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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/>

<a NAME="E1:46"/>
(  <a href="algstr_0.html#G3" title="ALGSTR_0:aggr.3">multMagma</a>(# the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <a href="monoid_0.html#K5" title="MONOID_0:func.5">&lt;NAT,+,0&gt;</a> ,the <a href="algstr_0.html#U2" title="ALGSTR_0:sel.2">multF</a> of <a href="monoid_0.html#K5" title="MONOID_0:func.5">&lt;NAT,+,0&gt;</a>  #) <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="monoid_0.html#K4" title="MONOID_0:func.4">&lt;NAT,+&gt;</a>  &amp;  <a href="monoid_1.html#K13" title="MONOID_1:func.13">MultiSet_over</a> <font color="Maroon" title="c1">X</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="monoid_1.html#K12" title="MONOID_1:func.12">.:</a> <a href="monoid_0.html#K5" title="MONOID_0:func.5">&lt;NAT,+,0&gt;</a> ,<font color="Maroon" title="c1">X</font> &amp;  <a href="binop_1.html#K3" title="BINOP_1:func.3">the_unity_wrt</a> <font color="Maroon">H<sub>1</sub></font>( <a href="monoid_0.html#K4" title="MONOID_0:func.4">&lt;NAT,+&gt;</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" title="MONOID_0:th.44">MONOID_0:44</a>, <a class="ref" href="monoid_0.html#D22" title="MONOID_0:def.22">MONOID_0:def 22</a></i>;<br/>
<b>hence </b><a NAME="E2:46"/>
( the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <span class="p1">(<span class="default"><a href="monoid_1.html#K13" title="MONOID_1:func.13">MultiSet_over</a> <font color="Maroon" title="c1">X</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="fraenkel.html#K1" title="FRAENKEL:func.1">Funcs</a> <font color="Maroon" title="c1">X</font>,<a href="numbers.html#K5" title="NUMBERS:func.5">NAT</a>  &amp; the <a href="algstr_0.html#U2" title="ALGSTR_0:sel.2">multF</a> of <span class="p1">(<span class="default"><a href="monoid_1.html#K13" title="MONOID_1:func.13">MultiSet_over</a> <font color="Maroon" title="c1">X</font></span>)</span> <a href="funct_2.html#R1" title="FUNCT_2:pred.1">=</a> <a href="binop_2.html#K47" title="BINOP_2:func.47">addnat</a> ,<a href="numbers.html#K5" title="NUMBERS:func.5">NAT</a>  <a href="monoid_1.html#K8" title="MONOID_1:func.8">.:</a> <font color="Maroon" title="c1">X</font> &amp;  <a href="struct_0.html#K5" title="STRUCT_0:func.5">1.</a> <span class="p1">(<span class="default"><a href="monoid_1.html#K13" title="MONOID_1:func.13">MultiSet_over</a> <font color="Maroon" title="c1">X</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c1">X</font> <a href="monoid_1.html#K5" title="MONOID_1:func.5">--&gt;</a> <a href="numbers.html#K6" title="NUMBERS:func.6">0</a>  )
 <b>by </b><i><a class="ref" href="monoid_1.html#T18" target="_self" title="MONOID_1:th.18">Th18</a>, <a class="ref" href="monoid_1.html#T23" target="_self" title="MONOID_1:th.23">Th23</a>, <a class="ref" href="monoid_0.html#T52" title="MONOID_0:th.52">MONOID_0:52</a></i>;<br/>


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