ring_nf at w
case intro.intro.intro.intro.intro
a b c : ℤθ
k j1 j2 j3 : ℤ
w :
  ↑(unit ^ (3 * k + 2)) =
    { f := (3 * j1 + 1) * -5 + 6 * (3 * j3) * -4 - 2 * (3 * j2) * -4 - 2 * (3 * j3) * -14,
      g := (3 * j1 + 1) * -14 + 3 * j2 * -5 + 16 * (3 * j3) * -4 - 6 * (3 * j2) * -4 - 6 * (3 * j3) * -14,
      h := (3 * j1 + 1) * -4 + 3 * j3 * -5 + 3 * j2 * -14 + 3 * (3 * j3) * -4 - 3 * (3 * j2) * -4 - 3 * (3 * j3) * -14 }
s : ↑(unit ^ (3 * k)) = { f := 3 * j1 + 1, g := 3 * j2, h := 3 * j3 }
⊢ (↑(unit ^ (3 * k + 2))).f % 3 = 1 ∧ (↑(unit ^ (3 * k + 2))).g % 3 = 1 ∧ (↑(unit ^ (3 * k + 2))).h % 3 = 2
case intro.intro.intro.intro.intro
a b c : ℤθ
k j1 j2 j3 : ℤ
s : ↑(unit ^ (3 * k)) = { f := 3 * j1 + 1, g := 3 * j2, h := 3 * j3 }
w :
  ↑(unit ^ (2 + k * 3)) =
    { f := -5 - j1 * 15 + j3 * 12 + j2 * 24, g := -14 - j1 * 42 + j3 * 60 + j2 * 57,
      h := -4 - j1 * 12 + (j3 * 75 - j2 * 6) }
⊢ (↑(unit ^ (3 * k + 2))).f % 3 = 1 ∧ (↑(unit ^ (3 * k + 2))).g % 3 = 1 ∧ (↑(unit ^ (3 * k + 2))).h % 3 = 2