ProofNum.step_dg: law of lawful-fields@0.1.1.0
Import: import lawful-fields@0.1.1.0/proof_num.bend as ProofNum
Lines 391-402 of lawful-fields@0.1.1.0/proof_num.bend: https://jend.leeeet.dev/read.txt?path=lawful-fields@0.1.1.0/proof_num.bend&start_line=391&end_line=402

import Base
import lawful-fields@0.1.1.0/defs.bend as F

# After byte x, from value a, by the digit test (dg).
law step_dg:
  for +acc: U32
  for +x: U32
  for +M: Nat
  for +q: Nat
  for +dg: Bool
  for +hdg: {DG(x) == dg : Bool}
  for +hm: {Nat.pow(2n, 32n) == M : Nat}
  for +hcq: {U32.to_nat(429496729) == q : Nat}
  for +hq: {Nat.add(Nat.mul(q, 10n), 6n) == M : Nat}
  Inv(Bool.and(dg, FT(acc, x)), NA(acc, x), F.dec.push(Some{U32.to_nat(acc)}, F.digit.if(x, dg)), M)

Uses (29):
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=Bool
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=Bool.and
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=Bool.or
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=Equal.sym
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=Maybe
  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_lt
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=Nat.mul
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=Nat.pow
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=Nat.sub
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=U32
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=U32.is_eq
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=U32.is_ge
  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.is_lt
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=U32.sub
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=U32.to_nat
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=Unit
  https://jend.leeeet.dev/definition.txt?path=lawful-arrays@0.1.0.0/proof_base.bend&name=and_true_l
  https://jend.leeeet.dev/definition.txt?path=lawful-arrays@0.1.0.0/proof_base.bend&name=and_true_r
  https://jend.leeeet.dev/definition.txt?path=lawful-fields@0.1.1.0/defs.bend&name=dec.push
  https://jend.leeeet.dev/definition.txt?path=lawful-fields@0.1.1.0/defs.bend&name=digit.if
  https://jend.leeeet.dev/definition.txt?path=lawful-fields@0.1.1.0/proof_num.bend&name=DG
  https://jend.leeeet.dev/definition.txt?path=lawful-fields@0.1.1.0/proof_num.bend&name=FITSU
  https://jend.leeeet.dev/definition.txt?path=lawful-fields@0.1.1.0/proof_num.bend&name=FT
  https://jend.leeeet.dev/definition.txt?path=lawful-fields@0.1.1.0/proof_num.bend&name=Inv
  https://jend.leeeet.dev/definition.txt?path=lawful-fields@0.1.1.0/proof_num.bend&name=NA
  https://jend.leeeet.dev/definition.txt?path=lawful-fields@0.1.1.0/proof_num.bend&name=step_fb