(** Extensional equality between trees. *)
Parameter beq: forall (A: Type), (A -> A -> bool) -> t A -> t A -> bool.

(* Specifications: *)
Axiom beq_correct:
forall (A: Type) (eqA: A -> A -> bool) (t1 t2: t A),
beq eqA t1 t2 = true <->
(forall (x: elt),
match get x t1, get x t2 with
| None, None => True
| Some y1, Some y2 => eqA y1 y2 = true
| _, _ => False
end).
Axiom beq_correct:
forall (A: Type) (eqA: A -> A -> bool) (t1 t2: t A),
beq eqA t1 t2 = true <->
(forall (x: elt),
match get x t1, get x t2 with
| None, None => True
| Some y1, Some y2 => eqA y1 y2 = true
| _, _ => False
end).