ring_theory.artinian ⟷ Mathlib.RingTheory.Artinian

mathlib commit https://github.com/leanprover-community/mathlib/commit/65a1391a0106c9204fe45bc73a039f056558cb83

@@ -515,7 +515,8 @@ theorem isNilpotent_jacobson_bot : IsNilpotent (Ideal.jacobson (⊥ : Ideal R))
     exact lt_of_le_of_ne le_sup_left fun h => H <| h.symm ▸ le_sup_right
   have : Ideal.span {x} * Jac ^ (n + 1) ≤ ⊥
   calc
-    Ideal.span {x} * Jac ^ (n + 1) = Ideal.span {x} * Jac * Jac ^ n := by rw [pow_succ, ← mul_assoc]
+    Ideal.span {x} * Jac ^ (n + 1) = Ideal.span {x} * Jac * Jac ^ n := by
+      rw [pow_succ', ← mul_assoc]
     _ ≤ J * Jac ^ n := (mul_le_mul (by rwa [mul_comm]) le_rfl)
     _ = ⊥ := by simp [J]
   refine' hxJ (mem_annihilator.2 fun y hy => (mem_bot R).1 _)
@@ -538,7 +539,7 @@ theorem localization_surjective : Function.Surjective (algebraMap R L) :=
   swap; · exact ⟨r₁ * r₂, by rw [IsLocalization.mk'_eq_mul_mk'_one, map_mul, h]⟩
   obtain ⟨n, r, hr⟩ := IsArtinian.exists_pow_succ_smul_dvd (s : R) (1 : R)
   use r
-  rw [smul_eq_mul, smul_eq_mul, pow_succ', mul_assoc] at hr
+  rw [smul_eq_mul, smul_eq_mul, pow_succ, mul_assoc] at hr
   apply_fun algebraMap R L at hr
   simp only [map_mul, ← Submonoid.coe_pow] at hr
   rw [← IsLocalization.mk'_one L, IsLocalization.mk'_eq_iff_eq, mul_one, Submonoid.coe_one, ←

mathlib commit https://github.com/leanprover-community/mathlib/commit/65a1391a0106c9204fe45bc73a039f056558cb83

@@ -254,7 +254,7 @@ theorem eventually_codisjoint_ker_pow_range_pow (f : M →ₗ[R] M) :
   obtain ⟨n, w⟩ :=
     monotone_stabilizes (f.iterate_range.comp ⟨fun n => n + 1, fun n m w => by linarith⟩)
   specialize w (n + 1 + n) (by linarith)
-  dsimp at w 
+  dsimp at w
   refine' ⟨n + 1, Nat.succ_ne_zero _, _⟩
   simp_rw [eq_top_iff', mem_sup]
   intro x
@@ -275,7 +275,7 @@ theorem surjective_of_injective_endomorphism (f : M →ₗ[R] M) (s : Injective
   by
   obtain ⟨n, ne, w⟩ := exists_endomorphism_iterate_ker_sup_range_eq_top f
   rw [linear_map.ker_eq_bot.mpr (LinearMap.iterate_injective s n), bot_sup_eq,
-    LinearMap.range_eq_top] at w 
+    LinearMap.range_eq_top] at w
   exact LinearMap.surjective_of_iterate_surjective Ne w
 #align is_artinian.surjective_of_injective_endomorphism IsArtinian.surjective_of_injective_endomorphism
 -/
@@ -338,7 +338,7 @@ variable {M}
 theorem exists_pow_succ_smul_dvd (r : R) (x : M) : ∃ (n : ℕ) (y : M), r ^ n.succ • y = r ^ n • x :=
   by
   obtain ⟨n, hn⟩ := IsArtinian.range_smul_pow_stabilizes M r
-  simp_rw [SetLike.ext_iff] at hn 
+  simp_rw [SetLike.ext_iff] at hn
   exact ⟨n, by simpa using hn n.succ n.le_succ (r ^ n • x)⟩
 #align is_artinian.exists_pow_succ_smul_dvd IsArtinian.exists_pow_succ_smul_dvd
 -/
@@ -431,8 +431,8 @@ theorem isArtinian_of_fg_of_artinian {R M} [Ring R] [AddCommGroup M] [Module R M
       change ∑ i in s.attach, (c • f i) • _ = _
       simp only [smul_eq_mul, mul_smul]
       exact finset.smul_sum.symm
-  rintro ⟨n, hn⟩; change n ∈ N at hn 
-  rw [← hs, ← Set.image_id ↑s, Finsupp.mem_span_image_iff_total] at hn 
+  rintro ⟨n, hn⟩; change n ∈ N at hn
+  rw [← hs, ← Set.image_id ↑s, Finsupp.mem_span_image_iff_total] at hn
   rcases hn with ⟨l, hl1, hl2⟩
   refine' ⟨fun x => l x, Subtype.ext _⟩
   change ∑ i in s.attach, l i • (i : M) = n
@@ -492,7 +492,7 @@ theorem isNilpotent_jacobson_bot : IsNilpotent (Ideal.jacobson (⊥ : Ideal R))
   suffices J = ⊤ by
     have hJ : J • Jac ^ n = ⊥ := annihilator_smul (Jac ^ n)
     simpa only [this, top_smul, Ideal.zero_eq_bot] using hJ
-  by_contra hJ; change J ≠ ⊤ at hJ 
+  by_contra hJ; change J ≠ ⊤ at hJ
   rcases IsArtinian.set_has_minimal {J' : Ideal R | J < J'} ⟨⊤, hJ.lt_top⟩ with
     ⟨J', hJJ' : J < J', hJ' : ∀ I, J < I → ¬I < J'⟩
   rcases SetLike.exists_of_lt hJJ' with ⟨x, hxJ', hxJ⟩
@@ -538,9 +538,9 @@ theorem localization_surjective : Function.Surjective (algebraMap R L) :=
   swap; · exact ⟨r₁ * r₂, by rw [IsLocalization.mk'_eq_mul_mk'_one, map_mul, h]⟩
   obtain ⟨n, r, hr⟩ := IsArtinian.exists_pow_succ_smul_dvd (s : R) (1 : R)
   use r
-  rw [smul_eq_mul, smul_eq_mul, pow_succ', mul_assoc] at hr 
-  apply_fun algebraMap R L at hr 
-  simp only [map_mul, ← Submonoid.coe_pow] at hr 
+  rw [smul_eq_mul, smul_eq_mul, pow_succ', mul_assoc] at hr
+  apply_fun algebraMap R L at hr
+  simp only [map_mul, ← Submonoid.coe_pow] at hr
   rw [← IsLocalization.mk'_one L, IsLocalization.mk'_eq_iff_eq, mul_one, Submonoid.coe_one, ←
     (IsLocalization.map_units L (s ^ n)).hMul_left_cancel hr, map_mul]
 #align is_artinian_ring.localization_surjective IsArtinianRing.localization_surjective

mathlib commit https://github.com/leanprover-community/mathlib/commit/65a1391a0106c9204fe45bc73a039f056558cb83

@@ -47,7 +47,7 @@ open Set
 open scoped BigOperators Pointwise
 
 #print IsArtinian /-
-/- ./././Mathport/Syntax/Translate/Command.lean:404:30: infer kinds are unsupported in Lean 4: #[`wellFounded_submodule_lt] [] -/
+/- ./././Mathport/Syntax/Translate/Command.lean:400:30: infer kinds are unsupported in Lean 4: #[`wellFounded_submodule_lt] [] -/
 /-- `is_artinian R M` is the proposition that `M` is an Artinian `R`-module,
 implemented as the well-foundedness of submodule inclusion.
 -/

mathlib commit https://github.com/leanprover-community/mathlib/commit/65a1391a0106c9204fe45bc73a039f056558cb83

@@ -504,8 +504,15 @@ theorem isNilpotent_jacobson_bot : IsNilpotent (Ideal.jacobson (⊥ : Ideal R))
       exact ⟨le_sup_left, ⟨x, mem_sup_right (mem_span_singleton_self x), hxJ⟩⟩
   have : J ⊔ Jac • Ideal.span {x} ≤ J ⊔ Ideal.span {x} :=
     sup_le_sup_left (smul_le.2 fun _ _ _ => Submodule.smul_mem _ _) _
-  have : Jac * Ideal.span {x} ≤ J := by classical
-  --Need version 4 of Nakayamas lemma on Stacks
+  have : Jac * Ideal.span {x} ≤ J := by
+    classical
+    --Need version 4 of Nakayamas lemma on Stacks
+    by_contra H
+    refine'
+      H
+        (smul_sup_le_of_le_smul_of_le_jacobson_bot (fg_span_singleton _) le_rfl
+          (this.eq_of_not_lt (hJ' _ _)).ge)
+    exact lt_of_le_of_ne le_sup_left fun h => H <| h.symm ▸ le_sup_right
   have : Ideal.span {x} * Jac ^ (n + 1) ≤ ⊥
   calc
     Ideal.span {x} * Jac ^ (n + 1) = Ideal.span {x} * Jac * Jac ^ n := by rw [pow_succ, ← mul_assoc]

mathlib commit https://github.com/leanprover-community/mathlib/commit/65a1391a0106c9204fe45bc73a039f056558cb83

@@ -504,15 +504,8 @@ theorem isNilpotent_jacobson_bot : IsNilpotent (Ideal.jacobson (⊥ : Ideal R))
       exact ⟨le_sup_left, ⟨x, mem_sup_right (mem_span_singleton_self x), hxJ⟩⟩
   have : J ⊔ Jac • Ideal.span {x} ≤ J ⊔ Ideal.span {x} :=
     sup_le_sup_left (smul_le.2 fun _ _ _ => Submodule.smul_mem _ _) _
-  have : Jac * Ideal.span {x} ≤ J := by
-    classical
-    --Need version 4 of Nakayamas lemma on Stacks
-    by_contra H
-    refine'
-      H
-        (smul_sup_le_of_le_smul_of_le_jacobson_bot (fg_span_singleton _) le_rfl
-          (this.eq_of_not_lt (hJ' _ _)).ge)
-    exact lt_of_le_of_ne le_sup_left fun h => H <| h.symm ▸ le_sup_right
+  have : Jac * Ideal.span {x} ≤ J := by classical
+  --Need version 4 of Nakayamas lemma on Stacks
   have : Ideal.span {x} * Jac ^ (n + 1) ≤ ⊥
   calc
     Ideal.span {x} * Jac ^ (n + 1) = Ideal.span {x} * Jac * Jac ^ n := by rw [pow_succ, ← mul_assoc]

mathlib commit https://github.com/leanprover-community/mathlib/commit/65a1391a0106c9204fe45bc73a039f056558cb83

@@ -47,7 +47,7 @@ open Set
 open scoped BigOperators Pointwise
 
 #print IsArtinian /-
-/- ./././Mathport/Syntax/Translate/Command.lean:394:30: infer kinds are unsupported in Lean 4: #[`wellFounded_submodule_lt] [] -/
+/- ./././Mathport/Syntax/Translate/Command.lean:404:30: infer kinds are unsupported in Lean 4: #[`wellFounded_submodule_lt] [] -/
 /-- `is_artinian R M` is the proposition that `M` is an Artinian `R`-module,
 implemented as the well-foundedness of submodule inclusion.
 -/

mathlib commit https://github.com/leanprover-community/mathlib/commit/65a1391a0106c9204fe45bc73a039f056558cb83

@@ -83,7 +83,7 @@ instance isArtinian_submodule' [IsArtinian R M] (N : Submodule R M) : IsArtinian
 
 #print isArtinian_of_le /-
 theorem isArtinian_of_le {s t : Submodule R M} [ht : IsArtinian R t] (h : s ≤ t) : IsArtinian R s :=
-  isArtinian_of_injective (Submodule.ofLe h) (Submodule.ofLe_injective h)
+  isArtinian_of_injective (Submodule.inclusion h) (Submodule.inclusion_injective h)
 #align is_artinian_of_le isArtinian_of_le
 -/
 

mathlib commit https://github.com/leanprover-community/mathlib/commit/19c869efa56bbb8b500f2724c0b77261edbfa28c

@@ -244,11 +244,11 @@ theorem induction {P : Submodule R M → Prop} (hgt : ∀ I, (∀ J < I, P J) 
 #align is_artinian.induction IsArtinian.induction
 -/
 
-#print IsArtinian.exists_endomorphism_iterate_ker_sup_range_eq_top /-
+#print LinearMap.eventually_codisjoint_ker_pow_range_pow /-
 /-- For any endomorphism of a Artinian module, there is some nontrivial iterate
 with disjoint kernel and range.
 -/
-theorem exists_endomorphism_iterate_ker_sup_range_eq_top (f : M →ₗ[R] M) :
+theorem eventually_codisjoint_ker_pow_range_pow (f : M →ₗ[R] M) :
     ∃ n : ℕ, n ≠ 0 ∧ (f ^ n).ker ⊔ (f ^ n).range = ⊤ :=
   by
   obtain ⟨n, w⟩ :=
@@ -266,7 +266,7 @@ theorem exists_endomorphism_iterate_ker_sup_range_eq_top (f : M →ₗ[R] M) :
     simp [iterate_add_apply]
   · use(f ^ (n + 1)) y
     simp
-#align is_artinian.exists_endomorphism_iterate_ker_sup_range_eq_top IsArtinian.exists_endomorphism_iterate_ker_sup_range_eq_top
+#align is_artinian.exists_endomorphism_iterate_ker_sup_range_eq_top LinearMap.eventually_codisjoint_ker_pow_range_pow
 -/
 
 #print IsArtinian.surjective_of_injective_endomorphism /-

mathlib commit https://github.com/leanprover-community/mathlib/commit/ce64cd319bb6b3e82f31c2d38e79080d377be451

@@ -3,8 +3,8 @@ Copyright (c) 2021 Chris Hughes. All rights reserved.
 Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Chris Hughes
 -/
-import Mathbin.RingTheory.Nakayama
-import Mathbin.Data.SetLike.Fintype
+import RingTheory.Nakayama
+import Data.SetLike.Fintype
 
 #align_import ring_theory.artinian from "leanprover-community/mathlib"@"38df578a6450a8c5142b3727e3ae894c2300cae0"
 
@@ -47,7 +47,7 @@ open Set
 open scoped BigOperators Pointwise
 
 #print IsArtinian /-
-/- ./././Mathport/Syntax/Translate/Command.lean:393:30: infer kinds are unsupported in Lean 4: #[`wellFounded_submodule_lt] [] -/
+/- ./././Mathport/Syntax/Translate/Command.lean:394:30: infer kinds are unsupported in Lean 4: #[`wellFounded_submodule_lt] [] -/
 /-- `is_artinian R M` is the proposition that `M` is an Artinian `R`-module,
 implemented as the well-foundedness of submodule inclusion.
 -/

mathlib commit https://github.com/leanprover-community/mathlib/commit/32a7e535287f9c73f2e4d2aef306a39190f0b504

@@ -542,7 +542,7 @@ theorem localization_surjective : Function.Surjective (algebraMap R L) :=
   apply_fun algebraMap R L at hr 
   simp only [map_mul, ← Submonoid.coe_pow] at hr 
   rw [← IsLocalization.mk'_one L, IsLocalization.mk'_eq_iff_eq, mul_one, Submonoid.coe_one, ←
-    (IsLocalization.map_units L (s ^ n)).mul_left_cancel hr, map_mul]
+    (IsLocalization.map_units L (s ^ n)).hMul_left_cancel hr, map_mul]
 #align is_artinian_ring.localization_surjective IsArtinianRing.localization_surjective
 -/
 

mathlib commit https://github.com/leanprover-community/mathlib/commit/63721b2c3eba6c325ecf8ae8cca27155a4f6306f

@@ -264,7 +264,7 @@ theorem exists_endomorphism_iterate_ker_sup_range_eq_top (f : M →ₗ[R] M) :
   constructor
   · rw [LinearMap.mem_ker, LinearMap.map_sub, ← hy, sub_eq_zero, pow_add]
     simp [iterate_add_apply]
-  · use (f ^ (n + 1)) y
+  · use(f ^ (n + 1)) y
     simp
 #align is_artinian.exists_endomorphism_iterate_ker_sup_range_eq_top IsArtinian.exists_endomorphism_iterate_ker_sup_range_eq_top
 -/

mathlib commit https://github.com/leanprover-community/mathlib/commit/8ea5598db6caeddde6cb734aa179cc2408dbd345

@@ -2,15 +2,12 @@
 Copyright (c) 2021 Chris Hughes. All rights reserved.
 Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Chris Hughes
-
-! This file was ported from Lean 3 source module ring_theory.artinian
-! leanprover-community/mathlib commit 38df578a6450a8c5142b3727e3ae894c2300cae0
-! Please do not edit these lines, except to modify the commit id
-! if you have ported upstream changes.
 -/
 import Mathbin.RingTheory.Nakayama
 import Mathbin.Data.SetLike.Fintype
 
+#align_import ring_theory.artinian from "leanprover-community/mathlib"@"38df578a6450a8c5142b3727e3ae894c2300cae0"
+
 /-!
 # Artinian rings and modules
 

mathlib commit https://github.com/leanprover-community/mathlib/commit/9fb8964792b4237dac6200193a0d533f1b3f7423

@@ -50,7 +50,7 @@ open Set
 open scoped BigOperators Pointwise
 
 #print IsArtinian /-
-/- ./././Mathport/Syntax/Translate/Command.lean:394:30: infer kinds are unsupported in Lean 4: #[`wellFounded_submodule_lt] [] -/
+/- ./././Mathport/Syntax/Translate/Command.lean:393:30: infer kinds are unsupported in Lean 4: #[`wellFounded_submodule_lt] [] -/
 /-- `is_artinian R M` is the proposition that `M` is an Artinian `R`-module,
 implemented as the well-foundedness of submodule inclusion.
 -/
@@ -69,14 +69,14 @@ variable [Module R M] [Module R P] [Module R N]
 
 open IsArtinian
 
-include R
-
+#print isArtinian_of_injective /-
 theorem isArtinian_of_injective (f : M →ₗ[R] P) (h : Function.Injective f) [IsArtinian R P] :
     IsArtinian R M :=
   ⟨Subrelation.wf
       (fun A B hAB => show A.map f < B.map f from Submodule.map_strictMono_of_injective h hAB)
       (InvImage.wf (Submodule.map f) (IsArtinian.wellFounded_submodule_lt R P))⟩
 #align is_artinian_of_injective isArtinian_of_injective
+-/
 
 #print isArtinian_submodule' /-
 instance isArtinian_submodule' [IsArtinian R M] (N : Submodule R M) : IsArtinian R N :=
@@ -84,12 +84,15 @@ instance isArtinian_submodule' [IsArtinian R M] (N : Submodule R M) : IsArtinian
 #align is_artinian_submodule' isArtinian_submodule'
 -/
 
+#print isArtinian_of_le /-
 theorem isArtinian_of_le {s t : Submodule R M} [ht : IsArtinian R t] (h : s ≤ t) : IsArtinian R s :=
   isArtinian_of_injective (Submodule.ofLe h) (Submodule.ofLe_injective h)
 #align is_artinian_of_le isArtinian_of_le
+-/
 
 variable (M)
 
+#print isArtinian_of_surjective /-
 theorem isArtinian_of_surjective (f : M →ₗ[R] P) (hf : Function.Surjective f) [IsArtinian R M] :
     IsArtinian R P :=
   ⟨Subrelation.wf
@@ -97,13 +100,17 @@ theorem isArtinian_of_surjective (f : M →ₗ[R] P) (hf : Function.Surjective f
         show A.comap f < B.comap f from Submodule.comap_strictMono_of_surjective hf hAB)
       (InvImage.wf (Submodule.comap f) (IsArtinian.wellFounded_submodule_lt _ _))⟩
 #align is_artinian_of_surjective isArtinian_of_surjective
+-/
 
 variable {M}
 
+#print isArtinian_of_linearEquiv /-
 theorem isArtinian_of_linearEquiv (f : M ≃ₗ[R] P) [IsArtinian R M] : IsArtinian R P :=
   isArtinian_of_surjective _ f.toLinearMap f.toEquiv.Surjective
 #align is_artinian_of_linear_equiv isArtinian_of_linearEquiv
+-/
 
+#print isArtinian_of_range_eq_ker /-
 theorem isArtinian_of_range_eq_ker [IsArtinian R M] [IsArtinian R P] (f : M →ₗ[R] N) (g : N →ₗ[R] P)
     (hf : Function.Injective f) (hg : Function.Surjective g) (h : f.range = g.ker) :
     IsArtinian R N :=
@@ -112,11 +119,14 @@ theorem isArtinian_of_range_eq_ker [IsArtinian R M] [IsArtinian R P] (f : M →
       (Submodule.comap g) (Submodule.map g) (Submodule.gciMapComap hf) (Submodule.giMapComap hg)
       (by simp [Submodule.map_comap_eq, inf_comm]) (by simp [Submodule.comap_map_eq, h])⟩
 #align is_artinian_of_range_eq_ker isArtinian_of_range_eq_ker
+-/
 
+#print isArtinian_prod /-
 instance isArtinian_prod [IsArtinian R M] [IsArtinian R P] : IsArtinian R (M × P) :=
   isArtinian_of_range_eq_ker (LinearMap.inl R M P) (LinearMap.snd R M P) LinearMap.inl_injective
     LinearMap.snd_surjective (LinearMap.range_inl R M P)
 #align is_artinian_prod isArtinian_prod
+-/
 
 #print isArtinian_of_finite /-
 instance (priority := 100) isArtinian_of_finite [Finite M] : IsArtinian R M :=
@@ -160,13 +170,16 @@ section Ring
 
 variable {R M : Type _} [Ring R] [AddCommGroup M] [Module R M]
 
+#print isArtinian_iff_wellFounded /-
 theorem isArtinian_iff_wellFounded :
     IsArtinian R M ↔ WellFounded ((· < ·) : Submodule R M → Submodule R M → Prop) :=
   ⟨fun h => h.1, IsArtinian.mk⟩
 #align is_artinian_iff_well_founded isArtinian_iff_wellFounded
+-/
 
 variable {R M}
 
+#print IsArtinian.finite_of_linearIndependent /-
 theorem IsArtinian.finite_of_linearIndependent [Nontrivial R] [IsArtinian R M] {s : Set M}
     (hs : LinearIndependent R (coe : s → M)) : s.Finite :=
   by
@@ -190,39 +203,51 @@ theorem IsArtinian.finite_of_linearIndependent [Nontrivial R] [IsArtinian R M] {
       conv_rhs => rw [GT.gt, lt_iff_le_not_le, this, this, ← lt_iff_le_not_le]
       simp⟩
 #align is_artinian.finite_of_linear_independent IsArtinian.finite_of_linearIndependent
+-/
 
+#print set_has_minimal_iff_artinian /-
 /-- A module is Artinian iff every nonempty set of submodules has a minimal submodule among them.
 -/
 theorem set_has_minimal_iff_artinian :
     (∀ a : Set <| Submodule R M, a.Nonempty → ∃ M' ∈ a, ∀ I ∈ a, ¬I < M') ↔ IsArtinian R M := by
   rw [isArtinian_iff_wellFounded, WellFounded.wellFounded_iff_has_min]
 #align set_has_minimal_iff_artinian set_has_minimal_iff_artinian
+-/
 
+#print IsArtinian.set_has_minimal /-
 theorem IsArtinian.set_has_minimal [IsArtinian R M] (a : Set <| Submodule R M) (ha : a.Nonempty) :
     ∃ M' ∈ a, ∀ I ∈ a, ¬I < M' :=
   set_has_minimal_iff_artinian.mpr ‹_› a ha
 #align is_artinian.set_has_minimal IsArtinian.set_has_minimal
+-/
 
+#print monotone_stabilizes_iff_artinian /-
 /-- A module is Artinian iff every decreasing chain of submodules stabilizes. -/
 theorem monotone_stabilizes_iff_artinian :
     (∀ f : ℕ →o (Submodule R M)ᵒᵈ, ∃ n, ∀ m, n ≤ m → f n = f m) ↔ IsArtinian R M := by
   rw [isArtinian_iff_wellFounded]; exact well_founded.monotone_chain_condition.symm
 #align monotone_stabilizes_iff_artinian monotone_stabilizes_iff_artinian
+-/
 
 namespace IsArtinian
 
 variable [IsArtinian R M]
 
+#print IsArtinian.monotone_stabilizes /-
 theorem monotone_stabilizes (f : ℕ →o (Submodule R M)ᵒᵈ) : ∃ n, ∀ m, n ≤ m → f n = f m :=
   monotone_stabilizes_iff_artinian.mpr ‹_› f
 #align is_artinian.monotone_stabilizes IsArtinian.monotone_stabilizes
+-/
 
+#print IsArtinian.induction /-
 /-- If `∀ I > J, P I` implies `P J`, then `P` holds for all submodules. -/
 theorem induction {P : Submodule R M → Prop} (hgt : ∀ I, (∀ J < I, P J) → P I) (I : Submodule R M) :
     P I :=
   (wellFounded_submodule_lt R M).recursion I hgt
 #align is_artinian.induction IsArtinian.induction
+-/
 
+#print IsArtinian.exists_endomorphism_iterate_ker_sup_range_eq_top /-
 /-- For any endomorphism of a Artinian module, there is some nontrivial iterate
 with disjoint kernel and range.
 -/
@@ -245,7 +270,9 @@ theorem exists_endomorphism_iterate_ker_sup_range_eq_top (f : M →ₗ[R] M) :
   · use (f ^ (n + 1)) y
     simp
 #align is_artinian.exists_endomorphism_iterate_ker_sup_range_eq_top IsArtinian.exists_endomorphism_iterate_ker_sup_range_eq_top
+-/
 
+#print IsArtinian.surjective_of_injective_endomorphism /-
 /-- Any injective endomorphism of an Artinian module is surjective. -/
 theorem surjective_of_injective_endomorphism (f : M →ₗ[R] M) (s : Injective f) : Surjective f :=
   by
@@ -254,12 +281,16 @@ theorem surjective_of_injective_endomorphism (f : M →ₗ[R] M) (s : Injective
     LinearMap.range_eq_top] at w 
   exact LinearMap.surjective_of_iterate_surjective Ne w
 #align is_artinian.surjective_of_injective_endomorphism IsArtinian.surjective_of_injective_endomorphism
+-/
 
+#print IsArtinian.bijective_of_injective_endomorphism /-
 /-- Any injective endomorphism of an Artinian module is bijective. -/
 theorem bijective_of_injective_endomorphism (f : M →ₗ[R] M) (s : Injective f) : Bijective f :=
   ⟨s, surjective_of_injective_endomorphism f s⟩
 #align is_artinian.bijective_of_injective_endomorphism IsArtinian.bijective_of_injective_endomorphism
+-/
 
+#print IsArtinian.disjoint_partial_infs_eventually_top /-
 /-- A sequence `f` of submodules of a artinian module,
 with the supremum `f (n+1)` and the infinum of `f 0`, ..., `f n` being ⊤,
 is eventually ⊤.
@@ -279,6 +310,7 @@ theorem disjoint_partial_infs_eventually_top (f : ℕ → Submodule R M)
   refine' ⟨n, fun m p => _⟩
   exact (h m).eq_bot_of_ge (sup_eq_left.1 <| (w (m + 1) <| le_add_right p).symm.trans <| w m p)
 #align is_artinian.disjoint_partial_infs_eventually_top IsArtinian.disjoint_partial_infs_eventually_top
+-/
 
 end IsArtinian
 
@@ -305,12 +337,14 @@ theorem range_smul_pow_stabilizes (r : R) :
 
 variable {M}
 
+#print IsArtinian.exists_pow_succ_smul_dvd /-
 theorem exists_pow_succ_smul_dvd (r : R) (x : M) : ∃ (n : ℕ) (y : M), r ^ n.succ • y = r ^ n • x :=
   by
   obtain ⟨n, hn⟩ := IsArtinian.range_smul_pow_stabilizes M r
   simp_rw [SetLike.ext_iff] at hn 
   exact ⟨n, by simpa using hn n.succ n.le_succ (r ^ n • x)⟩
 #align is_artinian.exists_pow_succ_smul_dvd IsArtinian.exists_pow_succ_smul_dvd
+-/
 
 end IsArtinian
 
@@ -351,20 +385,27 @@ theorem isArtinianRing_iff {R} [Ring R] : IsArtinianRing R ↔ IsArtinian R R :=
 #align is_artinian_ring_iff isArtinianRing_iff
 -/
 
+#print Ring.isArtinian_of_zero_eq_one /-
 theorem Ring.isArtinian_of_zero_eq_one {R} [Ring R] (h01 : (0 : R) = 1) : IsArtinianRing R :=
   have := subsingleton_of_zero_eq_one h01
   inferInstance
 #align ring.is_artinian_of_zero_eq_one Ring.isArtinian_of_zero_eq_one
+-/
 
+#print isArtinian_of_submodule_of_artinian /-
 theorem isArtinian_of_submodule_of_artinian (R M) [Ring R] [AddCommGroup M] [Module R M]
     (N : Submodule R M) (h : IsArtinian R M) : IsArtinian R N := by infer_instance
 #align is_artinian_of_submodule_of_artinian isArtinian_of_submodule_of_artinian
+-/
 
+#print isArtinian_of_quotient_of_artinian /-
 theorem isArtinian_of_quotient_of_artinian (R) [Ring R] (M) [AddCommGroup M] [Module R M]
     (N : Submodule R M) (h : IsArtinian R M) : IsArtinian R (M ⧸ N) :=
   isArtinian_of_surjective M (Submodule.mkQ N) (Submodule.Quotient.mk_surjective N)
 #align is_artinian_of_quotient_of_artinian isArtinian_of_quotient_of_artinian
+-/
 
+#print isArtinian_of_tower /-
 /-- If `M / S / R` is a scalar tower, and `M / R` is Artinian, then `M / S` is
 also Artinian. -/
 theorem isArtinian_of_tower (R) {S M} [CommRing R] [Ring S] [AddCommGroup M] [Algebra R S]
@@ -373,7 +414,9 @@ theorem isArtinian_of_tower (R) {S M} [CommRing R] [Ring S] [AddCommGroup M] [Al
   rw [isArtinian_iff_wellFounded] at h ⊢
   refine' (Submodule.restrictScalarsEmbedding R S M).WellFounded h
 #align is_artinian_of_tower isArtinian_of_tower
+-/
 
+#print isArtinian_of_fg_of_artinian /-
 theorem isArtinian_of_fg_of_artinian {R M} [Ring R] [AddCommGroup M] [Module R M]
     (N : Submodule R M) [IsArtinianRing R] (hN : N.FG) : IsArtinian R N :=
   by
@@ -400,31 +443,40 @@ theorem isArtinian_of_fg_of_artinian {R M} [Ring R] [AddCommGroup M] [Module R M
   refine' Finset.sum_subset hl1 fun x _ hx => _
   rw [Finsupp.not_mem_support_iff.1 hx, zero_smul]
 #align is_artinian_of_fg_of_artinian isArtinian_of_fg_of_artinian
+-/
 
+#print isArtinian_of_fg_of_artinian' /-
 theorem isArtinian_of_fg_of_artinian' {R M} [Ring R] [AddCommGroup M] [Module R M]
     [IsArtinianRing R] (h : (⊤ : Submodule R M).FG) : IsArtinian R M :=
   have : IsArtinian R (⊤ : Submodule R M) := isArtinian_of_fg_of_artinian _ h
   isArtinian_of_linearEquiv (LinearEquiv.ofTop (⊤ : Submodule R M) rfl)
 #align is_artinian_of_fg_of_artinian' isArtinian_of_fg_of_artinian'
+-/
 
+#print isArtinian_span_of_finite /-
 /-- In a module over a artinian ring, the submodule generated by finitely many vectors is
 artinian. -/
 theorem isArtinian_span_of_finite (R) {M} [Ring R] [AddCommGroup M] [Module R M] [IsArtinianRing R]
     {A : Set M} (hA : A.Finite) : IsArtinian R (Submodule.span R A) :=
   isArtinian_of_fg_of_artinian _ (Submodule.fg_def.mpr ⟨A, hA, rfl⟩)
 #align is_artinian_span_of_finite isArtinian_span_of_finite
+-/
 
+#print Function.Surjective.isArtinianRing /-
 theorem Function.Surjective.isArtinianRing {R} [Ring R] {S} [Ring S] {F} [RingHomClass F R S]
     {f : F} (hf : Function.Surjective f) [H : IsArtinianRing R] : IsArtinianRing S :=
   by
   rw [isArtinianRing_iff, isArtinian_iff_wellFounded] at H ⊢
   exact (Ideal.orderEmbeddingOfSurjective f hf).WellFounded H
 #align function.surjective.is_artinian_ring Function.Surjective.isArtinianRing
+-/
 
+#print isArtinianRing_range /-
 instance isArtinianRing_range {R} [Ring R] {S} [Ring S] (f : R →+* S) [IsArtinianRing R] :
     IsArtinianRing f.range :=
   f.rangeRestrict_surjective.IsArtinianRing
 #align is_artinian_ring_range isArtinianRing_range
+-/
 
 namespace IsArtinianRing
 
@@ -432,6 +484,7 @@ open IsArtinian
 
 variable {R : Type _} [CommRing R] [IsArtinianRing R]
 
+#print IsArtinianRing.isNilpotent_jacobson_bot /-
 theorem isNilpotent_jacobson_bot : IsNilpotent (Ideal.jacobson (⊥ : Ideal R)) :=
   by
   let Jac := Ideal.jacobson (⊥ : Ideal R)
@@ -472,13 +525,13 @@ theorem isNilpotent_jacobson_bot : IsNilpotent (Ideal.jacobson (⊥ : Ideal R))
   refine' this (mul_mem_mul (mem_span_singleton_self x) _)
   rwa [← hn (n + 1) (Nat.le_succ _)]
 #align is_artinian_ring.is_nilpotent_jacobson_bot IsArtinianRing.isNilpotent_jacobson_bot
+-/
 
 section Localization
 
 variable (S : Submonoid R) (L : Type _) [CommRing L] [Algebra R L] [IsLocalization S L]
 
