(* ********************************************************************** *)
(** ** Type substitution preserves subtyping (10) *)

Lemma sub_through_subst_tt : forall Q E F Z S T P,
sub (F ++ Z ~ bind_sub Q ++ E) S T ->
sub E P Q ->
sub (map (subst_tb Z P) F ++ E) (subst_tt Z P S) (subst_tt Z P T).