match Γ with
| (𝚺, _) => intro; simp [hP.iff]
| (𝚷, _) => intro; simp [hP.iff]
| (𝚫, _) => exact ⟨
  fun v ↦ by rcases p; simpa [HSemiformula.rew] using hP.proper.rew Rew.emb v,
  by intro; simp [hP.df.iff]⟩
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
p : HSemisentence L k Γ
hP : Defined P p
⊢ DefinedWithParam P (HSemiformula.rew Rew.emb p)
no goals