-- Lean 4 proof step from Mathlib.CategoryTheory.Monoidal.DayConvolution (hypothesis)
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
⊢ CategoryStruct.comp (Y :=
      tensorObj.{v₂, u₂} (𝒞 := inst_1) ((tensor C ⋙ @convolution _ _ _ _ inst_2 inst_3 F G _).obj (x, y)) (H.obj z))
      (NatTrans.app (unit F G) (x, y) ▷ H.obj z)
      (CategoryStruct.comp (Y :=
        (tensor C ⋙ @convolution _ _ _ _ inst_2 inst_3 (@convolution _ _ _ _ inst_2 inst_3 F G _) H _).obj
          (tensorObj.{v₁, u₁} (𝒞 := inst) x y, z))
        (NatTrans.app (unit (@convolution _ _ _ _ inst_2 inst_3 F G _) H) (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))) =
    Iso.hom (α_ (F.obj x) ((G, H).1.obj (y, z).1) ((G, H).2.obj (y, z).2)) ≫
      F.obj x ◁ NatTrans.app (unit G H) (y, z) ≫
        NatTrans.app (unit F (@convolution _ _ _ _ inst_2 inst_3 G H _)) (x, tensorObj.{v₁, u₁} (𝒞 := inst) y z) ≫
          (@convolution _ _ _ _ inst_2 inst_3 F (@convolution _ _ _ _ inst_2 inst_3 G H _) _).map
            (Iso.inv (α_ (x, tensorObj.{v₁, u₁} (𝒞 := inst) y z).1 y z))
have this : 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 _))