(** 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_add2 : forall s' s i j x, NoDupA s -> NoDupA s' -> eqB i j -> ~ InA x s -> equivlistA s' (x::s) -> eqB (fold_right f i s') (f x (fold_right f j s)).