Notation andb_true_intro2 :=
  (fun b1 b2 H1 H2 => andb_prop_intro b1 b2 (conj H1 H2))
  (only parsing).

(* Specifications: *)
Lemma andb_prop_elim : forall a b:bool, Is_true (a && b) -> Is_true a /\ Is_true b.