Theorems · Theorem · group theory

AddMonoidHom.map_finsum_mem

∀ {α : Type u_1} {M : Type u_5} {N : Type u_6} [inst : AddCommMonoid M] [inst_1 : AddCommMonoid N] {s : Set α}
  (f : α → M) (g : M →+ N), s.Finite → g (∑ᶠ (j : α) (_ : j ∈ s), f j) = ∑ᶠ (i : α) (_ : i ∈ s), g (f i)

Given an additive monoid homomorphism g : M →* N and a function f : α → M, the value of g at the sum of f i over i ∈ s equals the sum of g (f i) over s.

Defined in

Mathlib.Algebra.BigOperators.Finprod

Cited by

5 results in Mathlib

Foundations

Depth 80 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

AddCommMonoidAddCommMonoid