Hint Resolve @FF_left : norm.
Ltac norm := auto with norm.

(* Specifications: *)
Lemma add_andp: forall {A: Type} `{NatDed A} (P Q: A), P |-- Q -> P = P && Q.
Lemma andp_comm  {A}{NA: NatDed A}:
forall P Q: A,  P && Q = Q && P.