(** More properties of [fold] : behavior with respect to Above/Below *)

Lemma fold_4 :
forall s s' x (A : Type) (eqA : A -> A -> Prop)
(st : Equivalence eqA) (i : A) (f : elt -> A -> A),
Proper (E.eq==>eqA==>eqA) f ->
Below x s -> Add x s s' -> eqA (fold f s' i) (fold f s (f x i)).