-- 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 (@convolution _ _ _ _ inst_2 inst_4 F G _)
inst_13 : DayConvolution H F
inst_14 : DayConvolution (@convolution _ _ _ _ inst_2 inst_4 H F _) G
inst_15 : DayConvolution H G
inst_16 : DayConvolution F (@convolution _ _ _ _ inst_2 inst_4 H G _)
inst_17 : DayConvolution F H
inst_18 : DayConvolution (@convolution _ _ _ _ inst_2 inst_4 F H _) G
x y z : C
⊢ Eq (α :=
    (F ⊠ G ⊠ H).obj (x, y, z) ⟶
      (Functor.prod (𝟭 C) (tensor C) ⋙
            tensor C ⋙ @convolution _ _ _ _ inst_2 inst_4 (@convolution _ _ _ _ inst_2 inst_4 H F _) G _).obj
        (x, y, z))
    (NatTrans.app
      (ExternalProduct.extensionUnitRight (@convolution _ _ _ _ inst_2 inst_4 G H _) (unit G H) F ≫
        Functor.whiskerLeft (Functor.prod (𝟭 C) (tensor C))
          (CategoryStruct.comp (Y :=
            tensor C ⋙ @convolution _ _ _ _ inst_2 inst_4 F (@convolution _ _ _ _ inst_2 inst_4 G H _) _)
            (unit F (@convolution _ _ _ _ inst_2 inst_4 G H _))
            (Functor.whiskerLeft (tensor C)
              (CategoryStruct.comp (Y :=
                @convolution _ _ _ _ inst_2 inst_4 (@convolution _ _ _ _ inst_2 inst_4 F G _) H _)
                (Iso.inv (associator F G H))
                (CategoryStruct.comp (Y :=
                  @convolution _ _ _ _ inst_2 inst_4 H (@convolution _ _ _ _ inst_2 inst_4 F G _) _)
                  (Iso.hom (braiding (@convolution _ _ _ _ inst_2 inst_4 F G _) H)) (Iso.inv (associator H F G)))))))
      (x, y, z))
    (NatTrans.app
      (ExternalProduct.extensionUnitRight (@convolution _ _ _ _ inst_2 inst_4 G H _) (unit G H) F ≫
        Functor.whiskerLeft (Functor.prod (𝟭 C) (tensor C))
          (CategoryStruct.comp (Y :=
            tensor C ⋙ @convolution _ _ _ _ inst_2 inst_4 F (@convolution _ _ _ _ inst_2 inst_4 G H _) _)
            (unit F (@convolution _ _ _ _ inst_2 inst_4 G H _))
            (Functor.whiskerLeft (tensor C)
              (CategoryStruct.comp (Y :=
                @convolution _ _ _ _ inst_2 inst_4 F (@convolution _ _ _ _ inst_2 inst_4 H G _) _)
                (map (𝟙 F) (Iso.hom (braiding G H)))
                (CategoryStruct.comp (Y :=
                  @convolution _ _ _ _ inst_2 inst_4 (@convolution _ _ _ _ inst_2 inst_4 F H _) G _)
                  (Iso.inv (associator F H G)) (map (Iso.hom (braiding F H)) (𝟙 G)))))))
      (x, y, z))
have hγ : Eq (α :=
  tensorObj.{v₂, u₂} (𝒞 := inst_1) (F.obj x) (tensorObj.{v₂, u₂} (𝒞 := inst_1) (G.obj y) (H.obj z)) ⟶
    (@convolution _ _ _ _ inst_2 inst_4 (@convolution _ _ _ _ inst_2 inst_4 H F _) G _).obj
      (tensorObj.{v₁, u₁} (𝒞 := inst) x (tensorObj.{v₁, u₁} (𝒞 := inst) y z)))
  (CategoryStruct.comp (Y :=
      tensorObj.{v₂, u₂} (𝒞 := inst_1) (F.obj x)
        ((@convolution _ _ _ _ inst_2 inst_4 G H _).obj (tensorObj.{v₁, u₁} (𝒞 := inst) y z)))
      (𝟙 (F.obj x) ▷ tensorObj.{v₂, u₂} (𝒞 := inst_1) (G.obj y) (H.obj z) ≫ F.obj x ◁ NatTrans.app (unit G H) (y, z))
      (CategoryStruct.comp (Y :=
        (@convolution _ _ _ _ inst_2 inst_4 F (@convolution _ _ _ _ inst_2 inst_4 G H _) _).obj
