match Γ with
| 𝚺 => rcases h with ⟨p, h⟩; exact ⟨p.negPi, h.negPi⟩
| 𝚷 => rcases h with ⟨p, h⟩; exact ⟨p.negSigma, h.negSigma⟩
| 𝚫 => rcases h with ⟨p, h⟩; exact ⟨p.negDelta, h.not⟩
L : Language
inst✝⁹ : L.ORing
ξ : Type v
n : ℕ
M : Type u_1
inst✝⁸ : Zero M
inst✝⁷ : One M
inst✝⁶ : Add M
inst✝⁵ : Mul M
inst✝⁴ : LT M
inst✝³ : M ⊧ₘ* 𝐏𝐀⁻
inst✝² : Structure L M
inst✝¹ : Structure.ORing L M
inst✝ : Structure.Monotone L M
Γ✝ : HierarchySymbol
k : ℕ
P Q : (Fin k → M) → Prop
m : ℕ
Γ : SigmaPiDelta
h : Definable L (Γ.alt, m) P
⊢ Definable L (Γ, m) fun v => ¬P v
no goals