English
For a function, HasStrictDerivAt f f' x is equivalent to HasStrictFDerivAt f f' x when we view derivatives in the Fréchet sense with the appropriate identification.
Русский
Для функции эквивалентны строгая производная и строгий фDerivAt через соответствующее соответствие Фрете.
LaTeX
$$$\\text{HasStrictDerivAt}(f,f',x) \\iff \\text{HasStrictFDerivAt}(f,f',x).$$$
Lean4
/-- Derivative of `f` at the point `x` within the set `s`, if it exists. Zero otherwise.
If the derivative exists (i.e., `∃ f', HasDerivWithinAt f f' s x`), then
`f x' = f x + (x' - x) • derivWithin f s x + o(x' - x)` where `x'` converges to `x` inside `s`.
-/
def derivWithin (f : 𝕜 → F) (s : Set 𝕜) (x : 𝕜) :=
fderivWithin 𝕜 f s x 1
