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

@@ -4,9 +4,9 @@ Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Jujian Zhang
 -/
 import CategoryTheory.Preadditive.Injective
-import Algebra.Category.Module.EpiMono
+import Algebra.Category.ModuleCat.EpiMono
 import RingTheory.Ideal.Basic
-import LinearAlgebra.LinearPmap
+import LinearAlgebra.LinearPMap
 
 #align_import algebra.module.injective from "leanprover-community/mathlib"@"bd15ff41b70f5e2cc210f26f25a8d5c53b20d3de"
 

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

@@ -225,12 +225,12 @@ instance ExtensionOf.inhabited : Inhabited (ExtensionOf i f)
           map_add' := fun x y =>
             by
             have eq1 : _ + _ = (x + y).1 := congr_arg₂ (· + ·) x.2.choose_spec y.2.choose_spec
-            rw [← map_add, ← (x + y).2.choose_spec] at eq1 
+            rw [← map_add, ← (x + y).2.choose_spec] at eq1
             rw [← Fact.out (Function.Injective i) eq1, map_add]
           map_smul' := fun r x =>
             by
             have eq1 : r • _ = (r • x).1 := congr_arg ((· • ·) r) x.2.choose_spec
-            rw [← LinearMap.map_smul, ← (r • x).2.choose_spec] at eq1 
+            rw [← LinearMap.map_smul, ← (r • x).2.choose_spec] at eq1
             rw [RingHom.id_apply, ← Fact.out (Function.Injective i) eq1, LinearMap.map_smul] }
       le := le_refl _
       is_extension := fun m =>
@@ -265,9 +265,9 @@ private theorem extensionOfMax_adjoin.aux1 {y : N}
     ∃ (a : (extensionOfMax i f).domain) (b : R), x.1 = a.1 + b • y :=
   by
   have mem1 : x.1 ∈ (_ : Set _) := x.2
-  rw [Submodule.coe_sup] at mem1 
+  rw [Submodule.coe_sup] at mem1
   rcases mem1 with ⟨a, b, a_mem, b_mem : b ∈ (Submodule.span R _ : Submodule R N), eq1⟩
-  rw [Submodule.mem_span_singleton] at b_mem 
+  rw [Submodule.mem_span_singleton] at b_mem
   rcases b_mem with ⟨z, eq2⟩
   exact ⟨⟨a, a_mem⟩, z, by rw [← eq1, ← eq2]⟩
 
@@ -378,15 +378,15 @@ theorem ExtensionOfMaxAdjoin.extensionToFun_wd (h : Module.Baer R Q) {y : N}
       (extensionOfMax i f).toLinearPMap a + ExtensionOfMaxAdjoin.extendIdealTo i f h y r :=
   by
   cases' a with a ha
-  rw [Subtype.coe_mk] at eq1 
+  rw [Subtype.coe_mk] at eq1
   have eq2 :
     (extension_of_max_adjoin.fst i x - a : N) = (r - extension_of_max_adjoin.snd i x) • y := by
     rwa [extension_of_max_adjoin.eqn, ← sub_eq_zero, ← sub_sub_sub_eq, sub_eq_zero, ← sub_smul] at
-      eq1 
+      eq1
   have eq3 :=
     extension_of_max_adjoin.extend_ideal_to_eq i f h (r - extension_of_max_adjoin.snd i x)
       (by rw [← eq2] <;> exact Submodule.sub_mem _ (extension_of_max_adjoin.fst i x).2 ha)
-  simp only [map_sub, sub_smul, sub_eq_iff_eq_add] at eq3 
+  simp only [map_sub, sub_smul, sub_eq_iff_eq_add] at eq3
   unfold extension_of_max_adjoin.extension_to_fun
   rw [eq3, ← add_assoc, ← (extension_of_max i f).toLinearPMap.map_add, AddMemClass.mk_add_mk]
   congr

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

@@ -113,15 +113,13 @@ variable {R Q} {M N : Type max u v} [AddCommGroup M] [AddCommGroup N]
 
 variable [Module R M] [Module R N] (i : M →ₗ[R] N) (f : M →ₗ[R] Q)
 
-#print Module.Baer.ExtensionOf /-
 /-- If we view `M` as a submodule of `N` via the injective linear map `i : M ↪ N`, then a submodule
 between `M` and `N` is a submodule `N'` of `N`. To prove Baer's criterion, we need to consider
 pairs of `(N', f')` such that `M ≤ N' ≤ N` and `f'` extends `f`. -/
 structure ExtensionOf extends LinearPMap R N Q where
   le : i.range ≤ domain
   is_extension : ∀ m : M, f m = to_linear_pmap ⟨i m, le ⟨m, rfl⟩⟩
-#align module.Baer.extension_of Module.Baer.ExtensionOf
--/
+#align module.Baer.extension_of Module.Baer.ExtensionOfₓ
 
 section Ext
 

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

@@ -3,10 +3,10 @@ Copyright (c) 2022 Jujian Zhang. All rights reserved.
 Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Jujian Zhang
 -/
-import Mathbin.CategoryTheory.Preadditive.Injective
-import Mathbin.Algebra.Category.Module.EpiMono
-import Mathbin.RingTheory.Ideal.Basic
-import Mathbin.LinearAlgebra.LinearPmap
+import CategoryTheory.Preadditive.Injective
+import Algebra.Category.Module.EpiMono
+import RingTheory.Ideal.Basic
+import LinearAlgebra.LinearPmap
 
 #align_import algebra.module.injective from "leanprover-community/mathlib"@"bd15ff41b70f5e2cc210f26f25a8d5c53b20d3de"
 

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

@@ -2,17 +2,14 @@
 Copyright (c) 2022 Jujian Zhang. All rights reserved.
 Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Jujian Zhang
-
-! This file was ported from Lean 3 source module algebra.module.injective
-! leanprover-community/mathlib commit bd15ff41b70f5e2cc210f26f25a8d5c53b20d3de
-! Please do not edit these lines, except to modify the commit id
-! if you have ported upstream changes.
 -/
 import Mathbin.CategoryTheory.Preadditive.Injective
 import Mathbin.Algebra.Category.Module.EpiMono
 import Mathbin.RingTheory.Ideal.Basic
 import Mathbin.LinearAlgebra.LinearPmap
 
+#align_import algebra.module.injective from "leanprover-community/mathlib"@"bd15ff41b70f5e2cc210f26f25a8d5c53b20d3de"
+
 /-!
 # Injective modules
 

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

@@ -130,6 +130,7 @@ section Ext
 
 variable {i f}
 
+#print Module.Baer.ExtensionOf.ext /-
 @[ext]
 theorem ExtensionOf.ext {a b : ExtensionOf i f} (domain_eq : a.domain = b.domain)
     (to_fun_eq :
@@ -140,7 +141,9 @@ theorem ExtensionOf.ext {a b : ExtensionOf i f} (domain_eq : a.domain = b.domain
   congr
   exact LinearPMap.ext domain_eq to_fun_eq
 #align module.Baer.extension_of.ext Module.Baer.ExtensionOf.ext
+-/
 
+#print Module.Baer.ExtensionOf.ext_iff /-
 theorem ExtensionOf.ext_iff {a b : ExtensionOf i f} :
     a = b ↔
       ∃ domain_eq : a.domain = b.domain,
@@ -148,6 +151,7 @@ theorem ExtensionOf.ext_iff {a b : ExtensionOf i f} :
   ⟨fun r => r ▸ ⟨rfl, fun x y h => congr_arg a.toFun <| by exact_mod_cast h⟩, fun ⟨h1, h2⟩ =>
     ExtensionOf.ext h1 h2⟩
 #align module.Baer.extension_of.ext_iff Module.Baer.ExtensionOf.ext_iff
+-/
 
 end Ext
 
@@ -172,6 +176,7 @@ instance : SemilatticeInf (ExtensionOf i f) :=
 
 variable {R i f}
 
+#print Module.Baer.chain_linearPMap_of_chain_extensionOf /-
 theorem chain_linearPMap_of_chain_extensionOf {c : Set (ExtensionOf i f)}
     (hchain : IsChain (· ≤ ·) c) :
     IsChain (· ≤ ·) <| (fun x : ExtensionOf i f => x.toLinearPMap) '' c :=
@@ -179,7 +184,9 @@ theorem chain_linearPMap_of_chain_extensionOf {c : Set (ExtensionOf i f)}
   rintro _ ⟨a, a_mem, rfl⟩ _ ⟨b, b_mem, rfl⟩ neq
   exact hchain a_mem b_mem (ne_of_apply_ne _ neq)
 #align module.Baer.chain_linear_pmap_of_chain_extension_of Module.Baer.chain_linearPMap_of_chain_extensionOf
+-/
 
+#print Module.Baer.ExtensionOf.max /-
 /-- The maximal element of every nonempty chain of `extension_of i f`. -/
 def ExtensionOf.max {c : Set (ExtensionOf i f)} (hchain : IsChain (· ≤ ·) c)
     (hnonempty : c.Nonempty) : ExtensionOf i f :=
@@ -201,16 +208,20 @@ def ExtensionOf.max {c : Set (ExtensionOf i f)} (hchain : IsChain (· ≤ ·) c)
         LinearPMap.sSup_apply (IsChain.directedOn <| chain_linear_pmap_of_chain_extension_of hchain)
           ((Set.mem_image _ _ _).mpr ⟨hnonempty.some, hnonempty.some_spec, rfl⟩) ⟨i m, h1⟩ }
 #align module.Baer.extension_of.max Module.Baer.ExtensionOf.max
+-/
 
+#print Module.Baer.ExtensionOf.le_max /-
 theorem ExtensionOf.le_max {c : Set (ExtensionOf i f)} (hchain : IsChain (· ≤ ·) c)
     (hnonempty : c.Nonempty) (a : ExtensionOf i f) (ha : a ∈ c) :
     a ≤ ExtensionOf.max hchain hnonempty :=
   LinearPMap.le_sSup (IsChain.directedOn <| chain_linearPMap_of_chain_extensionOf hchain) <|
     (Set.mem_image _ _ _).mpr ⟨a, ha, rfl⟩
 #align module.Baer.extension_of.le_max Module.Baer.ExtensionOf.le_max
+-/
 
 variable (i f) [Fact <| Function.Injective i]
 
+#print Module.Baer.ExtensionOf.inhabited /-
 instance ExtensionOf.inhabited : Inhabited (ExtensionOf i f)
     where default :=
     { domain := i.range
@@ -233,19 +244,24 @@ instance ExtensionOf.inhabited : Inhabited (ExtensionOf i f)
         congr
         exact Fact.out (Function.Injective i) (⟨i m, ⟨_, rfl⟩⟩ : i.range).2.choose_spec.symm }
 #align module.Baer.extension_of.inhabited Module.Baer.ExtensionOf.inhabited
+-/
 
+#print Module.Baer.extensionOfMax /-
 /-- Since every nonempty chain has a maximal element, by Zorn's lemma, there is a maximal
 `extension_of i f`. -/
 def extensionOfMax : ExtensionOf i f :=
   (@zorn_nonempty_partialOrder (ExtensionOf i f) _ ⟨Inhabited.default⟩ fun c hchain hnonempty =>
       ⟨ExtensionOf.max hchain hnonempty, ExtensionOf.le_max hchain hnonempty⟩).some
 #align module.Baer.extension_of_max Module.Baer.extensionOfMax
+-/
 
+#print Module.Baer.extensionOfMax_is_max /-
 theorem extensionOfMax_is_max :
     ∀ a : ExtensionOf i f, extensionOfMax i f ≤ a → a = extensionOfMax i f :=
   (@zorn_nonempty_partialOrder (ExtensionOf i f) _ ⟨Inhabited.default⟩ fun c hchain hnonempty =>
       ⟨ExtensionOf.max hchain hnonempty, ExtensionOf.le_max hchain hnonempty⟩).choose_spec
 #align module.Baer.extension_of_max_is_max Module.Baer.extensionOfMax_is_max
+-/
 
 variable {f}
 
@@ -260,29 +276,38 @@ private theorem extensionOfMax_adjoin.aux1 {y : N}
   rcases b_mem with ⟨z, eq2⟩
   exact ⟨⟨a, a_mem⟩, z, by rw [← eq1, ← eq2]⟩
 
+#print Module.Baer.ExtensionOfMaxAdjoin.fst /-
 /-- If `x ∈ M ⊔ ⟨y⟩`, then `x = m + r • y`, `fst` pick an arbitrary such `m`.-/
 def ExtensionOfMaxAdjoin.fst {y : N} (x : (extensionOfMax i f).domain ⊔ Submodule.span R {y}) :
     (extensionOfMax i f).domain :=
   (ExtensionOfMaxAdjoin.aux1 i x).some
 #align module.Baer.extension_of_max_adjoin.fst Module.Baer.ExtensionOfMaxAdjoin.fst
+-/
 
+#print Module.Baer.ExtensionOfMaxAdjoin.snd /-
 /-- If `x ∈ M ⊔ ⟨y⟩`, then `x = m + r • y`, `snd` pick an arbitrary such `r`.-/
 def ExtensionOfMaxAdjoin.snd {y : N} (x : (extensionOfMax i f).domain ⊔ Submodule.span R {y}) : R :=
   (ExtensionOfMaxAdjoin.aux1 i x).choose_spec.some
 #align module.Baer.extension_of_max_adjoin.snd Module.Baer.ExtensionOfMaxAdjoin.snd
+-/
 
+#print Module.Baer.ExtensionOfMaxAdjoin.eqn /-
 theorem ExtensionOfMaxAdjoin.eqn {y : N} (x : (extensionOfMax i f).domain ⊔ Submodule.span R {y}) :
     ↑x = ↑(ExtensionOfMaxAdjoin.fst i x) + ExtensionOfMaxAdjoin.snd i x • y :=
   (ExtensionOfMaxAdjoin.aux1 i x).choose_spec.choose_spec
 #align module.Baer.extension_of_max_adjoin.eqn Module.Baer.ExtensionOfMaxAdjoin.eqn
+-/
 
 variable (f)
 
+#print Module.Baer.ExtensionOfMaxAdjoin.ideal /-
 /-- the ideal `I = {r | r • y ∈ N}`-/
 def ExtensionOfMaxAdjoin.ideal (y : N) : Ideal R :=
   (extensionOfMax i f).domain.comap ((LinearMap.id : R →ₗ[R] R).smul_right y)
 #align module.Baer.extension_of_max_adjoin.ideal Module.Baer.ExtensionOfMaxAdjoin.ideal
+-/
 
+#print Module.Baer.ExtensionOfMaxAdjoin.idealTo /-
 /-- A linear map `I ⟶ Q` by `x ↦ f' (x • y)` where `f'` is the maximal extension-/
 def ExtensionOfMaxAdjoin.idealTo (y : N) : ExtensionOfMaxAdjoin.ideal i f y →ₗ[R] Q
     where
@@ -290,19 +315,25 @@ def ExtensionOfMaxAdjoin.idealTo (y : N) : ExtensionOfMaxAdjoin.ideal i f y →
   map_add' z1 z2 := by simp [← (extension_of_max i f).toLinearPMap.map_add, add_smul]
   map_smul' z1 z2 := by simp [← (extension_of_max i f).toLinearPMap.map_smul, mul_smul] <;> rfl
 #align module.Baer.extension_of_max_adjoin.ideal_to Module.Baer.ExtensionOfMaxAdjoin.idealTo
+-/
 
+#print Module.Baer.ExtensionOfMaxAdjoin.extendIdealTo /-
 /-- Since we assumed `Q` being Baer, the linear map `x ↦ f' (x • y) : I ⟶ Q` extends to `R ⟶ Q`,
 call this extended map `φ`-/
 def ExtensionOfMaxAdjoin.extendIdealTo (h : Module.Baer R Q) (y : N) : R →ₗ[R] Q :=
   (h (ExtensionOfMaxAdjoin.ideal i f y) (ExtensionOfMaxAdjoin.idealTo i f y)).some
 #align module.Baer.extension_of_max_adjoin.extend_ideal_to Module.Baer.ExtensionOfMaxAdjoin.extendIdealTo
+-/
 
+#print Module.Baer.ExtensionOfMaxAdjoin.extendIdealTo_is_extension /-
 theorem ExtensionOfMaxAdjoin.extendIdealTo_is_extension (h : Module.Baer R Q) (y : N) :
     ∀ (x : R) (mem : x ∈ ExtensionOfMaxAdjoin.ideal i f y),
       ExtensionOfMaxAdjoin.extendIdealTo i f h y x = ExtensionOfMaxAdjoin.idealTo i f y ⟨x, mem⟩ :=
   (h (ExtensionOfMaxAdjoin.ideal i f y) (ExtensionOfMaxAdjoin.idealTo i f y)).choose_spec
 #align module.Baer.extension_of_max_adjoin.extend_ideal_to_is_extension Module.Baer.ExtensionOfMaxAdjoin.extendIdealTo_is_extension
+-/
 
+#print Module.Baer.ExtensionOfMaxAdjoin.extendIdealTo_wd' /-
 theorem ExtensionOfMaxAdjoin.extendIdealTo_wd' (h : Module.Baer R Q) {y : N} (r : R)
     (eq1 : r • y = 0) : ExtensionOfMaxAdjoin.extendIdealTo i f h y r = 0 :=
   by
@@ -311,7 +342,9 @@ theorem ExtensionOfMaxAdjoin.extendIdealTo_wd' (h : Module.Baer R Q) {y : N} (r
   simp only [extension_of_max_adjoin.ideal_to, LinearMap.coe_mk, eq1, Subtype.coe_mk, ←
     ZeroMemClass.zero_def, (extension_of_max i f).toLinearPMap.map_zero]
 #align module.Baer.extension_of_max_adjoin.extend_ideal_to_wd' Module.Baer.ExtensionOfMaxAdjoin.extendIdealTo_wd'
+-/
 
+#print Module.Baer.ExtensionOfMaxAdjoin.extendIdealTo_wd /-
 theorem ExtensionOfMaxAdjoin.extendIdealTo_wd (h : Module.Baer R Q) {y : N} (r r' : R)
     (eq1 : r • y = r' • y) :
     ExtensionOfMaxAdjoin.extendIdealTo i f h y r = ExtensionOfMaxAdjoin.extendIdealTo i f h y r' :=
@@ -320,7 +353,9 @@ theorem ExtensionOfMaxAdjoin.extendIdealTo_wd (h : Module.Baer R Q) {y : N} (r r
   convert extension_of_max_adjoin.extend_ideal_to_wd' i f h (r - r') _
   rw [sub_smul, sub_eq_zero, eq1]
 #align module.Baer.extension_of_max_adjoin.extend_ideal_to_wd Module.Baer.ExtensionOfMaxAdjoin.extendIdealTo_wd
+-/
 
+#print Module.Baer.ExtensionOfMaxAdjoin.extendIdealTo_eq /-
 theorem ExtensionOfMaxAdjoin.extendIdealTo_eq (h : Module.Baer R Q) {y : N} (r : R)
     (hr : r • y ∈ (extensionOfMax i f).domain) :
     ExtensionOfMaxAdjoin.extendIdealTo i f h y r = (extensionOfMax i f).toLinearPMap ⟨r • y, hr⟩ :=
@@ -328,7 +363,9 @@ theorem ExtensionOfMaxAdjoin.extendIdealTo_eq (h : Module.Baer R Q) {y : N} (r :
   simp only [extension_of_max_adjoin.extend_ideal_to_is_extension i f h _ _ hr,
     extension_of_max_adjoin.ideal_to, LinearMap.coe_mk, Subtype.coe_mk]
 #align module.Baer.extension_of_max_adjoin.extend_ideal_to_eq Module.Baer.ExtensionOfMaxAdjoin.extendIdealTo_eq
+-/
 
+#print Module.Baer.ExtensionOfMaxAdjoin.extensionToFun /-
 /-- We can finally define a linear map `M ⊔ ⟨y⟩ ⟶ Q` by `x + r • y ↦ f x + φ r`
 -/
 def ExtensionOfMaxAdjoin.extensionToFun (h : Module.Baer R Q) {y : N} :
@@ -336,7 +373,9 @@ def ExtensionOfMaxAdjoin.extensionToFun (h : Module.Baer R Q) {y : N} :
   (extensionOfMax i f).toLinearPMap (ExtensionOfMaxAdjoin.fst i x) +
     ExtensionOfMaxAdjoin.extendIdealTo i f h y (ExtensionOfMaxAdjoin.snd i x)
 #align module.Baer.extension_of_max_adjoin.extension_to_fun Module.Baer.ExtensionOfMaxAdjoin.extensionToFun
+-/
 
