PROOF.comm: def of bend-osdev-gf@0.1.1.0
Import: import bend-osdev-gf@0.1.1.0/PROOF.bend as PROOF
Lines 1729-1732 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=1729&end_line=1732

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

def comm(+a: G.Gf8Bits, +b: G.Gf8Bits, +p: G.Gf8Bits) -> {G.Gf8Bits.mul(a, b, p) == G.Gf8Bits.mul(b, a, p) : G.Gf8Bits}:
  %dec(a) : {G.Gf8Bits.mul(_, b, p) == G.Gf8Bits.mul(b, a, p) : G.Gf8Bits}
  %dec(a) : {G.Gf8Bits.mul(ss(bl(a), basis()), b, p) == G.Gf8Bits.mul(b, _, p) : G.Gf8Bits}
  Equal.trans(G.Gf8Bits, G.Gf8Bits.mul(ss(bl(a), basis()), b, p), ss(bl(a), ml(basis(), b, p)), G.Gf8Bits.mul(b, ss(bl(a), basis()), p), lin_l(bl(a), basis(), b, p), Equal.trans(G.Gf8Bits, ss(bl(a), ml(basis(), b, p)), ss(bl(a), mr(basis(), b, p)), G.Gf8Bits.mul(b, ss(bl(a), basis()), p), Equal.cong(List<&2, G.Gf8Bits>, G.Gf8Bits, l => ss(bl(a), l), ml(basis(), b, p), mr(basis(), b, p), mlr(b, p)), Equal.sym(G.Gf8Bits, G.Gf8Bits.mul(b, ss(bl(a), basis()), p), ss(bl(a), mr(basis(), b, p)), lin_r(bl(a), basis(), b, p))))

Uses (15):
  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=Equal.trans
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=List
  https://jend.leeeet.dev/definition.txt?path=bend-osdev-gf@0.1.1.0/PROOF.bend&name=basis
  https://jend.leeeet.dev/definition.txt?path=bend-osdev-gf@0.1.1.0/PROOF.bend&name=bl
  https://jend.leeeet.dev/definition.txt?path=bend-osdev-gf@0.1.1.0/PROOF.bend&name=dec
  https://jend.leeeet.dev/definition.txt?path=bend-osdev-gf@0.1.1.0/PROOF.bend&name=lin_l
  https://jend.leeeet.dev/definition.txt?path=bend-osdev-gf@0.1.1.0/PROOF.bend&name=lin_r
  https://jend.leeeet.dev/definition.txt?path=bend-osdev-gf@0.1.1.0/PROOF.bend&name=ml
  https://jend.leeeet.dev/definition.txt?path=bend-osdev-gf@0.1.1.0/PROOF.bend&name=mlr
  https://jend.leeeet.dev/definition.txt?path=bend-osdev-gf@0.1.1.0/PROOF.bend&name=mr
  https://jend.leeeet.dev/definition.txt?path=bend-osdev-gf@0.1.1.0/PROOF.bend&name=ss
  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