Theorems · Theorem · sequences and series

hasProd_nat_add_iff

∀ {G : Type u_2} [inst : CommGroup G] {g : G} [inst_1 : TopologicalSpace G] [IsTopologicalGroup G] {f : ℕ → G} (k : ℕ),
  HasProd (fun n => f (n + k)) g ↔ HasProd f (g * ∏ i ∈ Finset.range k, f i)

Defined in

Mathlib.Topology.Algebra.InfiniteSum.NatInt

Cited by

1 results in Mathlib

Foundations

Depth 88 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CommGroupTopologicalSpaceIsTopologicalGroup