+#print Module.Baer.ExtensionOfMaxAdjoin.extensionToFun_wd /-
 theorem ExtensionOfMaxAdjoin.extensionToFun_wd (h : Module.Baer R Q) {y : N}
     (x : (extensionOfMax i f).domain ⊔ Submodule.span R {y}) (a : (extensionOfMax i f).domain)
     (r : R) (eq1 : ↑x = ↑a + r • y) :
@@ -360,7 +399,9 @@ theorem ExtensionOfMaxAdjoin.extensionToFun_wd (h : Module.Baer R Q) {y : N}
   rw [Subtype.coe_mk, add_sub, ← eq1]
   exact eq_sub_of_add_eq (extension_of_max_adjoin.eqn _ _).symm
 #align module.Baer.extension_of_max_adjoin.extension_to_fun_wd Module.Baer.ExtensionOfMaxAdjoin.extensionToFun_wd
+-/
 
+#print Module.Baer.extensionOfMaxAdjoin /-
 /-- The linear map `M ⊔ ⟨y⟩ ⟶ Q` by `x + r • y ↦ f x + φ r` is an extension of `f`-/
 def extensionOfMaxAdjoin (h : Module.Baer R Q) (y : N) : ExtensionOf i f
     where
@@ -398,7 +439,9 @@ def extensionOfMaxAdjoin (h : Module.Baer R Q) (y : N) : ExtensionOf i f
       extension_of_max_adjoin.extension_to_fun_wd i f h _ ⟨i m, _⟩ 0 _, map_zero, add_zero]
     simp
 #align module.Baer.extension_of_max_adjoin Module.Baer.extensionOfMaxAdjoin
+-/
 
+#print Module.Baer.extensionOfMax_le /-
 theorem extensionOfMax_le (h : Module.Baer R Q) {y : N} :
     extensionOfMax i f ≤ extensionOfMaxAdjoin i f h y :=
   ⟨le_sup_left, fun x x' EQ => by
@@ -407,7 +450,9 @@ theorem extensionOfMax_le (h : Module.Baer R Q) {y : N} :
     rw [extension_of_max_adjoin.extension_to_fun_wd i f h x' x 0 (by simp [EQ]), map_zero,
       add_zero]⟩
 #align module.Baer.extension_of_max_le Module.Baer.extensionOfMax_le
+-/
 
+#print Module.Baer.extensionOfMax_to_submodule_eq_top /-
 theorem extensionOfMax_to_submodule_eq_top (h : Module.Baer R Q) :
     (extensionOfMax i f).domain = ⊤ :=
   by
@@ -416,6 +461,7 @@ theorem extensionOfMax_to_submodule_eq_top (h : Module.Baer R Q) :
     Submodule.mem_sup]
   exact ⟨0, Submodule.zero_mem _, y, Submodule.mem_span_singleton_self _, zero_add _⟩
 #align module.Baer.extension_of_max_to_submodule_eq_top Module.Baer.extensionOfMax_to_submodule_eq_top
+-/
 
 #print Module.Baer.injective /-
 /-- **Baer's criterion** for injective module : a Baer module is an injective module, i.e. if every

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

@@ -167,8 +167,8 @@ instance : Inf (ExtensionOf i f)
 instance : SemilatticeInf (ExtensionOf i f) :=
   Function.Injective.semilatticeInf ExtensionOf.toLinearPmap
     (fun X Y h =>
-      ExtensionOf.ext (by rw [h]) fun x y h' => by induction h; congr ; exact_mod_cast h')
-    fun X Y => LinearPMap.ext rfl fun x y h => by congr ; exact_mod_cast h
+      ExtensionOf.ext (by rw [h]) fun x y h' => by induction h; congr; exact_mod_cast h')
+    fun X Y => LinearPMap.ext rfl fun x y h => by congr; exact_mod_cast h
 
 variable {R i f}
 
@@ -219,12 +219,12 @@ instance ExtensionOf.inhabited : Inhabited (ExtensionOf i f)
           map_add' := fun x y =>
             by
             have eq1 : _ + _ = (x + y).1 := congr_arg₂ (· + ·) x.2.choose_spec y.2.choose_spec
-            rw [← map_add, ← (x + y).2.choose_spec] at eq1
+            rw [← map_add, ← (x + y).2.choose_spec] at eq1 
             rw [← Fact.out (Function.Injective i) eq1, map_add]
           map_smul' := fun r x =>
             by
             have eq1 : r • _ = (r • x).1 := congr_arg ((· • ·) r) x.2.choose_spec
-            rw [← LinearMap.map_smul, ← (r • x).2.choose_spec] at eq1
+            rw [← LinearMap.map_smul, ← (r • x).2.choose_spec] at eq1 
             rw [RingHom.id_apply, ← Fact.out (Function.Injective i) eq1, LinearMap.map_smul] }
       le := le_refl _
       is_extension := fun m =>
@@ -251,12 +251,12 @@ variable {f}
 
 private theorem extensionOfMax_adjoin.aux1 {y : N}
     (x : (extensionOfMax i f).domain ⊔ Submodule.span R {y}) :
-    ∃ (a : (extensionOfMax i f).domain)(b : R), x.1 = a.1 + b • y :=
+    ∃ (a : (extensionOfMax i f).domain) (b : R), x.1 = a.1 + b • y :=
   by
   have mem1 : x.1 ∈ (_ : Set _) := x.2
-  rw [Submodule.coe_sup] at mem1
+  rw [Submodule.coe_sup] at mem1 
   rcases mem1 with ⟨a, b, a_mem, b_mem : b ∈ (Submodule.span R _ : Submodule R N), eq1⟩
-  rw [Submodule.mem_span_singleton] at b_mem
+  rw [Submodule.mem_span_singleton] at b_mem 
   rcases b_mem with ⟨z, eq2⟩
   exact ⟨⟨a, a_mem⟩, z, by rw [← eq1, ← eq2]⟩
 
@@ -344,15 +344,15 @@ theorem ExtensionOfMaxAdjoin.extensionToFun_wd (h : Module.Baer R Q) {y : N}
       (extensionOfMax i f).toLinearPMap a + ExtensionOfMaxAdjoin.extendIdealTo i f h y r :=
   by
   cases' a with a ha
-  rw [Subtype.coe_mk] at eq1
+  rw [Subtype.coe_mk] at eq1 
   have eq2 :
     (extension_of_max_adjoin.fst i x - a : N) = (r - extension_of_max_adjoin.snd i x) • y := by
     rwa [extension_of_max_adjoin.eqn, ← sub_eq_zero, ← sub_sub_sub_eq, sub_eq_zero, ← sub_smul] at
-      eq1
+      eq1 
   have eq3 :=
     extension_of_max_adjoin.extend_ideal_to_eq i f h (r - extension_of_max_adjoin.snd i x)
       (by rw [← eq2] <;> exact Submodule.sub_mem _ (extension_of_max_adjoin.fst i x).2 ha)
-  simp only [map_sub, sub_smul, sub_eq_iff_eq_add] at eq3
+  simp only [map_sub, sub_smul, sub_eq_iff_eq_add] at eq3 
   unfold extension_of_max_adjoin.extension_to_fun
   rw [eq3, ← add_assoc, ← (extension_of_max i f).toLinearPMap.map_add, AddMemClass.mk_add_mk]
   congr

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

@@ -130,9 +130,6 @@ section Ext
 
 variable {i f}
 
-/- warning: module.Baer.extension_of.ext -> Module.Baer.ExtensionOf.ext is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align module.Baer.extension_of.ext Module.Baer.ExtensionOf.extₓ'. -/
 @[ext]
 theorem ExtensionOf.ext {a b : ExtensionOf i f} (domain_eq : a.domain = b.domain)
     (to_fun_eq :
@@ -144,9 +141,6 @@ theorem ExtensionOf.ext {a b : ExtensionOf i f} (domain_eq : a.domain = b.domain
   exact LinearPMap.ext domain_eq to_fun_eq
 #align module.Baer.extension_of.ext Module.Baer.ExtensionOf.ext
 
-/- warning: module.Baer.extension_of.ext_iff -> Module.Baer.ExtensionOf.ext_iff is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align module.Baer.extension_of.ext_iff Module.Baer.ExtensionOf.ext_iffₓ'. -/
 theorem ExtensionOf.ext_iff {a b : ExtensionOf i f} :
     a = b ↔
       ∃ domain_eq : a.domain = b.domain,
@@ -178,9 +172,6 @@ instance : SemilatticeInf (ExtensionOf i f) :=
 
 variable {R i f}
 
-/- warning: module.Baer.chain_linear_pmap_of_chain_extension_of -> Module.Baer.chain_linearPMap_of_chain_extensionOf is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align module.Baer.chain_linear_pmap_of_chain_extension_of Module.Baer.chain_linearPMap_of_chain_extensionOfₓ'. -/
 theorem chain_linearPMap_of_chain_extensionOf {c : Set (ExtensionOf i f)}
     (hchain : IsChain (· ≤ ·) c) :
     IsChain (· ≤ ·) <| (fun x : ExtensionOf i f => x.toLinearPMap) '' c :=
@@ -189,9 +180,6 @@ theorem chain_linearPMap_of_chain_extensionOf {c : Set (ExtensionOf i f)}
   exact hchain a_mem b_mem (ne_of_apply_ne _ neq)
 #align module.Baer.chain_linear_pmap_of_chain_extension_of Module.Baer.chain_linearPMap_of_chain_extensionOf
 
-/- warning: module.Baer.extension_of.max -> Module.Baer.ExtensionOf.max is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align module.Baer.extension_of.max Module.Baer.ExtensionOf.maxₓ'. -/
 /-- The maximal element of every nonempty chain of `extension_of i f`. -/
 def ExtensionOf.max {c : Set (ExtensionOf i f)} (hchain : IsChain (· ≤ ·) c)
     (hnonempty : c.Nonempty) : ExtensionOf i f :=
@@ -214,9 +202,6 @@ def ExtensionOf.max {c : Set (ExtensionOf i f)} (hchain : IsChain (· ≤ ·) c)
           ((Set.mem_image _ _ _).mpr ⟨hnonempty.some, hnonempty.some_spec, rfl⟩) ⟨i m, h1⟩ }
 #align module.Baer.extension_of.max Module.Baer.ExtensionOf.max
 
-/- warning: module.Baer.extension_of.le_max -> Module.Baer.ExtensionOf.le_max is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align module.Baer.extension_of.le_max Module.Baer.ExtensionOf.le_maxₓ'. -/
 theorem ExtensionOf.le_max {c : Set (ExtensionOf i f)} (hchain : IsChain (· ≤ ·) c)
     (hnonempty : c.Nonempty) (a : ExtensionOf i f) (ha : a ∈ c) :
     a ≤ ExtensionOf.max hchain hnonempty :=
@@ -226,9 +211,6 @@ theorem ExtensionOf.le_max {c : Set (ExtensionOf i f)} (hchain : IsChain (· ≤
 
 variable (i f) [Fact <| Function.Injective i]
 
-/- warning: module.Baer.extension_of.inhabited -> Module.Baer.ExtensionOf.inhabited is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align module.Baer.extension_of.inhabited Module.Baer.ExtensionOf.inhabitedₓ'. -/
 instance ExtensionOf.inhabited : Inhabited (ExtensionOf i f)
     where default :=
     { domain := i.range
@@ -252,9 +234,6 @@ instance ExtensionOf.inhabited : Inhabited (ExtensionOf i f)
         exact Fact.out (Function.Injective i) (⟨i m, ⟨_, rfl⟩⟩ : i.range).2.choose_spec.symm }
 #align module.Baer.extension_of.inhabited Module.Baer.ExtensionOf.inhabited
 
-/- warning: module.Baer.extension_of_max -> Module.Baer.extensionOfMax is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align module.Baer.extension_of_max Module.Baer.extensionOfMaxₓ'. -/
 /-- Since every nonempty chain has a maximal element, by Zorn's lemma, there is a maximal
 `extension_of i f`. -/
 def extensionOfMax : ExtensionOf i f :=
@@ -262,9 +241,6 @@ def extensionOfMax : ExtensionOf i f :=
       ⟨ExtensionOf.max hchain hnonempty, ExtensionOf.le_max hchain hnonempty⟩).some
 #align module.Baer.extension_of_max Module.Baer.extensionOfMax
 
-/- warning: module.Baer.extension_of_max_is_max -> Module.Baer.extensionOfMax_is_max is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align module.Baer.extension_of_max_is_max Module.Baer.extensionOfMax_is_maxₓ'. -/
 theorem extensionOfMax_is_max :
     ∀ a : ExtensionOf i f, extensionOfMax i f ≤ a → a = extensionOfMax i f :=
   (@zorn_nonempty_partialOrder (ExtensionOf i f) _ ⟨Inhabited.default⟩ fun c hchain hnonempty =>
@@ -284,26 +260,17 @@ private theorem extensionOfMax_adjoin.aux1 {y : N}
   rcases b_mem with ⟨z, eq2⟩
   exact ⟨⟨a, a_mem⟩, z, by rw [← eq1, ← eq2]⟩
 
-/- warning: module.Baer.extension_of_max_adjoin.fst -> Module.Baer.ExtensionOfMaxAdjoin.fst is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align module.Baer.extension_of_max_adjoin.fst Module.Baer.ExtensionOfMaxAdjoin.fstₓ'. -/
 /-- If `x ∈ M ⊔ ⟨y⟩`, then `x = m + r • y`, `fst` pick an arbitrary such `m`.-/
 def ExtensionOfMaxAdjoin.fst {y : N} (x : (extensionOfMax i f).domain ⊔ Submodule.span R {y}) :
     (extensionOfMax i f).domain :=
   (ExtensionOfMaxAdjoin.aux1 i x).some
 #align module.Baer.extension_of_max_adjoin.fst Module.Baer.ExtensionOfMaxAdjoin.fst
 
-/- warning: module.Baer.extension_of_max_adjoin.snd -> Module.Baer.ExtensionOfMaxAdjoin.snd is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align module.Baer.extension_of_max_adjoin.snd Module.Baer.ExtensionOfMaxAdjoin.sndₓ'. -/
 /-- If `x ∈ M ⊔ ⟨y⟩`, then `x = m + r • y`, `snd` pick an arbitrary such `r`.-/
 def ExtensionOfMaxAdjoin.snd {y : N} (x : (extensionOfMax i f).domain ⊔ Submodule.span R {y}) : R :=
   (ExtensionOfMaxAdjoin.aux1 i x).choose_spec.some
 #align module.Baer.extension_of_max_adjoin.snd Module.Baer.ExtensionOfMaxAdjoin.snd
 
-/- warning: module.Baer.extension_of_max_adjoin.eqn -> Module.Baer.ExtensionOfMaxAdjoin.eqn is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align module.Baer.extension_of_max_adjoin.eqn Module.Baer.ExtensionOfMaxAdjoin.eqnₓ'. -/
 theorem ExtensionOfMaxAdjoin.eqn {y : N} (x : (extensionOfMax i f).domain ⊔ Submodule.span R {y}) :
     ↑x = ↑(ExtensionOfMaxAdjoin.fst i x) + ExtensionOfMaxAdjoin.snd i x • y :=
   (ExtensionOfMaxAdjoin.aux1 i x).choose_spec.choose_spec
@@ -311,17 +278,11 @@ theorem ExtensionOfMaxAdjoin.eqn {y : N} (x : (extensionOfMax i f).domain ⊔ Su
 
 variable (f)
 
-/- warning: module.Baer.extension_of_max_adjoin.ideal -> Module.Baer.ExtensionOfMaxAdjoin.ideal is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align module.Baer.extension_of_max_adjoin.ideal Module.Baer.ExtensionOfMaxAdjoin.idealₓ'. -/
 /-- the ideal `I = {r | r • y ∈ N}`-/
 def ExtensionOfMaxAdjoin.ideal (y : N) : Ideal R :=
   (extensionOfMax i f).domain.comap ((LinearMap.id : R →ₗ[R] R).smul_right y)
 #align module.Baer.extension_of_max_adjoin.ideal Module.Baer.ExtensionOfMaxAdjoin.ideal
 
-/- warning: module.Baer.extension_of_max_adjoin.ideal_to -> Module.Baer.ExtensionOfMaxAdjoin.idealTo is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align module.Baer.extension_of_max_adjoin.ideal_to Module.Baer.ExtensionOfMaxAdjoin.idealToₓ'. -/
 /-- A linear map `I ⟶ Q` by `x ↦ f' (x • y)` where `f'` is the maximal extension-/
 def ExtensionOfMaxAdjoin.idealTo (y : N) : ExtensionOfMaxAdjoin.ideal i f y →ₗ[R] Q
     where
@@ -330,27 +291,18 @@ def ExtensionOfMaxAdjoin.idealTo (y : N) : ExtensionOfMaxAdjoin.ideal i f y →
   map_smul' z1 z2 := by simp [← (extension_of_max i f).toLinearPMap.map_smul, mul_smul] <;> rfl
 #align module.Baer.extension_of_max_adjoin.ideal_to Module.Baer.ExtensionOfMaxAdjoin.idealTo
 
-/- warning: module.Baer.extension_of_max_adjoin.extend_ideal_to -> Module.Baer.ExtensionOfMaxAdjoin.extendIdealTo is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align module.Baer.extension_of_max_adjoin.extend_ideal_to Module.Baer.ExtensionOfMaxAdjoin.extendIdealToₓ'. -/
 /-- Since we assumed `Q` being Baer, the linear map `x ↦ f' (x • y) : I ⟶ Q` extends to `R ⟶ Q`,
 call this extended map `φ`-/
 def ExtensionOfMaxAdjoin.extendIdealTo (h : Module.Baer R Q) (y : N) : R →ₗ[R] Q :=
   (h (ExtensionOfMaxAdjoin.ideal i f y) (ExtensionOfMaxAdjoin.idealTo i f y)).some
 #align module.Baer.extension_of_max_adjoin.extend_ideal_to Module.Baer.ExtensionOfMaxAdjoin.extendIdealTo
 
-/- warning: module.Baer.extension_of_max_adjoin.extend_ideal_to_is_extension -> Module.Baer.ExtensionOfMaxAdjoin.extendIdealTo_is_extension is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align module.Baer.extension_of_max_adjoin.extend_ideal_to_is_extension Module.Baer.ExtensionOfMaxAdjoin.extendIdealTo_is_extensionₓ'. -/
 theorem ExtensionOfMaxAdjoin.extendIdealTo_is_extension (h : Module.Baer R Q) (y : N) :
     ∀ (x : R) (mem : x ∈ ExtensionOfMaxAdjoin.ideal i f y),
       ExtensionOfMaxAdjoin.extendIdealTo i f h y x = ExtensionOfMaxAdjoin.idealTo i f y ⟨x, mem⟩ :=
   (h (ExtensionOfMaxAdjoin.ideal i f y) (ExtensionOfMaxAdjoin.idealTo i f y)).choose_spec
 #align module.Baer.extension_of_max_adjoin.extend_ideal_to_is_extension Module.Baer.ExtensionOfMaxAdjoin.extendIdealTo_is_extension
 
-/- warning: module.Baer.extension_of_max_adjoin.extend_ideal_to_wd' -> Module.Baer.ExtensionOfMaxAdjoin.extendIdealTo_wd' is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align module.Baer.extension_of_max_adjoin.extend_ideal_to_wd' Module.Baer.ExtensionOfMaxAdjoin.extendIdealTo_wd'ₓ'. -/
 theorem ExtensionOfMaxAdjoin.extendIdealTo_wd' (h : Module.Baer R Q) {y : N} (r : R)
     (eq1 : r • y = 0) : ExtensionOfMaxAdjoin.extendIdealTo i f h y r = 0 :=
   by
@@ -360,9 +312,6 @@ theorem ExtensionOfMaxAdjoin.extendIdealTo_wd' (h : Module.Baer R Q) {y : N} (r
     ZeroMemClass.zero_def, (extension_of_max i f).toLinearPMap.map_zero]
 #align module.Baer.extension_of_max_adjoin.extend_ideal_to_wd' Module.Baer.ExtensionOfMaxAdjoin.extendIdealTo_wd'
 
