Theorems · Theorem · functional analysis
hasStrictDerivAt_exp_of_mem_ball
∀ {𝕂 : Type u_1} [inst : NontriviallyNormedField 𝕂] [CompleteSpace 𝕂] [CharZero 𝕂] {x : 𝕂},
x ∈ Metric.eball 0 (NormedSpace.expSeries 𝕂 𝕂).radius → HasStrictDerivAt NormedSpace.exp (NormedSpace.exp x) xThe exponential map in a complete normed field 𝕂 of characteristic zero has strict derivative
NormedSpace.exp x at any point x in the disk of convergence.
- Cited by
- 2 results in Mathlib
- Foundations
- Depth 190 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites16
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coeproof · cited by 62,936
- Setstatement · cited by 53,352
- NontriviallyNormedFieldstatement and proof · cited by 8,742
- mul_oneproof · cited by 3,885
- CompleteSpacestatement and proof · cited by 2,532
- CharZerostatement and proof · cited by 932
- Metric.eballstatement and proof · cited by 294
- smul_applyproof · cited by 229
- HasStrictDerivAtstatement · cited by 163
- NormedSpace.expstatement and proof · cited by 157
- FormalMultilinearSeries.radiusstatement and proof · cited by 150
- NormedSpace.expSeriesstatement and proof · cited by 68
Cited by2
Results whose statement or proof uses this declaration.
- hasStrictDerivAt_expproof · cited by 1
- hasDerivAt_exp_of_mem_ballproof · cited by 0