exact ⟨.mkSigma (∃' p.val) (by simp), by intro v; simp [hp.df.iff]⟩
case mk.intro
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
s : ℕ
P : (Fin k → M) → M → Prop
p : HSemiformula L M k.succ (𝚺, s + 1)
hp : DefinedWithParam (fun w => P (fun x => w x.succ) (w 0)) p
⊢ Definable L (𝚺, s + 1) fun v => ∃ x, P v x
no goals