hasFDerivWithinAt — Mathlib

English

For a function f : F → G and a subset s ⊆ F, the Frenet-derivative within of f ∘ iso on iso^{-1}(s) equals the Frenet-derivative within of f on s composed with iso, i.e., fderivWithin 𝕜 (f ∘ iso) (iso^{-1} s) x = (fderivWithin 𝕜 f s (iso x)).comp (iso).

Русский

Для функции f : F → G и подмножества s ⊆ F, локальная производная Фрéша внутри композиции f ∘ iso на iso^{-1}(s) равна композиции производной внутри f на s с iso, т.е. fderivWithin 𝕜 (f ∘ iso) (iso^{-1} s) x = (fderivWithin 𝕜 f s (iso x)).comp (iso).

LaTeX

$$$ fderivWithin 𝕜 (f \\circ iso) (iso^{-1} s) x = (fderivWithin 𝕜 f s (iso x)).comp (iso) $$$

Lean4

@[fun_prop]
protected theorem hasFDerivWithinAt : HasFDerivWithinAt iso (iso : E →L[𝕜] F) s x :=
  (iso : E ≃L[𝕜] F).hasFDerivWithinAt

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