have t1 : ((unit ) ^ (3 * b):ℤθ).f % 3 = 1 :=
  by
    norm_cast
case left.succ.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
w : ↑(unit ^ (3 * (b + 1))) = ↑(unit ^ (3 * b)) * ↑unit ^ 3
⊢ (↑(unit ^ (3 * (b + 1)))).f % 3 = 1 ∧ (↑(unit ^ (3 * (b + 1)))).g % 3 = 0 ∧ (↑(unit ^ (3 * (b + 1)))).h % 3 = 0
case left.succ.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
w : ↑(unit ^ (3 * (b + 1))) = ↑(unit ^ (3 * b)) * ↑unit ^ 3
t1 : (↑(unit ^ (3 * b))).f % 3 = 1
⊢ (↑(unit ^ (3 * (b + 1)))).f % 3 = 1 ∧ (↑(unit ^ (3 * (b + 1)))).g % 3 = 0 ∧ (↑(unit ^ (3 * (b + 1)))).h % 3 = 0