Theorems · Theorem · real analysis
contDiffOn_univ
∀ {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}
{n : WithTop ℕ∞}, ContDiffOn 𝕜 n f Set.univ ↔ ContDiff 𝕜 n f- Defined in
- Mathlib.Analysis.Calculus.ContDiff.Defs
- Cited by
- 25 results in Mathlib
- Foundations
- Depth 193 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites26
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- NormedAddCommGroupstatement and proof · cited by 15,752
- NormedSpacestatement and proof · cited by 12,499
- Top.topproof · cited by 9,680
- NontriviallyNormedFieldstatement and proof · cited by 8,742
- ENatstatement and proof · cited by 4,985
- Set.univstatement and proof · cited by 3,945
- WithTopstatement and proof · cited by 3,754
- nhdsWithinproof · cited by 1,912
- WithTop.someproof · cited by 1,128
- FormalMultilinearSeriesproof · cited by 615
- le_topproof · cited by 411
- ContDiffstatement and proof · cited by 352
Cited by25
Results whose statement or proof uses this declaration.
- ContDiff.compproof · cited by 48
- ContDiff.contDiffOnproof · cited by 38
- ContDiff.comp_contDiffOnproof · cited by 20
- ContDiff.of_leproof · cited by 18
- ContDiff.differentiableproof · cited by 15
- Function.HasTemperateGrowth.compproof · cited by 12
- ContDiff.prodMkproof · cited by 11
- contDiff_zeroproof · cited by 9
- contMDiff_iff_contDiffproof · cited by 6
- contDiff_iff_continuous_differentiableproof · cited by 6
- AnalyticOn.contDiffproof · cited by 2
- ContDiff.fun_comp_contDiffOnproof · cited by 2