(** Adding a valuation function on all elements of a set. *)

Definition sum (f:elt -> nat)(s:t) := fold (fun x => plus (f x)) s 0.Notation compat_opL := (Proper (E.eq==>Logic.eq==>Logic.eq)).Notation transposeL := (transpose Logic.eq).

Lemma sum_compat : forall f g, Proper (E.eq==>Logic.eq) f -> Proper (E.eq==>Logic.eq) g -> forall s, (forall x, In x s -> f x=g x) -> sum f s=sum g s.