ProofDigits.hk_step: law of lawful-fields@0.1.1.0
Import: import lawful-fields@0.1.1.0/proof_digits.bend as ProofDigits
Lines 529-534 of lawful-fields@0.1.1.0/proof_digits.bend: https://jend.leeeet.dev/read.txt?path=lawful-fields@0.1.1.0/proof_digits.bend&start_line=529&end_line=534

import Base

# n <= BK(1 + j) gives n / 10 <= BK(j).
law hk_step:
  for +n: U32
  for +j: Nat
  for +hk: {Nat.is_le(U32.to_nat(n), U32.to_nat(BK(1n+j))) == True{} : Bool}
  {Nat.is_le(U32.to_nat(U32.div(n, 10)), U32.to_nat(BK(j))) == True{} : Bool}

Uses (17):
  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.div
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=Nat.is_le
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=U32
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=U32.div
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=U32.is_le
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=U32.to_nat
  https://jend.leeeet.dev/definition.txt?path=lawful-arrays@0.1.0.0/proof_base.bend&name=subst
  https://jend.leeeet.dev/definition.txt?path=lawful-fields@0.1.1.0/proof_digits.bend&name=BK
  https://jend.leeeet.dev/definition.txt?path=lawful-fields@0.1.1.0/proof_digits.bend&name=bk_step
  https://jend.leeeet.dev/definition.txt?path=lawful-fields@0.1.1.0/proof_digits.bend&name=div_mono10
  https://jend.leeeet.dev/definition.txt?path=lawful-words@0.1.0.0/proof_nat.bend&name=le_trans
  https://jend.leeeet.dev/definition.txt?path=lawful-words@0.1.0.0/proof_u32.bend&name=is_le_to_nat
  https://jend.leeeet.dev/definition.txt?path=lawful-words@0.1.0.0/proof_u32.bend&name=to_nat_div