Theorems · Theorem · number theory
schnirelmannDensity_le_of_notMem
∀ {A : Set ℕ} [inst : DecidablePred fun x => x ∈ A] {k : ℕ}, k ∉ A → schnirelmannDensity A ≤ 1 - (↑k)⁻¹If k is omitted from the set, its Schnirelmann density is upper bounded by 1 - k⁻¹.
- Defined in
- Mathlib.Combinatorics.Schnirelmann
- Cited by
- 2 results in Mathlib
- Foundations
- Depth 120 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- DecidablePred
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites29
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Setstatement and proof · cited by 53,352
- Realstatement and proof · cited by 25,697
- Finsetproof · cited by 13,712
- Finset.cardproof · cited by 2,327
- Nat.cast_zeroproof · cited by 1,870
- LT.lt.ne'proof · cited by 1,417
- le_of_ltproof · cited by 1,175
- Finset.filterproof · cited by 949
- sub_zeroproof · cited by 938
- one_divproof · cited by 624
- LE.le.trans_eqproof · cited by 328
- Finset.Iocproof · cited by 301
Cited by2
Results whose statement or proof uses this declaration.
- schnirelmannDensity_eq_zero_of_one_notMemproof · cited by 3
- schnirelmannDensity_eq_one_iffproof · cited by 1