Theorems · Theorem · real analysis
ContDiff.fun_comp
∀ {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 : NormedSpace 𝕜 E] [inst_3 : NormedAddCommGroup F] [inst_4 : NormedSpace 𝕜 F]
[inst_5 : NormedAddCommGroup G] [inst_6 : NormedSpace 𝕜 G] {n : WithTop ℕ∞} {g : F → G} {f : E → F},
ContDiff 𝕜 n g → ContDiff 𝕜 n f → ContDiff 𝕜 n fun x => g (f x)- Defined in
- Mathlib.Analysis.Calculus.ContDiff.Comp
- Cited by
- 10 results in Mathlib
- Foundations
- Depth 195 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites7
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- NormedAddCommGroupstatement and proof · cited by 15,752
- NormedSpacestatement and proof · cited by 12,499
- NontriviallyNormedFieldstatement and proof · cited by 8,742
- ENatstatement and proof · cited by 4,985
- WithTopstatement and proof · cited by 3,754
- ContDiffstatement and proof · cited by 352
- ContDiff.compproof · cited by 48
Cited by10
Results whose statement or proof uses this declaration.
- Manifold.exists_lt_locally_constant_of_riemannianEDist_ltproof · cited by 3
- Manifold.IsImmersionAtOfComplement.contMDiffOnproof · cited by 2
- Convex.curveIntegral_segment_add_eq_of_hasFDerivWithinAt_symmetricproof · cited by 1
- ContDiff.differentiable_deriv_twoproof · cited by 1
- MeasureTheory.lintegral_pow_le_pow_lintegral_fderivproof · cited by 1
- MeasureTheory.lintegral_pow_le_pow_lintegral_fderiv_auxproof · cited by 1
- MeasureTheory.eLpNorm_le_eLpNorm_fderiv_of_eq_innerproof · cited by 1
- ContDiff.deriv'proof · cited by 0
- ContDiff.lineMapproof · cited by 0
- AffineMap.contDiff_lineMapproof · cited by 0