Notation NoDup := (NoDupA E.eq).Notation InA := (InA E.eq).

Lemma fold_2 : forall s s' x (A : Type) (eqA : A -> A -> Prop) (st : Equivalence eqA) (i : A) (f : elt -> A -> A), compat_op E.eq eqA f -> transpose eqA f -> ~ In x s -> Add x s s' -> eqA (fold f s' i) (f x (fold f s i)).