Theorems · Theorem · group theory
Finset.sum_disjiUnion
∀ {ι : Type u_1} {κ : Type u_2} {M : Type u_4} [inst : AddCommMonoid M] {f : ι → M} (s : Finset κ) (t : κ → Finset ι)
(h : (↑s).PairwiseDisjoint t), ∑ x ∈ s.disjiUnion t h, f x = ∑ i ∈ s, ∑ x ∈ t i, f x- Cited by
- 10 results in Mathlib
- Foundations
- Depth 63 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.
Cites14
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
- Multisetproof · cited by 2,627
- Multiset.mapproof · cited by 876
- Finset.valproof · cited by 438
- Set.PairwiseDisjointstatement and proof · cited by 275
- Finset.sum_const_zeroproof · cited by 219
- Multiset.bindproof · cited by 59
- Finset.disjiUnionstatement · cited by 37
- LeftCommutativeproof · cited by 20
Cited by10
Results whose statement or proof uses this declaration.
- Finset.sum_fiberwise_of_maps_toproof · cited by 12
- Finset.sum_sigmaproof · cited by 12
- Finset.sum_biUnionproof · cited by 10
- Finset.sum_fiberwise_eq_sum_filterproof · cited by 3
- Finsupp.sum_uncurry_indexproof · cited by 2
- Finset.sum_smul_sum_eq_sum_permproof · cited by 2
- Finset.sum_powersetproof · cited by 1
- Finset.sum_eq_sum_range_sdiffproof · cited by 1
- List.sum_fixedLengthDigits_sumproof · cited by 1
- Finset.sum_pow_eq_sum_piAntidiag_of_commuteproof · cited by 1