          (tensorObj.{v₁, u₁} (𝒞 := inst) x (tensorObj.{v₁, u₁} (𝒞 := inst) y z)))
        (NatTrans.app (unit F (@convolution _ _ _ _ inst_2 inst_4 G H _)) (x, tensorObj.{v₁, u₁} (𝒞 := inst) y z))
        (CategoryStruct.comp (Y :=
          (@convolution _ _ _ _ inst_2 inst_4 (@convolution _ _ _ _ inst_2 inst_4 F G _) H _).obj
            (tensorObj.{v₁, u₁} (𝒞 := inst) x (tensorObj.{v₁, u₁} (𝒞 := inst) y z)))
          (NatTrans.app (Iso.inv (associator F G H))
            (tensorObj.{v₁, u₁} (𝒞 := inst) x (tensorObj.{v₁, u₁} (𝒞 := inst) y z)))
          (CategoryStruct.comp (Y :=
            (@convolution _ _ _ _ inst_2 inst_4 H (@convolution _ _ _ _ inst_2 inst_4 F G _) _).obj
              (tensorObj.{v₁, u₁} (𝒞 := inst) x (tensorObj.{v₁, u₁} (𝒞 := inst) y z)))
            (NatTrans.app (Iso.hom (braiding (@convolution _ _ _ _ inst_2 inst_4 F G _) H))
              (tensorObj.{v₁, u₁} (𝒞 := inst) x (tensorObj.{v₁, u₁} (𝒞 := inst) y z)))
            (NatTrans.app (Iso.inv (associator H F G))
              (tensorObj.{v₁, u₁} (𝒞 := inst) x (tensorObj.{v₁, u₁} (𝒞 := inst) y z)))))) :
    tensorObj.{v₂, u₂} (𝒞 := inst_1) (F.obj x) (tensorObj.{v₂, u₂} (𝒞 := inst_1) (G.obj y) (H.obj z)) ⟶
      (@convolution _ _ _ _ inst_2 inst_4 (@convolution _ _ _ _ inst_2 inst_4 H F _) G _).obj
        (tensorObj.{v₁, u₁} (𝒞 := inst) x (tensorObj.{v₁, u₁} (𝒞 := inst) y z)))
  (CategoryStruct.comp (Y :=
      tensorObj.{v₂, u₂} (𝒞 := inst_1) (F.obj x)
        ((@convolution _ _ _ _ inst_2 inst_4 G H _).obj (tensorObj.{v₁, u₁} (𝒞 := inst) y z)))
      (𝟙 (F.obj x) ▷ tensorObj.{v₂, u₂} (𝒞 := inst_1) (G.obj y) (H.obj z) ≫ F.obj x ◁ NatTrans.app (unit G H) (y, z))
      (CategoryStruct.comp (Y :=
        (@convolution _ _ _ _ inst_2 inst_4 F (@convolution _ _ _ _ inst_2 inst_4 G H _) _).obj
          (tensorObj.{v₁, u₁} (𝒞 := inst) x (tensorObj.{v₁, u₁} (𝒞 := inst) y z)))
        (NatTrans.app (unit F (@convolution _ _ _ _ inst_2 inst_4 G H _)) (x, tensorObj.{v₁, u₁} (𝒞 := inst) y z))
        (CategoryStruct.comp (Y :=
          (@convolution _ _ _ _ inst_2 inst_4 F (@convolution _ _ _ _ inst_2 inst_4 H G _) _).obj
            (tensorObj.{v₁, u₁} (𝒞 := inst) x (tensorObj.{v₁, u₁} (𝒞 := inst) y z)))
          (NatTrans.app (map (𝟙 F) (Iso.hom (braiding G H)))
            (tensorObj.{v₁, u₁} (𝒞 := inst) x (tensorObj.{v₁, u₁} (𝒞 := inst) y z)))
          (CategoryStruct.comp (Y :=
            (@convolution _ _ _ _ inst_2 inst_4 (@convolution _ _ _ _ inst_2 inst_4 F H _) G _).obj
              (tensorObj.{v₁, u₁} (𝒞 := inst) x (tensorObj.{v₁, u₁} (𝒞 := inst) y z)))
            (NatTrans.app (Iso.inv (associator F H G))
              (tensorObj.{v₁, u₁} (𝒞 := inst) x (tensorObj.{v₁, u₁} (𝒞 := inst) y z)))
            (NatTrans.app (map (Iso.hom (braiding F H)) (𝟙 G))
              (tensorObj.{v₁, u₁} (𝒞 := inst) x (tensorObj.{v₁, u₁} (𝒞 := inst) y z)))))) :
    tensorObj.{v₂, u₂} (𝒞 := inst_1) (F.obj x) (tensorObj.{v₂, u₂} (𝒞 := inst_1) (G.obj y) (H.obj z)) ⟶
      (@convolution _ _ _ _ inst_2 inst_4 (@convolution _ _ _ _ inst_2 inst_4 H F _) G _).obj
        (tensorObj.{v₁, u₁} (𝒞 := inst) x (tensorObj.{v₁, u₁} (𝒞 := inst) y z)))
Tactic: dsimp