-- Lean 4 proof step from Mathlib.CategoryTheory.Monoidal.DayConvolution (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 : 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
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 _) _))))
⊢ 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 dsimp : 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_3 F (@convolution _ _ _ _ inst_2 inst_3 G H _) _).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_3 F G _).obj (tensorObj.{v₁, u₁} (𝒞 := inst) x y)) (H.obj z))
      (NatTrans.app (unit F G) (x, y) ▷ H.obj z)
      (NatTrans.app (unit (@convolution _ _ _ _ inst_2 inst_3 F G _) H) (tensorObj.{v₁, u₁} (𝒞 := inst) x y, z) ≫
        NatTrans.app
          ((@convolution _ _ _ _ inst_2 inst_3 (@convolution _ _ _ _ inst_2 inst_3 F G _) H _).descOfIsLeftKanExtension
            (unit (@convolution _ _ _ _ inst_2 inst_3 F G _) H)
            (@convolution _ _ _ _ inst_2 inst_3 F (@convolution _ _ _ _ inst_2 inst_3 G H _) _)
            ((@convolution _ _ _ _ inst_2 inst_3 F G _ ⊠ H).descOfIsLeftKanExtension
              (extensionUnitLeft (@convolution _ _ _ _ inst_2 inst_3 F G _) (unit F G) H)
              (tensor C ⋙ @convolution _ _ _ _ inst_2 inst_3 F (@convolution _ _ _ _ inst_2 inst_3 G H _) _)
              (((Equiv.symm
                      (FullyFaithful.homEquiv
                        (Equivalence.fullyFaithfulFunctor (Equivalence.congrLeft (prod.associativity C C C)))) :
                    (prod.inverseAssociator C C C ⋙ (F ⊠ G) ⊠ H ⟶
                        prod.inverseAssociator C C C ⋙
                          Functor.prod (tensor C) (𝟭 C) ⋙
                            tensor C ⋙
                              @convolution _ _ _ _ inst_2 inst_3 F (@convolution _ _ _ _ inst_2 inst_3 G H _) _) ≃
                      ((F ⊠ G) ⊠ H ⟶
                        Functor.prod (tensor C) (𝟭 C) ⋙
                          tensor C ⋙
                            @convolution _ _ _ _ inst_2 inst_3 F (@convolution _ _ _ _ inst_2 inst_3 G H _) _)) :
                  (a :
                      prod.inverseAssociator C C C ⋙ (F ⊠ G) ⊠ H ⟶
                        prod.inverseAssociator C C C ⋙ (tensor C).prod (𝟭 C) ⋙ tensor C ⋙ F ⊛ G ⊛ H) →
                    (F ⊠ G) ⊠ H ⟶ (tensor C).prod (𝟭 C) ⋙ tensor C ⋙ F ⊛ G ⊛ H)
                ((ConcreteCategory.hom (FC := TypeCat.Fun)
                      (𝟙
                        (prod.inverseAssociator C C C ⋙ (F ⊠ G) ⊠ H ⟶
                          prod.inverseAssociator C C C ⋙
                            Functor.prod (tensor C) (𝟭 C) ⋙
                              tensor C ⋙
                                @convolution _ _ _ _ inst_2 inst_3 F (@convolution _ _ _ _ inst_2 inst_3 G H _) _)) :
                    (a :
                        prod.inverseAssociator C C C ⋙ (F ⊠ G) ⊠ H ⟶
                          (prod.inverseAssociator C C C ⋙ (tensor C).prod (𝟭 C) ⋙ tensor C) ⋙ F ⊛ G ⊛ H) →
                      prod.inverseAssociator C C C ⋙ (F ⊠ G) ⊠ H ⟶
                        prod.inverseAssociator C C C ⋙ (tensor C).prod (𝟭 C) ⋙ tensor C ⋙ F ⊛ G ⊛ H)
