-- Module: Mathlib.CategoryTheory.Monoidal.DayConvolution
Goal:
C_1 : Type u₁
inst : Category.{v₁, u₁} C_1
V_1 : Type u₂
inst_1 : Category.{v₂, u₂} V_1
inst_2 : MonoidalCategory.{v₁, u₁} C_1
inst_3 : MonoidalCategory.{v₂, u₂} V_1
C : Type u₁
inst_4 : Category.{v₁, u₁} C
V : Type u₂
inst_5 : Category.{v₂, u₂} V
inst_6 : MonoidalCategory.{v₁, u₁} C
inst_7 : MonoidalCategory.{v₂, u₂} V
D : Type u₃
inst_8 : Category.{v₃, u₃} D
inst_9 : MonoidalCategoryStruct.{v₃, u₃} D
inst_10 : LawfulDayConvolutionMonoidalCategoryStruct.{v₁, v₂, v₃, u₁, u₂, u₃} C V D
inst_11 :
  ∀ (v : V) (d : C), Limits.PreservesColimitsOfShape (CostructuredArrow.{v₁, v₁, u₁, u₁} (tensor C) d) (tensorLeft v)
inst_12 :
  ∀ (v : V) (d : C), Limits.PreservesColimitsOfShape (CostructuredArrow.{v₁, v₁, u₁, u₁} (tensor C) d) (tensorRight v)
inst_13 :
  ∀ (v : V) (d : C),
    Limits.PreservesColimitsOfShape.{0, v₁, v₂, v₂, u₂, u₂}
      (CostructuredArrow (Functor.fromPUnit (tensorUnit.{v₁, u₁} C (𝒞 := inst_4))) d) (tensorLeft v)
inst_14 :
  ∀ (v : V) (d : C),
    Limits.PreservesColimitsOfShape.{0, v₁, v₂, v₂, u₂, u₂}
      (CostructuredArrow (Functor.fromPUnit (tensorUnit.{v₁, u₁} C (𝒞 := inst_4))) d) (tensorRight v)
inst_15 :
  ∀ (v : V) (d : C × C),
    Limits.PreservesColimitsOfShape
      (CostructuredArrow.{v₁, v₁, u₁, u₁} (Functor.prod (𝟭 C) (Functor.fromPUnit (tensorUnit.{v₁, u₁} C (𝒞 := inst_4))))
        d)
      (tensorRight v)
inst_16 :
  ∀ (v : V) (d : C × C),
    Limits.PreservesColimitsOfShape (CostructuredArrow.{v₁, v₁, u₁, u₁} (Functor.prod (tensor C) (𝟭 C)) d)
      (tensorRight v)
x y : D
fst snd : C
a :
  Eq.{v₂ + 1} (α :=
    tensorObj.{v₂, u₂} (𝒞 := inst_5)
        (Functor.obj.{v₁, v₂, u₁, u₂} (Functor.obj (@ι C _ V _ inst_6 inst_7 D _ inst_9 _) x) fst)
        (Functor.obj.{v₁, v₂, u₁, u₂} (Functor.obj (@ι C _ V _ inst_6 inst_7 D _ inst_9 _) y) snd) ⟶
      Functor.obj.{v₁, v₂, u₁, u₂}
        (Functor.obj (@ι C _ V _ inst_6 inst_7 D _ inst_9 _) (tensorObj.{v₃, u₃} (𝒞 := inst_8) x y))
        (tensorObj.{v₁, u₁} (𝒞 := inst_4) fst snd))
    (NatTrans.app
        (unit (Functor.obj (@ι C _ V _ inst_6 inst_7 D _ inst_9 _) x)
          (Functor.obj (@ι C _ V _ inst_6 inst_7 D _ inst_9 _) y))
        (fst, snd) :
      Functor.obj.{v₁, v₂, u₁, u₂}
          (Functor.obj (@ι C _ V _ inst_6 inst_7 D _ inst_9 _) x ⊠
            Functor.obj (@ι C _ V _ inst_6 inst_7 D _ inst_9 _) y)
          (fst, snd) ⟶
        Functor.obj.{v₁, v₂, u₁, u₂}
          (tensor C ⋙ Functor.obj (@ι C _ V _ inst_6 inst_7 D _ inst_9 _) (tensorObj.{v₃, u₃} (𝒞 := inst_8) x y))
          (fst, snd))
    (NatTrans.app
        (unit (Functor.obj (@ι C _ V _ inst_6 inst_7 D _ inst_9 _) x)
          (Functor.obj (@ι C _ V _ inst_6 inst_7 D _ inst_9 _) y))
        (fst, snd) ≫
      𝟙
        (Functor.obj.{v₁, v₂, u₁, u₂}
          (Functor.obj (@ι C _ V _ inst_6 inst_7 D _ inst_9 _) (tensorObj.{v₃, u₃} (𝒞 := inst_8) x y))
          (tensorObj.{v₁, u₁} (𝒞 := inst_4) fst snd)))
⊢ Eq.{v₂ + 1} (α :=
    tensorObj.{v₂, u₂} (𝒞 := inst_5)
        (Functor.obj.{v₁, v₂, u₁, u₂} (Functor.obj (@ι C _ V _ inst_6 inst_7 D _ inst_9 _) x) fst)
        (Functor.obj.{v₁, v₂, u₁, u₂} (Functor.obj (@ι C _ V _ inst_6 inst_7 D _ inst_9 _) y) snd) ⟶
      Functor.obj.{v₁, v₂, u₁, u₂}
        (@DayConvolution.convolution _ _ _ _ inst_6 inst_7 (Functor.obj (@ι C _ V _ inst_6 inst_7 D _ inst_9 _) x)
          (Functor.obj (@ι C _ V _ inst_6 inst_7 D _ inst_9 _) y) _)
        (tensorObj.{v₁, u₁} (𝒞 := inst_4) fst snd))
    (NatTrans.app
        (unit (Functor.obj (@ι C _ V _ inst_6 inst_7 D _ inst_9 _) x)
          (Functor.obj (@ι C _ V _ inst_6 inst_7 D _ inst_9 _) y))
        (fst, snd) :
      Functor.obj.{v₁, v₂, u₁, u₂}
          (Functor.obj (@ι C _ V _ inst_6 inst_7 D _ inst_9 _) x ⊠
            Functor.obj (@ι C _ V _ inst_6 inst_7 D _ inst_9 _) y)
          (fst, snd) ⟶
        Functor.obj.{v₁, v₂, u₁, u₂}
          (tensor C ⋙
            @DayConvolution.convolution _ _ _ _ inst_6 inst_7 (Functor.obj (@ι C _ V _ inst_6 inst_7 D _ inst_9 _) x)
              (Functor.obj (@ι C _ V _ inst_6 inst_7 D _ inst_9 _) y) _)
          (fst, snd))
    (NatTrans.app
        (unit (Functor.obj (@ι C _ V _ inst_6 inst_7 D _ inst_9 _) x)
          (Functor.obj (@ι C _ V _ inst_6 inst_7 D _ inst_9 _) y))
        (fst, snd) ≫
      𝟙
        (Functor.obj.{v₁, v₂, u₁, u₂}
          (Functor.obj (@ι C _ V _ inst_6 inst_7 D _ inst_9 _) (tensorObj.{v₃, u₃} (𝒞 := inst_8) x y))
          (tensorObj.{v₁, u₁} (𝒞 := inst_4) fst snd)))

Tactic:
dsimp [DayConvolution.convolution]

Premises used: CategoryTheory.MonoidalCategory.DayConvolution.convolution