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<span class="kw">given </span><font color="Maroon" title="c5">p</font> being   <a href="int_2.html#NM1" title="INT_2:NM.1">Prime</a><span class="kw"> such that </span><a NAME="E2:163"/><span class="lab"><font color="Green" title="E123">A1</font></span>: 
<font color="Maroon" title="c5">p</font> <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> 130
 <span class="kw">and </span><br/><a NAME="E3:163"/><span class="lab"><font color="Green" title="E124">A2</font></span>: 
<font color="Maroon" title="c5">p</font> <a href="number08.html#R3" title="NUMBER08:pred.3">satisfies_Sierpinski_problem_105</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="E4:163"/>
<font color="Maroon" title="c5">p</font> <a href="xxreal_0.html#NR3" title="XXREAL_0:NR.3">&lt;</a> 130 <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:163"><span class="lab"><font color="Green" title="E123">A1</font></span></a>, <a class="ref" href="nat_1.html#T13" onmouseover="rs('nat_1/T13')" onmouseout="rh()">NAT_1:13</a></span>;<br/>
<div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="163_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="E1:163_1"/><span class="kw">then </span>
( <font color="Maroon" title="c5">p</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 2 or <font color="Maroon" title="c5">p</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 3 or <font color="Maroon" title="c5">p</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 5 or <font color="Maroon" title="c5">p</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 7 or <font color="Maroon" title="c5">p</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 11 or <font color="Maroon" title="c5">p</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 13 or <font color="Maroon" title="c5">p</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 17 or <font color="Maroon" title="c5">p</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 19 or <font color="Maroon" title="c5">p</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 23 or <font color="Maroon" title="c5">p</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 29 or <font color="Maroon" title="c5">p</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 31 or <font color="Maroon" title="c5">p</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 37 or <font color="Maroon" title="c5">p</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 41 or <font color="Maroon" title="c5">p</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 43 or <font color="Maroon" title="c5">p</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 47 or <font color="Maroon" title="c5">p</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 53 or <font color="Maroon" title="c5">p</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 59 or <font color="Maroon" title="c5">p</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 61 or <font color="Maroon" title="c5">p</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 67 or <font color="Maroon" title="c5">p</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 71 or <font color="Maroon" title="c5">p</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 73 or <font color="Maroon" title="c5">p</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 79 or <font color="Maroon" title="c5">p</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 83 or <font color="Maroon" title="c5">p</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 89 or <font color="Maroon" title="c5">p</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 97 or <font color="Maroon" title="c5">p</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 101 or <font color="Maroon" title="c5">p</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 103 or <font color="Maroon" title="c5">p</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 107 or <font color="Maroon" title="c5">p</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 109 or <font color="Maroon" title="c5">p</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 113 or <font color="Maroon" title="c5">p</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 127 )
 </span><span class="kw">by</span> <span class="lab"><a class="ref" href="xprimet1.html#T61" onmouseover="rs('xprimet1/T61')" onmouseout="rh()">XPRIMET1:61</a></span>;<br/><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="163_1_1"><span class="kw">suppose </span></a><a NAME="E1:163_1_1"/>
<font color="Maroon" title="c5">p</font> <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"> contradiction</span><br/><div class="add"><span class="kw">hence </span><a NAME="E2:163_1_1"/>
contradiction
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E3:163"><span class="lab"><font color="Green" title="E124">A2</font></span></a>, <a class="ref" href="number08.html#T81" target="_self" onmouseover="rs('number08/T81')" onmouseout="rh()">Th81</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="163_1_2"><span class="kw">suppose </span></a><a NAME="E1:163_1_2"/>
<font color="Maroon" title="c5">p</font> <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"> contradiction</span><br/><div class="add"><span class="kw">hence </span><a NAME="E2:163_1_2"/>
contradiction
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E3:163"><span class="lab"><font color="Green" title="E124">A2</font></span></a>, <a class="ref" href="number08.html#T81" target="_self" onmouseover="rs('number08/T81')" onmouseout="rh()">Th81</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="163_1_3"><span class="kw">suppose </span></a><a NAME="E1:163_1_3"/>
