Definition projf2 (a:A) (b:B) :=
  quotient_projection T (f a b).

(* Specifications: *)
Lemma projf2_well_defined: forall (a1 a2:A) (b1 b2:B), R a1 a2 -> S b1 b2 -> projf2 a1 b1 = projf2 a2 b2.