ProofNum.FITS0: law of lawful-fields@0.1.1.0
Import: import lawful-fields@0.1.1.0/proof_num.bend as ProofNum
Lines 154-160 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=154&end_line=160

import Base

# a < q, or a = q and k <= 5, exactly when 10a + k < 10q + 6 (k a digit).
law FITS0:
  for +a: Nat
  for +q: Nat
  for +k: Nat
  for +hk: {Nat.is_le(k, 9n) == True{} : Bool}
  {Bool.or(Nat.is_lt(a, q), Bool.and(Nat.is_eq(a, q), Nat.is_le(k, 5n))) == Nat.is_lt(Nat.add(Nat.mul(a, 10n), k), Nat.add(Nat.mul(q, 10n), 6n)) : Bool}

Uses (14):
  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=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.add
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=Nat.is_eq
  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.mul
  https://jend.leeeet.dev/definition.txt?path=lawful-words@0.1.0.0/proof_nat.bend&name=le_add_r
  https://jend.leeeet.dev/definition.txt?path=lawful-words@0.1.0.0/proof_nat.bend&name=lt_le_trans
  https://jend.leeeet.dev/definition.txt?path=lawful-words@0.1.0.0/proof_nat.bend&name=lt_succ_iff