Theorems · Theorem · functional analysis
hasStrictDerivAt_exp_zero_of_radius_pos
∀ {𝕂 : Type u_1} [inst : NontriviallyNormedField 𝕂] [CompleteSpace 𝕂] [CharZero 𝕂],
0 < (NormedSpace.expSeries 𝕂 𝕂).radius → HasStrictDerivAt NormedSpace.exp 1 0The exponential map in a complete normed field 𝕂 of characteristic zero has strict derivative
1 at zero, as long as it converges on a neighborhood of zero.
- Cited by
- 2 results in Mathlib
- Foundations
- Depth 183 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites10
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- ENNRealstatement · cited by 9,879
- NontriviallyNormedFieldstatement and proof · cited by 8,742
- CompleteSpacestatement and proof · cited by 2,532
- CharZerostatement and proof · cited by 932
- HasStrictDerivAtstatement · cited by 163
- NormedSpace.expstatement · cited by 157
- FormalMultilinearSeries.radiusstatement and proof · cited by 150
- NormedSpace.expSeriesstatement and proof · cited by 68
- HasStrictFDerivAt.hasStrictDerivAtproof · cited by 18
- hasStrictFDerivAt_exp_zero_of_radius_posproof · cited by 3
Cited by2
Results whose statement or proof uses this declaration.
- hasStrictDerivAt_exp_zeroproof · cited by 1
- hasDerivAt_exp_zero_of_radius_posproof · cited by 0