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<b>let </b><font color="Maroon">n</font> be  <a href="abian.html#V1">even</a>  <a href="subset_1.html#M2">Element</a> of  <a href="numbers.html#K5">NAT</a> ;<br/>

<font color="Maroon">n</font> = 
<span class="p1">(<span class="default">2 <a href="nat_1.html#K2">*</a> <span class="p2">(<span class="default"><font color="Maroon">n</font> <a href="nat_1.html#K5">div</a> 2</span>)</span></span>)</span> <a href="nat_1.html#K1">+</a> <span class="p1">(<span class="default"><font color="Maroon">n</font> <a href="nat_1.html#K6">mod</a> 2</span>)</span>
<b>by </b><i><a class="ref" href="nat_1.html#T47">NAT_1:47</a></i>
<br/>.= 
<span class="p1">(<span class="default">2 <a href="nat_1.html#K2">*</a> <span class="p2">(<span class="default"><font color="Maroon">n</font> <a href="nat_1.html#K5">div</a> 2</span>)</span></span>)</span> <a href="nat_1.html#K1">+</a> 0
<b>by </b><i/>
;<br/>
<b>hence </b><a NAME="E2:27"/>
<font color="Maroon">n</font> <a href="nat_1.html#K5">div</a> 2 <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><font color="Maroon">n</font> <a href="nat_1.html#K1">+</a> 1</span>)</span> <a href="nat_1.html#K5">div</a> 2
 <b>by </b><i><a class="ref" href="nat_1.html#D1">NAT_1:def 1</a></i>;<br/>


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