-/- warning: module.Baer.extension_of_max_adjoin.extend_ideal_to_wd -> Module.Baer.ExtensionOfMaxAdjoin.extendIdealTo_wd is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align module.Baer.extension_of_max_adjoin.extend_ideal_to_wd Module.Baer.ExtensionOfMaxAdjoin.extendIdealTo_wdₓ'. -/
 theorem ExtensionOfMaxAdjoin.extendIdealTo_wd (h : Module.Baer R Q) {y : N} (r r' : R)
     (eq1 : r • y = r' • y) :
     ExtensionOfMaxAdjoin.extendIdealTo i f h y r = ExtensionOfMaxAdjoin.extendIdealTo i f h y r' :=
@@ -372,9 +321,6 @@ theorem ExtensionOfMaxAdjoin.extendIdealTo_wd (h : Module.Baer R Q) {y : N} (r r
   rw [sub_smul, sub_eq_zero, eq1]
 #align module.Baer.extension_of_max_adjoin.extend_ideal_to_wd Module.Baer.ExtensionOfMaxAdjoin.extendIdealTo_wd
 
-/- warning: module.Baer.extension_of_max_adjoin.extend_ideal_to_eq -> Module.Baer.ExtensionOfMaxAdjoin.extendIdealTo_eq is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align module.Baer.extension_of_max_adjoin.extend_ideal_to_eq Module.Baer.ExtensionOfMaxAdjoin.extendIdealTo_eqₓ'. -/
 theorem ExtensionOfMaxAdjoin.extendIdealTo_eq (h : Module.Baer R Q) {y : N} (r : R)
     (hr : r • y ∈ (extensionOfMax i f).domain) :
     ExtensionOfMaxAdjoin.extendIdealTo i f h y r = (extensionOfMax i f).toLinearPMap ⟨r • y, hr⟩ :=
@@ -383,9 +329,6 @@ theorem ExtensionOfMaxAdjoin.extendIdealTo_eq (h : Module.Baer R Q) {y : N} (r :
     extension_of_max_adjoin.ideal_to, LinearMap.coe_mk, Subtype.coe_mk]
 #align module.Baer.extension_of_max_adjoin.extend_ideal_to_eq Module.Baer.ExtensionOfMaxAdjoin.extendIdealTo_eq
 
-/- warning: module.Baer.extension_of_max_adjoin.extension_to_fun -> Module.Baer.ExtensionOfMaxAdjoin.extensionToFun is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align module.Baer.extension_of_max_adjoin.extension_to_fun Module.Baer.ExtensionOfMaxAdjoin.extensionToFunₓ'. -/
 /-- We can finally define a linear map `M ⊔ ⟨y⟩ ⟶ Q` by `x + r • y ↦ f x + φ r`
 -/
 def ExtensionOfMaxAdjoin.extensionToFun (h : Module.Baer R Q) {y : N} :
@@ -394,9 +337,6 @@ def ExtensionOfMaxAdjoin.extensionToFun (h : Module.Baer R Q) {y : N} :
     ExtensionOfMaxAdjoin.extendIdealTo i f h y (ExtensionOfMaxAdjoin.snd i x)
 #align module.Baer.extension_of_max_adjoin.extension_to_fun Module.Baer.ExtensionOfMaxAdjoin.extensionToFun
 
-/- warning: module.Baer.extension_of_max_adjoin.extension_to_fun_wd -> Module.Baer.ExtensionOfMaxAdjoin.extensionToFun_wd is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align module.Baer.extension_of_max_adjoin.extension_to_fun_wd Module.Baer.ExtensionOfMaxAdjoin.extensionToFun_wdₓ'. -/
 theorem ExtensionOfMaxAdjoin.extensionToFun_wd (h : Module.Baer R Q) {y : N}
     (x : (extensionOfMax i f).domain ⊔ Submodule.span R {y}) (a : (extensionOfMax i f).domain)
     (r : R) (eq1 : ↑x = ↑a + r • y) :
@@ -421,9 +361,6 @@ theorem ExtensionOfMaxAdjoin.extensionToFun_wd (h : Module.Baer R Q) {y : N}
   exact eq_sub_of_add_eq (extension_of_max_adjoin.eqn _ _).symm
 #align module.Baer.extension_of_max_adjoin.extension_to_fun_wd Module.Baer.ExtensionOfMaxAdjoin.extensionToFun_wd
 
-/- warning: module.Baer.extension_of_max_adjoin -> Module.Baer.extensionOfMaxAdjoin is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align module.Baer.extension_of_max_adjoin Module.Baer.extensionOfMaxAdjoinₓ'. -/
 /-- The linear map `M ⊔ ⟨y⟩ ⟶ Q` by `x + r • y ↦ f x + φ r` is an extension of `f`-/
 def extensionOfMaxAdjoin (h : Module.Baer R Q) (y : N) : ExtensionOf i f
     where
@@ -462,9 +399,6 @@ def extensionOfMaxAdjoin (h : Module.Baer R Q) (y : N) : ExtensionOf i f
     simp
 #align module.Baer.extension_of_max_adjoin Module.Baer.extensionOfMaxAdjoin
 
-/- warning: module.Baer.extension_of_max_le -> Module.Baer.extensionOfMax_le is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align module.Baer.extension_of_max_le Module.Baer.extensionOfMax_leₓ'. -/
 theorem extensionOfMax_le (h : Module.Baer R Q) {y : N} :
     extensionOfMax i f ≤ extensionOfMaxAdjoin i f h y :=
   ⟨le_sup_left, fun x x' EQ => by
@@ -474,9 +408,6 @@ theorem extensionOfMax_le (h : Module.Baer R Q) {y : N} :
       add_zero]⟩
 #align module.Baer.extension_of_max_le Module.Baer.extensionOfMax_le
 
-/- warning: module.Baer.extension_of_max_to_submodule_eq_top -> Module.Baer.extensionOfMax_to_submodule_eq_top is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align module.Baer.extension_of_max_to_submodule_eq_top Module.Baer.extensionOfMax_to_submodule_eq_topₓ'. -/
 theorem extensionOfMax_to_submodule_eq_top (h : Module.Baer R Q) :
     (extensionOfMax i f).domain = ⊤ :=
   by

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

@@ -173,15 +173,8 @@ instance : Inf (ExtensionOf i f)
 instance : SemilatticeInf (ExtensionOf i f) :=
   Function.Injective.semilatticeInf ExtensionOf.toLinearPmap
     (fun X Y h =>
-      ExtensionOf.ext (by rw [h]) fun x y h' =>
-        by
-        induction h
-        congr
-        exact_mod_cast h')
-    fun X Y =>
-    LinearPMap.ext rfl fun x y h => by
-      congr
-      exact_mod_cast h
+      ExtensionOf.ext (by rw [h]) fun x y h' => by induction h; congr ; exact_mod_cast h')
+    fun X Y => LinearPMap.ext rfl fun x y h => by congr ; exact_mod_cast h
 
 variable {R i f}
 
@@ -503,13 +496,9 @@ protected theorem injective (h : Module.Baer R Q) : Module.Injective R Q :=
       ⟨{  toFun := fun y =>
             (extension_of_max i f).toLinearPMap
               ⟨y, (extension_of_max_to_submodule_eq_top i f h).symm ▸ trivial⟩
-          map_add' := fun x y => by
-            rw [← LinearPMap.map_add]
-            congr
-          map_smul' := fun r x => by
-            rw [← LinearPMap.map_smul]
-            congr },
-        fun x => ((extension_of_max i f).is_extension x).symm⟩ }
+          map_add' := fun x y => by rw [← LinearPMap.map_add]; congr
+          map_smul' := fun r x => by rw [← LinearPMap.map_smul]; congr }, fun x =>
+        ((extension_of_max i f).is_extension x).symm⟩ }
 #align module.Baer.injective Module.Baer.injective
 -/
 

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

@@ -131,10 +131,7 @@ section Ext
 variable {i f}
 
 /- warning: module.Baer.extension_of.ext -> Module.Baer.ExtensionOf.ext is a dubious translation:
-lean 3 declaration is
-  forall {R : Type.{u1}} [_inst_1 : Ring.{u1} R] {Q : Type.{max u1 u2}} [_inst_2 : AddCommGroup.{max u1 u2} Q] [_inst_3 : Module.{u1, max u1 u2} R Q (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{max u1 u2} Q _inst_2)] {M : Type.{max u1 u2}} {N : Type.{max u1 u2}} [_inst_4 : AddCommGroup.{max u1 u2} M] [_inst_5 : AddCommGroup.{max u1 u2} N] [_inst_6 : Module.{u1, max u1 u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{max u1 u2} M _inst_4)] [_inst_7 : Module.{u1, max u1 u2} R N (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{max u1 u2} N _inst_5)] {i : LinearMap.{u1, u1, max u1 u2, max u1 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 N (AddCommGroup.toAddCommMonoid.{max u1 u2} M _inst_4) (AddCommGroup.toAddCommMonoid.{max u1 u2} N _inst_5) _inst_6 _inst_7} {f : LinearMap.{u1, u1, max u1 u2, max u1 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 Q (AddCommGroup.toAddCommMonoid.{max u1 u2} M _inst_4) (AddCommGroup.toAddCommMonoid.{max u1 u2} Q _inst_2) _inst_6 _inst_3} {a : Module.Baer.ExtensionOf.{u1, u2} R _inst_1 Q _inst_2 _inst_3 M N _inst_4 _inst_5 _inst_6 _inst_7 i f} {b : Module.Baer.ExtensionOf.{u1, u2} R _inst_1 Q _inst_2 _inst_3 M N _inst_4 _inst_5 _inst_6 _inst_7 i f}, (Eq.{succ (max u1 u2)} (Submodule.{u1, max u1 u2} R N (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{max u1 u2} N _inst_5) _inst_7) (LinearPMap.domain.{u1, max u1 u2, max u1 u2} R _inst_1 N _inst_5 _inst_7 Q _inst_2 _inst_3 (Module.Baer.ExtensionOf.toLinearPmap.{u1, u2} R _inst_1 Q _inst_2 _inst_3 M N _inst_4 _inst_5 _inst_6 _inst_7 i f a)) (LinearPMap.domain.{u1, max u1 u2, max u1 u2} R _inst_1 N _inst_5 _inst_7 Q _inst_2 _inst_3 (Module.Baer.ExtensionOf.toLinearPmap.{u1, u2} R 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 Case conversion may be inaccurate. Consider using '#align module.Baer.extension_of.ext Module.Baer.ExtensionOf.extₓ'. -/
 @[ext]
 theorem ExtensionOf.ext {a b : ExtensionOf i f} (domain_eq : a.domain = b.domain)
@@ -148,10 +145,7 @@ theorem ExtensionOf.ext {a b : ExtensionOf i f} (domain_eq : a.domain = b.domain
 #align module.Baer.extension_of.ext Module.Baer.ExtensionOf.ext
 
 /- warning: module.Baer.extension_of.ext_iff -> Module.Baer.ExtensionOf.ext_iff is a dubious translation:
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 Case conversion may be inaccurate. Consider using '#align module.Baer.extension_of.ext_iff Module.Baer.ExtensionOf.ext_iffₓ'. -/
 theorem ExtensionOf.ext_iff {a b : ExtensionOf i f} :
     a = b ↔
@@ -192,10 +186,7 @@ instance : SemilatticeInf (ExtensionOf i f) :=
 variable {R i f}
 
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+<too large>
 Case conversion may be inaccurate. Consider using '#align module.Baer.chain_linear_pmap_of_chain_extension_of Module.Baer.chain_linearPMap_of_chain_extensionOfₓ'. -/
 theorem chain_linearPMap_of_chain_extensionOf {c : Set (ExtensionOf i f)}
     (hchain : IsChain (· ≤ ·) c) :
@@ -206,10 +197,7 @@ theorem chain_linearPMap_of_chain_extensionOf {c : Set (ExtensionOf i f)}
 #align module.Baer.chain_linear_pmap_of_chain_extension_of Module.Baer.chain_linearPMap_of_chain_extensionOf
 
 /- warning: module.Baer.extension_of.max -> Module.Baer.ExtensionOf.max is a dubious translation:
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+<too large>
 Case conversion may be inaccurate. Consider using '#align module.Baer.extension_of.max Module.Baer.ExtensionOf.maxₓ'. -/
 /-- The maximal element of every nonempty chain of `extension_of i f`. -/
 def ExtensionOf.max {c : Set (ExtensionOf i f)} (hchain : IsChain (· ≤ ·) c)
@@ -234,10 +222,7 @@ def ExtensionOf.max {c : Set (ExtensionOf i f)} (hchain : IsChain (· ≤ ·) c)
 #align module.Baer.extension_of.max Module.Baer.ExtensionOf.max
 
 /- warning: module.Baer.extension_of.le_max -> Module.Baer.ExtensionOf.le_max is a dubious translation:
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+<too large>
 Case conversion may be inaccurate. Consider using '#align module.Baer.extension_of.le_max Module.Baer.ExtensionOf.le_maxₓ'. -/
 theorem ExtensionOf.le_max {c : Set (ExtensionOf i f)} (hchain : IsChain (· ≤ ·) c)
     (hnonempty : c.Nonempty) (a : ExtensionOf i f) (ha : a ∈ c) :
@@ -249,10 +234,7 @@ theorem ExtensionOf.le_max {c : Set (ExtensionOf i f)} (hchain : IsChain (· ≤
 variable (i f) [Fact <| Function.Injective i]
 
 /- warning: module.Baer.extension_of.inhabited -> Module.Baer.ExtensionOf.inhabited is a dubious translation:
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 Case conversion may be inaccurate. Consider using '#align module.Baer.extension_of.inhabited Module.Baer.ExtensionOf.inhabitedₓ'. -/
 instance ExtensionOf.inhabited : Inhabited (ExtensionOf i f)
     where default :=
@@ -278,10 +260,7 @@ instance ExtensionOf.inhabited : Inhabited (ExtensionOf i f)
 #align module.Baer.extension_of.inhabited Module.Baer.ExtensionOf.inhabited
 
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 Case conversion may be inaccurate. Consider using '#align module.Baer.extension_of_max Module.Baer.extensionOfMaxₓ'. -/
 /-- Since every nonempty chain has a maximal element, by Zorn's lemma, there is a maximal
 `extension_of i f`. -/
@@ -291,10 +270,7 @@ def extensionOfMax : ExtensionOf i f :=
 #align module.Baer.extension_of_max Module.Baer.extensionOfMax
 
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 Case conversion may be inaccurate. Consider using '#align module.Baer.extension_of_max_is_max Module.Baer.extensionOfMax_is_maxₓ'. -/
 theorem extensionOfMax_is_max :
     ∀ a : ExtensionOf i f, extensionOfMax i f ≤ a → a = extensionOfMax i f :=
@@ -314,13 +290,9 @@ private theorem extensionOfMax_adjoin.aux1 {y : N}
   rw [Submodule.mem_span_singleton] at b_mem
   rcases b_mem with ⟨z, eq2⟩
   exact ⟨⟨a, a_mem⟩, z, by rw [← eq1, ← eq2]⟩
-#align module.Baer.extension_of_max_adjoin.aux1 Module.Baer.extensionOfMax_adjoin.aux1
 
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 Case conversion may be inaccurate. Consider using '#align module.Baer.extension_of_max_adjoin.fst Module.Baer.ExtensionOfMaxAdjoin.fstₓ'. -/
 /-- If `x ∈ M ⊔ ⟨y⟩`, then `x = m + r • y`, `fst` pick an arbitrary such `m`.-/
 def ExtensionOfMaxAdjoin.fst {y : N} (x : (extensionOfMax i f).domain ⊔ Submodule.span R {y}) :
@@ -329,10 +301,7 @@ def ExtensionOfMaxAdjoin.fst {y : N} (x : (extensionOfMax i f).domain ⊔ Submod
 #align module.Baer.extension_of_max_adjoin.fst Module.Baer.ExtensionOfMaxAdjoin.fst
 
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 Case conversion may be inaccurate. Consider using '#align module.Baer.extension_of_max_adjoin.snd Module.Baer.ExtensionOfMaxAdjoin.sndₓ'. -/
 /-- If `x ∈ M ⊔ ⟨y⟩`, then `x = m + r • y`, `snd` pick an arbitrary such `r`.-/
 def ExtensionOfMaxAdjoin.snd {y : N} (x : (extensionOfMax i f).domain ⊔ Submodule.span R {y}) : R :=
@@ -340,10 +309,7 @@ def ExtensionOfMaxAdjoin.snd {y : N} (x : (extensionOfMax i f).domain ⊔ Submod
 #align module.Baer.extension_of_max_adjoin.snd Module.Baer.ExtensionOfMaxAdjoin.snd
 
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(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 Q (AddCommGroup.toAddCommMonoid.{max u1 u2} M _inst_4) (AddCommGroup.toAddCommMonoid.{max u1 u2} Q _inst_2) _inst_6 _inst_3} [_inst_8 : Fact (Function.Injective.{succ (max u1 u2), succ (max u1 u2)} M N (coeFn.{succ (max u1 u2), succ (max u1 u2)} (LinearMap.{u1, u1, max u1 u2, max u1 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 N (AddCommGroup.toAddCommMonoid.{max u1 u2} M _inst_4) (AddCommGroup.toAddCommMonoid.{max u1 u2} N _inst_5) _inst_6 _inst_7) (fun (_x : LinearMap.{u1, u1, max u1 u2, max u1 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 N (AddCommGroup.toAddCommMonoid.{max u1 u2} M 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+<too large>
 Case conversion may be inaccurate. Consider using '#align module.Baer.extension_of_max_adjoin.eqn Module.Baer.ExtensionOfMaxAdjoin.eqnₓ'. -/
 theorem ExtensionOfMaxAdjoin.eqn {y : N} (x : (extensionOfMax i f).domain ⊔ Submodule.span R {y}) :
     ↑x = ↑(ExtensionOfMaxAdjoin.fst i x) + ExtensionOfMaxAdjoin.snd i x • y :=
@@ -353,10 +319,7 @@ theorem ExtensionOfMaxAdjoin.eqn {y : N} (x : (extensionOfMax i f).domain ⊔ Su
 variable (f)
 
 /- warning: module.Baer.extension_of_max_adjoin.ideal -> Module.Baer.ExtensionOfMaxAdjoin.ideal is a dubious translation:
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 Case conversion may be inaccurate. Consider using '#align module.Baer.extension_of_max_adjoin.ideal Module.Baer.ExtensionOfMaxAdjoin.idealₓ'. -/
 /-- the ideal `I = {r | r • y ∈ N}`-/
 def ExtensionOfMaxAdjoin.ideal (y : N) : Ideal R :=
@@ -364,10 +327,7 @@ def ExtensionOfMaxAdjoin.ideal (y : N) : Ideal R :=
 #align module.Baer.extension_of_max_adjoin.ideal Module.Baer.ExtensionOfMaxAdjoin.ideal
 
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 Case conversion may be inaccurate. Consider using '#align module.Baer.extension_of_max_adjoin.ideal_to Module.Baer.ExtensionOfMaxAdjoin.idealToₓ'. -/
 /-- A linear map `I ⟶ Q` by `x ↦ f' (x • y)` where `f'` is the maximal extension-/
 def ExtensionOfMaxAdjoin.idealTo (y : N) : ExtensionOfMaxAdjoin.ideal i f y →ₗ[R] Q
@@ -378,10 +338,7 @@ def ExtensionOfMaxAdjoin.idealTo (y : N) : ExtensionOfMaxAdjoin.ideal i f y →
 #align module.Baer.extension_of_max_adjoin.ideal_to Module.Baer.ExtensionOfMaxAdjoin.idealTo
 
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 Case conversion may be inaccurate. Consider using '#align module.Baer.extension_of_max_adjoin.extend_ideal_to Module.Baer.ExtensionOfMaxAdjoin.extendIdealToₓ'. -/
 /-- Since we assumed `Q` being Baer, the linear map `x ↦ f' (x • y) : I ⟶ Q` extends to `R ⟶ Q`,
 call this extended map `φ`-/
@@ -390,10 +347,7 @@ def ExtensionOfMaxAdjoin.extendIdealTo (h : Module.Baer R Q) (y : N) : R →ₗ[
 #align module.Baer.extension_of_max_adjoin.extend_ideal_to Module.Baer.ExtensionOfMaxAdjoin.extendIdealTo
 
