Definition 1.6.2.  Let X, Y, Z be sets, :X × Y → Z be an operation, x ∈ X, y ∈ Y. We define
xy
by:
x(X × Y → Z(a, b) ↦ ca,b)y:= cx,y  (ca,b ∈ Z for each a ∈ X and b ∈ Y) = ((x, y))
Equality.  No proof.