Theorems · Theorem · global analysis
DifferentiableWithinAt.mono_of_mem_nhdsWithin
∀ {𝕜 : Type u_1} [inst : NontriviallyNormedField 𝕜] {E : Type u_2} [inst_1 : AddCommGroup E] [inst_2 : Module 𝕜 E]
[inst_3 : TopologicalSpace E] {F : Type u_3} [inst_4 : AddCommGroup F] [inst_5 : Module 𝕜 F]
[inst_6 : TopologicalSpace F] {f : E → F} {x : E} {s : Set E},
DifferentiableWithinAt 𝕜 f s x → ∀ {t : Set E}, s ∈ nhdsWithin x t → DifferentiableWithinAt 𝕜 f t x- Defined in
- Mathlib.Analysis.Calculus.FDeriv.Basic
- Cited by
- 7 results in Mathlib
- Foundations
- Depth 163 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.
- Setstatement and proof · cited by 53,352
- TopologicalSpacestatement and proof · cited by 24,529
- Modulestatement and proof · cited by 20,661
- AddCommGroupstatement and proof · cited by 12,871
- NontriviallyNormedFieldstatement and proof · cited by 8,742
- Filterstatement · cited by 8,121
- nhdsWithinstatement and proof · cited by 1,912
- DifferentiableWithinAtstatement and proof · cited by 453
- DifferentiableWithinAt.hasFDerivWithinAtproof · cited by 132
- HasFDerivWithinAt.differentiableWithinAtproof · cited by 65
- HasFDerivWithinAt.mono_of_mem_nhdsWithinproof · cited by 6
Cited by7
Results whose statement or proof uses this declaration.
- differentiableWithinAt_localInvariantPropproof · cited by 13
- hasDerivWithinAt_taylorWithinEvalproof · cited by 2
- Complex.isConservativeOn_and_continuousOn_iff_isDifferentiableOnproof · cited by 1
- hasDerivWithinAt_taylor_coeff_withinproof · cited by 1
- taylorWithinEval_hasDerivAt_Iooproof · cited by 1
- DifferentiableWithinAt.congr_nhdsproof · cited by 1
- HasFPowerSeriesWithinOnBall.differentiableOnproof · cited by 0