Module VeriStarSound := VSS.
(********duplicate temporarily a lemma from wellformed_sound. Maybe some of the lemmas there Repair import-structire later****** ********)
(************end of duplicated lemma ********)
(* Definition agree_except (x: var) (s s': state) : Prop := (forall x', x' <> x -> stack_get (stk s) (Some x') = stack_get (stk s') (Some x')) /\ hp s = hp s'.  Lemma agree_except_refl: forall x s, agree_except x s s. Hint Resolve agree_except_refl.  Definition existsv (nextv: var) (P: spred) : spred := fun s => exists s', agree_except nextv s s' /\ P s'. *)
Definition existsv (nextv: var) (P: spred) : spred :=
fun s => exists y,  P (State (env_set nextv y (stk s)) (hp s)).
Definition fresh {A} (f: A -> var) (a: A) (x: var) : Prop :=  Ident.lt (f a) x.
Ltac do_fresh1 :=
repeat match goal with H: Ile _ _ |- _ => revert H
| H: Ident.lt _ _ |- _ => revert H
| H: fresh _ _ _ |- _ => revert H end;
clear;
unfold fresh; simpl;
repeat ((rewrite freshmax_list_app || rewrite freshmax_list_rev
|| rewrite varmax_minid || rewrite varmax_minid'); simpl).
Ltac do_fresh :=
do_fresh1; intros;
repeat match goal with
|  H: Ident.lt (var_max _ _) _ |- _ => apply var_max_split in H; destruct H
end;
repeat apply var_max_intro; auto;
try solve [etransitivity; eauto].
(*  repeat rewrite Zpos_succ_morphism in *; solve [auto | omega]. *)
Definition set_in_state nextv z s := State (env_set nextv z (stk s)) (hp s).

Lemma space_atom_denote_agree:
forall a s nextv z,
fresh freshmax_space_atom a nextv ->
space_atom_denote a s ->
space_atom_denote a (set_in_state nextv z s).