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<b>let </b><font color="Maroon" title="c1">k</font> be   <a href="int_1.html#NM1" title="INT_1:NM.1">Integer</a>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> ( 1 <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> <font color="Maroon" title="c1">k</font> implies <font color="Maroon" title="c1">k</font> is   <a href="nat_1.html#NM1" title="NAT_1:NM.1">Nat</a> )</span><br/>

<b>assume </b><a NAME="E1:3"/>
1 <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> <font color="Maroon" title="c1">k</font>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> <font color="Maroon" title="c1">k</font> is   <a href="nat_1.html#NM1" title="NAT_1:NM.1">Nat</a></span><br/>

<b>then reconsider </b><font color="Maroon" title="c2">k</font> = <font color="Maroon" title="c1">k</font> as    <a href="subset_1.html#M2" title="SUBSET_1:mode.2">Element</a> of  <a href="numbers.html#K5" title="NUMBERS:func.5">NAT</a>  <b>by </b><i><a class="ref" href="int_1.html#T16" title="INT_1:th.16">INT_1:16</a></i>;<br/>
<a NAME="E3:3"/>
<font color="Maroon" title="c2">k</font> is   <a href="nat_1.html#NM1" title="NAT_1:NM.1">Nat</a>
 
;<br/>
<b>hence </b><a NAME="E4:3"/>
<font color="Maroon" title="c1">k</font> is   <a href="nat_1.html#NM1" title="NAT_1:NM.1">Nat</a>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> verum</span><br/>


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