Theorems · Theorem · combinatorics
Finset.card_eq_iff_eq_univ
∀ {α : Type u_1} [inst : Fintype α] (s : Finset α), s.card = Fintype.card α ↔ s = Finset.univ- Defined in
- Mathlib.Data.Fintype.Card
- Cited by
- 6 results in Mathlib
- Foundations
- Depth 58 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 and proof · cited by 3,473
- Finset.cardstatement · cited by 2,327
- Fintype.cardstatement · cited by 1,386
- Finset.card_univproof · cited by 58
- Finset.eq_univ_of_cardproof · cited by 5
Cited by6
Results whose statement or proof uses this declaration.
- set_fintype_card_eq_univ_iffproof · cited by 3
- Finset.card_lt_iff_ne_univproof · cited by 3
- Configuration.Nondegenerate.exists_injective_of_card_leproof · cited by 2
- SSet.subcomplex_le_horn_iffproof · cited by 2
- Set.Sized.subsingleton'proof · cited by 0
- SimpleGraph.degree_eq_card_sub_oneproof · cited by 0