U32.u32_to_nat_from_nat: law of bend-mathlib@0.8.1.0
Import: import bend-mathlib@0.8.1.0/u32.bend as U32
Lines 701-705 of bend-mathlib@0.8.1.0/u32.bend: https://jend.leeeet.dev/read.txt?path=bend-mathlib@0.8.1.0/u32.bend&start_line=701&end_line=705

import Base
import bend-mathlib@0.8.1.0/nat.bend as MNat

# Converting a natural below 2^32 to U32 and back is the identity: k < 2^32 implies to_nat (from_nat k) = k.
law u32_to_nat_from_nat:
  for k: Nat
  for h: MNat.lt(k, Nat.pow(2n, 32n))
  {U32.to_nat(U32.from_nat(k)) == k : Nat}

Uses (6):
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=Nat
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=Nat.pow
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=U32.from_nat
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=U32.to_nat
  https://jend.leeeet.dev/definition.txt?path=bend-mathlib@0.8.1.0/nat.bend&name=lt
  https://jend.leeeet.dev/definition.txt?path=bend-mathlib@0.8.1.0/u32.bend&name=internal_u32_to_nat_from_nat