Theorem: HasFDerivAt.clm_comp_const (ForML/ContinuousLinearMap.lean)

State before:
𝕜 : Type u_1
α : Type u_2
E : Type u_3
F : Type u_4
G : Type u_5
inst✝⁸ : NontriviallyNormedField 𝕜
inst✝⁷ : NormedAddCommGroup α
inst✝⁶ : NormedSpace 𝕜 α
inst✝⁵ : NormedAddCommGroup E
inst✝⁴ : NormedSpace 𝕜 E
inst✝³ : NormedAddCommGroup F
inst✝² : NormedSpace 𝕜 F
inst✝¹ : NormedAddCommGroup G
inst✝ : NormedSpace 𝕜 G
c : α → F →L[𝕜] G
u : E →L[𝕜] F
c' : α →L[𝕜] F →L[𝕜] G
x : α
hc : HasFDerivAt c c' x
⊢ HasFDerivAt (fun y => ContinuousLinearMap.comp (c y) u)
    (ContinuousLinearMap.comp ((ContinuousLinearMap.flip (ContinuousLinearMap.compL 𝕜 E F G)) u) c') x
Tactic:
refine HasFDerivAt.congr_fderiv (HasFDerivAt.clm_comp hc (hasFDerivAt_const u x)) ?_
State after:
𝕜 : Type u_1
α : Type u_2
E : Type u_3
F : Type u_4
G : Type u_5
inst✝⁸ : NontriviallyNormedField 𝕜
inst✝⁷ : NormedAddCommGroup α
inst✝⁶ : NormedSpace 𝕜 α
inst✝⁵ : NormedAddCommGroup E
inst✝⁴ : NormedSpace 𝕜 E
inst✝³ : NormedAddCommGroup F
inst✝² : NormedSpace 𝕜 F
inst✝¹ : NormedAddCommGroup G
inst✝ : NormedSpace 𝕜 G
c : α → F →L[𝕜] G
u : E →L[𝕜] F
c' : α →L[𝕜] F →L[𝕜] G
x : α
hc : HasFDerivAt c c' x
⊢ ContinuousLinearMap.comp ((ContinuousLinearMap.compL 𝕜 E F G) (c x)) 0 +
      ContinuousLinearMap.comp ((ContinuousLinearMap.flip (ContinuousLinearMap.compL 𝕜 E F G)) u) c' =
    ContinuousLinearMap.comp ((ContinuousLinearMap.flip (ContinuousLinearMap.compL 𝕜 E F G)) u) c'

State before:
𝕜 : Type u_1
α : Type u_2
E : Type u_3
F : Type u_4
G : Type u_5
inst✝⁸ : NontriviallyNormedField 𝕜
inst✝⁷ : NormedAddCommGroup α
inst✝⁶ : NormedSpace 𝕜 α
inst✝⁵ : NormedAddCommGroup E
inst✝⁴ : NormedSpace 𝕜 E
inst✝³ : NormedAddCommGroup F
inst✝² : NormedSpace 𝕜 F
inst✝¹ : NormedAddCommGroup G
inst✝ : NormedSpace 𝕜 G
c : α → F →L[𝕜] G
u : E →L[𝕜] F
c' : α →L[𝕜] F →L[𝕜] G
x : α
hc : HasFDerivAt c c' x
⊢ ContinuousLinearMap.comp ((ContinuousLinearMap.compL 𝕜 E F G) (c x)) 0 +
      ContinuousLinearMap.comp ((ContinuousLinearMap.flip (ContinuousLinearMap.compL 𝕜 E F G)) u) c' =
    ContinuousLinearMap.comp ((ContinuousLinearMap.flip (ContinuousLinearMap.compL 𝕜 E F G)) u) c'
Tactic:
rw [ContinuousLinearMap.comp_zero, zero_add]
State after:
no goals