atTop_mul_one_le — Mathlib

English

A simp-annotated form of tendsto atBot_iff for order isomorphisms.

Русский

Упрощенная через simp форма tendsto atBot_iff для изоморфизмов порядка.

LaTeX

$$$\\forall l f, (e:\\\\alpha \\simeq_o \\beta),\\; \\operatorname{Tendsto}(\\lambda x. e(f(x)))\,l\\operatorname{atBot} \\iff \\operatorname{Tendsto} f\,l\\operatorname{atBot}$$$

Lean4

@[to_additive]
theorem atTop_mul_one_le (hf : Tendsto f l atTop) (hg : ∀ x, 1 ≤ g x) : Tendsto (fun x => f x * g x) l atTop :=
  hf.atTop_mul_one_eventuallyLE <| .of_forall hg

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