exact this.of_iff <| by intro v; simp [lt_succ_iff_le]
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
P : (Fin k → M) → M → Prop
f : (Fin k → M) → M
hf : DefinableFunction L (𝚺, m + 1) f
h : Definable L (Γ, m + 1) fun w => P (fun x => w x.succ) (w 0)
this : Definable L (Γ, m + 1) fun v => ∀ x < f v + 1, P v x
⊢ Definable L (Γ, m + 1) fun v => ∀ x ≤ f v, P v x
no goals