End Continuity.
Module Kleene.
(* just for this proof, we want that nat is a poset under <= *)
(* in other scopes, we'll use the equality as ordering *)
Section NatPoset.

(* Specifications: *)
Lemma nat_refl x : x <= x. Proof. by []. Qed.
Lemma nat_asym x y : x <= y -> y <= x -> x = y.
Definition nat_chain := Chain nat_chain_axiom.