mfderivWithin_univ — Mathlib

English

Alternative formulation: invertible mfderivWithin implies MDifferentiableWithinAt.

Русский

Альтернативная формулировка: обратимый mfderivWithin влечет MDifferentiableWithinAt.

LaTeX

$$$(mfderivWithin I I' f s x).IsInvertible \Rightarrow MDifferentiableWithinAt I I' f s x$$$

Lean4

@[simp, mfld_simps]
theorem mfderivWithin_univ : mfderivWithin I I' f univ = mfderiv I I' f :=
  by
  ext x : 1
  simp only [mfderivWithin, mfderiv, mfld_simps]
  rw [mdifferentiableWithinAt_univ]

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