Theorems · Theorem · global analysis
Differentiable.comp_differentiableOn
∀ {𝕜 : Type u_1} [inst : NontriviallyNormedField 𝕜] {E : Type u_2} [inst_1 : NormedAddCommGroup E]
[inst_2 : NormedSpace 𝕜 E] {F : Type u_3} [inst_3 : NormedAddCommGroup F] [inst_4 : NormedSpace 𝕜 F] {G : Type u_4}
[inst_5 : NormedAddCommGroup G] [inst_6 : NormedSpace 𝕜 G] {f : E → F} {s : Set E} {g : F → G},
Differentiable 𝕜 g → DifferentiableOn 𝕜 f s → DifferentiableOn 𝕜 (g ∘ f) s- Defined in
- Mathlib.Analysis.Calculus.FDeriv.Comp
- Cited by
- 6 results in Mathlib
- Foundations
- Depth 171 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
- DifferentiableOnstatement and proof · cited by 419
- Differentiablestatement and proof · cited by 298
- Set.mapsTo_univproof · cited by 55
- Differentiable.differentiableOnproof · cited by 40
- DifferentiableOn.compproof · cited by 5
Cited by6
Results whose statement or proof uses this declaration.
- InnerProductSpace.HarmonicOnNhd.exists_analyticOnNhd_ball_re_eqproof · cited by 4
- Complex.affine_of_mapsTo_ball_of_norm_dslope_eq_divproof · cited by 2
- norm_sub_le_integral_of_norm_deriv_le_of_leproof · cited by 1
- Complex.dist_le_mul_div_pow_of_mapsTo_ball_of_isLittleOproof · cited by 1
- DifferentiableOn.fstproof · cited by 0
- DifferentiableOn.sndproof · cited by 0