no goals
R : Type u_2
M : Type u_1
P : Type ?u.119271
N : Type w
inst✝⁶ : Semiring R
inst✝⁵ : AddCommMonoid M
inst✝⁴ : Module R M
inst✝³ : AddCommMonoid N
inst✝² : Module R N
inst✝¹ : AddCommMonoid P
inst✝ : Module R P
⊢ (∀ (f : ℕ →o Submodule R M), ∃ n, ∀ (m : ℕ), n ≤ m → ↑f n = ↑f m) ↔ IsNoetherian R M
rw [isNoetherian_iff_wellFounded, WellFounded.monotone_chain_condition]