PROOF.tl.zero_l: def of bend-osdev-gf@0.1.1.0
Import: import bend-osdev-gf@0.1.1.0/PROOF.bend as PROOF
Lines 7850-7854 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=7850&end_line=7854

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

# a product with a factor whose table zero test is true is 0
def tl.zero_l(+f: G.Gf8Field, +a: U32, +b: U32, +h: {U32.is_eq(G.Gf8.elt(a), 0) == True{} : Bool}) -> {G.Gf8.mul(f, a, b) == 0 : U32}:
  %Equal.sym(U32, G.Gf8.mul(f, a, b), G.Gf8.mul(f, G.Gf8.elt(a), b), mul_elt_l(f, a, b)) : {_ == 0 : U32}
  %Equal.sym(U32, G.Gf8.elt(a), 0, GC.gc.elt0(a, h)) : {G.Gf8.mul(f, _, b) == 0 : U32}
  Laws.mul_zero(f, b)

Uses (10):
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=Bool
  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=Base/base.bend&name=U32.is_eq
  https://jend.leeeet.dev/definition.txt?path=bend-osdev-gf@0.1.1.0/LAWS.bend&name=mul_zero
  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
  https://jend.leeeet.dev/definition.txt?path=bend-osdev-gf@0.1.1.0/proof_tab_cases.bend&name=gc.elt0