-- Lean 4 proof step from Mathlib.CategoryTheory.Monoidal.DayConvolution (goal)
Goal:
C_1 : Type u₁
inst : Category.{v₁, u₁} C_1
V_1 : Type u₂
inst_1 : Category.{v₂, u₂} V_1
inst_2 : MonoidalCategory.{v₁, u₁} C_1
inst_3 : MonoidalCategory.{v₂, u₂} V_1
C : Type u₁
inst_4 : Category.{v₁, u₁} C
V : Type u₂
inst_5 : Category.{v₂, u₂} V
inst_6 : MonoidalCategory.{v₁, u₁} C
inst_7 : MonoidalCategory.{v₂, u₂} V
D : Type u₃
inst_8 : Category.{v₃, u₃} D
inst_9 : InducedLawfulDayConvolutionMonoidalCategoryStructCore.{v₁, v₂, v₃, u₁, u₂, u₃} C V D
d d' : D
⊢ Eq (α :=
    Quiver.Hom (V := Functor.{v₁, v₂, u₁, u₂} (C × C) V)
      (Functor.obj (@ι C _ V _ inst_6 inst_7 D _ _) d ⊠ Functor.obj (@ι C _ V _ inst_6 inst_7 D _ _) d')
      (Functor.obj (Functor.obj (Functor.whiskeringLeft (C × C) C V) (tensor C))
        (StructuredArrow.right (D := Functor.{v₁, v₂, u₁, u₂} (C × C) V) (S :=
          Functor.obj (@ι C _ V _ inst_6 inst_7 D _ _) d ⊠ Functor.obj (@ι C _ V _ inst_6 inst_7 D _ _) d') (T :=
          Functor.obj (Functor.whiskeringLeft (C × C) C V) (tensor C))
          (Functor.LeftExtension.mk
            (Functor.obj (@ι C _ V _ inst_6 inst_7 D _ _)
              (@tensorObj.{v₁, v₂, v₃, u₁, u₂, u₃} C inst_4 V inst_5 inst_6 inst_7 _ inst_8 _ d d'))
            { app := fun (x : C × C) ↦ convolutionUnitApp V d d' x.1 x.2, naturality := ⋯ }))))
    (CategoryStruct.comp (Y :=
      Functor.obj (Functor.obj (Functor.whiskeringLeft (C × C) C V) (tensor C))
        (StructuredArrow.right (S :=
          Functor.obj (@ι C _ V _ inst_6 inst_7 D _ _) d ⊠ Functor.obj (@ι C _ V _ inst_6 inst_7 D _ _) d') (T :=
          Functor.obj (Functor.whiskeringLeft (C × C) C V) (tensor C))
          (Functor.LeftExtension.mk
            (@DayConvolution.convolution _ _ _ _ inst_6 inst_7 (Functor.obj (@ι C _ V _ inst_6 inst_7 D _ _) d)
              (Functor.obj (@ι C _ V _ inst_6 inst_7 D _ _) d') _)
            (DayConvolution.unit (Functor.obj (@ι C _ V _ inst_6 inst_7 D _ _) d)
              (Functor.obj (@ι C _ V _ inst_6 inst_7 D _ _) d')))))
      (StructuredArrow.hom
        (Functor.LeftExtension.mk
          (@DayConvolution.convolution _ _ _ _ inst_6 inst_7 (Functor.obj (@ι C _ V _ inst_6 inst_7 D _ _) d)
            (Functor.obj (@ι C _ V _ inst_6 inst_7 D _ _) d') _)
          (DayConvolution.unit (Functor.obj (@ι C _ V _ inst_6 inst_7 D _ _) d)
            (Functor.obj (@ι C _ V _ inst_6 inst_7 D _ _) d'))))
      (Functor.map (Functor.obj (Functor.whiskeringLeft (C × C) C V) (tensor C))
        (Iso.hom (Iso.symm (tensorObjIsoConvolution C V d d')))))
    (StructuredArrow.hom
      (Functor.LeftExtension.mk
        (Functor.obj (@ι C _ V _ inst_6 inst_7 D _ _)
