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<a NAME="E1:115"/><i><font color="Green">E28</font></i>: 
(  <a href="binop_2.html#K47">addnat</a>  <a href="setwiseo.html#NR1" target="_self">has_a_unity</a>  &amp;  <a href="binop_1.html#K3">the_unity_wrt</a> <a href="binop_2.html#K47">addnat</a>  <a href="hidden.html#R1">=</a> 0 )
 
<b>by </b><i><a class="ref" href="monoid_0.html#D12" target="_self">Def12</a>, <a class="ref" href="monoid_0.html#D20" target="_self">Def20</a></i>;<br/>
<a NAME="E2:115"/>
 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#K47">addnat</a> 
 
<b>by </b><i><a class="ref" href="setwiseo.html#D2">SETWISEO:def 2</a></i>;<br/>
<b>hence </b><a NAME="E3:115"/>
0 <a href="binop_1.html#R3">is_a_unity_wrt</a>  <a href="binop_2.html#K47">addnat</a> 
 <b>by </b><i>, <a class="ref" href="binop_1.html#D8">BINOP_1:def 8</a></i>;<br/>

<b>thus </b><a NAME="E4:115"/>
 <a href="binop_2.html#K47">addnat</a>  is <a href="monoid_0.html#V9" target="_self">uniquely-decomposable</a>
 <b>by </b><i>, <a class="ref" href="monoid_0.html#D20" target="_self">Def20</a></i>;<br/>


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