(*
 Lemma agree_except_sym:
  forall x s s', agree_except x s s' -> agree_except x s' s.
 Proof.
 unfold agree_except; intuition. symmetry. apply H0; auto.
 Qed.
*)

Axiom env_reset2: forall s x z, env_set x (env_get s x) (env_set x z s) = s.

Lemma permute_sigma0: forall sigma0 (a: space_atom) sigma, Permutation (sigma0 ++ a :: sigma) (a :: sigma0 ++ sigma).