Theorems · Theorem · real analysis
ContDiff.of_le
∀ {𝕜 : Type u} [inst : NontriviallyNormedField 𝕜] {E : Type uE} [inst_1 : NormedAddCommGroup E]
[inst_2 : NormedSpace 𝕜 E] {F : Type uF} [inst_3 : NormedAddCommGroup F] [inst_4 : NormedSpace 𝕜 F] {f : E → F}
{m n : WithTop ℕ∞}, ContDiff 𝕜 n f → m ≤ n → ContDiff 𝕜 m f- Defined in
- Mathlib.Analysis.Calculus.ContDiff.Defs
- Cited by
- 18 results in Mathlib
- Foundations
- Depth 194 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites8
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
- ContDiffOn.of_leproof · cited by 25
- contDiffOn_univproof · cited by 25
Cited by18
Results whose statement or proof uses this declaration.
- ContDiff.continuousproof · cited by 23
- SchwartzMap.smoothproof · cited by 6
- ContDiff.continuous_iteratedFDerivproof · cited by 6
- ContDiff.continuous_derivproof · cited by 5
- ContDiff.continuous_fderivproof · cited by 5
- ContDiff.differentiable_iteratedFDerivproof · cited by 4
- Function.HasTemperateGrowth.addproof · cited by 4
- IsOpen.exists_contDiff_support_eqproof · cited by 2
- contDiff_stereoInvFunAuxproof · cited by 2
- VectorFourier.norm_iteratedFDeriv_fourierPowSMulRightproof · cited by 2
- differentiable_sigmoidproof · cited by 2
- iteratedFDeriv_comp_const_smulproof · cited by 1