-include S
-
+#print IsArtinianRing.localization_surjective /-
 /-- Localizing an artinian ring can only reduce the amount of elements. -/
 theorem localization_surjective : Function.Surjective (algebraMap R L) :=
   by
@@ -494,10 +547,13 @@ theorem localization_surjective : Function.Surjective (algebraMap R L) :=
   rw [← IsLocalization.mk'_one L, IsLocalization.mk'_eq_iff_eq, mul_one, Submonoid.coe_one, ←
     (IsLocalization.map_units L (s ^ n)).mul_left_cancel hr, map_mul]
 #align is_artinian_ring.localization_surjective IsArtinianRing.localization_surjective
+-/
 
+#print IsArtinianRing.localization_artinian /-
 theorem localization_artinian : IsArtinianRing L :=
   (localization_surjective S L).IsArtinianRing
 #align is_artinian_ring.localization_artinian IsArtinianRing.localization_artinian
+-/
 
 /-- `is_artinian_ring.localization_artinian` can't be made an instance, as it would make `S` + `R`
 into metavariables. However, this is safe. -/

mathlib commit https://github.com/leanprover-community/mathlib/commit/a3e83f0fa4391c8740f7d773a7a9b74e311ae2a3

@@ -385,17 +385,17 @@ theorem isArtinian_of_fg_of_artinian {R M} [Ring R] [AddCommGroup M] [Module R M
   · fapply LinearMap.mk
     · exact fun f => ⟨∑ i in s.attach, f i • i.1, N.sum_mem fun c _ => N.smul_mem _ <| this _ c.2⟩
     · intro f g; apply Subtype.eq
-      change (∑ i in s.attach, (f i + g i) • _) = _
+      change ∑ i in s.attach, (f i + g i) • _ = _
       simp only [add_smul, Finset.sum_add_distrib]; rfl
     · intro c f; apply Subtype.eq
-      change (∑ i in s.attach, (c • f i) • _) = _
+      change ∑ i in s.attach, (c • f i) • _ = _
       simp only [smul_eq_mul, mul_smul]
       exact finset.smul_sum.symm
   rintro ⟨n, hn⟩; change n ∈ N at hn 
   rw [← hs, ← Set.image_id ↑s, Finsupp.mem_span_image_iff_total] at hn 
   rcases hn with ⟨l, hl1, hl2⟩
   refine' ⟨fun x => l x, Subtype.ext _⟩
-  change (∑ i in s.attach, l i • (i : M)) = n
+  change ∑ i in s.attach, l i • (i : M) = n
   rw [@Finset.sum_attach M M s _ fun i => l i • i, ← hl2, Finsupp.total_apply, Finsupp.sum, eq_comm]
   refine' Finset.sum_subset hl1 fun x _ hx => _
   rw [Finsupp.not_mem_support_iff.1 hx, zero_smul]

mathlib commit https://github.com/leanprover-community/mathlib/commit/7e5137f579de09a059a5ce98f364a04e221aabf0

@@ -468,7 +468,6 @@ theorem isNilpotent_jacobson_bot : IsNilpotent (Ideal.jacobson (⊥ : Ideal R))
     Ideal.span {x} * Jac ^ (n + 1) = Ideal.span {x} * Jac * Jac ^ n := by rw [pow_succ, ← mul_assoc]
     _ ≤ J * Jac ^ n := (mul_le_mul (by rwa [mul_comm]) le_rfl)
     _ = ⊥ := by simp [J]
-    
   refine' hxJ (mem_annihilator.2 fun y hy => (mem_bot R).1 _)
   refine' this (mul_mem_mul (mem_span_singleton_self x) _)
   rwa [← hn (n + 1) (Nat.le_succ _)]

mathlib commit https://github.com/leanprover-community/mathlib/commit/5f25c089cb34db4db112556f23c50d12da81b297

@@ -50,7 +50,7 @@ open Set
 open scoped BigOperators Pointwise
 
 #print IsArtinian /-
-/- ./././Mathport/Syntax/Translate/Command.lean:393:30: infer kinds are unsupported in Lean 4: #[`wellFounded_submodule_lt] [] -/
+/- ./././Mathport/Syntax/Translate/Command.lean:394:30: infer kinds are unsupported in Lean 4: #[`wellFounded_submodule_lt] [] -/
 /-- `is_artinian R M` is the proposition that `M` is an Artinian `R`-module,
 implemented as the well-foundedness of submodule inclusion.
 -/
@@ -174,8 +174,8 @@ theorem IsArtinian.finite_of_linearIndependent [Nontrivial R] [IsArtinian R M] {
     by_contradiction fun hf =>
       (RelEmbedding.wellFounded_iff_no_descending_seq.1 (well_founded_submodule_lt R M)).elim' _
   have f : ℕ ↪ s := Set.Infinite.natEmbedding s hf
-  have : ∀ n, coe ∘ f '' { m | n ≤ m } ⊆ s := by rintro n x ⟨y, hy₁, rfl⟩; exact (f y).2
-  have : ∀ a b : ℕ, a ≤ b ↔ span R (coe ∘ f '' { m | b ≤ m }) ≤ span R (coe ∘ f '' { m | a ≤ m }) :=
+  have : ∀ n, coe ∘ f '' {m | n ≤ m} ⊆ s := by rintro n x ⟨y, hy₁, rfl⟩; exact (f y).2
+  have : ∀ a b : ℕ, a ≤ b ↔ span R (coe ∘ f '' {m | b ≤ m}) ≤ span R (coe ∘ f '' {m | a ≤ m}) :=
     by
     intro a b
     rw [span_le_span_iff hs (this b) (this a),
@@ -183,7 +183,7 @@ theorem IsArtinian.finite_of_linearIndependent [Nontrivial R] [IsArtinian R M] {
     simp only [Set.mem_setOf_eq]
     exact ⟨fun hab x => le_trans hab, fun h => h _ le_rfl⟩
   exact
-    ⟨⟨fun n => span R (coe ∘ f '' { m | n ≤ m }), fun x y => by
+    ⟨⟨fun n => span R (coe ∘ f '' {m | n ≤ m}), fun x y => by
         simp (config := { contextual := true }) [le_antisymm_iff, (this _ _).symm]⟩,
       by
       intro a b
@@ -443,7 +443,7 @@ theorem isNilpotent_jacobson_bot : IsNilpotent (Ideal.jacobson (⊥ : Ideal R))
     have hJ : J • Jac ^ n = ⊥ := annihilator_smul (Jac ^ n)
     simpa only [this, top_smul, Ideal.zero_eq_bot] using hJ
   by_contra hJ; change J ≠ ⊤ at hJ 
-  rcases IsArtinian.set_has_minimal { J' : Ideal R | J < J' } ⟨⊤, hJ.lt_top⟩ with
+  rcases IsArtinian.set_has_minimal {J' : Ideal R | J < J'} ⟨⊤, hJ.lt_top⟩ with
     ⟨J', hJJ' : J < J', hJ' : ∀ I, J < I → ¬I < J'⟩
   rcases SetLike.exists_of_lt hJJ' with ⟨x, hxJ', hxJ⟩
   obtain rfl : J ⊔ Ideal.span {x} = J' :=
@@ -456,13 +456,13 @@ theorem isNilpotent_jacobson_bot : IsNilpotent (Ideal.jacobson (⊥ : Ideal R))
     sup_le_sup_left (smul_le.2 fun _ _ _ => Submodule.smul_mem _ _) _
   have : Jac * Ideal.span {x} ≤ J := by
     classical
-      --Need version 4 of Nakayamas lemma on Stacks
-      by_contra H
-      refine'
-        H
-          (smul_sup_le_of_le_smul_of_le_jacobson_bot (fg_span_singleton _) le_rfl
-            (this.eq_of_not_lt (hJ' _ _)).ge)
-      exact lt_of_le_of_ne le_sup_left fun h => H <| h.symm ▸ le_sup_right
+    --Need version 4 of Nakayamas lemma on Stacks
+    by_contra H
+    refine'
+      H
+        (smul_sup_le_of_le_smul_of_le_jacobson_bot (fg_span_singleton _) le_rfl
+          (this.eq_of_not_lt (hJ' _ _)).ge)
+    exact lt_of_le_of_ne le_sup_left fun h => H <| h.symm ▸ le_sup_right
   have : Ideal.span {x} * Jac ^ (n + 1) ≤ ⊥
   calc
     Ideal.span {x} * Jac ^ (n + 1) = Ideal.span {x} * Jac * Jac ^ n := by rw [pow_succ, ← mul_assoc]
@@ -490,7 +490,7 @@ theorem localization_surjective : Function.Surjective (algebraMap R L) :=
   obtain ⟨n, r, hr⟩ := IsArtinian.exists_pow_succ_smul_dvd (s : R) (1 : R)
   use r
   rw [smul_eq_mul, smul_eq_mul, pow_succ', mul_assoc] at hr 
-  apply_fun algebraMap R L  at hr 
+  apply_fun algebraMap R L at hr 
   simp only [map_mul, ← Submonoid.coe_pow] at hr 
   rw [← IsLocalization.mk'_one L, IsLocalization.mk'_eq_iff_eq, mul_one, Submonoid.coe_one, ←
     (IsLocalization.map_units L (s ^ n)).mul_left_cancel hr, map_mul]

mathlib commit https://github.com/leanprover-community/mathlib/commit/cca40788df1b8755d5baf17ab2f27dacc2e17acb

@@ -232,7 +232,7 @@ theorem exists_endomorphism_iterate_ker_sup_range_eq_top (f : M →ₗ[R] M) :
   obtain ⟨n, w⟩ :=
     monotone_stabilizes (f.iterate_range.comp ⟨fun n => n + 1, fun n m w => by linarith⟩)
   specialize w (n + 1 + n) (by linarith)
-  dsimp at w
+  dsimp at w 
   refine' ⟨n + 1, Nat.succ_ne_zero _, _⟩
   simp_rw [eq_top_iff', mem_sup]
   intro x
@@ -251,7 +251,7 @@ theorem surjective_of_injective_endomorphism (f : M →ₗ[R] M) (s : Injective
   by
   obtain ⟨n, ne, w⟩ := exists_endomorphism_iterate_ker_sup_range_eq_top f
   rw [linear_map.ker_eq_bot.mpr (LinearMap.iterate_injective s n), bot_sup_eq,
-    LinearMap.range_eq_top] at w
+    LinearMap.range_eq_top] at w 
   exact LinearMap.surjective_of_iterate_surjective Ne w
 #align is_artinian.surjective_of_injective_endomorphism IsArtinian.surjective_of_injective_endomorphism
 
@@ -298,17 +298,17 @@ theorem range_smul_pow_stabilizes (r : R) :
           (r ^ n • LinearMap.id : M →ₗ[R] M).range = (r ^ m • LinearMap.id : M →ₗ[R] M).range :=
   monotone_stabilizes
     ⟨fun n => (r ^ n • LinearMap.id : M →ₗ[R] M).range, fun n m h x ⟨y, hy⟩ =>
-      ⟨r ^ (m - n) • y, by dsimp at hy⊢;
+      ⟨r ^ (m - n) • y, by dsimp at hy ⊢;
         rw [← smul_assoc, smul_eq_mul, ← pow_add, ← hy, add_tsub_cancel_of_le h]⟩⟩
 #align is_artinian.range_smul_pow_stabilizes IsArtinian.range_smul_pow_stabilizes
 -/
 
 variable {M}
 
-theorem exists_pow_succ_smul_dvd (r : R) (x : M) : ∃ (n : ℕ)(y : M), r ^ n.succ • y = r ^ n • x :=
+theorem exists_pow_succ_smul_dvd (r : R) (x : M) : ∃ (n : ℕ) (y : M), r ^ n.succ • y = r ^ n • x :=
   by
   obtain ⟨n, hn⟩ := IsArtinian.range_smul_pow_stabilizes M r
-  simp_rw [SetLike.ext_iff] at hn
+  simp_rw [SetLike.ext_iff] at hn 
   exact ⟨n, by simpa using hn n.succ n.le_succ (r ^ n • x)⟩
 #align is_artinian.exists_pow_succ_smul_dvd IsArtinian.exists_pow_succ_smul_dvd
 
@@ -370,7 +370,7 @@ also Artinian. -/
 theorem isArtinian_of_tower (R) {S M} [CommRing R] [Ring S] [AddCommGroup M] [Algebra R S]
     [Module S M] [Module R M] [IsScalarTower R S M] (h : IsArtinian R M) : IsArtinian S M :=
   by
-  rw [isArtinian_iff_wellFounded] at h⊢
+  rw [isArtinian_iff_wellFounded] at h ⊢
   refine' (Submodule.restrictScalarsEmbedding R S M).WellFounded h
 #align is_artinian_of_tower isArtinian_of_tower
 
@@ -391,8 +391,8 @@ theorem isArtinian_of_fg_of_artinian {R M} [Ring R] [AddCommGroup M] [Module R M
       change (∑ i in s.attach, (c • f i) • _) = _
       simp only [smul_eq_mul, mul_smul]
       exact finset.smul_sum.symm
-  rintro ⟨n, hn⟩; change n ∈ N at hn
-  rw [← hs, ← Set.image_id ↑s, Finsupp.mem_span_image_iff_total] at hn
+  rintro ⟨n, hn⟩; change n ∈ N at hn 
+  rw [← hs, ← Set.image_id ↑s, Finsupp.mem_span_image_iff_total] at hn 
   rcases hn with ⟨l, hl1, hl2⟩
   refine' ⟨fun x => l x, Subtype.ext _⟩
   change (∑ i in s.attach, l i • (i : M)) = n
@@ -417,7 +417,7 @@ theorem isArtinian_span_of_finite (R) {M} [Ring R] [AddCommGroup M] [Module R M]
 theorem Function.Surjective.isArtinianRing {R} [Ring R] {S} [Ring S] {F} [RingHomClass F R S]
     {f : F} (hf : Function.Surjective f) [H : IsArtinianRing R] : IsArtinianRing S :=
   by
-  rw [isArtinianRing_iff, isArtinian_iff_wellFounded] at H⊢
+  rw [isArtinianRing_iff, isArtinian_iff_wellFounded] at H ⊢
   exact (Ideal.orderEmbeddingOfSurjective f hf).WellFounded H
 #align function.surjective.is_artinian_ring Function.Surjective.isArtinianRing
 
@@ -442,7 +442,7 @@ theorem isNilpotent_jacobson_bot : IsNilpotent (Ideal.jacobson (⊥ : Ideal R))
   suffices J = ⊤ by
     have hJ : J • Jac ^ n = ⊥ := annihilator_smul (Jac ^ n)
     simpa only [this, top_smul, Ideal.zero_eq_bot] using hJ
-  by_contra hJ; change J ≠ ⊤ at hJ
+  by_contra hJ; change J ≠ ⊤ at hJ 
   rcases IsArtinian.set_has_minimal { J' : Ideal R | J < J' } ⟨⊤, hJ.lt_top⟩ with
     ⟨J', hJJ' : J < J', hJ' : ∀ I, J < I → ¬I < J'⟩
   rcases SetLike.exists_of_lt hJJ' with ⟨x, hxJ', hxJ⟩
@@ -489,9 +489,9 @@ theorem localization_surjective : Function.Surjective (algebraMap R L) :=
   swap; · exact ⟨r₁ * r₂, by rw [IsLocalization.mk'_eq_mul_mk'_one, map_mul, h]⟩
   obtain ⟨n, r, hr⟩ := IsArtinian.exists_pow_succ_smul_dvd (s : R) (1 : R)
   use r
-  rw [smul_eq_mul, smul_eq_mul, pow_succ', mul_assoc] at hr
-  apply_fun algebraMap R L  at hr
-  simp only [map_mul, ← Submonoid.coe_pow] at hr
+  rw [smul_eq_mul, smul_eq_mul, pow_succ', mul_assoc] at hr 
+  apply_fun algebraMap R L  at hr 
+  simp only [map_mul, ← Submonoid.coe_pow] at hr 
   rw [← IsLocalization.mk'_one L, IsLocalization.mk'_eq_iff_eq, mul_one, Submonoid.coe_one, ←
     (IsLocalization.map_units L (s ^ n)).mul_left_cancel hr, map_mul]
 #align is_artinian_ring.localization_surjective IsArtinianRing.localization_surjective

mathlib commit https://github.com/leanprover-community/mathlib/commit/cca40788df1b8755d5baf17ab2f27dacc2e17acb

@@ -491,7 +491,7 @@ theorem localization_surjective : Function.Surjective (algebraMap R L) :=
   use r
   rw [smul_eq_mul, smul_eq_mul, pow_succ', mul_assoc] at hr
   apply_fun algebraMap R L  at hr
-  simp only [map_mul, ← [anonymous]] at hr
+  simp only [map_mul, ← Submonoid.coe_pow] at hr
   rw [← IsLocalization.mk'_one L, IsLocalization.mk'_eq_iff_eq, mul_one, Submonoid.coe_one, ←
     (IsLocalization.map_units L (s ^ n)).mul_left_cancel hr, map_mul]
 #align is_artinian_ring.localization_surjective IsArtinianRing.localization_surjective

mathlib commit https://github.com/leanprover-community/mathlib/commit/917c3c072e487b3cccdbfeff17e75b40e45f66cb

@@ -47,7 +47,7 @@ Artinian, artinian, Artinian ring, Artinian module, artinian ring, artinian modu
 
 open Set
 
-open BigOperators Pointwise
+open scoped BigOperators Pointwise
 
 #print IsArtinian /-
 /- ./././Mathport/Syntax/Translate/Command.lean:393:30: infer kinds are unsupported in Lean 4: #[`wellFounded_submodule_lt] [] -/

mathlib commit https://github.com/leanprover-community/mathlib/commit/917c3c072e487b3cccdbfeff17e75b40e45f66cb

@@ -71,12 +71,6 @@ open IsArtinian
 
 include R
 
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 theorem isArtinian_of_injective (f : M →ₗ[R] P) (h : Function.Injective f) [IsArtinian R P] :
     IsArtinian R M :=
   ⟨Subrelation.wf
@@ -90,24 +84,12 @@ instance isArtinian_submodule' [IsArtinian R M] (N : Submodule R M) : IsArtinian
 #align is_artinian_submodule' isArtinian_submodule'
 -/
 
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 theorem isArtinian_of_le {s t : Submodule R M} [ht : IsArtinian R t] (h : s ≤ t) : IsArtinian R s :=
   isArtinian_of_injective (Submodule.ofLe h) (Submodule.ofLe_injective h)
 #align is_artinian_of_le isArtinian_of_le
 
 variable (M)
 
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 theorem isArtinian_of_surjective (f : M →ₗ[R] P) (hf : Function.Surjective f) [IsArtinian R M] :
     IsArtinian R P :=
   ⟨Subrelation.wf
@@ -118,19 +100,10 @@ theorem isArtinian_of_surjective (f : M →ₗ[R] P) (hf : Function.Surjective f
 
 variable {M}
 
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 theorem isArtinian_of_linearEquiv (f : M ≃ₗ[R] P) [IsArtinian R M] : IsArtinian R P :=
   isArtinian_of_surjective _ f.toLinearMap f.toEquiv.Surjective
 #align is_artinian_of_linear_equiv isArtinian_of_linearEquiv
 
-/- warning: is_artinian_of_range_eq_ker -> isArtinian_of_range_eq_ker is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align is_artinian_of_range_eq_ker isArtinian_of_range_eq_kerₓ'. -/
 theorem isArtinian_of_range_eq_ker [IsArtinian R M] [IsArtinian R P] (f : M →ₗ[R] N) (g : N →ₗ[R] P)
     (hf : Function.Injective f) (hg : Function.Surjective g) (h : f.range = g.ker) :
     IsArtinian R N :=
@@ -140,12 +113,6 @@ theorem isArtinian_of_range_eq_ker [IsArtinian R M] [IsArtinian R P] (f : M →
       (by simp [Submodule.map_comap_eq, inf_comm]) (by simp [Submodule.comap_map_eq, h])⟩
 #align is_artinian_of_range_eq_ker isArtinian_of_range_eq_ker
 
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 instance isArtinian_prod [IsArtinian R M] [IsArtinian R P] : IsArtinian R (M × P) :=
   isArtinian_of_range_eq_ker (LinearMap.inl R M P) (LinearMap.snd R M P) LinearMap.inl_injective
     LinearMap.snd_surjective (LinearMap.range_inl R M P)
@@ -193,12 +160,6 @@ section Ring
 
 variable {R M : Type _} [Ring R] [AddCommGroup M] [Module R M]
 
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 theorem isArtinian_iff_wellFounded :
     IsArtinian R M ↔ WellFounded ((· < ·) : Submodule R M → Submodule R M → Prop) :=
   ⟨fun h => h.1, IsArtinian.mk⟩
@@ -206,12 +167,6 @@ theorem isArtinian_iff_wellFounded :
 
 variable {R M}
 
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 theorem IsArtinian.finite_of_linearIndependent [Nontrivial R] [IsArtinian R M] {s : Set M}
     (hs : LinearIndependent R (coe : s → M)) : s.Finite :=
   by
@@ -236,12 +191,6 @@ theorem IsArtinian.finite_of_linearIndependent [Nontrivial R] [IsArtinian R M] {
       simp⟩
 #align is_artinian.finite_of_linear_independent IsArtinian.finite_of_linearIndependent
 
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 /-- A module is Artinian iff every nonempty set of submodules has a minimal submodule among them.
 -/
 theorem set_has_minimal_iff_artinian :
@@ -249,20 +198,11 @@ theorem set_has_minimal_iff_artinian :
   rw [isArtinian_iff_wellFounded, WellFounded.wellFounded_iff_has_min]
 #align set_has_minimal_iff_artinian set_has_minimal_iff_artinian
 
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 theorem IsArtinian.set_has_minimal [IsArtinian R M] (a : Set <| Submodule R M) (ha : a.Nonempty) :
     ∃ M' ∈ a, ∀ I ∈ a, ¬I < M' :=
   set_has_minimal_iff_artinian.mpr ‹_› a ha
 #align is_artinian.set_has_minimal IsArtinian.set_has_minimal
 
-/- warning: monotone_stabilizes_iff_artinian -> monotone_stabilizes_iff_artinian is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align monotone_stabilizes_iff_artinian monotone_stabilizes_iff_artinianₓ'. -/
 /-- A module is Artinian iff every decreasing chain of submodules stabilizes. -/
 theorem monotone_stabilizes_iff_artinian :
     (∀ f : ℕ →o (Submodule R M)ᵒᵈ, ∃ n, ∀ m, n ≤ m → f n = f m) ↔ IsArtinian R M := by
@@ -273,28 +213,16 @@ namespace IsArtinian
 
 variable [IsArtinian R M]
 
-/- warning: is_artinian.monotone_stabilizes -> IsArtinian.monotone_stabilizes is a dubious translation:
-<too large>
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 theorem monotone_stabilizes (f : ℕ →o (Submodule R M)ᵒᵈ) : ∃ n, ∀ m, n ≤ m → f n = f m :=
   monotone_stabilizes_iff_artinian.mpr ‹_› f
 #align is_artinian.monotone_stabilizes IsArtinian.monotone_stabilizes
 
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-Case conversion may be inaccurate. Consider using '#align is_artinian.induction IsArtinian.inductionₓ'. -/
 /-- If `∀ I > J, P I` implies `P J`, then `P` holds for all submodules. -/
 theorem induction {P : Submodule R M → Prop} (hgt : ∀ I, (∀ J < I, P J) → P I) (I : Submodule R M) :
     P I :=
   (wellFounded_submodule_lt R M).recursion I hgt
 #align is_artinian.induction IsArtinian.induction
 
-/- warning: is_artinian.exists_endomorphism_iterate_ker_sup_range_eq_top -> IsArtinian.exists_endomorphism_iterate_ker_sup_range_eq_top is a dubious translation:
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 /-- For any endomorphism of a Artinian module, there is some nontrivial iterate
 with disjoint kernel and range.
 -/
@@ -318,12 +246,6 @@ theorem exists_endomorphism_iterate_ker_sup_range_eq_top (f : M →ₗ[R] M) :
     simp
 #align is_artinian.exists_endomorphism_iterate_ker_sup_range_eq_top IsArtinian.exists_endomorphism_iterate_ker_sup_range_eq_top
 
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 /-- Any injective endomorphism of an Artinian module is surjective. -/
 theorem surjective_of_injective_endomorphism (f : M →ₗ[R] M) (s : Injective f) : Surjective f :=
   by
@@ -333,20 +255,11 @@ theorem surjective_of_injective_endomorphism (f : M →ₗ[R] M) (s : Injective
   exact LinearMap.surjective_of_iterate_surjective Ne w
 #align is_artinian.surjective_of_injective_endomorphism IsArtinian.surjective_of_injective_endomorphism
 
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 /-- Any injective endomorphism of an Artinian module is bijective. -/
 theorem bijective_of_injective_endomorphism (f : M →ₗ[R] M) (s : Injective f) : Bijective f :=
   ⟨s, surjective_of_injective_endomorphism f s⟩
 #align is_artinian.bijective_of_injective_endomorphism IsArtinian.bijective_of_injective_endomorphism
 
-/- warning: is_artinian.disjoint_partial_infs_eventually_top -> IsArtinian.disjoint_partial_infs_eventually_top is a dubious translation:
-<too large>
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 /-- A sequence `f` of submodules of a artinian module,
 with the supremum `f (n+1)` and the infinum of `f 0`, ..., `f n` being ⊤,
 is eventually ⊤.
@@ -392,12 +305,6 @@ theorem range_smul_pow_stabilizes (r : R) :
 
 variable {M}
 
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 theorem exists_pow_succ_smul_dvd (r : R) (x : M) : ∃ (n : ℕ)(y : M), r ^ n.succ • y = r ^ n • x :=
   by
   obtain ⟨n, hn⟩ := IsArtinian.range_smul_pow_stabilizes M r
@@ -444,44 +351,20 @@ theorem isArtinianRing_iff {R} [Ring R] : IsArtinianRing R ↔ IsArtinian R R :=
 #align is_artinian_ring_iff isArtinianRing_iff
 -/
 
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 theorem Ring.isArtinian_of_zero_eq_one {R} [Ring R] (h01 : (0 : R) = 1) : IsArtinianRing R :=
   have := subsingleton_of_zero_eq_one h01
   inferInstance
 #align ring.is_artinian_of_zero_eq_one Ring.isArtinian_of_zero_eq_one
 
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 theorem isArtinian_of_submodule_of_artinian (R M) [Ring R] [AddCommGroup M] [Module R M]
     (N : Submodule R M) (h : IsArtinian R M) : IsArtinian R N := by infer_instance
 #align is_artinian_of_submodule_of_artinian isArtinian_of_submodule_of_artinian
 
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 theorem isArtinian_of_quotient_of_artinian (R) [Ring R] (M) [AddCommGroup M] [Module R M]
     (N : Submodule R M) (h : IsArtinian R M) : IsArtinian R (M ⧸ N) :=
   isArtinian_of_surjective M (Submodule.mkQ N) (Submodule.Quotient.mk_surjective N)
 #align is_artinian_of_quotient_of_artinian isArtinian_of_quotient_of_artinian
 
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 /-- If `M / S / R` is a scalar tower, and `M / R` is Artinian, then `M / S` is
 also Artinian. -/
 theorem isArtinian_of_tower (R) {S M} [CommRing R] [Ring S] [AddCommGroup M] [Algebra R S]
@@ -491,12 +374,6 @@ theorem isArtinian_of_tower (R) {S M} [CommRing R] [Ring S] [AddCommGroup M] [Al
   refine' (Submodule.restrictScalarsEmbedding R S M).WellFounded h
 #align is_artinian_of_tower isArtinian_of_tower
 
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 theorem isArtinian_of_fg_of_artinian {R M} [Ring R] [AddCommGroup M] [Module R M]
     (N : Submodule R M) [IsArtinianRing R] (hN : N.FG) : IsArtinian R N :=
   by
@@ -524,24 +401,12 @@ theorem isArtinian_of_fg_of_artinian {R M} [Ring R] [AddCommGroup M] [Module R M
   rw [Finsupp.not_mem_support_iff.1 hx, zero_smul]
 #align is_artinian_of_fg_of_artinian isArtinian_of_fg_of_artinian
 
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 theorem isArtinian_of_fg_of_artinian' {R M} [Ring R] [AddCommGroup M] [Module R M]
     [IsArtinianRing R] (h : (⊤ : Submodule R M).FG) : IsArtinian R M :=
   have : IsArtinian R (⊤ : Submodule R M) := isArtinian_of_fg_of_artinian _ h
   isArtinian_of_linearEquiv (LinearEquiv.ofTop (⊤ : Submodule R M) rfl)
 #align is_artinian_of_fg_of_artinian' isArtinian_of_fg_of_artinian'
 
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 /-- In a module over a artinian ring, the submodule generated by finitely many vectors is
 artinian. -/
 theorem isArtinian_span_of_finite (R) {M} [Ring R] [AddCommGroup M] [Module R M] [IsArtinianRing R]
@@ -549,12 +414,6 @@ theorem isArtinian_span_of_finite (R) {M} [Ring R] [AddCommGroup M] [Module R M]
   isArtinian_of_fg_of_artinian _ (Submodule.fg_def.mpr ⟨A, hA, rfl⟩)
 #align is_artinian_span_of_finite isArtinian_span_of_finite
 
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 theorem Function.Surjective.isArtinianRing {R} [Ring R] {S} [Ring S] {F} [RingHomClass F R S]
     {f : F} (hf : Function.Surjective f) [H : IsArtinianRing R] : IsArtinianRing S :=
   by
@@ -562,12 +421,6 @@ theorem Function.Surjective.isArtinianRing {R} [Ring R] {S} [Ring S] {F} [RingHo
   exact (Ideal.orderEmbeddingOfSurjective f hf).WellFounded H
 #align function.surjective.is_artinian_ring Function.Surjective.isArtinianRing
 
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 instance isArtinianRing_range {R} [Ring R] {S} [Ring S] (f : R →+* S) [IsArtinianRing R] :
     IsArtinianRing f.range :=
   f.rangeRestrict_surjective.IsArtinianRing
@@ -579,12 +432,6 @@ open IsArtinian
 
 variable {R : Type _} [CommRing R] [IsArtinianRing R]
 
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 theorem isNilpotent_jacobson_bot : IsNilpotent (Ideal.jacobson (⊥ : Ideal R)) :=
   by
   let Jac := Ideal.jacobson (⊥ : Ideal R)
@@ -633,12 +480,6 @@ variable (S : Submonoid R) (L : Type _) [CommRing L] [Algebra R L] [IsLocalizati
 
 include S
 
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-Case conversion may be inaccurate. Consider using '#align is_artinian_ring.localization_surjective IsArtinianRing.localization_surjectiveₓ'. -/
 /-- Localizing an artinian ring can only reduce the amount of elements. -/
 theorem localization_surjective : Function.Surjective (algebraMap R L) :=
   by
@@ -655,12 +496,6 @@ theorem localization_surjective : Function.Surjective (algebraMap R L) :=
     (IsLocalization.map_units L (s ^ n)).mul_left_cancel hr, map_mul]
 #align is_artinian_ring.localization_surjective IsArtinianRing.localization_surjective
 
-/- warning: is_artinian_ring.localization_artinian -> IsArtinianRing.localization_artinian is a dubious translation:
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-but is expected to have type
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-Case conversion may be inaccurate. Consider using '#align is_artinian_ring.localization_artinian IsArtinianRing.localization_artinianₓ'. -/
 theorem localization_artinian : IsArtinianRing L :=
   (localization_surjective S L).IsArtinianRing
 #align is_artinian_ring.localization_artinian IsArtinianRing.localization_artinian

mathlib commit https://github.com/leanprover-community/mathlib/commit/917c3c072e487b3cccdbfeff17e75b40e45f66cb

