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(*                                                                  *)
(*  The Why3 Verification Platform   /   The Why3 Development Team  *)
(*  Copyright 2010-2024 --  Inria - CNRS - Paris-Saclay University  *)
(*                                                                  *)
(*  This software is distributed under the terms of the GNU Lesser  *)
(*  General Public License version 2.1, with the special exception  *)
(*  on linking described in file LICENSE.                           *)
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(* This file is generated by Why3's Coq-realize driver *)
(* Beware! Only edit allowed sections below    *)
Require Import BuiltIn.
Require BuiltIn.

(* Why3 assumption *)
Definition is_none {a:Type} {a_WT:WhyType a} (o:Init.Datatypes.option a) :
    Prop :=
  match o with
  | Init.Datatypes.None => True
  | Init.Datatypes.Some _ => False
  end.

(* Why3 goal *)
Lemma is_none'spec {a:Type} {a_WT:WhyType a} :
  forall (o:Init.Datatypes.option a), is_none o <-> (o = Init.Datatypes.None).
Proof.
intros o.
split.
now destruct o.
now intros ->.
Qed.

Global Instance option_WhyType : forall T {T_WT : WhyType T}, WhyType (option T).
Proof.
split.
apply @None.
intros [x|] [y|] ; try (now right) ; try (now left).
destruct (why_decidable_eq x y) as [E|E].
left.
now apply f_equal.
right.
contradict E.
now injection E.
Qed.
