(************************************************************************)
(*         *   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)         *)
(************************************************************************)
(* Certified Haskell Prelude. * Author: Matthieu Sozeau * Institution: LRI, CNRS UMR 8623 - UniversitÃcopyright Paris Sud *              91405 Orsay, France *)
Set Implicit Arguments.
Unset Strict Implicit.
Goal not True == not (not False) -> ((not True -> True)) \/ True.
intros.
clrewrite H.
clrewrite <- H.
right ; auto.
Defined.
Definition reduced_thm := Eval compute in Unnamed_thm.
(* Print reduced_thm. *)

Lemma foo [ Setoid a R ] : True. (* forall x y, R x y -> x -> y. *)
Goal forall A B C (H : A <-> B) (H' : B <-> C), A /\ B <-> B /\ C.