Theorems · Theorem · group theory
Finset.mulIndicator_biUnion_apply
∀ {ι : Type u_1} {κ : Type u_2} {β : Type u_4} [inst : CommMonoid β] (s : Finset ι) (t : ι → Set κ) {f : κ → β},
(↑s).PairwiseDisjoint t → ∀ (x : κ), (⋃ i ∈ s, t i).mulIndicator f x = ∏ i ∈ s, (t i).mulIndicator f x- Cited by
- 0 results in Mathlib
- Foundations
- Depth 62 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- CommMonoid
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Cites9
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Setstatement and proof · cited by 53,352
- Finsetstatement and proof · cited by 13,712
- SetLike.coestatement and proof · cited by 8,199
- Set.iUnionstatement · cited by 2,483
- Finset.prodstatement and proof · cited by 2,356
- CommMonoidstatement and proof · cited by 2,264
- Set.PairwiseDisjointstatement and proof · cited by 275
- Set.mulIndicatorstatement and proof · cited by 163
- Finset.mulIndicator_biUnionproof · cited by 2
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