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<a NAME="E1:113"/><i><font color="Green" title="E51">A1</font></i>: 
(  <a href="binop_2.html#K47" title="BINOP_2:func.47">addnat</a>  <a href="setwiseo.html#NR1" title="SETWISEO:NR.1">has_a_unity</a>  &amp;  <a href="binop_1.html#K3" title="BINOP_1:func.3">the_unity_wrt</a> <a href="binop_2.html#K47" title="BINOP_2:func.47">addnat</a>  <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="numbers.html#K6" title="NUMBERS:func.6">0</a>  )
 
<b>by </b><i><a class="ref" href="monoid_0.html#T44" target="_self" title="MONOID_0:th.44">Th44</a>, <a class="ref" href="monoid_0.html#T49" target="_self" title="MONOID_0:th.49">Th49</a></i>;<br/>
<a NAME="E2:113"/>
 ex <font color="Olive" title="b1">n</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>  st <font color="Olive" title="b1">n</font> <a href="binop_1.html#R3" title="BINOP_1:pred.3">is_a_unity_wrt</a>  <a href="binop_2.html#K47" title="BINOP_2:func.47">addnat</a> 
 
<b>by </b><i><a class="ref" href="setwiseo.html#D2" title="SETWISEO:def.2">SETWISEO:def 2</a></i>;<br/>
<b>hence </b><a NAME="E3:113"/>
 <a href="numbers.html#K6" title="NUMBERS:func.6">0</a>  <a href="binop_1.html#R3" title="BINOP_1:pred.3">is_a_unity_wrt</a>  <a href="binop_2.html#K47" title="BINOP_2:func.47">addnat</a> 
 <b>by </b><i><a class="txt" href="monoid_0.html#E1:113"><i><font color="Green" title="E51">A1</font></i></a>, <a class="ref" href="binop_1.html#D8" title="BINOP_1:def.8">BINOP_1:def 8</a></i>;<br/>

<b>thus </b><a NAME="E4:113"/>
 <a href="binop_2.html#K47" title="BINOP_2:func.47">addnat</a>  is <a href="monoid_0.html#V9" title="MONOID_0:attr.9">uniquely-decomposable</a>
 <b>by </b><i><a class="ref" href="monoid_0.html#D20" target="_self" title="MONOID_0:def.20">Def20</a>, <a class="ref" href="monoid_0.html#T49" target="_self" title="MONOID_0:th.49">Th49</a></i>;<br/>


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