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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>set </b><font color="Maroon">c<sub>2</sub></font> = <font color="Maroon">c<sub>1</sub></font> <a href="monoid_0.html#K11" target="_self">*+^+&lt;0&gt;</a> ;<br/>
<a NAME="E1:129"/>
(  <a href="group_1.html#G1">HGrStr</a>(# the <a href="struct_0.html#U1">carrier</a> of <span class="p1">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="monoid_0.html#K11" target="_self">*+^+&lt;0&gt;</a> </span>)</span>,the <a href="group_1.html#U1">mult</a> of <span class="p1">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="monoid_0.html#K11" target="_self">*+^+&lt;0&gt;</a> </span>)</span> #) <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>1</sub></font> <a href="monoid_0.html#K10" target="_self">*+^</a>  &amp;  <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#K11" target="_self">*+^+&lt;0&gt;</a> ) <a href="hidden.html#R1">=</a> <font color="Maroon">H<sub>3</sub></font>(<font color="Maroon">c<sub>1</sub></font> <a href="monoid_0.html#K11" target="_self">*+^+&lt;0&gt;</a> ) &amp;  <a href="binop_1.html#K3">the_unity_wrt</a> the <a href="group_1.html#U1">mult</a> of <span class="p1">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="monoid_0.html#K10" target="_self">*+^</a> </span>)</span> <a href="hidden.html#R1">=</a>  <a href="xboole_0.html#K1">{}</a>  )
 
<b>by </b><i><a class="ref" href="monoid_0.html#D22" target="_self">Def22</a>, <a class="ref" href="monoid_0.html#T19" target="_self">Th19</a>, <a class="ref" href="monoid_0.html#T69" target="_self">Th69</a></i>;<br/>
<b>hence </b><a NAME="E2:129"/>
( the <a href="struct_0.html#U1">carrier</a> of <span class="p1">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="monoid_0.html#K11" target="_self">*+^+&lt;0&gt;</a> </span>)</span> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>1</sub></font> <a href="finseq_2.html#K3">*</a>  &amp; the <a href="group_1.html#U1">mult</a> of <span class="p1">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="monoid_0.html#K11" target="_self">*+^+&lt;0&gt;</a> </span>)</span> <a href="funct_2.html#R1">=</a> <font color="Maroon">c<sub>1</sub></font> <a href="monoid_0.html#K12" target="_self">-concatenation</a>  &amp; the <a href="vectsp_1.html#U1">unity</a> of <span class="p1">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="monoid_0.html#K11" target="_self">*+^+&lt;0&gt;</a> </span>)</span> <a href="hidden.html#R1">=</a>  <a href="xboole_0.html#K1">{}</a>  )
 <b>by </b><i><a class="ref" href="monoid_0.html#D34" target="_self">Def34</a></i>;<br/>


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