PROOF.ak: def of bend-osdev-gf@0.1.1.0
Import: import bend-osdev-gf@0.1.1.0/PROOF.bend as PROOF
Lines 1748-1753 of bend-osdev-gf@0.1.1.0/PROOF.bend: https://jend.leeeet.dev/read.txt?path=bend-osdev-gf@0.1.1.0/PROOF.bend&start_line=1748&end_line=1753

import Base
import bend-osdev-gf@0.1.1.0/gf.bend as G

def ak(n: Nat, +b: G.Gf8Bits, +c: G.Gf8Bits, +p: G.Gf8Bits) -> {G.Gf8Bits.mul(xk(n, b, p), c, p) == xk(n, G.Gf8Bits.mul(b, c, p), p) : G.Gf8Bits}:
  match n:
    case 0n:
      {==}
    case 1n+k:
      Equal.trans(G.Gf8Bits, G.Gf8Bits.mul(xk(k, G.Gf8Bits.x(b, p), p), c, p), xk(k, G.Gf8Bits.mul(G.Gf8Bits.x(b, p), c, p), p), xk(k, G.Gf8Bits.x(G.Gf8Bits.mul(b, c, p), p), p), ak(k, G.Gf8Bits.x(b, p), c, p), Equal.cong(G.Gf8Bits, G.Gf8Bits, z => xk(k, z, p), G.Gf8Bits.mul(G.Gf8Bits.x(b, p), c, p), G.Gf8Bits.x(G.Gf8Bits.mul(b, c, p), p), ax(b, c, p)))

Uses (8):
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=Equal.cong
  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=bend-osdev-gf@0.1.1.0/PROOF.bend&name=ax
  https://jend.leeeet.dev/definition.txt?path=bend-osdev-gf@0.1.1.0/PROOF.bend&name=xk
  https://jend.leeeet.dev/definition.txt?path=bend-osdev-gf@0.1.1.0/gf.bend&name=Gf8Bits
  https://jend.leeeet.dev/definition.txt?path=bend-osdev-gf@0.1.1.0/gf.bend&name=Gf8Bits.mul
  https://jend.leeeet.dev/definition.txt?path=bend-osdev-gf@0.1.1.0/gf.bend&name=Gf8Bits.x