Theorems · Theorem · combinatorics
Set.powersetCard.eq_empty_iff
∀ {α : Type u_1} {n : ℕ} [Finite α], Set.powersetCard α n = ∅ ↔ Nat.card α < n- Defined in
- Mathlib.Data.Set.PowersetCard
- Cited by
- 0 results in Mathlib
- Foundations
- Depth 100 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- Finite
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites10
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Setstatement · cited by 53,352
- Finsetstatement · cited by 13,712
- Finitestatement and proof · cited by 3,029
- Nat.cardstatement and proof · cited by 844
- Set.toFiniteproof · cited by 174
- Set.powersetCardstatement and proof · cited by 100
- Nat.card_coe_set_eqproof · cited by 19
- Set.ncard_eq_zeroproof · cited by 7
- Set.powersetCard.cardproof · cited by 5
- Nat.choose_eq_zero_iffproof · cited by 4
Cited by0
Results whose statement or proof uses this declaration.
Nothing cites this yet.