Theorems · Theorem · global analysis
differentiableWithinAt_id
∀ {𝕜 : Type u_1} [inst : NontriviallyNormedField 𝕜] {E : Type u_2} [inst_1 : AddCommGroup E] [inst_2 : Module 𝕜 E]
[inst_3 : TopologicalSpace E] {x : E} {s : Set E}, DifferentiableWithinAt 𝕜 id s x- Defined in
- Mathlib.Analysis.Calculus.FDeriv.Basic
- Cited by
- 7 results in Mathlib
- Foundations
- Depth 168 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.
- 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
- DifferentiableWithinAtstatement · cited by 453
- DifferentiableAt.differentiableWithinAtproof · cited by 96
- differentiableAt_idproof · cited by 63
Cited by7
Results whose statement or proof uses this declaration.
- DifferentiableWithinAt.of_dslopeproof · cited by 3
- differentiableWithinAt_fun_idproof · cited by 3
- Real.differentiableWithinAt_arcsin_Iicproof · cited by 2
- differentiableWithinAt_dslope_of_neproof · cited by 2
- not_differentiableWithinAt_of_deriv_tendsto_atBot_Iioproof · cited by 2
- iteratedDerivWithin_comp_const_smulproof · cited by 1
- differentiableWithinAt_powproof · cited by 0