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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) *)
(************************************************************************)
Inductive T : Set :=
| A : T
| B : T -> T.
Lemma lem1 : forall x y : T, {x = y} + {x <> y}.
decide equality.
Qed.
Lemma lem1' : forall x y : T, x = y \/ x <> y.
decide equality.
Qed.
Lemma lem1'' : forall x y : T, {x <> y} + {x = y}.
decide equality.
Qed.
Lemma lem1''' : forall x y : T, x <> y \/ x = y.
decide equality.
Qed.
Lemma lem2 : forall x y : T, {x = y} + {x <> y}.
intros x y.
decide equality.
Qed.
Lemma lem4 : forall x y : T, {x = y} + {x <> y}.
intros x y.
compare x y; auto.
Qed.
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