(** Matching between states *)

Inductive match_states: Csem.state -> state -> Prop :=
  | match_exprstates: forall f r k e m tf sl tk le dest a tmps,
      tr_function f tf ->
      tr_top tge e le m dest r sl a tmps ->
      match_cont_exp dest a k tk ->
      match_states (Csem.ExprState f r k e m)
                   (State tf Sskip (Kseqlist sl tk) e le m)
  | match_regularstates: forall f s k e m tf ts tk le,
      tr_function f tf ->
      tr_stmt s ts ->
      match_cont k tk ->
      match_states (Csem.State f s k e m)
                   (State tf ts tk e le m)
  | match_callstates: forall fd args k m tfd tk,
      tr_fundef fd tfd ->
      match_cont k tk ->
      match_states (Csem.Callstate fd args k m)
                   (Callstate tfd args tk m)
  | match_returnstates: forall res k m tk,
      match_cont k tk ->
      match_states (Csem.Returnstate res k m)
                   (Returnstate res tk m)
  | match_stuckstate: forall S,
      match_states Csem.Stuckstate S.(** Matching between states *)

Inductive match_states: Csem.state -> state -> Prop :=
  | match_exprstates: forall f r k e m tf sl tk le dest a tmps,
      tr_function f tf ->
      tr_top tge e le m dest r sl a tmps ->
      match_cont_exp dest a k tk ->
      match_states (Csem.ExprState f r k e m)
                   (State tf Sskip (Kseqlist sl tk) e le m)
  | match_regularstates: forall f s k e m tf ts tk le,
      tr_function f tf ->
      tr_stmt s ts ->
      match_cont k tk ->
      match_states (Csem.State f s k e m)
                   (State tf ts tk e le m)
  | match_callstates: forall fd args k m tfd tk,
      tr_fundef fd tfd ->
      match_cont k tk ->
      match_states (Csem.Callstate fd args k m)
                   (Callstate tfd args tk m)
  | match_returnstates: forall res k m tk,
      match_cont k tk ->
      match_states (Csem.Returnstate res k m)
                   (Returnstate res tk m)
  | match_stuckstate: forall S,
      match_states Csem.Stuckstate S.(** Matching between states *)

Inductive match_states: Csem.state -> state -> Prop :=
  | match_exprstates: forall f r k e m tf sl tk le dest a tmps,
      tr_function f tf ->
      tr_top tge e le m dest r sl a tmps ->
      match_cont_exp dest a k tk ->
      match_states (Csem.ExprState f r k e m)
                   (State tf Sskip (Kseqlist sl tk) e le m)
  | match_regularstates: forall f s k e m tf ts tk le,
      tr_function f tf ->
      tr_stmt s ts ->
      match_cont k tk ->
      match_states (Csem.State f s k e m)
                   (State tf ts tk e le m)
  | match_callstates: forall fd args k m tfd tk,
      tr_fundef fd tfd ->
      match_cont k tk ->
      match_states (Csem.Callstate fd args k m)
                   (Callstate tfd args tk m)
  | match_returnstates: forall res k m tk,
      match_cont k tk ->
      match_states (Csem.Returnstate res k m)
                   (Returnstate res tk m)
  | match_stuckstate: forall S,
      match_states Csem.Stuckstate S.(** Matching between states *)

Inductive match_states: Csem.state -> state -> Prop :=
  | match_exprstates: forall f r k e m tf sl tk le dest a tmps,
      tr_function f tf ->
      tr_top tge e le m dest r sl a tmps ->
      match_cont_exp dest a k tk ->
      match_states (Csem.ExprState f r k e m)
                   (State tf Sskip (Kseqlist sl tk) e le m)
  | match_regularstates: forall f s k e m tf ts tk le,
      tr_function f tf ->
      tr_stmt s ts ->
      match_cont k tk ->
      match_states (Csem.State f s k e m)
                   (State tf ts tk e le m)
  | match_callstates: forall fd args k m tfd tk,
      tr_fundef fd tfd ->
      match_cont k tk ->
      match_states (Csem.Callstate fd args k m)
                   (Callstate tfd args tk m)
  | match_returnstates: forall res k m tk,
      match_cont k tk ->
      match_states (Csem.Returnstate res k m)
                   (Returnstate res tk m)
  | match_stuckstate: forall S,
      match_states Csem.Stuckstate S.(** Matching between states *)

Inductive match_states: Csem.state -> state -> Prop :=
  | match_exprstates: forall f r k e m tf sl tk le dest a tmps,
      tr_function f tf ->
      tr_top tge e le m dest r sl a tmps ->
      match_cont_exp dest a k tk ->
      match_states (Csem.ExprState f r k e m)
                   (State tf Sskip (Kseqlist sl tk) e le m)
  | match_regularstates: forall f s k e m tf ts tk le,
      tr_function f tf ->
      tr_stmt s ts ->
      match_cont k tk ->
      match_states (Csem.State f s k e m)
                   (State tf ts tk e le m)
  | match_callstates: forall fd args k m tfd tk,
      tr_fundef fd tfd ->
      match_cont k tk ->
      match_states (Csem.Callstate fd args k m)
                   (Callstate tfd args tk m)
  | match_returnstates: forall res k m tk,
      match_cont k tk ->
      match_states (Csem.Returnstate res k m)
                   (Returnstate res tk m)
  | match_stuckstate: forall S,
      match_states Csem.Stuckstate S.(** Matching between states *)

Inductive match_states: Csem.state -> state -> Prop :=
  | match_exprstates: forall f r k e m tf sl tk le dest a tmps,
      tr_function f tf ->
      tr_top tge e le m dest r sl a tmps ->
      match_cont_exp dest a k tk ->
      match_states (Csem.ExprState f r k e m)
                   (State tf Sskip (Kseqlist sl tk) e le m)
  | match_regularstates: forall f s k e m tf ts tk le,
      tr_function f tf ->
      tr_stmt s ts ->
      match_cont k tk ->
      match_states (Csem.State f s k e m)
                   (State tf ts tk e le m)
  | match_callstates: forall fd args k m tfd tk,
      tr_fundef fd tfd ->
      match_cont k tk ->
      match_states (Csem.Callstate fd args k m)
                   (Callstate tfd args tk m)
  | match_returnstates: forall res k m tk,
      match_cont k tk ->
      match_states (Csem.Returnstate res k m)
                   (Returnstate res tk m)
  | match_stuckstate: forall S,
      match_states Csem.Stuckstate S.

(* Specifications: *)
Lemma tr_select_switch: forall n ls tls, tr_lblstmts ls tls -> tr_lblstmts (Csem.select_switch n ls) (select_switch n tls).
Lemma tr_seq_of_labeled_statement: forall ls tls, tr_lblstmts ls tls -> tr_stmt (Csem.seq_of_labeled_statement ls) (seq_of_labeled_statement tls).