Definition induced2 :=
induced_function2 induced1 equivR eq_fn_equiv well_defined_induced1.
Definition eval (b:quotient S) (f:quotient S->C): C := f b.

(* Specifications: *)
Lemma well_defined_eval: forall (b:quotient S) (f g:quotient S->C),
eq_fn f g -> eval b f = eval b g.