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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) *)
(************************************************************************)
Require Import ssreflect ssrbool.
Set Implicit Arguments.
Inductive wf T : bool -> option T -> Type :=
| wf_f : wf false None
| wf_t : forall x, wf true (Some x).
Derive Inversion wf_inv with (forall T b (o : option T), wf b o) Sort Prop.
Lemma Problem T b (o : option T) :
wf b o ->
match b with
| true => exists x, o = Some x
| false => o = None
end.
Proof.
by case: b; elim/wf_inv=> //; case: o=> // a *; exists a.
Qed.
|
