Theorems · Theorem · group theory
Finset.sum_preimage_of_bij
∀ {ι : Type u_1} {κ : Type u_2} {β : Type u_3} [inst : AddCommMonoid β] (f : ι → κ) (s : Finset κ)
(hf : Set.BijOn f (f ⁻¹' ↑s) ↑s) (g : κ → β), ∑ x ∈ s.preimage f ⋯, g (f x) = ∑ x ∈ s, g x- Cited by
- 1 results in Mathlib
- Foundations
- Depth 80 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.
Cites11
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
- AddCommMonoidstatement and proof · cited by 12,281
- SetLike.coestatement and proof · cited by 8,199
- Finset.sumstatement · cited by 5,195
- Set.preimagestatement and proof · cited by 4,946
- Set.rangeproof · cited by 4,705
- Set.BijOnstatement and proof · cited by 168
- Finset.preimagestatement · cited by 108
- Set.BijOn.injOnstatement and proof · cited by 42
- Finset.sum_preimageproof · cited by 6
- Set.BijOn.subset_rangeproof · cited by 2
Cited by1
Results whose statement or proof uses this declaration.
- Finsupp.sum_comapDomainproof · cited by 1