Theorems · Theorem · group theory
prod_indicator_apply
∀ {ι : Type u_1} {κ : Type u_2} {R : Type u_5} [inst : CommSemiring R] (s : Finset ι) (f : ι → Set κ) (g : ι → κ → R)
(j : κ), ∏ i ∈ s, (f i).indicator (g i) j = (⋂ x ∈ s, f x).indicator (∏ i ∈ s, g i) j- Defined in
- Mathlib.Algebra.BigOperators.Pi
- Cited by
- 4 results in Mathlib
- Foundations
- Depth 60 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- CommSemiring
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.
- Setstatement and proof · cited by 53,352
- Finsetstatement and proof · cited by 13,712
- CommSemiringstatement and proof · cited by 10,911
- Finset.prodstatement and proof · cited by 2,356
- Set.iInterstatement and proof · cited by 1,084
- Set.indicatorstatement and proof · cited by 723
- Finset.prod_congrproof · cited by 646
- Set.indicator_of_memproof · cited by 161
- Set.indicator_of_notMemproof · cited by 154
- Finset.prod_applyproof · cited by 70
- Finset.prod_eq_zeroproof · cited by 44
Cited by4
Results whose statement or proof uses this declaration.
- Finset.inclusion_exclusion_sum_biUnionproof · cited by 2
- Finset.indicator_biUnion_eq_sum_powersetproof · cited by 1
- prod_indicatorproof · cited by 1
- prod_indicator_const_applyproof · cited by 0