PROOF.AP.and_zero: def of bend-osdev-array@0.1.0.1
Import: import bend-osdev-array@0.1.0.1/PROOF.bend as PROOF
Lines 875-884 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=875&end_line=884

import Base

def AP.and_zero(n: Nat, w: Word(n)) -> {Word.and(n, w, Word.zero(n)) == Word.zero(n) : Word(n)}:
  match n:
    case 0n:
      {==}
    case 1n+ +q:
      match w:
        case WCon{False{}, t}:
          AP.wcon_cong(q, False{}, Word.and(q, t, Word.zero(q)), Word.zero(q), AP.and_zero(q, t))
        case WCon{True{}, t}:
          AP.wcon_cong(q, False{}, Word.and(q, t, Word.zero(q)), Word.zero(q), AP.and_zero(q, t))

Uses (7):
  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.Con
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=Word.and
  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.wcon_cong