Theorem: HasDerivAt.of_deriv (ForML/Util.lean)

State before:
𝕜 : Type u_1
𝕜' : Type u_2
F : Type u_3
inst✝⁶ : NontriviallyNormedField 𝕜
inst✝⁵ : NontriviallyNormedField 𝕜'
inst✝⁴ : NormedAlgebra 𝕜 𝕜'
inst✝³ : NontriviallyNormedField F
inst✝² : NormedAlgebra 𝕜 F
inst✝¹ : NormedAlgebra 𝕜' F
inst✝ : IsScalarTower 𝕜 𝕜' F
x : 𝕜
f f' : 𝕜 → F
h : DifferentiableAt 𝕜 f x
h' : _root_.deriv f x = f' x
⊢ HasDerivAt f (f' x) x
Tactic:
rw [← h']
State after:
𝕜 : Type u_1
𝕜' : Type u_2
F : Type u_3
inst✝⁶ : NontriviallyNormedField 𝕜
inst✝⁵ : NontriviallyNormedField 𝕜'
inst✝⁴ : NormedAlgebra 𝕜 𝕜'
inst✝³ : NontriviallyNormedField F
inst✝² : NormedAlgebra 𝕜 F
inst✝¹ : NormedAlgebra 𝕜' F
inst✝ : IsScalarTower 𝕜 𝕜' F
x : 𝕜
f f' : 𝕜 → F
h : DifferentiableAt 𝕜 f x
h' : _root_.deriv f x = f' x
⊢ HasDerivAt f (_root_.deriv f x) x

State before:
𝕜 : Type u_1
𝕜' : Type u_2
F : Type u_3
inst✝⁶ : NontriviallyNormedField 𝕜
inst✝⁵ : NontriviallyNormedField 𝕜'
inst✝⁴ : NormedAlgebra 𝕜 𝕜'
inst✝³ : NontriviallyNormedField F
inst✝² : NormedAlgebra 𝕜 F
inst✝¹ : NormedAlgebra 𝕜' F
inst✝ : IsScalarTower 𝕜 𝕜' F
x : 𝕜
f f' : 𝕜 → F
h : DifferentiableAt 𝕜 f x
h' : _root_.deriv f x = f' x
⊢ HasDerivAt f (_root_.deriv f x) x
Tactic:
exact h.hasDerivAt
State after:
no goals