(** ** Matching between C#minor's variable environment and Cminor's stack pointer *)

Inductive match_var (f: meminj) (sp: block): option (block * Z) -> option Z -> Prop :=
  | match_var_local: forall b sz ofs,
      val_inject f (Vptr b Int.zero) (Vptr sp (Int.repr ofs)) ->
      match_var f sp (Some(b, sz)) (Some ofs)
  | match_var_global:
      match_var f sp None None.(** ** Matching between C#minor's variable environment and Cminor's stack pointer *)

Inductive match_var (f: meminj) (sp: block): option (block * Z) -> option Z -> Prop :=
  | match_var_local: forall b sz ofs,
      val_inject f (Vptr b Int.zero) (Vptr sp (Int.repr ofs)) ->
      match_var f sp (Some(b, sz)) (Some ofs)
  | match_var_global:
      match_var f sp None None.(** ** Matching between C#minor's variable environment and Cminor's stack pointer *)

Inductive match_var (f: meminj) (sp: block): option (block * Z) -> option Z -> Prop :=
  | match_var_local: forall b sz ofs,
      val_inject f (Vptr b Int.zero) (Vptr sp (Int.repr ofs)) ->
      match_var f sp (Some(b, sz)) (Some ofs)
  | match_var_global:
      match_var f sp None None.Ltac geninv x :=
  let H := fresh in (generalize x; intro H; inv H).

(* Specifications: *)
Lemma match_env_invariant: forall f1 cenv e sp lo hi f2, match_env f1 cenv e sp lo hi -> inject_incr f1 f2 -> (forall b delta, f2 b = Some(sp, delta) -> f1 b = Some(sp, delta)) -> (forall b, Plt b lo -> f2 b = f1 b) -> match_env f2 cenv e sp lo hi.
Lemma match_env_invariant: forall f1 cenv e sp lo hi f2, match_env f1 cenv e sp lo hi -> inject_incr f1 f2 -> (forall b delta, f2 b = Some(sp, delta) -> f1 b = Some(sp, delta)) -> (forall b, Plt b lo -> f2 b = f1 b) -> match_env f2 cenv e sp lo hi.