Theorems · Theorem · group theory
Finset.prod_disjiUnion
∀ {ι : Type u_1} {κ : Type u_2} {M : Type u_4} [inst : CommMonoid 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
- 6 results in Mathlib
- Foundations
- Depth 63 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- CommMonoid
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
- SetLike.coestatement and proof · cited by 8,199
- Multisetproof · cited by 2,627
- Finset.prodstatement · cited by 2,356
- CommMonoidstatement and proof · cited by 2,264
- Multiset.mapproof · cited by 876
- Finset.valproof · cited by 438
- Set.PairwiseDisjointstatement and proof · cited by 275
- Finset.prod_const_oneproof · cited by 100
- Multiset.bindproof · cited by 59
- Finset.disjiUnionstatement · cited by 37
- LeftCommutativeproof · cited by 20
Cited by6
Results whose statement or proof uses this declaration.
- Finset.prod_sigmaproof · cited by 10
- Finset.prod_fiberwise_of_maps_toproof · cited by 5
- Finset.prod_biUnionproof · cited by 3
- Finset.prod_fiberwise_eq_prod_filterproof · cited by 1
- Finset.prod_eq_prod_range_sdiffproof · cited by 0
- Finset.prod_powersetproof · cited by 0