(** Matching between program states. *)
Inductive match_stackframes: Linear.stackframe -> Linear.stackframe -> Prop :=
| match_stackframe_intro:
forall f sp rs c tf tc before after,
match_function f tf ->
match_code c tc ->
match_stackframes
(Stackframe f sp rs c)
(Stackframe tf sp rs (add_delta_ranges before after tc)).
Inductive match_states: Linear.state ->  Linear.state -> Prop :=
| match_states_instr:
forall s f sp c rs m tf ts tc
(STACKS: list_forall2 match_stackframes s ts)
(TRF: match_function f tf)
(TRC: match_code c tc),
match_states (State s f sp c rs m)
(State ts tf sp tc rs m)
| match_states_call:
forall s f rs m tf ts,
list_forall2 match_stackframes s ts ->
transf_fundef f = OK tf ->
match_states (Callstate s f rs m)
(Callstate ts tf rs m)
| match_states_return:
forall s rs m ts,
list_forall2 match_stackframes s ts ->
match_states (Returnstate s rs m)
(Returnstate ts rs m).

Lemma parent_locset_match:
forall s ts,
list_forall2 match_stackframes s ts ->
parent_locset ts = parent_locset s.