          (@tensorObj.{v₁, v₂, v₃, u₁, u₂, u₃} C inst_4 V inst_5 inst_6 inst_7 _ inst_8 _ d d'))
        { app := fun (x : C × C) ↦ convolutionUnitApp V d d' x.1 x.2, naturality := ⋯ }))
have w : ∀ (x y : C),
  Eq.{v₂ + 1} (α :=
    Functor.obj.{v₁, v₂, u₁, u₂}
        (Functor.obj (@ι C _ V _ inst_6 inst_7 D _ _) d ⊠ Functor.obj (@ι C _ V _ inst_6 inst_7 D _ _) d') (x, y) ⟶
      Functor.obj.{v₁, v₂, u₁, u₂}
        (Functor.obj (Functor.obj (Functor.whiskeringLeft (C × C) C V) (tensor C))
          (StructuredArrow.right (D := Functor.{v₁, v₂, u₁, u₂} (C × C) V) (S :=
            Functor.obj (@ι C _ V _ inst_6 inst_7 D _ _) d ⊠ Functor.obj (@ι C _ V _ inst_6 inst_7 D _ _) d') (T :=
            Functor.obj (Functor.whiskeringLeft (C × C) C V) (tensor C))
            (Functor.LeftExtension.mk
              (Functor.obj (@ι C _ V _ inst_6 inst_7 D _ _)
                (@tensorObj.{v₁, v₂, v₃, u₁, u₂, u₃} C inst_4 V inst_5 inst_6 inst_7 _ inst_8 _ d d'))
              { app := fun (x : C × C) ↦ convolutionUnitApp V d d' x.1 x.2, naturality := sorry })))
        (x, y))
    (NatTrans.app
      (CategoryStruct.comp (Y :=
        Functor.obj (Functor.obj (Functor.whiskeringLeft (C × C) C V) (tensor C))
          (StructuredArrow.right (S :=
            Functor.obj (@ι C _ V _ inst_6 inst_7 D _ _) d ⊠ Functor.obj (@ι C _ V _ inst_6 inst_7 D _ _) d') (T :=
            Functor.obj (Functor.whiskeringLeft (C × C) C V) (tensor C))
            (Functor.LeftExtension.mk
              (@DayConvolution.convolution _ _ _ _ inst_6 inst_7 (Functor.obj (@ι C _ V _ inst_6 inst_7 D _ _) d)
                (Functor.obj (@ι C _ V _ inst_6 inst_7 D _ _) d') _)
              (DayConvolution.unit (Functor.obj (@ι C _ V _ inst_6 inst_7 D _ _) d)
                (Functor.obj (@ι C _ V _ inst_6 inst_7 D _ _) d')))))
        (StructuredArrow.hom
          (Functor.LeftExtension.mk
            (@DayConvolution.convolution _ _ _ _ inst_6 inst_7 (Functor.obj (@ι C _ V _ inst_6 inst_7 D _ _) d)
              (Functor.obj (@ι C _ V _ inst_6 inst_7 D _ _) d') _)
            (DayConvolution.unit (Functor.obj (@ι C _ V _ inst_6 inst_7 D _ _) d)
              (Functor.obj (@ι C _ V _ inst_6 inst_7 D _ _) d'))))
        (Functor.map (Functor.obj (Functor.whiskeringLeft (C × C) C V) (tensor C))
          (Iso.hom (Iso.symm (tensorObjIsoConvolution C V d d')))))
      (x, y))
    (NatTrans.app
      (StructuredArrow.hom
        (Functor.LeftExtension.mk
          (Functor.obj (@ι C _ V _ inst_6 inst_7 D _ _)
            (@tensorObj.{v₁, v₂, v₃, u₁, u₂, u₃} C inst_4 V inst_5 inst_6 inst_7 _ inst_8 _ d d'))
          { app := fun (x : C × C) ↦ convolutionUnitApp V d d' x.1 x.2, naturality := sorry }))
      (x, y))
Tactic: ext ⟨x, y⟩