Theorems · Theorem · real analysis
HasDerivAt.eventually_ne
∀ {𝕜 : Type u} [inst : NontriviallyNormedField 𝕜] {F : Type v} [inst_1 : NormedAddCommGroup F]
[inst_2 : NormedSpace 𝕜 F] {f : 𝕜 → F} {f' : F} {x : 𝕜} {c : F},
HasDerivAt f f' x → f' ≠ 0 → ∀ᶠ (z : 𝕜) in nhdsWithin x {x}ᶜ, f z ≠ c- Defined in
- Mathlib.Analysis.Calculus.Deriv.Inverse
- Cited by
- 0 results in Mathlib
- Foundations
- Depth 171 from the axioms · uses propext, Classical.choice, Quot.sound
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Cites11
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Setstatement · 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
- Filter.Eventuallystatement and proof · cited by 3,134
- Compl.complstatement · cited by 2,925
- nhdsWithinstatement and proof · cited by 1,912
- HasDerivAtstatement and proof · cited by 493
- Set.compl_eq_univ_sdiffproof · cited by 43
- hasDerivWithinAt_univproof · cited by 18
- HasDerivWithinAt.eventually_neproof · cited by 2
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