(* Lemma typecheck_environ_join_switch2: forall sl Delta rho, typecheck_environ Delta rho -> typecheck_environ (join_tycon_labeled sl Delta) rho.  Lemma typecheck_environ_join_switch1: forall n sl rho Delta, typecheck_environ (update_tycon Delta (seq_of_labeled_statement (select_switch n sl))) rho -> typecheck_environ (join_tycon_labeled sl Delta) rho. *)

Lemma prop_subp:
forall A (NA: ageable A) (P Q: Prop) (w: nat),
(P -> Q) -> app_pred (!! P >=> !! Q)  w.