-- 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
D : Type u₃
inst_4 : Category.{v₃, u₃} D
inst_5 : InducedLawfulDayConvolutionMonoidalCategoryStructCore.{v₁, v₂, v₃, u₁, u₂, u₃} C V D
inst_6 :
  ∀ (v : V) (d : C), Limits.PreservesColimitsOfShape (CostructuredArrow.{v₁, v₁, u₁, u₁} (tensor C) d) (tensorLeft v)
inst_7 :
  ∀ (v : V) (d : C), Limits.PreservesColimitsOfShape (CostructuredArrow.{v₁, v₁, u₁, u₁} (tensor C) d) (tensorRight v)
inst_8 :
  ∀ (v : V) (d : C),
    Limits.PreservesColimitsOfShape.{0, v₁, v₂, v₂, u₂, u₂}
      (CostructuredArrow (Functor.fromPUnit (MonoidalCategoryStruct.tensorUnit.{v₁, u₁} C (𝒞 := inst))) d)
      (tensorRight v)
inst_9 :
  ∀ (v : V) (d : C),
    Limits.PreservesColimitsOfShape.{0, v₁, v₂, v₂, u₂, u₂}
      (CostructuredArrow (Functor.fromPUnit (MonoidalCategoryStruct.tensorUnit.{v₁, u₁} C (𝒞 := inst))) d)
      (tensorLeft v)
d₁ d₁' d₂ d₂' : D
f : d₁ ⟶ d₂
f' : d₁' ⟶ d₂'
⊢ Eq (α :=
    Quiver.Hom (V := Functor.{v₁, v₂, u₁, u₂} C V)
      (Functor.obj (@ι C _ V _ inst_2 inst_3 D _ _)
        (@tensorObj.{v₁, v₂, v₃, u₁, u₂, u₃} C inst V inst_1 inst_2 inst_3 _ inst_4 _ d₁ d₁'))
      (Functor.obj (@ι C _ V _ inst_2 inst_3 D _ _)
        (@tensorObj.{v₁, v₂, v₃, u₁, u₂, u₃} C inst V inst_1 inst_2 inst_3 _ inst_4 _ d₂ d₂')))
    (Iso.hom (tensorObjIsoConvolution C V d₁ d₁') ≫
      DayConvolution.map (Functor.map (@ι C _ V _ inst_2 inst_3 D _ _) f)
          (Functor.map (@ι C _ V _ inst_2 inst_3 D _ _) f') ≫
        Iso.inv (tensorObjIsoConvolution C V d₂ d₂'))
    (DayConvolution.map (Functor.map (@ι C _ V _ inst_2 inst_3 D _ _) f)
      (Functor.map (@ι C _ V _ inst_2 inst_3 D _ _) f'))
have a : Eq (α :=
  Functor.obj (C := Functor.{v₁, v₂, u₁, u₂} C V)
    (Functor.obj (Functor.whiskeringLeft (C × C) C V) (tensor C) ⋙
      Functor.obj coyoneda
        (Opposite.op
          (Functor.obj (@ι C _ V _ inst_2 inst_3 D _ _) d₁ ⊠ Functor.obj (@ι C _ V _ inst_2 inst_3 D _ _) d₁')))
    (Functor.obj (@ι C _ V _ inst_2 inst_3 D _ _)
      (@tensorObj.{v₁, v₂, v₃, u₁, u₂, u₃} C inst V inst_1 inst_2 inst_3 _ inst_4 _ d₂ d₂')))
  ((Functor.CorepresentableBy.homEquiv
          (DayConvolution.corepresentableBy (Functor.obj (@ι C _ V _ inst_2 inst_3 D _ _) d₁)
            (Functor.obj (@ι C _ V _ inst_2 inst_3 D _ _) d₁')) :
        (a : (ι C V D).obj d₁ ⊛ (ι C V D).obj d₁' ⟶ (ι C V D).obj (tensorObj C V d₂ d₂')) →
          ((Functor.whiskeringLeft (C × C) C V).obj (tensor C) ⋙
                coyoneda.obj (Opposite.op ((ι C V D).obj d₁ ⊠ (ι C V D).obj d₁'))).obj
            ((ι C V D).obj (tensorObj C V d₂ d₂')))
      (Iso.hom (tensorObjIsoConvolution C V d₁ d₁') ≫
        DayConvolution.map (Functor.map (@ι C _ V _ inst_2 inst_3 D _ _) f)
            (Functor.map (@ι C _ V _ inst_2 inst_3 D _ _) f') ≫
          Iso.inv (tensorObjIsoConvolution C V d₂ d₂')) :
    Functor.obj (C := Functor.{v₁, v₂, u₁, u₂} C V)
      (Functor.obj (Functor.whiskeringLeft (C × C) C V) (tensor C) ⋙
        Functor.obj coyoneda
          (Opposite.op
            (Functor.obj (@ι C _ V _ inst_2 inst_3 D _ _) d₁ ⊠ Functor.obj (@ι C _ V _ inst_2 inst_3 D _ _) d₁')))
      (Functor.obj (@ι C _ V _ inst_2 inst_3 D _ _)
        (@tensorObj.{v₁, v₂, v₃, u₁, u₂, u₃} C inst V inst_1 inst_2 inst_3 _ inst_4 _ d₂ d₂')))
  ((Functor.CorepresentableBy.homEquiv
          (DayConvolution.corepresentableBy (Functor.obj (@ι C _ V _ inst_2 inst_3 D _ _) d₁)
            (Functor.obj (@ι C _ V _ inst_2 inst_3 D _ _) d₁')) :
        (a : (ι C V D).obj d₁ ⊛ (ι C V D).obj d₁' ⟶ (ι C V D).obj (tensorObj C V d₂ d₂')) →
          ((Functor.whiskeringLeft (C × C) C V).obj (tensor C) ⋙
                coyoneda.obj (Opposite.op ((ι C V D).obj d₁ ⊠ (ι C V D).obj d₁'))).obj
            ((ι C V D).obj (tensorObj C V d₂ d₂')))
      (DayConvolution.map (Functor.map (@ι C _ V _ inst_2 inst_3 D _ _) f)
        (Functor.map (@ι C _ V _ inst_2 inst_3 D _ _) f')) :
    Functor.obj (C := Functor.{v₁, v₂, u₁, u₂} C V)
      (Functor.obj (Functor.whiskeringLeft (C × C) C V) (tensor C) ⋙
        Functor.obj coyoneda
          (Opposite.op
            (Functor.obj (@ι C _ V _ inst_2 inst_3 D _ _) d₁ ⊠ Functor.obj (@ι C _ V _ inst_2 inst_3 D _ _) d₁')))
      (Functor.obj (@ι C _ V _ inst_2 inst_3 D _ _)
        (@tensorObj.{v₁, v₂, v₃, u₁, u₂, u₃} C inst V inst_1 inst_2 inst_3 _ inst_4 _ d₂ d₂')))
Tactic: apply (convolutions C V d₁ d₁').corepresentableBy.homEquiv.injective