(** Two-argument functions that allow to reorder their arguments. *)
Definition transpose2 (f : A -> B -> B) :=
  forall (x y : A) (z z': B), eqB z z' -> eqB (f x (f y z)) (f y (f x z')).(** A version of transpose with restriction on where it should hold *)
Definition transpose_restr2 (R : A -> A -> Prop)(f : A -> B -> B) :=
  forall (x y : A) (z z': B), R x y -> eqB z z' -> eqB (f x (f y z)) (f y (f x z')).

Lemma fold_right_equivlistA_restr2 : forall s s' i j, NoDupA s -> NoDupA s' -> ForallOrdPairs R s -> equivlistA s s' -> eqB i j -> eqB (fold_right f i s) (fold_right f j s').