exact finite_comprehension₁! this
  ⟨f, fun i ↦ by rintro ⟨hi, _⟩; exact lt_of_mem hi⟩
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
f s : M
this : 𝚺₁-Predicate fun x => x ∈ f ∧ π₁ x ∈ s
⊢ ∃! g, ∀ (x : M), x ∈ g ↔ x ∈ f ∧ π₁ x ∈ s
no goals