(************************************************************************)
(*         *   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.                  *)
case: (X in _ = X) / eqP => _.
match goal with |- (x == x) = true => myadmit end.
match goal with |- (x == x) = false => myadmit end.
Qed.

Lemma test1 x : (x == x) = (x + x.+1 == 2 * x + 1).