Theorems · Theorem · combinatorics
Set.powersetCard.exist_mem_powersetCard_of_inf
∀ (α : Type u_1) (n : ℕ), 0 < n → ∀ [Infinite α] (a : α), ∃ s ∈ Set.powersetCard α n, a ∈ s
- Defined in
- Mathlib.Data.Set.PowersetCard
- Cited by
- 0 results in Mathlib
- Foundations
- Depth 65 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- Infinite
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Cites8
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Setstatement · cited by 53,352
- Finsetstatement and proof · cited by 13,712
- Finset.cardproof · cited by 2,327
- Infinitestatement and proof · cited by 352
- Finset.card_singletonproof · cited by 144
- Set.powersetCardstatement · cited by 100
- Infinite.exists_superset_card_eqproof · cited by 3
- Set.powersetCard.mem_iffproof · cited by 2
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