erdos_868.parts.i

Let $A$ be an additive basis of order $2$, let $f(n)$ denote the number of ways in which $n$ can be written as the sum of two elements from $A$. If $f(n) \to \infty$ as $n \to \infty$, then must $A$ contain a minimal additive basis of order $2$?

theorem erdos_868.parts.i :
    answer(sorry) ↔ ∀ (A : Set ℕ), A.IsAsymptoticAddBasisOfOrder 2 →
      atTop.Tendsto (fun n => ncard_add_repr A 2 n) atTop → ∃ B ⊆ A,
      B.IsAsymptoticAddBasisOfOrder 2 ∧ ∀ b ∈ B, ¬(B \ {b}).IsAsymptoticAddBasisOfOrder 2

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