Theorems · Theorem · real analysis
IsBoundedLinearMap.contDiff
∀ {𝕜 : Type u_1} {E : Type u_2} {F : Type u_3} [inst : NontriviallyNormedField 𝕜] [inst_1 : NormedAddCommGroup E]
[inst_2 : NormedSpace 𝕜 E] [inst_3 : NormedAddCommGroup F] [inst_4 : NormedSpace 𝕜 F] {f : E → F} {n : WithTop ℕ∞},
IsBoundedLinearMap 𝕜 f → ContDiff 𝕜 n fUnbundled bounded linear functions are C^n.
- Defined in
- Mathlib.Analysis.Calculus.ContDiff.Basic
- Cited by
- 6 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.
Cites11
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
- NontriviallyNormedFieldstatement and proof · cited by 8,742
- ENatstatement and proof · cited by 4,985
- Set.univproof · cited by 3,945
- WithTopstatement and proof · cited by 3,754
- ContDiffstatement · cited by 352
- IsBoundedLinearMapstatement and proof · cited by 39
- IsBoundedLinearMap.toContinuousLinearMapproof · cited by 9
- AnalyticOnNhd.contDiffproof · cited by 7
- ContinuousLinearMap.analyticOnNhdproof · cited by 5
Cited by6
Results whose statement or proof uses this declaration.
- contDiff_idproof · cited by 40
- ContinuousLinearMap.contDiffproof · cited by 18
- contDiff_sndproof · cited by 10
- contDiff_fstproof · cited by 9
- contDiff_negproof · cited by 8
- contDiff_addproof · cited by 2