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<span class="kw">assume </span><a NAME="E1:102"/>
 <a href="newton.html#K13" title="NEWTON:func.13">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:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> contradiction</span><br/>

<span class="kw">then </span><span class="kw">consider </span><font color="Maroon" title="c1">x</font> being    <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a> <span class="kw"> such that </span><br/><a NAME="E3:102"/><span class="lab"><font color="Green" title="E50">A1</font></span>: 
<font color="Maroon" title="c1">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="newton.html#K13" title="NEWTON:func.13">SetPrimenumber</a> 2
 <span class="kw">by</span> <span class="lab"><a class="ref" href="xboole_0.html#D1" title="XBOOLE_0:def.1">XBOOLE_0:def 1</a></span>;<br/>
<span class="kw">reconsider </span><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> <span class="kw">by</span> <span class="lab"><a class="txt" href="#E3:102"><span class="lab"><font color="Green" title="E50">A1</font></span></a></span>;<br/>
<a NAME="E5:102"/><span class="lab"><font color="Green" title="E51">A2</font></span>: 
<font color="Maroon" title="c2">x</font> is  <a href="int_2.html#V1" title="INT_2:attr.1">prime</a> 
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E3:102"><span class="lab"><font color="Green" title="E50">A1</font></span></a>, <a class="ref" href="newton.html#D7" target="_self" title="NEWTON:def.7">Def7</a></span>;<br/>
<a NAME="E6:102"/>
<font color="Maroon" title="c2">x</font> <a href="xxreal_0.html#NR3" title="XXREAL_0:NR.3">&lt;</a> 2
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E3:102"><span class="lab"><font color="Green" title="E50">A1</font></span></a>, <a class="ref" href="newton.html#D7" target="_self" title="NEWTON:def.7">Def7</a></span>;<br/>
<a NAME="E7:102"/><span class="kw">then </span>
(  <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>  )
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E5:102"><span class="lab"><font color="Green" title="E51">A2</font></span></a>, <a class="ref" href="nat_1.html#T27" title="NAT_1:th.27">NAT_1:27</a></span>;<br/>
<span class="kw">hence </span><a NAME="E8:102"/>
contradiction
 <span class="kw">by</span> <span class="lab"><a class="ref" href="int_2.html#D5" title="INT_2:def.5">INT_2:def 5</a></span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> verum</span><br/>


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