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

<b>assume </b><a NAME="E1:26"/>
<font color="Maroon" title="c1">j</font> <a href="xxreal_0.html#NR3" title="XXREAL_0:NR.3">&lt;</a> 1
 ;<br/>

<a NAME="E2:26"/><b>then </b>
<font color="Maroon" title="c1">j</font> <a href="xxreal_0.html#NR3" title="XXREAL_0:NR.3">&lt;</a> 0 <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1
 
;<br/>
<a NAME="E3:26"/><b>then </b><i><font color="Green" title="E11">A1</font></i>: 
<font color="Maroon" title="c1">j</font> <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> 0
 
<b>by </b><i><a class="ref" href="nat_1.html#T13" target="_self" title="NAT_1:th.13">Th38</a></i>;<br/>
<b>assume </b><a NAME="E4:26"/>
<font color="Maroon" title="c1">j</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> 0
 ;<br/>

<b>hence </b><a NAME="E5:26"/>
contradiction
 <b>by </b><i><a class="txt" href="nat_1.html#E3:26"><i><font color="Green" title="E11">A1</font></i></a>, <a class="ref" href="nat_1.html#T2" target="_self" title="NAT_1:th.2">Th18</a></i>;<br/>


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