PROOF.AP.sp: def of bend-osdev-array@0.1.0.1
Import: import bend-osdev-array@0.1.0.1/PROOF.bend as PROOF
Lines 364-373 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=364&end_line=373

import Base

def AP.sp(n: Nat, d: Nat) -> {Word.shl.put(n, False{}, AP.pw(n, d)) == AP.pw(n, 1n+d) : Word(n)}:
  match n:
    case 0n:
      {==}
    case 1n+ +q:
      match d:
        case 0n:
          AP.wcon_cong(q, False{}, Word.shl.put(q, True{}, Word.zero(q)), AP.pw(q, 0n), AP.spz(q))
        case 1n+ +e:
          AP.wcon_cong(q, False{}, Word.shl.put(q, False{}, AP.pw(q, e)), AP.pw(q, 1n+e), AP.sp(q, e))

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.shl.put
  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.pw
  https://jend.leeeet.dev/definition.txt?path=bend-osdev-array@0.1.0.1/PROOF.bend&name=AP.spz
  https://jend.leeeet.dev/definition.txt?path=bend-osdev-array@0.1.0.1/PROOF.bend&name=AP.wcon_cong