@@ -167,9 +167,7 @@ instance isArtinian_pi {R ι : Type _} [Finite ι] :
     (by
       intro α β e hα M _ _ _ _
       exact isArtinian_of_linearEquiv (LinearEquiv.piCongrLeft R M e))
-    (by
-      intro M _ _ _ _
-      infer_instance)
+    (by intro M _ _ _ _; infer_instance)
     (by
       intro α _ ih M _ _ _ _
       exact isArtinian_of_linearEquiv (LinearEquiv.piOptionEquivProd R).symm)
@@ -221,10 +219,7 @@ theorem IsArtinian.finite_of_linearIndependent [Nontrivial R] [IsArtinian R M] {
     by_contradiction fun hf =>
       (RelEmbedding.wellFounded_iff_no_descending_seq.1 (well_founded_submodule_lt R M)).elim' _
   have f : ℕ ↪ s := Set.Infinite.natEmbedding s hf
-  have : ∀ n, coe ∘ f '' { m | n ≤ m } ⊆ s :=
-    by
-    rintro n x ⟨y, hy₁, rfl⟩
-    exact (f y).2
+  have : ∀ n, coe ∘ f '' { m | n ≤ m } ⊆ s := by rintro n x ⟨y, hy₁, rfl⟩; exact (f y).2
   have : ∀ a b : ℕ, a ≤ b ↔ span R (coe ∘ f '' { m | b ≤ m }) ≤ span R (coe ∘ f '' { m | a ≤ m }) :=
     by
     intro a b
@@ -270,10 +265,8 @@ theorem IsArtinian.set_has_minimal [IsArtinian R M] (a : Set <| Submodule R M) (
 Case conversion may be inaccurate. Consider using '#align monotone_stabilizes_iff_artinian monotone_stabilizes_iff_artinianₓ'. -/
 /-- A module is Artinian iff every decreasing chain of submodules stabilizes. -/
 theorem monotone_stabilizes_iff_artinian :
-    (∀ f : ℕ →o (Submodule R M)ᵒᵈ, ∃ n, ∀ m, n ≤ m → f n = f m) ↔ IsArtinian R M :=
-  by
-  rw [isArtinian_iff_wellFounded]
-  exact well_founded.monotone_chain_condition.symm
+    (∀ f : ℕ →o (Submodule R M)ᵒᵈ, ∃ n, ∀ m, n ≤ m → f n = f m) ↔ IsArtinian R M := by
+  rw [isArtinian_iff_wellFounded]; exact well_founded.monotone_chain_condition.symm
 #align monotone_stabilizes_iff_artinian monotone_stabilizes_iff_artinian
 
 namespace IsArtinian
@@ -315,10 +308,7 @@ theorem exists_endomorphism_iterate_ker_sup_range_eq_top (f : M →ₗ[R] M) :
   refine' ⟨n + 1, Nat.succ_ne_zero _, _⟩
   simp_rw [eq_top_iff', mem_sup]
   intro x
-  have : (f ^ (n + 1)) x ∈ (f ^ (n + 1 + n + 1)).range :=
-    by
-    rw [← w]
-    exact mem_range_self _
+  have : (f ^ (n + 1)) x ∈ (f ^ (n + 1 + n + 1)).range := by rw [← w]; exact mem_range_self _
   rcases this with ⟨y, hy⟩
   use x - (f ^ (n + 1)) y
   constructor
@@ -395,8 +385,7 @@ theorem range_smul_pow_stabilizes (r : R) :
           (r ^ n • LinearMap.id : M →ₗ[R] M).range = (r ^ m • LinearMap.id : M →ₗ[R] M).range :=
   monotone_stabilizes
     ⟨fun n => (r ^ n • LinearMap.id : M →ₗ[R] M).range, fun n m h x ⟨y, hy⟩ =>
-      ⟨r ^ (m - n) • y, by
-        dsimp at hy⊢
+      ⟨r ^ (m - n) • y, by dsimp at hy⊢;
         rw [← smul_assoc, smul_eq_mul, ← pow_add, ← hy, add_tsub_cancel_of_le h]⟩⟩
 #align is_artinian.range_smul_pow_stabilizes IsArtinian.range_smul_pow_stabilizes
 -/
@@ -518,18 +507,14 @@ theorem isArtinian_of_fg_of_artinian {R M} [Ring R] [AddCommGroup M] [Module R M
   refine' @isArtinian_of_surjective ((↑s : Set M) → R) _ _ _ (Pi.module _ _ _) _ _ _ isArtinian_pi
   · fapply LinearMap.mk
     · exact fun f => ⟨∑ i in s.attach, f i • i.1, N.sum_mem fun c _ => N.smul_mem _ <| this _ c.2⟩
-    · intro f g
-      apply Subtype.eq
+    · intro f g; apply Subtype.eq
       change (∑ i in s.attach, (f i + g i) • _) = _
-      simp only [add_smul, Finset.sum_add_distrib]
-      rfl
-    · intro c f
-      apply Subtype.eq
+      simp only [add_smul, Finset.sum_add_distrib]; rfl
+    · intro c f; apply Subtype.eq
       change (∑ i in s.attach, (c • f i) • _) = _
       simp only [smul_eq_mul, mul_smul]
       exact finset.smul_sum.symm
-  rintro ⟨n, hn⟩
-  change n ∈ N at hn
+  rintro ⟨n, hn⟩; change n ∈ N at hn
   rw [← hs, ← Set.image_id ↑s, Finsupp.mem_span_image_iff_total] at hn
   rcases hn with ⟨l, hl1, hl2⟩
   refine' ⟨fun x => l x, Subtype.ext _⟩
@@ -610,8 +595,7 @@ theorem isNilpotent_jacobson_bot : IsNilpotent (Ideal.jacobson (⊥ : Ideal R))
   suffices J = ⊤ by
     have hJ : J • Jac ^ n = ⊥ := annihilator_smul (Jac ^ n)
     simpa only [this, top_smul, Ideal.zero_eq_bot] using hJ
-  by_contra hJ
-  change J ≠ ⊤ at hJ
+  by_contra hJ; change J ≠ ⊤ at hJ
   rcases IsArtinian.set_has_minimal { J' : Ideal R | J < J' } ⟨⊤, hJ.lt_top⟩ with
     ⟨J', hJJ' : J < J', hJ' : ∀ I, J < I → ¬I < J'⟩
   rcases SetLike.exists_of_lt hJJ' with ⟨x, hxJ', hxJ⟩

mathlib commit https://github.com/leanprover-community/mathlib/commit/917c3c072e487b3cccdbfeff17e75b40e45f66cb

@@ -129,10 +129,7 @@ theorem isArtinian_of_linearEquiv (f : M ≃ₗ[R] P) [IsArtinian R M] : IsArtin
 #align is_artinian_of_linear_equiv isArtinian_of_linearEquiv
 
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_inst_4) (AddCommGroup.toAddCommMonoid.{u2} P _inst_3) _inst_7 _inst_6 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (Ring.toSemiring.{u4} R _inst_1)))) g)) -> (IsArtinian.{u4, u1} R N (Ring.toSemiring.{u4} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} N _inst_4) _inst_7)
+<too large>
 Case conversion may be inaccurate. Consider using '#align is_artinian_of_range_eq_ker isArtinian_of_range_eq_kerₓ'. -/
 theorem isArtinian_of_range_eq_ker [IsArtinian R M] [IsArtinian R P] (f : M →ₗ[R] N) (g : N →ₗ[R] P)
     (hf : Function.Injective f) (hg : Function.Surjective g) (h : f.range = g.ker) :
@@ -269,10 +266,7 @@ theorem IsArtinian.set_has_minimal [IsArtinian R M] (a : Set <| Submodule R M) (
 #align is_artinian.set_has_minimal IsArtinian.set_has_minimal
 
 /- warning: monotone_stabilizes_iff_artinian -> monotone_stabilizes_iff_artinian is a dubious translation:
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+<too large>
 Case conversion may be inaccurate. Consider using '#align monotone_stabilizes_iff_artinian monotone_stabilizes_iff_artinianₓ'. -/
 /-- A module is Artinian iff every decreasing chain of submodules stabilizes. -/
 theorem monotone_stabilizes_iff_artinian :
@@ -287,10 +281,7 @@ namespace IsArtinian
 variable [IsArtinian R M]
 
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+<too large>
 Case conversion may be inaccurate. Consider using '#align is_artinian.monotone_stabilizes IsArtinian.monotone_stabilizesₓ'. -/
 theorem monotone_stabilizes (f : ℕ →o (Submodule R M)ᵒᵈ) : ∃ n, ∀ m, n ≤ m → f n = f m :=
   monotone_stabilizes_iff_artinian.mpr ‹_› f
@@ -309,10 +300,7 @@ theorem induction {P : Submodule R M → Prop} (hgt : ∀ I, (∀ J < I, P J) 
 #align is_artinian.induction IsArtinian.induction
 
 /- warning: is_artinian.exists_endomorphism_iterate_ker_sup_range_eq_top -> IsArtinian.exists_endomorphism_iterate_ker_sup_range_eq_top is a dubious translation:
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+<too large>
 Case conversion may be inaccurate. Consider using '#align is_artinian.exists_endomorphism_iterate_ker_sup_range_eq_top IsArtinian.exists_endomorphism_iterate_ker_sup_range_eq_topₓ'. -/
 /-- For any endomorphism of a Artinian module, there is some nontrivial iterate
 with disjoint kernel and range.
@@ -367,10 +355,7 @@ theorem bijective_of_injective_endomorphism (f : M →ₗ[R] M) (s : Injective f
 #align is_artinian.bijective_of_injective_endomorphism IsArtinian.bijective_of_injective_endomorphism
 
 /- warning: is_artinian.disjoint_partial_infs_eventually_top -> IsArtinian.disjoint_partial_infs_eventually_top is a dubious translation:
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_inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3))) f)) n) (FunLike.coe.{succ u1, succ u1, succ u1} (Equiv.{succ u1, succ u1} (Submodule.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (OrderDual.{u1} (Submodule.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3))) (Submodule.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (fun (_x : Submodule.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) => (fun (x._@.Mathlib.Logic.Equiv.Defs._hyg.812 : Submodule.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) => OrderDual.{u1} (Submodule.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3)) _x) (Equiv.instFunLikeEquiv.{succ u1, succ u1} (Submodule.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (OrderDual.{u1} (Submodule.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3))) (OrderDual.toDual.{u1} (Submodule.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3)) (f (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))))) -> (Exists.{1} Nat (fun (n : Nat) => forall (m : Nat), (LE.le.{0} Nat instLENat n m) -> (Eq.{succ u1} (Submodule.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (f m) (Top.top.{u1} (Submodule.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.instTopSubmodule.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3)))))
+<too large>
 Case conversion may be inaccurate. Consider using '#align is_artinian.disjoint_partial_infs_eventually_top IsArtinian.disjoint_partial_infs_eventually_topₓ'. -/
 /-- A sequence `f` of submodules of a artinian module,
 with the supremum `f (n+1)` and the infinum of `f 0`, ..., `f n` being ⊤,

mathlib commit https://github.com/leanprover-community/mathlib/commit/8d33f09cd7089ecf074b4791907588245aec5d1b

@@ -75,7 +75,7 @@ include R
 lean 3 declaration is
   forall {R : Type.{u1}} {M : Type.{u2}} {P : Type.{u3}} [_inst_1 : Ring.{u1} R] [_inst_2 : AddCommGroup.{u2} M] [_inst_3 : AddCommGroup.{u3} P] [_inst_5 : Module.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2)] [_inst_6 : Module.{u1, u3} R P (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} P _inst_3)] (f : LinearMap.{u1, u1, u2, u3} R R (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) M P (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u3} P _inst_3) _inst_5 _inst_6), (Function.Injective.{succ u2, succ u3} M P (coeFn.{max (succ u2) (succ u3), max (succ u2) (succ u3)} (LinearMap.{u1, u1, u2, u3} R R (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) M P (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u3} P _inst_3) _inst_5 _inst_6) (fun (_x : LinearMap.{u1, u1, u2, u3} R R (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) M P (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u3} P _inst_3) _inst_5 _inst_6) => M -> P) (LinearMap.hasCoeToFun.{u1, u1, u2, u3} R R M P (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u3} P _inst_3) _inst_5 _inst_6 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1)))) f)) -> (forall [_inst_8 : IsArtinian.{u1, u3} R P (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} P _inst_3) _inst_6], IsArtinian.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_5)
 but is expected to have type
-  forall {R : Type.{u3}} {M : Type.{u2}} {P : Type.{u1}} [_inst_1 : Ring.{u3} R] [_inst_2 : AddCommGroup.{u2} M] [_inst_3 : AddCommGroup.{u1} P] [_inst_5 : Module.{u3, u2} R M (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2)] [_inst_6 : Module.{u3, u1} R P (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} P _inst_3)] (f : LinearMap.{u3, u3, u2, u1} R R (Ring.toSemiring.{u3} R _inst_1) (Ring.toSemiring.{u3} R _inst_1) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (Ring.toSemiring.{u3} R _inst_1))) M P (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} P _inst_3) _inst_5 _inst_6), (Function.Injective.{succ u2, succ u1} M P (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (LinearMap.{u3, u3, u2, u1} R R (Ring.toSemiring.{u3} R _inst_1) (Ring.toSemiring.{u3} R _inst_1) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (Ring.toSemiring.{u3} R _inst_1))) M P (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} P _inst_3) _inst_5 _inst_6) M (fun (_x : M) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : M) => P) _x) (LinearMap.instFunLikeLinearMap.{u3, u3, u2, u1} R R M P (Ring.toSemiring.{u3} R _inst_1) (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} P _inst_3) _inst_5 _inst_6 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (Ring.toSemiring.{u3} R _inst_1)))) f)) -> (forall [_inst_8 : IsArtinian.{u3, u1} R P (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} P _inst_3) _inst_6], IsArtinian.{u3, u2} R M (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_5)
+  forall {R : Type.{u3}} {M : Type.{u2}} {P : Type.{u1}} [_inst_1 : Ring.{u3} R] [_inst_2 : AddCommGroup.{u2} M] [_inst_3 : AddCommGroup.{u1} P] [_inst_5 : Module.{u3, u2} R M (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2)] [_inst_6 : Module.{u3, u1} R P (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} P _inst_3)] (f : LinearMap.{u3, u3, u2, u1} R R (Ring.toSemiring.{u3} R _inst_1) (Ring.toSemiring.{u3} R _inst_1) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (Ring.toSemiring.{u3} R _inst_1))) M P (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} P _inst_3) _inst_5 _inst_6), (Function.Injective.{succ u2, succ u1} M P (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (LinearMap.{u3, u3, u2, u1} R R (Ring.toSemiring.{u3} R _inst_1) (Ring.toSemiring.{u3} R _inst_1) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (Ring.toSemiring.{u3} R _inst_1))) M P (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} P _inst_3) _inst_5 _inst_6) M (fun (_x : M) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : M) => P) _x) (LinearMap.instFunLikeLinearMap.{u3, u3, u2, u1} R R M P (Ring.toSemiring.{u3} R _inst_1) (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} P _inst_3) _inst_5 _inst_6 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (Ring.toSemiring.{u3} R _inst_1)))) f)) -> (forall [_inst_8 : IsArtinian.{u3, u1} R P (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} P _inst_3) _inst_6], IsArtinian.{u3, u2} R M (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_5)
 Case conversion may be inaccurate. Consider using '#align is_artinian_of_injective isArtinian_of_injectiveₓ'. -/
 theorem isArtinian_of_injective (f : M →ₗ[R] P) (h : Function.Injective f) [IsArtinian R P] :
     IsArtinian R M :=
@@ -106,7 +106,7 @@ variable (M)
 lean 3 declaration is
   forall {R : Type.{u1}} (M : Type.{u2}) {P : Type.{u3}} [_inst_1 : Ring.{u1} R] [_inst_2 : AddCommGroup.{u2} M] [_inst_3 : AddCommGroup.{u3} P] [_inst_5 : Module.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2)] [_inst_6 : Module.{u1, u3} R P (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} P _inst_3)] (f : LinearMap.{u1, u1, u2, u3} R R (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) M P (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u3} P _inst_3) _inst_5 _inst_6), (Function.Surjective.{succ u2, succ u3} M P (coeFn.{max (succ u2) (succ u3), max (succ u2) (succ u3)} (LinearMap.{u1, u1, u2, u3} R R (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) M P (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u3} P _inst_3) _inst_5 _inst_6) (fun (_x : LinearMap.{u1, u1, u2, u3} R R (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) M P (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u3} P _inst_3) _inst_5 _inst_6) => M -> P) (LinearMap.hasCoeToFun.{u1, u1, u2, u3} R R M P (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u3} P _inst_3) _inst_5 _inst_6 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1)))) f)) -> (forall [_inst_8 : IsArtinian.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_5], IsArtinian.{u1, u3} R P (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} P _inst_3) _inst_6)
 but is expected to have type
-  forall {R : Type.{u3}} (M : Type.{u2}) {P : Type.{u1}} [_inst_1 : Ring.{u3} R] [_inst_2 : AddCommGroup.{u2} M] [_inst_3 : AddCommGroup.{u1} P] [_inst_5 : Module.{u3, u2} R M (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2)] [_inst_6 : Module.{u3, u1} R P (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} P _inst_3)] (f : LinearMap.{u3, u3, u2, u1} R R (Ring.toSemiring.{u3} R _inst_1) (Ring.toSemiring.{u3} R _inst_1) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (Ring.toSemiring.{u3} R _inst_1))) M P (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} P _inst_3) _inst_5 _inst_6), (Function.Surjective.{succ u2, succ u1} M P (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (LinearMap.{u3, u3, u2, u1} R R (Ring.toSemiring.{u3} R _inst_1) (Ring.toSemiring.{u3} R _inst_1) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (Ring.toSemiring.{u3} R _inst_1))) M P (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} P _inst_3) _inst_5 _inst_6) M (fun (_x : M) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : M) => P) _x) (LinearMap.instFunLikeLinearMap.{u3, u3, u2, u1} R R M P (Ring.toSemiring.{u3} R _inst_1) (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} P _inst_3) _inst_5 _inst_6 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (Ring.toSemiring.{u3} R _inst_1)))) f)) -> (forall [_inst_8 : IsArtinian.{u3, u2} R M (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_5], IsArtinian.{u3, u1} R P (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} P _inst_3) _inst_6)
+  forall {R : Type.{u3}} (M : Type.{u2}) {P : Type.{u1}} [_inst_1 : Ring.{u3} R] [_inst_2 : AddCommGroup.{u2} M] [_inst_3 : AddCommGroup.{u1} P] [_inst_5 : Module.{u3, u2} R M (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2)] [_inst_6 : Module.{u3, u1} R P (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} P _inst_3)] (f : LinearMap.{u3, u3, u2, u1} R R (Ring.toSemiring.{u3} R _inst_1) (Ring.toSemiring.{u3} R _inst_1) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (Ring.toSemiring.{u3} R _inst_1))) M P (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} P _inst_3) _inst_5 _inst_6), (Function.Surjective.{succ u2, succ u1} M P (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (LinearMap.{u3, u3, u2, u1} R R (Ring.toSemiring.{u3} R _inst_1) (Ring.toSemiring.{u3} R _inst_1) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (Ring.toSemiring.{u3} R _inst_1))) M P (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} P _inst_3) _inst_5 _inst_6) M (fun (_x : M) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : M) => P) _x) (LinearMap.instFunLikeLinearMap.{u3, u3, u2, u1} R R M P (Ring.toSemiring.{u3} R _inst_1) (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} P _inst_3) _inst_5 _inst_6 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (Ring.toSemiring.{u3} R _inst_1)))) f)) -> (forall [_inst_8 : IsArtinian.{u3, u2} R M (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_5], IsArtinian.{u3, u1} R P (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} P _inst_3) _inst_6)
 Case conversion may be inaccurate. Consider using '#align is_artinian_of_surjective isArtinian_of_surjectiveₓ'. -/
 theorem isArtinian_of_surjective (f : M →ₗ[R] P) (hf : Function.Surjective f) [IsArtinian R M] :
     IsArtinian R P :=
@@ -132,7 +132,7 @@ theorem isArtinian_of_linearEquiv (f : M ≃ₗ[R] P) [IsArtinian R M] : IsArtin
 lean 3 declaration is
   forall {R : Type.{u1}} {M : Type.{u2}} {P : Type.{u3}} {N : Type.{u4}} [_inst_1 : Ring.{u1} R] [_inst_2 : AddCommGroup.{u2} M] [_inst_3 : AddCommGroup.{u3} P] [_inst_4 : AddCommGroup.{u4} N] [_inst_5 : Module.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2)] [_inst_6 : Module.{u1, u3} R P (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} P _inst_3)] [_inst_7 : Module.{u1, u4} R N (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u4} N _inst_4)] [_inst_8 : IsArtinian.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_5] [_inst_9 : IsArtinian.{u1, u3} R P (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} P _inst_3) _inst_6] (f : LinearMap.{u1, u1, u2, u4} R R (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) M N (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u4} N _inst_4) _inst_5 _inst_7) (g : LinearMap.{u1, u1, u4, u3} R R (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) N P (AddCommGroup.toAddCommMonoid.{u4} N _inst_4) (AddCommGroup.toAddCommMonoid.{u3} P _inst_3) _inst_7 _inst_6), (Function.Injective.{succ u2, succ u4} M N (coeFn.{max (succ u2) (succ u4), max (succ u2) (succ u4)} (LinearMap.{u1, u1, u2, u4} R R (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) M N (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u4} N _inst_4) _inst_5 _inst_7) (fun (_x : LinearMap.{u1, u1, u2, u4} R R (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) M N (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u4} N _inst_4) _inst_5 _inst_7) => M -> N) (LinearMap.hasCoeToFun.{u1, u1, u2, u4} R R M N (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u4} N _inst_4) _inst_5 _inst_7 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1)))) f)) -> (Function.Surjective.{succ u4, succ u3} N P (coeFn.{max (succ u4) (succ u3), max (succ u4) (succ u3)} (LinearMap.{u1, u1, u4, u3} R R (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) N P (AddCommGroup.toAddCommMonoid.{u4} N _inst_4) (AddCommGroup.toAddCommMonoid.{u3} P _inst_3) _inst_7 _inst_6) (fun (_x : LinearMap.{u1, u1, u4, u3} R R (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) N P (AddCommGroup.toAddCommMonoid.{u4} N _inst_4) (AddCommGroup.toAddCommMonoid.{u3} P _inst_3) _inst_7 _inst_6) => N -> P) (LinearMap.hasCoeToFun.{u1, u1, u4, u3} R R N P (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u4} N _inst_4) (AddCommGroup.toAddCommMonoid.{u3} P _inst_3) _inst_7 _inst_6 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1)))) g)) -> (Eq.{succ u4} (Submodule.{u1, u4} R N (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u4} N _inst_4) _inst_7) (LinearMap.range.{u1, u1, u2, u4, max u2 u4} R R M N (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u4} N _inst_4) _inst_5 _inst_7 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (LinearMap.{u1, u1, u2, u4} R R (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) M N (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u4} N _inst_4) _inst_5 _inst_7) (LinearMap.semilinearMapClass.{u1, u1, u2, u4} R R M N (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u4} N _inst_4) _inst_5 _inst_7 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1)))) (RingHomSurjective.ids.{u1} R (Ring.toSemiring.{u1} R _inst_1)) f) (LinearMap.ker.{u1, u1, u4, u3, max u4 u3} R R N P (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u4} N _inst_4) (AddCommGroup.toAddCommMonoid.{u3} P _inst_3) _inst_7 _inst_6 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (LinearMap.{u1, u1, u4, u3} R R (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) N P (AddCommGroup.toAddCommMonoid.{u4} N _inst_4) (AddCommGroup.toAddCommMonoid.{u3} P _inst_3) _inst_7 _inst_6) (LinearMap.semilinearMapClass.{u1, u1, u4, u3} R R N P (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u4} N _inst_4) (AddCommGroup.toAddCommMonoid.{u3} P _inst_3) _inst_7 _inst_6 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1)))) g)) -> (IsArtinian.{u1, u4} R N (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u4} N _inst_4) _inst_7)
 but is expected to have type
-  forall {R : Type.{u4}} {M : Type.{u3}} {P : Type.{u2}} {N : Type.{u1}} [_inst_1 : Ring.{u4} R] [_inst_2 : AddCommGroup.{u3} M] [_inst_3 : AddCommGroup.{u2} P] [_inst_4 : AddCommGroup.{u1} N] [_inst_5 : Module.{u4, u3} R M (Ring.toSemiring.{u4} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2)] [_inst_6 : Module.{u4, u2} R P (Ring.toSemiring.{u4} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} P _inst_3)] [_inst_7 : Module.{u4, u1} R N (Ring.toSemiring.{u4} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} N _inst_4)] [_inst_8 : IsArtinian.{u4, u3} R M (Ring.toSemiring.{u4} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) _inst_5] [_inst_9 : IsArtinian.{u4, u2} R P (Ring.toSemiring.{u4} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} P _inst_3) _inst_6] (f : LinearMap.{u4, u4, u3, u1} R R (Ring.toSemiring.{u4} R _inst_1) (Ring.toSemiring.{u4} R _inst_1) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (Ring.toSemiring.{u4} R _inst_1))) M N (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} N _inst_4) _inst_5 _inst_7) (g : LinearMap.{u4, u4, u1, u2} R R (Ring.toSemiring.{u4} R _inst_1) (Ring.toSemiring.{u4} R _inst_1) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (Ring.toSemiring.{u4} R _inst_1))) N P (AddCommGroup.toAddCommMonoid.{u1} N _inst_4) (AddCommGroup.toAddCommMonoid.{u2} P _inst_3) _inst_7 _inst_6), (Function.Injective.{succ u3, succ u1} M N (FunLike.coe.{max (succ u3) (succ u1), succ u3, succ u1} (LinearMap.{u4, u4, u3, u1} R R (Ring.toSemiring.{u4} R _inst_1) (Ring.toSemiring.{u4} R _inst_1) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (Ring.toSemiring.{u4} R _inst_1))) M N (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} N _inst_4) _inst_5 _inst_7) M (fun (_x : M) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : M) => N) _x) (LinearMap.instFunLikeLinearMap.{u4, u4, u3, u1} R R M N (Ring.toSemiring.{u4} R _inst_1) (Ring.toSemiring.{u4} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} N _inst_4) _inst_5 _inst_7 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (Ring.toSemiring.{u4} R _inst_1)))) f)) -> (Function.Surjective.{succ u1, succ u2} N P (FunLike.coe.{max (succ u2) (succ u1), succ u1, succ u2} (LinearMap.{u4, u4, u1, u2} R R (Ring.toSemiring.{u4} R _inst_1) (Ring.toSemiring.{u4} R _inst_1) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (Ring.toSemiring.{u4} R _inst_1))) N P (AddCommGroup.toAddCommMonoid.{u1} N _inst_4) (AddCommGroup.toAddCommMonoid.{u2} P _inst_3) _inst_7 _inst_6) N (fun (_x : N) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : N) => P) _x) (LinearMap.instFunLikeLinearMap.{u4, u4, u1, u2} R R N P (Ring.toSemiring.{u4} R _inst_1) (Ring.toSemiring.{u4} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} N _inst_4) (AddCommGroup.toAddCommMonoid.{u2} P _inst_3) _inst_7 _inst_6 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (Ring.toSemiring.{u4} R _inst_1)))) g)) -> (Eq.{succ u1} (Submodule.{u4, u1} R N (Ring.toSemiring.{u4} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} N _inst_4) _inst_7) (LinearMap.range.{u4, u4, u3, u1, max u3 u1} R R M N (Ring.toSemiring.{u4} R _inst_1) (Ring.toSemiring.{u4} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} N _inst_4) _inst_5 _inst_7 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (Ring.toSemiring.{u4} R _inst_1))) (LinearMap.{u4, u4, u3, u1} R R (Ring.toSemiring.{u4} R _inst_1) (Ring.toSemiring.{u4} R _inst_1) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (Ring.toSemiring.{u4} R _inst_1))) M N (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} N _inst_4) _inst_5 _inst_7) (LinearMap.semilinearMapClass.{u4, u4, u3, u1} R R M N (Ring.toSemiring.{u4} R _inst_1) (Ring.toSemiring.{u4} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} N _inst_4) _inst_5 _inst_7 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (Ring.toSemiring.{u4} R _inst_1)))) (RingHomSurjective.ids.{u4} R (Ring.toSemiring.{u4} R _inst_1)) f) (LinearMap.ker.{u4, u4, u1, u2, max u2 u1} R R N P (Ring.toSemiring.{u4} R _inst_1) (Ring.toSemiring.{u4} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} N _inst_4) (AddCommGroup.toAddCommMonoid.{u2} P _inst_3) _inst_7 _inst_6 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (Ring.toSemiring.{u4} R _inst_1))) (LinearMap.{u4, u4, u1, u2} R R (Ring.toSemiring.{u4} R _inst_1) (Ring.toSemiring.{u4} R _inst_1) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (Ring.toSemiring.{u4} R _inst_1))) N P (AddCommGroup.toAddCommMonoid.{u1} N _inst_4) (AddCommGroup.toAddCommMonoid.{u2} P _inst_3) _inst_7 _inst_6) (LinearMap.semilinearMapClass.{u4, u4, u1, u2} R R N P (Ring.toSemiring.{u4} R _inst_1) (Ring.toSemiring.{u4} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} N _inst_4) (AddCommGroup.toAddCommMonoid.{u2} P _inst_3) _inst_7 _inst_6 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (Ring.toSemiring.{u4} R _inst_1)))) g)) -> (IsArtinian.{u4, u1} R N (Ring.toSemiring.{u4} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} N _inst_4) _inst_7)
+  forall {R : Type.{u4}} {M : Type.{u3}} {P : Type.{u2}} {N : Type.{u1}} [_inst_1 : Ring.{u4} R] [_inst_2 : AddCommGroup.{u3} M] [_inst_3 : AddCommGroup.{u2} P] [_inst_4 : AddCommGroup.{u1} N] [_inst_5 : Module.{u4, u3} R M (Ring.toSemiring.{u4} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2)] [_inst_6 : Module.{u4, u2} R P (Ring.toSemiring.{u4} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} P _inst_3)] [_inst_7 : Module.{u4, u1} R N (Ring.toSemiring.{u4} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} N _inst_4)] [_inst_8 : IsArtinian.{u4, u3} R M (Ring.toSemiring.{u4} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) _inst_5] [_inst_9 : IsArtinian.{u4, u2} R P (Ring.toSemiring.{u4} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} P _inst_3) _inst_6] (f : LinearMap.{u4, u4, u3, u1} R R (Ring.toSemiring.{u4} R _inst_1) (Ring.toSemiring.{u4} R _inst_1) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (Ring.toSemiring.{u4} R _inst_1))) M N (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} N _inst_4) _inst_5 _inst_7) (g : LinearMap.{u4, u4, u1, u2} R R (Ring.toSemiring.{u4} R _inst_1) (Ring.toSemiring.{u4} R _inst_1) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (Ring.toSemiring.{u4} R _inst_1))) N P (AddCommGroup.toAddCommMonoid.{u1} N _inst_4) (AddCommGroup.toAddCommMonoid.{u2} P _inst_3) _inst_7 _inst_6), (Function.Injective.{succ u3, succ u1} M N (FunLike.coe.{max (succ u3) (succ u1), succ u3, succ u1} (LinearMap.{u4, u4, u3, u1} R R (Ring.toSemiring.{u4} R _inst_1) (Ring.toSemiring.{u4} R _inst_1) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (Ring.toSemiring.{u4} R _inst_1))) M N (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} N _inst_4) _inst_5 _inst_7) M (fun (_x : M) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : M) => N) _x) (LinearMap.instFunLikeLinearMap.{u4, u4, u3, u1} R R M N (Ring.toSemiring.{u4} R _inst_1) (Ring.toSemiring.{u4} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} N _inst_4) _inst_5 _inst_7 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (Ring.toSemiring.{u4} R _inst_1)))) f)) -> (Function.Surjective.{succ u1, succ u2} N P (FunLike.coe.{max (succ u2) (succ u1), succ u1, succ u2} (LinearMap.{u4, u4, u1, u2} R R (Ring.toSemiring.{u4} R _inst_1) (Ring.toSemiring.{u4} R _inst_1) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (Ring.toSemiring.{u4} R _inst_1))) N P (AddCommGroup.toAddCommMonoid.{u1} N _inst_4) (AddCommGroup.toAddCommMonoid.{u2} P _inst_3) _inst_7 _inst_6) N (fun (_x : N) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : N) => P) _x) (LinearMap.instFunLikeLinearMap.{u4, u4, u1, u2} R R N P (Ring.toSemiring.{u4} R _inst_1) (Ring.toSemiring.{u4} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} N _inst_4) (AddCommGroup.toAddCommMonoid.{u2} P _inst_3) _inst_7 _inst_6 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (Ring.toSemiring.{u4} R _inst_1)))) g)) -> (Eq.{succ u1} (Submodule.{u4, u1} R N (Ring.toSemiring.{u4} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} N _inst_4) _inst_7) (LinearMap.range.{u4, u4, u3, u1, max u3 u1} R R M N (Ring.toSemiring.{u4} R _inst_1) (Ring.toSemiring.{u4} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} N _inst_4) _inst_5 _inst_7 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (Ring.toSemiring.{u4} R _inst_1))) (LinearMap.{u4, u4, u3, u1} R R (Ring.toSemiring.{u4} R _inst_1) (Ring.toSemiring.{u4} R _inst_1) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (Ring.toSemiring.{u4} R _inst_1))) M N (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} N _inst_4) _inst_5 _inst_7) (LinearMap.semilinearMapClass.{u4, u4, u3, u1} R R M N (Ring.toSemiring.{u4} R _inst_1) (Ring.toSemiring.{u4} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} N _inst_4) _inst_5 _inst_7 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (Ring.toSemiring.{u4} R _inst_1)))) (RingHomSurjective.ids.{u4} R (Ring.toSemiring.{u4} R _inst_1)) f) (LinearMap.ker.{u4, u4, u1, u2, max u2 u1} R R N P (Ring.toSemiring.{u4} R _inst_1) (Ring.toSemiring.{u4} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} N _inst_4) (AddCommGroup.toAddCommMonoid.{u2} P _inst_3) _inst_7 _inst_6 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (Ring.toSemiring.{u4} R _inst_1))) (LinearMap.{u4, u4, u1, u2} R R (Ring.toSemiring.{u4} R _inst_1) (Ring.toSemiring.{u4} R _inst_1) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (Ring.toSemiring.{u4} R _inst_1))) N P (AddCommGroup.toAddCommMonoid.{u1} N _inst_4) (AddCommGroup.toAddCommMonoid.{u2} P _inst_3) _inst_7 _inst_6) (LinearMap.semilinearMapClass.{u4, u4, u1, u2} R R N P (Ring.toSemiring.{u4} R _inst_1) (Ring.toSemiring.{u4} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} N _inst_4) (AddCommGroup.toAddCommMonoid.{u2} P _inst_3) _inst_7 _inst_6 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (Ring.toSemiring.{u4} R _inst_1)))) g)) -> (IsArtinian.{u4, u1} R N (Ring.toSemiring.{u4} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} N _inst_4) _inst_7)
 Case conversion may be inaccurate. Consider using '#align is_artinian_of_range_eq_ker isArtinian_of_range_eq_kerₓ'. -/
 theorem isArtinian_of_range_eq_ker [IsArtinian R M] [IsArtinian R P] (f : M →ₗ[R] N) (g : N →ₗ[R] P)
     (hf : Function.Injective f) (hg : Function.Surjective g) (h : f.range = g.ker) :
@@ -344,7 +344,7 @@ theorem exists_endomorphism_iterate_ker_sup_range_eq_top (f : M →ₗ[R] M) :
 lean 3 declaration is
   forall {R : Type.{u1}} {M : Type.{u2}} [_inst_1 : Ring.{u1} R] [_inst_2 : AddCommGroup.{u2} M] [_inst_3 : Module.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2)] [_inst_4 : IsArtinian.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3] (f : LinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 _inst_3), (Function.Injective.{succ u2, succ u2} M M (coeFn.{succ u2, succ u2} (LinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 _inst_3) (fun (_x : LinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 _inst_3) => M -> M) (LinearMap.hasCoeToFun.{u1, u1, u2, u2} R R M M (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 _inst_3 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1)))) f)) -> (Function.Surjective.{succ u2, succ u2} M M (coeFn.{succ u2, succ u2} (LinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 _inst_3) (fun (_x : LinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 _inst_3) => M -> M) (LinearMap.hasCoeToFun.{u1, u1, u2, u2} R R M M (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 _inst_3 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1)))) f))
 but is expected to have type
-  forall {R : Type.{u2}} {M : Type.{u1}} [_inst_1 : Ring.{u2} R] [_inst_2 : AddCommGroup.{u1} M] [_inst_3 : Module.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2)] [_inst_4 : IsArtinian.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3] (f : LinearMap.{u2, u2, u1, u1} R R (Ring.toSemiring.{u2} R _inst_1) (Ring.toSemiring.{u2} R _inst_1) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (Ring.toSemiring.{u2} R _inst_1))) M M (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3 _inst_3), (Function.Injective.{succ u1, succ u1} M M (FunLike.coe.{succ u1, succ u1, succ u1} (LinearMap.{u2, u2, u1, u1} R R (Ring.toSemiring.{u2} R _inst_1) (Ring.toSemiring.{u2} R _inst_1) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (Ring.toSemiring.{u2} R _inst_1))) M M (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3 _inst_3) M (fun (_x : M) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : M) => M) _x) (LinearMap.instFunLikeLinearMap.{u2, u2, u1, u1} R R M M (Ring.toSemiring.{u2} R _inst_1) (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3 _inst_3 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (Ring.toSemiring.{u2} R _inst_1)))) f)) -> (Function.Surjective.{succ u1, succ u1} M M (FunLike.coe.{succ u1, succ u1, succ u1} (LinearMap.{u2, u2, u1, u1} R R (Ring.toSemiring.{u2} R _inst_1) (Ring.toSemiring.{u2} R _inst_1) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (Ring.toSemiring.{u2} R _inst_1))) M M (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3 _inst_3) M (fun (_x : M) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : M) => M) _x) (LinearMap.instFunLikeLinearMap.{u2, u2, u1, u1} R R M M (Ring.toSemiring.{u2} R _inst_1) (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3 _inst_3 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (Ring.toSemiring.{u2} R _inst_1)))) f))
+  forall {R : Type.{u2}} {M : Type.{u1}} [_inst_1 : Ring.{u2} R] [_inst_2 : AddCommGroup.{u1} M] [_inst_3 : Module.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2)] [_inst_4 : IsArtinian.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3] (f : LinearMap.{u2, u2, u1, u1} R R (Ring.toSemiring.{u2} R _inst_1) (Ring.toSemiring.{u2} R _inst_1) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (Ring.toSemiring.{u2} R _inst_1))) M M (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3 _inst_3), (Function.Injective.{succ u1, succ u1} M M (FunLike.coe.{succ u1, succ u1, succ u1} (LinearMap.{u2, u2, u1, u1} R R (Ring.toSemiring.{u2} R _inst_1) (Ring.toSemiring.{u2} R _inst_1) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (Ring.toSemiring.{u2} R _inst_1))) M M (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3 _inst_3) M (fun (_x : M) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : M) => M) _x) (LinearMap.instFunLikeLinearMap.{u2, u2, u1, u1} R R M M (Ring.toSemiring.{u2} R _inst_1) (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3 _inst_3 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (Ring.toSemiring.{u2} R _inst_1)))) f)) -> (Function.Surjective.{succ u1, succ u1} M M (FunLike.coe.{succ u1, succ u1, succ u1} (LinearMap.{u2, u2, u1, u1} R R (Ring.toSemiring.{u2} R _inst_1) (Ring.toSemiring.{u2} R _inst_1) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (Ring.toSemiring.{u2} R _inst_1))) M M (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3 _inst_3) M (fun (_x : M) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : M) => M) _x) (LinearMap.instFunLikeLinearMap.{u2, u2, u1, u1} R R M M (Ring.toSemiring.{u2} R _inst_1) (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3 _inst_3 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (Ring.toSemiring.{u2} R _inst_1)))) f))
 Case conversion may be inaccurate. Consider using '#align is_artinian.surjective_of_injective_endomorphism IsArtinian.surjective_of_injective_endomorphismₓ'. -/
 /-- Any injective endomorphism of an Artinian module is surjective. -/
 theorem surjective_of_injective_endomorphism (f : M →ₗ[R] M) (s : Injective f) : Surjective f :=
@@ -359,7 +359,7 @@ theorem surjective_of_injective_endomorphism (f : M →ₗ[R] M) (s : Injective
 lean 3 declaration is
   forall {R : Type.{u1}} {M : Type.{u2}} [_inst_1 : Ring.{u1} R] [_inst_2 : AddCommGroup.{u2} M] [_inst_3 : Module.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2)] [_inst_4 : IsArtinian.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3] (f : LinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 _inst_3), (Function.Injective.{succ u2, succ u2} M M (coeFn.{succ u2, succ u2} (LinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 _inst_3) (fun (_x : LinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 _inst_3) => M -> M) (LinearMap.hasCoeToFun.{u1, u1, u2, u2} R R M M (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 _inst_3 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1)))) f)) -> (Function.Bijective.{succ u2, succ u2} M M (coeFn.{succ u2, succ u2} (LinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 _inst_3) (fun (_x : LinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 _inst_3) => M -> M) (LinearMap.hasCoeToFun.{u1, u1, u2, u2} R R M M (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 _inst_3 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1)))) f))
 but is expected to have type
-  forall {R : Type.{u2}} {M : Type.{u1}} [_inst_1 : Ring.{u2} R] [_inst_2 : AddCommGroup.{u1} M] [_inst_3 : Module.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2)] [_inst_4 : IsArtinian.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3] (f : LinearMap.{u2, u2, u1, u1} R R (Ring.toSemiring.{u2} R _inst_1) (Ring.toSemiring.{u2} R _inst_1) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (Ring.toSemiring.{u2} R _inst_1))) M M (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3 _inst_3), (Function.Injective.{succ u1, succ u1} M M (FunLike.coe.{succ u1, succ u1, succ u1} (LinearMap.{u2, u2, u1, u1} R R (Ring.toSemiring.{u2} R _inst_1) (Ring.toSemiring.{u2} R _inst_1) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (Ring.toSemiring.{u2} R _inst_1))) M M (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3 _inst_3) M (fun (_x : M) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : M) => M) _x) (LinearMap.instFunLikeLinearMap.{u2, u2, u1, u1} R R M M (Ring.toSemiring.{u2} R _inst_1) (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3 _inst_3 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (Ring.toSemiring.{u2} R _inst_1)))) f)) -> (Function.Bijective.{succ u1, succ u1} M M (FunLike.coe.{succ u1, succ u1, succ u1} (LinearMap.{u2, u2, u1, u1} R R (Ring.toSemiring.{u2} R _inst_1) (Ring.toSemiring.{u2} R _inst_1) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (Ring.toSemiring.{u2} R _inst_1))) M M (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3 _inst_3) M (fun (_x : M) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : M) => M) _x) (LinearMap.instFunLikeLinearMap.{u2, u2, u1, u1} R R M M (Ring.toSemiring.{u2} R _inst_1) (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3 _inst_3 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (Ring.toSemiring.{u2} R _inst_1)))) f))
+  forall {R : Type.{u2}} {M : Type.{u1}} [_inst_1 : Ring.{u2} R] [_inst_2 : AddCommGroup.{u1} M] [_inst_3 : Module.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2)] [_inst_4 : IsArtinian.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3] (f : LinearMap.{u2, u2, u1, u1} R R (Ring.toSemiring.{u2} R _inst_1) (Ring.toSemiring.{u2} R _inst_1) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (Ring.toSemiring.{u2} R _inst_1))) M M (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3 _inst_3), (Function.Injective.{succ u1, succ u1} M M (FunLike.coe.{succ u1, succ u1, succ u1} (LinearMap.{u2, u2, u1, u1} R R (Ring.toSemiring.{u2} R _inst_1) (Ring.toSemiring.{u2} R _inst_1) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (Ring.toSemiring.{u2} R _inst_1))) M M (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3 _inst_3) M (fun (_x : M) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : M) => M) _x) (LinearMap.instFunLikeLinearMap.{u2, u2, u1, u1} R R M M (Ring.toSemiring.{u2} R _inst_1) (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3 _inst_3 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (Ring.toSemiring.{u2} R _inst_1)))) f)) -> (Function.Bijective.{succ u1, succ u1} M M (FunLike.coe.{succ u1, succ u1, succ u1} (LinearMap.{u2, u2, u1, u1} R R (Ring.toSemiring.{u2} R _inst_1) (Ring.toSemiring.{u2} R _inst_1) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (Ring.toSemiring.{u2} R _inst_1))) M M (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3 _inst_3) M (fun (_x : M) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : M) => M) _x) (LinearMap.instFunLikeLinearMap.{u2, u2, u1, u1} R R M M (Ring.toSemiring.{u2} R _inst_1) (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3 _inst_3 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (Ring.toSemiring.{u2} R _inst_1)))) f))
 Case conversion may be inaccurate. Consider using '#align is_artinian.bijective_of_injective_endomorphism IsArtinian.bijective_of_injective_endomorphismₓ'. -/
 /-- Any injective endomorphism of an Artinian module is bijective. -/
 theorem bijective_of_injective_endomorphism (f : M →ₗ[R] M) (s : Injective f) : Bijective f :=

