(************************************************************************)
(*         *   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)         *)
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(** * DecimalFacts : some facts about Decimal numbers *)
(** Normalization on little-endian numbers *)
Fixpoint nztail d :=
match d with
| Nil => Nil
| D0 d => match nztail d with Nil => Nil | d' => D0 d' end
| D1 d => D1 (nztail d)
| D2 d => D2 (nztail d)
| D3 d => D3 (nztail d)
| D4 d => D4 (nztail d)
| D5 d => D5 (nztail d)
| D6 d => D6 (nztail d)
| D7 d => D7 (nztail d)
| D8 d => D8 (nztail d)
| D9 d => D9 (nztail d)
end.
Definition lnorm d :=
match nztail d with
| Nil => zero
| d => d
end.

Lemma nzhead_rev d : nztail d <> Nil ->
nzhead (rev d) = rev (nztail d).