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<a NAME="E1:111"/>
(  <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>  &amp;  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>  )
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="monoid_0.html#T40" target="_self" title="MONOID_0:th.40">Th44</a>, <a class="ref" href="monoid_0.html#T43" target="_self" title="MONOID_0:th.43">Th49</a>, <a class="ref" href="setwiseo.html#D2" title="SETWISEO:def.2">SETWISEO:def 2</a></span>;<br/>
<span class="kw">hence </span><a NAME="E2:111"/>
 <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> 
 <span class="kw">by</span> <span class="lab"><a class="ref" href="binop_1.html#D8" title="BINOP_1:def.8">BINOP_1:def 8</a></span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide">  <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> </span><br/>

<span class="kw">thus </span><a NAME="E3:111"/>
 <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> 
 <span class="kw">by</span> <span class="lab"><a class="ref" href="monoid_0.html#D20" target="_self" title="MONOID_0:def.20">Def20</a>, <a class="ref" href="monoid_0.html#T43" target="_self" title="MONOID_0:th.43">Th49</a></span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> verum</span><br/>


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