dsimp at w
case intro.intro.intro.intro.intro
a b c : ℤθ
k j1 j2 j3 : ℤ
w :
  ↑(unit ^ (3 * k + 1)) =
    {
      f :=
        { f := 3 * j1 + 1, g := 3 * j2, h := 3 * j3 }.f * { f := -1, g := -3, h := -1 }.f +
              6 * { f := 3 * j1 + 1, g := 3 * j2, h := 3 * j3 }.h * { f := -1, g := -3, h := -1 }.h -
            2 * { f := 3 * j1 + 1, g := 3 * j2, h := 3 * j3 }.g * { f := -1, g := -3, h := -1 }.h -
          2 * { f := 3 * j1 + 1, g := 3 * j2, h := 3 * j3 }.h * { f := -1, g := -3, h := -1 }.g,
      g :=
        { f := 3 * j1 + 1, g := 3 * j2, h := 3 * j3 }.f * { f := -1, g := -3, h := -1 }.g +
                { f := 3 * j1 + 1, g := 3 * j2, h := 3 * j3 }.g * { f := -1, g := -3, h := -1 }.f +
              16 * { f := 3 * j1 + 1, g := 3 * j2, h := 3 * j3 }.h * { f := -1, g := -3, h := -1 }.h -
            6 * { f := 3 * j1 + 1, g := 3 * j2, h := 3 * j3 }.g * { f := -1, g := -3, h := -1 }.h -
          6 * { f := 3 * j1 + 1, g := 3 * j2, h := 3 * j3 }.h * { f := -1, g := -3, h := -1 }.g,
      h :=
        { f := 3 * j1 + 1, g := 3 * j2, h := 3 * j3 }.f * { f := -1, g := -3, h := -1 }.h +
                  { f := 3 * j1 + 1, g := 3 * j2, h := 3 * j3 }.h * { f := -1, g := -3, h := -1 }.f +
                { f := 3 * j1 + 1, g := 3 * j2, h := 3 * j3 }.g * { f := -1, g := -3, h := -1 }.g +
              3 * { f := 3 * j1 + 1, g := 3 * j2, h := 3 * j3 }.h * { f := -1, g := -3, h := -1 }.h -
            3 * { f := 3 * j1 + 1, g := 3 * j2, h := 3 * j3 }.g * { f := -1, g := -3, h := -1 }.h -
          3 * { f := 3 * j1 + 1, g := 3 * j2, h := 3 * j3 }.h * { f := -1, g := -3, h := -1 }.g }
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
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