simpa [show u.Positive from by simpa using pos] using ih rfl
case intro.intro.intro.intro.refl.intro.intro
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✝ n₁ : ℕ
ω : Rew L μ₁ n₁ μ₂ n✝
u : Semiterm L μ₁ (n₁ + 1)
pos : (ω.q u).Positive
p : Semiformula L μ₁ (n₁ + 1)
a✝ : Hierarchy Γ✝ s✝ (ω.q.hom p)
ih :
  ∀ {n₁_1 : ℕ} {ω_1 : Rew L μ₁ n₁_1 μ₂ (n✝ + 1)} {p_1 : Semiformula L μ₁ n₁_1},
    ω_1.hom p_1 = ω.q.hom p → Hierarchy Γ✝ s✝ p_1
⊢ Hierarchy Γ✝ s✝ (“(∀[#0 < !!u] !p)”)
no goals