ring_nf at w
case intro.intro.intro.intro.intro
a b c : ℤθ
k j1 j2 j3 : ℤ
w :
  ↑(unit ^ (3 * k + 1)) =
    { f := (3 * j1 + 1) * -1 + 6 * (3 * j3) * -1 - 2 * (3 * j2) * -1 - 2 * (3 * j3) * -3,
      g := (3 * j1 + 1) * -3 + 3 * j2 * -1 + 16 * (3 * j3) * -1 - 6 * (3 * j2) * -1 - 6 * (3 * j3) * -3,
      h := (3 * j1 + 1) * -1 + 3 * j3 * -1 + 3 * j2 * -3 + 3 * (3 * j3) * -1 - 3 * (3 * j2) * -1 - 3 * (3 * j3) * -3 }
s : ↑(unit ^ (3 * k)) = { f := 3 * j1 + 1, g := 3 * j2, h := 3 * j3 }
⊢ (↑(unit ^ (3 * k + 1))).f % 3 = 2 ∧ (↑(unit ^ (3 * k + 1))).g % 3 = 0 ∧ (↑(unit ^ (3 * k + 1))).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 ^ (1 + k * 3)) = { f := -1 - j1 * 3 + j2 * 6, g := -3 - j1 * 9 + j3 * 6 + j2 * 15, h := -1 - j1 * 3 + j3 * 15 }
⊢ (↑(unit ^ (3 * k + 1))).f % 3 = 2 ∧ (↑(unit ^ (3 * k + 1))).g % 3 = 0 ∧ (↑(unit ^ (3 * k + 1))).h % 3 = 2