fderiv_continuousAlternatingMap_apply_const_apply

English

Equality form: fderivWithin 𝕜 (λ y, (c y) u) s x equals the flip-alternating application of fderivWithin 𝕜 c s x to u.

Русский

Эквивалентность: fderivWithin ... равен flips...

LaTeX

$$$fderivWithin 𝕜 (λ y. (c(y))u) s x = (fderivWithin 𝕜 c s x).flipAlternating u.$$$

Lean4

/-- Application of a `ContinuousAlternatingMap` to a constant commutes with `fderiv`. -/
theorem fderiv_continuousAlternatingMap_apply_const_apply (hc : DifferentiableAt 𝕜 c x) (u : ι → F) (m : E) :
    (fderiv 𝕜 (fun y ↦ (c y) u) x) m = (fderiv 𝕜 c x) m u := by simp [fderiv_continuousAlternatingMap_apply_const hc]

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