Theorems · Theorem · number theory
schnirelmannDensity_le_div
∀ {A : Set ℕ} [inst : DecidablePred fun x => x ∈ A] {n : ℕ},
n ≠ 0 → schnirelmannDensity A ≤ ↑{a ∈ Finset.Ioc 0 n | a ∈ A}.card / ↑n- Defined in
- Mathlib.Combinatorics.Schnirelmann
- Cited by
- 2 results in Mathlib
- Foundations
- Depth 117 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.
Cites11
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
- Set.rangeproof · cited by 4,705
- Finset.cardstatement and proof · cited by 2,327
- Finset.filterstatement and proof · cited by 949
- Finset.Iocstatement and proof · cited by 301
- Nat.cast_nonneg'proof · cited by 245
- Ne.bot_ltproof · cited by 116
- div_nonnegproof · cited by 103
- schnirelmannDensitystatement · cited by 35
- ciInf_leproof · cited by 25
Cited by2
Results whose statement or proof uses this declaration.
- schnirelmannDensity_le_of_leproof · cited by 3
- schnirelmannDensity_mul_le_card_filterproof · cited by 1