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<b>let </b><font color="Maroon">n1</font> be    <a href="subset_1.html#M2">Element</a> of  <a href="numbers.html#K5">NAT</a> , <font color="Maroon">n2</font> be    <a href="subset_1.html#M2">Element</a> of  <a href="numbers.html#K5">NAT</a> ;<br/><b>let </b><font color="Maroon">m1</font> be   <a href="struct_0.html#NM1">Element</a> of <a href="monoid_0.html#K9" target="_self">&lt;NAT,*,1&gt;</a> , <font color="Maroon">m2</font> be   <a href="struct_0.html#NM1">Element</a> of <a href="monoid_0.html#K9" target="_self">&lt;NAT,*,1&gt;</a> ;<br/>



<a NAME="E1:123"/>
 <a href="group_1.html#G1">HGrStr</a>(# the <a href="struct_0.html#U1">carrier</a> of <a href="monoid_0.html#K9" target="_self">&lt;NAT,*,1&gt;</a> ,the <a href="group_1.html#U1">mult</a> of <a href="monoid_0.html#K9" target="_self">&lt;NAT,*,1&gt;</a>  #) <a href="hidden.html#R1">=</a>  <a href="monoid_0.html#K8" target="_self">&lt;NAT,*&gt;</a> 
 
<b>by </b><i/>;<br/>
<b>then reconsider </b><font color="Maroon">x1</font> = <font color="Maroon">m1</font>, <font color="Maroon">x2</font> = <font color="Maroon">m2</font> as   <a href="struct_0.html#NM1">Element</a> of <a href="monoid_0.html#K8" target="_self">&lt;NAT,*&gt;</a>  ;<br/>
<a NAME="E3:123"/>
<font color="Maroon">x1</font> <a href="group_1.html#K10">*</a> <font color="Maroon">x2</font> <a href="hidden.html#R1">=</a> <font color="Maroon">m1</font> <a href="group_1.html#K10">*</a> <font color="Maroon">m2</font>
 
<b>by </b><i/>;<br/>
<b>hence </b><a NAME="E4:123"/>
( <font color="Maroon">n1</font> <a href="hidden.html#R1">=</a> <font color="Maroon">m1</font> &amp; <font color="Maroon">n2</font> <a href="hidden.html#R1">=</a> <font color="Maroon">m2</font> implies <font color="Maroon">m1</font> <a href="group_1.html#K10">*</a> <font color="Maroon">m2</font> <a href="hidden.html#R1">=</a> <font color="Maroon">n1</font> <a href="binop_2.html#K24">*</a> <font color="Maroon">n2</font> )
 <b>by </b><i><a class="ref" href="monoid_0.html#T4" target="_self">Th4</a></i>;<br/>


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