(** ** Semantic preservation for statements *)

(** The simulation diagram for the translation of statements and functions
  is a "plus" diagram of the form
<<
           I
     S1 ------- R1
     |          |
   t |        + | t
     v          v
     S2 ------- R2
           I                         I
>>

The invariant [I] is the [match_states] predicate that we now define.
*)

Inductive match_transl: stmt -> cont -> stmt -> cont -> Prop :=
  | match_transl_0: forall ts tk,
      match_transl ts tk ts tk
  | match_transl_1: forall ts tk,
      match_transl (Sblock ts) tk ts (Kblock tk).(** ** Semantic preservation for statements *)

(** The simulation diagram for the translation of statements and functions
  is a "plus" diagram of the form
<<
           I
     S1 ------- R1
     |          |
   t |        + | t
     v          v
     S2 ------- R2
           I                         I
>>

The invariant [I] is the [match_states] predicate that we now define.
*)

Inductive match_transl: stmt -> cont -> stmt -> cont -> Prop :=
  | match_transl_0: forall ts tk,
      match_transl ts tk ts tk
  | match_transl_1: forall ts tk,
      match_transl (Sblock ts) tk ts (Kblock tk).(** ** Semantic preservation for statements *)

(** The simulation diagram for the translation of statements and functions
  is a "plus" diagram of the form
<<
           I
     S1 ------- R1
     |          |
   t |        + | t
     v          v
     S2 ------- R2
           I                         I
>>

The invariant [I] is the [match_states] predicate that we now define.
*)

Inductive match_transl: stmt -> cont -> stmt -> cont -> Prop :=
  | match_transl_0: forall ts tk,
      match_transl ts tk ts tk
  | match_transl_1: forall ts tk,
      match_transl (Sblock ts) tk ts (Kblock tk).

Lemma match_transl_step: forall ts tk ts' tk' f te le m, match_transl (Sblock ts) tk ts' tk' -> star step tge (State f ts' tk' te le m) E0 (State f ts (Kblock tk) te le m).