Theorems · Theorem · real analysis
IsOpen.isOpen_inter_preimage_of_deriv_eq_zero
∀ {𝕜 : Type u_3} {G : Type u_4} [inst : RCLike 𝕜] [inst_1 : NormedAddCommGroup G] [inst_2 : NormedSpace 𝕜 G] {f : 𝕜 → G}
{s : Set 𝕜}, IsOpen s → DifferentiableOn 𝕜 f s → Set.EqOn (deriv f) 0 s → ∀ (t : Set G), IsOpen (s ∩ f ⁻¹' t)- Defined in
- Mathlib.Analysis.Calculus.MeanValue
- Cited by
- 0 results in Mathlib
- Foundations
- Depth 195 from the axioms · uses propext, Classical.choice, Quot.sound
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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
- NormedAddCommGroupstatement and proof · cited by 15,752
- NormedSpacestatement and proof · cited by 12,499
- Set.preimagestatement · cited by 4,946
- RCLikestatement and proof · cited by 2,829
- IsOpenstatement and proof · cited by 2,400
- derivstatement and proof · cited by 676
- Set.EqOnstatement and proof · cited by 603
- DifferentiableOnstatement and proof · cited by 419
- ContinuousLinearMap.toSpanSingleton.congr_simpproof · cited by 12
- ContinuousLinearMap.toSpanSingleton_zeroproof · cited by 5
- IsOpen.isOpen_inter_preimage_of_fderiv_eq_zeroproof · cited by 3
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