ProofDigits.R: law of lawful-fields@0.1.1.0
Import: import lawful-fields@0.1.1.0/proof_digits.bend as ProofDigits
Lines 585-597 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=585&end_line=597

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

# With n <= BK(k) the fuel k suffices; q = n / 10 and the spec's fuel f >= q.
law R:
  for +k: Nat
  for +small: Bool
  for +q: Nat
  for +f: Nat
  for +n: U32
  for +acc: List<&2, U32>
  for +hs: {U32.is_lt(n, 10) == small : Bool}
  for +hq: {Nat.div(U32.to_nat(n), 10n) == q : Nat}
  for +hk: {Nat.is_le(U32.to_nat(n), U32.to_nat(BK(k))) == True{} : Bool}
  for +hf: {Nat.is_le(q, f) == True{} : Bool}
  {FC.put_dec.digits(k, small, n, acc) == lgo(f, q, DG(U32.to_nat(n)), acc) : List<&2, U32>}

Uses (38):
  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=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=List
  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_le
  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.mod
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=Nat.mul
  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-arrays@0.1.0.0/proof_base.bend&name=succ_ne_zero
  https://jend.leeeet.dev/definition.txt?path=lawful-arrays@0.1.0.0/proof_base.bend&name=true_ne_false
  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=DG
  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=dg_eq
  https://jend.leeeet.dev/definition.txt?path=lawful-fields@0.1.1.0/proof_digits.bend&name=dg_small
  https://jend.leeeet.dev/definition.txt?path=lawful-fields@0.1.1.0/proof_digits.bend&name=dlt
  https://jend.leeeet.dev/definition.txt?path=lawful-fields@0.1.1.0/proof_digits.bend&name=ge10
  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-fields@0.1.1.0/proof_digits.bend&name=lgo
  https://jend.leeeet.dev/definition.txt?path=lawful-fields@0.1.1.0/proof_digits.bend&name=lt10
  https://jend.leeeet.dev/definition.txt?path=lawful-words@0.1.0.0/proof_nat.bend&name=div_mod
  https://jend.leeeet.dev/definition.txt?path=lawful-words@0.1.0.0/proof_nat.bend&name=div_small
  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_nat.bend&name=mod_lt
  https://jend.leeeet.dev/definition.txt?path=lawful-words@0.1.0.0/proof_u32.bend&name=to_nat_div