Theorems · Theorem · ring theory

AddMonoidAlgebra.map_sum

∀ {ι : Type u_1} {R : Type u_3} {S : Type u_4} {M : Type u_6} [inst : Semiring R] [inst_1 : Semiring S] (f : R →+ S)
  (s : Finset ι) (x : ι → AddMonoidAlgebra R M),
  AddMonoidAlgebra.map f (∑ i ∈ s, x i) = ∑ i ∈ s, AddMonoidAlgebra.map f (x i)

Defined in

Mathlib.Algebra.MonoidAlgebra.MapDomain

Cited by

0 results in Mathlib

Foundations

Depth 75 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

SemiringSemiring