Definition const_chain := Chain const_chainP.

(* Specifications: *)
Lemma proj1_mono : monotone (@fst T1 T2).
Lemma proj2_mono : monotone (@snd T1 T2).
Lemma diag_mono : monotone (fun x : T => (x, x)).
Lemma proj1_diagE : proj1_chain diag_chain = s.
Lemma proj2_diagE : proj2_chain diag_chain = s.
Lemma app_mono x : monotone (fun f : A -> T => f x).
Lemma dapp_mono x : monotone (fun f : dfunPoset T => f x).
Lemma nat_chain_axiom : chain_axiom (@PredT nat).