Library Coq.Numbers.DecimalR


Proofs that conversions between decimal numbers and R are bijections.

Require Import Decimal DecimalFacts DecimalPos DecimalZ DecimalQ Rdefinitions.

Lemma of_IQmake_to_decimal num den :
  match IQmake_to_decimal num den with
  | None => True
  | Some (DecimalExp _ _ _) => False
  | Some (Decimal i f) =>
    of_decimal (Decimal i f) = IRQ (QArith_base.Qmake num den)

Lemma of_to (q:IR) : forall d, to_decimal q = Some d -> of_decimal d = q.

Lemma to_of (d:decimal) : to_decimal (of_decimal d) = Some (dnorm d).

Some consequences