Theorems · Theorem · combinatorics
Finset.card_compl
∀ {α : Type u_1} [inst : DecidableEq α] [inst_1 : Fintype α] (s : Finset α), sᶜ.card = Fintype.card α - s.card- Defined in
- Mathlib.Data.Fintype.Card
- Cited by
- 34 results in Mathlib
- Foundations
- Depth 72 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- DecidableEqFintype
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites6
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
- Compl.complstatement · cited by 2,925
- Finset.cardstatement · cited by 2,327
- Fintype.cardstatement · cited by 1,386
- Finset.card_univ_sdiffproof · cited by 3
Cited by34
Results whose statement or proof uses this declaration.
- Fintype.card_subtype_complproof · cited by 16
- Finset.card_add_card_complproof · cited by 6
- Fintype.card_compl_setproof · cited by 5
- alternatingGroup.isMultiplyPretransitiveproof · cited by 4
- Affine.Simplex.faceOppositeCentroid_vsub_point_eq_smul_sum_vsubproof · cited by 4
- Equiv.Perm.card_fixedPointsproof · cited by 4
- SimpleGraph.IsTree.card_edgeFinsetproof · cited by 3
- SimpleGraph.antitoneOn_extremalNumber_div_choose_twoproof · cited by 3
- Equiv.Perm.card_compl_support_modEqproof · cited by 3
- IsUpperSet.card_inter_le_finsetproof · cited by 2
- Set.Sized.complsproof · cited by 2
- Configuration.Nondegenerate.exists_injective_of_card_leproof · cited by 2