------------------------------------------------------------------------
-- The Agda standard library
--
-- Properties of showing natural numbers
------------------------------------------------------------------------
{-# OPTIONS --cubical-compatible --safe #-}
open import Data.Digit.Properties using (toDigits-injective; showDigit-injective)
import Data.List.Properties as Listₚ
open import Data.Nat.Base using (ℕ)
open import Data.Nat.Properties using (_≤?_)
open import Data.Nat.Show using (charsInBase)
open import Function.Base using (_∘_)
open import Relation.Nullary.Decidable.Core using (True)
open import Relation.Binary.PropositionalEquality.Core using (_≡_)
module Data.Nat.Show.Properties where
module _ (base : ℕ) {base≥2 : True (2 ≤? base)} {base≤16 : True (base ≤? 16)} where
private
charsInBase-base = charsInBase base {base≥2} {base≤16}
toDigits-injective-base = toDigits-injective base {base≥2} {base≥2}
showDigit-injective-base = showDigit-injective base {base≤16} {base≤16}
charsInBase-injective : ∀ n m → charsInBase-base n ≡ charsInBase-base m → n ≡ m
charsInBase-injective n m = toDigits-injective-base _ _
∘ Listₚ.reverse-injective
∘ Listₚ.map-injective (showDigit-injective-base _ _)
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