Theorems · Theorem · real analysis
Differentiable.comp_diffContOnCl
∀ {𝕜 : Type u_1} {E : Type u_2} {F : Type u_3} {G : Type u_4} [inst : NontriviallyNormedField 𝕜]
[inst_1 : NormedAddCommGroup E] [inst_2 : NormedAddCommGroup F] [inst_3 : NormedSpace 𝕜 E] [inst_4 : NormedSpace 𝕜 F]
[inst_5 : NormedAddCommGroup G] [inst_6 : NormedSpace 𝕜 G] {f : E → F} {g : G → E} {t : Set G},
Differentiable 𝕜 f → DiffContOnCl 𝕜 g t → DiffContOnCl 𝕜 (f ∘ g) t- Defined in
- Mathlib.Analysis.Calculus.DiffContOnCl
- Cited by
- 2 results in Mathlib
- Foundations
- Depth 172 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
- Differentiablestatement and proof · cited by 298
- DiffContOnClstatement and proof · cited by 92
- Set.mapsTo_imageproof · cited by 71
- Differentiable.diffContOnClproof · cited by 15
- DiffContOnCl.compproof · cited by 10
Cited by2
Results whose statement or proof uses this declaration.
- Complex.norm_max_aux₂proof · cited by 1
- Complex.norm_deriv_le_of_forall_mem_sphere_norm_leproof · cited by 1