e : ℂ → ℂ
e' : ℂ
z : ℝ
h : HasDerivAt e e' ↑z
A : HasFDerivAt ofReal' ofRealClm z
⊢ HasDerivAt (fun x => (e ↑x).re) e'.re z
e : ℂ → ℂ
e' : ℂ
z : ℝ
h : HasDerivAt e e' ↑z
⊢ HasDerivAt (fun x => (e ↑x).re) e'.re z
have A : HasFDerivAt ((↑) : ℝ → ℂ) ofRealClm z := ofRealClm.hasFDerivAt
e : ℂ → ℂ
e' : ℂ
z : ℝ
h : HasDerivAt e e' ↑z
A : HasFDerivAt ofReal' ofRealClm z
B : HasFDerivAt e (ContinuousLinearMap.restrictScalars ℝ (ContinuousLinearMap.smulRight 1 e')) (↑ofRealClm z)
⊢ HasDerivAt (fun x => (e ↑x).re) e'.re z
e : ℂ → ℂ
e' : ℂ
z : ℝ
h : HasDerivAt e e' ↑z
A : HasFDerivAt ofReal' ofRealClm z
⊢ HasDerivAt (fun x => (e ↑x).re) e'.re z
have B :
  HasFDerivAt e ((ContinuousLinearMap.smulRight 1 e' : ℂ →L[ℂ] ℂ).restrictScalars ℝ)
    (ofRealClm z) :=
  h.hasFDerivAt.restrictScalars ℝ
e : ℂ → ℂ
e' : ℂ
z : ℝ
h : HasDerivAt e e' ↑z
A : HasFDerivAt ofReal' ofRealClm z
B : HasFDerivAt e (ContinuousLinearMap.restrictScalars ℝ (ContinuousLinearMap.smulRight 1 e')) (↑ofRealClm z)
C : HasFDerivAt re reClm (e (↑ofRealClm z))
⊢ HasDerivAt (fun x => (e ↑x).re) e'.re z
e : ℂ → ℂ
e' : ℂ
z : ℝ
h : HasDerivAt e e' ↑z
A : HasFDerivAt ofReal' ofRealClm z
B : HasFDerivAt e (ContinuousLinearMap.restrictScalars ℝ (ContinuousLinearMap.smulRight 1 e')) (↑ofRealClm z)
⊢ HasDerivAt (fun x => (e ↑x).re) e'.re z
have C : HasFDerivAt re reClm (e (ofRealClm z)) := reClm.hasFDerivAt
case h.e'_7
e : ℂ → ℂ
e' : ℂ
z : ℝ
h : HasDerivAt e e' ↑z
A : HasFDerivAt ofReal' ofRealClm z
B : HasFDerivAt e (ContinuousLinearMap.restrictScalars ℝ (ContinuousLinearMap.smulRight 1 e')) (↑ofRealClm z)
C : HasFDerivAt re reClm (e (↑ofRealClm z))
⊢ e'.re =
    ↑(ContinuousLinearMap.comp reClm
          (ContinuousLinearMap.comp (ContinuousLinearMap.restrictScalars ℝ (ContinuousLinearMap.smulRight 1 e'))
            ofRealClm))
      1
e : ℂ → ℂ
e' : ℂ
z : ℝ
h : HasDerivAt e e' ↑z
A : HasFDerivAt ofReal' ofRealClm z
B : HasFDerivAt e (ContinuousLinearMap.restrictScalars ℝ (ContinuousLinearMap.smulRight 1 e')) (↑ofRealClm z)
C : HasFDerivAt re reClm (e (↑ofRealClm z))
⊢ HasDerivAt (fun x => (e ↑x).re) e'.re z
convert (C.comp z (B.comp z A)).hasDerivAt
case h.e'_7
e : ℂ → ℂ
e' : ℂ
z : ℝ
h : HasDerivAt e e' ↑z
A : HasFDerivAt ofReal' ofRealClm z
B : HasFDerivAt e (ContinuousLinearMap.restrictScalars ℝ (ContinuousLinearMap.smulRight 1 e')) (↑ofRealClm z)
C : HasFDerivAt re reClm (e (↑ofRealClm z))
⊢ e'.re = ↑reClm (↑(ContinuousLinearMap.restrictScalars ℝ (ContinuousLinearMap.smulRight 1 e')) (↑ofRealClm 1))
case h.e'_7
e : ℂ → ℂ
e' : ℂ
z : ℝ
h : HasDerivAt e e' ↑z
A : HasFDerivAt ofReal' ofRealClm z
B : HasFDerivAt e (ContinuousLinearMap.restrictScalars ℝ (ContinuousLinearMap.smulRight 1 e')) (↑ofRealClm z)
C : HasFDerivAt re reClm (e (↑ofRealClm z))
⊢ e'.re =
    ↑(ContinuousLinearMap.comp reClm
          (ContinuousLinearMap.comp (ContinuousLinearMap.restrictScalars ℝ (ContinuousLinearMap.smulRight 1 e'))
            ofRealClm))
      1
rw [ContinuousLinearMap.comp_apply, ContinuousLinearMap.comp_apply]
no goals
case h.e'_7
e : ℂ → ℂ
e' : ℂ
z : ℝ
h : HasDerivAt e e' ↑z
A : HasFDerivAt ofReal' ofRealClm z
B : HasFDerivAt e (ContinuousLinearMap.restrictScalars ℝ (ContinuousLinearMap.smulRight 1 e')) (↑ofRealClm z)
C : HasFDerivAt re reClm (e (↑ofRealClm z))
⊢ e'.re = ↑reClm (↑(ContinuousLinearMap.restrictScalars ℝ (ContinuousLinearMap.smulRight 1 e')) (↑ofRealClm 1))
simp