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<b>let </b><font color="Maroon">a</font> be    <a href="subset_1.html#M2">Element</a> of  <a href="numbers.html#K5">NAT</a> ;<br/><b>let </b><font color="Maroon">b</font> be    <a href="subset_1.html#M2">Element</a> of  <a href="numbers.html#K5">NAT</a> ;<br/>



<b>assume </b><a NAME="E1:75"/><i><font color="Green">E40</font></i>: 
( <font color="Maroon">a</font> <a href="nat_1.html#R1">divides</a> <font color="Maroon">b</font> &amp; <font color="Maroon">b</font> <a href="xxreal_0.html#NR3" target="_self">&lt;</a> <font color="Maroon">a</font> &amp; not <font color="Maroon">b</font> <a href="hidden.html#R1">=</a> 0 )
 ;<br/>

<a NAME="E2:75"/><b>then </b>
<font color="Maroon">b</font> <a href="xxreal_0.html#NR4" target="_self">&gt;</a> 0
 
;<br/>
<b>hence </b><a NAME="E3:75"/>
contradiction
 <b>by </b><i><a class="txt" href="wsierp_1.html#E14"><i><font color="Green">Lemma53</font></i></a>, <a class="ref" href="nat_1.html#T54">NAT_1:54</a></i>;<br/>


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