Theorems · Theorem · combinatorics
IsLowerSet.card_inter_le_finset
∀ {α : Type u_1} [inst : DecidableEq α] {𝒜 ℬ : Finset (Finset α)} [inst_1 : Fintype α],
IsLowerSet ↑𝒜 → IsUpperSet ↑ℬ → 2 ^ Fintype.card α * (𝒜 ∩ ℬ).card ≤ 𝒜.card * ℬ.cardHarris-Kleitman inequality: Lower sets and upper sets of finsets anticorrelate.
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 82 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- DecidableEqFintype
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites10
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Finsetstatement and proof · cited by 13,712
- SetLike.coestatement and proof · cited by 8,199
- Fintypestatement and proof · cited by 7,736
- Finset.cardstatement and proof · cited by 2,327
- mul_commproof · cited by 2,262
- Fintype.cardstatement and proof · cited by 1,386
- IsLowerSetstatement and proof · cited by 167
- IsUpperSetstatement and proof · cited by 148
- Finset.inter_commproof · cited by 25
- IsUpperSet.card_inter_le_finsetproof · cited by 2
Cited by1
Results whose statement or proof uses this declaration.
- IsUpperSet.le_card_inter_finsetproof · cited by 0