Theorems · Theorem · group theory
prod_indicator_const_apply
∀ {ι : Type u_1} {κ : Type u_2} {R : Type u_5} [inst : CommSemiring R] (s : Finset ι) (f : ι → Set κ) (g : κ → R)
(j : κ), ∏ i ∈ s, (f i).indicator g j = (⋂ x ∈ s, f x).indicator (g ^ s.card) j- Defined in
- Mathlib.Algebra.BigOperators.Pi
- Cited by
- 0 results in Mathlib
- Foundations
- Depth 61 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- CommSemiring
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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
- CommSemiringstatement and proof · cited by 10,911
- Finset.prodstatement · cited by 2,356
- Finset.cardstatement and proof · cited by 2,327
- Set.iInterstatement and proof · cited by 1,084
- Set.indicatorstatement and proof · cited by 723
- Finset.prod_constproof · cited by 154
- prod_indicator_applyproof · cited by 4
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