Group has Latin Square Property/Additive Notation

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

Then $G$ satisfies the Latin square property.

That is, for all $a, b \in G$, there exists a unique $g \in G$ such that $a + g = b$.

Similarly, there exists a unique $h \in G$ such that $h + a = b$.

Proof
From Group has Latin Square Property, we have that:

and: