Theorems · Theorem · field theory
Finset.dens_eq_sum_dens_fiberwise
∀ {α : Type u_3} {β : Type u_4} [inst : Fintype β] {s : Finset α} [inst_1 : DecidableEq α] {f : β → α} {t : Finset β},
Set.MapsTo f ↑t ↑s → t.dens = ∑ a ∈ s, {b ∈ t | f b = a}.dens- Defined in
- Mathlib.Algebra.BigOperators.Field
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 91 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- FintypeDecidableEq
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites12
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
- SetLike.coestatement and proof · cited by 8,199
- Fintypestatement and proof · cited by 7,736
- Finset.sumstatement and proof · cited by 5,195
- Finset.cardproof · cited by 2,327
- Fintype.cardproof · cited by 1,386
- Finset.filterstatement and proof · cited by 949
- Set.MapsTostatement and proof · cited by 732
- NNRatstatement · cited by 523
- Finset.densstatement · cited by 55
- Nat.cast_sumproof · cited by 38
- Finset.card_eq_sum_card_fiberwiseproof · cited by 11
Cited by1
Results whose statement or proof uses this declaration.
- Finset.dens_eq_sum_dens_imageproof · cited by 0