Theorems · Theorem · group theory
Finset.prod_union_inter
∀ {ι : Type u_1} {M : Type u_4} {s₁ s₂ : Finset ι} [inst : CommMonoid M] {f : ι → M} [inst_1 : DecidableEq ι],
(∏ x ∈ s₁ ∪ s₂, f x) * ∏ x ∈ s₁ ∩ s₂, 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
- CommMonoidDecidableEq
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites4
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
- Finset.prodstatement · cited by 2,356
- CommMonoidstatement and proof · cited by 2,264
- Finset.fold_union_interproof · cited by 2
Cited by4
Results whose statement or proof uses this declaration.
- Finset.prod_unionproof · cited by 31
- HasProd.nat_mul_negproof · cited by 2
- finprod_mem_union_interproof · cited by 1
- Nat.prod_primeFactors_gcd_mul_prod_primeFactors_mulproof · cited by 1