English
For hf differentiable within at 𝕜′, hs UniqueDiffWithinAt 𝕜 s x, DifferentiableWithinAt 𝕜 f s x is equivalent to the existence of a g' with g'.restrictScalars 𝕜 = fderivWithin 𝕜 f s x.
Русский
Для hf дифференцируемости внутри s по 𝕜′ и при условии уникального различия 𝕜 внутри s, x: DifferentiableWithinAt 𝕜 f s x эквивалентна существованию g' с g'.restrictScalars 𝕜 = fderivWithin 𝕜 f s x.
LaTeX
$$DifferentiableWithinAt 𝕜 f s x ↔ (DifferentiableWithinAt 𝕜' f s x ∧ ∃ g' : E →L[𝕜'] F, g'.restrictScalars 𝕜 = fderivWithin 𝕜 f s x)$$
Lean4
@[fun_prop]
protected theorem star (h : DifferentiableWithinAt 𝕜 f s x) : DifferentiableWithinAt 𝕜 (fun y => star (f y)) s x :=
h.hasFDerivWithinAt.star.differentiableWithinAt
