let uniq := 2^x.1 * 3^x.2
case mk.mk
f : ↑(𝒫 Set.univ) → ↑(𝒫 Set.univ) :=
  fun a_set_of_nxn =>
    { val := {x | ∃ x_1 ∈ ↑a_set_of_nxn, 2 ^ x_1.1 * 3 ^ x_1.2 = x},
      property := (_ : {x | ∃ x_1 ∈ ↑a_set_of_nxn, 2 ^ x_1.1 * 3 ^ x_1.2 = x} ∈ 𝒫 Set.univ) }
p : Set (ℕ × ℕ)
property✝¹ : p ∈ 𝒫 Set.univ
q : Set (ℕ × ℕ)
property✝ : q ∈ 𝒫 Set.univ
heq : ∀ (x : ℕ), (∃ a b, (a, b) ∈ p ∧ 2 ^ a * 3 ^ b = x) ↔ ∃ a b, (a, b) ∈ q ∧ 2 ^ a * 3 ^ b = x
x : ℕ × ℕ
⊢ x ∈ p ↔ x ∈ q
case mk.mk
f : ↑(𝒫 Set.univ) → ↑(𝒫 Set.univ) :=
  fun a_set_of_nxn =>
    { val := {x | ∃ x_1 ∈ ↑a_set_of_nxn, 2 ^ x_1.1 * 3 ^ x_1.2 = x},
      property := (_ : {x | ∃ x_1 ∈ ↑a_set_of_nxn, 2 ^ x_1.1 * 3 ^ x_1.2 = x} ∈ 𝒫 Set.univ) }
p : Set (ℕ × ℕ)
property✝¹ : p ∈ 𝒫 Set.univ
q : Set (ℕ × ℕ)
property✝ : q ∈ 𝒫 Set.univ
heq : ∀ (x : ℕ), (∃ a b, (a, b) ∈ p ∧ 2 ^ a * 3 ^ b = x) ↔ ∃ a b, (a, b) ∈ q ∧ 2 ^ a * 3 ^ b = x
x : ℕ × ℕ
uniq : ℕ := 2 ^ x.1 * 3 ^ x.2
⊢ x ∈ p ↔ x ∈ q