Notation bool_6 := eq_true_not_negb (only parsing).

(* Specifications: *)
Lemma absurd_eq_bool : forall b b':bool, False -> b = b'.
Lemma absurd_eq_true : forall b, False -> b = true.
Lemma trans_eq_bool : forall x y z:bool, x = y -> y = z -> x = z.
Lemma Is_true_eq_true : forall x:bool, Is_true x -> x = true.
Lemma Is_true_eq_left : forall x:bool, x = true -> Is_true x.
Lemma Is_true_eq_right : forall x:bool, true = x -> Is_true x.