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<b>let </b><font color="Maroon" title="c1">n</font> be   <a href="nat_1.html#NM1" title="NAT_1:NM.1">Nat</a>;<br/>

<b>assume </b><a NAME="E1:50"/><i><font color="Green" title="E18">A1</font></i>: 
<font color="Maroon" title="c1">n</font> <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> 5
 ;<br/>

<b>assume </b><a NAME="E2:50"/><i><font color="Green" title="E19">A2</font></i>: 
( not <font color="Maroon" title="c1">n</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 0 &amp; not <font color="Maroon" title="c1">n</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 1 &amp; not <font color="Maroon" title="c1">n</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 2 &amp; not <font color="Maroon" title="c1">n</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 3 &amp; not <font color="Maroon" title="c1">n</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 4 &amp; not <font color="Maroon" title="c1">n</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 5 )
 ;<br/>

<a NAME="E3:50"/><b>then </b>
<font color="Maroon" title="c1">n</font> <a href="xxreal_0.html#NR3" title="XXREAL_0:NR.3">&lt;</a> 4 <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1
 
<b>by </b><i><a class="txt" href="nat_1.html#E1:50"><i><font color="Green" title="E18">A1</font></i></a>, <a class="ref" href="real_1.html#D5" title="REAL_1:def.5">REAL_1:def 5</a></i>;<br/>
<a NAME="E4:50"/><b>then </b>
<font color="Maroon" title="c1">n</font> <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> 4
 
<b>by </b><i><a class="ref" href="nat_1.html#T13" target="_self" title="NAT_1:th.13">Th38</a></i>;<br/>
<b>hence </b><a NAME="E5:50"/>
contradiction
 <b>by </b><i><a class="txt" href="nat_1.html#E2:50"><i><font color="Green" title="E19">A2</font></i></a>, <a class="ref" href="nat_1.html#T29" target="_self" title="NAT_1:th.29">Th85</a></i>;<br/>


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