(************************************************************************)
(*         *      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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(** * HexadecimalQ  Proofs that conversions between hexadecimal numbers and [Q] are bijections. *)

Lemma of_to (q:IQ) : forall d, to_hexadecimal q = Some d -> of_hexadecimal d = q.
Definition dnorm (d:hexadecimal) : hexadecimal :=
let norm_i i f :=
match i with
| Pos i => Pos (unorm i)
| Neg i => match nzhead (app i f) with Nil => Pos zero | _ => Neg (unorm i) end
end in
match d with
| Hexadecimal i f => Hexadecimal (norm_i i f) f
| HexadecimalExp i f e =>
match Decimal.norm e with
| Decimal.Pos Decimal.zero => Hexadecimal (norm_i i f) f
| e => HexadecimalExp (norm_i i f) f e
end
end.