-- Lean 4 proof step from Mathlib.CategoryTheory.Monoidal.DayConvolution.Braided (goal)
Goal:
C : Type u₁
inst : Category.{v₁, u₁} C
V : Type u₂
inst_1 : Category.{v₂, u₂} V
inst_2 : MonoidalCategory.{v₁, u₁} C
inst_3 : BraidedCategory.{v₁, u₁} C
inst_4 : MonoidalCategory.{v₂, u₂} V
inst_5 : BraidedCategory.{v₂, u₂} V
F G : Functor.{v₁, v₂, u₁, u₂} C V
inst_6 :
  ∀ (v : V) (d : C), Limits.PreservesColimitsOfShape (CostructuredArrow.{v₁, v₁, u₁, u₁} (tensor C) d) (tensorLeft v)
inst_7 :
  ∀ (v : V) (d : C), Limits.PreservesColimitsOfShape (CostructuredArrow.{v₁, v₁, u₁, u₁} (tensor C) d) (tensorRight v)
H : Functor.{v₁, v₂, u₁, u₂} C V
inst_8 : DayConvolution F G
inst_9 : DayConvolution G H
inst_10 : DayConvolution F (@convolution _ _ _ _ inst_2 inst_4 G H _)
inst_11 : DayConvolution (@convolution _ _ _ _ inst_2 inst_4 F G _) H
inst_12 : DayConvolution H F
inst_13 : DayConvolution G (@convolution _ _ _ _ inst_2 inst_4 H F _)
inst_14 : DayConvolution (@convolution _ _ _ _ inst_2 inst_4 G H _) F
inst_15 : DayConvolution G F
inst_16 : DayConvolution (@convolution _ _ _ _ inst_2 inst_4 G F _) H
inst_17 : DayConvolution F H
inst_18 : DayConvolution G (@convolution _ _ _ _ inst_2 inst_4 F H _)
z x y : C
⊢ Eq (α :=
    ((F ⊠ G) ⊠ H).obj ((x, y), z) ⟶
      (Functor.prod (tensor C) (𝟭 C) ⋙
            tensor C ⋙ @convolution _ _ _ _ inst_2 inst_4 G (@convolution _ _ _ _ inst_2 inst_4 H F _) _).obj
        ((x, y), z))
    (NatTrans.app
      (ExternalProduct.extensionUnitLeft (@convolution _ _ _ _ inst_2 inst_4 F G _) (unit F G) H ≫
        Functor.whiskerLeft (Functor.prod (tensor C) (𝟭 C))
          (CategoryStruct.comp (Y :=
            tensor C ⋙ @convolution _ _ _ _ inst_2 inst_4 (@convolution _ _ _ _ inst_2 inst_4 F G _) H _)
            (unit (@convolution _ _ _ _ inst_2 inst_4 F G _) H)
            (Functor.whiskerLeft (tensor C)
              (CategoryStruct.comp (Y :=
                @convolution _ _ _ _ inst_2 inst_4 F (@convolution _ _ _ _ inst_2 inst_4 G H _) _)
                (Iso.hom (associator F G H))
                (CategoryStruct.comp (Y :=
                  @convolution _ _ _ _ inst_2 inst_4 (@convolution _ _ _ _ inst_2 inst_4 G H _) F _)
                  (Iso.hom (braiding F (@convolution _ _ _ _ inst_2 inst_4 G H _))) (Iso.hom (associator G H F)))))))
      ((x, y), z))
    (NatTrans.app
      (ExternalProduct.extensionUnitLeft (@convolution _ _ _ _ inst_2 inst_4 F G _) (unit F G) H ≫
        Functor.whiskerLeft (Functor.prod (tensor C) (𝟭 C))
          (CategoryStruct.comp (Y :=
            tensor C ⋙ @convolution _ _ _ _ inst_2 inst_4 (@convolution _ _ _ _ inst_2 inst_4 F G _) H _)
            (unit (@convolution _ _ _ _ inst_2 inst_4 F G _) H)
            (Functor.whiskerLeft (tensor C)
              (CategoryStruct.comp (Y :=
                @convolution _ _ _ _ inst_2 inst_4 (@convolution _ _ _ _ inst_2 inst_4 G F _) H _)
                (map (Iso.hom (braiding F G)) (𝟙 H))
                (CategoryStruct.comp (Y :=
                  @convolution _ _ _ _ inst_2 inst_4 G (@convolution _ _ _ _ inst_2 inst_4 F H _) _)
                  (Iso.hom (associator G F H)) (map (𝟙 G) (Iso.hom (braiding F H))))))))
      ((x, y), z))
have hγ : Eq (α :=
  tensorObj.{v₂, u₂} (𝒞 := inst_1) (tensorObj.{v₂, u₂} (𝒞 := inst_1) (F.obj x) (G.obj y)) (H.obj z) ⟶
    (@convolution _ _ _ _ inst_2 inst_4 G (@convolution _ _ _ _ inst_2 inst_4 H F _) _).obj
      (tensorObj.{v₁, u₁} (𝒞 := inst) (tensorObj.{v₁, u₁} (𝒞 := inst) x y) z))
  (CategoryStruct.comp (Y :=
      tensorObj.{v₂, u₂} (𝒞 := inst_1)
