Theorems · Theorem · combinatorics
IsAntichain.sperner
- 1000+ list: Sperner's theorem
∀ {α : Type u_2} [inst : Fintype α] {𝒜 : Finset (Finset α)},
IsAntichain (fun x1 x2 => x1 ⊆ x2) ↑𝒜 → 𝒜.card ≤ (Fintype.card α).choose (Fintype.card α / 2)Sperner's theorem. The size of an antichain in Finset α is bounded by the size of the
maximal layer in Finset α. This precisely means that Finset α is a Sperner order.
- Defined in
- Mathlib.Combinatorics.SetFamily.LYM
- Cited by
- 0 results in Mathlib
- Foundations
- Depth 90 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- Fintype
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Cites22
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- SetLike.coestatement and proof · cited by 8,199
- Fintypestatement and proof · cited by 7,736
- Finset.sumproof · cited by 5,195
- mul_oneproof · cited by 3,885
- Finset.cardstatement and proof · cited by 2,327
- Nat.cast_zeroproof · cited by 1,870
- Fintype.cardstatement and proof · cited by 1,386
- NNRatproof · cited by 523
- Nat.choosestatement and proof · cited by 494
- nsmul_eq_mulproof · cited by 369
- Finset.sum_constproof · cited by 254
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