Theorems · Theorem · functional analysis
not_differentiableAt_norm_zero
∀ (E : Type u_1) [inst : NormedAddCommGroup E] [inst_1 : NormedSpace ℝ E] [Nontrivial E], ¬DifferentiableAt ℝ (fun x => ‖x‖) 0
- Defined in
- Mathlib.Analysis.Calculus.FDeriv.Norm
- Cited by
- 4 results in Mathlib
- Foundations
- Depth 186 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites16
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
- NormedAddCommGroupstatement and proof · cited by 15,752
- NormedSpacestatement and proof · cited by 12,499
- Norm.normstatement and proof · cited by 5,413
- one_mulproof · cited by 2,841
- Nontrivialstatement and proof · cited by 2,416
- absproof · cited by 1,814
- zero_smulproof · cited by 716
- ne_of_gtproof · cited by 637
- div_oneproof · cited by 629
- DifferentiableAtstatement and proof · cited by 617
- norm_smulproof · cited by 242
Cited by4
Results whose statement or proof uses this declaration.
- fderiv_norm_smulproof · cited by 2
- DifferentiableAt.differentiableAt_norm_of_smulproof · cited by 1
- norm_fderiv_normproof · cited by 0
- ContDiffAt.contDiffAt_norm_of_smulproof · cited by 0