Theorems · Theorem · combinatorics
Finset.mem_powersetCard_univ
∀ {α : Type u_1} [inst : Fintype α] {s : Finset α} {k : ℕ}, s ∈ Finset.powersetCard k Finset.univ ↔ s.card = k- Defined in
- Mathlib.Data.Fintype.Powerset
- Cited by
- 3 results in Mathlib
- Foundations
- Depth 65 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- Fintype
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites7
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
- Fintypestatement and proof · cited by 7,736
- Finset.univstatement · cited by 3,473
- Finset.cardstatement · cited by 2,327
- Finset.subset_univproof · cited by 60
- Finset.powersetCardstatement · cited by 60
- Finset.mem_powersetCardproof · cited by 14
Cited by3
Results whose statement or proof uses this declaration.
- Finset.subset_powersetCard_univ_iffproof · cited by 2
- Finset.card_shatterer_le_sum_vcDimproof · cited by 0
- MvPolynomial.esymm_eq_sum_subtypeproof · cited by 0