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(*         *   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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(* (c) Copyright 2006-2016 Microsoft Corporation and Inria.                  *)
Goal forall m n p, n <= p -> m <= n -> m <= p.
by move=> m n p le_n_p /leq_trans; apply.
Undo 1.
by move=> m n p le_n_p /leq_trans /(_ le_n_p) le_m_p; exact: le_m_p.
Undo 1.
by move=> m n p le_n_p /leq_trans ->.
Qed.
Goal forall P Q X : Prop, Q -> (True -> X -> Q = P) -> X -> P.
by move=> P Q X q V /V <-.
Qed.
by move=> a b; repeat move=> /andP []; move=> *.
Qed.
by move=> a b /andP /andP /andP [] //.
Qed.
by move=> a b /andP /andP /(@andP a) [] //.
Qed.
by move=> a b /andP [_ /andP [_ //]].
Qed.
by move=> a b; apply/andP/andP=> ?; apply/andP/andP/andP; rewrite andbC; apply/andP.
Qed.

Lemma test5:  forall C I A O, (True -> O) -> (O -> A) -> (True -> A -> I) -> (I -> C) -> C.