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Theorems · Theorem · combinatorics

Finset.subset_powersetCard_univ_iff

∀ {α : Type u_1} [inst : Fintype α] {𝒜 : Finset (Finset α)} {r : ℕ},
  𝒜 ⊆ Finset.powersetCard r Finset.univ ↔ Set.Sized r ↑𝒜
Defined in
Mathlib.Data.Finset.Slice
Cited by
2 results in Mathlib
Foundations
Depth 66 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes
Fintype
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Around this declaration

Dashed lines are statement dependencies; solid lines are citations in proofs.

Set.Sized.card_le · cited by 2Sized.card_leSet.Sized.subset_powersetCard_univ · cited by 0Sized.subset_powersetCard…Finset · cited by 13712FinsetSetLike.coe · cited by 8199SetLike.coeFintype · cited by 7736FintypeFinset.univ · cited by 3473Finset.univFinset.card · cited by 2327Finset.cardFinset.mem_coe · cited by 91Finset.mem_coeFinset.powersetCard · cited by 60Finset.powersetCardSet.Sized · cited by 35Set.SizedFinset.mem_powersetCard_univ · cited by 3Finset.mem_powersetCard_u…Finset.subset_powersetCard_un…CITED BYCITES

Cites9

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Cited by2

Results whose statement or proof uses this declaration.