LAWS.nat_div_mod: law of lawful-words@0.1.0.0
Import: import lawful-words@0.1.0.0/LAWS.bend as LAWS
Lines 491-495 of lawful-words@0.1.0.0/LAWS.bend: https://jend.leeeet.dev/read.txt?path=lawful-words@0.1.0.0/LAWS.bend&start_line=491&end_line=495

import Base

# a = (a / b) * b + a % b (also for b = 0: a / 0 = 0 and a % 0 = a).
law nat_div_mod:
  for a: Nat
  for b: Nat
  {Nat.add(Nat.mul(Nat.div(a, b), b), Nat.mod(a, b)) == a : 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.add
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=Nat.div
  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.mul
  https://jend.leeeet.dev/definition.txt?path=lawful-words@0.1.0.0/proof_nat.bend&name=div_mod