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<b>let </b><font color="Maroon">X</font> be    <a href="hidden.html#M1">set</a> ;<br/>

<a NAME="E1:46"/>
(  <a href="group_1.html#G1">HGrStr</a>(# the <a href="struct_0.html#U1">carrier</a> of <a href="monoid_0.html#K6">&lt;NAT,+,0&gt;</a> ,the <a href="group_1.html#U1">mult</a> of <a href="monoid_0.html#K6">&lt;NAT,+,0&gt;</a>  #) <a href="hidden.html#R1">=</a>  <a href="monoid_0.html#K5">&lt;NAT,+&gt;</a>  &amp;  <a href="monoid_1.html#K13" target="_self">MultiSet_over</a> <font color="Maroon">X</font> <a href="hidden.html#R1">=</a>  <a href="monoid_1.html#K12" target="_self">.:</a> <a href="monoid_0.html#K6">&lt;NAT,+,0&gt;</a> ,<font color="Maroon">X</font> &amp;  <a href="binop_1.html#K3">the_unity_wrt</a> <font color="Maroon">H<sub>1</sub></font>( <a href="monoid_0.html#K5">&lt;NAT,+&gt;</a> ) <a href="hidden.html#R1">=</a> 0 )
 
<b>by </b><i><a class="ref" href="monoid_0.html#T44">MONOID_0:44</a>, <a class="ref" href="monoid_0.html#D22">MONOID_0:def 22</a></i>;<br/>
<b>hence </b><a NAME="E2:46"/>
( the <a href="struct_0.html#U1">carrier</a> of <span class="p1">(<span class="default"><a href="monoid_1.html#K13" target="_self">MultiSet_over</a> <font color="Maroon">X</font></span>)</span> <a href="hidden.html#R1">=</a>  <a href="fraenkel.html#K1">Funcs</a> <font color="Maroon">X</font>,<a href="numbers.html#K5">NAT</a>  &amp; the <a href="group_1.html#U1">mult</a> of <span class="p1">(<span class="default"><a href="monoid_1.html#K13" target="_self">MultiSet_over</a> <font color="Maroon">X</font></span>)</span> <a href="funct_2.html#R1">=</a> <a href="binop_2.html#K47">addnat</a> ,<a href="numbers.html#K5">NAT</a>  <a href="monoid_1.html#K8" target="_self">.:</a> <font color="Maroon">X</font> &amp; the <a href="vectsp_1.html#U1">unity</a> of <span class="p1">(<span class="default"><a href="monoid_1.html#K13" target="_self">MultiSet_over</a> <font color="Maroon">X</font></span>)</span> <a href="hidden.html#R1">=</a> <font color="Maroon">X</font> <a href="monoid_1.html#K5" target="_self">--&gt;</a> 0 )
 <b>by </b><i>, , <a class="ref" href="monoid_0.html#T52">MONOID_0:52</a></i>;<br/>


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