(************************************************************************)
(*         *      The Rocq Prover / The Rocq Development Team           *)
(*  v      *         Copyright INRIA, CNRS and contributors             *)
(* <O___,, * (see version control and CREDITS file for authors & dates) *)
(*   \VV/  **************************************************************)
(*    //   *    This file is distributed under the terms of the         *)
(*         *     GNU Lesser General Public License Version 2.1          *)
(*         *     (see LICENSE file for the text of the license)         *)
(************************************************************************)

(** * A typeclass to ease the handling of decidable properties. *)

(** A proposition is decidable whenever it is reflected by a boolean. *)

Class Decidable (P : Prop) := {
  Decidable_witness : bool;
  Decidable_spec : Decidable_witness = true <-> P
}.(************************************************************************)
(*         *      The Rocq Prover / The Rocq Development Team           *)
(*  v      *         Copyright INRIA, CNRS and contributors             *)
(* <O___,, * (see version control and CREDITS file for authors & dates) *)
(*   \VV/  **************************************************************)
(*    //   *    This file is distributed under the terms of the         *)
(*         *     GNU Lesser General Public License Version 2.1          *)
(*         *     (see LICENSE file for the text of the license)         *)
(************************************************************************)

(** * A typeclass to ease the handling of decidable properties. *)

(** A proposition is decidable whenever it is reflected by a boolean. *)

Class Decidable (P : Prop) := {
  Decidable_witness : bool;
  Decidable_spec : Decidable_witness = true <-> P
}.(************************************************************************)
(*         *      The Rocq Prover / The Rocq Development Team           *)
(*  v      *         Copyright INRIA, CNRS and contributors             *)
(* <O___,, * (see version control and CREDITS file for authors & dates) *)
(*   \VV/  **************************************************************)
(*    //   *    This file is distributed under the terms of the         *)
(*         *     GNU Lesser General Public License Version 2.1          *)
(*         *     (see LICENSE file for the text of the license)         *)
(************************************************************************)

(** * A typeclass to ease the handling of decidable properties. *)

(** A proposition is decidable whenever it is reflected by a boolean. *)

Class Decidable (P : Prop) := {
  Decidable_witness : bool;
  Decidable_spec : Decidable_witness = true <-> P
}.

(* Specifications: *)
Lemma Decidable_sound : forall P (H : Decidable P), Decidable_witness = true -> P.
Lemma Decidable_complete : forall P (H : Decidable P), P -> Decidable_witness = true.
Lemma Decidable_sound_alt : forall P (H : Decidable P), ~ P -> Decidable_witness = false.
Lemma Decidable_complete_alt : forall P (H : Decidable P), Decidable_witness = false -> ~ P.