Theorems · Theorem · global analysis
ContDiffAt.norm
∀ (𝕜 : Type u_1) {E : Type u_2} [inst : RCLike 𝕜] [inst_1 : NormedAddCommGroup E] [InnerProductSpace 𝕜 E]
[inst : NormedSpace ℝ E] {G : Type u_4} [inst_2 : NormedAddCommGroup G] [inst_3 : NormedSpace ℝ G] {f : G → E} {x : G}
{n : WithTop ℕ∞}, ContDiffAt ℝ n f x → f x ≠ 0 → ContDiffAt ℝ n (fun y => ‖f y‖) x- Cited by
- 4 results in Mathlib
- Foundations
- Depth 209 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites11
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 · cited by 5,413
- ENatstatement and proof · cited by 4,985
- WithTopstatement and proof · cited by 3,754
- InnerProductSpacestatement and proof · cited by 3,523
- RCLikestatement and proof · cited by 2,829
- ContDiffAtstatement and proof · cited by 262
- ContDiffAt.compproof · cited by 34
- contDiffAt_normproof · cited by 4
Cited by4
Results whose statement or proof uses this declaration.
- DifferentiableWithinAt.normproof · cited by 2
- ContDiffAt.distproof · cited by 1
- ContDiffAt.absproof · cited by 1
- ContDiff.normproof · cited by 0