Theorems · Theorem · logic and foundations
Set.fintypeCard_eq_ncard
∀ {α : Type u_1} (s : Set α) [inst : Fintype ↑s], Fintype.card ↑s = s.ncard- Defined in
- Mathlib.Data.Set.Card
- Cited by
- 13 results in Mathlib
- Foundations
- Depth 94 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.
- Setstatement and proof · cited by 53,352
- Fintypestatement and proof · cited by 7,736
- Set.Elemstatement and proof · cited by 7,166
- Fintype.cardstatement and proof · cited by 1,386
- Set.ncardstatement · cited by 344
- Set.toFinset_cardproof · cited by 63
- Set.ncard_eq_toFinset_card'proof · cited by 9
Cited by13
Results whose statement or proof uses this declaration.
- finrank_span_le_cardproof · cited by 8
- Ideal.ncard_primesOver_mul_ramificationIdxIn_mul_inertiaDegInproof · cited by 5
- SimpleGraph.Subgraph.IsMatching.even_cardproof · cited by 5
- IsPGroup.card_modEq_card_fixedPointsproof · cited by 4
- exists_finset_linearIndependent_of_le_rankproof · cited by 3
- LinearIndependent.finite_of_le_span_finiteproof · cited by 2
- Group.nat_card_center_add_sum_card_noncenter_eq_cardproof · cited by 1
- SimpleGraph.ConnectedComponent.odd_matches_node_outsideproof · cited by 1
- Module.Basis.le_spanproof · cited by 1
- sum_conjClasses_card_eq_cardproof · cited by 1
- RootPairing.ncard_eq_finrank_of_linearIndepOn_ofproof · cited by 1
- Group.card_center_add_sum_card_noncenter_eq_cardproof · cited by 0