erdos_434.parts.ii

Let $k \le n$. Out of all $A\subseteq\{1, \dots, n\}$ of size $|A| = k$, does $A = \{n, n - 1, \dots, n - k + 1\}$ maximise the number of integers not representable as the sum of finitely many elements from $A$ (with repetitions allowed)?

theorem erdos_434.parts.ii : answer(sorry) ↔ ∀ᵉ (n ≥ 1) (k ≥ 1), k ≤ n →
    IsGreatest
      { Nat.NcardUnrepresentable S | (S : Set ℕ) (_ : S ⊆ Set.Icc 1 n) (_ : S.ncard = k) }
      (Nat.NcardUnrepresentable <| Set.Icc (n - k + 1 : ℕ) n)

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