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(*         *      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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(** The type [bool] is defined in the prelude as [[ Inductive bool : Set := true : bool | false : bool ]] *)
(** Most of the lemmas in this file are trivial by case analysis *)
Local Ltac Tauto.intuition_solver ::= auto with bool.
Ltac destr_bool :=
intros; destruct_all bool; simpl in *; trivial; try discriminate.
(** Interpretation of booleans as propositions *)
Definition Is_true (b:bool) :=
match b with
| true => True
| false => False
end.
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(** * Decidability *)
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(* Specifications: *)
Lemma bool_dec : forall b1 b2 : bool, {b1 = b2} + {b1 <> b2}.
#[global]
Hint Resolve diff_true_false : bool.
Lemma diff_false_true : false <> true.
#[global]
Hint Resolve diff_false_true : bool.