        ((@convolution _ _ _ _ inst_2 inst_4 F G _).obj (tensorObj.{v₁, u₁} (𝒞 := inst) x y)) (H.obj z))
      (NatTrans.app (unit F G) (x, y) ▷ H.obj z ≫
        (@convolution _ _ _ _ inst_2 inst_4 F G _).obj (tensorObj.{v₁, u₁} (𝒞 := inst) x y) ◁ 𝟙 (H.obj z))
      (CategoryStruct.comp (Y :=
        (@convolution _ _ _ _ inst_2 inst_4 (@convolution _ _ _ _ inst_2 inst_4 F G _) H _).obj
          (tensorObj.{v₁, u₁} (𝒞 := inst) (tensorObj.{v₁, u₁} (𝒞 := inst) x y) z))
        (NatTrans.app (unit (@convolution _ _ _ _ inst_2 inst_4 F G _) H) (tensorObj.{v₁, u₁} (𝒞 := inst) x y, z))
        (CategoryStruct.comp (Y :=
          (@convolution _ _ _ _ inst_2 inst_4 F (@convolution _ _ _ _ inst_2 inst_4 G H _) _).obj
            (tensorObj.{v₁, u₁} (𝒞 := inst) (tensorObj.{v₁, u₁} (𝒞 := inst) x y) z))
          (NatTrans.app (Iso.hom (associator F G H))
            (tensorObj.{v₁, u₁} (𝒞 := inst) (tensorObj.{v₁, u₁} (𝒞 := inst) x y) z))
          (CategoryStruct.comp (Y :=
            (@convolution _ _ _ _ inst_2 inst_4 (@convolution _ _ _ _ inst_2 inst_4 G H _) F _).obj
              (tensorObj.{v₁, u₁} (𝒞 := inst) (tensorObj.{v₁, u₁} (𝒞 := inst) x y) z))
            (NatTrans.app (Iso.hom (braiding F (@convolution _ _ _ _ inst_2 inst_4 G H _)))
              (tensorObj.{v₁, u₁} (𝒞 := inst) (tensorObj.{v₁, u₁} (𝒞 := inst) x y) z))
            (NatTrans.app (Iso.hom (associator G H F))
              (tensorObj.{v₁, u₁} (𝒞 := inst) (tensorObj.{v₁, u₁} (𝒞 := inst) x y) z))))) :
    tensorObj.{v₂, u₂} (𝒞 := inst_1) (tensorObj.{v₂, u₂} (𝒞 := inst_1) (F.obj x) (G.obj y)) (H.obj z) ⟶
      (@convolution _ _ _ _ inst_2 inst_4 G (@convolution _ _ _ _ inst_2 inst_4 H F _) _).obj
        (tensorObj.{v₁, u₁} (𝒞 := inst) (tensorObj.{v₁, u₁} (𝒞 := inst) x y) z))
  (CategoryStruct.comp (Y :=
      tensorObj.{v₂, u₂} (𝒞 := inst_1)
        ((@convolution _ _ _ _ inst_2 inst_4 F G _).obj (tensorObj.{v₁, u₁} (𝒞 := inst) x y)) (H.obj z))
      (NatTrans.app (unit F G) (x, y) ▷ H.obj z ≫
        (@convolution _ _ _ _ inst_2 inst_4 F G _).obj (tensorObj.{v₁, u₁} (𝒞 := inst) x y) ◁ 𝟙 (H.obj z))
      (CategoryStruct.comp (Y :=
        (@convolution _ _ _ _ inst_2 inst_4 (@convolution _ _ _ _ inst_2 inst_4 F G _) H _).obj
          (tensorObj.{v₁, u₁} (𝒞 := inst) (tensorObj.{v₁, u₁} (𝒞 := inst) x y) z))
        (NatTrans.app (unit (@convolution _ _ _ _ inst_2 inst_4 F G _) H) (tensorObj.{v₁, u₁} (𝒞 := inst) x y, z))
        (CategoryStruct.comp (Y :=
          (@convolution _ _ _ _ inst_2 inst_4 (@convolution _ _ _ _ inst_2 inst_4 G F _) H _).obj
            (tensorObj.{v₁, u₁} (𝒞 := inst) (tensorObj.{v₁, u₁} (𝒞 := inst) x y) z))
          (NatTrans.app (map (Iso.hom (braiding F G)) (𝟙 H))
            (tensorObj.{v₁, u₁} (𝒞 := inst) (tensorObj.{v₁, u₁} (𝒞 := inst) x y) z))
          (CategoryStruct.comp (Y :=
            (@convolution _ _ _ _ inst_2 inst_4 G (@convolution _ _ _ _ inst_2 inst_4 F H _) _).obj
              (tensorObj.{v₁, u₁} (𝒞 := inst) (tensorObj.{v₁, u₁} (𝒞 := inst) x y) z))
            (NatTrans.app (Iso.hom (associator G F H))
              (tensorObj.{v₁, u₁} (𝒞 := inst) (tensorObj.{v₁, u₁} (𝒞 := inst) x y) z))
            (NatTrans.app (map (𝟙 G) (Iso.hom (braiding F H)))
              (tensorObj.{v₁, u₁} (𝒞 := inst) (tensorObj.{v₁, u₁} (𝒞 := inst) x y) z))))) :
    tensorObj.{v₂, u₂} (𝒞 := inst_1) (tensorObj.{v₂, u₂} (𝒞 := inst_1) (F.obj x) (G.obj y)) (H.obj z) ⟶
      (@convolution _ _ _ _ inst_2 inst_4 G (@convolution _ _ _ _ inst_2 inst_4 H F _) _).obj
        (tensorObj.{v₁, u₁} (𝒞 := inst) (tensorObj.{v₁, u₁} (𝒞 := inst) x y) z))
Tactic: dsimp