Theorems · Theorem · real analysis
contDiffOn_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] {s : Set E}
{f : E → F}, ContDiffOn 𝕜 0 f s ↔ ContinuousOn f s- Defined in
- Mathlib.Analysis.Calculus.ContDiff.Defs
- Cited by
- 5 results in Mathlib
- Foundations
- Depth 178 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites22
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coeproof · cited by 62,936
- 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
- ENatstatement and proof · cited by 4,985
- WithTopstatement and proof · cited by 3,754
- le_antisymmproof · cited by 2,068
- nhdsWithinproof · cited by 1,912
- Nat.cast_zeroproof · cited by 1,870
- ContinuousOnstatement and proof · cited by 1,411
- FormalMultilinearSeriesproof · cited by 615
Cited by5
Results whose statement or proof uses this declaration.
- contDiff_zeroproof · cited by 9
- ODE.continuousOn_compproof · cited by 3
- contMDiffOn_zero_iffproof · cited by 1
- MeasureTheory.contDiffOn_convolution_right_with_param_auxproof · cited by 1
- contDiffWithinAt_zeroproof · cited by 0