fst — Mathlib

English

The HasStrictFDerivAt for fst is obtained from the general fst derivative functor: HasStrictFDerivAt Prod.fst ...

Русский

Генерализация производной fst в виде HasStrictFDerivAt для проекции fst.

LaTeX

$$$\text{HasStrictFDerivAt}\big(\mathrm{Prod.fst}, \mathrm{fst}\, 𝕜\, E\, F, p\big)$$$

Lean4

@[fun_prop]
protected theorem fst (h : HasStrictFDerivAt f₂ f₂' x) :
    HasStrictFDerivAt (fun x => (f₂ x).1) ((fst 𝕜 F G).comp f₂') x :=
  hasStrictFDerivAt_fst.comp x h

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