-- Lean 4 proof step from Mathlib.Algebra.Category.Ring.FilteredColimits (goal)
Goal:
J : Type v
inst : SmallCategory J
F : J ⥤ SemiRingCat
inst_1 : IsFiltered J
j : J
x :
  ((F ⋙
          forget₂ SemiRingCat (FC := fun (R S : SemiRingCat) ↦ (↑R : Type (max u v)) →+* (↑S : Type (max u v))) (CC :=
            carrier) MonCat (FD := fun (x1 x2 : MonCat) ↦ (↑x1 : Type (max u v)) →* (↑x2 : Type (max u v))) (CD :=
            MonCat.carrier)) ⋙
        forget MonCat (FC := fun (x1 x2 : MonCat) ↦ (↑x1 : Type (max u v)) →* (↑x2 : Type (max u v))) (CC :=
          MonCat.carrier)).obj
    j
⊢ MonCat.FilteredColimits.M.mk
      (F ⋙
        forget₂ SemiRingCat (FC := fun (R S : SemiRingCat) ↦ (↑R : Type (max u v)) →+* (↑S : Type (max u v))) (CC :=
          carrier) MonCat (FD := fun (x1 x2 : MonCat) ↦ (↑x1 : Type (max u v)) →* (↑x2 : Type (max u v))) (CD :=
          MonCat.carrier))
      (Sigma.mk (β := fun (j : J) ↦
        (↑(Functor.obj
              (forget₂ SemiRingCat (FC := fun (R S : SemiRingCat) ↦ (↑R : Type (max u v)) →+* (↑S : Type (max u v)))
                (CC := carrier) MonCat (FD := fun (x1 x2 : MonCat) ↦ (↑x1 : Type (max u v)) →* (↑x2 : Type (max u v)))
                (CD := MonCat.carrier))
              (F.obj j)) :
          Type (max u v)))
        j (0 * x)) =
    AddMonCat.FilteredColimits.M.mk
      ((F ⋙
          forget₂ SemiRingCat (FC := fun (R S : SemiRingCat) ↦ (↑R : Type (max u v)) →+* (↑S : Type (max u v))) (CC :=
            carrier) AddCommMonCat (FD := fun (x1 x2 : AddCommMonCat) ↦
            (↑x1 : Type (max u v)) →+ (↑x2 : Type (max u v))) (CD := AddCommMonCat.carrier)) ⋙
        forget₂ AddCommMonCat (FC := fun (x1 x2 : AddCommMonCat) ↦ (↑x1 : Type (max u v)) →+ (↑x2 : Type (max u v)))
          (CC := AddCommMonCat.carrier) AddMonCat (FD := fun (x1 x2 : AddMonCat) ↦
          (↑x1 : Type (max u v)) →+ (↑x2 : Type (max u v))) (CD := AddMonCat.carrier))
      (Sigma.mk (β := fun (j : J) ↦
        (↑(Functor.obj
              (forget₂ SemiRingCat (FC := fun (R S : SemiRingCat) ↦ (↑R : Type (max u v)) →+* (↑S : Type (max u v)))
                (CC := carrier) AddCommMonCat (FD := fun (x1 x2 : AddCommMonCat) ↦
                (↑x1 : Type (max u v)) →+ (↑x2 : Type (max u v))) (CD := AddCommMonCat.carrier))
              (F.obj j)) :
          Type (max u v)))
        j 0)
have rw : MonCat.FilteredColimits.M.mk
    (F ⋙
      forget₂ SemiRingCat (FC := fun (R S : SemiRingCat) ↦ (↑R : Type (max u v)) →+* (↑S : Type (max u v))) (CC :=
        carrier) MonCat (FD := fun (x1 x2 : MonCat) ↦ (↑x1 : Type (max u v)) →* (↑x2 : Type (max u v))) (CD :=
        MonCat.carrier))
    (Sigma.mk (β := fun (j : J) ↦
      (↑(Functor.obj
            (forget₂ SemiRingCat (FC := fun (R S : SemiRingCat) ↦ (↑R : Type (max u v)) →+* (↑S : Type (max u v)))
              (CC := carrier) MonCat (FD := fun (x1 x2 : MonCat) ↦ (↑x1 : Type (max u v)) →* (↑x2 : Type (max u v)))
              (CD := MonCat.carrier))
            (F.obj j)) :
        Type (max u v)))
      j 0) =
  AddMonCat.FilteredColimits.M.mk
    ((F ⋙
        forget₂ SemiRingCat (FC := fun (R S : SemiRingCat) ↦ (↑R : Type (max u v)) →+* (↑S : Type (max u v))) (CC :=
          carrier) AddCommMonCat (FD := fun (x1 x2 : AddCommMonCat) ↦ (↑x1 : Type (max u v)) →+ (↑x2 : Type (max u v)))
          (CD := AddCommMonCat.carrier)) ⋙
      forget₂ AddCommMonCat (FC := fun (x1 x2 : AddCommMonCat) ↦ (↑x1 : Type (max u v)) →+ (↑x2 : Type (max u v)))
        (CC := AddCommMonCat.carrier) AddMonCat (FD := fun (x1 x2 : AddMonCat) ↦
        (↑x1 : Type (max u v)) →+ (↑x2 : Type (max u v))) (CD := AddMonCat.carrier))
    (Sigma.mk (β := fun (j : J) ↦
      (↑(Functor.obj
            (forget₂ SemiRingCat (FC := fun (R S : SemiRingCat) ↦ (↑R : Type (max u v)) →+* (↑S : Type (max u v)))
              (CC := carrier) AddCommMonCat (FD := fun (x1 x2 : AddCommMonCat) ↦
              (↑x1 : Type (max u v)) →+ (↑x2 : Type (max u v))) (CD := AddCommMonCat.carrier))
            (F.obj j)) :
        Type (max u v)))
      j 0)
Tactic: rw [zero_mul x]