                  (CategoryStruct.comp (Y :=
                    (Functor.prod (𝟭 C) (tensor C) ⋙ tensor C) ⋙
                      @convolution _ _ _ _ inst_2 inst_3 F (@convolution _ _ _ _ inst_2 inst_3 G H _) _)
                    (CategoryStruct.comp (Y := F ⊠ G ⊠ H)
                      (Iso.inv
                        (NatIso.ofComponents
                          (fun (x : C × C × C) ↦ Iso.symm (α_ (F.obj x.1) (G.obj x.2.1) (H.obj x.2.2))) sorry))
                      (((F ⊠ @convolution _ _ _ _ inst_2 inst_3 G H _).homEquivOfIsLeftKanExtension
                            (extensionUnitRight (@convolution _ _ _ _ inst_2 inst_3 G H _) (unit G H) F)
                            (tensor C ⋙
                              @convolution _ _ _ _ inst_2 inst_3 F (@convolution _ _ _ _ inst_2 inst_3 G H _) _) :
                          (a : F ⊠ G ⊛ H ⟶ tensor C ⋙ F ⊛ G ⊛ H) →
                            F ⊠ G ⊠ H ⟶ (𝟭 C).prod (tensor C) ⋙ tensor C ⋙ F ⊛ G ⊛ H)
                        ((CorepresentableBy.homEquiv (corepresentableBy F (@convolution _ _ _ _ inst_2 inst_3 G H _)) :
                            (a : F ⊛ G ⊛ H ⟶ F ⊛ G ⊛ H) → F ⊠ G ⊛ H ⟶ tensor C ⋙ F ⊛ G ⊛ H)
                          (𝟙 (@convolution _ _ _ _ inst_2 inst_3 F (@convolution _ _ _ _ inst_2 inst_3 G H _) _)))))
                    (NatTrans.app
                      (Functor.map (whiskeringLeft (C × C × C) C V)
                        (Iso.inv (NatIso.ofComponents (fun (x : C × C × C) ↦ α_ x.1 x.2.1 x.2.2) sorry)))
                      (@convolution _ _ _ _ inst_2 inst_3 F (@convolution _ _ _ _ inst_2 inst_3 G 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_3 F (@convolution _ _ _ _ inst_2 inst_3 G H _) _).obj
        (tensorObj.{v₁, u₁} (𝒞 := inst) (tensorObj.{v₁, u₁} (𝒞 := inst) x y) z))
  (Iso.hom (α_ (F.obj x) (G.obj y) (H.obj z)) ≫
      CategoryStruct.comp (Y :=
        tensorObj.{v₂, u₂} (𝒞 := inst_1) (F.obj x)
          ((@convolution _ _ _ _ inst_2 inst_3 G H _).obj (tensorObj.{v₁, u₁} (𝒞 := inst) y z)))
        (F.obj x ◁ NatTrans.app (unit G H) (y, z) :
          tensorObj.{v₂, u₂} (𝒞 := inst_1) (F.obj x) (tensorObj.{v₂, u₂} (𝒞 := inst_1) (G.obj y) (H.obj z)) ⟶
            tensorObj.{v₂, u₂} (𝒞 := inst_1) (F.obj x)
              ((@convolution _ _ _ _ inst_2 inst_3 G H _).obj (tensorObj.{v₁, u₁} (𝒞 := inst) 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 y z)) :
          tensorObj.{v₂, u₂} (𝒞 := inst_1) (F.obj x)
              ((@convolution _ _ _ _ inst_2 inst_3 G H _).obj (tensorObj.{v₁, u₁} (𝒞 := inst) y z)) ⟶
            (@convolution _ _ _ _ inst_2 inst_3 F (@convolution _ _ _ _ inst_2 inst_3 G H _) _).obj
              (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_3 F (@convolution _ _ _ _ inst_2 inst_3 G H _) _).obj
        (tensorObj.{v₁, u₁} (𝒞 := inst) (tensorObj.{v₁, u₁} (𝒞 := inst) x y) z))
Tactic: dsimp [associator, Coyoneda.fullyFaithful, corepresentableBy₂,
    corepresentableBy₂', Functor.CorepresentableBy.ofIso, corepresentableBy₂,
    Functor.corepresentableByEquiv, associatorCorepresentingIso] at this ⊢