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+<too large>
 Case conversion may be inaccurate. Consider using '#align module.Baer.extension_of_max_adjoin.extend_ideal_to_is_extension Module.Baer.ExtensionOfMaxAdjoin.extendIdealTo_is_extensionₓ'. -/
 theorem ExtensionOfMaxAdjoin.extendIdealTo_is_extension (h : Module.Baer R Q) (y : N) :
     ∀ (x : R) (mem : x ∈ ExtensionOfMaxAdjoin.ideal i f y),
@@ -402,10 +356,7 @@ theorem ExtensionOfMaxAdjoin.extendIdealTo_is_extension (h : Module.Baer R Q) (y
 #align module.Baer.extension_of_max_adjoin.extend_ideal_to_is_extension Module.Baer.ExtensionOfMaxAdjoin.extendIdealTo_is_extension
 
 /- warning: module.Baer.extension_of_max_adjoin.extend_ideal_to_wd' -> Module.Baer.ExtensionOfMaxAdjoin.extendIdealTo_wd' is a dubious translation:
-lean 3 declaration is
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 Case conversion may be inaccurate. Consider using '#align module.Baer.extension_of_max_adjoin.extend_ideal_to_wd' Module.Baer.ExtensionOfMaxAdjoin.extendIdealTo_wd'ₓ'. -/
 theorem ExtensionOfMaxAdjoin.extendIdealTo_wd' (h : Module.Baer R Q) {y : N} (r : R)
     (eq1 : r • y = 0) : ExtensionOfMaxAdjoin.extendIdealTo i f h y r = 0 :=
@@ -417,10 +368,7 @@ theorem ExtensionOfMaxAdjoin.extendIdealTo_wd' (h : Module.Baer R Q) {y : N} (r
 #align module.Baer.extension_of_max_adjoin.extend_ideal_to_wd' Module.Baer.ExtensionOfMaxAdjoin.extendIdealTo_wd'
 
 /- warning: module.Baer.extension_of_max_adjoin.extend_ideal_to_wd -> Module.Baer.ExtensionOfMaxAdjoin.extendIdealTo_wd is a dubious translation:
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 Case conversion may be inaccurate. Consider using '#align module.Baer.extension_of_max_adjoin.extend_ideal_to_wd Module.Baer.ExtensionOfMaxAdjoin.extendIdealTo_wdₓ'. -/
 theorem ExtensionOfMaxAdjoin.extendIdealTo_wd (h : Module.Baer R Q) {y : N} (r r' : R)
     (eq1 : r • y = r' • y) :
@@ -432,10 +380,7 @@ theorem ExtensionOfMaxAdjoin.extendIdealTo_wd (h : Module.Baer R Q) {y : N} (r r
 #align module.Baer.extension_of_max_adjoin.extend_ideal_to_wd Module.Baer.ExtensionOfMaxAdjoin.extendIdealTo_wd
 
 /- warning: module.Baer.extension_of_max_adjoin.extend_ideal_to_eq -> Module.Baer.ExtensionOfMaxAdjoin.extendIdealTo_eq is a dubious translation:
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 Case conversion may be inaccurate. Consider using '#align module.Baer.extension_of_max_adjoin.extend_ideal_to_eq Module.Baer.ExtensionOfMaxAdjoin.extendIdealTo_eqₓ'. -/
 theorem ExtensionOfMaxAdjoin.extendIdealTo_eq (h : Module.Baer R Q) {y : N} (r : R)
     (hr : r • y ∈ (extensionOfMax i f).domain) :
@@ -446,10 +391,7 @@ theorem ExtensionOfMaxAdjoin.extendIdealTo_eq (h : Module.Baer R Q) {y : N} (r :
 #align module.Baer.extension_of_max_adjoin.extend_ideal_to_eq Module.Baer.ExtensionOfMaxAdjoin.extendIdealTo_eq
 
 /- warning: module.Baer.extension_of_max_adjoin.extension_to_fun -> Module.Baer.ExtensionOfMaxAdjoin.extensionToFun is a dubious translation:
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 Case conversion may be inaccurate. Consider using '#align module.Baer.extension_of_max_adjoin.extension_to_fun Module.Baer.ExtensionOfMaxAdjoin.extensionToFunₓ'. -/
 /-- We can finally define a linear map `M ⊔ ⟨y⟩ ⟶ Q` by `x + r • y ↦ f x + φ r`
 -/
@@ -460,10 +402,7 @@ def ExtensionOfMaxAdjoin.extensionToFun (h : Module.Baer R Q) {y : N} :
 #align module.Baer.extension_of_max_adjoin.extension_to_fun Module.Baer.ExtensionOfMaxAdjoin.extensionToFun
 
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 Case conversion may be inaccurate. Consider using '#align module.Baer.extension_of_max_adjoin.extension_to_fun_wd Module.Baer.ExtensionOfMaxAdjoin.extensionToFun_wdₓ'. -/
 theorem ExtensionOfMaxAdjoin.extensionToFun_wd (h : Module.Baer R Q) {y : N}
     (x : (extensionOfMax i f).domain ⊔ Submodule.span R {y}) (a : (extensionOfMax i f).domain)
@@ -490,10 +429,7 @@ theorem ExtensionOfMaxAdjoin.extensionToFun_wd (h : Module.Baer R Q) {y : N}
 #align module.Baer.extension_of_max_adjoin.extension_to_fun_wd Module.Baer.ExtensionOfMaxAdjoin.extensionToFun_wd
 
 /- warning: module.Baer.extension_of_max_adjoin -> Module.Baer.extensionOfMaxAdjoin is a dubious translation:
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 Case conversion may be inaccurate. Consider using '#align module.Baer.extension_of_max_adjoin Module.Baer.extensionOfMaxAdjoinₓ'. -/
 /-- The linear map `M ⊔ ⟨y⟩ ⟶ Q` by `x + r • y ↦ f x + φ r` is an extension of `f`-/
 def extensionOfMaxAdjoin (h : Module.Baer R Q) (y : N) : ExtensionOf i f
@@ -534,10 +470,7 @@ def extensionOfMaxAdjoin (h : Module.Baer R Q) (y : N) : ExtensionOf i f
 #align module.Baer.extension_of_max_adjoin Module.Baer.extensionOfMaxAdjoin
 
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 Case conversion may be inaccurate. Consider using '#align module.Baer.extension_of_max_le Module.Baer.extensionOfMax_leₓ'. -/
 theorem extensionOfMax_le (h : Module.Baer R Q) {y : N} :
     extensionOfMax i f ≤ extensionOfMaxAdjoin i f h y :=
@@ -549,10 +482,7 @@ theorem extensionOfMax_le (h : Module.Baer R Q) {y : N} :
 #align module.Baer.extension_of_max_le Module.Baer.extensionOfMax_le
 
 /- warning: module.Baer.extension_of_max_to_submodule_eq_top -> Module.Baer.extensionOfMax_to_submodule_eq_top is a dubious translation:
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-  forall {R : Type.{u1}} [_inst_1 : Ring.{u1} R] {Q : TypeMax.{u2, u1}} [_inst_2 : AddCommGroup.{max u1 u2} Q] [_inst_3 : Module.{u1, max u1 u2} R Q (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{max u1 u2} Q _inst_2)] {M : Type.{max u1 u2}} {N : Type.{max u1 u2}} [_inst_4 : AddCommGroup.{max u1 u2} M] [_inst_5 : AddCommGroup.{max u1 u2} N] [_inst_6 : Module.{u1, max u1 u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{max u1 u2} M _inst_4)] [_inst_7 : Module.{u1, max u1 u2} R N (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{max u1 u2} N _inst_5)] (i : LinearMap.{u1, u1, max u1 u2, max u1 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 N (AddCommGroup.toAddCommMonoid.{max u1 u2} M _inst_4) (AddCommGroup.toAddCommMonoid.{max u1 u2} N _inst_5) _inst_6 _inst_7) (f : LinearMap.{u1, u1, max u1 u2, max u1 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 Q (AddCommGroup.toAddCommMonoid.{max u1 u2} M _inst_4) (AddCommGroup.toAddCommMonoid.{max u1 u2} Q _inst_2) _inst_6 _inst_3) [_inst_8 : Fact (Function.Injective.{max (succ u1) (succ u2), max (succ u1) (succ u2)} M N (FunLike.coe.{max (succ u1) (succ u2), max (succ u1) (succ u2), max (succ u1) (succ u2)} (LinearMap.{u1, u1, max u1 u2, max u1 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 N (AddCommGroup.toAddCommMonoid.{max u1 u2} M _inst_4) (AddCommGroup.toAddCommMonoid.{max u1 u2} N _inst_5) _inst_6 _inst_7) M (fun (_x : M) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : M) => N) _x) (LinearMap.instFunLikeLinearMap.{u1, u1, max u1 u2, max u1 u2} R R M N (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{max u1 u2} M _inst_4) (AddCommGroup.toAddCommMonoid.{max u1 u2} N _inst_5) _inst_6 _inst_7 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1)))) i))], (Module.Baer.{u1, u2} R _inst_1 Q _inst_2 _inst_3) -> (Eq.{max (succ u1) (succ u2)} (Submodule.{u1, max u1 u2} R N (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{max u1 u2} N _inst_5) _inst_7) (LinearPMap.domain.{u1, max u1 u2, max u1 u2} R _inst_1 N _inst_5 _inst_7 Q _inst_2 _inst_3 (Module.Baer.ExtensionOf.toLinearPMap.{u1, u2} R _inst_1 Q _inst_2 _inst_3 M N _inst_4 _inst_5 _inst_6 _inst_7 i f (Module.Baer.extensionOfMax.{u1, u2} R _inst_1 Q _inst_2 _inst_3 M N _inst_4 _inst_5 _inst_6 _inst_7 i f _inst_8))) (Top.top.{max u1 u2} (Submodule.{u1, max u1 u2} R N (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{max u1 u2} N _inst_5) _inst_7) (Submodule.instTopSubmodule.{u1, max u1 u2} R N (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{max u1 u2} N _inst_5) _inst_7)))
+<too large>
 Case conversion may be inaccurate. Consider using '#align module.Baer.extension_of_max_to_submodule_eq_top Module.Baer.extensionOfMax_to_submodule_eq_topₓ'. -/
 theorem extensionOfMax_to_submodule_eq_top (h : Module.Baer R Q) :
     (extensionOfMax i f).domain = ⊤ :=

