continuousWithinAt_Icc_iff_Ici — Mathlib

English

If f converges to a1 and g converges to a2 along a filter b, and f x ≤ g x frequently, then a1 ≤ a2.

Русский

Если f сходится к a1 и g сходится к a2 вдоль фильтра b, и нечасто выполняется f x ≤ g x, то a1 ≤ a2.

LaTeX

$$$\text{If } \text{Tendsto } f b (\mathcal{N} a_1) \text{ and } \text{Tendsto } g b (\mathcal{N} a_2) \text{ and } \text{Frequent}(f \le g) \text{ then } a_1 \le a_2.$$$

Lean4

@[simp]
theorem continuousWithinAt_Icc_iff_Ici (h : a < b) :
    ContinuousWithinAt f (Icc a b) a ↔ ContinuousWithinAt f (Ici a) a := by
  simp only [ContinuousWithinAt, nhdsWithin_Icc_eq_nhdsGE h]

Похожие утверждения