hasDerivWithinAt_iff_tendsto_slope'

English

If a monotone derivative is considered at a non-isolated point, then the derivative is nonnegative.

Русский

Если производная монотонна на области и точка не изолирована, то производная неотрицательна.

LaTeX

$$$0 \\le g'$$$

Lean4

theorem hasDerivWithinAt_iff_tendsto_slope' (hs : x ∉ s) :
    HasDerivWithinAt f f' s x ↔ Tendsto (slope f x) (𝓝[s] x) (𝓝 f') := by
  rw [hasDerivWithinAt_iff_tendsto_slope, diff_singleton_eq_self hs]

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