Theorems · Theorem · group theory

map_sum

∀ {ι : Type u_1} {M : Type u_3} {N : Type u_4} [inst : AddCommMonoid M] [inst_1 : AddCommMonoid N] {G : Type u_7}
  [inst_2 : FunLike G M N] [AddMonoidHomClass G M N] (g : G) (f : ι → M) (s : Finset ι),
  g (∑ x ∈ s, f x) = ∑ x ∈ s, g (f x)

Defined in

Mathlib.Algebra.BigOperators.Group.Finset.Defs

Cited by

455 results in Mathlib

Foundations

Depth 15 from the axioms, rests on 95 definitions · uses propext, Quot.sound

Assumes

AddCommMonoidAddCommMonoidFunLikeAddMonoidHomClass