Theorems · Theorem · logic and foundations
Set.eq_univ_iff_ncard
∀ {α : Type u_1} [Finite α] (s : Set α), s = Set.univ ↔ s.ncard = Nat.card α- Defined in
- Mathlib.Data.Set.Card
- Cited by
- 4 results in Mathlib
- Foundations
- Depth 101 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.
Cites11
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Setstatement and proof · cited by 53,352
- Set.univstatement · cited by 3,945
- Finitestatement and proof · cited by 3,029
- Compl.complproof · cited by 2,925
- Nat.cardstatement and proof · cited by 844
- Set.ncardstatement and proof · cited by 344
- Set.toFiniteproof · cited by 174
- Set.ncard_add_ncard_complproof · cited by 16
- left_eq_addproof · cited by 15
- Set.compl_empty_iffproof · cited by 11
- Set.ncard_eq_zeroproof · cited by 7
Cited by4
Results whose statement or proof uses this declaration.
- MulAction.IsPreprimitive.of_prime_cardproof · cited by 3
- MulAction.isTrivialBlock_of_card_le_twoproof · cited by 1
- Set.powersetCard.isPreprimitive_permproof · cited by 1
- AddAction.IsPreprimitive.of_prime_cardproof · cited by 0