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

@@ -252,7 +252,7 @@ variable (i f) [Fact <| Function.Injective i]
 lean 3 declaration is
   forall {R : Type.{u1}} [_inst_1 : Ring.{u1} R] {Q : Type.{max u1 u2}} [_inst_2 : AddCommGroup.{max u1 u2} Q] [_inst_3 : Module.{u1, max u1 u2} R Q (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{max u1 u2} Q _inst_2)] {M : Type.{max u1 u2}} {N : Type.{max u1 u2}} [_inst_4 : AddCommGroup.{max u1 u2} M] [_inst_5 : AddCommGroup.{max u1 u2} N] [_inst_6 : Module.{u1, max u1 u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{max u1 u2} M _inst_4)] [_inst_7 : Module.{u1, max u1 u2} R N (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{max u1 u2} N _inst_5)] (i : LinearMap.{u1, u1, max u1 u2, max u1 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 N (AddCommGroup.toAddCommMonoid.{max u1 u2} M _inst_4) (AddCommGroup.toAddCommMonoid.{max u1 u2} N _inst_5) _inst_6 _inst_7) (f : LinearMap.{u1, u1, max u1 u2, max u1 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 Q (AddCommGroup.toAddCommMonoid.{max u1 u2} M _inst_4) (AddCommGroup.toAddCommMonoid.{max u1 u2} Q _inst_2) _inst_6 _inst_3) [_inst_8 : Fact (Function.Injective.{succ (max u1 u2), succ (max u1 u2)} M N (coeFn.{succ (max u1 u2), succ (max u1 u2)} (LinearMap.{u1, u1, max u1 u2, max u1 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 N (AddCommGroup.toAddCommMonoid.{max u1 u2} M _inst_4) (AddCommGroup.toAddCommMonoid.{max u1 u2} N _inst_5) _inst_6 _inst_7) (fun (_x : LinearMap.{u1, u1, max u1 u2, max u1 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 N (AddCommGroup.toAddCommMonoid.{max u1 u2} M _inst_4) (AddCommGroup.toAddCommMonoid.{max u1 u2} N _inst_5) _inst_6 _inst_7) => M -> N) (LinearMap.hasCoeToFun.{u1, u1, max u1 u2, max u1 u2} R R M N (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{max u1 u2} M _inst_4) (AddCommGroup.toAddCommMonoid.{max u1 u2} N _inst_5) _inst_6 _inst_7 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1)))) i))], Inhabited.{max (succ u1) (succ u2)} (Module.Baer.ExtensionOf.{u1, u2} R _inst_1 Q _inst_2 _inst_3 M N _inst_4 _inst_5 _inst_6 _inst_7 i f)
 but is expected to have type
-  forall {R : Type.{u1}} [_inst_1 : Ring.{u1} R] {Q : TypeMax.{u2, u1}} [_inst_2 : AddCommGroup.{max u1 u2} Q] [_inst_3 : Module.{u1, max u1 u2} R Q (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{max u1 u2} Q _inst_2)] {M : Type.{max u1 u2}} {N : Type.{max u1 u2}} [_inst_4 : AddCommGroup.{max u1 u2} M] [_inst_5 : AddCommGroup.{max u1 u2} N] [_inst_6 : Module.{u1, max u1 u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{max u1 u2} M _inst_4)] [_inst_7 : Module.{u1, max u1 u2} R N (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{max u1 u2} N _inst_5)] (i : LinearMap.{u1, u1, max u1 u2, max u1 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 N (AddCommGroup.toAddCommMonoid.{max u1 u2} M _inst_4) (AddCommGroup.toAddCommMonoid.{max u1 u2} N _inst_5) _inst_6 _inst_7) (f : LinearMap.{u1, u1, max u1 u2, max u1 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 Q (AddCommGroup.toAddCommMonoid.{max u1 u2} M _inst_4) (AddCommGroup.toAddCommMonoid.{max u1 u2} Q _inst_2) _inst_6 _inst_3) [_inst_8 : Fact (Function.Injective.{max (succ u1) (succ u2), max (succ u1) (succ u2)} M N (FunLike.coe.{max (succ u1) (succ u2), max (succ u1) (succ u2), max (succ u1) (succ u2)} (LinearMap.{u1, u1, max u1 u2, max u1 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 N (AddCommGroup.toAddCommMonoid.{max u1 u2} M _inst_4) (AddCommGroup.toAddCommMonoid.{max u1 u2} N _inst_5) _inst_6 _inst_7) M (fun (_x : M) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : M) => N) _x) (LinearMap.instFunLikeLinearMap.{u1, u1, max u1 u2, max u1 u2} R R M N (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{max u1 u2} M _inst_4) (AddCommGroup.toAddCommMonoid.{max u1 u2} N _inst_5) _inst_6 _inst_7 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1)))) i))], Inhabited.{max (succ u2) (succ u1)} (Module.Baer.ExtensionOf.{u1, u2} R _inst_1 Q _inst_2 _inst_3 M N _inst_4 _inst_5 _inst_6 _inst_7 i f)
+  forall {R : Type.{u1}} [_inst_1 : Ring.{u1} R] {Q : TypeMax.{u2, u1}} [_inst_2 : AddCommGroup.{max u1 u2} Q] [_inst_3 : Module.{u1, max u1 u2} R Q (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{max u1 u2} Q _inst_2)] {M : Type.{max u1 u2}} {N : Type.{max u1 u2}} [_inst_4 : AddCommGroup.{max u1 u2} M] [_inst_5 : AddCommGroup.{max u1 u2} N] [_inst_6 : Module.{u1, max u1 u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{max u1 u2} M _inst_4)] [_inst_7 : Module.{u1, max u1 u2} R N (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{max u1 u2} N _inst_5)] (i : LinearMap.{u1, u1, max u1 u2, max u1 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 N (AddCommGroup.toAddCommMonoid.{max u1 u2} M _inst_4) (AddCommGroup.toAddCommMonoid.{max u1 u2} N _inst_5) _inst_6 _inst_7) (f : LinearMap.{u1, u1, max u1 u2, max u1 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 Q (AddCommGroup.toAddCommMonoid.{max u1 u2} M _inst_4) (AddCommGroup.toAddCommMonoid.{max u1 u2} Q _inst_2) _inst_6 _inst_3) [_inst_8 : Fact (Function.Injective.{max (succ u1) (succ u2), max (succ u1) (succ u2)} M N (FunLike.coe.{max (succ u1) (succ u2), max (succ u1) (succ u2), max (succ u1) (succ u2)} (LinearMap.{u1, u1, max u1 u2, max u1 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 N (AddCommGroup.toAddCommMonoid.{max u1 u2} M _inst_4) (AddCommGroup.toAddCommMonoid.{max u1 u2} N _inst_5) _inst_6 _inst_7) M (fun (_x : M) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : M) => N) _x) (LinearMap.instFunLikeLinearMap.{u1, u1, max u1 u2, max u1 u2} R R M N (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{max u1 u2} M _inst_4) (AddCommGroup.toAddCommMonoid.{max u1 u2} N _inst_5) _inst_6 _inst_7 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1)))) i))], Inhabited.{max (succ u2) (succ u1)} (Module.Baer.ExtensionOf.{u1, u2} R _inst_1 Q _inst_2 _inst_3 M N _inst_4 _inst_5 _inst_6 _inst_7 i f)
 Case conversion may be inaccurate. Consider using '#align module.Baer.extension_of.inhabited Module.Baer.ExtensionOf.inhabitedₓ'. -/
 instance ExtensionOf.inhabited : Inhabited (ExtensionOf i f)
     where default :=
@@ -281,7 +281,7 @@ instance ExtensionOf.inhabited : Inhabited (ExtensionOf i f)
 lean 3 declaration is
   forall {R : Type.{u1}} [_inst_1 : Ring.{u1} R] {Q : Type.{max u1 u2}} [_inst_2 : AddCommGroup.{max u1 u2} Q] [_inst_3 : Module.{u1, max u1 u2} R Q (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{max u1 u2} Q _inst_2)] {M : Type.{max u1 u2}} {N : Type.{max u1 u2}} [_inst_4 : AddCommGroup.{max u1 u2} M] [_inst_5 : AddCommGroup.{max u1 u2} N] [_inst_6 : Module.{u1, max u1 u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{max u1 u2} M _inst_4)] [_inst_7 : Module.{u1, max u1 u2} R N (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{max u1 u2} N _inst_5)] (i : LinearMap.{u1, u1, max u1 u2, max u1 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 N (AddCommGroup.toAddCommMonoid.{max u1 u2} M _inst_4) (AddCommGroup.toAddCommMonoid.{max u1 u2} N _inst_5) _inst_6 _inst_7) (f : LinearMap.{u1, u1, max u1 u2, max u1 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 Q (AddCommGroup.toAddCommMonoid.{max u1 u2} M _inst_4) (AddCommGroup.toAddCommMonoid.{max u1 u2} Q _inst_2) _inst_6 _inst_3) [_inst_8 : Fact (Function.Injective.{succ (max u1 u2), succ (max u1 u2)} M N (coeFn.{succ (max u1 u2), succ (max u1 u2)} (LinearMap.{u1, u1, max u1 u2, max u1 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 N (AddCommGroup.toAddCommMonoid.{max u1 u2} M _inst_4) (AddCommGroup.toAddCommMonoid.{max u1 u2} N _inst_5) _inst_6 _inst_7) (fun (_x : LinearMap.{u1, u1, max u1 u2, max u1 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 N (AddCommGroup.toAddCommMonoid.{max u1 u2} M _inst_4) (AddCommGroup.toAddCommMonoid.{max u1 u2} N _inst_5) _inst_6 _inst_7) => M -> N) (LinearMap.hasCoeToFun.{u1, u1, max u1 u2, max u1 u2} R R M N (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{max u1 u2} M _inst_4) (AddCommGroup.toAddCommMonoid.{max u1 u2} N _inst_5) _inst_6 _inst_7 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1)))) i))], Module.Baer.ExtensionOf.{u1, u2} R _inst_1 Q _inst_2 _inst_3 M N _inst_4 _inst_5 _inst_6 _inst_7 i f
 but is expected to have type
-  forall {R : Type.{u1}} [_inst_1 : Ring.{u1} R] {Q : TypeMax.{u2, u1}} [_inst_2 : AddCommGroup.{max u1 u2} Q] [_inst_3 : Module.{u1, max u1 u2} R Q (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{max u1 u2} Q _inst_2)] {M : Type.{max u1 u2}} {N : Type.{max u1 u2}} [_inst_4 : AddCommGroup.{max u1 u2} M] [_inst_5 : AddCommGroup.{max u1 u2} N] [_inst_6 : Module.{u1, max u1 u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{max u1 u2} M _inst_4)] [_inst_7 : Module.{u1, max u1 u2} R N (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{max u1 u2} N _inst_5)] (i : LinearMap.{u1, u1, max u1 u2, max u1 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 N (AddCommGroup.toAddCommMonoid.{max u1 u2} M _inst_4) (AddCommGroup.toAddCommMonoid.{max u1 u2} N _inst_5) _inst_6 _inst_7) (f : LinearMap.{u1, u1, max u1 u2, max u1 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 Q (AddCommGroup.toAddCommMonoid.{max u1 u2} M _inst_4) (AddCommGroup.toAddCommMonoid.{max u1 u2} Q _inst_2) _inst_6 _inst_3) [_inst_8 : Fact (Function.Injective.{max (succ u1) (succ u2), max (succ u1) (succ u2)} M N (FunLike.coe.{max (succ u1) (succ u2), max (succ u1) (succ u2), max (succ u1) (succ u2)} (LinearMap.{u1, u1, max u1 u2, max u1 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 N (AddCommGroup.toAddCommMonoid.{max u1 u2} M _inst_4) (AddCommGroup.toAddCommMonoid.{max u1 u2} N _inst_5) _inst_6 _inst_7) M (fun (_x : M) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : M) => N) _x) (LinearMap.instFunLikeLinearMap.{u1, u1, max u1 u2, max u1 u2} R R M N (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{max u1 u2} M _inst_4) (AddCommGroup.toAddCommMonoid.{max u1 u2} N _inst_5) _inst_6 _inst_7 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1)))) i))], Module.Baer.ExtensionOf.{u1, u2} R _inst_1 Q _inst_2 _inst_3 M N _inst_4 _inst_5 _inst_6 _inst_7 i f
+  forall {R : Type.{u1}} [_inst_1 : Ring.{u1} R] {Q : TypeMax.{u2, u1}} [_inst_2 : AddCommGroup.{max u1 u2} Q] [_inst_3 : Module.{u1, max u1 u2} R Q (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{max u1 u2} Q _inst_2)] {M : Type.{max u1 u2}} {N : Type.{max u1 u2}} [_inst_4 : AddCommGroup.{max u1 u2} M] [_inst_5 : AddCommGroup.{max u1 u2} N] [_inst_6 : Module.{u1, max u1 u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{max u1 u2} M _inst_4)] [_inst_7 : Module.{u1, max u1 u2} R N (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{max u1 u2} N _inst_5)] (i : LinearMap.{u1, u1, max u1 u2, max u1 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 N (AddCommGroup.toAddCommMonoid.{max u1 u2} M _inst_4) (AddCommGroup.toAddCommMonoid.{max u1 u2} N _inst_5) _inst_6 _inst_7) (f : LinearMap.{u1, u1, max u1 u2, max u1 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 Q (AddCommGroup.toAddCommMonoid.{max u1 u2} M _inst_4) (AddCommGroup.toAddCommMonoid.{max u1 u2} Q _inst_2) _inst_6 _inst_3) [_inst_8 : Fact (Function.Injective.{max (succ u1) (succ u2), max (succ u1) (succ u2)} M N (FunLike.coe.{max (succ u1) (succ u2), max (succ u1) (succ u2), max (succ u1) (succ u2)} (LinearMap.{u1, u1, max u1 u2, max u1 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 N (AddCommGroup.toAddCommMonoid.{max u1 u2} M _inst_4) (AddCommGroup.toAddCommMonoid.{max u1 u2} N _inst_5) _inst_6 _inst_7) M (fun (_x : M) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : M) => N) _x) (LinearMap.instFunLikeLinearMap.{u1, u1, max u1 u2, max u1 u2} R R M N (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{max u1 u2} M _inst_4) (AddCommGroup.toAddCommMonoid.{max u1 u2} N _inst_5) _inst_6 _inst_7 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1)))) i))], Module.Baer.ExtensionOf.{u1, u2} R _inst_1 Q _inst_2 _inst_3 M N _inst_4 _inst_5 _inst_6 _inst_7 i f
 Case conversion may be inaccurate. Consider using '#align module.Baer.extension_of_max Module.Baer.extensionOfMaxₓ'. -/
 /-- Since every nonempty chain has a maximal element, by Zorn's lemma, there is a maximal
 `extension_of i f`. -/
@@ -294,7 +294,7 @@ def extensionOfMax : ExtensionOf i f :=
 lean 3 declaration is
   forall {R : Type.{u1}} [_inst_1 : Ring.{u1} R] {Q : Type.{max u1 u2}} [_inst_2 : AddCommGroup.{max u1 u2} Q] [_inst_3 : Module.{u1, max u1 u2} R Q (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{max u1 u2} Q _inst_2)] {M : Type.{max u1 u2}} {N : Type.{max u1 u2}} [_inst_4 : AddCommGroup.{max u1 u2} M] [_inst_5 : AddCommGroup.{max u1 u2} N] [_inst_6 : Module.{u1, max u1 u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{max u1 u2} M _inst_4)] [_inst_7 : Module.{u1, max u1 u2} R N (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{max u1 u2} N _inst_5)] (i : LinearMap.{u1, u1, max u1 u2, max u1 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 N (AddCommGroup.toAddCommMonoid.{max u1 u2} M _inst_4) (AddCommGroup.toAddCommMonoid.{max u1 u2} N _inst_5) _inst_6 _inst_7) (f : LinearMap.{u1, u1, max u1 u2, max u1 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 Q (AddCommGroup.toAddCommMonoid.{max u1 u2} M _inst_4) (AddCommGroup.toAddCommMonoid.{max u1 u2} Q _inst_2) _inst_6 _inst_3) [_inst_8 : Fact (Function.Injective.{succ (max u1 u2), succ (max u1 u2)} M N (coeFn.{succ (max u1 u2), succ (max u1 u2)} (LinearMap.{u1, u1, max u1 u2, max u1 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 N (AddCommGroup.toAddCommMonoid.{max u1 u2} M _inst_4) (AddCommGroup.toAddCommMonoid.{max u1 u2} N _inst_5) _inst_6 _inst_7) (fun (_x : LinearMap.{u1, u1, max u1 u2, max u1 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 N (AddCommGroup.toAddCommMonoid.{max u1 u2} M _inst_4) (AddCommGroup.toAddCommMonoid.{max u1 u2} N _inst_5) _inst_6 _inst_7) => M -> N) (LinearMap.hasCoeToFun.{u1, u1, max u1 u2, max u1 u2} R R M N (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{max u1 u2} M _inst_4) (AddCommGroup.toAddCommMonoid.{max u1 u2} N _inst_5) _inst_6 _inst_7 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1)))) i))] (a : Module.Baer.ExtensionOf.{u1, u2} R _inst_1 Q _inst_2 _inst_3 M N _inst_4 _inst_5 _inst_6 _inst_7 i f), (LE.le.{max u1 u2} (Module.Baer.ExtensionOf.{u1, u2} R _inst_1 Q _inst_2 _inst_3 M N _inst_4 _inst_5 _inst_6 _inst_7 i f) (Preorder.toHasLe.{max u1 u2} (Module.Baer.ExtensionOf.{u1, u2} R _inst_1 Q _inst_2 _inst_3 M N _inst_4 _inst_5 _inst_6 _inst_7 i f) (PartialOrder.toPreorder.{max u1 u2} (Module.Baer.ExtensionOf.{u1, u2} R _inst_1 Q _inst_2 _inst_3 M N _inst_4 _inst_5 _inst_6 _inst_7 i f) (SemilatticeInf.toPartialOrder.{max u1 u2} (Module.Baer.ExtensionOf.{u1, u2} R _inst_1 Q _inst_2 _inst_3 M N _inst_4 _inst_5 _inst_6 _inst_7 i f) (Module.Baer.ExtensionOf.semilatticeInf.{u1, u2} R _inst_1 Q _inst_2 _inst_3 M N _inst_4 _inst_5 _inst_6 _inst_7 i f)))) (Module.Baer.extensionOfMax.{u1, u2} R _inst_1 Q _inst_2 _inst_3 M N _inst_4 _inst_5 _inst_6 _inst_7 i f _inst_8) a) -> (Eq.{max (succ u1) (succ u2)} (Module.Baer.ExtensionOf.{u1, u2} R _inst_1 Q _inst_2 _inst_3 M N _inst_4 _inst_5 _inst_6 _inst_7 i f) a (Module.Baer.extensionOfMax.{u1, u2} R _inst_1 Q _inst_2 _inst_3 M N _inst_4 _inst_5 _inst_6 _inst_7 i f _inst_8))
 but is expected to have type
-  forall {R : Type.{u1}} [_inst_1 : Ring.{u1} R] {Q : TypeMax.{u2, u1}} [_inst_2 : AddCommGroup.{max u1 u2} Q] [_inst_3 : Module.{u1, max u1 u2} R Q (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{max u1 u2} Q _inst_2)] {M : Type.{max u1 u2}} {N : Type.{max u1 u2}} [_inst_4 : AddCommGroup.{max u1 u2} M] [_inst_5 : AddCommGroup.{max u1 u2} N] [_inst_6 : Module.{u1, max u1 u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{max u1 u2} M _inst_4)] [_inst_7 : Module.{u1, max u1 u2} R N (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{max u1 u2} N _inst_5)] (i : LinearMap.{u1, u1, max u1 u2, max u1 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 N (AddCommGroup.toAddCommMonoid.{max u1 u2} M _inst_4) (AddCommGroup.toAddCommMonoid.{max u1 u2} N _inst_5) _inst_6 _inst_7) (f : LinearMap.{u1, u1, max u1 u2, max u1 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 Q (AddCommGroup.toAddCommMonoid.{max u1 u2} M _inst_4) (AddCommGroup.toAddCommMonoid.{max u1 u2} Q _inst_2) _inst_6 _inst_3) [_inst_8 : Fact (Function.Injective.{max (succ u1) (succ u2), max (succ u1) (succ u2)} M N (FunLike.coe.{max (succ u1) (succ u2), max (succ u1) (succ u2), max (succ u1) (succ u2)} (LinearMap.{u1, u1, max u1 u2, max u1 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 N (AddCommGroup.toAddCommMonoid.{max u1 u2} M _inst_4) (AddCommGroup.toAddCommMonoid.{max u1 u2} N _inst_5) _inst_6 _inst_7) M (fun (_x : M) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : M) => N) _x) (LinearMap.instFunLikeLinearMap.{u1, u1, max u1 u2, max u1 u2} R R M N (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{max u1 u2} M _inst_4) (AddCommGroup.toAddCommMonoid.{max u1 u2} N _inst_5) _inst_6 _inst_7 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1)))) i))] (a : Module.Baer.ExtensionOf.{u1, u2} R _inst_1 Q _inst_2 _inst_3 M N _inst_4 _inst_5 _inst_6 _inst_7 i f), (LE.le.{max u1 u2} (Module.Baer.ExtensionOf.{u1, u2} R _inst_1 Q _inst_2 _inst_3 M N _inst_4 _inst_5 _inst_6 _inst_7 i f) (Preorder.toLE.{max u1 u2} (Module.Baer.ExtensionOf.{u1, u2} R _inst_1 Q _inst_2 _inst_3 M N _inst_4 _inst_5 _inst_6 _inst_7 i f) (PartialOrder.toPreorder.{max u1 u2} (Module.Baer.ExtensionOf.{u1, u2} R _inst_1 Q _inst_2 _inst_3 M N _inst_4 _inst_5 _inst_6 _inst_7 i f) (SemilatticeInf.toPartialOrder.{max u1 u2} (Module.Baer.ExtensionOf.{u1, u2} R _inst_1 Q _inst_2 _inst_3 M N _inst_4 _inst_5 _inst_6 _inst_7 i f) (Module.Baer.instSemilatticeInfExtensionOf.{u1, u2} R _inst_1 Q _inst_2 _inst_3 M N _inst_4 _inst_5 _inst_6 _inst_7 i f)))) (Module.Baer.extensionOfMax.{u1, u2} R _inst_1 Q _inst_2 _inst_3 M N _inst_4 _inst_5 _inst_6 _inst_7 i f _inst_8) a) -> (Eq.{max (succ u1) (succ u2)} (Module.Baer.ExtensionOf.{u1, u2} R _inst_1 Q _inst_2 _inst_3 M N _inst_4 _inst_5 _inst_6 _inst_7 i f) a (Module.Baer.extensionOfMax.{u1, u2} R _inst_1 Q _inst_2 _inst_3 M N _inst_4 _inst_5 _inst_6 _inst_7 i f _inst_8))
