Theorems · Theorem · real analysis
deriv_eqOn
∀ {𝕜 : Type u} [inst : NontriviallyNormedField 𝕜] {F : Type v} [inst_1 : NormedAddCommGroup F]
[inst_2 : NormedSpace 𝕜 F] {f : 𝕜 → F} {s : Set 𝕜} {f' : 𝕜 → F},
IsOpen s → (∀ x ∈ s, HasDerivWithinAt f (f' x) s x) → Set.EqOn (deriv f) f' s- Defined in
- Mathlib.Analysis.Calculus.Deriv.Basic
- Cited by
- 7 results in Mathlib
- Foundations
- Depth 171 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites11
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
- IsOpenstatement and proof · cited by 2,400
- derivstatement · cited by 676
- Set.EqOnstatement · cited by 603
- HasDerivWithinAtstatement and proof · cited by 333
- HasDerivWithinAt.derivWithinproof · cited by 62
- IsOpen.uniqueDiffWithinAtproof · cited by 7
- derivWithin_of_isOpenproof · cited by 7
Cited by7
Results whose statement or proof uses this declaration.
- monotoneOn_of_hasDerivWithinAt_nonnegproof · cited by 1
- convexOn_of_hasDerivWithinAt2_nonnegproof · cited by 0
- strictMonoOn_of_hasDerivWithinAt_posproof · cited by 0
- strictAntiOn_of_hasDerivWithinAt_negproof · cited by 0
- LSeries_deriv_eqOnproof · cited by 0
- antitoneOn_of_hasDerivWithinAt_nonposproof · cited by 0
- concaveOn_of_hasDerivWithinAt2_nonposproof · cited by 0