Theorems · Theorem · group theory
Finset.prod_disjUnion
∀ {ι : Type u_1} {M : Type u_4} {s₁ s₂ : Finset ι} [inst : CommMonoid M] {f : ι → M} (h : Disjoint s₁ s₂),
∏ x ∈ s₁.disjUnion s₂ h, f x = (∏ x ∈ s₁, f x) * ∏ x ∈ s₂, f x- Cited by
- 4 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.
Cites8
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
- one_mulproof · cited by 2,841
- Finset.prodstatement and proof · cited by 2,356
- CommMonoidstatement and proof · cited by 2,264
- Disjointstatement and proof · cited by 2,201
- Finset.disjUnionstatement and proof · cited by 55
- Finset.foldproof · cited by 46
- Finset.fold_disjUnionproof · cited by 2
Cited by4
Results whose statement or proof uses this declaration.
- Finset.prod_disjSumproof · cited by 6
- IsCompl.prod_mul_prodproof · cited by 2
- UniqueFactorizationMonoid.radical_mulproof · cited by 2
- Finset.prod_prod_Ioi_mul_eq_prod_prod_off_diagproof · cited by 1