differentiableOn — Mathlib

English

For an iso: E ≃L[𝕜] F, and any f : G → E, differentiability of f ∘ iso at x is equivalent to differentiability of f at iso x.

Русский

Пусть iso: E ≃L[𝕜] F и f: G → E. Тогда различение d(f ∘ iso) в точке x эквивалентно дифференцируемости f в точке iso(x).

LaTeX

$$$\\operatorname{Differentiable}_{\\mathbb{k}}(\\,f \\circ iso\\,)(x) \\iff \\operatorname{Differentiable}_{\\mathbb{k}} f(iso(x))$$$

Lean4

@[fun_prop]
protected theorem differentiableOn : DifferentiableOn 𝕜 iso s :=
  iso.differentiable.differentiableOn

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