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 *)

Lemma tr_simple:
forall e m,
(forall r v,
eval_simple_rvalue ge e m r v ->
forall le dst sl a tmps,
tr_expr le dst r sl a tmps ->
match dst with
| For_val => sl = nil /\ Csyntax.typeof r = typeof a /\ eval_expr tge e le m a v
| For_effects => sl = nil
| For_set sd =>
exists b, sl = do_set sd b
/\ Csyntax.typeof r = typeof b
/\ eval_expr tge e le m b v
end)
/\
(forall l b ofs,
eval_simple_lvalue ge e m l b ofs ->
forall le sl a tmps,
tr_expr le For_val l sl a tmps ->
sl = nil /\ Csyntax.typeof l = typeof a /\ eval_lvalue tge e le m a b ofs).