(** Soundness: if [step_expr] returns [Some ll], then every element of [ll] is a reduct. *)

(* Specifications: *)
Lemma context_compose:
forall k2 k3 C2, context k2 k3 C2 ->
forall k1 C1, context k1 k2 C1 ->
context k1 k3 (fun x => C2(C1 x))
with contextlist_compose:
forall k2 C2, contextlist k2 C2 ->
forall k1 C1, context k1 k2 C1 ->
contextlist k1 (fun x => C2(C1 x)).