have r2 := y_mod_three ((unit ^ ((3 : ℤ) * -(b : ℤ)) : ℤθˣ) : ℤθ).g 0 h2
case right.succ.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
w : ↑(unit ^ (3 * -(↑b + 1))) = ↑(unit ^ (3 * -↑b)) * ↑(unit ^ (-3))
c1 : ℤ
hc1 : (↑(unit ^ (3 * -↑b))).f = 3 * c1 + 1
⊢ (↑(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
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))
c1 : ℤ
hc1 : (↑(unit ^ (3 * -↑b))).f = 3 * c1 + 1
r2 : ∃ k, (↑(unit ^ (3 * -↑b))).g = 3 * k + 0
⊢ (↑(unit ^ (3 * -↑(b + 1)))).f % 3 = 1 ∧ (↑(unit ^ (3 * -↑(b + 1)))).g % 3 = 0 ∧ (↑(unit ^ (3 * -↑(b + 1)))).h % 3 = 0