Theorems · Theorem · sequences and series

tsum_setElem_eq_tsum_setElem_sdiff

∀ {α : Type u_1} {β : Type u_2} [inst : AddCommMonoid α] [inst_1 : TopologicalSpace α] {f : β → α} (s t : Set β),
  (∀ b ∈ t, f b = 0) → ∑' (a : ↑s), f ↑a = ∑' (a : ↑(s \ t)), f ↑a

If f b = 0 for all b ∈ t, then the sum of f a with a ∈ s is the same as the sum of f a with a ∈ s ∖ t.

Defined in

Mathlib.Topology.Algebra.InfiniteSum.Basic

Cited by

1 results in Mathlib

Foundations

Depth 84 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

AddCommMonoidTopologicalSpace