Theorems · Theorem · real analysis
HasDerivWithinAt.add
∀ {𝕜 : Type u} [inst : NontriviallyNormedField 𝕜] {F : Type v} [inst_1 : NormedAddCommGroup F]
[inst_2 : NormedSpace 𝕜 F] {f g : 𝕜 → F} {f' g' : F} {x : 𝕜} {s : Set 𝕜},
HasDerivWithinAt f f' s x → HasDerivWithinAt g g' s x → HasDerivWithinAt (f + g) (f' + g') s x- Defined in
- Mathlib.Analysis.Calculus.Deriv.Add
- Cited by
- 4 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.
Cites6
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
- HasDerivWithinAtstatement and proof · cited by 333
- HasDerivAtFilter.addproof · cited by 5
Cited by4
Results whose statement or proof uses this declaration.
- derivWithin_fun_addproof · cited by 2
- hasDerivWithinAt_taylorWithinEvalproof · cited by 2
- image_le_of_liminf_slope_right_le_deriv_boundaryproof · cited by 2
- HasDerivWithinAt.fun_addproof · cited by 0