differentiableOn_fun_neg_iff — Mathlib

English

DifferentiableOn 𝕜 (−f) s ⇔ DifferentiableOn 𝕜 f s (simp lemma).

Русский

Симпатическое лемма: DifferentiableOn 𝕜 (−f) s ⇔ DifferentiableOn 𝕜 f s.

LaTeX

$$$$ DifferentiableOn\ 𝕜\ (-f)\ s \iff DifferentiableOn\ 𝕜\ f\ s. $$$$

Lean4

@[simp]
theorem differentiableOn_fun_neg_iff : DifferentiableOn 𝕜 (fun y => -f y) s ↔ DifferentiableOn 𝕜 f s :=
  ⟨fun h => by simpa only [neg_neg] using h.fun_neg, fun h => h.neg⟩

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