Theorems · Theorem · combinatorics
Set.toFinset_singleton
∀ {α : Type u_1} (a : α) [inst : Fintype ↑{a}], {a}.toFinset = {a}- Defined in
- Mathlib.Data.Fintype.Sets
- Cited by
- 14 results in Mathlib
- Foundations
- Depth 59 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.
Cites6
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Setstatement · cited by 53,352
- Finsetstatement · cited by 13,712
- Fintypestatement and proof · cited by 7,736
- Set.Elemstatement and proof · cited by 7,166
- Finset.extproof · cited by 565
- Set.toFinsetstatement · cited by 217
Cited by14
Results whose statement or proof uses this declaration.
- MeasureTheory.Measure.count_singleton'proof · cited by 10
- Function.locallyFinsuppWithin.logCounting_single_eq_log_sub_constproof · cited by 4
- Affine.Simplex.affineSpan_pair_eq_altitude_iffproof · cited by 2
- alternatingGroup.coe_two_sylow_of_card_eq_fourproof · cited by 2
- LinearEquiv.sup_span_singleton_lt_topproof · cited by 1
- SimpleGraph.IsSRGWith.card_commonNeighbors_eq_of_adj_complproof · cited by 1
- SimpleGraph.neighborFinset_complproof · cited by 1
- SimpleGraph.IsSRGWith.card_commonNeighbors_eq_of_not_adj_complproof · cited by 1
- NumberField.InfinitePlace.nat_card_stabilizer_eq_one_or_twoproof · cited by 1
- SimpleGraph.card_commonNeighbors_topproof · cited by 1
- SimpleGraph.cycleGraph_neighborFinsetproof · cited by 1
- Group.card_dvd_prod_orderOfproof · cited by 0