Theorems · Theorem · real analysis
continuousAt_dslope_of_ne
∀ {𝕜 : Type u_1} {E : Type u_2} [inst : NontriviallyNormedField 𝕜] [inst_1 : NormedAddCommGroup E]
[inst_2 : NormedSpace 𝕜 E] {f : 𝕜 → E} {a b : 𝕜}, b ≠ a → (ContinuousAt (dslope f a) b ↔ ContinuousAt f b)- Defined in
- Mathlib.Analysis.Calculus.DSlope
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 167 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites9
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Setproof · 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
- Set.univproof · cited by 3,945
- ContinuousAtstatement · cited by 697
- ContinuousWithinAtproof · cited by 512
- dslopestatement and proof · cited by 40
- continuousWithinAt_dslope_of_neproof · cited by 2
Cited by1
Results whose statement or proof uses this declaration.
- Real.continuous_sincproof · cited by 1