Theorems · Theorem · global analysis
hasLineDerivWithinAt_zero
∀ {𝕜 : Type u_1} [inst : NontriviallyNormedField 𝕜] {F : Type u_2} [inst_1 : NormedAddCommGroup F]
[inst_2 : NormedSpace 𝕜 F] {E : Type u_3} [inst_3 : AddCommGroup E] [inst_4 : Module 𝕜 E] {f : E → F} {s : Set E}
{x : E}, HasLineDerivWithinAt 𝕜 f 0 s x 0- Cited by
- 1 results in Mathlib
- Foundations
- Depth 169 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
- Modulestatement and proof · cited by 20,661
- NormedAddCommGroupstatement and proof · cited by 15,752
- AddCommGroupstatement and proof · cited by 12,871
- NormedSpacestatement and proof · cited by 12,499
- NontriviallyNormedFieldstatement and proof · cited by 8,742
- Set.preimageproof · cited by 4,946
- add_zeroproof · cited by 2,707
- smul_zeroproof · cited by 665
- HasDerivWithinAt.congr_simpproof · cited by 29
- HasLineDerivWithinAtstatement · cited by 22
Cited by1
Results whose statement or proof uses this declaration.
- lineDifferentiableWithinAt_zeroproof · cited by 0