Hint Resolve @derives_refl.

(* Specifications: *)
Lemma andp_derives {A} `{ageable A}:
forall P Q P' Q': pred A, P |-- P' -> Q |-- Q' -> P && Q |-- P' && Q'.
Lemma orp_derives {A} `{ageable A}:
forall P Q P' Q': pred A, P |-- P' -> Q |-- Q' -> P || Q |-- P' || Q'.
Lemma exp_derives {A} `{HA : ageable A}:
forall B (P: B -> pred A) Q , (forall x:B, P x |-- Q x) -> (exp P |-- exp Q).
Lemma box_ext {A} `{agA : ageable A}: forall (M: modality) P Q,
box M (P <--> Q) |--  box M P <--> box M Q.
Lemma andp_pred_ext {A} `{agA : ageable A}: forall P Q P' Q',
(P <--> P') && (Q <--> Q') |--  (P && Q) <--> (P' && Q').
Lemma derives_TT {A}: forall (P: pred A), P |-- TT.
Hint Resolve @derives_TT.
Lemma sepcon_derives {A} {JA: Join A}{PA: Perm_alg A}:
forall p q p' q', (p |-- p') -> (q |-- q') -> (p * q |-- p' * q').
Lemma derives_e {A: Type}: forall p q (st: A),
(p |-- q) -> p st -> q st.
Lemma exp_derives {A} :
forall B (P: B -> pred A) Q , (forall x:B, P x |-- Q x) -> (exp P |-- exp Q).
Lemma unmodus_wand {A}  {JA: Join A}{PA: Perm_alg A}:
forall P Q R, Q = P * R ->  Q |-- P * (P -* Q).