no goals
E : Type ?u.455453
inst✝³ : NormedAddCommGroup E
inst✝² : NormedSpace ℝ E
F : Type ?u.455549
inst✝¹ : NormedAddCommGroup F
inst✝ : NormedSpace ℝ F
D : Set ℝ
hD : Convex ℝ D
f : ℝ → ℝ
hf : ContinuousOn f D
hf' : DifferentiableOn ℝ f (interior D)
hf'' : DifferentiableOn ℝ (deriv f) (interior D)
hf''_nonneg : ∀ (x : ℝ), x ∈ interior D → 0 ≤ (deriv^[2]) f x
⊢ DifferentiableOn ℝ (deriv f) (interior (interior D))
rwa [interior_interior]
no goals
E : Type ?u.455453
inst✝³ : NormedAddCommGroup E
inst✝² : NormedSpace ℝ E
F : Type ?u.455549
inst✝¹ : NormedAddCommGroup F
inst✝ : NormedSpace ℝ F
D : Set ℝ
hD : Convex ℝ D
f : ℝ → ℝ
hf : ContinuousOn f D
hf' : DifferentiableOn ℝ f (interior D)
hf'' : DifferentiableOn ℝ (deriv f) (interior D)
hf''_nonneg : ∀ (x : ℝ), x ∈ interior D → 0 ≤ (deriv^[2]) f x
⊢ ∀ (x : ℝ), x ∈ interior (interior D) → 0 ≤ deriv (deriv f) x
rwa [interior_interior]