Theorems · Theorem · ring theory
Fintype.prod_sum
∀ {ι : Type u_5} {R : Type u_7} [inst : Fintype ι] [inst_1 : CommSemiring R] [inst_2 : DecidableEq ι] {κ : ι → Type u_8}
[inst_3 : (i : ι) → Fintype (κ i)] (f : (i : ι) → κ i → R), ∏ i, ∑ j, f i j = ∑ x, ∏ i, f i (x i)A product of sums can be written as a sum of products.
- Defined in
- Mathlib.Algebra.BigOperators.Ring.Finset
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 79 from the axioms · uses propext, Classical.choice, Quot.sound
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.
- CommSemiringstatement and proof · cited by 10,911
- Fintypestatement and proof · cited by 7,736
- Finset.sumstatement · cited by 5,195
- Finset.univstatement and proof · cited by 3,473
- Finset.prodstatement · cited by 2,356
- Finset.prod_univ_sumproof · cited by 6
Cited by1
Results whose statement or proof uses this declaration.
- mem_convexHull_piproof · cited by 1