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<b>let </b><font color="Maroon">c<sub>1</sub></font> be  non <a href="xboole_0.html#V1">empty</a>  <a href="hidden.html#M1">set</a> ;<br/><b>let </b><font color="Maroon">c<sub>2</sub></font> be  non <a href="struct_0.html#V3">empty</a>  <a href="monoid_0.html#M2" target="_self">SubStr</a> of <font color="Maroon">c<sub>1</sub></font> <a href="monoid_0.html#K10" target="_self">*+^</a> ;<br/>



<a NAME="E1:133"/>
 <a href="binop_1.html#K3">the_unity_wrt</a> <font color="Maroon">H<sub>2</sub></font>(<font color="Maroon">c<sub>1</sub></font> <a href="monoid_0.html#K10" target="_self">*+^</a> ) <a href="hidden.html#R1">=</a>  <a href="xboole_0.html#K1">{}</a> 
 
<b>by </b><i><a class="ref" href="monoid_0.html#T69" target="_self">Th69</a></i>;<br/>
<b>hence </b><a NAME="E2:133"/>
(  <a href="xboole_0.html#K1">{}</a>  is   <a href="struct_0.html#NM1">Element</a> of <font color="Maroon">c<sub>2</sub></font> implies ( <font color="Maroon">c<sub>2</sub></font> is <a href="group_1.html#V2">unital</a> &amp;  <a href="binop_1.html#K3">the_unity_wrt</a> the <a href="group_1.html#U1">mult</a> of <font color="Maroon">c<sub>2</sub></font> <a href="hidden.html#R1">=</a>  <a href="xboole_0.html#K1">{}</a>  ) )
 <b>by </b><i><a class="ref" href="monoid_0.html#T32" target="_self">Th32</a></i>;<br/>


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