Definition empty : t := mk (M.empty elt) wf_empty.

(* Specifications: *)
Lemma repr_empty: forall a, repr empty a = a.
Lemma sameclass_empty: forall a b, sameclass empty a b -> a = b.
Lemma identify_order: forall x y, order (M.set a b uf.(m)) y x <-> order uf.(m) y x \/ (x = a /\ y = b).
Lemma repr_empty: forall a, repr empty a = a.
Lemma sameclass_empty: forall a b, sameclass empty a b -> a = b.
Lemma identify_order: forall x y, order (M.set a b uf.(m)) y x <-> order uf.(m) y x \/ (x = a /\ y = b).