(************************************************************************)
(*         *   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)         *)
(************************************************************************)
(************************************************************************)
refine
((fun x0 : nat => match x0 with
| O => _
| S p => _
end)).
Restart.
refine
(fun x0 : nat => match x0 as n return (n = n) with
| O => _
| S p => _
end). (* OK *)
Restart.
refine
(fun x0 : nat => match x0 as n return (n = n) with
| O => _
| S p => _
end). (* OK *)
Restart.
(** Refine [x0:nat]Cases x0 of O => ? | (S p) => ? end. (* cannot be executed *)
**)
Abort.
(************************************************************************)
refine (S _).
Abort.
(************************************************************************)
refine (fix f (x : nat) : x = x := _).
Restart.
refine
(fix f (x : nat) : x = x :=
match x as n return (n = n :>nat) with
| O => _
| S p => _
end).
Restart.
refine
(fix f (x : nat) : x = x :=
match x as n return (n = n) with
| O => _
| S p => _
end).
Restart.
refine
(fix f (x : nat) : x = x :=
match x as n return (n = n :>nat) with
| O => _
| S p => f_equal S _
end).
Restart.
refine
(fix f (x : nat) : x = x :=
match x as n return (n = n :>nat) with
| O => _
| S p => f_equal S _
end).
Abort.
(************************************************************************)
Parameter f : nat * nat -> nat -> nat.

Lemma essai : nat.