differentiableOn — Mathlib

English

Eq (nhdsWithin x s) (nhdsWithin x t) implies equivalence of differentiability within s and t at x.

Русский

Равенство nhdsWithin x s и nhdsWithin x t выводит эквивалентность дифференцируемости внутри s и t в точке x.

LaTeX

$$$\text{Eq }(\mathrm{nhdsWithin} x s)(\mathrm{nhdsWithin} x t) \Rightarrow \bigl( \mathrm{DifferentiableWithinAt } 𝕜 f s x \iff \mathrm{DifferentiableWithinAt } 𝕜 f t x \bigr)$$$

Lean4

@[fun_prop]
theorem differentiableOn (h : Differentiable 𝕜 f) : DifferentiableOn 𝕜 f s :=
  (differentiableOn_univ.2 h).mono (subset_univ _)

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