Theorems · Theorem · ring theory
Finset.sum_mul_sum
∀ {ι : Type u_1} {κ : Type u_2} {R : Type u_4} [inst : NonUnitalNonAssocSemiring R] (s : Finset ι) (t : Finset κ)
(f : ι → R) (g : κ → R), (∑ i ∈ s, f i) * ∑ j ∈ t, g j = ∑ i ∈ s, ∑ j ∈ t, f i * g j- Defined in
- Mathlib.Algebra.BigOperators.Ring.Finset
- Cited by
- 13 results in Mathlib
- Foundations
- Depth 56 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- NonUnitalNonAssocSemiring
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites5
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.sumstatement and proof · cited by 5,195
- Finset.sum_congrproof · cited by 2,323
- NonUnitalNonAssocSemiringstatement and proof · cited by 1,081
- Finset.sum_mulproof · cited by 112
Cited by13
Results whose statement or proof uses this declaration.
- Matrix.det_fromBlocks_zero₂₁proof · cited by 10
- ArithmeticFunction.IsMultiplicative.mulproof · cited by 5
- IsNilpotent.exp_add_of_commuteproof · cited by 3
- Choose.choose_modEq_choose_mod_mul_choose_divproof · cited by 2
- IncidenceAlgebra.prod_mul_prod'proof · cited by 2
- Finset.sum_sq_le_sq_sum_of_nonnegproof · cited by 1
- mk_mem_convexHull_prodproof · cited by 1
- Matrix.frobenius_nnnorm_mulproof · cited by 1
- gaussSum_mulproof · cited by 1
- Matrix.detp_mulproof · cited by 1
- Matrix.isAddUnit_detp_mul_detpproof · cited by 1
- PowerBasis.repr_mul_isIntegralproof · cited by 1