(* Define the subset type canonTree and show that it has
     decidable equality. *)

  Definition canonTree :=  { t:ShareTree | canonicalTree t }.

(* Specifications: *)
Lemma shareTree_dec_eq : forall x y:ShareTree, {x=y}+{x<>y}.
Lemma canonTree_eq : forall x y:canonTree, proj1_sig x = proj1_sig y -> x = y.
Lemma canonTree_eq_dec : forall x y:canonTree, {x=y}+{x<>y}.