Theorems · Theorem · sequences and series

HasProd.le_one

∀ {ι : Type u_1} {α : Type u_3} {L : SummationFilter ι} [inst : CommMonoid α] [inst_1 : Preorder α] [IsOrderedMonoid α]
  [inst_3 : TopologicalSpace α] [OrderClosedTopology α] {g : ι → α} {a : α} [L.NeBot],
  (∀ (i : ι), g i ≤ 1) → HasProd g a L → a ≤ 1

Defined in

Mathlib.Topology.Algebra.InfiniteSum.Order

Cited by

1 results in Mathlib

Foundations

Depth 75 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CommMonoidPreorderIsOrderedMonoidTopologicalSpaceOrderClosedTopologySummationFilter.NeBot