U32.u32_to_nat_from_nat_mod_sym: law of bend-mathlib@0.8.1.0
Import: import bend-mathlib@0.8.1.0/u32.bend as U32
Lines 1235-1238 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=1235&end_line=1238

import Base

# Converting any natural to U32 and back reduces it modulo 2^32: to_nat (from_nat k) = k % 2^32, reversed to rewrite toward the simple side.
law u32_to_nat_from_nat_mod_sym:
  for k: Nat
  {Nat.mod(k, Nat.pow(2n, 32n)) == U32.to_nat(U32.from_nat(k)) : Nat}

Uses (7):
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=Equal.sym
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=Nat
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=Nat.mod
  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/u32.bend&name=u32_to_nat_from_nat_mod