PROOF.comm_e5: def of bend-osdev-gf@0.1.1.0
Import: import bend-osdev-gf@0.1.1.0/PROOF.bend as PROOF
Lines 1697-1702 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=1697&end_line=1702

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

def comm_e5(+b: G.Gf8Bits, +p: G.Gf8Bits) -> {G.Gf8Bits.mul(G.Gf8Bits{False{}, False{}, False{}, False{}, False{}, True{}, False{}, False{}}, b, p) == G.Gf8Bits.mul(b, G.Gf8Bits{False{}, False{}, False{}, False{}, False{}, True{}, False{}, False{}}, p) : G.Gf8Bits}:
  match p:
    case G.Gf8Bits{+p0, +p1, +p2, +p3, +p4, +p5, +p6, +p7}:
      %dec(b) : {G.Gf8Bits.mul(G.Gf8Bits{False{}, False{}, False{}, False{}, False{}, True{}, False{}, False{}}, _, G.Gf8Bits{p0, p1, p2, p3, p4, p5, p6, p7}) == G.Gf8Bits.mul(b, G.Gf8Bits{False{}, False{}, False{}, False{}, False{}, True{}, False{}, False{}}, G.Gf8Bits{p0, p1, p2, p3, p4, p5, p6, p7}) : G.Gf8Bits}
      %dec(b) : {G.Gf8Bits.mul(G.Gf8Bits{False{}, False{}, False{}, False{}, False{}, True{}, False{}, False{}}, ss(bl(b), basis()), G.Gf8Bits{p0, p1, p2, p3, p4, p5, p6, p7}) == G.Gf8Bits.mul(_, G.Gf8Bits{False{}, False{}, False{}, False{}, False{}, True{}, False{}, False{}}, G.Gf8Bits{p0, p1, p2, p3, p4, p5, p6, p7}) : G.Gf8Bits}
      Equal.trans(G.Gf8Bits, G.Gf8Bits.mul(G.Gf8Bits{False{}, False{}, False{}, False{}, False{}, True{}, False{}, False{}}, ss(bl(b), basis()), G.Gf8Bits{p0, p1, p2, p3, p4, p5, p6, p7}), ss(bl(b), mr(basis(), G.Gf8Bits{False{}, False{}, False{}, False{}, False{}, True{}, False{}, False{}}, G.Gf8Bits{p0, p1, p2, p3, p4, p5, p6, p7})), G.Gf8Bits.mul(ss(bl(b), basis()), G.Gf8Bits{False{}, False{}, False{}, False{}, False{}, True{}, False{}, False{}}, G.Gf8Bits{p0, p1, p2, p3, p4, p5, p6, p7}), lin_r(bl(b), basis(), G.Gf8Bits{False{}, False{}, False{}, False{}, False{}, True{}, False{}, False{}}, G.Gf8Bits{p0, p1, p2, p3, p4, p5, p6, p7}), Equal.sym(G.Gf8Bits, G.Gf8Bits.mul(ss(bl(b), basis()), G.Gf8Bits{False{}, False{}, False{}, False{}, False{}, True{}, False{}, False{}}, G.Gf8Bits{p0, p1, p2, p3, p4, p5, p6, p7}), ss(bl(b), ml(basis(), G.Gf8Bits{False{}, False{}, False{}, False{}, False{}, True{}, False{}, False{}}, G.Gf8Bits{p0, p1, p2, p3, p4, p5, p6, p7})), lin_l(bl(b), basis(), G.Gf8Bits{False{}, False{}, False{}, False{}, False{}, True{}, False{}, False{}}, G.Gf8Bits{p0, p1, p2, p3, p4, p5, p6, p7})))

Uses (13):
  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=Equal.trans
  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=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