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<b>let </b><font color="Maroon">c<sub>1</sub></font> be    <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="group_1.html#V2">unital</a>  <a href="group_1.html#L1">HGrStr</a> ;<br/>



<a NAME="E1:40"/>
 <a href="monoid_1.html#K11" target="_self">.:</a> <font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>1</sub></font> <a href="hidden.html#R1">=</a>  <a href="vectsp_1.html#G1">multLoopStr</a>(# <span class="p1">(<span class="default"><a href="fraenkel.html#K1">Funcs</a> <font color="Maroon">c<sub>1</sub></font>,<font color="Maroon">H<sub>3</sub></font>(<font color="Maroon">c<sub>2</sub></font>)</span>)</span>,<span class="p1">(<span class="default"><font color="Maroon">H<sub>1</sub></font>(<font color="Maroon">c<sub>2</sub></font>),<font color="Maroon">H<sub>3</sub></font>(<font color="Maroon">c<sub>2</sub></font>) <a href="monoid_1.html#K8" target="_self">.:</a> <font color="Maroon">c<sub>1</sub></font></span>)</span>,<span class="p1">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="monoid_1.html#K5" target="_self">--&gt;</a> <span class="p2">(<span class="default"><a href="binop_1.html#K3">the_unity_wrt</a> <font color="Maroon">H<sub>1</sub></font>(<font color="Maroon">c<sub>2</sub></font>)</span>)</span></span>)</span> #)
 
<b>by </b><i><a class="ref" href="monoid_1.html#D3" target="_self">Def3</a></i>;<br/>
<b>hence </b><a NAME="E2:40"/>
the <a href="vectsp_1.html#U1">unity</a> of <span class="p1">(<span class="default"><a href="monoid_1.html#K11" target="_self">.:</a> <font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>1</sub></font> <a href="monoid_1.html#K5" target="_self">--&gt;</a> <span class="p1">(<span class="default"><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></span>)</span>
 ;<br/>


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