Section Normalize.
Context (A : Type).
Class Normalizes (m : relation A) (m' : relation A) : Prop :=
normalizes : relation_equivalence m m'.
(** Current strategy: add [flip] everywhere and reduce using [subrelation] afterwards. *)

Lemma proper_normalizes_proper `(Normalizes R0 R1, Proper A R1 m) : Proper R0 m.