Theorems · Theorem · real analysis
DiffContOnCl.mono
∀ {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 t : Set E},
DiffContOnCl 𝕜 f s → t ⊆ s → DiffContOnCl 𝕜 f t- Defined in
- Mathlib.Analysis.Calculus.DiffContOnCl
- Cited by
- 4 results in Mathlib
- Foundations
- Depth 165 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites10
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
- ContinuousOn.monoproof · cited by 156
- closure_monoproof · cited by 133
- DiffContOnClstatement and proof · cited by 92
- DifferentiableOn.monoproof · cited by 39
- DiffContOnCl.continuousOnproof · cited by 22
- DiffContOnCl.differentiableOnproof · cited by 16
Cited by4
Results whose statement or proof uses this declaration.
- Complex.norm_eq_norm_of_isMaxOn_of_ball_subsetproof · cited by 3
- PhragmenLindelof.horizontal_stripproof · cited by 3
- PhragmenLindelof.right_half_plane_of_tendsto_zero_on_realproof · cited by 2
- AnalyticAt.eventually_constant_or_nhds_le_map_nhds_auxproof · cited by 1