erdos_488

Let $A$ be a finite set and $$B=\{ n \geq 1 : a\mid n\textrm{ for some }a\in A\}.$$ Is it true that, for every $m>n\geq \max(A)$, $$\frac{\lvert B\cap [1,m]\rvert }{m}< 2\frac{\lvert B\cap [1,n]\rvert}{n}?$$

theorem erdos_488 : answer(sorry) ↔ ∀ (A : Finset ℕ), A.Nonempty →
    letI B

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