exact finite_comprehension₁! this
  ⟨⟪log a, log b⟫ + 1, fun i ↦ by
    rintro ⟨y, hy, z, hz, rfl⟩
    simp [lt_succ_iff_le]
    exact pair_le_pair (le_log_of_mem hy) (le_log_of_mem hz)⟩
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 b : M
this : 𝚺₁-Predicate fun x => ∃ y ∈ a, ∃ z ∈ b, x = ⟪y, z⟫
⊢ ∃! u, ∀ (x : M), x ∈ u ↔ ∃ y ∈ a, ∃ z ∈ b, x = ⟪y, z⟫
no goals