E : Type u_1
inst✝¹ : NormedAddCommGroup E
inst✝ : NormedSpace ℂ E
z : ℂ
f : ℂ → E
h : DifferentiableAt ℂ f z
hf' : deriv f z ≠ 0
⊢ IsConformalMap (ContinuousLinearMap.restrictScalars ℝ (fderiv ℂ f z))
E : Type u_1
inst✝¹ : NormedAddCommGroup E
inst✝ : NormedSpace ℂ E
z : ℂ
f : ℂ → E
h : DifferentiableAt ℂ f z
hf' : deriv f z ≠ 0
⊢ ConformalAt f z
rw [conformalAt_iff_isConformalMap_fderiv, (h.hasFDerivAt.restrictScalars ℝ).fderiv]
case nonzero
E : Type u_1
inst✝¹ : NormedAddCommGroup E
inst✝ : NormedSpace ℂ E
z : ℂ
f : ℂ → E
h : DifferentiableAt ℂ f z
hf' : deriv f z ≠ 0
⊢ fderiv ℂ f z ≠ 0
E : Type u_1
inst✝¹ : NormedAddCommGroup E
inst✝ : NormedSpace ℂ E
z : ℂ
f : ℂ → E
h : DifferentiableAt ℂ f z
hf' : deriv f z ≠ 0
⊢ IsConformalMap (ContinuousLinearMap.restrictScalars ℝ (fderiv ℂ f z))
apply isConformalMap_complex_linear
no goals
case nonzero
E : Type u_1
inst✝¹ : NormedAddCommGroup E
inst✝ : NormedSpace ℂ E
z : ℂ
f : ℂ → E
h : DifferentiableAt ℂ f z
hf' : deriv f z ≠ 0
⊢ fderiv ℂ f z ≠ 0
simpa only [Ne.def, ext_ring_iff]