mathlib commit https://github.com/leanprover-community/mathlib/commit/8d33f09cd7089ecf074b4791907588245aec5d1b

@@ -4,7 +4,7 @@ Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Chris Hughes
 
 ! This file was ported from Lean 3 source module ring_theory.artinian
-! leanprover-community/mathlib commit 210657c4ea4a4a7b234392f70a3a2a83346dfa90
+! leanprover-community/mathlib commit 38df578a6450a8c5142b3727e3ae894c2300cae0
 ! Please do not edit these lines, except to modify the commit id
 ! if you have ported upstream changes.
 -/
@@ -14,6 +14,9 @@ import Mathbin.Data.SetLike.Fintype
 /-!
 # Artinian rings and modules
 
+> THIS FILE IS SYNCHRONIZED WITH MATHLIB4.
+> Any changes to this file require a corresponding PR to mathlib4.
+
 
 A module satisfying these equivalent conditions is said to be an *Artinian* R-module
 if every decreasing chain of submodules is eventually constant, or equivalently,

mathlib commit https://github.com/leanprover-community/mathlib/commit/1b0a28e1c93409dbf6d69526863cd9984ef652ce

@@ -46,6 +46,7 @@ open Set
 
 open BigOperators Pointwise
 
+#print IsArtinian /-
 /- ./././Mathport/Syntax/Translate/Command.lean:393:30: infer kinds are unsupported in Lean 4: #[`wellFounded_submodule_lt] [] -/
 /-- `is_artinian R M` is the proposition that `M` is an Artinian `R`-module,
 implemented as the well-foundedness of submodule inclusion.
@@ -53,6 +54,7 @@ implemented as the well-foundedness of submodule inclusion.
 class IsArtinian (R M) [Semiring R] [AddCommMonoid M] [Module R M] : Prop where
   wellFounded_submodule_lt : WellFounded ((· < ·) : Submodule R M → Submodule R M → Prop)
 #align is_artinian IsArtinian
+-/
 
 section
 
@@ -66,6 +68,12 @@ open IsArtinian
 
 include R
 
+/- warning: is_artinian_of_injective -> isArtinian_of_injective is a dubious translation:
+lean 3 declaration is
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+but is expected to have type
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+Case conversion may be inaccurate. Consider using '#align is_artinian_of_injective isArtinian_of_injectiveₓ'. -/
 theorem isArtinian_of_injective (f : M →ₗ[R] P) (h : Function.Injective f) [IsArtinian R P] :
     IsArtinian R M :=
   ⟨Subrelation.wf
@@ -73,16 +81,30 @@ theorem isArtinian_of_injective (f : M →ₗ[R] P) (h : Function.Injective f) [
       (InvImage.wf (Submodule.map f) (IsArtinian.wellFounded_submodule_lt R P))⟩
 #align is_artinian_of_injective isArtinian_of_injective
 
+#print isArtinian_submodule' /-
 instance isArtinian_submodule' [IsArtinian R M] (N : Submodule R M) : IsArtinian R N :=
   isArtinian_of_injective N.Subtype Subtype.val_injective
 #align is_artinian_submodule' isArtinian_submodule'
+-/
 
+/- warning: is_artinian_of_le -> isArtinian_of_le is a dubious translation:
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+Case conversion may be inaccurate. Consider using '#align is_artinian_of_le isArtinian_of_leₓ'. -/
 theorem isArtinian_of_le {s t : Submodule R M} [ht : IsArtinian R t] (h : s ≤ t) : IsArtinian R s :=
   isArtinian_of_injective (Submodule.ofLe h) (Submodule.ofLe_injective h)
 #align is_artinian_of_le isArtinian_of_le
 
 variable (M)
 
+/- warning: is_artinian_of_surjective -> isArtinian_of_surjective is a dubious translation:
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+but is expected to have type
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+Case conversion may be inaccurate. Consider using '#align is_artinian_of_surjective isArtinian_of_surjectiveₓ'. -/
 theorem isArtinian_of_surjective (f : M →ₗ[R] P) (hf : Function.Surjective f) [IsArtinian R M] :
     IsArtinian R P :=
   ⟨Subrelation.wf
@@ -93,10 +115,22 @@ theorem isArtinian_of_surjective (f : M →ₗ[R] P) (hf : Function.Surjective f
 
 variable {M}
 
+/- warning: is_artinian_of_linear_equiv -> isArtinian_of_linearEquiv is a dubious translation:
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+but is expected to have type
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+Case conversion may be inaccurate. Consider using '#align is_artinian_of_linear_equiv isArtinian_of_linearEquivₓ'. -/
 theorem isArtinian_of_linearEquiv (f : M ≃ₗ[R] P) [IsArtinian R M] : IsArtinian R P :=
   isArtinian_of_surjective _ f.toLinearMap f.toEquiv.Surjective
 #align is_artinian_of_linear_equiv isArtinian_of_linearEquiv
 
+/- warning: is_artinian_of_range_eq_ker -> isArtinian_of_range_eq_ker is a dubious translation:
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_inst_4) (AddCommGroup.toAddCommMonoid.{u2} P _inst_3) _inst_7 _inst_6 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (Ring.toSemiring.{u4} R _inst_1)))) g)) -> (IsArtinian.{u4, u1} R N (Ring.toSemiring.{u4} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} N _inst_4) _inst_7)
+Case conversion may be inaccurate. Consider using '#align is_artinian_of_range_eq_ker isArtinian_of_range_eq_kerₓ'. -/
 theorem isArtinian_of_range_eq_ker [IsArtinian R M] [IsArtinian R P] (f : M →ₗ[R] N) (g : N →ₗ[R] P)
     (hf : Function.Injective f) (hg : Function.Surjective g) (h : f.range = g.ker) :
     IsArtinian R N :=
@@ -106,17 +140,26 @@ theorem isArtinian_of_range_eq_ker [IsArtinian R M] [IsArtinian R P] (f : M →
       (by simp [Submodule.map_comap_eq, inf_comm]) (by simp [Submodule.comap_map_eq, h])⟩
 #align is_artinian_of_range_eq_ker isArtinian_of_range_eq_ker
 
+/- warning: is_artinian_prod -> isArtinian_prod is a dubious translation:
+lean 3 declaration is
+  forall {R : Type.{u1}} {M : Type.{u2}} {P : Type.{u3}} [_inst_1 : Ring.{u1} R] [_inst_2 : AddCommGroup.{u2} M] [_inst_3 : AddCommGroup.{u3} P] [_inst_5 : Module.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2)] [_inst_6 : Module.{u1, u3} R P (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} P _inst_3)] [_inst_8 : IsArtinian.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_5] [_inst_9 : IsArtinian.{u1, u3} R P (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} P _inst_3) _inst_6], IsArtinian.{u1, max u2 u3} R (Prod.{u2, u3} M P) (Ring.toSemiring.{u1} R _inst_1) (Prod.addCommMonoid.{u2, u3} M P (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u3} P _inst_3)) (Prod.module.{u1, u2, u3} R M P (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u3} P _inst_3) _inst_5 _inst_6)
+but is expected to have type
+  forall {R : Type.{u1}} {M : Type.{u2}} {P : Type.{u3}} [_inst_1 : Ring.{u1} R] [_inst_2 : AddCommGroup.{u2} M] [_inst_3 : AddCommGroup.{u3} P] [_inst_5 : Module.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2)] [_inst_6 : Module.{u1, u3} R P (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} P _inst_3)] [_inst_8 : IsArtinian.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_5] [_inst_9 : IsArtinian.{u1, u3} R P (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} P _inst_3) _inst_6], IsArtinian.{u1, max u3 u2} R (Prod.{u2, u3} M P) (Ring.toSemiring.{u1} R _inst_1) (Prod.instAddCommMonoidSum.{u2, u3} M P (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u3} P _inst_3)) (Prod.module.{u1, u2, u3} R M P (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u3} P _inst_3) _inst_5 _inst_6)
+Case conversion may be inaccurate. Consider using '#align is_artinian_prod isArtinian_prodₓ'. -/
 instance isArtinian_prod [IsArtinian R M] [IsArtinian R P] : IsArtinian R (M × P) :=
   isArtinian_of_range_eq_ker (LinearMap.inl R M P) (LinearMap.snd R M P) LinearMap.inl_injective
     LinearMap.snd_surjective (LinearMap.range_inl R M P)
 #align is_artinian_prod isArtinian_prod
 
+#print isArtinian_of_finite /-
 instance (priority := 100) isArtinian_of_finite [Finite M] : IsArtinian R M :=
   ⟨Finite.wellFounded_of_trans_of_irrefl _⟩
 #align is_artinian_of_finite isArtinian_of_finite
+-/
 
 attribute [local elab_as_elim] Finite.induction_empty_option
 
+#print isArtinian_pi /-
 instance isArtinian_pi {R ι : Type _} [Finite ι] :
     ∀ {M : ι → Type _} [Ring R] [∀ i, AddCommGroup (M i)],
       ∀ [∀ i, Module R (M i)], ∀ [∀ i, IsArtinian R (M i)], IsArtinian R (∀ i, M i) :=
@@ -132,7 +175,9 @@ instance isArtinian_pi {R ι : Type _} [Finite ι] :
       exact isArtinian_of_linearEquiv (LinearEquiv.piOptionEquivProd R).symm)
     ι
 #align is_artinian_pi isArtinian_pi
+-/
 
+#print isArtinian_pi' /-
 /-- A version of `is_artinian_pi` for non-dependent functions. We need this instance because
 sometimes Lean fails to apply the dependent version in non-dependent settings (e.g., it fails to
 prove that `ι → ℝ` is finite dimensional over `ℝ`). -/
@@ -140,6 +185,7 @@ instance isArtinian_pi' {R ι M : Type _} [Ring R] [AddCommGroup M] [Module R M]
     [IsArtinian R M] : IsArtinian R (ι → M) :=
   isArtinian_pi
 #align is_artinian_pi' isArtinian_pi'
+-/
 
 end
 
@@ -149,6 +195,12 @@ section Ring
 
 variable {R M : Type _} [Ring R] [AddCommGroup M] [Module R M]
 
+/- warning: is_artinian_iff_well_founded -> isArtinian_iff_wellFounded is a dubious translation:
+lean 3 declaration is
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+but is expected to have type
+  forall {R : Type.{u2}} {M : Type.{u1}} [_inst_1 : Ring.{u2} R] [_inst_2 : AddCommGroup.{u1} M] [_inst_3 : Module.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2)], Iff (IsArtinian.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (WellFounded.{succ u1} (Submodule.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (fun (x._@.Mathlib.RingTheory.Artinian._hyg.1218 : Submodule.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (x._@.Mathlib.RingTheory.Artinian._hyg.1220 : Submodule.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) => LT.lt.{u1} (Submodule.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Preorder.toLT.{u1} (Submodule.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (PartialOrder.toPreorder.{u1} (Submodule.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (OmegaCompletePartialOrder.toPartialOrder.{u1} (Submodule.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (CompleteLattice.instOmegaCompletePartialOrder.{u1} (Submodule.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.completeLattice.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3))))) x._@.Mathlib.RingTheory.Artinian._hyg.1218 x._@.Mathlib.RingTheory.Artinian._hyg.1220))
+Case conversion may be inaccurate. Consider using '#align is_artinian_iff_well_founded isArtinian_iff_wellFoundedₓ'. -/
 theorem isArtinian_iff_wellFounded :
     IsArtinian R M ↔ WellFounded ((· < ·) : Submodule R M → Submodule R M → Prop) :=
   ⟨fun h => h.1, IsArtinian.mk⟩
@@ -156,6 +208,12 @@ theorem isArtinian_iff_wellFounded :
 
 variable {R M}
 
+/- warning: is_artinian.finite_of_linear_independent -> IsArtinian.finite_of_linearIndependent is a dubious translation:
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+Case conversion may be inaccurate. Consider using '#align is_artinian.finite_of_linear_independent IsArtinian.finite_of_linearIndependentₓ'. -/
 theorem IsArtinian.finite_of_linearIndependent [Nontrivial R] [IsArtinian R M] {s : Set M}
     (hs : LinearIndependent R (coe : s → M)) : s.Finite :=
   by
@@ -183,6 +241,12 @@ theorem IsArtinian.finite_of_linearIndependent [Nontrivial R] [IsArtinian R M] {
       simp⟩
 #align is_artinian.finite_of_linear_independent IsArtinian.finite_of_linearIndependent
 
+/- warning: set_has_minimal_iff_artinian -> set_has_minimal_iff_artinian is a dubious translation:
+lean 3 declaration is
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+but is expected to have type
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+Case conversion may be inaccurate. Consider using '#align set_has_minimal_iff_artinian set_has_minimal_iff_artinianₓ'. -/
 /-- A module is Artinian iff every nonempty set of submodules has a minimal submodule among them.
 -/
 theorem set_has_minimal_iff_artinian :
@@ -190,11 +254,23 @@ theorem set_has_minimal_iff_artinian :
   rw [isArtinian_iff_wellFounded, WellFounded.wellFounded_iff_has_min]
 #align set_has_minimal_iff_artinian set_has_minimal_iff_artinian
 
+/- warning: is_artinian.set_has_minimal -> IsArtinian.set_has_minimal is a dubious translation:
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+but is expected to have type
+  forall {R : Type.{u2}} {M : Type.{u1}} [_inst_1 : Ring.{u2} R] [_inst_2 : AddCommGroup.{u1} M] [_inst_3 : Module.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2)] [_inst_4 : IsArtinian.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3] (a : Set.{u1} (Submodule.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3)), (Set.Nonempty.{u1} (Submodule.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) a) -> (Exists.{succ u1} (Submodule.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (fun (M' : Submodule.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) => And (Membership.mem.{u1, u1} (Submodule.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Set.{u1} (Submodule.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3)) (Set.instMembershipSet.{u1} (Submodule.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3)) M' a) (forall (I : Submodule.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3), (Membership.mem.{u1, u1} (Submodule.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Set.{u1} (Submodule.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3)) (Set.instMembershipSet.{u1} (Submodule.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3)) I a) -> (Not (LT.lt.{u1} (Submodule.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Preorder.toLT.{u1} (Submodule.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (PartialOrder.toPreorder.{u1} (Submodule.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (OmegaCompletePartialOrder.toPartialOrder.{u1} (Submodule.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (CompleteLattice.instOmegaCompletePartialOrder.{u1} (Submodule.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.completeLattice.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3))))) I M')))))
+Case conversion may be inaccurate. Consider using '#align is_artinian.set_has_minimal IsArtinian.set_has_minimalₓ'. -/
 theorem IsArtinian.set_has_minimal [IsArtinian R M] (a : Set <| Submodule R M) (ha : a.Nonempty) :
     ∃ M' ∈ a, ∀ I ∈ a, ¬I < M' :=
   set_has_minimal_iff_artinian.mpr ‹_› a ha
 #align is_artinian.set_has_minimal IsArtinian.set_has_minimal
 
+/- warning: monotone_stabilizes_iff_artinian -> monotone_stabilizes_iff_artinian is a dubious translation:
+lean 3 declaration is
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(Submodule.setLike.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3))))) => Nat -> (OrderDual.{u2} (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3))) (OrderHom.hasCoeToFun.{0, u2} Nat (OrderDual.{u2} (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3)) (PartialOrder.toPreorder.{0} Nat (OrderedCancelAddCommMonoid.toPartialOrder.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring))) (OrderDual.preorder.{u2} (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (PartialOrder.toPreorder.{u2} (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (SetLike.partialOrder.{u2, u2} (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) M (Submodule.setLike.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3))))) f n) (coeFn.{succ u2, succ u2} (OrderHom.{0, u2} Nat (OrderDual.{u2} (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3)) (PartialOrder.toPreorder.{0} Nat (OrderedCancelAddCommMonoid.toPartialOrder.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring))) (OrderDual.preorder.{u2} (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (PartialOrder.toPreorder.{u2} (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (SetLike.partialOrder.{u2, u2} (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) M (Submodule.setLike.{u1, u2} R M 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(Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3))) (OrderHom.hasCoeToFun.{0, u2} Nat (OrderDual.{u2} (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3)) (PartialOrder.toPreorder.{0} Nat (OrderedCancelAddCommMonoid.toPartialOrder.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring))) (OrderDual.preorder.{u2} (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (PartialOrder.toPreorder.{u2} (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (SetLike.partialOrder.{u2, u2} (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) M (Submodule.setLike.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3))))) f m)))) (IsArtinian.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3)
+but is expected to have type
+  forall {R : Type.{u1}} {M : Type.{u2}} [_inst_1 : Ring.{u1} R] [_inst_2 : AddCommGroup.{u2} M] [_inst_3 : Module.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2)], Iff (forall (f : OrderHom.{0, u2} Nat (OrderDual.{u2} (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3)) (PartialOrder.toPreorder.{0} Nat (StrictOrderedSemiring.toPartialOrder.{0} Nat Nat.strictOrderedSemiring)) (OrderDual.preorder.{u2} (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (PartialOrder.toPreorder.{u2} (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (OmegaCompletePartialOrder.toPartialOrder.{u2} (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (CompleteLattice.instOmegaCompletePartialOrder.{u2} (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.completeLattice.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3)))))), Exists.{1} Nat (fun (n : Nat) => forall (m : Nat), (LE.le.{0} Nat instLENat n m) -> (Eq.{succ u2} (OrderDual.{u2} (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3)) (OrderHom.toFun.{0, u2} Nat (OrderDual.{u2} (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3)) (PartialOrder.toPreorder.{0} Nat (StrictOrderedSemiring.toPartialOrder.{0} Nat Nat.strictOrderedSemiring)) (OrderDual.preorder.{u2} (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (PartialOrder.toPreorder.{u2} (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (OmegaCompletePartialOrder.toPartialOrder.{u2} (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (CompleteLattice.instOmegaCompletePartialOrder.{u2} (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.completeLattice.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3))))) f n) (OrderHom.toFun.{0, u2} Nat (OrderDual.{u2} (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3)) (PartialOrder.toPreorder.{0} Nat (StrictOrderedSemiring.toPartialOrder.{0} Nat Nat.strictOrderedSemiring)) (OrderDual.preorder.{u2} (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (PartialOrder.toPreorder.{u2} (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (OmegaCompletePartialOrder.toPartialOrder.{u2} (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (CompleteLattice.instOmegaCompletePartialOrder.{u2} (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.completeLattice.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3))))) f m)))) (IsArtinian.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3)
+Case conversion may be inaccurate. Consider using '#align monotone_stabilizes_iff_artinian monotone_stabilizes_iff_artinianₓ'. -/
 /-- A module is Artinian iff every decreasing chain of submodules stabilizes. -/
 theorem monotone_stabilizes_iff_artinian :
     (∀ f : ℕ →o (Submodule R M)ᵒᵈ, ∃ n, ∀ m, n ≤ m → f n = f m) ↔ IsArtinian R M :=
@@ -207,16 +283,34 @@ namespace IsArtinian
 
 variable [IsArtinian R M]
 
+/- warning: is_artinian.monotone_stabilizes -> IsArtinian.monotone_stabilizes is a dubious translation:
+lean 3 declaration is
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(Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3))))) f m)))
+but is expected to have type
+  forall {R : Type.{u1}} {M : Type.{u2}} [_inst_1 : Ring.{u1} R] [_inst_2 : AddCommGroup.{u2} M] [_inst_3 : Module.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2)] [_inst_4 : IsArtinian.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3] (f : OrderHom.{0, u2} Nat (OrderDual.{u2} (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3)) (PartialOrder.toPreorder.{0} Nat (StrictOrderedSemiring.toPartialOrder.{0} Nat Nat.strictOrderedSemiring)) (OrderDual.preorder.{u2} (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (PartialOrder.toPreorder.{u2} (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (OmegaCompletePartialOrder.toPartialOrder.{u2} (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (CompleteLattice.instOmegaCompletePartialOrder.{u2} (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.completeLattice.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3)))))), Exists.{1} Nat (fun (n : Nat) => forall (m : Nat), (LE.le.{0} Nat instLENat n m) -> (Eq.{succ u2} (OrderDual.{u2} (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3)) (OrderHom.toFun.{0, u2} Nat (OrderDual.{u2} (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3)) (PartialOrder.toPreorder.{0} Nat (StrictOrderedSemiring.toPartialOrder.{0} Nat Nat.strictOrderedSemiring)) (OrderDual.preorder.{u2} (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (PartialOrder.toPreorder.{u2} (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (OmegaCompletePartialOrder.toPartialOrder.{u2} (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (CompleteLattice.instOmegaCompletePartialOrder.{u2} (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.completeLattice.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3))))) f n) (OrderHom.toFun.{0, u2} Nat (OrderDual.{u2} (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3)) (PartialOrder.toPreorder.{0} Nat (StrictOrderedSemiring.toPartialOrder.{0} Nat Nat.strictOrderedSemiring)) (OrderDual.preorder.{u2} (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (PartialOrder.toPreorder.{u2} (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (OmegaCompletePartialOrder.toPartialOrder.{u2} (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (CompleteLattice.instOmegaCompletePartialOrder.{u2} (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.completeLattice.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3))))) f m)))
+Case conversion may be inaccurate. Consider using '#align is_artinian.monotone_stabilizes IsArtinian.monotone_stabilizesₓ'. -/
 theorem monotone_stabilizes (f : ℕ →o (Submodule R M)ᵒᵈ) : ∃ n, ∀ m, n ≤ m → f n = f m :=
   monotone_stabilizes_iff_artinian.mpr ‹_› f
 #align is_artinian.monotone_stabilizes IsArtinian.monotone_stabilizes
 
+/- warning: is_artinian.induction -> IsArtinian.induction is a dubious translation:
+lean 3 declaration is
+  forall {R : Type.{u1}} {M : Type.{u2}} [_inst_1 : Ring.{u1} R] [_inst_2 : AddCommGroup.{u2} M] [_inst_3 : Module.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2)] [_inst_4 : IsArtinian.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3] {P : (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) -> Prop}, (forall (I : Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3), (forall (J : Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3), (LT.lt.{u2} (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Preorder.toHasLt.{u2} (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (PartialOrder.toPreorder.{u2} (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (SetLike.partialOrder.{u2, u2} (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) M (Submodule.setLike.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3)))) J I) -> (P J)) -> (P I)) -> (forall (I : Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3), P I)
+but is expected to have type
+  forall {R : Type.{u2}} {M : Type.{u1}} [_inst_1 : Ring.{u2} R] [_inst_2 : AddCommGroup.{u1} M] [_inst_3 : Module.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2)] [_inst_4 : IsArtinian.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3] {P : (Submodule.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) -> Prop}, (forall (I : Submodule.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3), (forall (J : Submodule.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3), (LT.lt.{u1} (Submodule.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Preorder.toLT.{u1} (Submodule.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (PartialOrder.toPreorder.{u1} (Submodule.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (OmegaCompletePartialOrder.toPartialOrder.{u1} (Submodule.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (CompleteLattice.instOmegaCompletePartialOrder.{u1} (Submodule.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.completeLattice.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3))))) J I) -> (P J)) -> (P I)) -> (forall (I : Submodule.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3), P I)
+Case conversion may be inaccurate. Consider using '#align is_artinian.induction IsArtinian.inductionₓ'. -/
 /-- If `∀ I > J, P I` implies `P J`, then `P` holds for all submodules. -/
 theorem induction {P : Submodule R M → Prop} (hgt : ∀ I, (∀ J < I, P J) → P I) (I : Submodule R M) :
     P I :=
   (wellFounded_submodule_lt R M).recursion I hgt
 #align is_artinian.induction IsArtinian.induction
 
+/- warning: is_artinian.exists_endomorphism_iterate_ker_sup_range_eq_top -> IsArtinian.exists_endomorphism_iterate_ker_sup_range_eq_top is a dubious translation:
+lean 3 declaration is
+  forall {R : Type.{u1}} {M : Type.{u2}} [_inst_1 : Ring.{u1} R] [_inst_2 : AddCommGroup.{u2} M] [_inst_3 : Module.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2)] [_inst_4 : IsArtinian.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3] (f : LinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 _inst_3), Exists.{1} Nat (fun (n : Nat) => And (Ne.{1} Nat n (OfNat.ofNat.{0} Nat 0 (OfNat.mk.{0} Nat 0 (Zero.zero.{0} Nat Nat.hasZero)))) (Eq.{succ u2} (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Sup.sup.{u2} (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (SemilatticeSup.toHasSup.{u2} (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Lattice.toSemilatticeSup.{u2} (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (ConditionallyCompleteLattice.toLattice.{u2} (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (CompleteLattice.toConditionallyCompleteLattice.{u2} (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.completeLattice.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3))))) (LinearMap.ker.{u1, u1, u2, u2, u2} R R M M (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 _inst_3 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (LinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 _inst_3) (LinearMap.semilinearMapClass.{u1, u1, u2, u2} R R M M (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 _inst_3 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1)))) (HPow.hPow.{u2, 0, u2} (LinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 _inst_3) Nat (LinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 _inst_3) (instHPow.{u2, 0} (LinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 _inst_3) Nat (Monoid.Pow.{u2} (LinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 _inst_3) (Module.End.monoid.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3))) f n)) (LinearMap.range.{u1, u1, u2, u2, u2} R R M M (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 _inst_3 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (LinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 _inst_3) (LinearMap.semilinearMapClass.{u1, u1, u2, u2} R R M M (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 _inst_3 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1)))) (RingHomSurjective.ids.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (HPow.hPow.{u2, 0, u2} (LinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 _inst_3) Nat (LinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 _inst_3) (instHPow.{u2, 0} (LinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 _inst_3) Nat (Monoid.Pow.{u2} (LinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 _inst_3) (Module.End.monoid.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3))) f n))) (Top.top.{u2} (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasTop.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3))))
+but is expected to have type
+  forall {R : Type.{u2}} {M : Type.{u1}} [_inst_1 : Ring.{u2} R] [_inst_2 : AddCommGroup.{u1} M] [_inst_3 : Module.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2)] [_inst_4 : IsArtinian.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3] (f : LinearMap.{u2, u2, u1, u1} R R (Ring.toSemiring.{u2} R _inst_1) (Ring.toSemiring.{u2} R _inst_1) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (Ring.toSemiring.{u2} R _inst_1))) M M (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3 _inst_3), Exists.{1} Nat (fun (n : Nat) => And (Ne.{1} Nat n (OfNat.ofNat.{0} Nat 0 (instOfNatNat 0))) (Eq.{succ u1} (Submodule.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Sup.sup.{u1} (Submodule.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (SemilatticeSup.toSup.{u1} (Submodule.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Lattice.toSemilatticeSup.{u1} (Submodule.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (ConditionallyCompleteLattice.toLattice.{u1} (Submodule.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (CompleteLattice.toConditionallyCompleteLattice.{u1} (Submodule.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.completeLattice.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3))))) (LinearMap.ker.{u2, u2, u1, u1, u1} R R M M (Ring.toSemiring.{u2} R _inst_1) (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3 _inst_3 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (Ring.toSemiring.{u2} R _inst_1))) (LinearMap.{u2, u2, u1, u1} R R (Ring.toSemiring.{u2} R _inst_1) (Ring.toSemiring.{u2} R _inst_1) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (Ring.toSemiring.{u2} R _inst_1))) M M (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3 _inst_3) (LinearMap.semilinearMapClass.{u2, u2, u1, u1} R R M M (Ring.toSemiring.{u2} R _inst_1) (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3 _inst_3 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (Ring.toSemiring.{u2} R _inst_1)))) (HPow.hPow.{u1, 0, u1} (LinearMap.{u2, u2, u1, u1} R R (Ring.toSemiring.{u2} R _inst_1) (Ring.toSemiring.{u2} R _inst_1) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (Ring.toSemiring.{u2} R _inst_1))) M M (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3 _inst_3) Nat (LinearMap.{u2, u2, u1, u1} R R (Ring.toSemiring.{u2} R _inst_1) (Ring.toSemiring.{u2} R _inst_1) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (Ring.toSemiring.{u2} R _inst_1))) M M (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3 _inst_3) (instHPow.{u1, 0} (LinearMap.{u2, u2, u1, u1} R R (Ring.toSemiring.{u2} R _inst_1) (Ring.toSemiring.{u2} R _inst_1) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (Ring.toSemiring.{u2} R _inst_1))) M M (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3 _inst_3) Nat (Monoid.Pow.{u1} (LinearMap.{u2, u2, u1, u1} R R (Ring.toSemiring.{u2} R _inst_1) (Ring.toSemiring.{u2} R _inst_1) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (Ring.toSemiring.{u2} R _inst_1))) M M (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3 _inst_3) (Module.End.monoid.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3))) f n)) (LinearMap.range.{u2, u2, u1, u1, u1} R R M M (Ring.toSemiring.{u2} R _inst_1) (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3 _inst_3 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (Ring.toSemiring.{u2} R _inst_1))) (LinearMap.{u2, u2, u1, u1} R R (Ring.toSemiring.{u2} R _inst_1) (Ring.toSemiring.{u2} R _inst_1) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (Ring.toSemiring.{u2} R _inst_1))) M M (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3 _inst_3) (LinearMap.semilinearMapClass.{u2, u2, u1, u1} R R M M (Ring.toSemiring.{u2} R _inst_1) (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3 _inst_3 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (Ring.toSemiring.{u2} R _inst_1)))) (RingHomSurjective.ids.{u2} R (Ring.toSemiring.{u2} R _inst_1)) (HPow.hPow.{u1, 0, u1} (LinearMap.{u2, u2, u1, u1} R R (Ring.toSemiring.{u2} R _inst_1) (Ring.toSemiring.{u2} R _inst_1) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (Ring.toSemiring.{u2} R _inst_1))) M M (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3 _inst_3) Nat (LinearMap.{u2, u2, u1, u1} R R (Ring.toSemiring.{u2} R _inst_1) (Ring.toSemiring.{u2} R _inst_1) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (Ring.toSemiring.{u2} R _inst_1))) M M (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3 _inst_3) (instHPow.{u1, 0} (LinearMap.{u2, u2, u1, u1} R R (Ring.toSemiring.{u2} R _inst_1) (Ring.toSemiring.{u2} R _inst_1) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (Ring.toSemiring.{u2} R _inst_1))) M M (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3 _inst_3) Nat (Monoid.Pow.{u1} (LinearMap.{u2, u2, u1, u1} R R (Ring.toSemiring.{u2} R _inst_1) (Ring.toSemiring.{u2} R _inst_1) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (Ring.toSemiring.{u2} R _inst_1))) M M (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3 _inst_3) (Module.End.monoid.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3))) f n))) (Top.top.{u1} (Submodule.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.instTopSubmodule.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3))))
+Case conversion may be inaccurate. Consider using '#align is_artinian.exists_endomorphism_iterate_ker_sup_range_eq_top IsArtinian.exists_endomorphism_iterate_ker_sup_range_eq_topₓ'. -/
 /-- For any endomorphism of a Artinian module, there is some nontrivial iterate
 with disjoint kernel and range.
 -/
@@ -243,6 +337,12 @@ theorem exists_endomorphism_iterate_ker_sup_range_eq_top (f : M →ₗ[R] M) :
     simp
 #align is_artinian.exists_endomorphism_iterate_ker_sup_range_eq_top IsArtinian.exists_endomorphism_iterate_ker_sup_range_eq_top
 
+/- warning: is_artinian.surjective_of_injective_endomorphism -> IsArtinian.surjective_of_injective_endomorphism is a dubious translation:
+lean 3 declaration is
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+Case conversion may be inaccurate. Consider using '#align is_artinian.surjective_of_injective_endomorphism IsArtinian.surjective_of_injective_endomorphismₓ'. -/
 /-- Any injective endomorphism of an Artinian module is surjective. -/
 theorem surjective_of_injective_endomorphism (f : M →ₗ[R] M) (s : Injective f) : Surjective f :=
   by
@@ -252,11 +352,23 @@ theorem surjective_of_injective_endomorphism (f : M →ₗ[R] M) (s : Injective
   exact LinearMap.surjective_of_iterate_surjective Ne w
 #align is_artinian.surjective_of_injective_endomorphism IsArtinian.surjective_of_injective_endomorphism
 
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 /-- Any injective endomorphism of an Artinian module is bijective. -/
 theorem bijective_of_injective_endomorphism (f : M →ₗ[R] M) (s : Injective f) : Bijective f :=
   ⟨s, surjective_of_injective_endomorphism f s⟩
 #align is_artinian.bijective_of_injective_endomorphism IsArtinian.bijective_of_injective_endomorphism
 
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(AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3))) => (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) -> (OrderDual.{u2} (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3))) (Equiv.hasCoeToFun.{succ u2, succ u2} (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (OrderDual.{u2} (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3))) (OrderDual.toDual.{u2} (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3))) f)) n) (coeFn.{succ u2, succ u2} (Equiv.{succ u2, succ u2} (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (OrderDual.{u2} (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} 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(instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))))) -> (Exists.{1} Nat (fun (n : Nat) => forall (m : Nat), (LE.le.{0} Nat Nat.hasLe n m) -> (Eq.{succ u2} (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (f m) (Top.top.{u2} (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasTop.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3)))))
+but is expected to have type
+  forall {R : Type.{u2}} {M : Type.{u1}} [_inst_1 : Ring.{u2} R] [_inst_2 : AddCommGroup.{u1} M] [_inst_3 : Module.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2)] [_inst_4 : IsArtinian.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3] (f : Nat -> (Submodule.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3)), (forall (n : Nat), Disjoint.{u1} (OrderDual.{u1} (Submodule.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3)) (OrderDual.partialOrder.{u1} (Submodule.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (OmegaCompletePartialOrder.toPartialOrder.{u1} (Submodule.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (CompleteLattice.instOmegaCompletePartialOrder.{u1} (Submodule.{u2, u1} R M 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_inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3))) f)) n) (FunLike.coe.{succ u1, succ u1, succ u1} (Equiv.{succ u1, succ u1} (Submodule.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (OrderDual.{u1} (Submodule.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3))) (Submodule.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (fun (_x : Submodule.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) => (fun (x._@.Mathlib.Logic.Equiv.Defs._hyg.812 : Submodule.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) => OrderDual.{u1} (Submodule.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3)) _x) (Equiv.instFunLikeEquiv.{succ u1, succ u1} (Submodule.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (OrderDual.{u1} (Submodule.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3))) (OrderDual.toDual.{u1} (Submodule.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3)) (f (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))))) -> (Exists.{1} Nat (fun (n : Nat) => forall (m : Nat), (LE.le.{0} Nat instLENat n m) -> (Eq.{succ u1} (Submodule.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (f m) (Top.top.{u1} (Submodule.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.instTopSubmodule.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3)))))
+Case conversion may be inaccurate. Consider using '#align is_artinian.disjoint_partial_infs_eventually_top IsArtinian.disjoint_partial_infs_eventually_topₓ'. -/
 /-- A sequence `f` of submodules of a artinian module,
 with the supremum `f (n+1)` and the infinum of `f 0`, ..., `f n` being ⊤,
 is eventually ⊤.
@@ -287,6 +399,7 @@ variable {R : Type _} (M : Type _) [CommRing R] [AddCommGroup M] [Module R M] [I
 
 namespace IsArtinian
 
+#print IsArtinian.range_smul_pow_stabilizes /-
 theorem range_smul_pow_stabilizes (r : R) :
     ∃ n : ℕ,
       ∀ m,
@@ -298,9 +411,16 @@ theorem range_smul_pow_stabilizes (r : R) :
         dsimp at hy⊢
         rw [← smul_assoc, smul_eq_mul, ← pow_add, ← hy, add_tsub_cancel_of_le h]⟩⟩
 #align is_artinian.range_smul_pow_stabilizes IsArtinian.range_smul_pow_stabilizes
+-/
 
 variable {M}
 
+/- warning: is_artinian.exists_pow_succ_smul_dvd -> IsArtinian.exists_pow_succ_smul_dvd is a dubious translation:
+lean 3 declaration is
+  forall {R : Type.{u1}} {M : Type.{u2}} [_inst_1 : CommRing.{u1} R] [_inst_2 : AddCommGroup.{u2} M] [_inst_3 : Module.{u1, u2} R M (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2)] [_inst_4 : IsArtinian.{u1, u2} R M (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3] (r : R) (x : M), Exists.{1} Nat (fun (n : Nat) => Exists.{succ u2} M (fun (y : M) => Eq.{succ u2} M (SMul.smul.{u1, u2} R M (SMulZeroClass.toHasSmul.{u1, u2} R M (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2)))) (SMulWithZero.toSmulZeroClass.{u1, u2} R M (MulZeroClass.toHasZero.{u1} R (MulZeroOneClass.toMulZeroClass.{u1} R (MonoidWithZero.toMulZeroOneClass.{u1} R (Semiring.toMonoidWithZero.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))))) (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2)))) (MulActionWithZero.toSMulWithZero.{u1, u2} R M (Semiring.toMonoidWithZero.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2)))) (Module.toMulActionWithZero.{u1, u2} R M (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3)))) (HPow.hPow.{u1, 0, u1} R Nat R (instHPow.{u1, 0} R Nat (Monoid.Pow.{u1} R (Ring.toMonoid.{u1} R (CommRing.toRing.{u1} R _inst_1)))) r (Nat.succ n)) y) (SMul.smul.{u1, u2} R M (SMulZeroClass.toHasSmul.{u1, u2} R M (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2)))) (SMulWithZero.toSmulZeroClass.{u1, u2} R M (MulZeroClass.toHasZero.{u1} R (MulZeroOneClass.toMulZeroClass.{u1} R (MonoidWithZero.toMulZeroOneClass.{u1} R (Semiring.toMonoidWithZero.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))))) (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2)))) (MulActionWithZero.toSMulWithZero.{u1, u2} R M (Semiring.toMonoidWithZero.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2)))) (Module.toMulActionWithZero.{u1, u2} R M (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3)))) (HPow.hPow.{u1, 0, u1} R Nat R (instHPow.{u1, 0} R Nat (Monoid.Pow.{u1} R (Ring.toMonoid.{u1} R (CommRing.toRing.{u1} R _inst_1)))) r n) x)))
+but is expected to have type
+  forall {R : Type.{u1}} {M : Type.{u2}} [_inst_1 : CommRing.{u1} R] [_inst_2 : AddCommGroup.{u2} M] [_inst_3 : Module.{u1, u2} R M (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2)] [_inst_4 : IsArtinian.{u1, u2} R M (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3] (r : R) (x : M), Exists.{1} Nat (fun (n : Nat) => Exists.{succ u2} M (fun (y : M) => Eq.{succ u2} M (HSMul.hSMul.{u1, u2, u2} R M M (instHSMul.{u1, u2} R M (SMulZeroClass.toSMul.{u1, u2} R M (NegZeroClass.toZero.{u2} M (SubNegZeroMonoid.toNegZeroClass.{u2} M (SubtractionMonoid.toSubNegZeroMonoid.{u2} M (SubtractionCommMonoid.toSubtractionMonoid.{u2} M (AddCommGroup.toDivisionAddCommMonoid.{u2} M _inst_2))))) (SMulWithZero.toSMulZeroClass.{u1, u2} R M (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (NegZeroClass.toZero.{u2} M (SubNegZeroMonoid.toNegZeroClass.{u2} M (SubtractionMonoid.toSubNegZeroMonoid.{u2} M (SubtractionCommMonoid.toSubtractionMonoid.{u2} M (AddCommGroup.toDivisionAddCommMonoid.{u2} M _inst_2))))) (MulActionWithZero.toSMulWithZero.{u1, u2} R M (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (NegZeroClass.toZero.{u2} M (SubNegZeroMonoid.toNegZeroClass.{u2} M (SubtractionMonoid.toSubNegZeroMonoid.{u2} M (SubtractionCommMonoid.toSubtractionMonoid.{u2} M (AddCommGroup.toDivisionAddCommMonoid.{u2} M _inst_2))))) (Module.toMulActionWithZero.{u1, u2} R M (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3))))) (HPow.hPow.{u1, 0, u1} R Nat R (instHPow.{u1, 0} R Nat (Monoid.Pow.{u1} R (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) r (Nat.succ n)) y) (HSMul.hSMul.{u1, u2, u2} R M M (instHSMul.{u1, u2} R M (SMulZeroClass.toSMul.{u1, u2} R M (NegZeroClass.toZero.{u2} M (SubNegZeroMonoid.toNegZeroClass.{u2} M (SubtractionMonoid.toSubNegZeroMonoid.{u2} M (SubtractionCommMonoid.toSubtractionMonoid.{u2} M (AddCommGroup.toDivisionAddCommMonoid.{u2} M _inst_2))))) (SMulWithZero.toSMulZeroClass.{u1, u2} R M (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (NegZeroClass.toZero.{u2} M (SubNegZeroMonoid.toNegZeroClass.{u2} M (SubtractionMonoid.toSubNegZeroMonoid.{u2} M (SubtractionCommMonoid.toSubtractionMonoid.{u2} M (AddCommGroup.toDivisionAddCommMonoid.{u2} M _inst_2))))) (MulActionWithZero.toSMulWithZero.{u1, u2} R M (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (NegZeroClass.toZero.{u2} M (SubNegZeroMonoid.toNegZeroClass.{u2} M (SubtractionMonoid.toSubNegZeroMonoid.{u2} M (SubtractionCommMonoid.toSubtractionMonoid.{u2} M (AddCommGroup.toDivisionAddCommMonoid.{u2} M _inst_2))))) (Module.toMulActionWithZero.{u1, u2} R M (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3))))) (HPow.hPow.{u1, 0, u1} R Nat R (instHPow.{u1, 0} R Nat (Monoid.Pow.{u1} R (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) r n) x)))
+Case conversion may be inaccurate. Consider using '#align is_artinian.exists_pow_succ_smul_dvd IsArtinian.exists_pow_succ_smul_dvdₓ'. -/
 theorem exists_pow_succ_smul_dvd (r : R) (x : M) : ∃ (n : ℕ)(y : M), r ^ n.succ • y = r ^ n • x :=
   by
   obtain ⟨n, hn⟩ := IsArtinian.range_smul_pow_stabilizes M r
@@ -312,6 +432,7 @@ end IsArtinian
 
 end CommRing
 
+#print IsArtinianRing /-
 -- TODO: Prove this for artinian modules
 -- /--
 -- If `M ⊕ N` embeds into `M`, for `M` noetherian over `R`, then `N` is trivial.
@@ -338,25 +459,52 @@ convenience in the commutative case. For a right Artinian ring, use `is_artinian
 def IsArtinianRing (R) [Ring R] :=
   IsArtinian R R
 #align is_artinian_ring IsArtinianRing
+-/
 
+#print isArtinianRing_iff /-
 theorem isArtinianRing_iff {R} [Ring R] : IsArtinianRing R ↔ IsArtinian R R :=
   Iff.rfl
 #align is_artinian_ring_iff isArtinianRing_iff
+-/
 
-theorem Ring.is_artinian_of_zero_eq_one {R} [Ring R] (h01 : (0 : R) = 1) : IsArtinianRing R :=
+/- warning: ring.is_artinian_of_zero_eq_one -> Ring.isArtinian_of_zero_eq_one is a dubious translation:
+lean 3 declaration is
+  forall {R : Type.{u1}} [_inst_1 : Ring.{u1} R], (Eq.{succ u1} R (OfNat.ofNat.{u1} R 0 (OfNat.mk.{u1} R 0 (Zero.zero.{u1} R (MulZeroClass.toHasZero.{u1} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R _inst_1)))))))) (OfNat.ofNat.{u1} R 1 (OfNat.mk.{u1} R 1 (One.one.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R _inst_1)))))))) -> (IsArtinianRing.{u1} R _inst_1)
+but is expected to have type
+  forall {R : Type.{u1}} [_inst_1 : Ring.{u1} R], (Eq.{succ u1} R (OfNat.ofNat.{u1} R 0 (Zero.toOfNat0.{u1} R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (Ring.toSemiring.{u1} R _inst_1))))) (OfNat.ofNat.{u1} R 1 (One.toOfNat1.{u1} R (Semiring.toOne.{u1} R (Ring.toSemiring.{u1} R _inst_1))))) -> (IsArtinianRing.{u1} R _inst_1)
+Case conversion may be inaccurate. Consider using '#align ring.is_artinian_of_zero_eq_one Ring.isArtinian_of_zero_eq_oneₓ'. -/
+theorem Ring.isArtinian_of_zero_eq_one {R} [Ring R] (h01 : (0 : R) = 1) : IsArtinianRing R :=
   have := subsingleton_of_zero_eq_one h01
   inferInstance
-#align ring.is_artinian_of_zero_eq_one Ring.is_artinian_of_zero_eq_one
-
+#align ring.is_artinian_of_zero_eq_one Ring.isArtinian_of_zero_eq_one
+
+/- warning: is_artinian_of_submodule_of_artinian -> isArtinian_of_submodule_of_artinian is a dubious translation:
+lean 3 declaration is
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+but is expected to have type
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+Case conversion may be inaccurate. Consider using '#align is_artinian_of_submodule_of_artinian isArtinian_of_submodule_of_artinianₓ'. -/
 theorem isArtinian_of_submodule_of_artinian (R M) [Ring R] [AddCommGroup M] [Module R M]
     (N : Submodule R M) (h : IsArtinian R M) : IsArtinian R N := by infer_instance
 #align is_artinian_of_submodule_of_artinian isArtinian_of_submodule_of_artinian
 
+/- warning: is_artinian_of_quotient_of_artinian -> isArtinian_of_quotient_of_artinian is a dubious translation:
+lean 3 declaration is
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+but is expected to have type
+  forall (R : Type.{u2}) [_inst_1 : Ring.{u2} R] (M : Type.{u1}) [_inst_2 : AddCommGroup.{u1} M] [_inst_3 : Module.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2)] (N : Submodule.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3), (IsArtinian.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) -> (IsArtinian.{u2, u1} R (HasQuotient.Quotient.{u1, u1} M (Submodule.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.hasQuotient.{u2, u1} R M _inst_1 _inst_2 _inst_3) N) (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} (HasQuotient.Quotient.{u1, u1} M (Submodule.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.hasQuotient.{u2, u1} R M _inst_1 _inst_2 _inst_3) N) (Submodule.Quotient.addCommGroup.{u2, u1} R M _inst_1 _inst_2 _inst_3 N)) (Submodule.Quotient.module.{u2, u1} R M _inst_1 _inst_2 _inst_3 N))
+Case conversion may be inaccurate. Consider using '#align is_artinian_of_quotient_of_artinian isArtinian_of_quotient_of_artinianₓ'. -/
 theorem isArtinian_of_quotient_of_artinian (R) [Ring R] (M) [AddCommGroup M] [Module R M]
     (N : Submodule R M) (h : IsArtinian R M) : IsArtinian R (M ⧸ N) :=
   isArtinian_of_surjective M (Submodule.mkQ N) (Submodule.Quotient.mk_surjective N)
 #align is_artinian_of_quotient_of_artinian isArtinian_of_quotient_of_artinian
 
+/- warning: is_artinian_of_tower -> isArtinian_of_tower is a dubious translation:
+lean 3 declaration is
+  forall (R : Type.{u1}) {S : Type.{u2}} {M : Type.{u3}} [_inst_1 : CommRing.{u1} R] [_inst_2 : Ring.{u2} S] [_inst_3 : AddCommGroup.{u3} M] [_inst_4 : Algebra.{u1, u2} R S (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u2} S _inst_2)] [_inst_5 : Module.{u2, u3} S M (Ring.toSemiring.{u2} S _inst_2) (AddCommGroup.toAddCommMonoid.{u3} M _inst_3)] [_inst_6 : Module.{u1, u3} R M (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u3} M _inst_3)] [_inst_7 : IsScalarTower.{u1, u2, u3} R S M (SMulZeroClass.toHasSmul.{u1, u2} R S (AddZeroClass.toHasZero.{u2} S (AddMonoid.toAddZeroClass.{u2} S (AddCommMonoid.toAddMonoid.{u2} S (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S (Ring.toSemiring.{u2} S _inst_2))))))) (SMulWithZero.toSmulZeroClass.{u1, u2} R S (MulZeroClass.toHasZero.{u1} R (MulZeroOneClass.toMulZeroClass.{u1} R (MonoidWithZero.toMulZeroOneClass.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) (AddZeroClass.toHasZero.{u2} S (AddMonoid.toAddZeroClass.{u2} S (AddCommMonoid.toAddMonoid.{u2} S (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S (Ring.toSemiring.{u2} S _inst_2))))))) (MulActionWithZero.toSMulWithZero.{u1, u2} R S (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddZeroClass.toHasZero.{u2} S (AddMonoid.toAddZeroClass.{u2} S (AddCommMonoid.toAddMonoid.{u2} S (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S (Ring.toSemiring.{u2} S _inst_2))))))) (Module.toMulActionWithZero.{u1, u2} R S (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S (Ring.toSemiring.{u2} S _inst_2)))) (Algebra.toModule.{u1, u2} R S (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u2} S _inst_2) _inst_4))))) (SMulZeroClass.toHasSmul.{u2, u3} S M (AddZeroClass.toHasZero.{u3} M (AddMonoid.toAddZeroClass.{u3} M (AddCommMonoid.toAddMonoid.{u3} M (AddCommGroup.toAddCommMonoid.{u3} M _inst_3)))) (SMulWithZero.toSmulZeroClass.{u2, u3} S M (MulZeroClass.toHasZero.{u2} S (MulZeroOneClass.toMulZeroClass.{u2} S (MonoidWithZero.toMulZeroOneClass.{u2} S (Semiring.toMonoidWithZero.{u2} S (Ring.toSemiring.{u2} S _inst_2))))) (AddZeroClass.toHasZero.{u3} M (AddMonoid.toAddZeroClass.{u3} M (AddCommMonoid.toAddMonoid.{u3} M (AddCommGroup.toAddCommMonoid.{u3} M _inst_3)))) (MulActionWithZero.toSMulWithZero.{u2, u3} S M (Semiring.toMonoidWithZero.{u2} S (Ring.toSemiring.{u2} S _inst_2)) (AddZeroClass.toHasZero.{u3} M (AddMonoid.toAddZeroClass.{u3} M (AddCommMonoid.toAddMonoid.{u3} M (AddCommGroup.toAddCommMonoid.{u3} M _inst_3)))) (Module.toMulActionWithZero.{u2, u3} S M (Ring.toSemiring.{u2} S _inst_2) (AddCommGroup.toAddCommMonoid.{u3} M _inst_3) _inst_5)))) (SMulZeroClass.toHasSmul.{u1, u3} R M (AddZeroClass.toHasZero.{u3} M (AddMonoid.toAddZeroClass.{u3} M (AddCommMonoid.toAddMonoid.{u3} M (AddCommGroup.toAddCommMonoid.{u3} M _inst_3)))) (SMulWithZero.toSmulZeroClass.{u1, u3} R M (MulZeroClass.toHasZero.{u1} R (MulZeroOneClass.toMulZeroClass.{u1} R (MonoidWithZero.toMulZeroOneClass.{u1} R (Semiring.toMonoidWithZero.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))))) (AddZeroClass.toHasZero.{u3} M (AddMonoid.toAddZeroClass.{u3} M (AddCommMonoid.toAddMonoid.{u3} M (AddCommGroup.toAddCommMonoid.{u3} M _inst_3)))) (MulActionWithZero.toSMulWithZero.{u1, u3} R M (Semiring.toMonoidWithZero.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddZeroClass.toHasZero.{u3} M (AddMonoid.toAddZeroClass.{u3} M (AddCommMonoid.toAddMonoid.{u3} M (AddCommGroup.toAddCommMonoid.{u3} M _inst_3)))) (Module.toMulActionWithZero.{u1, u3} R M (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u3} M _inst_3) _inst_6))))], (IsArtinian.{u1, u3} R M (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u3} M _inst_3) _inst_6) -> (IsArtinian.{u2, u3} S M (Ring.toSemiring.{u2} S _inst_2) (AddCommGroup.toAddCommMonoid.{u3} M _inst_3) _inst_5)
+but is expected to have type
+  forall (R : Type.{u3}) {S : Type.{u2}} {M : Type.{u1}} [_inst_1 : CommRing.{u3} R] [_inst_2 : Ring.{u2} S] [_inst_3 : AddCommGroup.{u1} M] [_inst_4 : Algebra.{u3, u2} R S (CommRing.toCommSemiring.{u3} R _inst_1) (Ring.toSemiring.{u2} S _inst_2)] [_inst_5 : Module.{u2, u1} S M (Ring.toSemiring.{u2} S _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M _inst_3)] [_inst_6 : Module.{u3, u1} R M (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_3)] [_inst_7 : IsScalarTower.{u3, u2, u1} R S M (Algebra.toSMul.{u3, u2} R S (CommRing.toCommSemiring.{u3} R _inst_1) (Ring.toSemiring.{u2} S _inst_2) _inst_4) (SMulZeroClass.toSMul.{u2, u1} S M (NegZeroClass.toZero.{u1} M (SubNegZeroMonoid.toNegZeroClass.{u1} M (SubtractionMonoid.toSubNegZeroMonoid.{u1} M (SubtractionCommMonoid.toSubtractionMonoid.{u1} M (AddCommGroup.toDivisionAddCommMonoid.{u1} M _inst_3))))) (SMulWithZero.toSMulZeroClass.{u2, u1} S M (MonoidWithZero.toZero.{u2} S (Semiring.toMonoidWithZero.{u2} S (Ring.toSemiring.{u2} S _inst_2))) (NegZeroClass.toZero.{u1} M (SubNegZeroMonoid.toNegZeroClass.{u1} M (SubtractionMonoid.toSubNegZeroMonoid.{u1} M (SubtractionCommMonoid.toSubtractionMonoid.{u1} M (AddCommGroup.toDivisionAddCommMonoid.{u1} M _inst_3))))) (MulActionWithZero.toSMulWithZero.{u2, u1} S M (Semiring.toMonoidWithZero.{u2} S (Ring.toSemiring.{u2} S _inst_2)) (NegZeroClass.toZero.{u1} M (SubNegZeroMonoid.toNegZeroClass.{u1} M (SubtractionMonoid.toSubNegZeroMonoid.{u1} M (SubtractionCommMonoid.toSubtractionMonoid.{u1} M (AddCommGroup.toDivisionAddCommMonoid.{u1} M _inst_3))))) (Module.toMulActionWithZero.{u2, u1} S M (Ring.toSemiring.{u2} S _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M _inst_3) _inst_5)))) (SMulZeroClass.toSMul.{u3, u1} R M (NegZeroClass.toZero.{u1} M (SubNegZeroMonoid.toNegZeroClass.{u1} M (SubtractionMonoid.toSubNegZeroMonoid.{u1} M (SubtractionCommMonoid.toSubtractionMonoid.{u1} M (AddCommGroup.toDivisionAddCommMonoid.{u1} M _inst_3))))) (SMulWithZero.toSMulZeroClass.{u3, u1} R M (CommMonoidWithZero.toZero.{u3} R (CommSemiring.toCommMonoidWithZero.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))) (NegZeroClass.toZero.{u1} M (SubNegZeroMonoid.toNegZeroClass.{u1} M (SubtractionMonoid.toSubNegZeroMonoid.{u1} M (SubtractionCommMonoid.toSubtractionMonoid.{u1} M (AddCommGroup.toDivisionAddCommMonoid.{u1} M _inst_3))))) (MulActionWithZero.toSMulWithZero.{u3, u1} R M (Semiring.toMonoidWithZero.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))) (NegZeroClass.toZero.{u1} M (SubNegZeroMonoid.toNegZeroClass.{u1} M (SubtractionMonoid.toSubNegZeroMonoid.{u1} M (SubtractionCommMonoid.toSubtractionMonoid.{u1} M (AddCommGroup.toDivisionAddCommMonoid.{u1} M _inst_3))))) (Module.toMulActionWithZero.{u3, u1} R M (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_3) _inst_6))))], (IsArtinian.{u3, u1} R M (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_3) _inst_6) -> (IsArtinian.{u2, u1} S M (Ring.toSemiring.{u2} S _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M _inst_3) _inst_5)
+Case conversion may be inaccurate. Consider using '#align is_artinian_of_tower isArtinian_of_towerₓ'. -/
 /-- If `M / S / R` is a scalar tower, and `M / R` is Artinian, then `M / S` is
 also Artinian. -/
 theorem isArtinian_of_tower (R) {S M} [CommRing R] [Ring S] [AddCommGroup M] [Algebra R S]
@@ -366,7 +514,13 @@ theorem isArtinian_of_tower (R) {S M} [CommRing R] [Ring S] [AddCommGroup M] [Al
   refine' (Submodule.restrictScalarsEmbedding R S M).WellFounded h
 #align is_artinian_of_tower isArtinian_of_tower
 
