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<b>let </b><font color="Maroon" title="c1">n1</font>, <font color="Maroon" title="c2">n2</font> be    <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/><b>let </b><font color="Maroon" title="c3">m1</font>, <font color="Maroon" title="c4">m2</font> be   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <a href="monoid_0.html#K9" title="MONOID_0:func.9">&lt;NAT,*,1&gt;</a> ;<br/>



<a NAME="E1:121"/>
 <a href="group_1.html#G1" title="GROUP_1:aggr.1">HGrStr</a>(# the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <a href="monoid_0.html#K9" title="MONOID_0:func.9">&lt;NAT,*,1&gt;</a> ,the <a href="group_1.html#U1" title="GROUP_1:sel.1">mult</a> of <a href="monoid_0.html#K9" title="MONOID_0:func.9">&lt;NAT,*,1&gt;</a>  #) <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="monoid_0.html#K8" title="MONOID_0:func.8">&lt;NAT,*&gt;</a> 
 
<b>by </b><i><a class="ref" href="monoid_0.html#D22" target="_self" title="MONOID_0:def.22">Def22</a></i>;<br/>
<b>then reconsider </b><font color="Maroon" title="c5">x1</font> = <font color="Maroon" title="c3">m1</font>, <font color="Maroon" title="c6">x2</font> = <font color="Maroon" title="c4">m2</font> as   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <a href="monoid_0.html#K8" title="MONOID_0:func.8">&lt;NAT,*&gt;</a>  ;<br/>
<a NAME="E3:121"/>
<font color="Maroon" title="c5">x1</font> <a href="group_1.html#K10" title="GROUP_1:func.10">*</a> <font color="Maroon" title="c6">x2</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c3">m1</font> <a href="group_1.html#K10" title="GROUP_1:func.10">*</a> <font color="Maroon" title="c4">m2</font>
 
<b>by </b><i><a class="ref" href="monoid_0.html#T20" target="_self" title="MONOID_0:th.20">Th20</a></i>;<br/>
<b>hence </b><a NAME="E4:121"/>
( <font color="Maroon" title="c1">n1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c3">m1</font> &amp; <font color="Maroon" title="c2">n2</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c4">m2</font> implies <font color="Maroon" title="c3">m1</font> <a href="group_1.html#K10" title="GROUP_1:func.10">*</a> <font color="Maroon" title="c4">m2</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c1">n1</font> <a href="binop_2.html#K24" title="BINOP_2:func.24">*</a> <font color="Maroon" title="c2">n2</font> )
 <b>by </b><i><a class="ref" href="monoid_0.html#T58" target="_self" title="MONOID_0:th.58">Th58</a></i>;<br/>


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