Notation Is_true_eq_true2 := Is_true_eq_right (only parsing).

(* Specifications: *)
Lemma eqb_refl : forall x:bool, Is_true (eqb x x).
Lemma eqb_eq : forall x y:bool, Is_true (eqb x y) -> x = y.
Lemma orb_prop_elim : forall a b:bool, Is_true (a || b) -> Is_true a \/ Is_true b.