(** Completeness part 2: if we can reduce to [Stuckstate], [step_expr] contains at least one [Stuckred] reduction. *)

(* Specifications: *)
Lemma not_stuckred_imm_safe:
forall m a k,
(forall C, ~In (C, Stuckred) (step_expr k a m)) -> imm_safe_t k a m.
Lemma not_imm_safe_stuck_red:
forall m a k C,
context k RV C ->
~imm_safe_t k a m ->
exists C', In (C', Stuckred) (step_expr RV (C a) m).