-theorem isArtinian_of_fG_of_artinian {R M} [Ring R] [AddCommGroup M] [Module R M]
+/- warning: is_artinian_of_fg_of_artinian -> isArtinian_of_fg_of_artinian is a dubious translation:
+lean 3 declaration is
+  forall {R : Type.{u1}} {M : Type.{u2}} [_inst_1 : Ring.{u1} R] [_inst_2 : AddCommGroup.{u2} M] [_inst_3 : Module.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2)] (N : Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) [_inst_4 : IsArtinianRing.{u1} R _inst_1], (Submodule.FG.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 N) -> (IsArtinian.{u1, u2} R (coeSort.{succ u2, succ (succ u2)} (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) M (Submodule.setLike.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3)) N) (Ring.toSemiring.{u1} R _inst_1) (Submodule.addCommMonoid.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 N) (Submodule.module.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 N))
+but is expected to have type
+  forall {R : Type.{u2}} {M : Type.{u1}} [_inst_1 : Ring.{u2} R] [_inst_2 : AddCommGroup.{u1} M] [_inst_3 : Module.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2)] (N : Submodule.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) [_inst_4 : IsArtinianRing.{u2} R _inst_1], (Submodule.FG.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3 N) -> (IsArtinian.{u2, u1} R (Subtype.{succ u1} M (fun (x : M) => Membership.mem.{u1, u1} M (Submodule.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (SetLike.instMembership.{u1, u1} (Submodule.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) M (Submodule.setLike.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3)) x N)) (Ring.toSemiring.{u2} R _inst_1) (Submodule.addCommMonoid.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3 N) (Submodule.module.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3 N))
+Case conversion may be inaccurate. Consider using '#align is_artinian_of_fg_of_artinian isArtinian_of_fg_of_artinianₓ'. -/
+theorem isArtinian_of_fg_of_artinian {R M} [Ring R] [AddCommGroup M] [Module R M]
     (N : Submodule R M) [IsArtinianRing R] (hN : N.FG) : IsArtinian R N :=
   by
   let ⟨s, hs⟩ := hN
@@ -395,21 +549,39 @@ theorem isArtinian_of_fG_of_artinian {R M} [Ring R] [AddCommGroup M] [Module R M
   rw [@Finset.sum_attach M M s _ fun i => l i • i, ← hl2, Finsupp.total_apply, Finsupp.sum, eq_comm]
   refine' Finset.sum_subset hl1 fun x _ hx => _
   rw [Finsupp.not_mem_support_iff.1 hx, zero_smul]
-#align is_artinian_of_fg_of_artinian isArtinian_of_fG_of_artinian
-
-theorem isArtinian_of_fG_of_artinian' {R M} [Ring R] [AddCommGroup M] [Module R M]
+#align is_artinian_of_fg_of_artinian isArtinian_of_fg_of_artinian
+
+/- warning: is_artinian_of_fg_of_artinian' -> isArtinian_of_fg_of_artinian' is a dubious translation:
+lean 3 declaration is
+  forall {R : Type.{u1}} {M : Type.{u2}} [_inst_1 : Ring.{u1} R] [_inst_2 : AddCommGroup.{u2} M] [_inst_3 : Module.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2)] [_inst_4 : IsArtinianRing.{u1} R _inst_1], (Submodule.FG.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 (Top.top.{u2} (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasTop.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3))) -> (IsArtinian.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3)
+but is expected to have type
+  forall {R : Type.{u2}} {M : Type.{u1}} [_inst_1 : Ring.{u2} R] [_inst_2 : AddCommGroup.{u1} M] [_inst_3 : Module.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2)] [_inst_4 : IsArtinianRing.{u2} R _inst_1], (Submodule.FG.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3 (Top.top.{u1} (Submodule.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.instTopSubmodule.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3))) -> (IsArtinian.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3)
+Case conversion may be inaccurate. Consider using '#align is_artinian_of_fg_of_artinian' isArtinian_of_fg_of_artinian'ₓ'. -/
+theorem isArtinian_of_fg_of_artinian' {R M} [Ring R] [AddCommGroup M] [Module R M]
     [IsArtinianRing R] (h : (⊤ : Submodule R M).FG) : IsArtinian R M :=
-  have : IsArtinian R (⊤ : Submodule R M) := isArtinian_of_fG_of_artinian _ h
+  have : IsArtinian R (⊤ : Submodule R M) := isArtinian_of_fg_of_artinian _ h
   isArtinian_of_linearEquiv (LinearEquiv.ofTop (⊤ : Submodule R M) rfl)
-#align is_artinian_of_fg_of_artinian' isArtinian_of_fG_of_artinian'
-
+#align is_artinian_of_fg_of_artinian' isArtinian_of_fg_of_artinian'
+
+/- warning: is_artinian_span_of_finite -> isArtinian_span_of_finite is a dubious translation:
+lean 3 declaration is
+  forall (R : Type.{u1}) {M : Type.{u2}} [_inst_1 : Ring.{u1} R] [_inst_2 : AddCommGroup.{u2} M] [_inst_3 : Module.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2)] [_inst_4 : IsArtinianRing.{u1} R _inst_1] {A : Set.{u2} M}, (Set.Finite.{u2} M A) -> (IsArtinian.{u1, u2} R (coeSort.{succ u2, succ (succ u2)} (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) M (Submodule.setLike.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3)) (Submodule.span.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 A)) (Ring.toSemiring.{u1} R _inst_1) (Submodule.addCommMonoid.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 (Submodule.span.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 A)) (Submodule.module.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 (Submodule.span.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 A)))
+but is expected to have type
+  forall (R : Type.{u2}) {M : Type.{u1}} [_inst_1 : Ring.{u2} R] [_inst_2 : AddCommGroup.{u1} M] [_inst_3 : Module.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2)] [_inst_4 : IsArtinianRing.{u2} R _inst_1] {A : Set.{u1} M}, (Set.Finite.{u1} M A) -> (IsArtinian.{u2, u1} R (Subtype.{succ u1} M (fun (x : M) => Membership.mem.{u1, u1} M (Submodule.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (SetLike.instMembership.{u1, u1} (Submodule.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) M (Submodule.setLike.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3)) x (Submodule.span.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3 A))) (Ring.toSemiring.{u2} R _inst_1) (Submodule.addCommMonoid.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3 (Submodule.span.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3 A)) (Submodule.module.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3 (Submodule.span.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3 A)))
+Case conversion may be inaccurate. Consider using '#align is_artinian_span_of_finite isArtinian_span_of_finiteₓ'. -/
 /-- In a module over a artinian ring, the submodule generated by finitely many vectors is
 artinian. -/
 theorem isArtinian_span_of_finite (R) {M} [Ring R] [AddCommGroup M] [Module R M] [IsArtinianRing R]
     {A : Set M} (hA : A.Finite) : IsArtinian R (Submodule.span R A) :=
-  isArtinian_of_fG_of_artinian _ (Submodule.fg_def.mpr ⟨A, hA, rfl⟩)
+  isArtinian_of_fg_of_artinian _ (Submodule.fg_def.mpr ⟨A, hA, rfl⟩)
 #align is_artinian_span_of_finite isArtinian_span_of_finite
 
+/- warning: function.surjective.is_artinian_ring -> Function.Surjective.isArtinianRing is a dubious translation:
+lean 3 declaration is
+  forall {R : Type.{u1}} [_inst_1 : Ring.{u1} R] {S : Type.{u2}} [_inst_2 : Ring.{u2} S] {F : Type.{u3}} [_inst_3 : RingHomClass.{u3, u1, u2} F R S (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R _inst_1)) (NonAssocRing.toNonAssocSemiring.{u2} S (Ring.toNonAssocRing.{u2} S _inst_2))] {f : F}, (Function.Surjective.{succ u1, succ u2} R S (coeFn.{succ u3, max (succ u1) (succ u2)} F (fun (_x : F) => R -> S) (FunLike.hasCoeToFun.{succ u3, succ u1, succ u2} F R (fun (_x : R) => S) (MulHomClass.toFunLike.{u3, u1, u2} F R S (Distrib.toHasMul.{u1} R (NonUnitalNonAssocSemiring.toDistrib.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R _inst_1))))) (Distrib.toHasMul.{u2} S (NonUnitalNonAssocSemiring.toDistrib.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (NonAssocRing.toNonAssocSemiring.{u2} S (Ring.toNonAssocRing.{u2} S _inst_2))))) (NonUnitalRingHomClass.toMulHomClass.{u3, u1, u2} F R S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (NonAssocRing.toNonAssocSemiring.{u2} S (Ring.toNonAssocRing.{u2} S _inst_2))) (RingHomClass.toNonUnitalRingHomClass.{u3, u1, u2} F R S (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R _inst_1)) (NonAssocRing.toNonAssocSemiring.{u2} S (Ring.toNonAssocRing.{u2} S _inst_2)) _inst_3)))) f)) -> (forall [H : IsArtinianRing.{u1} R _inst_1], IsArtinianRing.{u2} S _inst_2)
+but is expected to have type
+  forall {R : Type.{u3}} [_inst_1 : Ring.{u3} R] {S : Type.{u2}} [_inst_2 : Ring.{u2} S] {F : Type.{u1}} [_inst_3 : RingHomClass.{u1, u3, u2} F R S (Semiring.toNonAssocSemiring.{u3} R (Ring.toSemiring.{u3} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} S (Ring.toSemiring.{u2} S _inst_2))] {f : F}, (Function.Surjective.{succ u3, succ u2} R S (FunLike.coe.{succ u1, succ u3, succ u2} F R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => S) _x) (MulHomClass.toFunLike.{u1, u3, u2} F R S (NonUnitalNonAssocSemiring.toMul.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R (Ring.toSemiring.{u3} R _inst_1)))) (NonUnitalNonAssocSemiring.toMul.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S (Ring.toSemiring.{u2} S _inst_2)))) (NonUnitalRingHomClass.toMulHomClass.{u1, u3, u2} F R S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R (Ring.toSemiring.{u3} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S (Ring.toSemiring.{u2} S _inst_2))) (RingHomClass.toNonUnitalRingHomClass.{u1, u3, u2} F R S (Semiring.toNonAssocSemiring.{u3} R (Ring.toSemiring.{u3} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} S (Ring.toSemiring.{u2} S _inst_2)) _inst_3))) f)) -> (forall [H : IsArtinianRing.{u3} R _inst_1], IsArtinianRing.{u2} S _inst_2)
+Case conversion may be inaccurate. Consider using '#align function.surjective.is_artinian_ring Function.Surjective.isArtinianRingₓ'. -/
 theorem Function.Surjective.isArtinianRing {R} [Ring R] {S} [Ring S] {F} [RingHomClass F R S]
     {f : F} (hf : Function.Surjective f) [H : IsArtinianRing R] : IsArtinianRing S :=
   by
@@ -417,6 +589,12 @@ theorem Function.Surjective.isArtinianRing {R} [Ring R] {S} [Ring S] {F} [RingHo
   exact (Ideal.orderEmbeddingOfSurjective f hf).WellFounded H
 #align function.surjective.is_artinian_ring Function.Surjective.isArtinianRing
 
+/- warning: is_artinian_ring_range -> isArtinianRing_range is a dubious translation:
+lean 3 declaration is
+  forall {R : Type.{u1}} [_inst_1 : Ring.{u1} R] {S : Type.{u2}} [_inst_2 : Ring.{u2} S] (f : RingHom.{u1, u2} R S (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R _inst_1)) (NonAssocRing.toNonAssocSemiring.{u2} S (Ring.toNonAssocRing.{u2} S _inst_2))) [_inst_3 : IsArtinianRing.{u1} R _inst_1], IsArtinianRing.{u2} (coeSort.{succ u2, succ (succ u2)} (Subring.{u2} S _inst_2) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Subring.{u2} S _inst_2) S (Subring.setLike.{u2} S _inst_2)) (RingHom.range.{u1, u2} R S _inst_1 _inst_2 f)) (Subring.toRing.{u2} S _inst_2 (RingHom.range.{u1, u2} R S _inst_1 _inst_2 f))
+but is expected to have type
+  forall {R : Type.{u1}} [_inst_1 : Ring.{u1} R] {S : Type.{u2}} [_inst_2 : Ring.{u2} S] (f : RingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} S (Ring.toSemiring.{u2} S _inst_2))) [_inst_3 : IsArtinianRing.{u1} R _inst_1], IsArtinianRing.{u2} (Subtype.{succ u2} S (fun (x : S) => Membership.mem.{u2, u2} S (Subring.{u2} S _inst_2) (SetLike.instMembership.{u2, u2} (Subring.{u2} S _inst_2) S (Subring.instSetLikeSubring.{u2} S _inst_2)) x (RingHom.range.{u1, u2} R S _inst_1 _inst_2 f))) (Subring.toRing.{u2} S _inst_2 (RingHom.range.{u1, u2} R S _inst_1 _inst_2 f))
+Case conversion may be inaccurate. Consider using '#align is_artinian_ring_range isArtinianRing_rangeₓ'. -/
 instance isArtinianRing_range {R} [Ring R] {S} [Ring S] (f : R →+* S) [IsArtinianRing R] :
     IsArtinianRing f.range :=
   f.rangeRestrict_surjective.IsArtinianRing
@@ -428,6 +606,12 @@ open IsArtinian
 
 variable {R : Type _} [CommRing R] [IsArtinianRing R]
 
+/- warning: is_artinian_ring.is_nilpotent_jacobson_bot -> IsArtinianRing.isNilpotent_jacobson_bot is a dubious translation:
+lean 3 declaration is
+  forall {R : Type.{u1}} [_inst_1 : CommRing.{u1} R] [_inst_2 : IsArtinianRing.{u1} R (CommRing.toRing.{u1} R _inst_1)], IsNilpotent.{u1} (Ideal.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toHasZero.{u1} (Ideal.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} (Ideal.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Ideal.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Ideal.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (IdemSemiring.toSemiring.{u1} (Ideal.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Submodule.idemSemiring.{u1, u1} R (CommRing.toCommSemiring.{u1} R _inst_1) R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))))) (Monoid.Pow.{u1} (Ideal.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Ideal.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Ideal.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (IdemSemiring.toSemiring.{u1} (Ideal.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Submodule.idemSemiring.{u1, u1} R (CommRing.toCommSemiring.{u1} R _inst_1) R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))))) (Ideal.jacobson.{u1} R (CommRing.toRing.{u1} R _inst_1) (Bot.bot.{u1} (Ideal.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Submodule.hasBot.{u1, u1} R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))))))
+but is expected to have type
+  forall {R : Type.{u1}} [_inst_1 : CommRing.{u1} R] [_inst_2 : IsArtinianRing.{u1} R (CommRing.toRing.{u1} R _inst_1)], IsNilpotent.{u1} (Ideal.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} (Ideal.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommSemiring.toCommMonoidWithZero.{u1} (Ideal.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (IdemCommSemiring.toCommSemiring.{u1} (Ideal.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ideal.instIdemCommSemiringIdealToSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (Monoid.Pow.{u1} (Ideal.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Ideal.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Ideal.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (IdemSemiring.toSemiring.{u1} (Ideal.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Submodule.idemSemiring.{u1, u1} R (CommRing.toCommSemiring.{u1} R _inst_1) R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))))) (Ideal.jacobson.{u1} R (CommRing.toRing.{u1} R _inst_1) (Bot.bot.{u1} (Ideal.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Submodule.instBotSubmodule.{u1, u1} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))))
+Case conversion may be inaccurate. Consider using '#align is_artinian_ring.is_nilpotent_jacobson_bot IsArtinianRing.isNilpotent_jacobson_botₓ'. -/
 theorem isNilpotent_jacobson_bot : IsNilpotent (Ideal.jacobson (⊥ : Ideal R)) :=
   by
   let Jac := Ideal.jacobson (⊥ : Ideal R)
@@ -477,6 +661,12 @@ variable (S : Submonoid R) (L : Type _) [CommRing L] [Algebra R L] [IsLocalizati
 
 include S
 
+/- warning: is_artinian_ring.localization_surjective -> IsArtinianRing.localization_surjective is a dubious translation:
+lean 3 declaration is
+  forall {R : Type.{u1}} [_inst_1 : CommRing.{u1} R] [_inst_2 : IsArtinianRing.{u1} R (CommRing.toRing.{u1} R _inst_1)] (S : Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1)))))) (L : Type.{u2}) [_inst_3 : CommRing.{u2} L] [_inst_4 : Algebra.{u1, u2} R L (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u2} L (CommRing.toRing.{u2} L _inst_3))] [_inst_5 : IsLocalization.{u1, u2} R (CommRing.toCommSemiring.{u1} R _inst_1) S L (CommRing.toCommSemiring.{u2} L _inst_3) _inst_4], Function.Surjective.{succ u1, succ u2} R L (coeFn.{max (succ u1) (succ u2), max (succ u1) (succ u2)} (RingHom.{u1, u2} R L (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u2} L (Ring.toSemiring.{u2} L (CommRing.toRing.{u2} L _inst_3)))) (fun (_x : RingHom.{u1, u2} R L (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u2} L (Ring.toSemiring.{u2} L (CommRing.toRing.{u2} L _inst_3)))) => R -> L) (RingHom.hasCoeToFun.{u1, u2} R L (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u2} L (Ring.toSemiring.{u2} L (CommRing.toRing.{u2} L _inst_3)))) (algebraMap.{u1, u2} R L (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u2} L (CommRing.toRing.{u2} L _inst_3)) _inst_4))
+but is expected to have type
+  forall {R : Type.{u2}} [_inst_1 : CommRing.{u2} R] [_inst_2 : IsArtinianRing.{u2} R (CommRing.toRing.{u2} R _inst_1)] (S : Submonoid.{u2} R (MulZeroOneClass.toMulOneClass.{u2} R (NonAssocSemiring.toMulZeroOneClass.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))))) (L : Type.{u1}) [_inst_3 : CommRing.{u1} L] [_inst_4 : Algebra.{u2, u1} R L (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} L (CommRing.toCommSemiring.{u1} L _inst_3))] [_inst_5 : IsLocalization.{u2, u1} R (CommRing.toCommSemiring.{u2} R _inst_1) S L (CommRing.toCommSemiring.{u1} L _inst_3) _inst_4], Function.Surjective.{succ u2, succ u1} R L (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (RingHom.{u2, u1} R L (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} L (CommSemiring.toSemiring.{u1} L (CommRing.toCommSemiring.{u1} L _inst_3)))) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => L) _x) (MulHomClass.toFunLike.{max u2 u1, u2, u1} (RingHom.{u2, u1} R L (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} L (CommSemiring.toSemiring.{u1} L (CommRing.toCommSemiring.{u1} L _inst_3)))) R L (NonUnitalNonAssocSemiring.toMul.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (NonUnitalNonAssocSemiring.toMul.{u1} L (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} L (Semiring.toNonAssocSemiring.{u1} L (CommSemiring.toSemiring.{u1} L (CommRing.toCommSemiring.{u1} L _inst_3))))) (NonUnitalRingHomClass.toMulHomClass.{max u2 u1, u2, u1} (RingHom.{u2, u1} R L (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} L (CommSemiring.toSemiring.{u1} L (CommRing.toCommSemiring.{u1} L _inst_3)))) R L (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} L (Semiring.toNonAssocSemiring.{u1} L (CommSemiring.toSemiring.{u1} L (CommRing.toCommSemiring.{u1} L _inst_3)))) (RingHomClass.toNonUnitalRingHomClass.{max u2 u1, u2, u1} (RingHom.{u2, u1} R L (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} L (CommSemiring.toSemiring.{u1} L (CommRing.toCommSemiring.{u1} L _inst_3)))) R L (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} L (CommSemiring.toSemiring.{u1} L (CommRing.toCommSemiring.{u1} L _inst_3))) (RingHom.instRingHomClassRingHom.{u2, u1} R L (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} L (CommSemiring.toSemiring.{u1} L (CommRing.toCommSemiring.{u1} L _inst_3))))))) (algebraMap.{u2, u1} R L (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} L (CommRing.toCommSemiring.{u1} L _inst_3)) _inst_4))
+Case conversion may be inaccurate. Consider using '#align is_artinian_ring.localization_surjective IsArtinianRing.localization_surjectiveₓ'. -/
 /-- Localizing an artinian ring can only reduce the amount of elements. -/
 theorem localization_surjective : Function.Surjective (algebraMap R L) :=
   by
@@ -493,6 +683,12 @@ theorem localization_surjective : Function.Surjective (algebraMap R L) :=
     (IsLocalization.map_units L (s ^ n)).mul_left_cancel hr, map_mul]
 #align is_artinian_ring.localization_surjective IsArtinianRing.localization_surjective
 
+/- warning: is_artinian_ring.localization_artinian -> IsArtinianRing.localization_artinian is a dubious translation:
+lean 3 declaration is
+  forall {R : Type.{u1}} [_inst_1 : CommRing.{u1} R] [_inst_2 : IsArtinianRing.{u1} R (CommRing.toRing.{u1} R _inst_1)] (S : Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1)))))) (L : Type.{u2}) [_inst_3 : CommRing.{u2} L] [_inst_4 : Algebra.{u1, u2} R L (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u2} L (CommRing.toRing.{u2} L _inst_3))] [_inst_5 : IsLocalization.{u1, u2} R (CommRing.toCommSemiring.{u1} R _inst_1) S L (CommRing.toCommSemiring.{u2} L _inst_3) _inst_4], IsArtinianRing.{u2} L (CommRing.toRing.{u2} L _inst_3)
+but is expected to have type
+  forall {R : Type.{u2}} [_inst_1 : CommRing.{u2} R] [_inst_2 : IsArtinianRing.{u2} R (CommRing.toRing.{u2} R _inst_1)] (S : Submonoid.{u2} R (MulZeroOneClass.toMulOneClass.{u2} R (NonAssocSemiring.toMulZeroOneClass.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))))) (L : Type.{u1}) [_inst_3 : CommRing.{u1} L] [_inst_4 : Algebra.{u2, u1} R L (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} L (CommRing.toCommSemiring.{u1} L _inst_3))] [_inst_5 : IsLocalization.{u2, u1} R (CommRing.toCommSemiring.{u2} R _inst_1) S L (CommRing.toCommSemiring.{u1} L _inst_3) _inst_4], IsArtinianRing.{u1} L (CommRing.toRing.{u1} L _inst_3)
+Case conversion may be inaccurate. Consider using '#align is_artinian_ring.localization_artinian IsArtinianRing.localization_artinianₓ'. -/
 theorem localization_artinian : IsArtinianRing L :=
   (localization_surjective S L).IsArtinianRing
 #align is_artinian_ring.localization_artinian IsArtinianRing.localization_artinian

mathlib commit https://github.com/leanprover-community/mathlib/commit/0b9eaaa7686280fad8cce467f5c3c57ee6ce77f8

@@ -366,8 +366,8 @@ theorem isArtinian_of_tower (R) {S M} [CommRing R] [Ring S] [AddCommGroup M] [Al
   refine' (Submodule.restrictScalarsEmbedding R S M).WellFounded h
 #align is_artinian_of_tower isArtinian_of_tower
 
-theorem isArtinian_of_fg_of_artinian {R M} [Ring R] [AddCommGroup M] [Module R M]
-    (N : Submodule R M) [IsArtinianRing R] (hN : N.Fg) : IsArtinian R N :=
+theorem isArtinian_of_fG_of_artinian {R M} [Ring R] [AddCommGroup M] [Module R M]
+    (N : Submodule R M) [IsArtinianRing R] (hN : N.FG) : IsArtinian R N :=
   by
   let ⟨s, hs⟩ := hN
   haveI := Classical.decEq M
@@ -395,19 +395,19 @@ theorem isArtinian_of_fg_of_artinian {R M} [Ring R] [AddCommGroup M] [Module R M
   rw [@Finset.sum_attach M M s _ fun i => l i • i, ← hl2, Finsupp.total_apply, Finsupp.sum, eq_comm]
   refine' Finset.sum_subset hl1 fun x _ hx => _
   rw [Finsupp.not_mem_support_iff.1 hx, zero_smul]
-#align is_artinian_of_fg_of_artinian isArtinian_of_fg_of_artinian
+#align is_artinian_of_fg_of_artinian isArtinian_of_fG_of_artinian
 
-theorem isArtinian_of_fg_of_artinian' {R M} [Ring R] [AddCommGroup M] [Module R M]
-    [IsArtinianRing R] (h : (⊤ : Submodule R M).Fg) : IsArtinian R M :=
-  have : IsArtinian R (⊤ : Submodule R M) := isArtinian_of_fg_of_artinian _ h
+theorem isArtinian_of_fG_of_artinian' {R M} [Ring R] [AddCommGroup M] [Module R M]
+    [IsArtinianRing R] (h : (⊤ : Submodule R M).FG) : IsArtinian R M :=
+  have : IsArtinian R (⊤ : Submodule R M) := isArtinian_of_fG_of_artinian _ h
   isArtinian_of_linearEquiv (LinearEquiv.ofTop (⊤ : Submodule R M) rfl)
-#align is_artinian_of_fg_of_artinian' isArtinian_of_fg_of_artinian'
+#align is_artinian_of_fg_of_artinian' isArtinian_of_fG_of_artinian'
 
 /-- In a module over a artinian ring, the submodule generated by finitely many vectors is
 artinian. -/
 theorem isArtinian_span_of_finite (R) {M} [Ring R] [AddCommGroup M] [Module R M] [IsArtinianRing R]
     {A : Set M} (hA : A.Finite) : IsArtinian R (Submodule.span R A) :=
-  isArtinian_of_fg_of_artinian _ (Submodule.fg_def.mpr ⟨A, hA, rfl⟩)
+  isArtinian_of_fG_of_artinian _ (Submodule.fg_def.mpr ⟨A, hA, rfl⟩)
 #align is_artinian_span_of_finite isArtinian_span_of_finite
 
 theorem Function.Surjective.isArtinianRing {R} [Ring R] {S} [Ring S] {F} [RingHomClass F R S]

mathlib commit https://github.com/leanprover-community/mathlib/commit/09079525fd01b3dda35e96adaa08d2f943e1648c

@@ -46,7 +46,7 @@ open Set
 
 open BigOperators Pointwise
 
-/- ./././Mathport/Syntax/Translate/Command.lean:388:30: infer kinds are unsupported in Lean 4: #[`wellFounded_submodule_lt] [] -/
+/- ./././Mathport/Syntax/Translate/Command.lean:393:30: infer kinds are unsupported in Lean 4: #[`wellFounded_submodule_lt] [] -/
 /-- `is_artinian R M` is the proposition that `M` is an Artinian `R`-module,
 implemented as the well-foundedness of submodule inclusion.
 -/

mathlib commit https://github.com/leanprover-community/mathlib/commit/88fcb83fe7996142dfcfe7368d31304a9adc874a

@@ -4,7 +4,7 @@ Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Chris Hughes
 
 ! This file was ported from Lean 3 source module ring_theory.artinian
-! leanprover-community/mathlib commit 831c494092374cfe9f50591ed0ac81a25efc5b86
+! leanprover-community/mathlib commit 210657c4ea4a4a7b234392f70a3a2a83346dfa90
 ! Please do not edit these lines, except to modify the commit id
 ! if you have ported upstream changes.
 -/
@@ -186,13 +186,12 @@ theorem IsArtinian.finite_of_linearIndependent [Nontrivial R] [IsArtinian R M] {
 /-- A module is Artinian iff every nonempty set of submodules has a minimal submodule among them.
 -/
 theorem set_has_minimal_iff_artinian :
-    (∀ a : Set <| Submodule R M, a.Nonempty → ∃ M' ∈ a, ∀ I ∈ a, I ≤ M' → I = M') ↔
-      IsArtinian R M :=
-  by rw [isArtinian_iff_wellFounded, WellFounded.wellFounded_iff_has_min']
+    (∀ a : Set <| Submodule R M, a.Nonempty → ∃ M' ∈ a, ∀ I ∈ a, ¬I < M') ↔ IsArtinian R M := by
+  rw [isArtinian_iff_wellFounded, WellFounded.wellFounded_iff_has_min]
 #align set_has_minimal_iff_artinian set_has_minimal_iff_artinian
 
 theorem IsArtinian.set_has_minimal [IsArtinian R M] (a : Set <| Submodule R M) (ha : a.Nonempty) :
-    ∃ M' ∈ a, ∀ I ∈ a, I ≤ M' → I = M' :=
+    ∃ M' ∈ a, ∀ I ∈ a, ¬I < M' :=
   set_has_minimal_iff_artinian.mpr ‹_› a ha
 #align is_artinian.set_has_minimal IsArtinian.set_has_minimal
 
@@ -442,14 +441,14 @@ theorem isNilpotent_jacobson_bot : IsNilpotent (Ideal.jacobson (⊥ : Ideal R))
   by_contra hJ
   change J ≠ ⊤ at hJ
   rcases IsArtinian.set_has_minimal { J' : Ideal R | J < J' } ⟨⊤, hJ.lt_top⟩ with
-    ⟨J', hJJ' : J < J', hJ' : ∀ I, J < I → I ≤ J' → I = J'⟩
+    ⟨J', hJJ' : J < J', hJ' : ∀ I, J < I → ¬I < J'⟩
   rcases SetLike.exists_of_lt hJJ' with ⟨x, hxJ', hxJ⟩
   obtain rfl : J ⊔ Ideal.span {x} = J' :=
     by
-    refine' hJ' (J ⊔ Ideal.span {x}) _ _
+    apply eq_of_le_of_not_lt _ (hJ' (J ⊔ Ideal.span {x}) _)
+    · exact sup_le hJJ'.le (span_le.2 (singleton_subset_iff.2 hxJ'))
     · rw [SetLike.lt_iff_le_and_exists]
       exact ⟨le_sup_left, ⟨x, mem_sup_right (mem_span_singleton_self x), hxJ⟩⟩
-    · exact sup_le hJJ'.le (span_le.2 (singleton_subset_iff.2 hxJ'))
   have : J ⊔ Jac • Ideal.span {x} ≤ J ⊔ Ideal.span {x} :=
     sup_le_sup_left (smul_le.2 fun _ _ _ => Submodule.smul_mem _ _) _
   have : Jac * Ideal.span {x} ≤ J := by
@@ -457,7 +456,9 @@ theorem isNilpotent_jacobson_bot : IsNilpotent (Ideal.jacobson (⊥ : Ideal R))
       --Need version 4 of Nakayamas lemma on Stacks
       by_contra H
       refine'
-        H (smul_sup_le_of_le_smul_of_le_jacobson_bot (fg_span_singleton _) le_rfl (hJ' _ _ this).ge)
+        H
+          (smul_sup_le_of_le_smul_of_le_jacobson_bot (fg_span_singleton _) le_rfl
+            (this.eq_of_not_lt (hJ' _ _)).ge)
       exact lt_of_le_of_ne le_sup_left fun h => H <| h.symm ▸ le_sup_right
   have : Ideal.span {x} * Jac ^ (n + 1) ≤ ⊥
   calc

mathlib commit https://github.com/leanprover-community/mathlib/commit/4c586d291f189eecb9d00581aeb3dd998ac34442

@@ -462,7 +462,7 @@ theorem isNilpotent_jacobson_bot : IsNilpotent (Ideal.jacobson (⊥ : Ideal R))
   have : Ideal.span {x} * Jac ^ (n + 1) ≤ ⊥
   calc
     Ideal.span {x} * Jac ^ (n + 1) = Ideal.span {x} * Jac * Jac ^ n := by rw [pow_succ, ← mul_assoc]
-    _ ≤ J * Jac ^ n := mul_le_mul (by rwa [mul_comm]) le_rfl
+    _ ≤ J * Jac ^ n := (mul_le_mul (by rwa [mul_comm]) le_rfl)
     _ = ⊥ := by simp [J]
     
   refine' hxJ (mem_annihilator.2 fun y hy => (mem_bot R).1 _)

mathlib commit https://github.com/leanprover-community/mathlib/commit/bd9851ca476957ea4549eb19b40e7b5ade9428cc

Co-authored-by: Moritz Firsching <firsching@google.com>

@@ -475,7 +475,7 @@ theorem isNilpotent_jacobson_bot : IsNilpotent (Ideal.jacobson (⊥ : Ideal R))
   have : Ideal.span {x} * Jac ^ (n + 1) ≤ ⊥ := calc
     Ideal.span {x} * Jac ^ (n + 1) = Ideal.span {x} * Jac * Jac ^ n := by
       rw [pow_succ', ← mul_assoc]
-    _ ≤ J * Jac ^ n := (mul_le_mul (by rwa [mul_comm]) le_rfl)
+    _ ≤ J * Jac ^ n := mul_le_mul (by rwa [mul_comm]) le_rfl
     _ = ⊥ := by simp [J]
   refine' hxJ (mem_annihilator.2 fun y hy => (mem_bot R).1 _)
   refine' this (mul_mem_mul (mem_span_singleton_self x) _)

Also do the same for "/-A". This is a purely aesthetic change (and exhaustive).

@@ -72,7 +72,7 @@ variable [Module R M] [Module R P] [Module R N]
 
 open IsArtinian
 
-/-Porting note: added this version with `R` and `M` explicit because infer kinds are unsupported in
+/- Porting note: added this version with `R` and `M` explicit because infer kinds are unsupported in
 Lean 4-/
 theorem IsArtinian.wellFounded_submodule_lt (R M) [Semiring R] [AddCommMonoid M] [Module R M]
     [IsArtinian R M] : WellFounded ((· < ·) : Submodule R M → Submodule R M → Prop) :=

We change the following field in the definition of an additive commutative monoid:

 nsmul_succ : ∀ (n : ℕ) (x : G),
-  AddMonoid.nsmul (n + 1) x = x + AddMonoid.nsmul n x
+  AddMonoid.nsmul (n + 1) x = AddMonoid.nsmul n x + x

where the latter is more natural

We adjust the definitions of ^ in monoids, groups, etc. Originally there was a warning comment about why this natural order was preferred

use x * npowRec n x and not npowRec n x * x in the definition to make sure that definitional unfolding of npowRec is blocked, to avoid deep recursion issues.

but it seems to no longer apply.

Remarks on the PR :

• pow_succ and pow_succ' have switched their meanings.
• Most of the time, the proofs were adjusted by priming/unpriming one lemma, or exchanging left and right; a few proofs were more complicated to adjust.
• In particular, [Mathlib/NumberTheory/RamificationInertia.lean] used Ideal.IsPrime.mul_mem_pow which is defined in [Mathlib/RingTheory/DedekindDomain/Ideal.lean]. Changing the order of operation forced me to add the symmetric lemma Ideal.IsPrime.mem_pow_mul.
• the docstring for Cauchy condensation test in [Mathlib/Analysis/PSeries.lean] was mathematically incorrect, I added the mention that the function is antitone.

