Definition inj := fun p => (prop p && emp).
Definition star := sepcon.
Definition ex := @exp mpred Nveric.

(* Specifications: *)
Lemma himp_star_comm : forall P Q,
(star P Q) ===> (star Q P).
Lemma heq_star_comm : forall P Q,
(star P Q) <===> (star Q P).
Lemma heq_star_assoc : forall P Q R,
(star (star P Q) R) <===> (star P (star Q R)).
Lemma heq_star_emp_l : forall P, (star emp P) <===> P.
Lemma heq_star_emp_r : forall P, (star P emp) <===> P.
Lemma himp_star_frame : forall P Q R S,
P ===> Q -> R ===> S -> (star P R) ===> (star Q S).