Definition bot_set t := t = @Unfinished this W A.
Definition bot_prg := @Prog _ _ _ bot_set (erefl _).

(* Specifications: *)
(* Bottom satisfies any specification *)
Lemma bot_spec : bot_prg \In has_spec this W s.
Definition sup es := DTbin_make (@sup_spec es).
(* sup is an upper bound *)
Lemma sup_supB es e : e \In es -> leq e (sup es).
Definition ret := with_spec (DTbin_make ret_has_spec).