Notation bool_3 := eq_true_negb_classical (only parsing).

(* Specifications: *)
Lemma eq_true_negb_classical_iff : forall b:bool, negb b <> true <-> b = true.
Lemma eq_true_not_negb : forall b:bool, b <> true -> negb b = true.
Lemma eq_true_not_negb_iff : forall b:bool, b <> true <-> negb b = true.