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Theorems · Theorem · logic and foundations

Set.ncard_eq_toFinset_card

∀ {α : Type u_1} (s : Set α) (hs : autoParam s.Finite Set.ncard_eq_toFinset_card._auto_1), s.ncard = hs.toFinset.card
Defined in
Mathlib.Data.Set.Card
Cited by
21 results in Mathlib
Foundations
Depth 93 from the axioms · uses propext, Classical.choice, Quot.sound

Around this declaration

Dashed lines are statement dependencies; solid lines are citations in proofs.

Set.ncard_coe_finset · cited by 15Set.ncard_coe_finsetSet.one_lt_ncard · cited by 4Set.one_lt_ncardSet.two_lt_ncard_iff · cited by 3Set.two_lt_ncard_iffSet.ncard_le_one · cited by 3Set.ncard_le_oneSet.exists_union_disjoint_cardinal_eq_of_even · cited by 2Set.exists_union_disjoint…Ideal.height_le_height_add_spanFinrank_of_le · cited by 2Ideal.height_le_height_ad…Ideal.exists_finset_card_eq_height_of_isNoetherianRing · cited by 2Ideal.exists_finset_card_…ProbabilityTheory.map_ncard_setBernoulli_real_singleton · cited by 2ProbabilityTheory.map_nca…Set.three_lt_ncard_iff · cited by 1Set.three_lt_ncard_iffSet.eq_insert_of_ncard_eq_succ · cited by 1Set.eq_insert_of_ncard_eq…finsum_one · cited by 1finsum_oneSet.ncard_le_one_iff_subset_singleton · cited by 1Set.ncard_le_one_iff_subs…Set.exists_ne_of_one_lt_ncard · cited by 1Set.exists_ne_of_one_lt_n…SimpleGraph.IsClique.even_iff_exists_isMatching · cited by 1IsClique.even_iff_exists_…NumberField.InfinitePlace.unramifedPlacesOver_ncard_add_eq_finrank · cited by 1InfinitePlace.unramifedPl…Set · cited by 53352SetSet.Elem · cited by 7166Set.ElemFinset.card · cited by 2327Finset.cardSet.Finite · cited by 1814Set.FiniteFintype.card · cited by 1386Fintype.cardSet.Finite.toFinset · cited by 351Finite.toFinsetSet.ncard · cited by 344Set.ncardNat.card_eq_fintype_card · cited by 200Nat.card_eq_fintype_cardNat.card_coe_set_eq · cited by 19Nat.card_coe_set_eqSet.Finite.card_toFinset · cited by 2Finite.card_toFinsetSet.ncard_eq_toFinset_cardCITED BYCITES

Cites10

Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.

Cited by21

Results whose statement or proof uses this declaration.