use 1
A✝ B✝ : Set ℕ
n : ℕ
A B : Set ℕ
hA : 0 ∈ A
hB : 0 ∈ B
α : ℝ := schnirelmannDensity A
halpha : α = schnirelmannDensity A
β : ℝ := schnirelmannDensity B
hbeta : β = schnirelmannDensity B
dum : α * (1 - β) + β = α + β - α * β
main : ∀ (n : ℕ), (α * (1 - β) + β) * ↑n ≤ ↑(countelements (A + B) n)
⊢ Nonempty { n // n ≠ 0 }
case property
A✝ B✝ : Set ℕ
n : ℕ
A B : Set ℕ
hA : 0 ∈ A
hB : 0 ∈ B
α : ℝ := schnirelmannDensity A
halpha : α = schnirelmannDensity A
β : ℝ := schnirelmannDensity B
hbeta : β = schnirelmannDensity B
dum : α * (1 - β) + β = α + β - α * β
main : ∀ (n : ℕ), (α * (1 - β) + β) * ↑n ≤ ↑(countelements (A + B) n)
⊢ 1 ≠ 0