Section PRESERVATION.
Variable prog: Csyntax.program.
Variable tprog: Clight.program.
Hypothesis TRANSL: match_prog prog tprog.
Let ge := Csem.globalenv prog.
Let tge := Clight.globalenv tprog.
(** Invariance properties. *)
Proof (Genv.find_symbol_match (proj1 TRANSL)).
Proof (Genv.senv_match (proj1 TRANSL)).
(** Properties of smart constructors. *)
(** Translation of simple expressions. *)
Proof (proj1 tr_simple_nil).
Proof (proj2 tr_simple_nil).
(** Translation of [deref_loc] and [assign_loc] operations. *)
Remark deref_loc_translated:
forall ty m b ofs t v,
Csem.deref_loc ge ty m b ofs t v ->
match chunk_for_volatile_type ty with
| None => t = E0 /\ Clight.deref_loc ty m b ofs v
| Some chunk => volatile_load tge chunk m b ofs t v
end.
Remark assign_loc_translated:
forall ty m b ofs v t m',
Csem.assign_loc ge ty m b ofs v t m' ->
match chunk_for_volatile_type ty with
| None => t = E0 /\ Clight.assign_loc tge ty m b ofs v m'
| Some chunk => volatile_store tge chunk m b ofs v t m'
end.
(** Evaluation of simple expressions and of their translation *)
(** Commutation between the translation of expressions and left contexts. *)

Lemma typeof_context:
forall k1 k2 C, leftcontext k1 k2 C ->
forall e1 e2, Csyntax.typeof e1 = Csyntax.typeof e2 ->
Csyntax.typeof (C e1) = Csyntax.typeof (C e2).