Lemmas.add_no_carry: law of bend-kit-lemmas@0.1.1.0
Import: import bend-kit-lemmas@0.1.1.0/lemmas.bend as Lemmas
Lines 421-428 of bend-kit-lemmas@0.1.1.0/lemmas.bend: https://jend.leeeet.dev/read.txt?path=bend-kit-lemmas@0.1.1.0/lemmas.bend&start_line=421&end_line=428

import Base
import bend-mathlib@0.7.4.0/nat.bend as MNat

law add_no_carry:
  for q: Bool
  for +r: Nat
  for +m: Nat
  for +s: Nat
  for e: {Nat.add(r, scale(q, m)) == s : Nat}
  for h: MNat.lt(s, m)
  {r == s : Nat}

Uses (12):
  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.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=bend-kit-lemmas@0.1.1.0/lemmas.bend&name=lt_rw
  https://jend.leeeet.dev/definition.txt?path=bend-kit-lemmas@0.1.1.0/lemmas.bend&name=scale
  https://jend.leeeet.dev/definition.txt?path=bend-mathlib@0.8.1.0/nat.bend&name=add_zero_sym
  https://jend.leeeet.dev/definition.txt?path=bend-mathlib@0.8.1.0/nat.bend&name=le_add_left
  https://jend.leeeet.dev/definition.txt?path=bend-mathlib@0.8.1.0/nat.bend&name=lt
  https://jend.leeeet.dev/definition.txt?path=bend-mathlib@0.8.1.0/nat.bend&name=lt_irrefl
  https://jend.leeeet.dev/definition.txt?path=bend-mathlib@0.8.1.0/nat.bend&name=lt_of_le_of_lt