+  forall {R : Type.{u1}} [_inst_1 : Ring.{u1} R] {Q : TypeMax.{u2, u1}} [_inst_2 : AddCommGroup.{max u1 u2} Q] [_inst_3 : Module.{u1, max u1 u2} R Q (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{max u1 u2} Q _inst_2)] {M : Type.{max u1 u2}} {N : Type.{max u1 u2}} [_inst_4 : AddCommGroup.{max u1 u2} M] [_inst_5 : AddCommGroup.{max u1 u2} N] [_inst_6 : Module.{u1, max u1 u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{max u1 u2} M _inst_4)] [_inst_7 : Module.{u1, max u1 u2} R N (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{max u1 u2} N _inst_5)] (i : LinearMap.{u1, u1, max u1 u2, max u1 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 N (AddCommGroup.toAddCommMonoid.{max u1 u2} M _inst_4) (AddCommGroup.toAddCommMonoid.{max u1 u2} N _inst_5) _inst_6 _inst_7) (f : LinearMap.{u1, u1, max u1 u2, max u1 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 Q (AddCommGroup.toAddCommMonoid.{max u1 u2} M _inst_4) (AddCommGroup.toAddCommMonoid.{max u1 u2} Q _inst_2) _inst_6 _inst_3) [_inst_8 : Fact (Function.Injective.{max (succ u1) (succ u2), max (succ u1) (succ u2)} M N (FunLike.coe.{max (succ u1) (succ u2), max (succ u1) (succ u2), max (succ u1) (succ u2)} (LinearMap.{u1, u1, max u1 u2, max u1 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 N (AddCommGroup.toAddCommMonoid.{max u1 u2} M _inst_4) (AddCommGroup.toAddCommMonoid.{max u1 u2} N _inst_5) _inst_6 _inst_7) M (fun (_x : M) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : M) => N) _x) (LinearMap.instFunLikeLinearMap.{u1, u1, max u1 u2, max u1 u2} R R M N (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{max u1 u2} M _inst_4) (AddCommGroup.toAddCommMonoid.{max u1 u2} N _inst_5) _inst_6 _inst_7 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1)))) i))] (a : Module.Baer.ExtensionOf.{u1, u2} R _inst_1 Q _inst_2 _inst_3 M N _inst_4 _inst_5 _inst_6 _inst_7 i f), (LE.le.{max u1 u2} (Module.Baer.ExtensionOf.{u1, u2} R _inst_1 Q _inst_2 _inst_3 M N _inst_4 _inst_5 _inst_6 _inst_7 i f) (Preorder.toLE.{max u1 u2} (Module.Baer.ExtensionOf.{u1, u2} R _inst_1 Q _inst_2 _inst_3 M N _inst_4 _inst_5 _inst_6 _inst_7 i f) (PartialOrder.toPreorder.{max u1 u2} (Module.Baer.ExtensionOf.{u1, u2} R _inst_1 Q _inst_2 _inst_3 M N _inst_4 _inst_5 _inst_6 _inst_7 i f) (SemilatticeInf.toPartialOrder.{max u1 u2} (Module.Baer.ExtensionOf.{u1, u2} R _inst_1 Q _inst_2 _inst_3 M N _inst_4 _inst_5 _inst_6 _inst_7 i f) (Module.Baer.instSemilatticeInfExtensionOf.{u1, u2} R _inst_1 Q _inst_2 _inst_3 M N _inst_4 _inst_5 _inst_6 _inst_7 i f)))) (Module.Baer.extensionOfMax.{u1, u2} R _inst_1 Q _inst_2 _inst_3 M N _inst_4 _inst_5 _inst_6 _inst_7 i f _inst_8) a) -> (Eq.{max (succ u1) (succ u2)} (Module.Baer.ExtensionOf.{u1, u2} R _inst_1 Q _inst_2 _inst_3 M N _inst_4 _inst_5 _inst_6 _inst_7 i f) a (Module.Baer.extensionOfMax.{u1, u2} R _inst_1 Q _inst_2 _inst_3 M N _inst_4 _inst_5 _inst_6 _inst_7 i f _inst_8))
 Case conversion may be inaccurate. Consider using '#align module.Baer.extension_of_max_is_max Module.Baer.extensionOfMax_is_maxₓ'. -/
 theorem extensionOfMax_is_max :
     ∀ a : ExtensionOf i f, extensionOfMax i f ≤ a → a = extensionOfMax i f :=
@@ -320,7 +320,7 @@ private theorem extensionOfMax_adjoin.aux1 {y : N}
 lean 3 declaration is
   forall {R : Type.{u1}} [_inst_1 : Ring.{u1} R] {Q : Type.{max u1 u2}} [_inst_2 : AddCommGroup.{max u1 u2} Q] [_inst_3 : Module.{u1, max u1 u2} R Q (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{max u1 u2} Q _inst_2)] {M : Type.{max u1 u2}} {N : Type.{max u1 u2}} [_inst_4 : AddCommGroup.{max u1 u2} M] [_inst_5 : AddCommGroup.{max u1 u2} N] [_inst_6 : Module.{u1, max u1 u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{max u1 u2} M _inst_4)] [_inst_7 : Module.{u1, max u1 u2} R N (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{max u1 u2} N _inst_5)] (i : LinearMap.{u1, u1, max u1 u2, max u1 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 N (AddCommGroup.toAddCommMonoid.{max u1 u2} M _inst_4) (AddCommGroup.toAddCommMonoid.{max u1 u2} N _inst_5) _inst_6 _inst_7) {f : LinearMap.{u1, u1, max u1 u2, max u1 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 Q (AddCommGroup.toAddCommMonoid.{max u1 u2} M _inst_4) (AddCommGroup.toAddCommMonoid.{max u1 u2} Q _inst_2) _inst_6 _inst_3} [_inst_8 : Fact (Function.Injective.{succ (max u1 u2), succ (max u1 u2)} M N (coeFn.{succ (max u1 u2), succ (max u1 u2)} (LinearMap.{u1, u1, max u1 u2, max u1 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 N (AddCommGroup.toAddCommMonoid.{max u1 u2} M _inst_4) (AddCommGroup.toAddCommMonoid.{max u1 u2} N _inst_5) _inst_6 _inst_7) (fun (_x : LinearMap.{u1, u1, max u1 u2, max u1 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 N (AddCommGroup.toAddCommMonoid.{max u1 u2} M _inst_4) (AddCommGroup.toAddCommMonoid.{max u1 u2} N _inst_5) _inst_6 _inst_7) => M -> N) (LinearMap.hasCoeToFun.{u1, u1, max u1 u2, max u1 u2} R R M N (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{max u1 u2} M _inst_4) (AddCommGroup.toAddCommMonoid.{max u1 u2} N _inst_5) _inst_6 _inst_7 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1)))) i))] {y : N}, (coeSort.{succ (max u1 u2), succ (succ (max u1 u2))} (Submodule.{u1, max u1 u2} R N (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{max u1 u2} N _inst_5) _inst_7) Type.{max u1 u2} (SetLike.hasCoeToSort.{max u1 u2, max u1 u2} (Submodule.{u1, max u1 u2} R N (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{max u1 u2} N _inst_5) _inst_7) N (Submodule.setLike.{u1, max u1 u2} R N (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{max u1 u2} N _inst_5) _inst_7)) (Sup.sup.{max u1 u2} (Submodule.{u1, max u1 u2} R N (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{max u1 u2} N _inst_5) _inst_7) (SemilatticeSup.toHasSup.{max u1 u2} (Submodule.{u1, max u1 u2} R N (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{max u1 u2} N _inst_5) _inst_7) (Lattice.toSemilatticeSup.{max u1 u2} (Submodule.{u1, max u1 u2} R N (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{max u1 u2} N _inst_5) _inst_7) (ConditionallyCompleteLattice.toLattice.{max u1 u2} (Submodule.{u1, max u1 u2} R N (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{max u1 u2} N _inst_5) _inst_7) (CompleteLattice.toConditionallyCompleteLattice.{max u1 u2} (Submodule.{u1, max u1 u2} R N (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{max u1 u2} N _inst_5) _inst_7) (Submodule.completeLattice.{u1, max u1 u2} R N (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{max u1 u2} N _inst_5) _inst_7))))) (LinearPMap.domain.{u1, max u1 u2, max u1 u2} R _inst_1 N _inst_5 _inst_7 Q _inst_2 _inst_3 (Module.Baer.ExtensionOf.toLinearPmap.{u1, u2} R _inst_1 Q _inst_2 _inst_3 M N _inst_4 _inst_5 _inst_6 _inst_7 i f (Module.Baer.extensionOfMax.{u1, u2} R _inst_1 Q _inst_2 _inst_3 M N _inst_4 _inst_5 _inst_6 _inst_7 i f _inst_8))) (Submodule.span.{u1, max u1 u2} R N (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{max u1 u2} N _inst_5) _inst_7 (Singleton.singleton.{max u1 u2, max u1 u2} N (Set.{max u1 u2} N) (Set.hasSingleton.{max u1 u2} N) y)))) -> (coeSort.{succ (max u1 u2), succ (succ (max u1 u2))} (Submodule.{u1, max u1 u2} R N (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{max u1 u2} N _inst_5) _inst_7) Type.{max u1 u2} (SetLike.hasCoeToSort.{max u1 u2, max u1 u2} (Submodule.{u1, max u1 u2} R N (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{max u1 u2} N _inst_5) _inst_7) N (Submodule.setLike.{u1, max u1 u2} R N (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{max u1 u2} N _inst_5) _inst_7)) (LinearPMap.domain.{u1, max u1 u2, max u1 u2} R _inst_1 N _inst_5 _inst_7 Q _inst_2 _inst_3 (Module.Baer.ExtensionOf.toLinearPmap.{u1, u2} R _inst_1 Q _inst_2 _inst_3 M N _inst_4 _inst_5 _inst_6 _inst_7 i f (Module.Baer.extensionOfMax.{u1, u2} R _inst_1 Q _inst_2 _inst_3 M N _inst_4 _inst_5 _inst_6 _inst_7 i f _inst_8))))
 but is expected to have type
-  forall {R : Type.{u1}} [_inst_1 : Ring.{u1} R] {Q : TypeMax.{u2, u1}} [_inst_2 : AddCommGroup.{max u1 u2} Q] [_inst_3 : Module.{u1, max u1 u2} R Q (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{max u1 u2} Q _inst_2)] {M : Type.{max u1 u2}} {N : Type.{max u1 u2}} [_inst_4 : AddCommGroup.{max u1 u2} M] [_inst_5 : AddCommGroup.{max u1 u2} N] [_inst_6 : Module.{u1, max u1 u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{max u1 u2} M _inst_4)] [_inst_7 : Module.{u1, max u1 u2} R N (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{max u1 u2} N _inst_5)] (i : LinearMap.{u1, u1, max u1 u2, max u1 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 N (AddCommGroup.toAddCommMonoid.{max u1 u2} M _inst_4) (AddCommGroup.toAddCommMonoid.{max u1 u2} N _inst_5) _inst_6 _inst_7) {f : LinearMap.{u1, u1, max u1 u2, max u1 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 Q (AddCommGroup.toAddCommMonoid.{max u1 u2} M _inst_4) (AddCommGroup.toAddCommMonoid.{max u1 u2} Q _inst_2) _inst_6 _inst_3} [_inst_8 : Fact (Function.Injective.{max (succ u1) (succ u2), max (succ u1) (succ u2)} M N (FunLike.coe.{max (succ u1) (succ u2), max (succ u1) (succ u2), max (succ u1) (succ u2)} (LinearMap.{u1, u1, max u1 u2, max u1 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 N (AddCommGroup.toAddCommMonoid.{max u1 u2} M _inst_4) (AddCommGroup.toAddCommMonoid.{max u1 u2} N _inst_5) _inst_6 _inst_7) M (fun (_x : M) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : M) => N) _x) (LinearMap.instFunLikeLinearMap.{u1, u1, max u1 u2, max u1 u2} R R M N (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{max u1 u2} M _inst_4) (AddCommGroup.toAddCommMonoid.{max u1 u2} N _inst_5) _inst_6 _inst_7 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1)))) i))] {y : N}, (Subtype.{succ (max u1 u2)} N (fun (x : N) => Membership.mem.{max u1 u2, max u1 u2} N (Submodule.{u1, max u1 u2} R N (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{max u1 u2} N _inst_5) _inst_7) (SetLike.instMembership.{max u1 u2, max u1 u2} (Submodule.{u1, max u1 u2} R N (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{max u1 u2} N _inst_5) _inst_7) N (Submodule.setLike.{u1, max u1 u2} R N (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{max u1 u2} N _inst_5) _inst_7)) x (Module.Baer.supExtensionOfMaxSingleton.{u1, u2} R _inst_1 Q _inst_2 _inst_3 M N _inst_4 _inst_5 _inst_6 _inst_7 i f _inst_8 y))) -> (Subtype.{succ (max u1 u2)} N (fun (x : N) => Membership.mem.{max u1 u2, max u1 u2} N (Submodule.{u1, max u1 u2} R N (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{max u1 u2} N _inst_5) _inst_7) (SetLike.instMembership.{max u1 u2, max u1 u2} (Submodule.{u1, max u1 u2} R N (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{max u1 u2} N _inst_5) _inst_7) N (Submodule.setLike.{u1, max u1 u2} R N (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{max u1 u2} N _inst_5) _inst_7)) x (LinearPMap.domain.{u1, max u1 u2, max u1 u2} R _inst_1 N _inst_5 _inst_7 Q _inst_2 _inst_3 (Module.Baer.ExtensionOf.toLinearPMap.{u1, u2} R _inst_1 Q _inst_2 _inst_3 M N _inst_4 _inst_5 _inst_6 _inst_7 i f (Module.Baer.extensionOfMax.{u1, u2} R _inst_1 Q _inst_2 _inst_3 M N _inst_4 _inst_5 _inst_6 _inst_7 i f _inst_8)))))
+  forall {R : Type.{u1}} [_inst_1 : Ring.{u1} R] {Q : TypeMax.{u2, u1}} [_inst_2 : AddCommGroup.{max u1 u2} Q] [_inst_3 : Module.{u1, max u1 u2} R Q (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{max u1 u2} Q _inst_2)] {M : Type.{max u1 u2}} {N : Type.{max u1 u2}} [_inst_4 : AddCommGroup.{max u1 u2} M] [_inst_5 : AddCommGroup.{max u1 u2} N] [_inst_6 : Module.{u1, max u1 u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{max u1 u2} M _inst_4)] [_inst_7 : Module.{u1, max u1 u2} R N (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{max u1 u2} N _inst_5)] (i : LinearMap.{u1, u1, max u1 u2, max u1 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 N (AddCommGroup.toAddCommMonoid.{max u1 u2} M _inst_4) (AddCommGroup.toAddCommMonoid.{max u1 u2} N _inst_5) _inst_6 _inst_7) {f : LinearMap.{u1, u1, max u1 u2, max u1 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 Q (AddCommGroup.toAddCommMonoid.{max u1 u2} M _inst_4) (AddCommGroup.toAddCommMonoid.{max u1 u2} Q _inst_2) _inst_6 _inst_3} [_inst_8 : Fact (Function.Injective.{max (succ u1) (succ u2), max (succ u1) (succ u2)} M N (FunLike.coe.{max (succ u1) (succ u2), max (succ u1) (succ u2), max (succ u1) (succ u2)} (LinearMap.{u1, u1, max u1 u2, max u1 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 N (AddCommGroup.toAddCommMonoid.{max u1 u2} M _inst_4) (AddCommGroup.toAddCommMonoid.{max u1 u2} N _inst_5) _inst_6 _inst_7) M (fun (_x : M) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : M) => N) _x) (LinearMap.instFunLikeLinearMap.{u1, u1, max u1 u2, max u1 u2} R R M N (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{max u1 u2} M _inst_4) (AddCommGroup.toAddCommMonoid.{max u1 u2} N _inst_5) _inst_6 _inst_7 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1)))) i))] {y : N}, (Subtype.{succ (max u1 u2)} N (fun (x : N) => Membership.mem.{max u1 u2, max u1 u2} N (Submodule.{u1, max u1 u2} R N (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{max u1 u2} N _inst_5) _inst_7) (SetLike.instMembership.{max u1 u2, max u1 u2} (Submodule.{u1, max u1 u2} R N (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{max u1 u2} N _inst_5) _inst_7) N (Submodule.setLike.{u1, max u1 u2} R N (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{max u1 u2} N _inst_5) _inst_7)) x (Module.Baer.supExtensionOfMaxSingleton.{u1, u2} R _inst_1 Q _inst_2 _inst_3 M N _inst_4 _inst_5 _inst_6 _inst_7 i f _inst_8 y))) -> (Subtype.{succ (max u1 u2)} N (fun (x : N) => Membership.mem.{max u1 u2, max u1 u2} N (Submodule.{u1, max u1 u2} R N (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{max u1 u2} N _inst_5) _inst_7) (SetLike.instMembership.{max u1 u2, max u1 u2} (Submodule.{u1, max u1 u2} R N (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{max u1 u2} N _inst_5) _inst_7) N (Submodule.setLike.{u1, max u1 u2} R N (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{max u1 u2} N _inst_5) _inst_7)) x (LinearPMap.domain.{u1, max u1 u2, max u1 u2} R _inst_1 N _inst_5 _inst_7 Q _inst_2 _inst_3 (Module.Baer.ExtensionOf.toLinearPMap.{u1, u2} R _inst_1 Q _inst_2 _inst_3 M N _inst_4 _inst_5 _inst_6 _inst_7 i f (Module.Baer.extensionOfMax.{u1, u2} R _inst_1 Q _inst_2 _inst_3 M N _inst_4 _inst_5 _inst_6 _inst_7 i f _inst_8)))))
 Case conversion may be inaccurate. Consider using '#align module.Baer.extension_of_max_adjoin.fst Module.Baer.ExtensionOfMaxAdjoin.fstₓ'. -/
 /-- If `x ∈ M ⊔ ⟨y⟩`, then `x = m + r • y`, `fst` pick an arbitrary such `m`.-/
 def ExtensionOfMaxAdjoin.fst {y : N} (x : (extensionOfMax i f).domain ⊔ Submodule.span R {y}) :
@@ -332,7 +332,7 @@ def ExtensionOfMaxAdjoin.fst {y : N} (x : (extensionOfMax i f).domain ⊔ Submod
 lean 3 declaration is
   forall {R : Type.{u1}} [_inst_1 : Ring.{u1} R] {Q : Type.{max u1 u2}} [_inst_2 : AddCommGroup.{max u1 u2} Q] [_inst_3 : Module.{u1, max u1 u2} R Q (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{max u1 u2} Q _inst_2)] {M : Type.{max u1 u2}} {N : Type.{max u1 u2}} [_inst_4 : AddCommGroup.{max u1 u2} M] [_inst_5 : AddCommGroup.{max u1 u2} N] [_inst_6 : Module.{u1, max u1 u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{max u1 u2} M _inst_4)] [_inst_7 : Module.{u1, max u1 u2} R N (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{max u1 u2} N _inst_5)] (i : LinearMap.{u1, u1, max u1 u2, max u1 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 N (AddCommGroup.toAddCommMonoid.{max u1 u2} M _inst_4) (AddCommGroup.toAddCommMonoid.{max u1 u2} N _inst_5) _inst_6 _inst_7) {f : LinearMap.{u1, u1, max u1 u2, max u1 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 Q (AddCommGroup.toAddCommMonoid.{max u1 u2} M _inst_4) (AddCommGroup.toAddCommMonoid.{max u1 u2} Q _inst_2) _inst_6 _inst_3} [_inst_8 : Fact (Function.Injective.{succ (max u1 u2), succ (max u1 u2)} M N (coeFn.{succ (max u1 u2), succ (max u1 u2)} (LinearMap.{u1, u1, max u1 u2, max u1 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 N (AddCommGroup.toAddCommMonoid.{max u1 u2} M _inst_4) (AddCommGroup.toAddCommMonoid.{max u1 u2} N _inst_5) _inst_6 _inst_7) (fun (_x : LinearMap.{u1, u1, max u1 u2, max u1 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 N (AddCommGroup.toAddCommMonoid.{max u1 u2} M _inst_4) (AddCommGroup.toAddCommMonoid.{max u1 u2} N _inst_5) _inst_6 _inst_7) => M -> N) (LinearMap.hasCoeToFun.{u1, u1, max u1 u2, max u1 u2} R R M N (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{max u1 u2} M _inst_4) (AddCommGroup.toAddCommMonoid.{max u1 u2} N _inst_5) _inst_6 _inst_7 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1)))) i))] {y : N}, (coeSort.{succ (max u1 u2), succ (succ (max u1 u2))} (Submodule.{u1, max u1 u2} R N (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{max u1 u2} N _inst_5) _inst_7) Type.{max u1 u2} (SetLike.hasCoeToSort.{max u1 u2, max u1 u2} (Submodule.{u1, max u1 u2} R N (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{max u1 u2} N _inst_5) _inst_7) N (Submodule.setLike.{u1, max u1 u2} R N (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{max u1 u2} N _inst_5) _inst_7)) (Sup.sup.{max u1 u2} (Submodule.{u1, max u1 u2} R N (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{max u1 u2} N _inst_5) _inst_7) (SemilatticeSup.toHasSup.{max u1 u2} (Submodule.{u1, max u1 u2} R N (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{max u1 u2} N _inst_5) _inst_7) (Lattice.toSemilatticeSup.{max u1 u2} (Submodule.{u1, max u1 u2} R N (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{max u1 u2} N _inst_5) _inst_7) (ConditionallyCompleteLattice.toLattice.{max u1 u2} (Submodule.{u1, max u1 u2} R N (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{max u1 u2} N _inst_5) _inst_7) (CompleteLattice.toConditionallyCompleteLattice.{max u1 u2} (Submodule.{u1, max u1 u2} R N (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{max u1 u2} N _inst_5) _inst_7) (Submodule.completeLattice.{u1, max u1 u2} R N (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{max u1 u2} N _inst_5) _inst_7))))) (LinearPMap.domain.{u1, max u1 u2, max u1 u2} R _inst_1 N _inst_5 _inst_7 Q _inst_2 _inst_3 (Module.Baer.ExtensionOf.toLinearPmap.{u1, u2} R _inst_1 Q _inst_2 _inst_3 M N _inst_4 _inst_5 _inst_6 _inst_7 i f (Module.Baer.extensionOfMax.{u1, u2} R _inst_1 Q _inst_2 _inst_3 M N _inst_4 _inst_5 _inst_6 _inst_7 i f _inst_8))) (Submodule.span.{u1, max u1 u2} R N (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{max u1 u2} N _inst_5) _inst_7 (Singleton.singleton.{max u1 u2, max u1 u2} N (Set.{max u1 u2} N) (Set.hasSingleton.{max u1 u2} N) y)))) -> R
 but is expected to have type
