Theorems · Theorem · combinatorics
Finset.card_cons
∀ {α : Type u_1} {s : Finset α} {a : α} (h : a ∉ s), (Finset.cons a s h).card = s.card + 1- Defined in
- Mathlib.Data.Finset.Card
- Cited by
- 16 results in Mathlib
- Foundations
- Depth 56 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites5
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
- Finset.cardstatement · cited by 2,327
- Finset.valproof · cited by 438
- Finset.consstatement · cited by 221
- Multiset.card_consproof · cited by 19
Cited by16
Results whose statement or proof uses this declaration.
- Finset.card_Ico_eq_card_Icc_sub_oneproof · cited by 8
- partialSups_disjointedproof · cited by 5
- Fintype.card_optionproof · cited by 5
- Infinite.exists_superset_card_eqproof · cited by 3
- Finset.card_Iio_eq_card_Iic_sub_oneproof · cited by 3
- Finset.card_Ioo_eq_card_Ico_sub_oneproof · cited by 3
- Int.erdos_ginzburg_zivproof · cited by 2
- Finset.card_Ioi_eq_card_Ici_sub_oneproof · cited by 1
- Set.card_fintypeInsertOfNotMemproof · cited by 1
- SimpleGraph.card_edgeFinset_sup_edgeproof · cited by 1
- Fin.card_filter_univ_succproof · cited by 1
- Finset.card_insertNoneproof · cited by 0