hasFDerivAt — Mathlib

English

For f ∈ 𝓢(E, F), HasFDerivAt (SchwartzMap.instFunLike.coe f) (fderiv Real (SchwartzMap.instFunLike.coe f) x) x holds for every x.

Русский

Для f ∈ 𝓢(E, F) имеетHasFDerivAt (SchwartzMap.instFunLike.coe f) (fderiv Real (SchwartzMap.instFunLike.coe f) x) x для каждого x.

LaTeX

$$$HasFDerivAt\,(SchwartzMap.instFunLike.coe f)\,(fderiv\,Real\,(SchwartzMap.instFunLike.coe f)\,x)\,x$$$

Lean4

theorem hasFDerivAt (f : 𝓢(E, F)) (x : E) : HasFDerivAt f (fderiv ℝ f x) x :=
  f.differentiableAt.hasFDerivAt

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