Notation Decb X := (dec2bool (Dec X)).

(* Specifications: *)
Lemma Dec_reflect_eq (X Y: Prop) (d: dec X) (e: dec Y) :
Decb X = Decb Y <->  (X <-> Y).
Lemma Dec_auto (X: Prop) (d: dec X) :
X -> Dec X.
Lemma Dec_auto_not (X: Prop) (d: dec X) :
~ X -> ~ Dec X.
Lemma Dec_reflect_eq (X Y: Prop) (d: dec X) (e: dec Y) :
Decb X = Decb Y <->  (X <-> Y).
Lemma Dec_auto (X: Prop) (d: dec X) :
X -> Dec X.
Lemma Dec_auto_not (X: Prop) (d: dec X) :
~ X -> ~ Dec X.