unfold revDeriv2
K : Type
inst✝⁴ : RCLike K
X : Type
inst✝³ : SemiInnerProductSpace K X
Y : Type
inst✝² : SemiInnerProductSpace K Y
Z : Type
inst✝¹ : SemiInnerProductSpace K Z
W : Type
inst✝ : SemiInnerProductSpace K W
f : W → X → Y
⊢ (revDeriv2 K fun w x => -f w x) = fun w x =>
    let ydf := revDeriv2 K f w x;
    (-ydf.1, fun dy dw =>
      let dwx := ydf.2 (-dy) dw;
      dwx)
K : Type
inst✝⁴ : RCLike K
X : Type
inst✝³ : SemiInnerProductSpace K X
Y : Type
inst✝² : SemiInnerProductSpace K Y
Z : Type
inst✝¹ : SemiInnerProductSpace K Z
W : Type
inst✝ : SemiInnerProductSpace K W
f : W → X → Y
⊢ (fun w x =>
      ((fun w x => -f w x) w x, fun dy =>
        match (motive := W × X → W → W × X)
          semiAdjoint K
            (cderiv K
              (fun x =>
                match x with
                | (w, x) => (fun w x => -f w x) w x)
              (w, x))
            dy with
        | (dw, dx) => fun dw' => (dw' + dw, dx))) =
    fun w x =>
    let ydf :=
      (f w x, fun dy =>
        match (motive := W × X → W → W × X)
          semiAdjoint K
            (cderiv K
              (fun x =>
                match x with
                | (w, x) => f w x)
              (w, x))
            dy with
        | (dw, dx) => fun dw' => (dw' + dw, dx));
    (-ydf.1, fun dy dw =>
      let dwx := ydf.2 (-dy) dw;
      dwx)