<font color="Maroon" title="c5">p</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="E2:163_1_3"/>
contradiction
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E3:163"><span class="lab"><font color="Green" title="E124">A2</font></span></a>, <a class="ref" href="number08.html#T81" target="_self" onmouseover="rs('number08/T81')" onmouseout="rh()">Th81</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="163_1_4"><span class="kw">suppose </span></a><a NAME="E1:163_1_4"/>
<font color="Maroon" title="c5">p</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 7
 ; <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="E2:163_1_4"/>
contradiction
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E3:163"><span class="lab"><font color="Green" title="E124">A2</font></span></a>, <a class="ref" href="number08.html#T81" target="_self" onmouseover="rs('number08/T81')" onmouseout="rh()">Th81</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="163_1_5"><span class="kw">suppose </span></a><a NAME="E1:163_1_5"/>
<font color="Maroon" title="c5">p</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 11
 ; <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="E2:163_1_5"/>
contradiction
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E3:163"><span class="lab"><font color="Green" title="E124">A2</font></span></a>, <a class="ref" href="number08.html#T81" target="_self" onmouseover="rs('number08/T81')" onmouseout="rh()">Th81</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="163_1_6"><span class="kw">suppose </span></a><a NAME="E1:163_1_6"/>
<font color="Maroon" title="c5">p</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="E2:163_1_6"/>
contradiction
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E3:163"><span class="lab"><font color="Green" title="E124">A2</font></span></a>, <a class="ref" href="number08.html#T81" target="_self" onmouseover="rs('number08/T81')" onmouseout="rh()">Th81</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="163_1_7"><span class="kw">suppose </span></a><a NAME="E1:163_1_7"/>
<font color="Maroon" title="c5">p</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="E2:163_1_7"/>
contradiction
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E3:163"><span class="lab"><font color="Green" title="E124">A2</font></span></a>, <a class="ref" href="number08.html#T81" target="_self" onmouseover="rs('number08/T81')" onmouseout="rh()">Th81</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="163_1_8"><span class="kw">suppose </span></a><a NAME="E1:163_1_8"/>
<font color="Maroon" title="c5">p</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 19
 ; <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="E2:163_1_8"/>
contradiction
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E3:163"><span class="lab"><font color="Green" title="E124">A2</font></span></a>, <a class="ref" href="number08.html#T81" target="_self" onmouseover="rs('number08/T81')" onmouseout="rh()">Th81</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="163_1_9"><span class="kw">suppose </span></a><a NAME="E1:163_1_9"/>
<font color="Maroon" title="c5">p</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 23
 ; <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="E2:163_1_9"/>
contradiction
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E3:163"><span class="lab"><font color="Green" title="E124">A2</font></span></a>, <a class="ref" href="number08.html#T81" target="_self" onmouseover="rs('number08/T81')" onmouseout="rh()">Th81</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="163_1_10"><span class="kw">suppose </span></a><a NAME="E1:163_1_10"/>
<font color="Maroon" title="c5">p</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="E2:163_1_10"/>
contradiction
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E3:163"><span class="lab"><font color="Green" title="E124">A2</font></span></a>, <a class="ref" href="number08.html#T81" target="_self" onmouseover="rs('number08/T81')" onmouseout="rh()">Th81</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="163_1_11"><span class="kw">suppose </span></a><a NAME="E1:163_1_11"/>
<font color="Maroon" title="c5">p</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 31
 ; <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="E2:163_1_11"/>
contradiction
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E3:163"><span class="lab"><font color="Green" title="E124">A2</font></span></a>, <a class="txt" href="number08.html#E6"><span class="lab"><font color="Green" title="E6">Lm6</font></span></a>, <a class="ref" href="xprimes1.html#T2" onmouseover="rs('xprimes1/T2')" onmouseout="rh()">XPRIMES1:2</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="163_1_12"><span class="kw">suppose </span></a><a NAME="E1:163_1_12"/>
<font color="Maroon" title="c5">p</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="E2:163_1_12"/>
contradiction
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E3:163"><span class="lab"><font color="Green" title="E124">A2</font></span></a>, <a class="txt" href="number08.html#E132"><span class="lab"><font color="Green" title="E104">Lm38</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/></div><span class="kw">end;</span></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="163_1_13"><span class="kw">suppose </span></a><a NAME="E1:163_1_13"/>
<font color="Maroon" title="c5">p</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="E2:163_1_13"/>
contradiction
