PROOF.AP.sub_one: def of bend-osdev-array@0.1.0.1
Import: import bend-osdev-array@0.1.0.1/PROOF.bend as PROOF
Lines 473-482 of bend-osdev-array@0.1.0.1/PROOF.bend: https://jend.leeeet.dev/read.txt?path=bend-osdev-array@0.1.0.1/PROOF.bend&start_line=473&end_line=482

import Base

def AP.sub_one(n: Nat, d: Nat) -> {Word.sub(n, AP.pw(n, d), AP.pw(n, 0n)) == AP.lm(n, d) : Word(n)}:
  match n:
    case 0n:
      {==}
    case 1n+ +q:
      match d:
        case 0n:
          AP.wcon_cong(q, False{}, Word.adc(q, Word.zero(q), Word.zero(q), True{}, True{}), Word.zero(q), AP.z1(q))
        case 1n+ +e:
          AP.wcon_cong(q, True{}, Word.adc(q, AP.pw(q, e), Word.zero(q), True{}, False{}), AP.lm(q, e), AP.z2(q, e))

Uses (11):
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=Bool
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=Nat
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=Word
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=Word.adc
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=Word.sub
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=Word.zero
  https://jend.leeeet.dev/definition.txt?path=bend-osdev-array@0.1.0.1/PROOF.bend&name=AP.lm
  https://jend.leeeet.dev/definition.txt?path=bend-osdev-array@0.1.0.1/PROOF.bend&name=AP.pw
  https://jend.leeeet.dev/definition.txt?path=bend-osdev-array@0.1.0.1/PROOF.bend&name=AP.wcon_cong
  https://jend.leeeet.dev/definition.txt?path=bend-osdev-array@0.1.0.1/PROOF.bend&name=AP.z1
  https://jend.leeeet.dev/definition.txt?path=bend-osdev-array@0.1.0.1/PROOF.bend&name=AP.z2