LAWS.nat_div_mul_add: law of lawful-words@0.1.0.0
Import: import lawful-words@0.1.0.0/LAWS.bend as LAWS
Lines 563-569 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=563&end_line=569

import Base

# (q * b + r) / b = q and (q * b + r) % b = r, for r < b.
law nat_div_mul_add:
  for q: Nat
  for b: Nat
  for r: Nat
  for h: {Nat.is_lt(r, b) == True{} : Bool}
  {Nat.div(Nat.add(Nat.mul(q, b), r), b) == q : Nat}

Uses (7):
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=Bool
  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.is_lt
  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_mul_add