case ball pos _ ih =>
  simp [Rew.eq_lt_iff] at eq
  rcases eq with ⟨hp, ⟨u, rfl, s, hs, rfl⟩, p, rfl, rfl⟩
  simpa [show u.Positive from by simpa using pos] using ih rfl
L : Language
inst✝ : L.LT
μ : Type v
μ₁ : Type u_1
μ₂ : Type u_2
n₂ : ℕ
Γ : Polarity
s : ℕ
q : Semiformula L μ₂ n₂
Γ✝ : Polarity
s✝ n✝ : ℕ
p✝ : Semiformula L μ₂ (n✝ + 1)
t✝ : Semiterm L μ₂ (n✝ + 1)
pos : t✝.Positive
a✝ : Hierarchy Γ✝ s✝ p✝
ih : ∀ {n₁ : ℕ} {ω : Rew L μ₁ n₁ μ₂ (n✝ + 1)} {p : Semiformula L μ₁ n₁}, ω.hom p = p✝ → Hierarchy Γ✝ s✝ p
n₁ : ℕ
ω : Rew L μ₁ n₁ μ₂ n✝
p : Semiformula L μ₁ n₁
eq : ∃ p₁, ω.q.hom p₁ = (“#0 < !!t✝”) ∧ ∃ x, ω.q.hom x = p✝ ∧ p = ∀[p₁] x
⊢ Hierarchy Γ✝ s✝ p
no goals