Theorems · Theorem · sequences and series

tprod_eq_prod

∀ {α : Type u_1} {β : Type u_2} [inst : CommMonoid α] [inst_1 : TopologicalSpace α] {f : β → α} {L : SummationFilter β}
  [L.LeAtTop] {s : Finset β}, (∀ b ∉ s, f b = 1) → ∏'[L] (b : β), f b = ∏ b ∈ s, f b

Defined in

Mathlib.Topology.Algebra.InfiniteSum.Basic

Cited by

4 results in Mathlib

Foundations

Depth 78 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CommMonoidTopologicalSpaceSummationFilter.LeAtTop