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

<a NAME="E1:125"/>
 ex <font color="Olive">n</font> being   <a href="subset_1.html#M2">Element</a> of  <a href="numbers.html#K5">NAT</a>  st <font color="Olive">n</font> <a href="binop_1.html#R3">is_a_unity_wrt</a>  <a href="binop_2.html#K48">multnat</a> 
 
<b>by </b><i><a class="ref" href="setwiseo.html#D2">SETWISEO:def 2</a></i>;<br/>
<b>hence </b><a NAME="E2:125"/>
1 <a href="binop_1.html#R3">is_a_unity_wrt</a>  <a href="binop_2.html#K48">multnat</a> 
 <b>by </b><i><a class="ref" href="monoid_0.html#T6" target="_self">Th6</a>, <a class="txt" href="monoid_0.html#E27"><i><font color="Green">Lemma57</font></i></a>, <a class="ref" href="binop_1.html#D8">BINOP_1:def 8</a></i>;<br/>

<b>thus </b><a NAME="E3:125"/>
 <a href="binop_2.html#K48">multnat</a>  is <a href="monoid_0.html#V9" target="_self">uniquely-decomposable</a>
 <b>by </b><i>, <a class="ref" href="monoid_0.html#T6" target="_self">Th6</a></i>;<br/>


</div>
