Theorems · Theorem · ring theory
MonoidAlgebra.coeff_sum
∀ {R : Type u_1} {M : Type u_4} {ι : Type u_7} [inst : Semiring R] (s : Finset ι) (f : ι → MonoidAlgebra R M),
(∑ i ∈ s, f i).coeff = ∑ i ∈ s, (f i).coeff- Defined in
- Mathlib.Algebra.MonoidAlgebra.Defs
- Cited by
- 3 results in Mathlib
- Foundations
- Depth 74 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- Semiring
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.
- Semiringstatement and proof · cited by 13,802
- Finsetstatement and proof · cited by 13,712
- Finsuppstatement · cited by 5,255
- Finset.sumstatement · cited by 5,195
- MonoidAlgebrastatement and proof · cited by 590
- map_sumproof · cited by 455
- MonoidAlgebra.coeffstatement · cited by 224
- MonoidAlgebra.coeffAddEquivproof · cited by 11
Cited by3
Results whose statement or proof uses this declaration.
- Rep.FiniteCyclicGroup.leftRegular.range_norm_eq_ker_applyAsHom_subproof · cited by 1
- Representation.leftRegular_norm_eq_zero_iffproof · cited by 1
- MonoidAlgebra.map_sumproof · cited by 0