green_3

Suppose that $A \subset [0,1]$ is open and has measure greater than $\frac{1}{3}$. Is there a solution to $xy = z$ with $x, y, z \in A$?

theorem green_3 :
    answer(sorry) ↔ ∀ A : Set ℝ,
      IsOpen A → A ⊆ Icc 0 1 → volume A > 1/3 →
        ∃ x y z, x ∈ A ∧ y ∈ A ∧ z ∈ A ∧ x * y = z

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