ProofDigits.LN: law of lawful-fields@0.1.1.0
Import: import lawful-fields@0.1.1.0/proof_digits.bend as ProofDigits
Lines 637-646 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=637&end_line=646

import Base
import lawful-fields@0.1.1.0/fields.bend as FC

law LN:
  for +k: Nat
  for +small: Bool
  for +j: Nat
  for +n: U32
  for +acc: List<&2, U32>
  for +hs: {U32.is_lt(n, 10) == small : Bool}
  for +hk: {Nat.is_le(U32.to_nat(n), U32.to_nat(BK(j))) == True{} : Bool}
  for +hj: {Nat.is_le(j, k) == True{} : Bool}
  {Nat.is_le(List.length(&2, U32, FC.put_dec.digits(k, small, n, acc)), Nat.add(1n+j, List.length(&2, U32, acc))) == True{} : Bool}

Uses (21):
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=Bool
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=Empty.absurd
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=List
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=List.length
  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.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.add
  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_lt
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=U32.mod
  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=false_ne_true
  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/fields.bend&name=put_dec.digits
  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=ab0
  https://jend.leeeet.dev/definition.txt?path=lawful-fields@0.1.1.0/proof_digits.bend&name=hk_step
  https://jend.leeeet.dev/definition.txt?path=lawful-words@0.1.0.0/proof_nat.bend&name=add_succ
  https://jend.leeeet.dev/definition.txt?path=lawful-words@0.1.0.0/proof_nat.bend&name=le_add_l