Ltac Provide T := apply (@ltac_database_provide (boxer T)).Ltac ltac_database_get D T :=
  let A := fresh "TEMP" in evar (A:Boxer);
  let H := fresh "TEMP" in
  assert (H : ltac_database (boxer D) (boxer T) A);
  [ subst A; auto
  | subst A; match type of H with ltac_database _ _ (boxer ?L) =>
               generalize L end; clear H ].(* ---------------------------------------------------------------------- *)
(** ** On-the-fly removal of hypotheses *)

(** In a list of arguments [>> H1 H2 .. HN] passed to a tactic
    such as [lets] or [applys] or [forwards] or [specializes],
    the term [rm], an identity function, can be placed in front
    of the name of an hypothesis to be deleted. *)

Definition rm (A:Type) (X:A) := X.(** [rm_term E] removes one hypothesis that admits the same
    type as [E]. *)

Ltac rm_term E :=
  let T := type of E in
  match goal with H: T |- _ => try clear H end.(** [rm_inside E] calls [rm_term Ei] for any subterm
    of the form [rm Ei] found in E *)

Ltac rm_inside E :=
  let go E := rm_inside E in
  match E with
  | rm ?X => rm_term X
  | ?X1 ?X2 =>
     go X1; go X2
  | ?X1 ?X2 ?X3 =>
     go X1; go X2; go X3
  | ?X1 ?X2 ?X3 ?X4 =>
     go X1; go X2; go X3; go X4
  | ?X1 ?X2 ?X3 ?X4 ?X5 =>
     go X1; go X2; go X3; go X4; go X5
  | ?X1 ?X2 ?X3 ?X4 ?X5 ?X6 =>
     go X1; go X2; go X3; go X4; go X5; go X6
  | ?X1 ?X2 ?X3 ?X4 ?X5 ?X6 ?X7 =>
     go X1; go X2; go X3; go X4; go X5; go X6; go X7
  | ?X1 ?X2 ?X3 ?X4 ?X5 ?X6 ?X7 ?X8 =>
     go X1; go X2; go X3; go X4; go X5; go X6; go X7; go X8
  | ?X1 ?X2 ?X3 ?X4 ?X5 ?X6 ?X7 ?X8 ?X9 =>
     go X1; go X2; go X3; go X4; go X5; go X6; go X7; go X8; go X9
  | ?X1 ?X2 ?X3 ?X4 ?X5 ?X6 ?X7 ?X8 ?X9 ?X10 =>
     go X1; go X2; go X3; go X4; go X5; go X6; go X7; go X8; go X9; go X10
  | _ => idtac
  end.(** For faster performance, one may deactivate [rm_inside] by
    replacing the body of this definition with [idtac]. *)

Ltac fast_rm_inside E :=
  rm_inside E.Definition ltac_nat_from_int (x:BinInt.Z) : nat :=
  match x with
  | BinInt.Z0 => 0%nat
  | BinInt.Zpos p => BinPos.nat_of_P p
  | BinInt.Zneg p => 0%nat
  end.Ltac nat_from_number N :=
  match type of N with
  | nat => constr:(N)
  | BinInt.Z => let N' := constr:(ltac_nat_from_int N) in eval compute in N'
  end.

Lemma dup_lemma : forall P, P -> P -> P.