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(* Check that problems with several solutions are solved in 8.4 as in 8.2 and 8.3 *)
Inductive Fin: nat -> Set :=
| first k : Fin (S k)
| succ k: Fin k -> Fin (S k).
Lemma match_sym_eq_eq: forall (n1 n2: nat)(f: Fin n1)(e: n1 = n2),
f = match sym_eq e in (_ = l) return (Fin l) with refl_equal =>
match e in (_ = l) return (Fin l) with refl_equal => f end end.
Proof.
intros n1 n2 f e.
(* Next line has a dependent and a non dependent solution *)
(* 8.2 and 8.3 used to choose the dependent one which is the one to make *)
(* the goal progress *)
refine (match e return _ with refl_equal => _ end).
reflexivity.
Undo 2.
(** Check insensitivity to alphabetic order *)
refine (match e as a in _ = b return _ with refl_equal => _ end).
reflexivity.
Undo 2.
(** Check insensitivity to alphabetic order *)
refine (match e as z in _ = y return _ with refl_equal => _ end).
reflexivity.
Undo 2.
(* Next line similarly has a dependent and a non dependent solution *)
refine (match e with refl_equal => _ end).
reflexivity.
Qed.
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