#[global]
Hint Resolve andb_prop_intro: bool.
Notation andb_true_intro2 :=
(fun b1 b2 H1 H2 => andb_prop_intro b1 b2 (conj H1 H2))
(only parsing).

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