Theorems · Theorem · combinatorics
Set.toFinset_card
∀ {α : Type u_4} (s : Set α) [inst : Fintype ↑s], s.toFinset.card = Fintype.card ↑s- Defined in
- Mathlib.Data.Fintype.Card
- Cited by
- 63 results in Mathlib
- Foundations
- Depth 28 from the axioms · uses propext, Quot.sound
- Assumes
- Fintype
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites9
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
- Fintypestatement and proof · cited by 7,736
- Set.Elemstatement and proof · cited by 7,166
- Finset.univproof · cited by 3,473
- Finset.cardstatement · cited by 2,327
- Fintype.cardstatement · cited by 1,386
- Finset.valproof · cited by 438
- Set.toFinsetstatement · cited by 217
- Multiset.card_mapproof · cited by 57
Cited by63
Results whose statement or proof uses this declaration.
- Set.fintypeCard_eq_ncardproof · cited by 13
- Set.ncard_eq_toFinset_card'proof · cited by 9
- SimpleGraph.card_neighborSet_eq_degreeproof · cited by 9
- finrank_span_le_cardproof · cited by 8
- SimpleGraph.Subgraph.IsMatching.even_cardproof · cited by 5
- Fintype.card_compl_setproof · cited by 5
- SimpleGraph.card_incidenceFinset_eq_degreeproof · cited by 4
- Polynomial.eq_zero_of_natDegree_lt_card_of_eval_eq_zeroproof · cited by 4
- finrank_span_set_eq_cardproof · cited by 4
- Set.Finite.encard_eq_coe_toFinset_cardproof · cited by 4
- set_fintype_card_eq_univ_iffproof · cited by 3
- Cardinal.card_lt_card_of_right_finiteproof · cited by 3