ProofShift.ws.or_zero: def of bend-osdev-word64@0.1.1.0
Import: import bend-osdev-word64@0.1.1.0/proof_shift.bend as ProofShift
Lines 332-343 of bend-osdev-word64@0.1.1.0/proof_shift.bend: https://jend.leeeet.dev/read.txt?path=bend-osdev-word64@0.1.1.0/proof_shift.bend&start_line=332&end_line=343

import Base

def ws.or_zero(n: Nat, w: Word(n)) -> {Word.or(n, w, Word.zero(n)) == w : Word(n)}:
  match n:
    case 0n:
      match w:
        case WNil{}:
          {==}
    case 1n+ +p:
      match w:
        case WCon{False{}, +t}:
          ws.wcon_cong(p, False{}, Word.or(p, t, Word.zero(p)), t, ws.or_zero(p, t))
        case WCon{True{}, +t}:
          ws.wcon_cong(p, True{}, Word.or(p, t, Word.zero(p)), t, ws.or_zero(p, t))

Uses (8):
  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.Nil
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=Word.or
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=Word.zero
  https://jend.leeeet.dev/definition.txt?path=bend-osdev-word64@0.1.1.0/proof_shift.bend&name=ws.wcon_cong