Coset Product is Well-Defined/Proof 3

Proof
Let $N \lhd G$ where $G$ is a group.

Let $a, a', b, b' \in G: N \circ a = N \circ a', N \circ b = N \circ b'$.

We need to show that $N \circ a \circ b = N \circ a' \circ b'$.

So: