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(*         *   The Coq Proof Assistant / The Coq Development Team       *)
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(* <O___,, *       (see CREDITS file for the list of authors)           *)
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(*    //   *    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 after breaking all booleans *)
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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Hint Resolve diff_true_false : bool.
Hint Resolve diff_false_true : bool.
Hint Extern 1 (false <> true) => exact diff_false_true : core.

Lemma not_true_is_false : forall b:bool, b <> true -> b = false.