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.