@@ -473,7 +473,8 @@ theorem isNilpotent_jacobson_bot : IsNilpotent (Ideal.jacobson (⊥ : Ideal R))
       (le_sup_right.trans_eq (this.eq_of_not_lt (hJ' _ ?_)).symm)))
     exact lt_of_le_of_ne le_sup_left fun h => H <| h.symm ▸ le_sup_right
   have : Ideal.span {x} * Jac ^ (n + 1) ≤ ⊥ := calc
-    Ideal.span {x} * Jac ^ (n + 1) = Ideal.span {x} * Jac * Jac ^ n := by rw [pow_succ, ← mul_assoc]
+    Ideal.span {x} * Jac ^ (n + 1) = Ideal.span {x} * Jac * Jac ^ n := by
+      rw [pow_succ', ← mul_assoc]
     _ ≤ J * Jac ^ n := (mul_le_mul (by rwa [mul_comm]) le_rfl)
     _ = ⊥ := by simp [J]
   refine' hxJ (mem_annihilator.2 fun y hy => (mem_bot R).1 _)
@@ -494,7 +495,7 @@ theorem localization_surjective : Function.Surjective (algebraMap R L) := by
   · exact ⟨r₁ * r₂, by rw [IsLocalization.mk'_eq_mul_mk'_one, map_mul, h]⟩
   obtain ⟨n, r, hr⟩ := IsArtinian.exists_pow_succ_smul_dvd (s : R) (1 : R)
   use r
-  rw [smul_eq_mul, smul_eq_mul, pow_succ', mul_assoc] at hr
+  rw [smul_eq_mul, smul_eq_mul, pow_succ, mul_assoc] at hr
   apply_fun algebraMap R L at hr
   simp only [map_mul] at hr
   rw [← IsLocalization.mk'_one (M := S) L, IsLocalization.mk'_eq_iff_eq, mul_one, Submonoid.coe_one,

Empty lines were removed by executing the following Python script twice

import os
import re


# Loop through each file in the repository
for dir_path, dirs, files in os.walk('.'):
  for filename in files:
    if filename.endswith('.lean'):
      file_path = os.path.join(dir_path, filename)

      # Open the file and read its contents
      with open(file_path, 'r') as file:
        content = file.read()

      # Use a regular expression to replace sequences of "variable" lines separated by empty lines
      # with sequences without empty lines
      modified_content = re.sub(r'(variable.*\n)\n(variable(?! .* in))', r'\1\2', content)

      # Write the modified content back to the file
      with open(file_path, 'w') as file:
        file.write(modified_content)

@@ -67,9 +67,7 @@ class IsArtinian (R M) [Semiring R] [AddCommMonoid M] [Module R M] : Prop where
 section
 
 variable {R M P N : Type*}
-
 variable [Ring R] [AddCommGroup M] [AddCommGroup P] [AddCommGroup N]
-
 variable [Module R M] [Module R P] [Module R N]
 
 open IsArtinian

• Prove isSemisimple_of_mem_adjoin: if two commuting endomorphisms of a finite-dimensional vector space over a perfect field are both semisimple, then every endomorphism in the algebra generated by them (in particular their product and sum) is semisimple.

• In the same file LinearAlgebra/Semisimple.lean, eq_zero_of_isNilpotent_isSemisimple and isSemisimple_of_squarefree_aeval_eq_zero are golfed, and IsSemisimple.minpoly_squarefree is proved

RingTheory/SimpleModule.lean:

• Define IsSemisimpleRing R to mean that R is a semisimple R-module. add properties of simple modules and a characterization (they are exactly the quotients of the ring by maximal left ideals).

• The annihilator of a semisimple module is a radical ideal.

• Any module over a semisimple ring is semisimple.

• A finite product of semisimple rings is semisimple.

• Any quotient of a semisimple ring is semisimple.

• Add Artin--Wedderburn as a TODO (proof_wanted).

• Order/Atoms.lean: add the instance from IsSimpleOrder to ComplementedLattice, so that IsSimpleModule → IsSemisimpleModule is automatically inferred.

Prerequisites for showing a product of semisimple rings is semisimple:

• Algebra/Module/Submodule/Map.lean: generalize orderIsoMapComap so that it only requires RingHomSurjective rather than RingHomInvPair

• Algebra/Ring/CompTypeclasses.lean, Mathlib/Algebra/Ring/Pi.lean, Algebra/Ring/Prod.lean: add RingHomSurjective instances

RingTheory/Artinian.lean:

• quotNilradicalEquivPi: the quotient of a commutative Artinian ring R by its nilradical is isomorphic to the (finite) product of its quotients by maximal ideals (therefore a product of fields). equivPi: if the ring is moreover reduced, then the ring itself is a product of fields. Deduce that R is a semisimple ring and both R and R[X] are decomposition monoids. Requires RingEquiv.quotientBot in RingTheory/Ideal/QuotientOperations.lean.

• Data/Polynomial/Eval.lean: the polynomial ring over a finite product of rings is isomorphic to the product of polynomial rings over individual rings. (Used to show R[X] is a decomposition monoid.)

Other necessary results:

• FieldTheory/Minpoly/Field.lean: the minimal polynomial of an element in a reduced algebra over a field is radical.

• RingTheory/PowerBasis.lean: generalize PowerBasis.finiteDimensional and rename it to .finite.

Annihilator stuff, some of which do not end up being used:

• RingTheory/Ideal/Operations.lean: define Module.annihilator and redefine Submodule.annihilator in terms of it; add lemmas, including one that says an arbitrary intersection of radical ideals is radical. The new lemma Ideal.isRadical_iff_pow_one_lt depends on pow_imp_self_of_one_lt in Mathlib/Data/Nat/Interval.lean, which is also used to golf the proof of isRadical_iff_pow_one_lt.

• Algebra/Module/Torsion.lean: add a lemma and an instance (unused)

• Data/Polynomial/Module/Basic.lean: add a def (unused) and a lemma

• LinearAlgebra/AnnihilatingPolynomial.lean: add lemma span_minpoly_eq_annihilator

Some results about idempotent linear maps (projections) and idempotent elements, used to show that any (left) ideal in a semisimple ring is spanned by an idempotent element (unused):

• LinearAlgebra/Projection.lean: add def isIdempotentElemEquiv

• LinearAlgebra/Span.lean: add two lemmas

Co-authored-by: Junyan Xu <junyanxu.math@gmail.com>

@@ -3,8 +3,10 @@ Copyright (c) 2021 Chris Hughes. All rights reserved.
 Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Chris Hughes
 -/
-import Mathlib.RingTheory.Nakayama
 import Mathlib.Data.SetLike.Fintype
+import Mathlib.Algebra.Divisibility.Prod
+import Mathlib.RingTheory.Nakayama
+import Mathlib.RingTheory.SimpleModule
 import Mathlib.Tactic.RSuffices
 
 #align_import ring_theory.artinian from "leanprover-community/mathlib"@"210657c4ea4a4a7b234392f70a3a2a83346dfa90"
@@ -28,6 +30,21 @@ Let `R` be a ring and let `M` and `P` be `R`-modules. Let `N` be an `R`-submodul
   implemented as the predicate that the `<` relation on submodules is well founded.
 * `IsArtinianRing R` is the proposition that `R` is a left Artinian ring.
 
+## Main results
+
+* `IsArtinianRing.localization_surjective`: the canonical homomorphism from a commutative artinian
+  ring to any localization of itself is surjective.
+
+* `IsArtinianRing.isNilpotent_jacobson_bot`: the Jacobson radical of a commutative artinian ring
+  is a nilpotent ideal. (TODO: generalize to noncommutative rings.)
+
+* `IsArtinianRing.primeSpectrum_finite`, `IsArtinianRing.isMaximal_of_isPrime`: there are only
+  finitely prime ideals in a commutative artinian ring, and each of them is maximal.
+
+* `IsArtinianRing.equivPi`: a reduced commutative artinian ring `R` is isomorphic to a finite
+  product of fields (and therefore is a semisimple ring and a decomposition monoid; moreover
+  `R[X]` is also a decomposition monoid).
+
 ## References
 
 * [M. F. Atiyah and I. G. Macdonald, *Introduction to commutative algebra*][atiyah-macdonald]
@@ -402,6 +419,10 @@ instance isArtinian_of_fg_of_artinian' {R M} [Ring R] [AddCommGroup M] [Module R
   isArtinian_of_linearEquiv (LinearEquiv.ofTop (⊤ : Submodule R M) rfl)
 #align is_artinian_of_fg_of_artinian' isArtinian_of_fg_of_artinian'
 
+theorem IsArtinianRing.of_finite (R S) [CommRing R] [Ring S] [Algebra R S]
+    [IsArtinianRing R] [Module.Finite R S] : IsArtinianRing S :=
+  isArtinian_of_tower R isArtinian_of_fg_of_artinian'
+
 /-- In a module over an artinian ring, the submodule generated by finitely many vectors is
 artinian. -/
 theorem isArtinian_span_of_finite (R) {M} [Ring R] [AddCommGroup M] [Module R M] [IsArtinianRing R]
@@ -513,7 +534,7 @@ lemma primeSpectrum_finite : {I : Ideal R | I.IsPrime}.Finite := by
     inf_le_right.eq_of_not_lt (H (p ⊓ s.inf Subtype.val) ⟨insert p s, by simp⟩)
   rwa [← Subtype.ext <| (@isMaximal_of_isPrime _ _ _ _ q.2).eq_of_le p.2.1 hq2]
 
-variable (R) in
+variable (R)
 /--
 [Stacks Lemma 00J7](https://stacks.math.columbia.edu/tag/00J7)
 -/
@@ -521,5 +542,37 @@ lemma maximal_ideals_finite : {I : Ideal R | I.IsMaximal}.Finite := by
   simp_rw [← isPrime_iff_isMaximal]
   apply primeSpectrum_finite R
 
+@[local instance] lemma subtype_isMaximal_finite : Finite {I : Ideal R | I.IsMaximal} :=
+  (maximal_ideals_finite R).to_subtype
+
+/-- A temporary field instance on the quotients by maximal ideals. -/
+@[local instance] noncomputable def fieldOfSubtypeIsMaximal
+    (I : {I : Ideal R | I.IsMaximal}) : Field (R ⧸ I.1) :=
+  have := mem_setOf.mp I.2; Ideal.Quotient.field I.1
+
+/-- The quotient of a commutative artinian ring by its nilradical is isomorphic to
+a finite product of fields, namely the quotients by the maximal ideals. -/
+noncomputable def quotNilradicalEquivPi :
+    R ⧸ nilradical R ≃+* ∀ I : {I : Ideal R | I.IsMaximal}, R ⧸ I.1 :=
+  .trans (Ideal.quotEquivOfEq <| ext fun x ↦ by simp_rw [mem_nilradical,
+    nilpotent_iff_mem_prime, Submodule.mem_iInf, Subtype.forall, isPrime_iff_isMaximal, mem_setOf])
+  (Ideal.quotientInfRingEquivPiQuotient _ fun I J h ↦
+    Ideal.isCoprime_iff_sup_eq.mpr <| I.2.coprime_of_ne J.2 <| by rwa [Ne, Subtype.coe_inj])
+
+/-- A reduced commutative artinian ring is isomorphic to a finite product of fields,
+namely the quotients by the maximal ideals. -/
+noncomputable def equivPi [IsReduced R] : R ≃+* ∀ I : {I : Ideal R | I.IsMaximal}, R ⧸ I.1 :=
+  .trans (.symm <| .quotientBot R) <| .trans
+    (Ideal.quotEquivOfEq (nilradical_eq_zero R).symm) (quotNilradicalEquivPi R)
+
+instance [IsReduced R] : DecompositionMonoid R := MulEquiv.decompositionMonoid (equivPi R)
+
+instance [IsReduced R] : DecompositionMonoid (Polynomial R) :=
+  MulEquiv.decompositionMonoid <| (Polynomial.mapEquiv <| equivPi R).trans (Polynomial.piEquiv _)
+
+theorem isSemisimpleRing_of_isReduced [IsReduced R] : IsSemisimpleRing R :=
+  (equivPi R).symm.isSemisimpleRing
+
+proof_wanted IsSemisimpleRing.isArtinianRing [IsSemisimpleRing R] : IsArtinianRing R
 
 end IsArtinianRing

Classifies by adding issue number #10754 to porting notes claiming anything semantically equivalent to:

• "added instance"
• "new instance"
• "adding instance"
• "had to add this instance manually"

@@ -139,7 +139,7 @@ instance isArtinian_pi' {R ι M : Type*} [Ring R] [AddCommGroup M] [Module R M]
   isArtinian_pi
 #align is_artinian_pi' isArtinian_pi'
 
---porting note: new instance
+--porting note (#10754): new instance
 instance isArtinian_finsupp {R ι M : Type*} [Ring R] [AddCommGroup M] [Module R M] [Finite ι]
     [IsArtinian R M] : IsArtinian R (ι →₀ M) :=
   isArtinian_of_linearEquiv (Finsupp.linearEquivFunOnFinite _ _ _).symm

Co-authored-by: Patrick Massot <patrickmassot@free.fr> Co-authored-by: Scott Morrison <scott.morrison@gmail.com>

@@ -456,7 +456,7 @@ theorem isNilpotent_jacobson_bot : IsNilpotent (Ideal.jacobson (⊥ : Ideal R))
   have : Ideal.span {x} * Jac ^ (n + 1) ≤ ⊥ := calc
     Ideal.span {x} * Jac ^ (n + 1) = Ideal.span {x} * Jac * Jac ^ n := by rw [pow_succ, ← mul_assoc]
     _ ≤ J * Jac ^ n := (mul_le_mul (by rwa [mul_comm]) le_rfl)
-    _ = ⊥ := by simp
+    _ = ⊥ := by simp [J]
   refine' hxJ (mem_annihilator.2 fun y hy => (mem_bot R).1 _)
   refine' this (mul_mem_mul (mem_span_singleton_self x) _)
   rwa [← hn (n + 1) (Nat.le_succ _)]

I replaced a few "terminal" refine/refine's with exact.

The strategy was very simple-minded: essentially any refine whose following line had smaller indentation got replaced by exact and then I cleaned up the mess.

This PR certainly leaves some further terminal refines, but maybe the current change is beneficial.

@@ -372,7 +372,7 @@ instance isArtinian_of_quotient_of_artinian (R) [Ring R] (M) [AddCommGroup M] [M
 theorem isArtinian_of_tower (R) {S M} [CommRing R] [Ring S] [AddCommGroup M] [Algebra R S]
     [Module S M] [Module R M] [IsScalarTower R S M] (h : IsArtinian R M) : IsArtinian S M := by
   rw [isArtinian_iff_wellFounded] at h ⊢
-  refine' (Submodule.restrictScalarsEmbedding R S M).wellFounded h
+  exact (Submodule.restrictScalarsEmbedding R S M).wellFounded h
 #align is_artinian_of_tower isArtinian_of_tower
 
 instance (R) [CommRing R] [IsArtinianRing R] (I : Ideal R) : IsArtinianRing (R ⧸ I) :=

No changes to tactic file, it's just boring fixes throughout the library.

This follows on from #6964.

Co-authored-by: sgouezel <sebastien.gouezel@univ-rennes1.fr> Co-authored-by: Eric Wieser <wieser.eric@gmail.com>

@@ -453,8 +453,7 @@ theorem isNilpotent_jacobson_bot : IsNilpotent (Ideal.jacobson (⊥ : Ideal R))
     refine H (Ideal.mul_le_left.trans (le_of_le_smul_of_le_jacobson_bot (fg_span_singleton _) le_rfl
       (le_sup_right.trans_eq (this.eq_of_not_lt (hJ' _ ?_)).symm)))
     exact lt_of_le_of_ne le_sup_left fun h => H <| h.symm ▸ le_sup_right
-  have : Ideal.span {x} * Jac ^ (n + 1) ≤ ⊥
-  calc
+  have : Ideal.span {x} * Jac ^ (n + 1) ≤ ⊥ := calc
     Ideal.span {x} * Jac ^ (n + 1) = Ideal.span {x} * Jac * Jac ^ n := by rw [pow_succ, ← mul_assoc]
     _ ≤ J * Jac ^ n := (mul_le_mul (by rwa [mul_comm]) le_rfl)
     _ = ⊥ := by simp

@@ -508,7 +508,7 @@ lemma primeSpectrum_finite : {I : Ideal R | I.IsPrime}.Finite := by
   set Spec := {I : Ideal R | I.IsPrime}
   obtain ⟨_, ⟨s, rfl⟩, H⟩ := set_has_minimal
     (range (Finset.inf · Subtype.val : Finset Spec → Ideal R)) ⟨⊤, ∅, by simp⟩
-  refine ⟨⟨s, fun p ↦ ?_⟩⟩
+  refine Set.finite_def.2 ⟨s, fun p ↦ ?_⟩
   classical
   obtain ⟨q, hq1, hq2⟩ := p.2.inf_le'.mp <| inf_eq_right.mp <|
     inf_le_right.eq_of_not_lt (H (p ⊓ s.inf Subtype.val) ⟨insert p s, by simp⟩)

The FunLike hierarchy is very big and gets scanned through each time we need a coercion (via the CoeFun instance). It looks like unbundled inheritance suits Lean 4 better here. The only class that still extends FunLike is EquivLike, since that has a custom coe_injective' field that is easier to implement. All other classes should take FunLike or EquivLike as a parameter.

Zulip thread

Important changes

Previously, morphism classes would be Type-valued and extend FunLike:

/-- `MyHomClass F A B` states that `F` is a type of `MyClass.op`-preserving morphisms.
You should extend this class when you extend `MyHom`. -/
class MyHomClass (F : Type*) (A B : outParam <| Type*) [MyClass A] [MyClass B]
  extends FunLike F A B :=
(map_op : ∀ (f : F) (x y : A), f (MyClass.op x y) = MyClass.op (f x) (f y))

After this PR, they should be Prop-valued and take FunLike as a parameter:

/-- `MyHomClass F A B` states that `F` is a type of `MyClass.op`-preserving morphisms.
You should extend this class when you extend `MyHom`. -/
class MyHomClass (F : Type*) (A B : outParam <| Type*) [MyClass A] [MyClass B]
  [FunLike F A B] : Prop :=
(map_op : ∀ (f : F) (x y : A), f (MyClass.op x y) = MyClass.op (f x) (f y))

(Note that A B stay marked as outParam even though they are not purely required to be so due to the FunLike parameter already filling them in. This is required to see through type synonyms, which is important in the category theory library. Also, I think keeping them as outParam is slightly faster.)

Similarly, MyEquivClass should take EquivLike as a parameter.

As a result, every mention of [MyHomClass F A B] should become [FunLike F A B] [MyHomClass F A B].

Remaining issues

Slower (failing) search

While overall this gives some great speedups, there are some cases that are noticeably slower. In particular, a failing application of a lemma such as map_mul is more expensive. This is due to suboptimal processing of arguments. For example:

variable [FunLike F M N] [Mul M] [Mul N] (f : F) (x : M) (y : M)

theorem map_mul [MulHomClass F M N] : f (x * y) = f x * f y

example [AddHomClass F A B] : f (x * y) = f x * f y := map_mul f _ _

Before this PR, applying map_mul f gives the goals [Mul ?M] [Mul ?N] [MulHomClass F ?M ?N]. Since M and N are out_params, [MulHomClass F ?M ?N] is synthesized first, supplies values for ?M and ?N and then the Mul M and Mul N instances can be found.

After this PR, the goals become [FunLike F ?M ?N] [Mul ?M] [Mul ?N] [MulHomClass F ?M ?N]. Now [FunLike F ?M ?N] is synthesized first, supplies values for ?M and ?N and then the Mul M and Mul N instances can be found, before trying MulHomClass F M N which fails. Since the Mul hierarchy is very big, this can be slow to fail, especially when there is no such Mul instance.

A long-term but harder to achieve solution would be to specify the order in which instance goals get solved. For example, we'd like to change the arguments to map_mul to look like [FunLike F M N] [Mul M] [Mul N] [highPriority <| MulHomClass F M N] because MulHomClass fails or succeeds much faster than the others.

As a consequence, the simpNF linter is much slower since by design it tries and fails to apply many map_ lemmas. The same issue occurs a few times in existing calls to simp [map_mul], where map_mul is tried "too soon" and fails. Thanks to the speedup of leanprover/lean4#2478 the impact is very limited, only in files that already were close to the timeout.

simp not firing sometimes

This affects map_smulₛₗ and related definitions. For simp lemmas Lean apparently uses a slightly different mechanism to find instances, so that rw can find every argument to map_smulₛₗ successfully but simp can't: leanprover/lean4#3701.

Missing instances due to unification failing

Especially in the category theory library, we might sometimes have a type A which is also accessible as a synonym (Bundled A hA).1. Instance synthesis doesn't always work if we have f : A →* B but x * y : (Bundled A hA).1 or vice versa. This seems to be mostly fixed by keeping A B as outParams in MulHomClass F A B. (Presumably because Lean will do a definitional check A =?= (Bundled A hA).1 instead of using the syntax in the discrimination tree.)

Workaround for issues

The timeouts can be worked around for now by specifying which map_mul we mean, either as map_mul f for some explicit f, or as e.g. MonoidHomClass.map_mul.

map_smulₛₗ not firing as simp lemma can be worked around by going back to the pre-FunLike situation and making LinearMap.map_smulₛₗ a simp lemma instead of the generic map_smulₛₗ. Writing simp [map_smulₛₗ _] also works.

Co-authored-by: Matthew Ballard <matt@mrb.email> Co-authored-by: Scott Morrison <scott.morrison@gmail.com> Co-authored-by: Scott Morrison <scott@tqft.net> Co-authored-by: Anne Baanen <Vierkantor@users.noreply.github.com>

@@ -233,8 +233,9 @@ theorem eventually_codisjoint_ker_pow_range_pow (f : M →ₗ[R] M) :
   intro x
   rsuffices ⟨y, hy⟩ : ∃ y, (f ^ m) ((f ^ n) y) = (f ^ m) x
   · exact ⟨x - (f ^ n) y, by simp [hy], (f ^ n) y, by simp⟩
+  -- Note: #8386 had to change `mem_range` into `mem_range (f := _)`
   simp_rw [f.pow_apply n, f.pow_apply m, ← iterate_add_apply, ← f.pow_apply (m + n),
-    ← f.pow_apply m, ← mem_range, ← hn _ (n.le_add_left m), hn _ hm]
+    ← f.pow_apply m, ← mem_range (f := _), ← hn _ (n.le_add_left m), hn _ hm]
   exact LinearMap.mem_range_self (f ^ m) x
 #align is_artinian.exists_endomorphism_iterate_ker_sup_range_eq_top LinearMap.eventually_codisjoint_ker_pow_range_pow
 
@@ -408,7 +409,8 @@ theorem isArtinian_span_of_finite (R) {M} [Ring R] [AddCommGroup M] [Module R M]
   isArtinian_of_fg_of_artinian _ (Submodule.fg_def.mpr ⟨A, hA, rfl⟩)
 #align is_artinian_span_of_finite isArtinian_span_of_finite
 
-theorem Function.Surjective.isArtinianRing {R} [Ring R] {S} [Ring S] {F} [RingHomClass F R S]
+theorem Function.Surjective.isArtinianRing {R} [Ring R] {S} [Ring S] {F}
+    [FunLike F R S] [RingHomClass F R S]
     {f : F} (hf : Function.Surjective f) [H : IsArtinianRing R] : IsArtinianRing S := by
   rw [isArtinianRing_iff, isArtinian_iff_wellFounded] at H ⊢
   exact (Ideal.orderEmbeddingOfSurjective f hf).wellFounded H

Co-authored-by: Andrew Yang <36414270+erdOne@users.noreply.github.com>

@@ -448,8 +448,8 @@ theorem isNilpotent_jacobson_bot : IsNilpotent (Ideal.jacobson (⊥ : Ideal R))
     sup_le_sup_left (smul_le.2 fun _ _ _ => Submodule.smul_mem _ _) _
   have : Jac * Ideal.span {x} ≤ J := by -- Need version 4 of Nakayama's lemma on Stacks
     by_contra H
-    refine' H (smul_le_of_le_smul_of_le_jacobson_bot (fg_span_singleton _) le_rfl
-      (this.eq_of_not_lt (hJ' _ _)).ge)
+    refine H (Ideal.mul_le_left.trans (le_of_le_smul_of_le_jacobson_bot (fg_span_singleton _) le_rfl
+      (le_sup_right.trans_eq (this.eq_of_not_lt (hJ' _ ?_)).symm)))
     exact lt_of_le_of_ne le_sup_left fun h => H <| h.symm ▸ le_sup_right
   have : Ideal.span {x} * Jac ^ (n + 1) ≤ ⊥
   calc

I literally went through and regex'd some uses of cases', replacing them with rcases; this is meant to be a low effort PR as I hope that tools can do this in the future.

rcases is an easier replacement than cases, though with better tools we could in future do a second pass converting simple rcases added here (and existing ones) to cases.

@@ -243,7 +243,7 @@ lemma eventually_iInf_range_pow_eq (f : Module.End R M) :
   obtain ⟨n, hn : ∀ m, n ≤ m → LinearMap.range (f ^ n) = LinearMap.range (f ^ m)⟩ :=
     monotone_stabilizes f.iterateRange
   refine eventually_atTop.mpr ⟨n, fun l hl ↦ le_antisymm (iInf_le _ _) (le_iInf fun m ↦ ?_)⟩
-  cases' le_or_lt l m with h h
+  rcases le_or_lt l m with h | h
   · rw [← hn _ (hl.trans h), hn _ hl]
   · exact f.iterateRange.monotone h.le
 

Co-PR: #9088 (minimal prime ideals in Noetherian ring are finite)

@@ -498,4 +498,27 @@ instance isMaximal_of_isPrime (p : Ideal R) [p.IsPrime] : p.IsMaximal :=
       localization_surjective (nonZeroDivisors (R ⧸ p)) (FractionRing (R ⧸ p))⟩).isField _
     <| Field.toIsField <| FractionRing (R ⧸ p)
 
+lemma isPrime_iff_isMaximal (p : Ideal R) : p.IsPrime ↔ p.IsMaximal :=
+  ⟨fun _ ↦ isMaximal_of_isPrime p, fun h ↦ h.isPrime⟩
+
+variable (R) in
+lemma primeSpectrum_finite : {I : Ideal R | I.IsPrime}.Finite := by
+  set Spec := {I : Ideal R | I.IsPrime}
+  obtain ⟨_, ⟨s, rfl⟩, H⟩ := set_has_minimal
+    (range (Finset.inf · Subtype.val : Finset Spec → Ideal R)) ⟨⊤, ∅, by simp⟩
+  refine ⟨⟨s, fun p ↦ ?_⟩⟩
+  classical
+  obtain ⟨q, hq1, hq2⟩ := p.2.inf_le'.mp <| inf_eq_right.mp <|
+    inf_le_right.eq_of_not_lt (H (p ⊓ s.inf Subtype.val) ⟨insert p s, by simp⟩)
+  rwa [← Subtype.ext <| (@isMaximal_of_isPrime _ _ _ _ q.2).eq_of_le p.2.1 hq2]
+
+variable (R) in
+/--
+[Stacks Lemma 00J7](https://stacks.math.columbia.edu/tag/00J7)
+-/
+lemma maximal_ideals_finite : {I : Ideal R | I.IsMaximal}.Finite := by
+  simp_rw [← isPrime_iff_isMaximal]
+  apply primeSpectrum_finite R
+
+
 end IsArtinianRing

The names for lemmas about monotonicity of (a ^ ·) and (· ^ n) were a mess. This PR tidies up everything related by following the naming convention for (a * ·) and (· * b). Namely, (a ^ ·) is pow_right and (· ^ n) is pow_left in lemma names. All lemma renames follow the corresponding multiplication lemma names closely.

Renames

Algebra.GroupPower.Order

• pow_mono → pow_right_mono
• pow_le_pow → pow_le_pow_right
• pow_le_pow_of_le_left → pow_le_pow_left
• pow_lt_pow_of_lt_left → pow_lt_pow_left
• strictMonoOn_pow → pow_left_strictMonoOn
• pow_strictMono_right → pow_right_strictMono
• pow_lt_pow → pow_lt_pow_right
• pow_lt_pow_iff → pow_lt_pow_iff_right
• pow_le_pow_iff → pow_le_pow_iff_right
• self_lt_pow → lt_self_pow
• strictAnti_pow → pow_right_strictAnti
• pow_lt_pow_iff_of_lt_one → pow_lt_pow_iff_right_of_lt_one
• pow_lt_pow_of_lt_one → pow_lt_pow_right_of_lt_one
• lt_of_pow_lt_pow → lt_of_pow_lt_pow_left
• le_of_pow_le_pow → le_of_pow_le_pow_left
• pow_lt_pow₀ → pow_lt_pow_right₀

Algebra.GroupPower.CovariantClass

• pow_le_pow_of_le_left' → pow_le_pow_left'
• nsmul_le_nsmul_of_le_right → nsmul_le_nsmul_right
• pow_lt_pow' → pow_lt_pow_right'
• nsmul_lt_nsmul → nsmul_lt_nsmul_left
• pow_strictMono_left → pow_right_strictMono'
• nsmul_strictMono_right → nsmul_left_strictMono
• StrictMono.pow_right' → StrictMono.pow_const
• StrictMono.nsmul_left → StrictMono.const_nsmul
• pow_strictMono_right' → pow_left_strictMono
• nsmul_strictMono_left → nsmul_right_strictMono
• Monotone.pow_right → Monotone.pow_const
• Monotone.nsmul_left → Monotone.const_nsmul
• lt_of_pow_lt_pow' → lt_of_pow_lt_pow_left'
• lt_of_nsmul_lt_nsmul → lt_of_nsmul_lt_nsmul_right
• pow_le_pow' → pow_le_pow_right'
• nsmul_le_nsmul → nsmul_le_nsmul_left
• pow_le_pow_of_le_one' → pow_le_pow_right_of_le_one'
• nsmul_le_nsmul_of_nonpos → nsmul_le_nsmul_left_of_nonpos
• le_of_pow_le_pow' → le_of_pow_le_pow_left'
• le_of_nsmul_le_nsmul' → le_of_nsmul_le_nsmul_right'
• pow_le_pow_iff' → pow_le_pow_iff_right'
• nsmul_le_nsmul_iff → nsmul_le_nsmul_iff_left
• pow_lt_pow_iff' → pow_lt_pow_iff_right'
• nsmul_lt_nsmul_iff → nsmul_lt_nsmul_iff_left

Data.Nat.Pow

• Nat.pow_lt_pow_of_lt_left → Nat.pow_lt_pow_left
• Nat.pow_le_iff_le_left → Nat.pow_le_pow_iff_left
• Nat.pow_lt_iff_lt_left → Nat.pow_lt_pow_iff_left

Lemmas added

• pow_le_pow_iff_left
• pow_lt_pow_iff_left
• pow_right_injective
• pow_right_inj
• Nat.pow_le_pow_left to have the correct name since Nat.pow_le_pow_of_le_left is in Std.
• Nat.pow_le_pow_right to have the correct name since Nat.pow_le_pow_of_le_right is in Std.

Lemmas removed

• self_le_pow was a duplicate of le_self_pow.
• Nat.pow_lt_pow_of_lt_right is defeq to pow_lt_pow_right.
• Nat.pow_right_strictMono is defeq to pow_right_strictMono.
• Nat.pow_le_iff_le_right is defeq to pow_le_pow_iff_right.
• Nat.pow_lt_iff_lt_right is defeq to pow_lt_pow_iff_right.

Other changes

• A bunch of proofs have been golfed.
• Some lemma assumptions have been turned from 0 < n or 1 ≤ n to n ≠ 0.
• A few Nat lemmas have been protected.
• One docstring has been fixed.

@@ -427,7 +427,7 @@ variable {R : Type*} [CommRing R] [IsArtinianRing R]
 
 theorem isNilpotent_jacobson_bot : IsNilpotent (Ideal.jacobson (⊥ : Ideal R)) := by
   let Jac := Ideal.jacobson (⊥ : Ideal R)
-  let f : ℕ →o (Ideal R)ᵒᵈ := ⟨fun n => Jac ^ n, fun _ _ h => Ideal.pow_le_pow h⟩
+  let f : ℕ →o (Ideal R)ᵒᵈ := ⟨fun n => Jac ^ n, fun _ _ h => Ideal.pow_le_pow_right h⟩
   obtain ⟨n, hn⟩ : ∃ n, ∀ m, n ≤ m → Jac ^ n = Jac ^ m := IsArtinian.monotone_stabilizes f
   refine' ⟨n, _⟩
   let J : Ideal R := annihilator (Jac ^ n)

@@ -448,7 +448,7 @@ theorem isNilpotent_jacobson_bot : IsNilpotent (Ideal.jacobson (⊥ : Ideal R))
     sup_le_sup_left (smul_le.2 fun _ _ _ => Submodule.smul_mem _ _) _
   have : Jac * Ideal.span {x} ≤ J := by -- Need version 4 of Nakayama's lemma on Stacks
     by_contra H
-    refine' H (smul_sup_le_of_le_smul_of_le_jacobson_bot (fg_span_singleton _) le_rfl
+    refine' H (smul_le_of_le_smul_of_le_jacobson_bot (fg_span_singleton _) le_rfl
       (this.eq_of_not_lt (hJ' _ _)).ge)
     exact lt_of_le_of_ne le_sup_left fun h => H <| h.symm ▸ le_sup_right
   have : Ideal.span {x} * Jac ^ (n + 1) ≤ ⊥

@@ -231,8 +231,8 @@ theorem eventually_codisjoint_ker_pow_range_pow (f : M →ₗ[R] M) :
   refine eventually_atTop.mpr ⟨n, fun m hm ↦ codisjoint_iff.mpr ?_⟩
   simp_rw [← hn _ hm, Submodule.eq_top_iff', Submodule.mem_sup]
   intro x
-  suffices : ∃ y, (f ^ m) ((f ^ n) y) = (f ^ m) x
-  · obtain ⟨y, hy⟩ := this; exact ⟨x - (f ^ n) y, by simp [hy], (f ^ n) y, by simp⟩
+  rsuffices ⟨y, hy⟩ : ∃ y, (f ^ m) ((f ^ n) y) = (f ^ m) x
+  · exact ⟨x - (f ^ n) y, by simp [hy], (f ^ n) y, by simp⟩
   simp_rw [f.pow_apply n, f.pow_apply m, ← iterate_add_apply, ← f.pow_apply (m + n),
     ← f.pow_apply m, ← mem_range, ← hn _ (n.le_add_left m), hn _ hm]
   exact LinearMap.mem_range_self (f ^ m) x
@@ -260,7 +260,7 @@ theorem eventually_isCompl_ker_pow_range_pow [IsNoetherian R M] (f : M →ₗ[R]
 
 See also `LinearMap.eventually_isCompl_ker_pow_range_pow` for an alternative spelling. -/
 theorem isCompl_iSup_ker_pow_iInf_range_pow [IsNoetherian R M] (f : M →ₗ[R] M) :
-    IsCompl (⨆ n,LinearMap.ker (f ^ n)) (⨅ n, LinearMap.range (f ^ n)) := by
+    IsCompl (⨆ n, LinearMap.ker (f ^ n)) (⨅ n, LinearMap.range (f ^ n)) := by
   obtain ⟨k, hk⟩ := eventually_atTop.mp <| f.eventually_isCompl_ker_pow_range_pow.and <|
     f.eventually_iInf_range_pow_eq.and f.eventually_iSup_ker_pow_eq
   obtain ⟨h₁, h₂, h₃⟩ := hk k (le_refl k)

Note: the proof (due to Zassenhaus) makes no assumption about the characteristic of the coefficients.

