Theorems · Theorem · real analysis
Differentiable.diffContOnCl
∀ {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} {s : Set E},
Differentiable 𝕜 f → DiffContOnCl 𝕜 f s- Defined in
- Mathlib.Analysis.Calculus.DiffContOnCl
- Cited by
- 15 results in Mathlib
- Foundations
- Depth 170 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 and proof · 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
- Continuous.continuousOnproof · cited by 311
- Differentiablestatement and proof · cited by 298
- DiffContOnClstatement · cited by 92
- Differentiable.differentiableOnproof · cited by 40
- Differentiable.continuousproof · cited by 28
Cited by15
Results whose statement or proof uses this declaration.
- PhragmenLindelof.quadrant_Iproof · cited by 4
- PhragmenLindelof.horizontal_stripproof · cited by 3
- PhragmenLindelof.quadrant_IVproof · cited by 2
- Differentiable.comp_diffContOnClproof · cited by 2
- PhragmenLindelof.vertical_stripproof · cited by 2
- Complex.norm_le_of_forall_mem_frontier_norm_leproof · cited by 2
- Complex.norm_eqOn_closedBall_of_isMaxOnproof · cited by 2
- Complex.HadamardThreeLines.scale_diffContOnClproof · cited by 2
- PhragmenLindelof.quadrant_IIproof · cited by 2
- PhragmenLindelof.quadrant_IIIproof · cited by 1
- Complex.HadamardThreeLines.diffContOnCl_invInterpStripproof · cited by 1
- Complex.liouville_theorem_auxproof · cited by 1