Theorems · Theorem · ring theory
Fintype.prod_add
∀ {ι : Type u_5} {R : Type u_7} [inst : Fintype ι] [inst_1 : CommSemiring R] [inst_2 : DecidableEq ι] (f g : ι → R),
∏ a, (f a + g a) = ∑ t, (∏ a ∈ t, f a) * ∏ a ∈ tᶜ, g a- Defined in
- Mathlib.Algebra.BigOperators.Ring.Finset
- Cited by
- 0 results in Mathlib
- Foundations
- Depth 82 from the axioms · uses propext, Classical.choice, Quot.sound
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Cites10
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
- 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
- Compl.complstatement · cited by 2,925
- Finset.prodstatement and proof · cited by 2,356
- Finset.sum_congrproof · cited by 2,323
- Finset.prod_addproof · cited by 7
- Finset.powerset_univproof · cited by 6
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