mfderivWithin_of_isOpen — Mathlib

English

If nhdsWithin x s equals nhdsWithin x t and h is MDifferentiableWithinAt, then mfderivWithin equals mfderiv.

Русский

Если nhdsWithin x s равно nhdsWithin x t и h — MDifferentiableWithinAt, то mfderivWithin равен mfderiv.

LaTeX

$$$ (h : MDifferentiableWithinAt I I' f s x) (hst : 𝓝[s] x = 𝓝[t] x) : mfderivWithin I I' f s x = mfderivWithin I I' f t x $$$

Lean4

theorem mfderivWithin_of_isOpen (hs : IsOpen s) (hx : x ∈ s) : mfderivWithin I I' f s x = mfderiv I I' f x :=
  mfderivWithin_of_mem_nhds (hs.mem_nhds hx)

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