@@ -350,6 +350,9 @@ def IsArtinianRing (R) [Ring R] :=
 theorem isArtinianRing_iff {R} [Ring R] : IsArtinianRing R ↔ IsArtinian R R := Iff.rfl
 #align is_artinian_ring_iff isArtinianRing_iff
 
+instance DivisionRing.instIsArtinianRing {K : Type*} [DivisionRing K] : IsArtinianRing K :=
+  ⟨Finite.wellFounded_of_trans_of_irrefl _⟩
+
 theorem Ring.isArtinian_of_zero_eq_one {R} [Ring R] (h01 : (0 : R) = 1) : IsArtinianRing R :=
   have := subsingleton_of_zero_eq_one h01
   inferInstance
@@ -392,9 +395,9 @@ theorem isArtinian_of_fg_of_artinian {R M} [Ring R] [AddCommGroup M] [Module R M
     simp
 #align is_artinian_of_fg_of_artinian isArtinian_of_fg_of_artinian
 
-theorem isArtinian_of_fg_of_artinian' {R M} [Ring R] [AddCommGroup M] [Module R M]
-    [IsArtinianRing R] (h : (⊤ : Submodule R M).FG) : IsArtinian R M :=
-  have : IsArtinian R (⊤ : Submodule R M) := isArtinian_of_fg_of_artinian _ h
+instance isArtinian_of_fg_of_artinian' {R M} [Ring R] [AddCommGroup M] [Module R M]
+    [IsArtinianRing R] [Module.Finite R M] : IsArtinian R M :=
+  have : IsArtinian R (⊤ : Submodule R M) := isArtinian_of_fg_of_artinian _ Module.Finite.out
   isArtinian_of_linearEquiv (LinearEquiv.ofTop (⊤ : Submodule R M) rfl)
 #align is_artinian_of_fg_of_artinian' isArtinian_of_fg_of_artinian'
 

This matches Set.inclusion, Subring.inclusion, Subalgebra.inclusion, etc.

Also renames the homOfLe spellings in Algebra/Lie to match.

Note that we leave LieSubalgebra.ofLe, as this is a completely different statement!

As requested by @alreadydone.

@@ -76,7 +76,7 @@ instance isArtinian_submodule' [IsArtinian R M] (N : Submodule R M) : IsArtinian
 #align is_artinian_submodule' isArtinian_submodule'
 
 theorem isArtinian_of_le {s t : Submodule R M} [IsArtinian R t] (h : s ≤ t) : IsArtinian R s :=
-  isArtinian_of_injective (Submodule.ofLe h) (Submodule.ofLe_injective h)
+  isArtinian_of_injective (Submodule.inclusion h) (Submodule.inclusion_injective h)
 #align is_artinian_of_le isArtinian_of_le
 
 variable (M)

Especially the new lemma LinearMap.eventually_isCompl_ker_pow_range_pow

@@ -39,9 +39,7 @@ Artinian, artinian, Artinian ring, Artinian module, artinian ring, artinian modu
 
 -/
 
-open Set
-
-open BigOperators Pointwise
+open Set Filter BigOperators Pointwise
 
 /-- `IsArtinian R M` is the proposition that `M` is an Artinian `R`-module,
 implemented as the well-foundedness of submodule inclusion. -/
@@ -207,41 +205,80 @@ theorem monotone_stabilizes (f : ℕ →o (Submodule R M)ᵒᵈ) : ∃ n, ∀ m,
   monotone_stabilizes_iff_artinian.mpr ‹_› f
 #align is_artinian.monotone_stabilizes IsArtinian.monotone_stabilizes
 
+theorem eventuallyConst_of_isArtinian (f : ℕ →o (Submodule R M)ᵒᵈ) :
+    atTop.EventuallyConst f := by
+  simp_rw [eventuallyConst_atTop, eq_comm]
+  exact monotone_stabilizes f
+
 /-- If `∀ I > J, P I` implies `P J`, then `P` holds for all submodules. -/
 theorem induction {P : Submodule R M → Prop} (hgt : ∀ I, (∀ J < I, P J) → P I) (I : Submodule R M) :
     P I :=
   (wellFounded_submodule_lt R M).recursion I hgt
 #align is_artinian.induction IsArtinian.induction
 
-/-- For any endomorphism of an Artinian module, there is some nontrivial iterate
-with disjoint kernel and range. -/
-theorem exists_endomorphism_iterate_ker_sup_range_eq_top (f : M →ₗ[R] M) :
-    ∃ n : ℕ, n ≠ 0 ∧ LinearMap.ker (f ^ n) ⊔ LinearMap.range (f ^ n) = ⊤ := by
-  obtain ⟨n, w⟩ :=
-    monotone_stabilizes (f.iterateRange.comp ⟨fun n => n + 1, fun n m w => by linarith⟩)
-  specialize w (n + 1 + n) (by linarith)
-  dsimp at w
-  refine' ⟨n + 1, Nat.succ_ne_zero _, _⟩
-  simp_rw [eq_top_iff', mem_sup]
+end IsArtinian
+
+namespace LinearMap
+
+variable [IsArtinian R M]
+
+/-- For any endomorphism of an Artinian module, any sufficiently high iterate has codisjoint kernel
+and range. -/
+theorem eventually_codisjoint_ker_pow_range_pow (f : M →ₗ[R] M) :
+    ∀ᶠ n in atTop, Codisjoint (LinearMap.ker (f ^ n)) (LinearMap.range (f ^ n)) := by
+  obtain ⟨n, hn : ∀ m, n ≤ m → LinearMap.range (f ^ n) = LinearMap.range (f ^ m)⟩ :=
+    monotone_stabilizes f.iterateRange
+  refine eventually_atTop.mpr ⟨n, fun m hm ↦ codisjoint_iff.mpr ?_⟩
+  simp_rw [← hn _ hm, Submodule.eq_top_iff', Submodule.mem_sup]
   intro x
-  have : (f ^ (n + 1)) x ∈ LinearMap.range (f ^ (n + 1 + n + 1)) := by
-    rw [← w]
-    exact mem_range_self _
-  rcases this with ⟨y, hy⟩
-  use x - (f ^ (n + 1)) y
-  constructor
-  · rw [LinearMap.mem_ker, LinearMap.map_sub, ← hy, sub_eq_zero, pow_add]
-    simp [pow_add]
-  · use (f ^ (n + 1)) y
-    simp
-#align is_artinian.exists_endomorphism_iterate_ker_sup_range_eq_top IsArtinian.exists_endomorphism_iterate_ker_sup_range_eq_top
+  suffices : ∃ y, (f ^ m) ((f ^ n) y) = (f ^ m) x
+  · obtain ⟨y, hy⟩ := this; exact ⟨x - (f ^ n) y, by simp [hy], (f ^ n) y, by simp⟩
+  simp_rw [f.pow_apply n, f.pow_apply m, ← iterate_add_apply, ← f.pow_apply (m + n),
+    ← f.pow_apply m, ← mem_range, ← hn _ (n.le_add_left m), hn _ hm]
+  exact LinearMap.mem_range_self (f ^ m) x
+#align is_artinian.exists_endomorphism_iterate_ker_sup_range_eq_top LinearMap.eventually_codisjoint_ker_pow_range_pow
+
+lemma eventually_iInf_range_pow_eq (f : Module.End R M) :
+    ∀ᶠ n in atTop, ⨅ m, LinearMap.range (f ^ m) = LinearMap.range (f ^ n) := by
+  obtain ⟨n, hn : ∀ m, n ≤ m → LinearMap.range (f ^ n) = LinearMap.range (f ^ m)⟩ :=
+    monotone_stabilizes f.iterateRange
+  refine eventually_atTop.mpr ⟨n, fun l hl ↦ le_antisymm (iInf_le _ _) (le_iInf fun m ↦ ?_)⟩
+  cases' le_or_lt l m with h h
+  · rw [← hn _ (hl.trans h), hn _ hl]
+  · exact f.iterateRange.monotone h.le
+
+/-- This is the Fitting decomposition of the module `M` with respect to the endomorphism `f`.
+
+See also `LinearMap.isCompl_iSup_ker_pow_iInf_range_pow` for an alternative spelling. -/
+theorem eventually_isCompl_ker_pow_range_pow [IsNoetherian R M] (f : M →ₗ[R] M) :
+    ∀ᶠ n in atTop, IsCompl (LinearMap.ker (f ^ n)) (LinearMap.range (f ^ n)) := by
+  filter_upwards [f.eventually_disjoint_ker_pow_range_pow.and
+    f.eventually_codisjoint_ker_pow_range_pow] with n hn
+  simpa only [isCompl_iff]
+
+/-- This is the Fitting decomposition of the module `M` with respect to the endomorphism `f`.
+
+See also `LinearMap.eventually_isCompl_ker_pow_range_pow` for an alternative spelling. -/
+theorem isCompl_iSup_ker_pow_iInf_range_pow [IsNoetherian R M] (f : M →ₗ[R] M) :
+    IsCompl (⨆ n,LinearMap.ker (f ^ n)) (⨅ n, LinearMap.range (f ^ n)) := by
+  obtain ⟨k, hk⟩ := eventually_atTop.mp <| f.eventually_isCompl_ker_pow_range_pow.and <|
+    f.eventually_iInf_range_pow_eq.and f.eventually_iSup_ker_pow_eq
+  obtain ⟨h₁, h₂, h₃⟩ := hk k (le_refl k)
+  rwa [h₂, h₃]
+
+end LinearMap
+
+namespace IsArtinian
+
+variable [IsArtinian R M]
 
 /-- Any injective endomorphism of an Artinian module is surjective. -/
 theorem surjective_of_injective_endomorphism (f : M →ₗ[R] M) (s : Injective f) : Surjective f := by
-  obtain ⟨n, ne, w⟩ := exists_endomorphism_iterate_ker_sup_range_eq_top f
-  rw [LinearMap.ker_eq_bot.mpr (LinearMap.iterate_injective s n), bot_sup_eq,
-    LinearMap.range_eq_top] at w
-  exact LinearMap.surjective_of_iterate_surjective ne w
+  obtain ⟨n, hn⟩ := eventually_atTop.mp f.eventually_codisjoint_ker_pow_range_pow
+  specialize hn (n + 1) (n.le_add_right 1)
+  rw [codisjoint_iff, LinearMap.ker_eq_bot.mpr (LinearMap.iterate_injective s _), bot_sup_eq,
+    LinearMap.range_eq_top] at hn
+  exact LinearMap.surjective_of_iterate_surjective n.succ_ne_zero hn
 #align is_artinian.surjective_of_injective_endomorphism IsArtinian.surjective_of_injective_endomorphism
 
 /-- Any injective endomorphism of an Artinian module is bijective. -/
@@ -267,15 +304,6 @@ theorem disjoint_partial_infs_eventually_top (f : ℕ → Submodule R M)
   exact (h m).eq_bot_of_ge (sup_eq_left.1 <| (w (m + 1) <| le_add_right p).symm.trans <| w m p)
 #align is_artinian.disjoint_partial_infs_eventually_top IsArtinian.disjoint_partial_infs_eventually_top
 
-lemma _root_.LinearMap.exists_range_pow_eq_iInf (f : Module.End R M) :
-    ∃ (n : ℕ), ⨅ m, LinearMap.range (f ^ m) = LinearMap.range (f ^ n) := by
-  obtain ⟨n, hn : ∀ m, n ≤ m → LinearMap.range (f ^ n) = LinearMap.range (f ^ m)⟩ :=
-    monotone_stabilizes f.iterateRange
-  refine ⟨n, le_antisymm (iInf_le _ _) (le_iInf fun m ↦ ?_)⟩
-  cases' le_or_lt n m with h h
-  · rw [hn _ h]
-  · exact f.iterateRange.monotone h.le
-
 end IsArtinian
 
 end Ring

@@ -267,6 +267,15 @@ theorem disjoint_partial_infs_eventually_top (f : ℕ → Submodule R M)
   exact (h m).eq_bot_of_ge (sup_eq_left.1 <| (w (m + 1) <| le_add_right p).symm.trans <| w m p)
 #align is_artinian.disjoint_partial_infs_eventually_top IsArtinian.disjoint_partial_infs_eventually_top
 
+lemma _root_.LinearMap.exists_range_pow_eq_iInf (f : Module.End R M) :
+    ∃ (n : ℕ), ⨅ m, LinearMap.range (f ^ m) = LinearMap.range (f ^ n) := by
+  obtain ⟨n, hn : ∀ m, n ≤ m → LinearMap.range (f ^ n) = LinearMap.range (f ^ m)⟩ :=
+    monotone_stabilizes f.iterateRange
+  refine ⟨n, le_antisymm (iInf_le _ _) (le_iInf fun m ↦ ?_)⟩
+  cases' le_or_lt n m with h h
+  · rw [hn _ h]
+  · exact f.iterateRange.monotone h.le
+
 end IsArtinian
 
 end Ring

Also changes a lemma to instance and adds a new instance.

Co-authored-by: Jujian Zhang <jujian.zhang1998@outlook.com> Co-authored-by: Junyan Xu <junyanxu.math@gmail.com>

@@ -322,8 +322,8 @@ theorem isArtinian_of_submodule_of_artinian (R M) [Ring R] [AddCommGroup M] [Mod
     (N : Submodule R M) (_ : IsArtinian R M) : IsArtinian R N := inferInstance
 #align is_artinian_of_submodule_of_artinian isArtinian_of_submodule_of_artinian
 
-theorem isArtinian_of_quotient_of_artinian (R) [Ring R] (M) [AddCommGroup M] [Module R M]
-    (N : Submodule R M) (_ : IsArtinian R M) : IsArtinian R (M ⧸ N) :=
+instance isArtinian_of_quotient_of_artinian (R) [Ring R] (M) [AddCommGroup M] [Module R M]
+    (N : Submodule R M) [IsArtinian R M] : IsArtinian R (M ⧸ N) :=
   isArtinian_of_surjective M (Submodule.mkQ N) (Submodule.Quotient.mk_surjective N)
 #align is_artinian_of_quotient_of_artinian isArtinian_of_quotient_of_artinian
 
@@ -334,6 +334,9 @@ theorem isArtinian_of_tower (R) {S M} [CommRing R] [Ring S] [AddCommGroup M] [Al
   refine' (Submodule.restrictScalarsEmbedding R S M).wellFounded h
 #align is_artinian_of_tower isArtinian_of_tower
 
+instance (R) [CommRing R] [IsArtinianRing R] (I : Ideal R) : IsArtinianRing (R ⧸ I) :=
+  isArtinian_of_tower R inferInstance
+
 theorem isArtinian_of_fg_of_artinian {R M} [Ring R] [AddCommGroup M] [Module R M]
     (N : Submodule R M) [IsArtinianRing R] (hN : N.FG) : IsArtinian R N := by
   let ⟨s, hs⟩ := hN
@@ -418,28 +421,6 @@ theorem isNilpotent_jacobson_bot : IsNilpotent (Ideal.jacobson (⊥ : Ideal R))
   rwa [← hn (n + 1) (Nat.le_succ _)]
 #align is_artinian_ring.is_nilpotent_jacobson_bot IsArtinianRing.isNilpotent_jacobson_bot
 
-instance isMaximal_of_isPrime (p : Ideal R) [p.IsPrime] : p.IsMaximal :=
-  Ideal.Quotient.maximal_of_isField _
-  { exists_pair_ne := ⟨0, 1, zero_ne_one⟩
-    mul_comm := mul_comm
-    mul_inv_cancel := fun {x} hx => by
-      have : IsArtinianRing (R ⧸ p) := (@Ideal.Quotient.mk_surjective R _ p).isArtinianRing
-      obtain ⟨n, hn⟩ : ∃ (n : ℕ), Ideal.span {x^n} = Ideal.span {x^(n+1)}
-      · obtain ⟨n, h⟩ := IsArtinian.monotone_stabilizes (R := R ⧸ p) (M := R ⧸ p)
-          ⟨fun m => OrderDual.toDual (Ideal.span {x^m}), fun m n h y hy => by
-            dsimp [OrderDual.toDual] at *
-            rw [Ideal.mem_span_singleton] at hy ⊢
-            obtain ⟨z, rfl⟩ := hy
-            exact dvd_mul_of_dvd_left (pow_dvd_pow _ h) _⟩
-        exact ⟨n, h (n + 1) <| by norm_num⟩
-      have H : x^n ∈ Ideal.span {x^(n+1)}
-      { rw [← hn]; refine Submodule.subset_span (Set.mem_singleton _) }
-      rw [Ideal.mem_span_singleton] at H
-      obtain ⟨y, hy⟩ := H
-      rw [pow_add, mul_assoc, pow_one] at hy
-      conv_lhs at hy => rw [←mul_one (x^n)]
-      exact ⟨y, mul_left_cancel₀ (pow_ne_zero _ hx) hy.symm⟩ }
-
 section Localization
 
 variable (S : Submonoid R) (L : Type*) [CommRing L] [Algebra R L] [IsLocalization S L]
@@ -471,4 +452,10 @@ instance : IsArtinianRing (Localization S) :=
 
 end Localization
 
+instance isMaximal_of_isPrime (p : Ideal R) [p.IsPrime] : p.IsMaximal :=
+  Ideal.Quotient.maximal_of_isField _ <|
+    (MulEquiv.ofBijective _ ⟨IsFractionRing.injective (R ⧸ p) (FractionRing (R ⧸ p)),
+      localization_surjective (nonZeroDivisors (R ⧸ p)) (FractionRing (R ⧸ p))⟩).isField _
+    <| Field.toIsField <| FractionRing (R ⧸ p)
+
 end IsArtinianRing

prime ideals in artinian rings are maximal

@@ -418,6 +418,28 @@ theorem isNilpotent_jacobson_bot : IsNilpotent (Ideal.jacobson (⊥ : Ideal R))
   rwa [← hn (n + 1) (Nat.le_succ _)]
 #align is_artinian_ring.is_nilpotent_jacobson_bot IsArtinianRing.isNilpotent_jacobson_bot
 
+instance isMaximal_of_isPrime (p : Ideal R) [p.IsPrime] : p.IsMaximal :=
+  Ideal.Quotient.maximal_of_isField _
+  { exists_pair_ne := ⟨0, 1, zero_ne_one⟩
+    mul_comm := mul_comm
+    mul_inv_cancel := fun {x} hx => by
+      have : IsArtinianRing (R ⧸ p) := (@Ideal.Quotient.mk_surjective R _ p).isArtinianRing
+      obtain ⟨n, hn⟩ : ∃ (n : ℕ), Ideal.span {x^n} = Ideal.span {x^(n+1)}
+      · obtain ⟨n, h⟩ := IsArtinian.monotone_stabilizes (R := R ⧸ p) (M := R ⧸ p)
+          ⟨fun m => OrderDual.toDual (Ideal.span {x^m}), fun m n h y hy => by
+            dsimp [OrderDual.toDual] at *
+            rw [Ideal.mem_span_singleton] at hy ⊢
+            obtain ⟨z, rfl⟩ := hy
+            exact dvd_mul_of_dvd_left (pow_dvd_pow _ h) _⟩
+        exact ⟨n, h (n + 1) <| by norm_num⟩
+      have H : x^n ∈ Ideal.span {x^(n+1)}
+      { rw [← hn]; refine Submodule.subset_span (Set.mem_singleton _) }
+      rw [Ideal.mem_span_singleton] at H
+      obtain ⟨y, hy⟩ := H
+      rw [pow_add, mul_assoc, pow_one] at hy
+      conv_lhs at hy => rw [←mul_one (x^n)]
+      exact ⟨y, mul_left_cancel₀ (pow_ne_zero _ hx) hy.symm⟩ }
+
 section Localization
 
 variable (S : Submonoid R) (L : Type*) [CommRing L] [Algebra R L] [IsLocalization S L]

We remove all possible occurences of Type _ and Sort _ in favor of Type* and Sort*.

This has nice performance benefits.

@@ -51,7 +51,7 @@ class IsArtinian (R M) [Semiring R] [AddCommMonoid M] [Module R M] : Prop where
 
 section
 
-variable {R M P N : Type _}
+variable {R M P N : Type*}
 
 variable [Ring R] [AddCommGroup M] [AddCommGroup P] [AddCommGroup N]
 
@@ -119,8 +119,8 @@ instance (priority := 100) isArtinian_of_finite [Finite M] : IsArtinian R M :=
 -- Porting note: elab_as_elim can only be global and cannot be changed on an imported decl
 -- attribute [local elab_as_elim] Finite.induction_empty_option
 
-instance isArtinian_pi {R ι : Type _} [Finite ι] :
-    ∀ {M : ι → Type _} [Ring R] [∀ i, AddCommGroup (M i)],
+instance isArtinian_pi {R ι : Type*} [Finite ι] :
+    ∀ {M : ι → Type*} [Ring R] [∀ i, AddCommGroup (M i)],
       ∀ [∀ i, Module R (M i)], ∀ [∀ i, IsArtinian R (M i)], IsArtinian R (∀ i, M i) := by
   apply Finite.induction_empty_option _ _ _ ι
   · intro α β e hα M _ _ _ _
@@ -136,13 +136,13 @@ instance isArtinian_pi {R ι : Type _} [Finite ι] :
 /-- A version of `isArtinian_pi` for non-dependent functions. We need this instance because
 sometimes Lean fails to apply the dependent version in non-dependent settings (e.g., it fails to
 prove that `ι → ℝ` is finite dimensional over `ℝ`). -/
-instance isArtinian_pi' {R ι M : Type _} [Ring R] [AddCommGroup M] [Module R M] [Finite ι]
+instance isArtinian_pi' {R ι M : Type*} [Ring R] [AddCommGroup M] [Module R M] [Finite ι]
     [IsArtinian R M] : IsArtinian R (ι → M) :=
   isArtinian_pi
 #align is_artinian_pi' isArtinian_pi'
 
 --porting note: new instance
-instance isArtinian_finsupp {R ι M : Type _} [Ring R] [AddCommGroup M] [Module R M] [Finite ι]
+instance isArtinian_finsupp {R ι M : Type*} [Ring R] [AddCommGroup M] [Module R M] [Finite ι]
     [IsArtinian R M] : IsArtinian R (ι →₀ M) :=
   isArtinian_of_linearEquiv (Finsupp.linearEquivFunOnFinite _ _ _).symm
 
@@ -152,7 +152,7 @@ open IsArtinian Submodule Function
 
 section Ring
 
-variable {R M : Type _} [Ring R] [AddCommGroup M] [Module R M]
+variable {R M : Type*} [Ring R] [AddCommGroup M] [Module R M]
 
 theorem isArtinian_iff_wellFounded :
     IsArtinian R M ↔ WellFounded ((· < ·) : Submodule R M → Submodule R M → Prop) :=
@@ -273,7 +273,7 @@ end Ring
 
 section CommRing
 
-variable {R : Type _} (M : Type _) [CommRing R] [AddCommGroup M] [Module R M] [IsArtinian R M]
+variable {R : Type*} (M : Type*) [CommRing R] [AddCommGroup M] [Module R M] [IsArtinian R M]
 
 namespace IsArtinian
 
@@ -380,7 +380,7 @@ namespace IsArtinianRing
 
 open IsArtinian
 
-variable {R : Type _} [CommRing R] [IsArtinianRing R]
+variable {R : Type*} [CommRing R] [IsArtinianRing R]
 
 theorem isNilpotent_jacobson_bot : IsNilpotent (Ideal.jacobson (⊥ : Ideal R)) := by
   let Jac := Ideal.jacobson (⊥ : Ideal R)
@@ -420,7 +420,7 @@ theorem isNilpotent_jacobson_bot : IsNilpotent (Ideal.jacobson (⊥ : Ideal R))
 
 section Localization
 
-variable (S : Submonoid R) (L : Type _) [CommRing L] [Algebra R L] [IsLocalization S L]
+variable (S : Submonoid R) (L : Type*) [CommRing L] [Algebra R L] [IsLocalization S L]
 
 /-- Localizing an artinian ring can only reduce the amount of elements. -/
 theorem localization_surjective : Function.Surjective (algebraMap R L) := by

Also drop @[simp] on LinearMap.pow_apply.

@@ -231,7 +231,7 @@ theorem exists_endomorphism_iterate_ker_sup_range_eq_top (f : M →ₗ[R] M) :
   use x - (f ^ (n + 1)) y
   constructor
   · rw [LinearMap.mem_ker, LinearMap.map_sub, ← hy, sub_eq_zero, pow_add]
-    simp [iterate_add_apply]
+    simp [pow_add]
   · use (f ^ (n + 1)) y
     simp
 #align is_artinian.exists_endomorphism_iterate_ker_sup_range_eq_top IsArtinian.exists_endomorphism_iterate_ker_sup_range_eq_top

• depends on: #5966

Co-authored-by: Eric Wieser <wieser.eric@gmail.com> Co-authored-by: Scott Morrison <scott.morrison@gmail.com>

@@ -2,16 +2,13 @@
 Copyright (c) 2021 Chris Hughes. All rights reserved.
 Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Chris Hughes
-
-! This file was ported from Lean 3 source module ring_theory.artinian
-! leanprover-community/mathlib commit 210657c4ea4a4a7b234392f70a3a2a83346dfa90
-! Please do not edit these lines, except to modify the commit id
-! if you have ported upstream changes.
 -/
 import Mathlib.RingTheory.Nakayama
 import Mathlib.Data.SetLike.Fintype
 import Mathlib.Tactic.RSuffices
 
+#align_import ring_theory.artinian from "leanprover-community/mathlib"@"210657c4ea4a4a7b234392f70a3a2a83346dfa90"
+
 /-!
 # Artinian rings and modules
 

This PR is the result of running

find . -type f -name "*.lean" -exec sed -i -E 's/^( +)\. /\1· /' {} \;
find . -type f -name "*.lean" -exec sed -i -E 'N;s/^( +·)\n +(.*)$/\1 \2/;P;D' {} \;

which firstly replaces . focusing dots with · and secondly removes isolated instances of such dots, unifying them with the following line. A new rule is placed in the style linter to verify this.

@@ -344,8 +344,8 @@ theorem isArtinian_of_fg_of_artinian {R M} [Ring R] [AddCommGroup M] [Module R M
   haveI := Classical.decEq R
   have : ∀ x ∈ s, x ∈ N := fun x hx => hs ▸ Submodule.subset_span hx
   refine' @isArtinian_of_surjective _ ((↑s : Set M) →₀ R) N _ _ _ _ _ _ _ isArtinian_finsupp
-  . exact Finsupp.total (↑s : Set M) N R (fun i => ⟨i, hs ▸ subset_span i.2⟩)
-  . rw [← LinearMap.range_eq_top, eq_top_iff,
+  · exact Finsupp.total (↑s : Set M) N R (fun i => ⟨i, hs ▸ subset_span i.2⟩)
+  · rw [← LinearMap.range_eq_top, eq_top_iff,
        ← map_le_map_iff_of_injective (show Injective (Submodule.subtype N)
          from Subtype.val_injective), Submodule.map_top, range_subtype,
          ← Submodule.map_top, ← Submodule.map_comp, Submodule.map_top]

Changes are of the form

• some_tactic at h⊢ -> some_tactic at h ⊢
• some_tactic at h -> some_tactic at h

@@ -287,7 +287,7 @@ theorem range_smul_pow_stabilizes (r : R) :
   monotone_stabilizes
     ⟨fun n => LinearMap.range (r ^ n • LinearMap.id : M →ₗ[R] M), fun n m h x ⟨y, hy⟩ =>
       ⟨r ^ (m - n) • y, by
-        dsimp at hy⊢
+        dsimp at hy ⊢
         rw [← smul_assoc, smul_eq_mul, ← pow_add, ← hy, add_tsub_cancel_of_le h]⟩⟩
 #align is_artinian.range_smul_pow_stabilizes IsArtinian.range_smul_pow_stabilizes
 
@@ -333,7 +333,7 @@ theorem isArtinian_of_quotient_of_artinian (R) [Ring R] (M) [AddCommGroup M] [Mo
 /-- If `M / S / R` is a scalar tower, and `M / R` is Artinian, then `M / S` is also Artinian. -/
 theorem isArtinian_of_tower (R) {S M} [CommRing R] [Ring S] [AddCommGroup M] [Algebra R S]
     [Module S M] [Module R M] [IsScalarTower R S M] (h : IsArtinian R M) : IsArtinian S M := by
-  rw [isArtinian_iff_wellFounded] at h⊢
+  rw [isArtinian_iff_wellFounded] at h ⊢
   refine' (Submodule.restrictScalarsEmbedding R S M).wellFounded h
 #align is_artinian_of_tower isArtinian_of_tower
 
@@ -370,7 +370,7 @@ theorem isArtinian_span_of_finite (R) {M} [Ring R] [AddCommGroup M] [Module R M]
 
 theorem Function.Surjective.isArtinianRing {R} [Ring R] {S} [Ring S] {F} [RingHomClass F R S]
     {f : F} (hf : Function.Surjective f) [H : IsArtinianRing R] : IsArtinianRing S := by
-  rw [isArtinianRing_iff, isArtinian_iff_wellFounded] at H⊢
+  rw [isArtinianRing_iff, isArtinian_iff_wellFounded] at H ⊢
   exact (Ideal.orderEmbeddingOfSurjective f hf).wellFounded H
 #align function.surjective.is_artinian_ring Function.Surjective.isArtinianRing
 

Part 3 of #5001

@@ -27,7 +27,7 @@ itself, or simply Artinian if it is both left and right Artinian.
 
 Let `R` be a ring and let `M` and `P` be `R`-modules. Let `N` be an `R`-submodule of `M`.
 
-* `IsArtinian R M` is the proposition that `M` is a Artinian `R`-module. It is a class,
+* `IsArtinian R M` is the proposition that `M` is an Artinian `R`-module. It is a class,
   implemented as the predicate that the `<` relation on submodules is well founded.
 * `IsArtinianRing R` is the proposition that `R` is a left Artinian ring.
 
@@ -216,7 +216,7 @@ theorem induction {P : Submodule R M → Prop} (hgt : ∀ I, (∀ J < I, P J) 
   (wellFounded_submodule_lt R M).recursion I hgt
 #align is_artinian.induction IsArtinian.induction
 
-/-- For any endomorphism of a Artinian module, there is some nontrivial iterate
+/-- For any endomorphism of an Artinian module, there is some nontrivial iterate
 with disjoint kernel and range. -/
 theorem exists_endomorphism_iterate_ker_sup_range_eq_top (f : M →ₗ[R] M) :
     ∃ n : ℕ, n ≠ 0 ∧ LinearMap.ker (f ^ n) ⊔ LinearMap.range (f ^ n) = ⊤ := by

@@ -304,24 +304,6 @@ end IsArtinian
 
 end CommRing
 
--- TODO: Prove this for artinian modules
--- /--
--- If `M ⊕ N` embeds into `M`, for `M` noetherian over `R`, then `N` is trivial.
--- -/
--- universe w
--- variables {N : Type w} [add_comm_group N] [module R N]
--- noncomputable def is_noetherian.equiv_punit_of_prod_injective [is_noetherian R M]
---   (f : M × N →ₗ[R] M) (i : injective f) : N ≃ₗ[R] punit.{w+1} :=
--- begin
---   apply nonempty.some,
---   obtain ⟨n, w⟩ := is_noetherian.disjoint_partial_sups_eventually_bot (f.tailing i)
---     (f.tailings_disjoint_tailing i),
---   specialize w n (le_refl n),
---   apply nonempty.intro,
---   refine (f.tailing_linear_equiv i n).symm.trans _,
---   rw w,
---   exact submodule.bot_equiv_punit,
--- end
 /-- A ring is Artinian if it is Artinian as a module over itself.
 
 Strictly speaking, this should be called `IsLeftArtinianRing` but we omit the `Left` for

Removes an unneeded import that was accidentally included in #4104

@@ -11,7 +11,6 @@ Authors: Chris Hughes
 import Mathlib.RingTheory.Nakayama
 import Mathlib.Data.SetLike.Fintype
 import Mathlib.Tactic.RSuffices
-import Mathlib.Tactic.LibrarySearch
 
 /-!
 # Artinian rings and modules

Co-authored-by: ChrisHughes24 <chrishughes24@gmail.com> Co-authored-by: Chris Hughes <chrishughes24@gmail.com>