exact this.of_iff (fun k ↦
forall_congr' <| fun s ↦ iff_congr (by rfl) <| and_congr (by rfl) <| and_congr (by rfl)
⟨fun h i hi z _ hiz ↦ h i z hiz, fun h i z hiz ↦ h i (lt_of_mem_dom hiz) z (lt_of_mem_rng hiz) hiz⟩)
M : Type u_1
inst✝⁵ : Zero M
inst✝⁴ : One M
inst✝³ : Add M
inst✝² : Mul M
inst✝¹ : LT M
inst✝ : M ⊧ₘ* 𝐈𝚺₁
a : M
this : 𝚷₁-Predicate fun {k} => ∀ {s : M}, s ∈ a ^ˢ k ↔ Seq s ∧ lh s = k ∧ ∀ i < s, ∀ z < s, ⟪i, z⟫ ∈ s → z ∈ a
⊢ 𝚷₁-Predicate fun {k} => ∀ {s : M}, s ∈ a ^ˢ k ↔ Seq s ∧ lh s = k ∧ ∀ (i z : M), ⟪i, z⟫ ∈ s → z ∈ a
no goals