∀ {R : Type u_1} {M : Type u_2} {P : Type u_3} [inst : Semiring R] [inst_1 : AddCommMonoid M] [inst_2 : AddCommMonoid P]
  [inst_3 : Module R M] [inst_4 : Module R P] [IsNoetherian R P] (f : M →ₗ[R] P),
  Function.Injective ⇑f → IsNoetherian R M