Subset Product within Semigroup is Associative/Corollary

Corollary to Subset Product within Semigroup is Associative
Let $\struct {S, \circ}$ be a semigroup.

Then:

Proof
From the definition of Subset Product with Singleton:

The result then follows directly from Subset Product within Semigroup is Associative.

Also see

 * Subset Product within Commutative Structure is Commutative