Theorems · Theorem · global analysis
DifferentiableOn.neg
∀ {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] {f : E → F}
{s : Set E}, DifferentiableOn 𝕜 f s → DifferentiableOn 𝕜 (-f) s- Defined in
- Mathlib.Analysis.Calculus.FDeriv.Add
- Cited by
- 9 results in Mathlib
- Foundations
- Depth 170 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites6
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
- DifferentiableWithinAt.negproof · cited by 6
Cited by9
Results whose statement or proof uses this declaration.
- DifferentiableOn.fun_negproof · cited by 2
- Real.differentiableOn_negMulLogproof · cited by 2
- AntitoneOn.concaveOn_of_derivproof · cited by 2
- Convex.image_sub_le_mul_sub_of_deriv_leproof · cited by 2
- Convex.image_sub_lt_mul_sub_of_deriv_ltproof · cited by 2
- differentiableOn_negproof · cited by 1
- differentiableOn_fun_neg_iffproof · cited by 0
- DiffContOnCl.negproof · cited by 0
- differentiableOn_neg_iffproof · cited by 0