Theorems · Theorem · real analysis
UniformConcaveOn.neg
∀ {E : Type u_1} [inst : NormedAddCommGroup E] [inst_1 : NormedSpace ℝ E] {φ : ℝ → ℝ} {s : Set E} {f : E → ℝ},
UniformConcaveOn s φ f → UniformConvexOn s φ (-f)- Defined in
- Mathlib.Analysis.Convex.Strong
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 158 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites13
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
- Realstatement and proof · cited by 25,697
- NormedAddCommGroupstatement and proof · cited by 15,752
- NormedSpacestatement and proof · cited by 12,499
- Norm.normproof · cited by 5,413
- add_commproof · cited by 1,535
- sub_eq_add_negproof · cited by 1,023
- neg_negproof · cited by 960
- mul_negproof · cited by 590
- neg_add_revproof · cited by 236
- UniformConcaveOnstatement and proof · cited by 11
- UniformConvexOnstatement · cited by 11
Cited by1
Results whose statement or proof uses this declaration.
- UniformConvexOn.subproof · cited by 0