fun_add — Mathlib

English

In a field, for any constant c, fderivWithin (c · f) equals c times fderivWithin f.

Русский

В поле: fderivWithin (c · f) = c · fderivWithin f для любого c.

LaTeX

$$$ fderivWithin 𝕜 (c \cdot f) \, s \, x = c \cdot fderivWithin 𝕜 f \, s \, x$$$

Lean4

@[fun_prop]
nonrec theorem fun_add (hf : HasStrictFDerivAt f f' x) (hg : HasStrictFDerivAt g g' x) :
    HasStrictFDerivAt (fun y => f y + g y) (f' + g') x :=
  .of_isLittleO <|
    (hf.isLittleO.add hg.isLittleO).congr_left fun y =>
      by
      simp only [map_sub, add_apply]
      abel

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