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<b>let </b><font color="Maroon">n</font> be   <a href="nat_1.html#NM1">Nat</a>;<br/>

<b>assume </b><a NAME="E1:87"/><i><font color="Green">E31</font></i>: 
<font color="Maroon">n</font> <a href="xxreal_0.html#R1">&lt;=</a> 8
 ;<br/>

<b>assume </b><a NAME="E2:87"/><i><font color="Green">E32</font></i>: 
( not <font color="Maroon">n</font> <a href="hidden.html#R1">=</a> 0 &amp; not <font color="Maroon">n</font> <a href="hidden.html#R1">=</a> 1 &amp; not <font color="Maroon">n</font> <a href="hidden.html#R1">=</a> 2 &amp; not <font color="Maroon">n</font> <a href="hidden.html#R1">=</a> 3 &amp; not <font color="Maroon">n</font> <a href="hidden.html#R1">=</a> 4 &amp; not <font color="Maroon">n</font> <a href="hidden.html#R1">=</a> 5 &amp; not <font color="Maroon">n</font> <a href="hidden.html#R1">=</a> 6 &amp; not <font color="Maroon">n</font> <a href="hidden.html#R1">=</a> 7 &amp; not <font color="Maroon">n</font> <a href="hidden.html#R1">=</a> 8 )
 ;<br/>

<a NAME="E3:87"/><b>then </b>
<font color="Maroon">n</font> <a href="xxreal_0.html#NR3" target="_self">&lt;</a> 7 <a href="nat_1.html#K1" target="_self">+</a> 1
 
<b>by </b><i>, <a class="ref" href="real_1.html#D5">REAL_1:def 5</a></i>;<br/>
<a NAME="E4:87"/><b>then </b>
<font color="Maroon">n</font> <a href="xxreal_0.html#R1">&lt;=</a> 7
 
<b>by </b><i/>;<br/>
<b>hence </b><a NAME="E5:87"/>
contradiction
 <b>by </b><i>, <a class="ref" href="nat_1.html#T22" target="_self">Th22</a></i>;<br/>


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