exact finite_comprehension₁! this
  ⟨s, fun i ↦ by
    rintro ⟨hs, h⟩
    have : log s ∈ s := log_mem_of_pos <| pos_iff_ne_zero.mpr hs
    exact _root_.trans (lt_of_mem <| h (log s) this) (lt_of_mem this)⟩
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
s : M
this : 𝚺₁-Predicate fun x => s ≠ ∅ ∧ ∀ t ∈ s, x ∈ t
⊢ ∃! u, ∀ (x : M), x ∈ u ↔ s ≠ ∅ ∧ ∀ t ∈ s, x ∈ t
no goals