Theorems · Theorem · combinatorics
IsUpperSet.le_card_inter_finset
∀ {α : Type u_1} [inst : DecidableEq α] {𝒜 ℬ : Finset (Finset α)} [inst_1 : Fintype α],
IsUpperSet ↑𝒜 → IsUpperSet ↑ℬ → 𝒜.card * ℬ.card ≤ 2 ^ Fintype.card α * (𝒜 ∩ ℬ).cardHarris-Kleitman inequality: Any two upper sets of finsets correlate.
- Cited by
- 0 results in Mathlib
- Foundations
- Depth 83 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- DecidableEqFintype
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Cites27
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
- le_reflproof · cited by 2,061
- Fintype.cardstatement and proof · cited by 1,386
- le_imp_le_of_le_of_leproof · cited by 576
- mul_le_mul'proof · cited by 274
- IsLowerSetproof · cited by 167
- IsUpperSetstatement and proof · cited by 148
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