Theorems · Theorem · sequences and series

hasProd_one_iff_of_one_le

∀ {ι : Type u_4} {α : Type u_5} {L : SummationFilter ι} [inst : CommMonoid α] [inst_1 : PartialOrder α]
  [IsOrderedMonoid α] [inst_3 : TopologicalSpace α] [OrderClosedTopology α] {f : ι → α} [L.LeAtTop] [L.NeBot],
  (∀ (i : ι), 1 ≤ f i) → (HasProd f 1 L ↔ f = 1)

Defined in

Mathlib.Topology.Algebra.InfiniteSum.Order

Cited by

1 results in Mathlib

Foundations

Depth 77 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CommMonoidPartialOrderIsOrderedMonoidTopologicalSpaceOrderClosedTopologySummationFilter.LeAtTopSummationFilter.NeBot