Theorems · Theorem · real analysis
hasDerivAt_update
∀ {𝕜 : Type u_1} {ι : Type u_2} [inst : DecidableEq ι] [inst_1 : NontriviallyNormedField 𝕜] (x : ι → 𝕜) (i : ι) (y : 𝕜),
HasDerivAt (Function.update x i) (Pi.single i 1) y- Defined in
- Mathlib.Analysis.Calculus.Deriv.Pi
- Cited by
- 3 results in Mathlib
- Foundations
- Depth 172 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites19
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coeproof · cited by 62,936
- TopologicalSpaceproof · cited by 24,529
- Moduleproof · cited by 20,661
- RingHom.idproof · cited by 18,349
- AddCommGroupproof · cited by 12,871
- NontriviallyNormedFieldstatement and proof · cited by 8,742
- ContinuousLinearMapproof · cited by 5,352
- ContinuousSMulproof · cited by 1,016
- Pi.singlestatement and proof · cited by 518
- Function.updatestatement and proof · cited by 502
- HasDerivAtstatement and proof · cited by 493
- zero_applyproof · cited by 251
Cited by3
Results whose statement or proof uses this declaration.
- deriv_updateproof · cited by 2
- MeasureTheory.lintegral_pow_le_pow_lintegral_fderiv_auxproof · cited by 1
- hasDerivAt_singleproof · cited by 0