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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.
Require list.List.

(* Why3 goal *)
Definition hd {a:Type} {a_WT:WhyType a} : Init.Datatypes.list a -> a.
intros [|h _].
exact why_inhabitant.
exact h.
Defined.

(* Why3 goal *)
Lemma hd_cons {a:Type} {a_WT:WhyType a} :
  forall (x:a) (r:Init.Datatypes.list a),
  ((hd (Init.Datatypes.cons x r)) = x).
Proof.
now intros x r.
Qed.

(* Why3 goal *)
Definition tl {a:Type} {a_WT:WhyType a} :
  Init.Datatypes.list a -> Init.Datatypes.list a.
intros [|_ t].
exact nil.
exact t.
Defined.

(* Why3 goal *)
Lemma tl_cons {a:Type} {a_WT:WhyType a} :
  forall (x:a) (r:Init.Datatypes.list a),
  ((tl (Init.Datatypes.cons x r)) = r).
Proof.
now intros x r.
Qed.

