Theorems · Theorem · real analysis
contDiffWithinAt_univ
∀ {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} {n : WithTop ℕ∞}, ContDiffWithinAt 𝕜 n f Set.univ x ↔ ContDiffAt 𝕜 n f x- Defined in
- Mathlib.Analysis.Calculus.ContDiff.Defs
- Cited by
- 20 results in Mathlib
- Foundations
- Depth 173 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
- Set.univstatement · cited by 3,945
- WithTopstatement and proof · cited by 3,754
- ContDiffWithinAtstatement · cited by 283
- ContDiffAtstatement · cited by 262
Cited by20
Results whose statement or proof uses this declaration.
- ContDiffAt.analyticAtproof · cited by 11
- AnalyticAt.contDiffAtproof · cited by 8
- ContDiffAt.prodMkproof · cited by 8
- ContDiffAt.iteratedFDeriv_rightproof · cited by 4
- contMDiffAt_iff_contDiffAtproof · cited by 4
- ContDiffAt.negproof · cited by 3
- ContDiffAt.restrict_scalarsproof · cited by 3
- ContDiffAt.smulproof · cited by 2
- ContDiffAt.addproof · cited by 2
- contDiffAt_zeroproof · cited by 2
- ContDiffAt.const_smulproof · cited by 2
- ContDiffAt.smul_constproof · cited by 1