Theorems · Theorem · group theory

sum_apply

∀ {F : Type u_8} {α : Type u_9} {β : Type u_10} {ι : Type u_11} [inst : FunLike F α β] [inst_1 : AddCommMonoid β]
  [inst_2 : AddCommMonoid F] [IsZeroApply F α β] [IsAddApply F α β] (s : Finset ι) (f : ι → F) (x : α),
  (∑ i ∈ s, f i) x = ∑ i ∈ s, (f i) x

Defined in

Mathlib.Algebra.BigOperators.Pi

Cited by

83 results in Mathlib

Foundations

Depth 61 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

FunLikeAddCommMonoidAddCommMonoidIsZeroApplyIsAddApply