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

Lemma flip_arrow `(NA : Normalizes A R (flip R'''), NB : Normalizes B R' (flip R'')) :
Normalizes (A -> B) (R ==> R') (flip (R''' ==> R'')%signature).