Theorems · Theorem · group theory
Finset.prod_mulIndicator_subset
∀ {ι : Type u_1} {β : Type u_4} [inst : CommMonoid β] (f : ι → β) {s t : Finset ι},
s ⊆ t → ∏ i ∈ t, (↑s).mulIndicator f i = ∏ i ∈ s, f iTaking the product of an indicator function over a possibly larger finset is the same as taking the original function over the original finset.
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 69 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.
Cites6
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 · cited by 8,199
- Finset.prodstatement · cited by 2,356
- CommMonoidstatement and proof · cited by 2,264
- Set.mulIndicatorstatement · cited by 163
- Finset.prod_mulIndicator_subset_of_eq_oneproof · cited by 1
Cited by1
Results whose statement or proof uses this declaration.
- prod_eq_tprod_mulIndicatorproof · cited by 1