rw [unit_inv_cubed] at w
case right.succ.intro.intro.intro.intro.intro
a b✝ c : ℤθ
b : ℕ
h1 : (↑(unit ^ (3 * -↑b))).f % 3 = 1
h2 : (↑(unit ^ (3 * -↑b))).g % 3 = 0
h3 : (↑(unit ^ (3 * -↑b))).h % 3 = 0
p : Nat.succ b = b + 1
c1 : ℤ
hc1 : (↑(unit ^ (3 * -↑b))).f = 3 * c1 + 1
c2 : ℤ
hc2 : (↑(unit ^ (3 * -↑b))).g = 3 * c2
c3 : ℤ
w : ↑(unit ^ (3 * -(↑b + 1))) = { f := 3 * c1 + 1, g := 3 * c2, h := 3 * c3 } * ↑(unit ^ (-3))
hc3 : (↑(unit ^ (3 * -↑b))).h = 3 * c3
s : ↑(unit ^ (3 * -↑b)) = { f := 3 * c1 + 1, g := 3 * c2, h := 3 * c3 }
⊢ (↑(unit ^ (3 * -↑(b + 1)))).f % 3 = 1 ∧ (↑(unit ^ (3 * -↑(b + 1)))).g % 3 = 0 ∧ (↑(unit ^ (3 * -↑(b + 1)))).h % 3 = 0
case right.succ.intro.intro.intro.intro.intro
a b✝ c : ℤθ
b : ℕ
h1 : (↑(unit ^ (3 * -↑b))).f % 3 = 1
h2 : (↑(unit ^ (3 * -↑b))).g % 3 = 0
h3 : (↑(unit ^ (3 * -↑b))).h % 3 = 0
p : Nat.succ b = b + 1
c1 : ℤ
hc1 : (↑(unit ^ (3 * -↑b))).f = 3 * c1 + 1
c2 : ℤ
hc2 : (↑(unit ^ (3 * -↑b))).g = 3 * c2
c3 : ℤ
w : ↑(unit ^ (3 * -(↑b + 1))) = { f := 3 * c1 + 1, g := 3 * c2, h := 3 * c3 } * { f := 10591, g := 5553, h := 2139 }
hc3 : (↑(unit ^ (3 * -↑b))).h = 3 * c3
s : ↑(unit ^ (3 * -↑b)) = { f := 3 * c1 + 1, g := 3 * c2, h := 3 * c3 }
⊢ (↑(unit ^ (3 * -↑(b + 1)))).f % 3 = 1 ∧ (↑(unit ^ (3 * -↑(b + 1)))).g % 3 = 0 ∧ (↑(unit ^ (3 * -↑(b + 1)))).h % 3 = 0