Theorems · Theorem · group theory
Finset.sum_fiberwise_of_maps_to
∀ {ι : Type u_1} {κ : Type u_2} {M : Type u_4} [inst : AddCommMonoid M] {s : Finset ι} {t : Finset κ}
[inst_1 : DecidableEq κ] {g : ι → κ},
(∀ i ∈ s, g i ∈ t) → ∀ (f : ι → M), ∑ j ∈ t, ∑ i ∈ s with g i = j, f i = ∑ i ∈ s, f i- Cited by
- 12 results in Mathlib
- Foundations
- Depth 66 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- AddCommMonoidDecidableEq
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites9
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.coeproof · cited by 8,199
- Finset.sumstatement and proof · cited by 5,195
- Finset.filterstatement and proof · cited by 949
- Finset.mem_filterproof · cited by 185
- Finset.disjoint_leftproof · cited by 50
- Finset.sum_disjiUnionproof · cited by 10
- Finset.disjiUnion_filter_eq_of_maps_toproof · cited by 2
Cited by12
Results whose statement or proof uses this declaration.
- Finset.card_eq_sum_card_fiberwiseproof · cited by 11
- Finset.sum_image'proof · cited by 5
- Finset.sum_fiberwiseproof · cited by 4
- Finset.sum_fiberwise_of_maps_to'proof · cited by 3
- Algebra.Generators.map_toComp_kerproof · cited by 3
- Finset.exists_le_sum_fiber_of_maps_to_of_nsmul_le_sumproof · cited by 3
- Finset.exists_lt_sum_fiber_of_maps_to_of_nsmul_lt_sumproof · cited by 3
- finsum_mem_finset_product'proof · cited by 2
- BoxIntegral.Prepartition.sum_fiberwiseproof · cited by 2
- Finset.sum_fiberwise_le_sum_of_sum_fiber_nonnegproof · cited by 1
- Finset.sum_powerset_apply_cardproof · cited by 1
- KaehlerDifferential.range_kerCotangentToTensorproof · cited by 1