-- 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
U : Functor.{v₁, v₂, u₁, u₂} C V
inst_4 : DayConvolutionUnit U
F : Functor.{v₁, v₂, u₁, u₂} C V
inst_5 :
  ∀ (v : V) (d : C),
    Limits.PreservesColimitsOfShape.{0, v₁, v₂, v₂, u₂, u₂}
      (CostructuredArrow (fromPUnit (tensorUnit.{v₁, u₁} C (𝒞 := inst))) d) (tensorLeft v)
inst_6 : DayConvolution F U
x : C
⊢ Eq.{v₂ + 1} (α :=
    (Opposite.unop (Opposite.op (F ⊠ fromPUnit (tensorUnit.{v₂, u₂} V (𝒞 := inst_1))))).obj
        (x, { as := PUnit.unit : Discrete PUnit.{1} }) ⟶
      (obj
            (obj (whiskeringLeft (C × Discrete PUnit.{1}) (C × C) V)
              (Functor.prod (𝟭 C) (fromPUnit (tensorUnit.{v₁, u₁} C (𝒞 := inst)))))
            (obj (obj (whiskeringLeft (C × C) C V) (tensor C)) F)).obj
        (x, { as := PUnit.unit }))
    ((fun
          (t :
            (obj (whiskeringLeft (C × C) C V) (tensor C) ⋙
                  obj (whiskeringLeft (C × Discrete PUnit.{1}) (C × C) V)
                      (Functor.prod (𝟭 C) (fromPUnit (tensorUnit.{v₁, u₁} C (𝒞 := inst)))) ⋙
                    obj coyoneda (Opposite.op (F ⊠ fromPUnit (tensorUnit.{v₂, u₂} V (𝒞 := inst_1))))).obj
              F) ↦
        (t.app (x, { as := PUnit.unit }) :
          (Opposite.unop (Opposite.op (F ⊠ fromPUnit (tensorUnit.{v₂, u₂} V (𝒞 := inst_1))))).obj
              (x, { as := PUnit.unit : Discrete PUnit.{1} }) ⟶
            (obj
                  (obj (whiskeringLeft (C × Discrete PUnit.{1}) (C × C) V)
                    (Functor.prod (𝟭 C) (fromPUnit (tensorUnit.{v₁, u₁} C (𝒞 := inst)))))
                  (obj (obj (whiskeringLeft (C × C) C V) (tensor C)) F)).obj
              (x, { as := PUnit.unit })))
      ((CorepresentableBy.homEquiv (corepresentableByRight U F) :
          (a : F ⊛ U ⟶ F) →
            ((whiskeringLeft (C × C) C V).obj (tensor C) ⋙
                  (whiskeringLeft (C × Discrete PUnit.{1}) (C × C) V).obj ((𝟭 C).prod (fromPUnit (𝟙_ C))) ⋙
                    coyoneda.obj (Opposite.op (F ⊠ fromPUnit (𝟙_ V)))).obj
              F)
        ((Equiv.symm (CorepresentableBy.homEquiv (corepresentableByRight U F)) :
            (a :
                ((whiskeringLeft (C × C) C V).obj (tensor C) ⋙
                      (whiskeringLeft (C × Discrete PUnit.{1}) (C × C) V).obj ((𝟭 C).prod (fromPUnit (𝟙_ C))) ⋙
                        coyoneda.obj (Opposite.op (F ⊠ fromPUnit (𝟙_ V)))).obj
                  F) →
              F ⊛ U ⟶ F)
          ((ConcreteCategory.hom (FC := TypeCat.Fun)
                (NatTrans.app (Iso.hom (Iso.symm (rightUnitorCorepresentingIso F))) F) :
              (a : (fun (X : Type (max u₁ v₂)) ↦ X) ((coyoneda.obj (Opposite.op F)).obj F)) →
                (fun (X : Type (max u₁ v₂)) ↦ X)
                  (((whiskeringLeft (C × C) C V).obj (tensor C) ⋙
                        (whiskeringLeft (C × Discrete PUnit.{1}) (C × C) V).obj ((𝟭 C).prod (fromPUnit (𝟙_ C))) ⋙
                          coyoneda.obj (Opposite.op (F ⊠ fromPUnit (𝟙_ V)))).obj
                    F))
            (𝟙 (Opposite.unop (Opposite.op F)))))))
    ((fun
          (t :
            (obj (whiskeringLeft (C × C) C V) (tensor C) ⋙
                  obj (whiskeringLeft (C × Discrete PUnit.{1}) (C × C) V)
                      (Functor.prod (𝟭 C) (fromPUnit (tensorUnit.{v₁, u₁} C (𝒞 := inst)))) ⋙
                    obj coyoneda (Opposite.op (F ⊠ fromPUnit (tensorUnit.{v₂, u₂} V (𝒞 := inst_1))))).obj
              F) ↦
        (t.app (x, { as := PUnit.unit }) :
          (Opposite.unop (Opposite.op (F ⊠ fromPUnit (tensorUnit.{v₂, u₂} V (𝒞 := inst_1))))).obj
              (x, { as := PUnit.unit : Discrete PUnit.{1} }) ⟶
            (obj
                  (obj (whiskeringLeft (C × Discrete PUnit.{1}) (C × C) V)
                    (Functor.prod (𝟭 C) (fromPUnit (tensorUnit.{v₁, u₁} C (𝒞 := inst)))))
                  (obj (obj (whiskeringLeft (C × C) C V) (tensor C)) F)).obj
              (x, { as := PUnit.unit })))
      ((ConcreteCategory.hom (FC := TypeCat.Fun)
            (NatTrans.app (Iso.hom (Iso.symm (rightUnitorCorepresentingIso F))) F) :
          (a : (fun (X : Type (max u₁ v₂)) ↦ X) ((coyoneda.obj (Opposite.op F)).obj F)) →
            (fun (X : Type (max u₁ v₂)) ↦ X)
              (((whiskeringLeft (C × C) C V).obj (tensor C) ⋙
                    (whiskeringLeft (C × Discrete PUnit.{1}) (C × C) V).obj ((𝟭 C).prod (fromPUnit (𝟙_ C))) ⋙
                      coyoneda.obj (Opposite.op (F ⊠ fromPUnit (𝟙_ V)))).obj
                F))
        (𝟙 (Opposite.unop (Opposite.op F)))))

Tactic:
have := congrArg (fun t ↦ t.app (x, .mk PUnit.unit)) <|
      (corepresentableByRight U F).homEquiv.rightInverse_symm <|
        ((rightUnitorCorepresentingIso F).symm.hom.app F) (𝟙 _)