Theorem: SciLean.cderiv.let_rule (SciLean/Core/FunctionTransformations/CDeriv.lean)

State before:
K : Type u_1
inst✝⁸ : RCLike K
X : Type u_2
inst✝⁷ : Vec K X
Y : Type u_3
inst✝⁶ : Vec K Y
Z : Type u_4
inst✝⁵ : Vec K Z
W : Type ?u.20485
inst✝⁴ : Vec K W
ι : Type ?u.20496
inst✝³ : IndexType ι
inst✝² : LawfulIndexType ι
inst✝¹ : DecidableEq ι
E : ι → Type ?u.20523
inst✝ : (i : ι) → Vec K (E i)
f : X → Y → Z
g : X → Y
hf : CDifferentiable K fun xy => f xy.1 xy.2
hg : CDifferentiable K g
⊢ (cderiv K fun x =>
      let y := g x;
      f x y) =
    fun x =>
    let y := g x;
    fun dx =>
    let dy := cderiv K g x dx;
    let dz := cderiv K (fun xy => f xy.1 xy.2) (x, y) (dx, dy);
    dz
Tactic:
sorry_proof
State after:
no goals