Add Parametric Relation X Y: (X -> Y) (@ext_eq X Y)
  reflexivity proved by (@ext_eq_refl X Y)
  symmetry proved by (@ext_eq_sym X Y)
  transitivity proved by (@ext_eq_trans X Y)
    as ext_eq_rel.

Lemma ext_eq_rw (A B: Type) (f g: A -> B): ext_eq f g -> forall x, f x = g x.