><a NAME="E2:97_2_42"/>
6 <a href="nat_d.html#R1" title="NAT_D:pred.1">divides</a> 6 <a href="xcmplx_0.html#K3" title="XCMPLX_0:func.3">*</a> 31
 ;<br/><span class="kw">hence </span><a NAME="E3:97_2_42"/>
contradiction
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:97"><span class="lab"><font color="Green" title="E81">A1</font></span></a>, <a class="txt" href="#E1:97_2_42"><span class="lab"><font color="Green" title="E88">A</font></span></a>, <a class="ref" href="number07.html#T63" target="_self" onmouseover="rs('number07/T63')" onmouseout="rh()">Th63</a>, <a class="ref" href="xprimes0.html#T6" onmouseover="rs('xprimes0/T6')" onmouseout="rh()">XPRIMES0:6</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/></div><span class="kw">end;</span></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="97_2_43"><span class="kw">suppose </span></a><a NAME="E1:97_2_43"/>
<font color="Maroon" title="c17">n</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 189
 ; <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/><div class="add"><span class="kw">hence </span><a NAME="E2:97_2_43"/>
contradiction
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:97"><span class="lab"><font color="Green" title="E81">A1</font></span></a>, <a class="ref" href="number07.html#T61" target="_self" onmouseover="rs('number07/T61')" onmouseout="rh()">Th61</a>, <a class="ref" href="xprimes1.html#T191" onmouseover="rs('xprimes1/T191')" onmouseout="rh()">XPRIMES1:191</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/></div><span class="kw">end;</span></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="97_2_44"><span class="kw">suppose </span></a><a NAME="E1:97_2_44"/>
<font color="Maroon" title="c17">n</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 193
 ; <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/><div class="add"><span class="kw">hence </span><a NAME="E2:97_2_44"/>
contradiction
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:97"><span class="lab"><font color="Green" title="E81">A1</font></span></a>, <a class="ref" href="number07.html#T61" target="_self" onmouseover="rs('number07/T61')" onmouseout="rh()">Th61</a>, <a class="ref" href="xprimes1.html#T193" onmouseover="rs('xprimes1/T193')" onmouseout="rh()">XPRIMES1:193</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/></div><span class="kw">end;</span></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="97_2_45"><span class="kw">suppose </span></a><a NAME="E1:97_2_45"/>
<font color="Maroon" title="c17">n</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 197
 ; <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/><div class="add"><span class="kw">hence </span><a NAME="E2:97_2_45"/>
contradiction
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:97"><span class="lab"><font color="Green" title="E81">A1</font></span></a>, <a class="ref" href="number07.html#T61" target="_self" onmouseover="rs('number07/T61')" onmouseout="rh()">Th61</a>, <a class="ref" href="xprimes1.html#T197" onmouseover="rs('xprimes1/T197')" onmouseout="rh()">XPRIMES1:197</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/></div><span class="kw">end;</span></div></div><span class="kw">end;</span></div>

</div>
