intros.
extensionality w; apply prop_ext; split; unfold prop, andp; simpl; intros; intuition.
Qed.

(* Specifications: *)
Lemma TT_i  {A} : forall w: A,  TT w.
Hint Resolve @TT_i.
Lemma TT_and {A}: forall (Q: pred A), TT && Q = Q.
intros; unfold andp,  TT, prop; extensionality w.