Theorems · Theorem · order theory

Filter.Tendsto.atTop_mul_one_eventuallyLE

∀ {α : Type u_1} {M : Type u_2} [inst : CommMonoid M] [inst_1 : Preorder M] [IsOrderedMonoid M] {l : Filter α}
  {f g : α → M}, Filter.Tendsto f l Filter.atTop → 1 ≤ᶠ[l] g → Filter.Tendsto (fun x => f x * g x) l Filter.atTop

Defined in

Mathlib.Order.Filter.AtTopBot.Monoid

Cited by

3 results in Mathlib

Foundations

Depth 55 from the axioms · uses propext, Quot.sound

Assumes

CommMonoidPreorderIsOrderedMonoid