Theorems · Theorem · convex and discrete geometry
ConcaveOn.continuousOn_Ico
∀ {f : ℝ → ℝ} {y z : ℝ}, ConcaveOn ℝ (Set.Ico y z) f → ContinuousWithinAt f (Set.Ici y) y → ContinuousOn f (Set.Ico y z)- Defined in
- Mathlib.Analysis.Convex.Continuous
- Cited by
- 0 results in Mathlib
- Foundations
- Depth 177 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.
- Realstatement and proof · cited by 25,697
- ContinuousOnstatement · cited by 1,411
- Set.Icistatement and proof · cited by 1,070
- Set.Icostatement and proof · cited by 799
- ContinuousWithinAtstatement and proof · cited by 512
- ConcaveOnstatement and proof · cited by 159
- ConcaveOn.negproof · cited by 29
- ContinuousWithinAt.negproof · cited by 9
- ConvexOn.continuousOn_Icoproof · cited by 2
Cited by0
Results whose statement or proof uses this declaration.
Nothing cites this yet.