Coset Product is Well-Defined

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

Let $N$ be a normal subgroup of $G$.

Let $a, b \in G$.

Then the coset product:
 * $\paren {a \circ N} \circ \paren {b \circ N} = \paren {a \circ b} \circ N$

is well-defined.

Also see

 * Coset Product of Normal Subgroup is Consistent with Subset Product Definition‎
 * Congruence Modulo Normal Subgroup is Congruence Relation‎