PROOF.ml_x: def of bend-osdev-gf@0.1.1.0
Import: import bend-osdev-gf@0.1.1.0/PROOF.bend as PROOF
Lines 1734-1743 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=1734&end_line=1743

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

def ml_x(+b: G.Gf8Bits, +p: G.Gf8Bits) -> {ml(basis(), b, p) == xs(b, p) : List<&2, G.Gf8Bits>}:
  %me0(b, p) : {ml(basis(), b, p) == [_, xk(1n, b, p), xk(2n, b, p), xk(3n, b, p), xk(4n, b, p), xk(5n, b, p), xk(6n, b, p), xk(7n, b, p)] : List<&2, G.Gf8Bits>}
  %me1(b, p) : {ml(basis(), b, p) == [G.Gf8Bits.mul(G.Gf8Bits{True{}, False{}, False{}, False{}, False{}, False{}, False{}, False{}}, b, p), _, xk(2n, b, p), xk(3n, b, p), xk(4n, b, p), xk(5n, b, p), xk(6n, b, p), xk(7n, b, p)] : List<&2, G.Gf8Bits>}
  %me2(b, p) : {ml(basis(), b, p) == [G.Gf8Bits.mul(G.Gf8Bits{True{}, False{}, False{}, False{}, False{}, False{}, False{}, False{}}, b, p), G.Gf8Bits.mul(G.Gf8Bits{False{}, True{}, False{}, False{}, False{}, False{}, False{}, False{}}, b, p), _, xk(3n, b, p), xk(4n, b, p), xk(5n, b, p), xk(6n, b, p), xk(7n, b, p)] : List<&2, G.Gf8Bits>}
  %me3(b, p) : {ml(basis(), b, p) == [G.Gf8Bits.mul(G.Gf8Bits{True{}, False{}, False{}, False{}, False{}, False{}, False{}, False{}}, b, p), G.Gf8Bits.mul(G.Gf8Bits{False{}, True{}, False{}, False{}, False{}, False{}, False{}, False{}}, b, p), G.Gf8Bits.mul(G.Gf8Bits{False{}, False{}, True{}, False{}, False{}, False{}, False{}, False{}}, b, p), _, xk(4n, b, p), xk(5n, b, p), xk(6n, b, p), xk(7n, b, p)] : List<&2, G.Gf8Bits>}
  %me4(b, p) : {ml(basis(), b, p) == [G.Gf8Bits.mul(G.Gf8Bits{True{}, False{}, False{}, False{}, False{}, False{}, False{}, False{}}, b, p), G.Gf8Bits.mul(G.Gf8Bits{False{}, True{}, False{}, False{}, False{}, False{}, False{}, False{}}, b, p), G.Gf8Bits.mul(G.Gf8Bits{False{}, False{}, True{}, False{}, False{}, False{}, False{}, False{}}, b, p), G.Gf8Bits.mul(G.Gf8Bits{False{}, False{}, False{}, True{}, False{}, False{}, False{}, False{}}, b, p), _, xk(5n, b, p), xk(6n, b, p), xk(7n, b, p)] : List<&2, G.Gf8Bits>}
  %me5(b, p) : {ml(basis(), b, p) == [G.Gf8Bits.mul(G.Gf8Bits{True{}, False{}, False{}, False{}, False{}, False{}, False{}, False{}}, b, p), G.Gf8Bits.mul(G.Gf8Bits{False{}, True{}, False{}, False{}, False{}, False{}, False{}, False{}}, b, p), G.Gf8Bits.mul(G.Gf8Bits{False{}, False{}, True{}, False{}, False{}, False{}, False{}, False{}}, b, p), G.Gf8Bits.mul(G.Gf8Bits{False{}, False{}, False{}, True{}, False{}, False{}, False{}, False{}}, b, p), G.Gf8Bits.mul(G.Gf8Bits{False{}, False{}, False{}, False{}, True{}, False{}, False{}, False{}}, b, p), _, xk(6n, b, p), xk(7n, b, p)] : List<&2, G.Gf8Bits>}
  %me6(b, p) : {ml(basis(), b, p) == [G.Gf8Bits.mul(G.Gf8Bits{True{}, False{}, False{}, False{}, False{}, False{}, False{}, False{}}, b, p), G.Gf8Bits.mul(G.Gf8Bits{False{}, True{}, False{}, False{}, False{}, False{}, False{}, False{}}, b, p), G.Gf8Bits.mul(G.Gf8Bits{False{}, False{}, True{}, False{}, False{}, False{}, False{}, False{}}, b, p), G.Gf8Bits.mul(G.Gf8Bits{False{}, False{}, False{}, True{}, False{}, False{}, False{}, False{}}, b, p), G.Gf8Bits.mul(G.Gf8Bits{False{}, False{}, False{}, False{}, True{}, False{}, False{}, False{}}, b, p), G.Gf8Bits.mul(G.Gf8Bits{False{}, False{}, False{}, False{}, False{}, True{}, False{}, False{}}, b, p), _, xk(7n, b, p)] : List<&2, G.Gf8Bits>}
  %me7(b, p) : {ml(basis(), b, p) == [G.Gf8Bits.mul(G.Gf8Bits{True{}, False{}, False{}, False{}, False{}, False{}, False{}, False{}}, b, p), G.Gf8Bits.mul(G.Gf8Bits{False{}, True{}, False{}, False{}, False{}, False{}, False{}, False{}}, b, p), G.Gf8Bits.mul(G.Gf8Bits{False{}, False{}, True{}, False{}, False{}, False{}, False{}, False{}}, b, p), G.Gf8Bits.mul(G.Gf8Bits{False{}, False{}, False{}, True{}, False{}, False{}, False{}, False{}}, b, p), G.Gf8Bits.mul(G.Gf8Bits{False{}, False{}, False{}, False{}, True{}, False{}, False{}, False{}}, b, p), G.Gf8Bits.mul(G.Gf8Bits{False{}, False{}, False{}, False{}, False{}, True{}, False{}, False{}}, b, p), G.Gf8Bits.mul(G.Gf8Bits{False{}, False{}, False{}, False{}, False{}, False{}, True{}, False{}}, b, p), _] : List<&2, G.Gf8Bits>}
  {==}

Uses (16):
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=Bool
  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=me0
  https://jend.leeeet.dev/definition.txt?path=bend-osdev-gf@0.1.1.0/PROOF.bend&name=me1
  https://jend.leeeet.dev/definition.txt?path=bend-osdev-gf@0.1.1.0/PROOF.bend&name=me2
  https://jend.leeeet.dev/definition.txt?path=bend-osdev-gf@0.1.1.0/PROOF.bend&name=me3
  https://jend.leeeet.dev/definition.txt?path=bend-osdev-gf@0.1.1.0/PROOF.bend&name=me4
  https://jend.leeeet.dev/definition.txt?path=bend-osdev-gf@0.1.1.0/PROOF.bend&name=me5
  https://jend.leeeet.dev/definition.txt?path=bend-osdev-gf@0.1.1.0/PROOF.bend&name=me6
  https://jend.leeeet.dev/definition.txt?path=bend-osdev-gf@0.1.1.0/PROOF.bend&name=me7
  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=xk
  https://jend.leeeet.dev/definition.txt?path=bend-osdev-gf@0.1.1.0/PROOF.bend&name=xs
  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