Theorems · Theorem · real analysis
contDiffAt_id
∀ {𝕜 : Type u_1} {E : Type u_2} [inst : NontriviallyNormedField 𝕜] [inst_1 : NormedAddCommGroup E]
[inst_2 : NormedSpace 𝕜 E] {n : WithTop ℕ∞} {x : E}, ContDiffAt 𝕜 n id x- Defined in
- Mathlib.Analysis.Calculus.ContDiff.Basic
- Cited by
- 16 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.
Cites8
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 · cited by 262
- ContDiff.contDiffAtproof · cited by 106
- contDiff_idproof · cited by 40
Cited by16
Results whose statement or proof uses this declaration.
- ContDiffAt.fderiv_rightproof · cited by 5
- contDiffAt_normproof · cited by 4
- HarmonicAt.differentiableAt_complex_partialproof · cited by 3
- Real.contDiffAt_logproof · cited by 3
- contMDiffAt_localFrameCoeffproof · cited by 3
- Real.deriv_sqrt_auxproof · cited by 2
- UpperHalfPlane.contMDiffAt_ofComplexproof · cited by 2
- DifferentiableWithinAt.normproof · cited by 2
- DifferentiableWithinAt.norm_sqproof · cited by 1
- contDiffAt_fun_idproof · cited by 1
- Real.contDiffAt_rpow_const_of_neproof · cited by 1
- OpenPartialHomeomorph.contDiffOn_univUnitBall_symmproof · cited by 1