mfderivWithin — Mathlib

English

If h is MDifferentiableWithinAt, then mfderivWithin equals the MF-derivative value mfderivWithin I I' f s x.

Русский

Если h — MDifferentiableWithinAt, то mfderivWithin равен MF-производной mfderivWithin I I' f s x.

LaTeX

$$$ (h : MDifferentiableWithinAt I I' f s x) \Rightarrow (mfderivWithin I I' f s x = mfderiv I I' f x) $$$

Lean4

protected theorem mfderivWithin (h : MDifferentiableWithinAt I I' f s x) :
    mfderivWithin I I' f s x =
      fderivWithin 𝕜 (writtenInExtChartAt I I' x f :) ((extChartAt I x).symm ⁻¹' s ∩ range I) ((extChartAt I x) x) :=
  by simp only [mfderivWithin, h, if_pos]

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