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<b>let </b><font color="Maroon" title="c1">x</font> be    <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a> ;<br/>

<font color="Maroon">H<sub>1</sub></font>( <a href="monoid_0.html#K6" title="MONOID_0:func.6">&lt;NAT,+,0&gt;</a> ) = 
<font color="Maroon">H<sub>1</sub></font>( <a href="monoid_0.html#K5" title="MONOID_0:func.5">&lt;NAT,+&gt;</a> )
<b>by </b><i><a class="ref" href="monoid_0.html#T20" target="_self" title="MONOID_0:th.20">Th20</a></i>
<br/>.= 
 <a href="numbers.html#K5" title="NUMBERS:func.5">NAT</a> 
<b>by </b><i><a class="ref" href="monoid_0.html#D27" target="_self" title="MONOID_0:def.27">Def27</a></i>
;<br/>
<b>hence </b><a NAME="E2:109"/>
( <font color="Maroon" title="c1">x</font> is   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <a href="monoid_0.html#K6" title="MONOID_0:func.6">&lt;NAT,+,0&gt;</a>  iff <font color="Maroon" title="c1">x</font> is    <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>  )
 ;<br/>


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