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E3:163"><span class="lab"><font color="Green" title="E124">A2</font></span></a>, <a class="txt" href="number08.html#E133"><span class="lab"><font color="Green" title="E105">Lm39</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/></div><span class="kw">end;</span></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="163_1_14"><span class="kw">suppose </span></a><a NAME="E1:163_1_14"/>
<font color="Maroon" title="c5">p</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 43
 ; <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="E2:163_1_14"/>
contradiction
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E3:163"><span class="lab"><font color="Green" title="E124">A2</font></span></a>, <a class="txt" href="number08.html#E134"><span class="lab"><font color="Green" title="E106">Lm40</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/></div><span class="kw">end;</span></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="163_1_15"><span class="kw">suppose </span></a><a NAME="E1:163_1_15"/>
<font color="Maroon" title="c5">p</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 47
 ; <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="E2:163_1_15"/>
contradiction
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E3:163"><span class="lab"><font color="Green" title="E124">A2</font></span></a>, <a class="txt" href="number08.html#E135"><span class="lab"><font color="Green" title="E107">Lm41</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/></div><span class="kw">end;</span></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="163_1_16"><span class="kw">suppose </span></a><a NAME="E1:163_1_16"/>
<font color="Maroon" title="c5">p</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="E2:163_1_16"/>
contradiction
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E3:163"><span class="lab"><font color="Green" title="E124">A2</font></span></a>, <a class="txt" href="number08.html#E136"><span class="lab"><font color="Green" title="E108">Lm42</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/></div><span class="kw">end;</span></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="163_1_17"><span class="kw">suppose </span></a><a NAME="E1:163_1_17"/>
<font color="Maroon" title="c5">p</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 59
 ; <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="E2:163_1_17"/>
contradiction
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E3:163"><span class="lab"><font color="Green" title="E124">A2</font></span></a>, <a class="txt" href="number08.html#E137"><span class="lab"><font color="Green" title="E109">Lm43</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/></div><span class="kw">end;</span></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="163_1_18"><span class="kw">suppose </span></a><a NAME="E1:163_1_18"/>
<font color="Maroon" title="c5">p</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="E2:163_1_18"/>
contradiction
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E3:163"><span class="lab"><font color="Green" title="E124">A2</font></span></a>, <a class="txt" href="number08.html#E138"><span class="lab"><font color="Green" title="E110">Lm44</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/></div><span class="kw">end;</span></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="163_1_19"><span class="kw">suppose </span></a><a NAME="E1:163_1_19"/>
<font color="Maroon" title="c5">p</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 67
 ; <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="E2:163_1_19"/>
contradiction
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E3:163"><span class="lab"><font color="Green" title="E124">A2</font></span></a>, <a class="txt" href="number08.html#E139"><span class="lab"><font color="Green" title="E111">Lm45</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/></div><span class="kw">end;</span></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="163_1_20"><span class="kw">suppose </span></a><a NAME="E1:163_1_20"/>
<font color="Maroon" title="c5">p</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 71
 ; <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="E2:163_1_20"/>
contradiction
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E3:163"><span class="lab"><font color="Green" title="E124">A2</font></span></a>, <a class="txt" href="number08.html#E140"><span class="lab"><font color="Green" title="E112">Lm46</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/></div><span class="kw">end;</span></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="163_1_21"><span class="kw">suppose </span></a><a NAME="E1:163_1_21"/>
<font color="Maroon" title="c5">p</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="E2:163_1_21"/>
contradiction
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E3:163"><span class="lab"><font color="Green" title="E124">A2</font></span></a>, <a class="txt" href="number08.html#E141"><span class="lab"><font color="Green" title="E113">Lm47</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/></div><span class="kw">end;</span></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="163_1_22"><span class="kw">suppose </span></a><a NAME="E1:163_1_22"/>
<font color="Maroon" title="c5">p</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 79
 ; <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="E2:163_1_22"/>
contradiction
