PROOF.elt_pow: def of bend-osdev-gf@0.1.1.0
Import: import bend-osdev-gf@0.1.1.0/PROOF.bend as PROOF
Lines 1838-1845 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=1838&end_line=1845

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

def elt_pow(n: Nat, +f: G.Gf8Field, +a: U32) -> {G.Gf8.elt(G.Gf8.pow(f, a, n)) == G.Gf8.pow(f, a, n) : U32}:
  match n:
    case 0n:
      {==}
    case 1n+k:
      match f:
        case G.Gf8Field{+poly, +gen}:
          Equal.cong(G.Gf8Bits, U32, r => G.Gf8Bits.to(r), G.Gf8Bits.of(G.Gf8Bits.to(G.Gf8Bits.mul(G.Gf8Bits.of(a), G.Gf8Bits.of(G.Gf8.pow(G.Gf8Field{poly, gen}, a, k)), G.Gf8Bits.of(poly)))), G.Gf8Bits.mul(G.Gf8Bits.of(a), G.Gf8Bits.of(G.Gf8.pow(G.Gf8Field{poly, gen}, a, k)), G.Gf8Bits.of(poly)), ot(G.Gf8Bits.mul(G.Gf8Bits.of(a), G.Gf8Bits.of(G.Gf8.pow(G.Gf8Field{poly, gen}, a, k)), G.Gf8Bits.of(poly))))

Uses (11):
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=Equal.cong
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=Nat
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=U32
  https://jend.leeeet.dev/definition.txt?path=bend-osdev-gf@0.1.1.0/PROOF.bend&name=ot
  https://jend.leeeet.dev/definition.txt?path=bend-osdev-gf@0.1.1.0/gf.bend&name=Gf8.elt
  https://jend.leeeet.dev/definition.txt?path=bend-osdev-gf@0.1.1.0/gf.bend&name=Gf8.pow
  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.of
  https://jend.leeeet.dev/definition.txt?path=bend-osdev-gf@0.1.1.0/gf.bend&name=Gf8Bits.to
  https://jend.leeeet.dev/definition.txt?path=bend-osdev-gf@0.1.1.0/gf.bend&name=Gf8Field