Theorems · Theorem · sequences and series

tprod_one_add_ordered

∀ {ι : Type u_1} {α : Type u_3} [inst : CommSemiring α] [inst_1 : TopologicalSpace α] {f : ι → α}
  [inst_2 : LinearOrder ι] [inst_3 : LocallyFiniteOrderBot ι] [T2Space α] [ContinuousAdd α],
  (Summable fun i => f i * ∏ j < i, (1 + f j)) →
    (Multipliable fun x => 1 + f x) → ∏' (i : ι), (1 + f i) = 1 + ∑' (i : ι), f i * ∏ j < i, (1 + f j)

The infinite version of Finset.prod_one_add_ordered.

Defined in

Mathlib.Topology.Algebra.InfiniteSum.Ring

Cited by

1 results in Mathlib

Foundations

Depth 93 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CommSemiringTopologicalSpaceLinearOrderLocallyFiniteOrderBotT2SpaceContinuousAdd