Theorems · Theorem · group theory

finsum_add_distrib

∀ {α : Type u_1} {M : Type u_5} [inst : AddCommMonoid M] {f g : α → M},
  Function.HasFiniteSupport f →
    Function.HasFiniteSupport g → ∑ᶠ (i : α), (f i + g i) = ∑ᶠ (i : α), f i + ∑ᶠ (i : α), g i

If the additive supports of f and g are finite, then the sum of f i + g i equals the sum of f i plus the sum of g i.

Defined in

Mathlib.Algebra.BigOperators.Finprod

Cited by

4 results in Mathlib

Foundations

Depth 76 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

AddCommMonoid