Invertible Element of Associative Structure is Cancellable/Corollary
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Theorem
Let $\struct {S, \circ}$ be a monoid whose identity element is $e_S$.
An element of $\struct {S, \circ}$ which is invertible is also cancellable.
Proof
By definition, a monoid is an associative algebraic structure with an identity element.
The result follows from Invertible Element of Associative Structure is Cancellable.
$\blacksquare$