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<b>assume </b><a NAME="E1:92"/>
 <a href="newton.html#K14" title="NEWTON:func.14">SetPrimenumber</a> 2 <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a>  <a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a> 
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> contradiction</span><br/>

<b>then consider </b><font color="Maroon" title="c1">x</font> being    <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a> <b> such that </b><br/><a NAME="E3:92"/><i><font color="Green" title="E50">A1</font></i>: 
<font color="Maroon" title="c1">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="newton.html#K14" title="NEWTON:func.14">SetPrimenumber</a> 2
 <b>by </b><i><a class="ref" href="xboole_0.html#D1" title="XBOOLE_0:def.1">XBOOLE_0:def 1</a></i>;<br/>
<b>reconsider </b><font color="Maroon" title="c2">x</font> = <font color="Maroon" title="c1">x</font> as   <a href="nat_1.html#NM1" title="NAT_1:NM.1">Nat</a> <b>by </b><i><a class="txt" href="newton.html#E3:92"><i><font color="Green" title="E50">A1</font></i></a>, <a class="ref" href="ordinal1.html#D13" title="ORDINAL1:def.13">ORDINAL1:def 13</a></i>;<br/>
<a NAME="E5:92"/>
( <font color="Maroon" title="c2">x</font> <a href="xxreal_0.html#NR3" title="XXREAL_0:NR.3">&lt;</a> 2 &amp; <font color="Maroon" title="c2">x</font> is <a href="int_2.html#V1" title="INT_2:attr.1">prime</a> )
 
<b>by </b><i><a class="txt" href="newton.html#E3:92"><i><font color="Green" title="E50">A1</font></i></a>, <a class="ref" href="newton.html#D7" target="_self" title="NEWTON:def.7">Def7</a></i>;<br/>
<a NAME="E6:92"/><b>then </b>
(  <a href="numbers.html#K6" title="NUMBERS:func.6">0</a>  is <a href="int_2.html#V1" title="INT_2:attr.1">prime</a> or 1 is <a href="int_2.html#V1" title="INT_2:attr.1">prime</a> )
 
<b>by </b><i><a class="ref" href="nat_1.html#T27" title="NAT_1:th.27">NAT_1:27</a></i>;<br/>
<b>hence </b><a NAME="E7:92"/>
contradiction
 <b>by </b><i><a class="ref" href="int_2.html#D5" title="INT_2:def.5">INT_2:def 5</a></i>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> verum</span><br/>


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