Theorem: GetElem.getElem.arg_cont.revCDeriv_rule (SciLean/Data/ArrayType/Properties.lean)

State before:
K : Type
inst✝⁶ : RCLike K
Cont : Type
Idx Elem : outParam Type
inst✝⁵ : ArrayType Cont Idx Elem
inst✝⁴ : IndexType Idx
inst✝³ : LawfulIndexType Idx
inst✝² : DecidableEq Idx
X : Type
inst✝¹ : SemiInnerProductSpace K X
inst✝ : SemiInnerProductSpace K Elem
f : X → Cont
idx : Idx
hf : HasAdjDiff K f
⊢ (revDeriv K fun x => (f x)[idx]) = fun x =>
    let ydf := revDerivProj K Idx f x;
    (ydf.1[idx], fun delem => ydf.2 idx delem)
Tactic:
unfold revDeriv
State after:
K : Type
inst✝⁶ : RCLike K
Cont : Type
Idx Elem : outParam Type
inst✝⁵ : ArrayType Cont Idx Elem
inst✝⁴ : IndexType Idx
inst✝³ : LawfulIndexType Idx
inst✝² : DecidableEq Idx
X : Type
inst✝¹ : SemiInnerProductSpace K X
inst✝ : SemiInnerProductSpace K Elem
f : X → Cont
idx : Idx
hf : HasAdjDiff K f
⊢ (fun x => ((fun x => (f x)[idx]) x, semiAdjoint K (cderiv K (fun x => (f x)[idx]) x))) = fun x =>
    let ydf := revDerivProj K Idx f x;
    (ydf.1[idx], fun delem => ydf.2 idx delem)

State before:
K : Type
inst✝⁶ : RCLike K
Cont : Type
Idx Elem : outParam Type
inst✝⁵ : ArrayType Cont Idx Elem
inst✝⁴ : IndexType Idx
inst✝³ : LawfulIndexType Idx
inst✝² : DecidableEq Idx
X : Type
inst✝¹ : SemiInnerProductSpace K X
inst✝ : SemiInnerProductSpace K Elem
f : X → Cont
idx : Idx
hf : HasAdjDiff K f
⊢ (fun x => ((fun x => (f x)[idx]) x, semiAdjoint K (cderiv K (fun x => (f x)[idx]) x))) = fun x =>
    let ydf := revDerivProj K Idx f x;
    (ydf.1[idx], fun delem => ydf.2 idx delem)
Tactic:
conv =>
  lhs; fun_trans; fun_trans; simp
State after:
no goals