-  forall {R : Type.{u1}} [_inst_1 : Ring.{u1} R] {Q : TypeMax.{u2, u1}} [_inst_2 : AddCommGroup.{max u1 u2} Q] [_inst_3 : Module.{u1, max u1 u2} R Q (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{max u1 u2} Q _inst_2)] {M : Type.{max u1 u2}} {N : Type.{max u1 u2}} [_inst_4 : AddCommGroup.{max u1 u2} M] [_inst_5 : AddCommGroup.{max u1 u2} N] [_inst_6 : Module.{u1, max u1 u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{max u1 u2} M _inst_4)] [_inst_7 : Module.{u1, max u1 u2} R N (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{max u1 u2} N _inst_5)] (i : LinearMap.{u1, u1, max u1 u2, max u1 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 N (AddCommGroup.toAddCommMonoid.{max u1 u2} M _inst_4) (AddCommGroup.toAddCommMonoid.{max u1 u2} N _inst_5) _inst_6 _inst_7) {f : LinearMap.{u1, u1, max u1 u2, max u1 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 Q (AddCommGroup.toAddCommMonoid.{max u1 u2} M _inst_4) (AddCommGroup.toAddCommMonoid.{max u1 u2} Q _inst_2) _inst_6 _inst_3} [_inst_8 : Fact (Function.Injective.{max (succ u1) (succ u2), max (succ u1) (succ u2)} M N (FunLike.coe.{max (succ u1) (succ u2), max (succ u1) (succ u2), max (succ u1) (succ u2)} (LinearMap.{u1, u1, max u1 u2, max u1 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 N (AddCommGroup.toAddCommMonoid.{max u1 u2} M _inst_4) (AddCommGroup.toAddCommMonoid.{max u1 u2} N _inst_5) _inst_6 _inst_7) M (fun (_x : M) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : M) => N) _x) (LinearMap.instFunLikeLinearMap.{u1, u1, max u1 u2, max u1 u2} R R M N (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{max u1 u2} M _inst_4) (AddCommGroup.toAddCommMonoid.{max u1 u2} N _inst_5) _inst_6 _inst_7 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1)))) i))] {y : N}, (Subtype.{succ (max u1 u2)} N (fun (x : N) => Membership.mem.{max u1 u2, max u1 u2} N (Submodule.{u1, max u1 u2} R N (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{max u1 u2} N _inst_5) _inst_7) (SetLike.instMembership.{max u1 u2, max u1 u2} (Submodule.{u1, max u1 u2} R N (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{max u1 u2} N _inst_5) _inst_7) N (Submodule.setLike.{u1, max u1 u2} R N (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{max u1 u2} N _inst_5) _inst_7)) x (Module.Baer.supExtensionOfMaxSingleton.{u1, u2} R _inst_1 Q _inst_2 _inst_3 M N _inst_4 _inst_5 _inst_6 _inst_7 i f _inst_8 y))) -> R
+  forall {R : Type.{u1}} [_inst_1 : Ring.{u1} R] {Q : TypeMax.{u2, u1}} [_inst_2 : AddCommGroup.{max u1 u2} Q] [_inst_3 : Module.{u1, max u1 u2} R Q (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{max u1 u2} Q _inst_2)] {M : Type.{max u1 u2}} {N : Type.{max u1 u2}} [_inst_4 : AddCommGroup.{max u1 u2} M] [_inst_5 : AddCommGroup.{max u1 u2} N] [_inst_6 : Module.{u1, max u1 u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{max u1 u2} M _inst_4)] [_inst_7 : Module.{u1, max u1 u2} R N (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{max u1 u2} N _inst_5)] (i : LinearMap.{u1, u1, max u1 u2, max u1 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 N (AddCommGroup.toAddCommMonoid.{max u1 u2} M _inst_4) (AddCommGroup.toAddCommMonoid.{max u1 u2} N _inst_5) _inst_6 _inst_7) {f : LinearMap.{u1, u1, max u1 u2, max u1 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 Q (AddCommGroup.toAddCommMonoid.{max u1 u2} M _inst_4) (AddCommGroup.toAddCommMonoid.{max u1 u2} Q _inst_2) _inst_6 _inst_3} [_inst_8 : Fact (Function.Injective.{max (succ u1) (succ u2), max (succ u1) (succ u2)} M N (FunLike.coe.{max (succ u1) (succ u2), max (succ u1) (succ u2), max (succ u1) (succ u2)} (LinearMap.{u1, u1, max u1 u2, max u1 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 N (AddCommGroup.toAddCommMonoid.{max u1 u2} M _inst_4) (AddCommGroup.toAddCommMonoid.{max u1 u2} N _inst_5) _inst_6 _inst_7) M (fun (_x : M) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : M) => N) _x) (LinearMap.instFunLikeLinearMap.{u1, u1, max u1 u2, max u1 u2} R R M N (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{max u1 u2} M _inst_4) (AddCommGroup.toAddCommMonoid.{max u1 u2} N _inst_5) _inst_6 _inst_7 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1)))) i))] {y : N}, (Subtype.{succ (max u1 u2)} N (fun (x : N) => Membership.mem.{max u1 u2, max u1 u2} N (Submodule.{u1, max u1 u2} R N (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{max u1 u2} N _inst_5) _inst_7) (SetLike.instMembership.{max u1 u2, max u1 u2} (Submodule.{u1, max u1 u2} R N (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{max u1 u2} N _inst_5) _inst_7) N (Submodule.setLike.{u1, max u1 u2} R N (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{max u1 u2} N _inst_5) _inst_7)) x (Module.Baer.supExtensionOfMaxSingleton.{u1, u2} R _inst_1 Q _inst_2 _inst_3 M N _inst_4 _inst_5 _inst_6 _inst_7 i f _inst_8 y))) -> R
 Case conversion may be inaccurate. Consider using '#align module.Baer.extension_of_max_adjoin.snd Module.Baer.ExtensionOfMaxAdjoin.sndₓ'. -/
 /-- If `x ∈ M ⊔ ⟨y⟩`, then `x = m + r • y`, `snd` pick an arbitrary such `r`.-/
 def ExtensionOfMaxAdjoin.snd {y : N} (x : (extensionOfMax i f).domain ⊔ Submodule.span R {y}) : R :=
@@ -343,7 +343,7 @@ def ExtensionOfMaxAdjoin.snd {y : N} (x : (extensionOfMax i f).domain ⊔ Submod
 lean 3 declaration is
   forall {R : Type.{u1}} [_inst_1 : Ring.{u1} R] {Q : Type.{max u1 u2}} [_inst_2 : AddCommGroup.{max u1 u2} Q] [_inst_3 : Module.{u1, max u1 u2} R Q (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{max u1 u2} Q _inst_2)] {M : Type.{max u1 u2}} {N : Type.{max u1 u2}} [_inst_4 : AddCommGroup.{max u1 u2} M] [_inst_5 : AddCommGroup.{max u1 u2} N] [_inst_6 : Module.{u1, max u1 u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{max u1 u2} M _inst_4)] [_inst_7 : Module.{u1, max u1 u2} R N (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{max u1 u2} N _inst_5)] (i : LinearMap.{u1, u1, max u1 u2, max u1 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 N (AddCommGroup.toAddCommMonoid.{max u1 u2} M _inst_4) (AddCommGroup.toAddCommMonoid.{max u1 u2} N _inst_5) _inst_6 _inst_7) {f : LinearMap.{u1, u1, max u1 u2, max u1 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 Q (AddCommGroup.toAddCommMonoid.{max u1 u2} M _inst_4) (AddCommGroup.toAddCommMonoid.{max u1 u2} Q _inst_2) _inst_6 _inst_3} [_inst_8 : Fact (Function.Injective.{succ (max u1 u2), succ (max u1 u2)} M N (coeFn.{succ (max u1 u2), succ (max u1 u2)} (LinearMap.{u1, u1, max u1 u2, max u1 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 N (AddCommGroup.toAddCommMonoid.{max u1 u2} M _inst_4) (AddCommGroup.toAddCommMonoid.{max u1 u2} N _inst_5) _inst_6 _inst_7) (fun (_x : LinearMap.{u1, u1, max u1 u2, max u1 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 N (AddCommGroup.toAddCommMonoid.{max u1 u2} M _inst_4) (AddCommGroup.toAddCommMonoid.{max u1 u2} N _inst_5) _inst_6 _inst_7) => M -> N) (LinearMap.hasCoeToFun.{u1, u1, max u1 u2, max u1 u2} R R M N (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{max u1 u2} M _inst_4) (AddCommGroup.toAddCommMonoid.{max u1 u2} N _inst_5) _inst_6 _inst_7 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1)))) i))] {y : N} (x : coeSort.{succ (max u1 u2), succ (succ (max u1 u2))} (Submodule.{u1, max u1 u2} R N (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{max u1 u2} N _inst_5) _inst_7) Type.{max u1 u2} (SetLike.hasCoeToSort.{max u1 u2, max u1 u2} (Submodule.{u1, max u1 u2} R N (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{max u1 u2} N _inst_5) _inst_7) N (Submodule.setLike.{u1, max u1 u2} R N (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{max u1 u2} N _inst_5) _inst_7)) (Sup.sup.{max u1 u2} (Submodule.{u1, max u1 u2} 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_inst_5 _inst_7 Q _inst_2 _inst_3 (Module.Baer.ExtensionOf.toLinearPmap.{u1, u2} R _inst_1 Q _inst_2 _inst_3 M N _inst_4 _inst_5 _inst_6 _inst_7 i f (Module.Baer.extensionOfMax.{u1, u2} R _inst_1 Q _inst_2 _inst_3 M N _inst_4 _inst_5 _inst_6 _inst_7 i f _inst_8))) (Submodule.span.{u1, max u1 u2} R N (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{max u1 u2} N _inst_5) _inst_7 (Singleton.singleton.{max u1 u2, max u1 u2} N (Set.{max u1 u2} N) (Set.hasSingleton.{max u1 u2} N) y)))), Eq.{succ (max u1 u2)} N ((fun (a : Type.{max u1 u2}) (b : Type.{max u1 u2}) [self : HasLiftT.{succ (max u1 u2), succ (max u1 u2)} a b] => self.0) (coeSort.{succ (max u1 u2), succ (succ (max u1 u2))} (Submodule.{u1, max u1 u2} R N (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{max u1 u2} N _inst_5) _inst_7) Type.{max u1 u2} (SetLike.hasCoeToSort.{max u1 u2, max u1 u2} (Submodule.{u1, max u1 u2} R N (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{max u1 u2} N 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_inst_5 _inst_7 Q _inst_2 _inst_3 (Module.Baer.ExtensionOf.toLinearPmap.{u1, u2} R _inst_1 Q _inst_2 _inst_3 M N _inst_4 _inst_5 _inst_6 _inst_7 i f (Module.Baer.extensionOfMax.{u1, u2} R _inst_1 Q _inst_2 _inst_3 M N _inst_4 _inst_5 _inst_6 _inst_7 i f _inst_8)))) N (CoeTCₓ.coe.{succ (max u1 u2), succ (max u1 u2)} (coeSort.{succ (max u1 u2), succ (succ (max u1 u2))} (Submodule.{u1, max u1 u2} R N (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{max u1 u2} N _inst_5) _inst_7) Type.{max u1 u2} (SetLike.hasCoeToSort.{max u1 u2, max u1 u2} (Submodule.{u1, max u1 u2} R N (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{max u1 u2} N _inst_5) _inst_7) N (Submodule.setLike.{u1, max u1 u2} R N (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{max u1 u2} N _inst_5) _inst_7)) (LinearPMap.domain.{u1, max u1 u2, max u1 u2} R _inst_1 N _inst_5 _inst_7 Q _inst_2 _inst_3 (Module.Baer.ExtensionOf.toLinearPmap.{u1, u2} R _inst_1 Q _inst_2 _inst_3 M N _inst_4 _inst_5 _inst_6 _inst_7 i f (Module.Baer.extensionOfMax.{u1, u2} R _inst_1 Q _inst_2 _inst_3 M N _inst_4 _inst_5 _inst_6 _inst_7 i f _inst_8)))) N (coeBase.{succ (max u1 u2), succ (max u1 u2)} (coeSort.{succ (max u1 u2), succ (succ (max u1 u2))} (Submodule.{u1, max u1 u2} R N (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{max u1 u2} N _inst_5) _inst_7) Type.{max u1 u2} (SetLike.hasCoeToSort.{max u1 u2, max u1 u2} (Submodule.{u1, max u1 u2} R N (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{max u1 u2} N _inst_5) _inst_7) N (Submodule.setLike.{u1, max u1 u2} R N (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{max u1 u2} N _inst_5) _inst_7)) (LinearPMap.domain.{u1, max u1 u2, max u1 u2} R _inst_1 N _inst_5 _inst_7 Q _inst_2 _inst_3 (Module.Baer.ExtensionOf.toLinearPmap.{u1, u2} R _inst_1 Q _inst_2 _inst_3 M N _inst_4 _inst_5 _inst_6 _inst_7 i f (Module.Baer.extensionOfMax.{u1, u2} R _inst_1 Q _inst_2 _inst_3 M N _inst_4 _inst_5 _inst_6 _inst_7 i f _inst_8)))) N (coeSubtype.{succ (max u1 u2)} N (fun (x : N) => Membership.Mem.{max u1 u2, max u1 u2} N (Submodule.{u1, max u1 u2} R N (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{max u1 u2} N _inst_5) _inst_7) (SetLike.hasMem.{max u1 u2, max u1 u2} (Submodule.{u1, max u1 u2} R N (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{max u1 u2} N _inst_5) _inst_7) N (Submodule.setLike.{u1, max u1 u2} R N (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{max u1 u2} N _inst_5) _inst_7)) x (LinearPMap.domain.{u1, max u1 u2, max u1 u2} R _inst_1 N _inst_5 _inst_7 Q _inst_2 _inst_3 (Module.Baer.ExtensionOf.toLinearPmap.{u1, u2} R _inst_1 Q _inst_2 _inst_3 M N _inst_4 _inst_5 _inst_6 _inst_7 i f (Module.Baer.extensionOfMax.{u1, u2} R _inst_1 Q _inst_2 _inst_3 M N _inst_4 _inst_5 _inst_6 _inst_7 i f _inst_8)))))))) (Module.Baer.ExtensionOfMaxAdjoin.fst.{u1, u2} R _inst_1 Q _inst_2 _inst_3 M N _inst_4 _inst_5 _inst_6 _inst_7 i f _inst_8 y x)) (SMul.smul.{u1, max u1 u2} R N (SMulZeroClass.toHasSmul.{u1, max u1 u2} R N (AddZeroClass.toHasZero.{max u1 u2} N (AddMonoid.toAddZeroClass.{max u1 u2} N (AddCommMonoid.toAddMonoid.{max u1 u2} N (AddCommGroup.toAddCommMonoid.{max u1 u2} N _inst_5)))) (SMulWithZero.toSmulZeroClass.{u1, max u1 u2} R N (MulZeroClass.toHasZero.{u1} R (MulZeroOneClass.toMulZeroClass.{u1} R (MonoidWithZero.toMulZeroOneClass.{u1} R (Semiring.toMonoidWithZero.{u1} R (Ring.toSemiring.{u1} R _inst_1))))) (AddZeroClass.toHasZero.{max u1 u2} N (AddMonoid.toAddZeroClass.{max u1 u2} N (AddCommMonoid.toAddMonoid.{max u1 u2} N (AddCommGroup.toAddCommMonoid.{max u1 u2} N _inst_5)))) (MulActionWithZero.toSMulWithZero.{u1, max u1 u2} R N (Semiring.toMonoidWithZero.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (AddZeroClass.toHasZero.{max u1 u2} N (AddMonoid.toAddZeroClass.{max u1 u2} N (AddCommMonoid.toAddMonoid.{max u1 u2} N (AddCommGroup.toAddCommMonoid.{max u1 u2} N _inst_5)))) (Module.toMulActionWithZero.{u1, max u1 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 but is expected to have type
-  forall {R : Type.{u1}} [_inst_1 : Ring.{u1} R] {Q : TypeMax.{u2, u1}} [_inst_2 : AddCommGroup.{max u1 u2} Q] [_inst_3 : Module.{u1, max u1 u2} R Q (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{max u1 u2} Q _inst_2)] {M : Type.{max u1 u2}} {N : Type.{max u1 u2}} [_inst_4 : AddCommGroup.{max u1 u2} M] [_inst_5 : AddCommGroup.{max u1 u2} N] [_inst_6 : Module.{u1, max u1 u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{max u1 u2} M _inst_4)] [_inst_7 : Module.{u1, max u1 u2} R N (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{max u1 u2} N _inst_5)] (i : LinearMap.{u1, u1, max u1 u2, max u1 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 N (AddCommGroup.toAddCommMonoid.{max u1 u2} M _inst_4) (AddCommGroup.toAddCommMonoid.{max u1 u2} N _inst_5) _inst_6 _inst_7) {f : LinearMap.{u1, u1, max u1 u2, max u1 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 Q (AddCommGroup.toAddCommMonoid.{max u1 u2} M _inst_4) (AddCommGroup.toAddCommMonoid.{max u1 u2} Q _inst_2) _inst_6 _inst_3} [_inst_8 : Fact (Function.Injective.{max (succ u1) (succ u2), max (succ u1) (succ u2)} M N (FunLike.coe.{max (succ u1) (succ u2), max (succ u1) (succ u2), max (succ u1) (succ u2)} (LinearMap.{u1, u1, max u1 u2, max u1 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 N (AddCommGroup.toAddCommMonoid.{max u1 u2} M _inst_4) (AddCommGroup.toAddCommMonoid.{max u1 u2} N _inst_5) _inst_6 _inst_7) M (fun (_x : M) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : M) => N) _x) (LinearMap.instFunLikeLinearMap.{u1, u1, max u1 u2, max u1 u2} R R M N (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{max u1 u2} M _inst_4) (AddCommGroup.toAddCommMonoid.{max u1 u2} N _inst_5) _inst_6 _inst_7 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1)))) i))] {y : N} (x : Subtype.{succ (max u1 u2)} N (fun (x : N) => Membership.mem.{max u1 u2, max u1 u2} N (Submodule.{u1, max u1 u2} R N (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{max u1 u2} N _inst_5) _inst_7) (SetLike.instMembership.{max u1 u2, max u1 u2} (Submodule.{u1, max u1 u2} R N (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{max u1 u2} N _inst_5) _inst_7) N (Submodule.setLike.{u1, max u1 u2} R N (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{max u1 u2} N _inst_5) _inst_7)) x (Module.Baer.supExtensionOfMaxSingleton.{u1, u2} R _inst_1 Q _inst_2 _inst_3 M N _inst_4 _inst_5 _inst_6 _inst_7 i f _inst_8 y))), Eq.{max (succ u1) (succ u2)} N (Subtype.val.{succ (max u1 u2)} N (fun (x : N) => 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(SubtractionCommMonoid.toSubtractionMonoid.{max u1 u2} N (AddCommGroup.toDivisionAddCommMonoid.{max u1 u2} N _inst_5))))) (SMulWithZero.toSMulZeroClass.{u1, max u1 u2} R N (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (NegZeroClass.toZero.{max u1 u2} N (SubNegZeroMonoid.toNegZeroClass.{max u1 u2} N (SubtractionMonoid.toSubNegZeroMonoid.{max u1 u2} N (SubtractionCommMonoid.toSubtractionMonoid.{max u1 u2} N (AddCommGroup.toDivisionAddCommMonoid.{max u1 u2} N _inst_5))))) (MulActionWithZero.toSMulWithZero.{u1, max u1 u2} R N (Semiring.toMonoidWithZero.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (NegZeroClass.toZero.{max u1 u2} N (SubNegZeroMonoid.toNegZeroClass.{max u1 u2} N (SubtractionMonoid.toSubNegZeroMonoid.{max u1 u2} N (SubtractionCommMonoid.toSubtractionMonoid.{max u1 u2} N (AddCommGroup.toDivisionAddCommMonoid.{max u1 u2} N _inst_5))))) (Module.toMulActionWithZero.{u1, max u1 u2} R N (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{max u1 u2} N _inst_5) _inst_7))))) (Module.Baer.ExtensionOfMaxAdjoin.snd.{u1, u2} R _inst_1 Q _inst_2 _inst_3 M N _inst_4 _inst_5 _inst_6 _inst_7 i f _inst_8 y x) y))
+  forall {R : Type.{u1}} [_inst_1 : Ring.{u1} R] {Q : TypeMax.{u2, u1}} [_inst_2 : AddCommGroup.{max u1 u2} Q] [_inst_3 : Module.{u1, max u1 u2} R Q (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{max u1 u2} Q _inst_2)] {M : Type.{max u1 u2}} {N : Type.{max u1 u2}} [_inst_4 : AddCommGroup.{max u1 u2} M] [_inst_5 : AddCommGroup.{max u1 u2} N] [_inst_6 : Module.{u1, max u1 u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{max u1 u2} M _inst_4)] [_inst_7 : Module.{u1, max u1 u2} R N (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{max u1 u2} N _inst_5)] (i : LinearMap.{u1, u1, max u1 u2, max u1 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 N (AddCommGroup.toAddCommMonoid.{max u1 u2} M _inst_4) (AddCommGroup.toAddCommMonoid.{max u1 u2} N _inst_5) _inst_6 _inst_7) {f : LinearMap.{u1, u1, max u1 u2, max u1 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 Q (AddCommGroup.toAddCommMonoid.{max u1 u2} M _inst_4) (AddCommGroup.toAddCommMonoid.{max u1 u2} Q _inst_2) _inst_6 _inst_3} [_inst_8 : Fact (Function.Injective.{max (succ u1) (succ u2), max (succ u1) (succ u2)} M N (FunLike.coe.{max (succ u1) (succ u2), max (succ u1) (succ u2), max (succ u1) (succ u2)} (LinearMap.{u1, u1, max u1 u2, max u1 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 N (AddCommGroup.toAddCommMonoid.{max u1 u2} M _inst_4) (AddCommGroup.toAddCommMonoid.{max u1 u2} N _inst_5) _inst_6 _inst_7) M (fun (_x : M) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : M) => N) _x) (LinearMap.instFunLikeLinearMap.{u1, u1, max u1 u2, max u1 u2} R R M N (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{max u1 u2} M _inst_4) (AddCommGroup.toAddCommMonoid.{max u1 u2} N _inst_5) _inst_6 _inst_7 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1)))) i))] {y : N} (x : Subtype.{succ (max u1 u2)} N (fun (x : N) => Membership.mem.{max u1 u2, max u1 u2} N (Submodule.{u1, max u1 u2} R N (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{max u1 u2} N _inst_5) _inst_7) (SetLike.instMembership.{max u1 u2, max u1 u2} (Submodule.{u1, max u1 u2} R N (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{max u1 u2} N _inst_5) _inst_7) N (Submodule.setLike.{u1, max u1 u2} R N (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{max u1 u2} N _inst_5) _inst_7)) x (Module.Baer.supExtensionOfMaxSingleton.{u1, u2} R _inst_1 Q _inst_2 _inst_3 M N _inst_4 _inst_5 _inst_6 _inst_7 i f _inst_8 y))), Eq.{max (succ u1) (succ u2)} N (Subtype.val.{succ (max u1 u2)} N (fun (x : N) => 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(Submodule.{u1, max u1 u2} R N (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{max u1 u2} N _inst_5) _inst_7) N (Submodule.setLike.{u1, max u1 u2} R N (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{max u1 u2} N _inst_5) _inst_7) (LinearPMap.domain.{u1, max u1 u2, max u1 u2} R _inst_1 N _inst_5 _inst_7 Q _inst_2 _inst_3 (Module.Baer.ExtensionOf.toLinearPMap.{u1, u2} R _inst_1 Q _inst_2 _inst_3 M N _inst_4 _inst_5 _inst_6 _inst_7 i f (Module.Baer.extensionOfMax.{u1, u2} R _inst_1 Q _inst_2 _inst_3 M N _inst_4 _inst_5 _inst_6 _inst_7 i f _inst_8))))) (Module.Baer.ExtensionOfMaxAdjoin.fst.{u1, u2} R _inst_1 Q _inst_2 _inst_3 M N _inst_4 _inst_5 _inst_6 _inst_7 i f _inst_8 y x)) (HSMul.hSMul.{u1, max u1 u2, max u1 u2} R N N (instHSMul.{u1, max u1 u2} R N (SMulZeroClass.toSMul.{u1, max u1 u2} R N (NegZeroClass.toZero.{max u1 u2} N (SubNegZeroMonoid.toNegZeroClass.{max u1 u2} N (SubtractionMonoid.toSubNegZeroMonoid.{max u1 u2} N (SubtractionCommMonoid.toSubtractionMonoid.{max u1 u2} N (AddCommGroup.toDivisionAddCommMonoid.{max u1 u2} N _inst_5))))) (SMulWithZero.toSMulZeroClass.{u1, max u1 u2} R N (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (NegZeroClass.toZero.{max u1 u2} N (SubNegZeroMonoid.toNegZeroClass.{max u1 u2} N (SubtractionMonoid.toSubNegZeroMonoid.{max u1 u2} N (SubtractionCommMonoid.toSubtractionMonoid.{max u1 u2} N (AddCommGroup.toDivisionAddCommMonoid.{max u1 u2} N _inst_5))))) (MulActionWithZero.toSMulWithZero.{u1, max u1 u2} R N (Semiring.toMonoidWithZero.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (NegZeroClass.toZero.{max u1 u2} N (SubNegZeroMonoid.toNegZeroClass.{max u1 u2} N (SubtractionMonoid.toSubNegZeroMonoid.{max u1 u2} N (SubtractionCommMonoid.toSubtractionMonoid.{max u1 u2} N (AddCommGroup.toDivisionAddCommMonoid.{max u1 u2} N _inst_5))))) (Module.toMulActionWithZero.{u1, max u1 u2} R N (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{max u1 u2} N _inst_5) _inst_7))))) (Module.Baer.ExtensionOfMaxAdjoin.snd.{u1, u2} R _inst_1 Q _inst_2 _inst_3 M N _inst_4 _inst_5 _inst_6 _inst_7 i f _inst_8 y x) y))
