ProofDigits.dg_pair: law of lawful-fields@0.1.1.0
Import: import lawful-fields@0.1.1.0/proof_digits.bend as ProofDigits
Lines 102-108 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=102&end_line=108

import Base
import lawful-bytes@0.1.1.0/defs.bend as D
import lawful-bytes@0.1.1.0/bytes.bend as B
import lawful-fields@0.1.1.0/fields.bend as FC
import lawful-bytes@0.1.1.0/proof_core.bend as C
import lawful-arrays@0.1.0.0/proof_tree.bend as P

law dg_pair:
  for +n: Nat
  for +len: U32
  for +t: P.Tree<U32>
  for +j: U32
  for +ok: Bool
  {FC.digits.go(n, B.at(C.BT(len, t), j), j, ok) == (C.BT(len, t), Pair.snd(D.Bytes, Bool, FC.digits.go(n, B.at(C.BT(len, t), j), j, ok))) : D.Bytes & Bool}

Uses (18):
  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=Equal.sym
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=Nat
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=Pair
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=Pair.snd
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=Sigma
  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.is_ge
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=U32.is_le
  https://jend.leeeet.dev/definition.txt?path=lawful-arrays@0.1.0.0/proof_tree.bend&name=Tree
  https://jend.leeeet.dev/definition.txt?path=lawful-bytes@0.1.1.0/bytes.bend&name=at
  https://jend.leeeet.dev/definition.txt?path=lawful-bytes@0.1.1.0/defs.bend&name=Bytes
  https://jend.leeeet.dev/definition.txt?path=lawful-bytes@0.1.1.0/proof_core.bend&name=AT
  https://jend.leeeet.dev/definition.txt?path=lawful-bytes@0.1.1.0/proof_core.bend&name=BT
  https://jend.leeeet.dev/definition.txt?path=lawful-bytes@0.1.1.0/proof_core.bend&name=at_pair_t
  https://jend.leeeet.dev/definition.txt?path=lawful-fields@0.1.1.0/fields.bend&name=digits.go