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<b>let </b><font color="Maroon" title="c1">n</font>, <font color="Maroon" title="c2">k</font> be   <a href="nat_1.html#NM1" title="NAT_1:NM.1">Nat</a>;<br/>

<b>assume </b><a NAME="E1:13"/><i><font color="Green" title="E14">A1</font></i>: 
<font color="Maroon" title="c1">n</font> <a href="nat_d.html#R1" title="NAT_D:pred.1">divides</a> <font color="Maroon" title="c2">k</font>
 ;<br/>

<b>assume </b><a NAME="E2:13"/><i><font color="Green" title="E15">A2</font></i>: 
1 <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;</a> <font color="Maroon" title="c1">n</font>
 ;<br/>

<a NAME="E3:13"/><b>then </b>
1 <a href="binop_2.html#K23" title="BINOP_2:func.23">+</a> 1 <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;</a> <font color="Maroon" title="c1">n</font> <a href="real_1.html#K3" title="REAL_1:func.3">+</a> 1
 
<b>by </b><i><a class="ref" href="xreal_1.html#T8" title="XREAL_1:th.8">XREAL_1:8</a></i>;<br/>
<a NAME="E4:13"/><b>then </b>
2 <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> <font color="Maroon" title="c1">n</font>
 
<b>by </b><i><a class="ref" href="nat_1.html#T13" title="NAT_1:th.13">NAT_1:13</a></i>;<br/>
<b>then consider </b><font color="Maroon" title="c3">p</font> being    <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> such that </b><br/><a NAME="E6:13"/><i><font color="Green" title="E16">A3</font></i>: 
( <font color="Maroon" title="c3">p</font> is <a href="int_2.html#V1" title="INT_2:attr.1">prime</a> &amp; <font color="Maroon" title="c3">p</font> <a href="nat_d.html#R1" title="NAT_D:pred.1">divides</a> <font color="Maroon" title="c1">n</font> )
 <b>by </b><i><a class="ref" href="int_2.html#T48" title="INT_2:th.48">INT_2:48</a></i>;<br/>
<b>take </b>
<font color="Maroon" title="c3">p</font>
;<br/>

<b>thus </b><a NAME="E7:13"/>
<font color="Maroon" title="c3">p</font> <a href="nat_d.html#R1" title="NAT_D:pred.1">divides</a> <font color="Maroon" title="c2">k</font>
 <b>by </b><i><a class="txt" href="nat_4.html#E1:13"><i><font color="Green" title="E14">A1</font></i></a>, <a class="txt" href="nat_4.html#E6:13"><i><font color="Green" title="E16">A3</font></i></a>, <a class="ref" href="nat_d.html#T4" title="NAT_D:th.4">NAT_D:4</a></i>;<br/>

<b>thus </b><a NAME="E8:13"/>
<font color="Maroon" title="c3">p</font> <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> <font color="Maroon" title="c1">n</font>
 <b>by </b><i><a class="txt" href="nat_4.html#E2:13"><i><font color="Green" title="E15">A2</font></i></a>, <a class="txt" href="nat_4.html#E6:13"><i><font color="Green" title="E16">A3</font></i></a>, <a class="ref" href="nat_d.html#T7" title="NAT_D:th.7">NAT_D:7</a></i>;<br/>

<b>thus </b><a NAME="E9:13"/>
<font color="Maroon" title="c3">p</font> is <a href="int_2.html#V1" title="INT_2:attr.1">prime</a>
 <b>by </b><i><a class="txt" href="nat_4.html#E6:13"><i><font color="Green" title="E16">A3</font></i></a></i>;<br/>


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