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def ak

bend-osdev-gf@0.1.1.0 · PROOF.bend:1748

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

1748def 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}:
1749  match n:
1750    case 0n:
1751      {==}
1752    case 1n+k:
1753      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)

Used by (1)