Library Coq.Numbers.DecimalZ


DecimalZ

Proofs that conversions between decimal numbers and Z are bijections.

Require Import Decimal DecimalFacts DecimalPos DecimalN ZArith.

Lemma of_to (z:Z) : Z.of_int (Z.to_int z) = z.

Lemma to_of (d:int) : Z.to_int (Z.of_int d) = norm d.

Some consequences

Lemma to_int_inj n n' : Z.to_int n = Z.to_int n' -> n = n'.

Lemma to_int_surj d : exists n, Z.to_int n = norm d.

Lemma of_int_norm d : Z.of_int (norm d) = Z.of_int d.

Lemma of_inj d d' :
 Z.of_int d = Z.of_int d' -> norm d = norm d'.

Lemma of_iff d d' : Z.of_int d = Z.of_int d' <-> norm d = norm d'.