∀ {R : Type u_1} {A : Type u_2} {B : Type u_3} {C : Type u_4} [inst : CommRing R] [inst_1 : CommRing A]
  [inst_2 : CommRing B] [inst_3 : CommRing C] [inst_4 : Algebra R A] [inst_5 : Algebra R B] [inst_6 : Algebra R C]
  {f : A →ₐ[R] B} {g : B →ₐ[R] C},
  f.FinitePresentation → Function.Surjective ⇑g → (RingHom.ker g.toRingHom).FG → (g.comp f).FinitePresentation