PROOF.horner_lin_a: def of bend-osdev-gf@0.1.1.0
Import: import bend-osdev-gf@0.1.1.0/PROOF.bend as PROOF
Lines 435-443 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=435&end_line=443

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

def horner_lin_a(ps: List<&2, GfPb>, +A: G.Gf8Bits, +C: G.Gf8Bits, +b: G.Gf8Bits, +p: G.Gf8Bits) -> {G.Gf8Bits.horner(pl.x(ps), G.Gf8Bits.xor(A, C), b, p) == G.Gf8Bits.xor(G.Gf8Bits.horner(pl.l(ps), A, b, p), G.Gf8Bits.horner(pl.r(ps), C, b, p)) : G.Gf8Bits}:
  match ps:
    case Nil{}:
      {==}
    case Con{h, rest}:
      match h:
        case GfPb{+s, +t}:
          %Equal.sym(G.Gf8Bits, G.Gf8Bits.step(Bool.xor(s, t), G.Gf8Bits.xor(A, C), b, p), G.Gf8Bits.xor(G.Gf8Bits.step(s, A, b, p), G.Gf8Bits.step(t, C, b, p)), step_lin_a(s, t, A, C, b, p)) : {G.Gf8Bits.horner(pl.x(rest), _, b, p) == G.Gf8Bits.xor(G.Gf8Bits.horner(pl.l(rest), G.Gf8Bits.step(s, A, b, p), b, p), G.Gf8Bits.horner(pl.r(rest), G.Gf8Bits.step(t, C, b, p), b, p)) : G.Gf8Bits}
          horner_lin_a(rest, G.Gf8Bits.step(s, A, b, p), G.Gf8Bits.step(t, C, b, p), b, p)

Uses (12):
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=Bool.xor
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=Equal.sym
  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=GfPb
  https://jend.leeeet.dev/definition.txt?path=bend-osdev-gf@0.1.1.0/PROOF.bend&name=pl.l
  https://jend.leeeet.dev/definition.txt?path=bend-osdev-gf@0.1.1.0/PROOF.bend&name=pl.r
  https://jend.leeeet.dev/definition.txt?path=bend-osdev-gf@0.1.1.0/PROOF.bend&name=pl.x
  https://jend.leeeet.dev/definition.txt?path=bend-osdev-gf@0.1.1.0/PROOF.bend&name=step_lin_a
  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.horner
  https://jend.leeeet.dev/definition.txt?path=bend-osdev-gf@0.1.1.0/gf.bend&name=Gf8Bits.step
  https://jend.leeeet.dev/definition.txt?path=bend-osdev-gf@0.1.1.0/gf.bend&name=Gf8Bits.xor