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def pow_elt

bend-osdev-gf@0.1.1.0 · PROOF.bend:1862

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

1862def pow_elt(+n: Nat, +f: G.Gf8Field, +a: U32) -> {G.Gf8.pow(f, a, n) == G.Gf8.pow(f, G.Gf8.elt(a), n) : U32}:
1863  match n:
1864    case 0n:
1865      {==}
1866    case 1n+k:
1867      Equal.trans(U32, G.Gf8.mul(f, a, G.Gf8.pow(f, a, k)), G.Gf8.mul(f, G.Gf8.elt(a), G.Gf8.pow(f, a, k)), G.Gf8.mul(f, G.Gf8.elt(a), G.Gf8.pow(f, G.Gf8.elt(a), k)), mul_elt_l(f, a, G.Gf8.pow(f, a, k)), Equal.cong(U32, U32, z => G.Gf8.mul(f, G.Gf8.elt(a), z), G.Gf8.pow(f, a, k), G.Gf8.pow(f, G.Gf8.elt(a), k), pow_elt(k, f, a)))

Uses (9)

Used by (2)