Definition induced_eval (b:quotient S) :=
  induced_function (eval b) eq_fn_equiv (well_defined_eval b).Definition induced_function2arg (a:quotient R) (b:quotient S) : C :=
  induced_eval b (induced2 a).

Lemma induced_function2arg_correct: forall (a:A) (b:B), induced_function2arg (quotient_projection R a) (quotient_projection S b) = f a b.