Theorems · Theorem · sequences and series

hasProd_le

∀ {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] {f g : ι → α} {a₁ a₂ : α},
  (∀ (i : ι), f i ≤ g i) → HasProd f a₁ L → HasProd g a₂ L → ∀ [L.NeBot], a₁ ≤ a₂

Defined in

Mathlib.Topology.Algebra.InfiniteSum.Order

Cited by

6 results in Mathlib

Foundations

Depth 74 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CommMonoidPreorderIsOrderedMonoidTopologicalSpaceOrderClosedTopologySummationFilter.NeBot