Theorems · Theorem · group theory

finsum_sub_distrib

∀ {α : Type u_1} {G : Type u_4} [inst : SubtractionCommMonoid G] {f g : α → G},
  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 minus the sum of g i.

Defined in

Mathlib.Algebra.BigOperators.Finprod

Cited by

2 results in Mathlib

Foundations

Depth 79 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

SubtractionCommMonoid