Theorems · Theorem · sequences and series

hasProd_ite_div_hasProd

∀ {α : Type u_1} {β : Type u_2} {L : SummationFilter β} [inst : CommGroup α] [inst_1 : TopologicalSpace α]
  [IsTopologicalGroup α] {f : β → α} {a : α} [L.LeAtTop] [inst_4 : DecidableEq β],
  HasProd f a L → ∀ (b : β), HasProd (fun n => if n = b then 1 else f n) (a / f b) L

Defined in

Mathlib.Topology.Algebra.InfiniteSum.Group

Cited by

1 results in Mathlib

Foundations

Depth 87 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CommGroupTopologicalSpaceIsTopologicalGroupSummationFilter.LeAtTopDecidableEq