Theorems · Theorem · sequences and series

hasProd_of_isLUB_of_one_le

∀ {ι : Type u_1} {α : Type u_3} [inst : CommMonoid α] [inst_1 : LinearOrder α] [IsOrderedMonoid α]
  [inst_3 : TopologicalSpace α] [OrderTopology α] {f : ι → α} (i : α),
  (∀ (i : ι), 1 ≤ f i) → IsLUB (Set.range fun s => ∏ i ∈ s, f i) i → HasProd f i

Defined in

Mathlib.Topology.Algebra.InfiniteSum.Order

Cited by

0 results in Mathlib

Foundations

Depth 67 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CommMonoidLinearOrderIsOrderedMonoidTopologicalSpaceOrderTopology