Theorems · Theorem · combinatorics
IsUpperSet.card_inter_le_finset
∀ {α : Type u_1} [inst : DecidableEq α] {𝒜 ℬ : Finset (Finset α)} [inst_1 : Fintype α],
IsUpperSet ↑𝒜 → IsLowerSet ↑ℬ → 2 ^ Fintype.card α * (𝒜 ∩ ℬ).card ≤ 𝒜.card * ℬ.cardHarris-Kleitman inequality: Upper sets and lower sets of finsets anticorrelate.
- Cited by
- 2 results in Mathlib
- Foundations
- Depth 81 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.
Cites22
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Setproof · cited by 53,352
- Finsetstatement and proof · cited by 13,712
- SetLike.coestatement and proof · cited by 8,199
- Fintypestatement and proof · cited by 7,736
- Compl.complproof · cited by 2,925
- Finset.cardstatement and proof · cited by 2,327
- Fintype.cardstatement and proof · cited by 1,386
- IsLowerSetstatement and proof · cited by 167
- IsUpperSetstatement and proof · cited by 148
- inf_commproof · cited by 139
- Finset.card_sdiff_of_subsetproof · cited by 35
- Finset.card_complproof · cited by 34
Cited by2
Results whose statement or proof uses this declaration.
- IsLowerSet.card_inter_le_finsetproof · cited by 1
- Finset.card_biUnion_le_of_intersectingproof · cited by 0