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<b>let </b><font color="Maroon">c<sub>1</sub></font>, <font color="Maroon">c<sub>2</sub></font> be   <a href="nat_1.html#NM1">Nat</a>;<br/><b>let </b><font color="Maroon">c<sub>3</sub></font>, <font color="Maroon">c<sub>4</sub></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><a class="ref" href="monoid_0.html#D22" target="_self">Def22</a></i>;<br/>
<b>then reconsider </b><font color="Maroon">c<sub>5</sub></font> = <font color="Maroon">c<sub>3</sub></font>, <font color="Maroon">c<sub>6</sub></font> = <font color="Maroon">c<sub>4</sub></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">c<sub>5</sub></font> <a href="group_1.html#K10">*</a> <font color="Maroon">c<sub>6</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>3</sub></font> <a href="group_1.html#K10">*</a> <font color="Maroon">c<sub>4</sub></font>
 
<b>by </b><i><a class="ref" href="monoid_0.html#T20" target="_self">Th20</a></i>;<br/>
<b>hence </b><a NAME="E4:123"/>
( <font color="Maroon">c<sub>1</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>3</sub></font> &amp; <font color="Maroon">c<sub>2</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>4</sub></font> implies <font color="Maroon">c<sub>3</sub></font> <a href="group_1.html#K10">*</a> <font color="Maroon">c<sub>4</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>1</sub></font> <a href="binop_2.html#K24">*</a> <font color="Maroon">c<sub>2</sub></font> )
 <b>by </b><i><a class="ref" href="monoid_0.html#T58" target="_self">Th58</a></i>;<br/>


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