(************************************************************************)
(*         *      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)         *)
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(** * 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
}.
(** Alternative ways of specifying the reflection property. *)

(* 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.