Theorems · Theorem · real analysis
StrictConcaveOn.lt_slope_of_hasDerivWithinAt_Iio
∀ {S : Set ℝ} {f : ℝ → ℝ} {x y f' : ℝ},
StrictConcaveOn ℝ S f → x ∈ S → y ∈ S → x < y → HasDerivWithinAt f f' (Set.Iio y) y → f' < slope f x y- Defined in
- Mathlib.Analysis.Convex.Deriv
- Cited by
- 2 results in Mathlib
- Foundations
- Depth 172 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites12
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
- Set.Iiostatement and proof · cited by 1,166
- neg_negproof · cited by 960
- HasDerivWithinAtstatement and proof · cited by 333
- slopestatement and proof · cited by 147
- StrictConcaveOnstatement and proof · cited by 85
- neg_lt_negproof · cited by 20
- HasDerivWithinAt.negproof · cited by 14
- StrictConcaveOn.negproof · cited by 11
- slope_negproof · cited by 10
- StrictConvexOn.slope_lt_of_hasDerivWithinAt_Iioproof · cited by 4
Cited by2
Results whose statement or proof uses this declaration.
- StrictConcaveOn.lt_slope_of_hasDerivAtproof · cited by 1
- StrictConcaveOn.leftDeriv_lt_slopeproof · cited by 0