Theorems · Theorem · real analysis
contDiffWithinAt_singleton
∀ {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} {x : E}
{n : WithTop ℕ∞}, ContDiffWithinAt 𝕜 n f {x} x- Defined in
- Mathlib.Analysis.Calculus.ContDiff.Basic
- Cited by
- 2 results in Mathlib
- Foundations
- Depth 201 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites9
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Setstatement · cited by 53,352
- 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
- ContDiffWithinAtstatement · cited by 283
- ContDiffWithinAt.congrproof · cited by 13
- contDiffWithinAt_constproof · cited by 9
Cited by2
Results whose statement or proof uses this declaration.
- ODE.contDiffOn_nat_picard_Iccproof · cited by 1
- ODE.contDiffOn_enat_Icc_of_hasDerivWithinAtproof · cited by 0