Theorems · Theorem · real analysis
ContDiffAt.contDiffPointwiseHolderAt
∀ {E : Type u_1} {F : Type u_2} [inst : NormedAddCommGroup E] [inst_1 : NormedSpace ℝ E] [inst_2 : NormedAddCommGroup F]
[inst_3 : NormedSpace ℝ F] {k : ℕ} {f : E → F} {a : E} {n : WithTop ℕ∞},
ContDiffAt ℝ n f a → ↑k < n → ∀ (α : ↑unitInterval), ContDiffPointwiseHolderAt k α f aA $C^n$ map is a $C^{k+(α)}$ map for any k < n.
- Cited by
- 6 results in Mathlib
- Foundations
- Depth 200 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites17
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Realstatement and proof · cited by 25,697
- NormedAddCommGroupstatement and proof · cited by 15,752
- NormedSpacestatement and proof · cited by 12,499
- Set.Elemstatement and proof · cited by 7,166
- ENatstatement and proof · cited by 4,985
- WithTopstatement and proof · cited by 3,754
- LT.lt.leproof · cited by 2,189
- unitIntervalstatement and proof · cited by 607
- ContDiffAtstatement and proof · cited by 262
- Asymptotics.IsBigO.comp_tendstoproof · cited by 33
- ContDiffPointwiseHolderAtstatement · cited by 30
- ContDiffAt.of_leproof · cited by 10
Cited by6
Results whose statement or proof uses this declaration.
- ContinuousLinearMap.contDiffPointwiseHolderAtproof · cited by 3
- ContDiffPointwiseHolderAt.of_order_ltproof · cited by 1
- ContDiffPointwiseHolderAt.clm_applyproof · cited by 0
- ContDiffPointwiseHolderAt.constproof · cited by 0
- ContDiffPointwiseHolderAt.sndproof · cited by 0
- ContDiffPointwiseHolderAt.fstproof · cited by 0