(** ** Transitions preserve semantics *)

(** We define the semantics of states as follows.
  For a triple [mu, sigma, tau], we perform the moves [tau] in
  reverse sequential order, then the moves [mu ++ sigma] in parallel. *)

Definition statemove (st: state) (e: env) :=
  match st with
  | State mu sigma tau => exec_par (mu ++ sigma) (exec_seq_rev tau e)
  end.

Lemma exec_par_ident: forall m1 r m2 e, is_mill (m1 ++ (r, r) :: m2) -> exec_par (m1 ++ (r, r) :: m2) e = exec_par (m1 ++ m2) e.