Theorems · Theorem · real analysis
IsMaxOn.lineDerivWithin_eq_zero
∀ {E : Type u_1} [inst : AddCommGroup E] [inst_1 : Module ℝ E] {f : E → ℝ} {s : Set E} {a b : E},
IsMaxOn f s a → (∀ᶠ (t : ℝ) in nhds 0, a + t • b ∈ s) → lineDerivWithin ℝ f s a b = 0- Cited by
- 0 results in Mathlib
- Foundations
- Depth 178 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- AddCommGroupModule
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites10
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Setstatement and proof · cited by 53,352
- Realstatement and proof · cited by 25,697
- Modulestatement and proof · cited by 20,661
- AddCommGroupstatement and proof · cited by 12,871
- nhdsstatement and proof · cited by 5,554
- Filter.Eventuallystatement and proof · cited by 3,134
- IsMaxOnstatement and proof · cited by 114
- lineDerivWithinstatement · cited by 14
- IsMaxOn.isExtrproof · cited by 6
- IsExtrOn.lineDerivWithin_eq_zeroproof · cited by 2
Cited by0
Results whose statement or proof uses this declaration.
Nothing cites this yet.