PROOF.tl.mul_elt: def of bend-osdev-gf@0.1.1.0
Import: import bend-osdev-gf@0.1.1.0/PROOF.bend as PROOF
Lines 7856-7857 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=7856&end_line=7857

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

def tl.mul_elt(+f: G.Gf8Field, +a: U32, +b: U32) -> {G.Gf8.mul(f, G.Gf8.elt(a), G.Gf8.elt(b)) == G.Gf8.mul(f, a, b) : U32}:
  Equal.trans(U32, G.Gf8.mul(f, G.Gf8.elt(a), G.Gf8.elt(b)), G.Gf8.mul(f, a, G.Gf8.elt(b)), G.Gf8.mul(f, a, b), Equal.sym(U32, G.Gf8.mul(f, a, G.Gf8.elt(b)), G.Gf8.mul(f, G.Gf8.elt(a), G.Gf8.elt(b)), mul_elt_l(f, a, G.Gf8.elt(b))), Equal.trans(U32, G.Gf8.mul(f, a, G.Gf8.elt(b)), G.Gf8.mul(f, G.Gf8.elt(b), a), G.Gf8.mul(f, a, b), Laws.mul_comm(f, a, G.Gf8.elt(b)), Equal.trans(U32, G.Gf8.mul(f, G.Gf8.elt(b), a), G.Gf8.mul(f, b, a), G.Gf8.mul(f, a, b), Equal.sym(U32, G.Gf8.mul(f, b, a), G.Gf8.mul(f, G.Gf8.elt(b), a), mul_elt_l(f, b, a)), Laws.mul_comm(f, b, a))))

Uses (8):
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=Equal.sym
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=Equal.trans
  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/LAWS.bend&name=mul_comm
  https://jend.leeeet.dev/definition.txt?path=bend-osdev-gf@0.1.1.0/PROOF.bend&name=mul_elt_l
  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=Gf8Field