Theorems · Theorem · real analysis
IsExtrFilter.hasLineDerivAt_eq_zero
∀ {E : Type u_1} [inst : AddCommGroup E] [inst_1 : Module ℝ E] {f : E → ℝ} {a b : E} {f' : ℝ} {l : Filter E},
IsExtrFilter f l a → HasLineDerivAt ℝ f f' a b → Filter.Tendsto (fun t => a + t • b) (nhds 0) l → f' = 0- Cited by
- 3 results in Mathlib
- Foundations
- Depth 174 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.
Cites12
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Realstatement and proof · cited by 25,697
- Modulestatement and proof · cited by 20,661
- AddCommGroupstatement and proof · cited by 12,871
- Filterstatement and proof · cited by 8,121
- nhdsstatement and proof · cited by 5,554
- Filter.Tendstostatement and proof · cited by 3,814
- add_zeroproof · cited by 2,707
- zero_smulproof · cited by 716
- HasLineDerivAtstatement and proof · cited by 37
- IsExtrFilterstatement and proof · cited by 16
- IsLocalExtr.hasDerivAt_eq_zeroproof · cited by 3
- IsExtrFilter.comp_tendstoproof · cited by 2
Cited by3
Results whose statement or proof uses this declaration.
- IsExtrOn.hasLineDerivAt_eq_zeroproof · cited by 3
- IsExtrFilter.lineDeriv_eq_zeroproof · cited by 2
- IsLocalExtr.hasLineDerivAt_eq_zeroproof · cited by 2