Theorems · Theorem · real analysis
contDiff_one_iff_fderiv
∀ {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},
ContDiff 𝕜 1 f ↔ Differentiable 𝕜 f ∧ Continuous (fderiv 𝕜 f)- Defined in
- Mathlib.Analysis.Calculus.ContDiff.Defs
- Cited by
- 2 results in Mathlib
- Foundations
- Depth 198 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites15
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- RingHom.idstatement · cited by 18,349
- NormedAddCommGroupstatement and proof · cited by 15,752
- NormedSpacestatement and proof · cited by 12,499
- NontriviallyNormedFieldstatement and proof · cited by 8,742
- ContinuousLinearMapstatement · cited by 5,352
- ENatstatement and proof · cited by 4,985
- Set.univproof · cited by 3,945
- WithTopstatement and proof · cited by 3,754
- Continuousstatement and proof · cited by 2,592
- zero_addproof · cited by 2,366
- fderivstatement and proof · cited by 398
- ContDiffstatement and proof · cited by 352
Cited by2
Results whose statement or proof uses this declaration.
- ContDiff.continuous_fderivproof · cited by 5
- contDiff_norm_rpowproof · cited by 2