Definition induced_function3 : quotient R -> quotient S -> quotient T :=
  induced_function2arg projf2 equivR equivS projf2_well_defined.

(* Specifications: *)
Lemma induced_function3_correct: forall (a:A) (b:B), induced_function3 (quotient_projection R a) (quotient_projection S b) = quotient_projection T (f a b).