-- Module: Mathlib.CategoryTheory.Monoidal.DayConvolution
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 : MonoidalCategory.{v₂, u₂} V
F G : Functor.{v₁, v₂, u₁, u₂} C V
inst_4 : DayConvolution F G
H : Functor.{v₁, v₂, u₁, u₂} C V
inst_5 : DayConvolution G H
inst_6 : DayConvolution F (@convolution _ _ _ _ inst_2 inst_3 G H _)
inst_7 : DayConvolution (@convolution _ _ _ _ inst_2 inst_3 F G _) H
inst_8 :
  ∀ (v : V) (d : C), Limits.PreservesColimitsOfShape (CostructuredArrow.{v₁, v₁, u₁, u₁} (tensor C) d) (tensorLeft v)
inst_9 :
  ∀ (v : V) (d : C), Limits.PreservesColimitsOfShape (CostructuredArrow.{v₁, v₁, u₁, u₁} (tensor C) d) (tensorRight v)
x y z : C
⊢ Eq.{v₂ + 1} (α :=
    (Opposite.unop (Opposite.op ((F ⊠ G) ⊠ H))).obj ((x, y), z) ⟶
      (obj (obj (whiskeringLeft ((C × C) × C) (C × C) V) (Functor.prod (tensor C) (𝟭 C)))
            (obj (obj (whiskeringLeft (C × C) C V) (tensor C))
              (@convolution _ _ _ _ inst_2 inst_3 F (@convolution _ _ _ _ inst_2 inst_3 G H _) _))).obj
        ((x, y), z))
    ((fun
          (t :
            (obj (whiskeringLeft (C × C) C V) (tensor C) ⋙
                  obj (whiskeringLeft ((C × C) × C) (C × C) V) (Functor.prod (tensor C) (𝟭 C)) ⋙
                    obj coyoneda (Opposite.op ((F ⊠ G) ⊠ H))).obj
              (@convolution _ _ _ _ inst_2 inst_3 F (@convolution _ _ _ _ inst_2 inst_3 G H _) _)) ↦
        (t.app ((x, y), z) :
          (Opposite.unop (Opposite.op ((F ⊠ G) ⊠ H))).obj ((x, y), z) ⟶
            (obj (obj (whiskeringLeft ((C × C) × C) (C × C) V) (Functor.prod (tensor C) (𝟭 C)))
                  (obj (obj (whiskeringLeft (C × C) C V) (tensor C))
                    (@convolution _ _ _ _ inst_2 inst_3 F (@convolution _ _ _ _ inst_2 inst_3 G H _) _))).obj
              ((x, y), z)))
      ((CorepresentableBy.homEquiv (corepresentableBy₂' F G H) :
          (a : (F ⊛ G) ⊛ H ⟶ F ⊛ G ⊛ H) →
            ((whiskeringLeft (C × C) C V).obj (tensor C) ⋙
                  (whiskeringLeft ((C × C) × C) (C × C) V).obj ((tensor C).prod (𝟭 C)) ⋙
                    coyoneda.obj (Opposite.op ((F ⊠ G) ⊠ H))).obj
              (F ⊛ G ⊛ H))
        ((Equiv.symm (CorepresentableBy.homEquiv (corepresentableBy₂' F G H)) :
            (a :
                ((whiskeringLeft (C × C) C V).obj (tensor C) ⋙
                      (whiskeringLeft ((C × C) × C) (C × C) V).obj ((tensor C).prod (𝟭 C)) ⋙
                        coyoneda.obj (Opposite.op ((F ⊠ G) ⊠ H))).obj
                  (F ⊛ G ⊛ H)) →
              (F ⊛ G) ⊛ H ⟶ F ⊛ G ⊛ H)
          ((CorepresentableBy.homEquiv
                (CorepresentableBy.ofIso (corepresentableBy₂ F G H) (Iso.symm (associatorCorepresentingIso F G H))) :
              (a : F ⊛ G ⊛ H ⟶ F ⊛ G ⊛ H) →
                ((whiskeringLeft (C × C) C V).obj (tensor C) ⋙
                      (whiskeringLeft ((C × C) × C) (C × C) V).obj ((tensor C).prod (𝟭 C)) ⋙
                        coyoneda.obj (Opposite.op ((F ⊠ G) ⊠ H))).obj
                  (F ⊛ G ⊛ H))
            (𝟙 (@convolution _ _ _ _ inst_2 inst_3 F (@convolution _ _ _ _ inst_2 inst_3 G H _) _))))))
    ((fun
          (t :
            (obj (whiskeringLeft (C × C) C V) (tensor C) ⋙
                  obj (whiskeringLeft ((C × C) × C) (C × C) V) (Functor.prod (tensor C) (𝟭 C)) ⋙
                    obj coyoneda (Opposite.op ((F ⊠ G) ⊠ H))).obj
              (@convolution _ _ _ _ inst_2 inst_3 F (@convolution _ _ _ _ inst_2 inst_3 G H _) _)) ↦
        (t.app ((x, y), z) :
          (Opposite.unop (Opposite.op ((F ⊠ G) ⊠ H))).obj ((x, y), z) ⟶
            (obj (obj (whiskeringLeft ((C × C) × C) (C × C) V) (Functor.prod (tensor C) (𝟭 C)))
                  (obj (obj (whiskeringLeft (C × C) C V) (tensor C))
                    (@convolution _ _ _ _ inst_2 inst_3 F (@convolution _ _ _ _ inst_2 inst_3 G H _) _))).obj
              ((x, y), z)))
      ((CorepresentableBy.homEquiv
            (CorepresentableBy.ofIso (corepresentableBy₂ F G H) (Iso.symm (associatorCorepresentingIso F G H))) :
          (a : F ⊛ G ⊛ H ⟶ F ⊛ G ⊛ H) →
            ((whiskeringLeft (C × C) C V).obj (tensor C) ⋙
                  (whiskeringLeft ((C × C) × C) (C × C) V).obj ((tensor C).prod (𝟭 C)) ⋙
                    coyoneda.obj (Opposite.op ((F ⊠ G) ⊠ H))).obj
              (F ⊛ G ⊛ H))
        (𝟙 (@convolution _ _ _ _ inst_2 inst_3 F (@convolution _ _ _ _ inst_2 inst_3 G H _) _))))

Tactic:
have := congrArg (fun t ↦ t.app ((x, y), z)) <|
      (corepresentableBy₂' F G H).homEquiv.rightInverse_symm <|
        (corepresentableBy₂ F G H |>.ofIso
          (associatorCorepresentingIso F G H).symm |>.homEquiv (𝟙 _))