Theorems · Theorem · real analysis
contDiffAt_zero
∀ {𝕜 : Type u} [inst : NontriviallyNormedField 𝕜] {E : Type uE} [inst_1 : NormedAddCommGroup E]
[inst_2 : NormedSpace 𝕜 E] {F : Type uF} [inst_3 : NormedAddCommGroup F] [inst_4 : NormedSpace 𝕜 F] {f : E → F}
{x : E}, ContDiffAt 𝕜 0 f x ↔ ∃ u ∈ nhds x, ContinuousOn f u- Defined in
- Mathlib.Analysis.Calculus.ContDiff.Defs
- Cited by
- 2 results in Mathlib
- Foundations
- Depth 181 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites13
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
- NormedAddCommGroupstatement and proof · cited by 15,752
- NormedSpacestatement and proof · cited by 12,499
- NontriviallyNormedFieldstatement and proof · cited by 8,742
- Filterstatement · cited by 8,121
- nhdsstatement and proof · cited by 5,554
- ENatstatement · cited by 4,985
- WithTopstatement · cited by 3,754
- ContinuousOnstatement and proof · cited by 1,411
- ContDiffAtstatement · cited by 262
- Set.univ_interproof · cited by 258
- nhdsWithin_univproof · cited by 88
Cited by2
Results whose statement or proof uses this declaration.
- OpenPartialHomeomorph.contDiffAt_symmproof · cited by 3
- ContDiffAt.contDiffAt_norm_of_smulproof · cited by 0