<?xml version="1.0"?>
<div class="add">

<b>let </b><font color="Maroon" title="c1">n</font> be  <a href="abian.html#V1" title="ABIAN:attr.1">even</a>  <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of  <a href="numbers.html#K5" title="NUMBERS:func.5">NAT</a> ;<br/>

<font color="Maroon" title="c1">n</font> = 
<span class="p1">(<span class="default">2 <a href="nat_1.html#K2" title="NAT_1:func.2">*</a> <span class="p2">(<span class="default"><font color="Maroon" title="c1">n</font> <a href="nat_d.html#K3" title="NAT_D:func.3">div</a> 2</span>)</span></span>)</span> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> <span class="p1">(<span class="default"><font color="Maroon" title="c1">n</font> <a href="nat_d.html#K4" title="NAT_D:func.4">mod</a> 2</span>)</span>
<b>by </b><i><a class="ref" href="nat_d.html#T2" title="NAT_D:th.2">NAT_D:2</a></i>
<br/>.= 
<span class="p1">(<span class="default">2 <a href="nat_1.html#K2" title="NAT_1:func.2">*</a> <span class="p2">(<span class="default"><font color="Maroon" title="c1">n</font> <a href="nat_d.html#K3" title="NAT_D:func.3">div</a> 2</span>)</span></span>)</span> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 0
<b>by </b><i><a class="ref" href="nat_2.html#T23" target="_self" title="NAT_2:th.23">Th23</a></i>
;<br/>
<b>hence </b><a NAME="E2:27"/>
<font color="Maroon" title="c1">n</font> <a href="nat_d.html#K3" title="NAT_D:func.3">div</a> 2 <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><font color="Maroon" title="c1">n</font> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1</span>)</span> <a href="nat_d.html#K3" title="NAT_D:func.3">div</a> 2
 <b>by </b><i><a class="ref" href="nat_d.html#D1" title="NAT_D:def.1">NAT_D:def 1</a></i>;<br/>


</div>
