Theorems · Theorem · group theory
Finset.sum_preimage
∀ {ι : Type u_1} {κ : Type u_2} {β : Type u_3} [inst : AddCommMonoid β] (f : ι → κ) (s : Finset κ)
(hf : Set.InjOn f (f ⁻¹' ↑s)) (g : κ → β),
(∀ x ∈ s, x ∉ Set.range f → g x = 0) → ∑ x ∈ s.preimage f hf, g (f x) = ∑ x ∈ s, g x- Cited by
- 6 results in Mathlib
- Foundations
- Depth 79 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- AddCommMonoid
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.
- Setstatement · cited by 53,352
- Finsetstatement and proof · cited by 13,712
- AddCommMonoidstatement and proof · cited by 12,281
- SetLike.coestatement and proof · cited by 8,199
- Finset.sumstatement and proof · cited by 5,195
- Set.preimagestatement and proof · cited by 4,946
- Set.rangestatement and proof · cited by 4,705
- Set.InjOnstatement and proof · cited by 543
- Finset.preimagestatement · cited by 108
- Not.imp_symmproof · cited by 25
- Finset.sum_filter_of_neproof · cited by 11
- Finset.sum_preimage'proof · cited by 3
Cited by6
Results whose statement or proof uses this declaration.
- linearIndepOn_iff'proof · cited by 2
- Function.Injective.hasSum_comap_iffproof · cited by 2
- Finset.sum_preimage_of_bijproof · cited by 1
- Function.Injective.map_atTop_finsetSum_eqproof · cited by 1
- LinearMap.snd_prodOfFinsuppNatproof · cited by 0
- Function.Injective.hasSum_comap_iff_of_hasSupportproof · cited by 0