Definition config_det w k := forall w' k' w'' k'',
  step w k w' k' -> step w k w'' k'' -> w'=w'' /\ k'=k''.

(* Specifications: *)
Lemma step_safe' : forall w k w' k', safe w' k' -> step w k w' k' -> config_det w k -> safe w k.
Lemma safe_seq_assoc: forall w k c1 c2, safe w (Kseq c1 (Kseq c2 k)) -> safe w (Kseq (Sseq c1 c2) k).
Lemma step_compatible : forall c w w' k, step w (Kseq c Kstop) w' Kstop -> step w (Kseq c k) w' k.