Theorems · Theorem · real analysis
ContDiffAt.of_le
∀ {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}
{x : E} {m n : WithTop ℕ∞}, ContDiffAt 𝕜 n f x → m ≤ n → ContDiffAt 𝕜 m f x- Defined in
- Mathlib.Analysis.Calculus.ContDiff.Defs
- Cited by
- 10 results in Mathlib
- Foundations
- Depth 176 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites7
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
- WithTopstatement and proof · cited by 3,754
- ContDiffAtstatement and proof · cited by 262
- ContDiffWithinAt.of_leproof · cited by 22
Cited by10
Results whose statement or proof uses this declaration.
- ContDiffAt.contDiffPointwiseHolderAtproof · cited by 6
- ContDiffAt.hasStrictFDerivAt'proof · cited by 5
- ContDiffAt.isSymmSndFDerivAtproof · cited by 4
- Real.contDiffAt_arcsinproof · cited by 3
- OpenPartialHomeomorph.contDiffAt_symmproof · cited by 3
- IsOpen.exists_contDiff_support_eqproof · cited by 2
- ContDiffWithinAt.contDiffBumpproof · cited by 1
- VectorField.pullback_lieBracketproof · cited by 0
- map_add_eq_sum_add_integral_iteratedFDerivproof · cited by 0
- VectorField.fderiv_apply_lieBracketproof · cited by 0