(************************************************************************)
(*         *      The Rocq Prover / The Rocq Development Team           *)
(*  v      *         Copyright INRIA, CNRS and contributors             *)
(* <O___,, * (see version control and CREDITS file for authors & dates) *)
(*   \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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(** * DecimalQ  Proofs that conversions between decimal numbers and [Q] are bijections. *)

Lemma dnorm_spec_i d :
let (i, f) :=
match d with Decimal i f => (i, f) | DecimalExp i f _ => (i, f) end in
let i' := match dnorm d with Decimal i _ => i | DecimalExp i _ _ => i end in
match i with
| Pos i => i' = Pos (unorm i)
| Neg i =>
(i' = Neg (unorm i) /\ (nzhead i <> Nil \/ nzhead f <> Nil))
\/ (i' = Pos zero /\ (nzhead i = Nil /\ nzhead f = Nil))
end.