Section Fold_More.
Variables (A:Type)(eqA:A->A->Prop)(st:Equivalence eqA).
Variables (f:elt->A->A)(Comp:Proper (E.eq==>eqA==>eqA) f)(Ass:transpose eqA f).
(** ** Fold is a morphism *)
(** ** Fold and other set operators *)

Lemma add_fold : forall i s x, In x s ->
eqA (fold f (add x s) i) (fold f s i).