Theorems · Theorem · real analysis
derivWithin_Ioi_eq_Ici
∀ {E : Type u_1} [inst : NormedAddCommGroup E] [inst_1 : NormedSpace ℝ E] (f : ℝ → E) (x : ℝ),
derivWithin f (Set.Ioi x) x = derivWithin f (Set.Ici x) x- Defined in
- Mathlib.Analysis.Calculus.Deriv.Basic
- Cited by
- 2 results in Mathlib
- Foundations
- Depth 173 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites15
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
- NormedAddCommGroupstatement and proof · cited by 15,752
- NormedSpacestatement and proof · cited by 12,499
- Set.Ioistatement and proof · cited by 1,463
- Set.Icistatement and proof · cited by 1,070
- DifferentiableWithinAtproof · cited by 453
- HasDerivWithinAtproof · cited by 333
- derivWithinstatement and proof · cited by 258
- DifferentiableWithinAt.hasDerivWithinAtproof · cited by 85
- Set.self_mem_Iciproof · cited by 30
- derivWithin_zero_of_not_differentiableWithinAtproof · cited by 12
- uniqueDiffOn_Iciproof · cited by 4
Cited by2
Results whose statement or proof uses this declaration.
- stronglyMeasurable_derivWithin_Ioiproof · cited by 1
- measurable_derivWithin_Ioiproof · cited by 1