Theorems · Theorem · functional analysis
hasStrictFDerivAt_exp_smul_const_of_mem_ball
∀ (𝕂 : Type u_1) {𝕊 : Type u_2} {𝔸 : Type u_3} [inst : NontriviallyNormedField 𝕂] [CharZero 𝕂]
[inst_2 : NormedCommRing 𝕊] [inst_3 : NormedRing 𝔸] [inst_4 : NormedSpace 𝕂 𝕊] [inst_5 : NormedAlgebra 𝕂 𝔸]
[inst_6 : Algebra 𝕊 𝔸] [inst_7 : ContinuousSMul 𝕊 𝔸] [inst_8 : IsScalarTower 𝕂 𝕊 𝔸] [CompleteSpace 𝔸] (x : 𝔸) (t : 𝕊),
t • x ∈ Metric.eball 0 (NormedSpace.expSeries 𝕂 𝔸).radius →
HasStrictFDerivAt (fun u => NormedSpace.exp (u • x)) (NormedSpace.exp (t • x) • ContinuousLinearMap.smulRight 1 x) t- Cited by
- 3 results in Mathlib
- Foundations
- Depth 189 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites34
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
- RingHom.idstatement · cited by 18,349
- NormedSpacestatement and proof · cited by 12,499
- Algebrastatement and proof · cited by 11,388
- NontriviallyNormedFieldstatement and proof · cited by 8,742
- ContinuousLinearMapstatement · cited by 5,352
- IsScalarTowerstatement and proof · cited by 3,896
- CompleteSpacestatement and proof · cited by 2,532
- NormedAlgebrastatement and proof · cited by 1,165
- ContinuousSMulstatement and proof · cited by 1,016
- CharZerostatement and proof · cited by 932
Cited by3
Results whose statement or proof uses this declaration.
- hasStrictDerivAt_exp_smul_const_of_mem_ballproof · cited by 2
- hasStrictFDerivAt_exp_smul_const_of_mem_ball'proof · cited by 2
- hasStrictFDerivAt_exp_smul_constproof · cited by 0