Definition interp (lvar : list (COINCpoint * positive)) (Default : COINCpoint) : positive -> COINCpoint := 
  fun p => list_assoc_inv COINCpoint positive positive_dec lvar p Default.Ltac add_to_distinct_list x xs :=
  match xs with
    | nil     => constr:(x::xs)
    | x::_    => fail 1
    | ?y::?ys => let zs := add_to_distinct_list x ys in constr:(y::zs)
  end.Ltac collect_points_list Tpoint xs :=
  match goal with
    | N : Tpoint |- _ => let ys := add_to_distinct_list N xs in
                           collect_points_list Tpoint ys
    | _               => xs
  end.Ltac collect_points Tpoint := collect_points_list Tpoint (@nil Tpoint).Ltac number_aux Tpoint lvar cpt :=
  match constr:(lvar) with
    | nil          => constr:(@nil (prodT Tpoint positive))
    | cons ?H ?T => let scpt := eval vm_compute in (Pos.succ cpt) in
                    let lvar2 := number_aux Tpoint T scpt in
                      constr:(cons (@pairT  Tpoint positive H cpt) lvar2)
  end.Ltac number Tpoint lvar := number_aux Tpoint lvar (1%positive).Ltac build_numbered_points_list Tpoint := let lvar := collect_points Tpoint in number Tpoint lvar.Ltac List_assoc Tpoint elt lst :=
  match constr:(lst) with
    | nil => fail
    | (cons (@pairT Tpoint positive ?X1 ?X2) ?X3) =>
      match constr:(elt = X1) with
        | (?X1 = ?X1) => constr:(X2)
        | _ => List_assoc Tpoint elt X3
      end
  end.Definition Tagged P : Prop := P.

Lemma PropToTagged : forall P : Prop, P -> Tagged P.