Group is Cancellable Monoid

From ProofWiki
Jump to navigation Jump to search

Theorem

Let $\struct {G, \circ}$ be a group.

Then $\struct {G, \circ}$ is a cancellable monoid.


Proof

By definition, a group is a fortiori a monoid.

From Group Operation is Cancellable, $\circ$ is a cancellable operation in $G$.

Hence the result by definition of cancellable monoid.

$\blacksquare$


Sources