(************************************************************************)
(*         *   The Coq Proof Assistant / The Coq Development Team       *)
(*  v      *   INRIA, CNRS and contributors - Copyright 1999-2018       *)
(* <O___,, *       (see CREDITS file for the list of authors)           *)
(*   \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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(**** Tactics Tauto and Intuition ****)
(**** Tauto: Tactic for automating proof in Intuionnistic Propositional Calculus, based on the contraction-free LJT* of Dickhoff ****)
(**** Intuition: Simplifications of goals, based on LJT* calcul ****)
(**** Examples of intuitionistic tautologies ****)
Parameter A B C D E F : Prop.
Parameter even : nat -> Prop.
Parameter P : nat -> Prop.

(* This example took very much time (about 3mn on a PIII 450MHz in bytecode) with the old Tauto. Now, it's immediate (less than 1s). *)
Lemma critical_example2 : (~ A <-> B) -> (~ B <-> A) -> (~ ~ A <-> A).