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<b>let </b><font color="Maroon" title="c1">X</font> be    <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a> ;<br/><b>let </b><font color="Maroon" title="c2">G</font> be  non <a href="struct_0.html#V2" title="STRUCT_0:attr.2">empty</a> <a href="group_1.html#V1" title="GROUP_1:attr.1">unital</a>  <a href="algstr_0.html#L3" title="ALGSTR_0:struct.3">multMagma</a> ;<br/>



<a NAME="E1:40"/>
 <a href="monoid_1.html#K11" title="MONOID_1:func.11">.:</a> <font color="Maroon" title="c2">G</font>,<font color="Maroon" title="c1">X</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="algstr_0.html#G4" title="ALGSTR_0:aggr.4">multLoopStr</a>(# <span class="p1">(<span class="default"><a href="fraenkel.html#K1" title="FRAENKEL:func.1">Funcs</a> <font color="Maroon" title="c1">X</font>,<font color="Maroon">H<sub>3</sub></font>(<font color="Maroon" title="c2">G</font>)</span>)</span>,<span class="p1">(<span class="default"><font color="Maroon">H<sub>1</sub></font>(<font color="Maroon" title="c2">G</font>),<font color="Maroon">H<sub>3</sub></font>(<font color="Maroon" title="c2">G</font>) <a href="monoid_1.html#K8" title="MONOID_1:func.8">.:</a> <font color="Maroon" title="c1">X</font></span>)</span>,<span class="p1">(<span class="default"><font color="Maroon" title="c1">X</font> <a href="monoid_1.html#K5" title="MONOID_1:func.5">--&gt;</a> <span class="p2">(<span class="default"><a href="binop_1.html#K3" title="BINOP_1:func.3">the_unity_wrt</a> <font color="Maroon">H<sub>1</sub></font>(<font color="Maroon" title="c2">G</font>)</span>)</span></span>)</span> #)
 
<b>by </b><i><a class="ref" href="monoid_1.html#D3" target="_self" title="MONOID_1:def.3">Def3</a></i>;<br/>
<b>hence </b><a NAME="E2:40"/>
 <a href="struct_0.html#K5" title="STRUCT_0:func.5">1.</a> <span class="p1">(<span class="default"><a href="monoid_1.html#K11" title="MONOID_1:func.11">.:</a> <font color="Maroon" title="c2">G</font>,<font color="Maroon" title="c1">X</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c1">X</font> <a href="monoid_1.html#K5" title="MONOID_1:func.5">--&gt;</a> <span class="p1">(<span class="default"><a href="binop_1.html#K3" title="BINOP_1:func.3">the_unity_wrt</a> the <a href="algstr_0.html#U2" title="ALGSTR_0:sel.2">multF</a> of <font color="Maroon" title="c2">G</font></span>)</span>
 ;<br/>


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