PROOF.mul_elt_l: def of bend-osdev-gf@0.1.1.0
Import: import bend-osdev-gf@0.1.1.0/PROOF.bend as PROOF
Lines 1857-1860 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=1857&end_line=1860

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

def mul_elt_l(+f: G.Gf8Field, +a: U32, +b: U32) -> {G.Gf8.mul(f, a, b) == G.Gf8.mul(f, G.Gf8.elt(a), b) : U32}:
  match f:
    case G.Gf8Field{+poly, gen}:
      Equal.cong(G.Gf8Bits, U32, z => G.Gf8Bits.to(G.Gf8Bits.mul(z, G.Gf8Bits.of(b), G.Gf8Bits.of(poly))), G.Gf8Bits.of(a), G.Gf8Bits.of(G.Gf8Bits.to(G.Gf8Bits.of(a))), Equal.sym(G.Gf8Bits, G.Gf8Bits.of(G.Gf8Bits.to(G.Gf8Bits.of(a))), G.Gf8Bits.of(a), ot(G.Gf8Bits.of(a))))

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=Equal.sym
  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.mul
  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