Theorems · Theorem · real analysis
DiffContOnCl.mk_ball
∀ {𝕜 : Type u_1} {E : Type u_2} {F : Type u_3} [inst : NontriviallyNormedField 𝕜] [inst_1 : NormedAddCommGroup E]
[inst_2 : NormedAddCommGroup F] [inst_3 : NormedSpace 𝕜 E] [inst_4 : NormedSpace 𝕜 F] {f : E → F} {x : E} {r : ℝ},
DifferentiableOn 𝕜 f (Metric.ball x r) → ContinuousOn f (Metric.closedBall x r) → DiffContOnCl 𝕜 f (Metric.ball x r)- Defined in
- Mathlib.Analysis.Calculus.DiffContOnCl
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 157 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.
- Realstatement and proof · cited by 25,697
- NormedAddCommGroupstatement and proof · cited by 15,752
- NormedSpacestatement and proof · cited by 12,499
- NontriviallyNormedFieldstatement and proof · cited by 8,742
- ContinuousOnstatement and proof · cited by 1,411
- Metric.ballstatement and proof · cited by 735
- Metric.closedBallstatement and proof · cited by 704
- DifferentiableOnstatement and proof · cited by 419
- ContinuousOn.monoproof · cited by 156
- DiffContOnClstatement · cited by 92
- Metric.closure_ball_subset_closedBallproof · cited by 10
Cited by1
Results whose statement or proof uses this declaration.
- DifferentiableOn.diffContOnCl_ballproof · cited by 1