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E3:163"><span class="lab"><font color="Green" title="E124">A2</font></span></a>, <a class="txt" href="number08.html#E142"><span class="lab"><font color="Green" title="E114">Lm48</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/></div><span class="kw">end;</span></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="163_1_23"><span class="kw">suppose </span></a><a NAME="E1:163_1_23"/>
<font color="Maroon" title="c5">p</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 83
 ; <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="E2:163_1_23"/>
contradiction
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E3:163"><span class="lab"><font color="Green" title="E124">A2</font></span></a>, <a class="txt" href="number08.html#E143"><span class="lab"><font color="Green" title="E115">Lm49</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/></div><span class="kw">end;</span></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="163_1_24"><span class="kw">suppose </span></a><a NAME="E1:163_1_24"/>
<font color="Maroon" title="c5">p</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="E2:163_1_24"/>
contradiction
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E3:163"><span class="lab"><font color="Green" title="E124">A2</font></span></a>, <a class="txt" href="number08.html#E144"><span class="lab"><font color="Green" title="E116">Lm50</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/></div><span class="kw">end;</span></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="163_1_25"><span class="kw">suppose </span></a><a NAME="E1:163_1_25"/>
<font color="Maroon" title="c5">p</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="E2:163_1_25"/>
contradiction
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E3:163"><span class="lab"><font color="Green" title="E124">A2</font></span></a>, <a class="txt" href="number08.html#E145"><span class="lab"><font color="Green" title="E117">Lm51</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/></div><span class="kw">end;</span></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="163_1_26"><span class="kw">suppose </span></a><a NAME="E1:163_1_26"/>
<font color="Maroon" title="c5">p</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="E2:163_1_26"/>
contradiction
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E3:163"><span class="lab"><font color="Green" title="E124">A2</font></span></a>, <a class="txt" href="number08.html#E146"><span class="lab"><font color="Green" title="E118">Lm52</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/></div><span class="kw">end;</span></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="163_1_27"><span class="kw">suppose </span></a><a NAME="E1:163_1_27"/>
<font color="Maroon" title="c5">p</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 103
 ; <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="E2:163_1_27"/>
contradiction
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E3:163"><span class="lab"><font color="Green" title="E124">A2</font></span></a>, <a class="txt" href="number08.html#E147"><span class="lab"><font color="Green" title="E119">Lm53</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/></div><span class="kw">end;</span></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="163_1_28"><span class="kw">suppose </span></a><a NAME="E1:163_1_28"/>
<font color="Maroon" title="c5">p</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 107
 ; <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="E2:163_1_28"/>
contradiction
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E3:163"><span class="lab"><font color="Green" title="E124">A2</font></span></a>, <a class="txt" href="number08.html#E148"><span class="lab"><font color="Green" title="E120">Lm54</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/></div><span class="kw">end;</span></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="163_1_29"><span class="kw">suppose </span></a><a NAME="E1:163_1_29"/>
<font color="Maroon" title="c5">p</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="E2:163_1_29"/>
contradiction
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E3:163"><span class="lab"><font color="Green" title="E124">A2</font></span></a>, <a class="txt" href="number08.html#E149"><span class="lab"><font color="Green" title="E121">Lm55</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/></div><span class="kw">end;</span></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="163_1_30"><span class="kw">suppose </span></a><a NAME="E1:163_1_30"/>
<font color="Maroon" title="c5">p</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="E2:163_1_30"/>
contradiction
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E3:163"><span class="lab"><font color="Green" title="E124">A2</font></span></a>, <a class="txt" href="number08.html#E150"><span class="lab"><font color="Green" title="E122">Lm56</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/></div><span class="kw">end;</span></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="163_1_31"><span class="kw">suppose </span></a><a NAME="E1:163_1_31"/>
<font color="Maroon" title="c5">p</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 127
 ; <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="E2:163_1_31"/>
contradiction
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E3:163"><span class="lab"><font color="Green" title="E124">A2</font></span></a>, <a class="txt" href="number08.html#E7"><span class="lab"><font color="Green" title="E7">Lm7</font></span></a>, <a class="ref" href="xprimes1.html#T2" onmouseover="rs('xprimes1/T2')" onmouseout="rh()">XPRIMES1:2</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>
