Set Bullet Behavior "Strict Subproofs".
Instance CompSpecs : compspecs. make_compspecs prog. Defined.
Definition Vprog : varspecs. mk_varspecs prog. Defined.
Definition acquire_spec := DECLARE _acquire acquire_spec.
Definition release_spec := DECLARE _release release_spec.
Definition makelock_spec := DECLARE _makelock (makelock_spec _).
Definition freelock_spec := DECLARE _freelock (freelock_spec _).
Definition surely_malloc_spec :=
DECLARE _surely_malloc
WITH n:Z
PRE [ _n OF tuint ]
PROP (0 <= n <= Int.max_unsigned)
LOCAL (temp _n (Vint (Int.repr n)))
SEP ()
POST [ tptr tvoid ] EX p:_,
PROP ()
LOCAL (temp ret_temp p)
SEP (malloc_token Tsh n p * memory_block Tsh n p).
(* lock invariant for atomic locations *)
Definition tatomic := Tstruct _atomic_loc noattr.
Definition A_inv p l R := EX v : Z, !!(repable_signed v) &&
(field_at Tsh tatomic [StructField _val] (vint v) p * R v *
(weak_precise_mpred (R v) && emp) * malloc_token Tsh (sizeof tatomic) p * malloc_token Tsh (sizeof tlock) l).
Definition atomic_loc sh p R := !!(field_compatible tatomic [] p) &&
(EX lock : val, field_at sh tatomic [StructField _lock] lock p * lock_inv sh lock (A_inv p lock R)).

(* Specifications: *)
Lemma A_inv_super_non_expansive : forall n p l R,
compcert_rmaps.RML.R.approx n (A_inv p l R) =
compcert_rmaps.RML.R.approx n (A_inv p l (fun v => compcert_rmaps.RML.R.approx n (R v))).
Lemma atomic_loc_super_non_expansive : forall n sh p R,
compcert_rmaps.RML.R.approx n (atomic_loc sh p R) =
compcert_rmaps.RML.R.approx n (atomic_loc sh p (fun v => compcert_rmaps.RML.R.approx n (R v))).