ProofU32.divstep1: law of lawful-words@0.1.0.0
Import: import lawful-words@0.1.0.0/proof_u32.bend as ProofU32
Lines 642-652 of lawful-words@0.1.0.0/proof_u32.bend: https://jend.leeeet.dev/read.txt?path=lawful-words@0.1.0.0/proof_u32.bend&start_line=642&end_line=652

import Base
import lawful-words@0.1.0.0/proof_nat.bend as N

# One step of long division, as numbers (quotient bit 1, then 0).
law divstep1:
  for +q: Nat
  for +b: Nat
  for +r: Nat
  for +h: Nat
  for +a0: Bool
  for +r2: Nat
  for +e1: {Nat.add(Nat.mul(q, b), r) == h : Nat}
  for +e: {Nat.add(b, r2) == Nat.add(N.bn(a0), Nat.double(r)) : Nat}
  {Nat.add(Nat.mul(1n+Nat.double(q), b), r2) == Nat.add(N.bn(a0), Nat.double(h)) : Nat}

Uses (12):
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=Bool
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=Equal.sym
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=Equal.trans
  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.double
  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=add_assoc
  https://jend.leeeet.dev/definition.txt?path=lawful-words@0.1.0.0/proof_nat.bend&name=add_left_comm
  https://jend.leeeet.dev/definition.txt?path=lawful-words@0.1.0.0/proof_nat.bend&name=bn
  https://jend.leeeet.dev/definition.txt?path=lawful-words@0.1.0.0/proof_nat.bend&name=dbl_dist
  https://jend.leeeet.dev/definition.txt?path=lawful-words@0.1.0.0/proof_nat.bend&name=mul_dbl_l