 Case conversion may be inaccurate. Consider using '#align module.Baer.extension_of_max_adjoin.eqn Module.Baer.ExtensionOfMaxAdjoin.eqnₓ'. -/
 theorem ExtensionOfMaxAdjoin.eqn {y : N} (x : (extensionOfMax i f).domain ⊔ Submodule.span R {y}) :
     ↑x = ↑(ExtensionOfMaxAdjoin.fst i x) + ExtensionOfMaxAdjoin.snd i x • y :=
@@ -356,7 +356,7 @@ variable (f)
 lean 3 declaration is
   forall {R : Type.{u1}} [_inst_1 : Ring.{u1} R] {Q : Type.{max u1 u2}} [_inst_2 : AddCommGroup.{max u1 u2} Q] [_inst_3 : Module.{u1, max u1 u2} R Q (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{max u1 u2} Q _inst_2)] {M : Type.{max u1 u2}} {N : Type.{max u1 u2}} [_inst_4 : AddCommGroup.{max u1 u2} M] [_inst_5 : AddCommGroup.{max u1 u2} N] [_inst_6 : Module.{u1, max u1 u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{max u1 u2} M _inst_4)] [_inst_7 : Module.{u1, max u1 u2} R N (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{max u1 u2} N _inst_5)] (i : LinearMap.{u1, u1, max u1 u2, max u1 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 N (AddCommGroup.toAddCommMonoid.{max u1 u2} M _inst_4) (AddCommGroup.toAddCommMonoid.{max u1 u2} N _inst_5) _inst_6 _inst_7), (LinearMap.{u1, u1, max u1 u2, max u1 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 Q (AddCommGroup.toAddCommMonoid.{max u1 u2} M _inst_4) (AddCommGroup.toAddCommMonoid.{max u1 u2} Q _inst_2) _inst_6 _inst_3) -> (forall [_inst_8 : Fact (Function.Injective.{succ (max u1 u2), succ (max u1 u2)} M N (coeFn.{succ (max u1 u2), succ (max u1 u2)} (LinearMap.{u1, u1, max u1 u2, max u1 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 N (AddCommGroup.toAddCommMonoid.{max u1 u2} M _inst_4) (AddCommGroup.toAddCommMonoid.{max u1 u2} N _inst_5) _inst_6 _inst_7) (fun (_x : LinearMap.{u1, u1, max u1 u2, max u1 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 N (AddCommGroup.toAddCommMonoid.{max u1 u2} M _inst_4) (AddCommGroup.toAddCommMonoid.{max u1 u2} N _inst_5) _inst_6 _inst_7) => M -> N) (LinearMap.hasCoeToFun.{u1, u1, max u1 u2, max u1 u2} R R M N (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{max u1 u2} M _inst_4) (AddCommGroup.toAddCommMonoid.{max u1 u2} N _inst_5) _inst_6 _inst_7 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1)))) i))], N -> (Ideal.{u1} R (Ring.toSemiring.{u1} R _inst_1)))
 but is expected to have type
-  forall {R : Type.{u1}} [_inst_1 : Ring.{u1} R] {Q : TypeMax.{u2, u1}} [_inst_2 : AddCommGroup.{max u1 u2} Q] [_inst_3 : Module.{u1, max u1 u2} R Q (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{max u1 u2} Q _inst_2)] {M : Type.{max u1 u2}} {N : Type.{max u1 u2}} [_inst_4 : AddCommGroup.{max u1 u2} M] [_inst_5 : AddCommGroup.{max u1 u2} N] [_inst_6 : Module.{u1, max u1 u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{max u1 u2} M _inst_4)] [_inst_7 : Module.{u1, max u1 u2} R N (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{max u1 u2} N _inst_5)] (i : LinearMap.{u1, u1, max u1 u2, max u1 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 N (AddCommGroup.toAddCommMonoid.{max u1 u2} M _inst_4) (AddCommGroup.toAddCommMonoid.{max u1 u2} N _inst_5) _inst_6 _inst_7), (LinearMap.{u1, u1, max u1 u2, max u1 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 Q (AddCommGroup.toAddCommMonoid.{max u1 u2} M _inst_4) (AddCommGroup.toAddCommMonoid.{max u1 u2} Q _inst_2) _inst_6 _inst_3) -> (forall [_inst_8 : Fact (Function.Injective.{max (succ u1) (succ u2), max (succ u1) (succ u2)} M N (FunLike.coe.{max (succ u1) (succ u2), max (succ u1) (succ u2), max (succ u1) (succ u2)} (LinearMap.{u1, u1, max u1 u2, max u1 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 N (AddCommGroup.toAddCommMonoid.{max u1 u2} M _inst_4) (AddCommGroup.toAddCommMonoid.{max u1 u2} N _inst_5) _inst_6 _inst_7) M (fun (_x : M) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : M) => N) _x) (LinearMap.instFunLikeLinearMap.{u1, u1, max u1 u2, max u1 u2} R R M N (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{max u1 u2} M _inst_4) (AddCommGroup.toAddCommMonoid.{max u1 u2} N _inst_5) _inst_6 _inst_7 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1)))) i))], N -> (Ideal.{u1} R (Ring.toSemiring.{u1} R _inst_1)))
+  forall {R : Type.{u1}} [_inst_1 : Ring.{u1} R] {Q : TypeMax.{u2, u1}} [_inst_2 : AddCommGroup.{max u1 u2} Q] [_inst_3 : Module.{u1, max u1 u2} R Q (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{max u1 u2} Q _inst_2)] {M : Type.{max u1 u2}} {N : Type.{max u1 u2}} [_inst_4 : AddCommGroup.{max u1 u2} M] [_inst_5 : AddCommGroup.{max u1 u2} N] [_inst_6 : Module.{u1, max u1 u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{max u1 u2} M _inst_4)] [_inst_7 : Module.{u1, max u1 u2} R N (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{max u1 u2} N _inst_5)] (i : LinearMap.{u1, u1, max u1 u2, max u1 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 N (AddCommGroup.toAddCommMonoid.{max u1 u2} M _inst_4) (AddCommGroup.toAddCommMonoid.{max u1 u2} N _inst_5) _inst_6 _inst_7), (LinearMap.{u1, u1, max u1 u2, max u1 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 Q (AddCommGroup.toAddCommMonoid.{max u1 u2} M _inst_4) (AddCommGroup.toAddCommMonoid.{max u1 u2} Q _inst_2) _inst_6 _inst_3) -> (forall [_inst_8 : Fact (Function.Injective.{max (succ u1) (succ u2), max (succ u1) (succ u2)} M N (FunLike.coe.{max (succ u1) (succ u2), max (succ u1) (succ u2), max (succ u1) (succ u2)} (LinearMap.{u1, u1, max u1 u2, max u1 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 N (AddCommGroup.toAddCommMonoid.{max u1 u2} M _inst_4) (AddCommGroup.toAddCommMonoid.{max u1 u2} N _inst_5) _inst_6 _inst_7) M (fun (_x : M) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : M) => N) _x) (LinearMap.instFunLikeLinearMap.{u1, u1, max u1 u2, max u1 u2} R R M N (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{max u1 u2} M _inst_4) (AddCommGroup.toAddCommMonoid.{max u1 u2} N _inst_5) _inst_6 _inst_7 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1)))) i))], N -> (Ideal.{u1} R (Ring.toSemiring.{u1} R _inst_1)))
 Case conversion may be inaccurate. Consider using '#align module.Baer.extension_of_max_adjoin.ideal Module.Baer.ExtensionOfMaxAdjoin.idealₓ'. -/
 /-- the ideal `I = {r | r • y ∈ N}`-/
 def ExtensionOfMaxAdjoin.ideal (y : N) : Ideal R :=
@@ -367,7 +367,7 @@ def ExtensionOfMaxAdjoin.ideal (y : N) : Ideal R :=
 lean 3 declaration is
   forall {R : Type.{u1}} [_inst_1 : Ring.{u1} R] {Q : Type.{max u1 u2}} [_inst_2 : AddCommGroup.{max u1 u2} Q] [_inst_3 : Module.{u1, max u1 u2} R Q (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{max u1 u2} Q _inst_2)] {M : Type.{max u1 u2}} {N : Type.{max u1 u2}} [_inst_4 : AddCommGroup.{max u1 u2} M] [_inst_5 : AddCommGroup.{max u1 u2} N] [_inst_6 : Module.{u1, max u1 u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{max u1 u2} M _inst_4)] [_inst_7 : Module.{u1, max u1 u2} R N (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{max u1 u2} N _inst_5)] (i : LinearMap.{u1, u1, max u1 u2, max u1 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 N (AddCommGroup.toAddCommMonoid.{max u1 u2} M _inst_4) (AddCommGroup.toAddCommMonoid.{max u1 u2} N _inst_5) _inst_6 _inst_7) (f : LinearMap.{u1, u1, max u1 u2, max u1 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 Q (AddCommGroup.toAddCommMonoid.{max u1 u2} M _inst_4) (AddCommGroup.toAddCommMonoid.{max u1 u2} Q _inst_2) _inst_6 _inst_3) [_inst_8 : Fact (Function.Injective.{succ (max u1 u2), succ (max u1 u2)} M N (coeFn.{succ (max u1 u2), succ (max u1 u2)} (LinearMap.{u1, u1, max u1 u2, max u1 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 N (AddCommGroup.toAddCommMonoid.{max u1 u2} M _inst_4) (AddCommGroup.toAddCommMonoid.{max u1 u2} N _inst_5) _inst_6 _inst_7) (fun (_x : LinearMap.{u1, u1, max u1 u2, max u1 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 N (AddCommGroup.toAddCommMonoid.{max u1 u2} M _inst_4) (AddCommGroup.toAddCommMonoid.{max u1 u2} N _inst_5) _inst_6 _inst_7) => M -> N) (LinearMap.hasCoeToFun.{u1, u1, max u1 u2, max u1 u2} R R M N (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{max u1 u2} M _inst_4) (AddCommGroup.toAddCommMonoid.{max u1 u2} N _inst_5) _inst_6 _inst_7 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1)))) i))] (y : N), LinearMap.{u1, u1, u1, max u1 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))) (coeSort.{succ u1, succ (succ u1)} (Ideal.{u1} R (Ring.toSemiring.{u1} R _inst_1)) Type.{u1} (SetLike.hasCoeToSort.{u1, u1} (Ideal.{u1} R (Ring.toSemiring.{u1} R _inst_1)) R (Submodule.setLike.{u1, u1} R R (Ring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R _inst_1)))) (Module.Baer.ExtensionOfMaxAdjoin.ideal.{u1, u2} R _inst_1 Q _inst_2 _inst_3 M N _inst_4 _inst_5 _inst_6 _inst_7 i f _inst_8 y)) Q (Submodule.addCommMonoid.{u1, u1} R R (Ring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (Module.Baer.ExtensionOfMaxAdjoin.ideal.{u1, u2} R _inst_1 Q _inst_2 _inst_3 M N _inst_4 _inst_5 _inst_6 _inst_7 i f _inst_8 y)) (AddCommGroup.toAddCommMonoid.{max u1 u2} Q _inst_2) (Submodule.module.{u1, u1} R R (Ring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (Module.Baer.ExtensionOfMaxAdjoin.ideal.{u1, u2} R _inst_1 Q _inst_2 _inst_3 M N _inst_4 _inst_5 _inst_6 _inst_7 i f _inst_8 y)) _inst_3
 but is expected to have type
-  forall {R : Type.{u1}} [_inst_1 : Ring.{u1} R] {Q : TypeMax.{u2, u1}} [_inst_2 : AddCommGroup.{max u1 u2} Q] [_inst_3 : Module.{u1, max u1 u2} R Q (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{max u1 u2} Q _inst_2)] {M : Type.{max u1 u2}} {N : Type.{max u1 u2}} [_inst_4 : AddCommGroup.{max u1 u2} M] [_inst_5 : AddCommGroup.{max u1 u2} N] [_inst_6 : Module.{u1, max u1 u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{max u1 u2} M _inst_4)] [_inst_7 : Module.{u1, max u1 u2} R N (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{max u1 u2} N _inst_5)] (i : LinearMap.{u1, u1, max u1 u2, max u1 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 N (AddCommGroup.toAddCommMonoid.{max u1 u2} M _inst_4) (AddCommGroup.toAddCommMonoid.{max u1 u2} N _inst_5) _inst_6 _inst_7) (f : LinearMap.{u1, u1, max u1 u2, max u1 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 Q (AddCommGroup.toAddCommMonoid.{max u1 u2} M _inst_4) (AddCommGroup.toAddCommMonoid.{max u1 u2} Q _inst_2) _inst_6 _inst_3) [_inst_8 : Fact (Function.Injective.{max (succ u1) (succ u2), max (succ u1) (succ u2)} M N (FunLike.coe.{max (succ u1) (succ u2), max (succ u1) (succ u2), max (succ u1) (succ u2)} (LinearMap.{u1, u1, max u1 u2, max u1 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 N (AddCommGroup.toAddCommMonoid.{max u1 u2} M _inst_4) (AddCommGroup.toAddCommMonoid.{max u1 u2} N _inst_5) _inst_6 _inst_7) M (fun (_x : M) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : M) => N) _x) (LinearMap.instFunLikeLinearMap.{u1, u1, max u1 u2, max u1 u2} R R M N (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{max u1 u2} M _inst_4) (AddCommGroup.toAddCommMonoid.{max u1 u2} N _inst_5) _inst_6 _inst_7 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1)))) i))] (y : N), LinearMap.{u1, u1, u1, max u1 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))) (ModuleCat.carrier.{u1, u1} R _inst_1 (ModuleCat.of.{u1, u1} R _inst_1 (Subtype.{succ u1} R (fun (x : R) => Membership.mem.{u1, u1} R (Submodule.{u1, u1} R R (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} R (Ring.toAddCommGroup.{u1} R _inst_1)) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (SetLike.instMembership.{u1, u1} (Submodule.{u1, u1} R R (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} R (Ring.toAddCommGroup.{u1} R _inst_1)) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R 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(Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R _inst_1))) R (Submodule.setLike.{u1, u1} R R (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} R (Ring.toAddCommGroup.{u1} R _inst_1)) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R _inst_1)))) x (Module.Baer.ExtensionOfMaxAdjoin.ideal.{u1, u2} R _inst_1 Q _inst_2 _inst_3 M N _inst_4 _inst_5 _inst_6 _inst_7 i f _inst_8 y))) (Submodule.addCommGroup.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R _inst_1) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (Module.Baer.ExtensionOfMaxAdjoin.ideal.{u1, u2} R _inst_1 Q _inst_2 _inst_3 M N _inst_4 _inst_5 _inst_6 _inst_7 i f _inst_8 y)) (Submodule.module.{u1, u1} R R (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} R (Ring.toAddCommGroup.{u1} R _inst_1)) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (Module.Baer.ExtensionOfMaxAdjoin.ideal.{u1, u2} R _inst_1 Q _inst_2 _inst_3 M N _inst_4 _inst_5 _inst_6 _inst_7 i f _inst_8 y))))) (AddCommGroup.toAddCommMonoid.{max u1 u2} Q _inst_2) (ModuleCat.isModule.{u1, u1} R _inst_1 (ModuleCat.of.{u1, u1} R _inst_1 (Subtype.{succ u1} R (fun (x : R) => Membership.mem.{u1, u1} R (Submodule.{u1, u1} R R (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} R (Ring.toAddCommGroup.{u1} R _inst_1)) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (SetLike.instMembership.{u1, u1} (Submodule.{u1, u1} R R (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} R (Ring.toAddCommGroup.{u1} R _inst_1)) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R _inst_1))) R (Submodule.setLike.{u1, u1} R R (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} R (Ring.toAddCommGroup.{u1} R _inst_1)) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R _inst_1)))) x (Module.Baer.ExtensionOfMaxAdjoin.ideal.{u1, u2} R _inst_1 Q _inst_2 _inst_3 M N _inst_4 _inst_5 _inst_6 _inst_7 i f _inst_8 y))) (Submodule.addCommGroup.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R _inst_1) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (Module.Baer.ExtensionOfMaxAdjoin.ideal.{u1, u2} R _inst_1 Q _inst_2 _inst_3 M N _inst_4 _inst_5 _inst_6 _inst_7 i f _inst_8 y)) (Submodule.module.{u1, u1} R R (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} R (Ring.toAddCommGroup.{u1} R _inst_1)) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (Module.Baer.ExtensionOfMaxAdjoin.ideal.{u1, u2} R _inst_1 Q _inst_2 _inst_3 M N _inst_4 _inst_5 _inst_6 _inst_7 i f _inst_8 y)))) _inst_3
+  forall {R : Type.{u1}} [_inst_1 : Ring.{u1} R] {Q : TypeMax.{u2, u1}} [_inst_2 : AddCommGroup.{max u1 u2} Q] [_inst_3 : Module.{u1, max u1 u2} R Q (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{max u1 u2} Q _inst_2)] {M : Type.{max u1 u2}} {N : Type.{max u1 u2}} [_inst_4 : AddCommGroup.{max u1 u2} M] [_inst_5 : AddCommGroup.{max u1 u2} N] [_inst_6 : Module.{u1, max u1 u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{max u1 u2} M _inst_4)] [_inst_7 : Module.{u1, max u1 u2} R N (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{max u1 u2} N _inst_5)] (i : LinearMap.{u1, u1, max u1 u2, max u1 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 N (AddCommGroup.toAddCommMonoid.{max u1 u2} M _inst_4) (AddCommGroup.toAddCommMonoid.{max u1 u2} N _inst_5) _inst_6 _inst_7) (f : LinearMap.{u1, u1, max u1 u2, max u1 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 Q (AddCommGroup.toAddCommMonoid.{max u1 u2} M _inst_4) (AddCommGroup.toAddCommMonoid.{max u1 u2} Q _inst_2) _inst_6 _inst_3) [_inst_8 : Fact (Function.Injective.{max (succ u1) (succ u2), max (succ u1) (succ u2)} M N (FunLike.coe.{max (succ u1) (succ u2), max (succ u1) (succ u2), max (succ u1) (succ u2)} (LinearMap.{u1, u1, max u1 u2, max u1 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 N (AddCommGroup.toAddCommMonoid.{max u1 u2} M _inst_4) (AddCommGroup.toAddCommMonoid.{max u1 u2} N _inst_5) _inst_6 _inst_7) M (fun (_x : M) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : M) => N) _x) (LinearMap.instFunLikeLinearMap.{u1, u1, max u1 u2, max u1 u2} R R M N (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{max u1 u2} M _inst_4) (AddCommGroup.toAddCommMonoid.{max u1 u2} N _inst_5) _inst_6 _inst_7 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1)))) i))] (y : N), LinearMap.{u1, u1, u1, max u1 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))) (ModuleCat.carrier.{u1, u1} R _inst_1 (ModuleCat.of.{u1, u1} R _inst_1 (Subtype.{succ u1} R (fun (x : R) => Membership.mem.{u1, u1} R (Submodule.{u1, u1} R R (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} R (Ring.toAddCommGroup.{u1} R _inst_1)) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (SetLike.instMembership.{u1, u1} (Submodule.{u1, u1} R R (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} R (Ring.toAddCommGroup.{u1} R _inst_1)) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R _inst_1))) R (Submodule.setLike.{u1, u1} R R (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} R (Ring.toAddCommGroup.{u1} R _inst_1)) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R _inst_1)))) x (Module.Baer.ExtensionOfMaxAdjoin.ideal.{u1, u2} R _inst_1 Q _inst_2 _inst_3 M N _inst_4 _inst_5 _inst_6 _inst_7 i f _inst_8 y))) (Submodule.addCommGroup.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R _inst_1) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (Module.Baer.ExtensionOfMaxAdjoin.ideal.{u1, u2} R _inst_1 Q _inst_2 _inst_3 M N _inst_4 _inst_5 _inst_6 _inst_7 i f _inst_8 y)) (Submodule.module.{u1, u1} R R (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} R (Ring.toAddCommGroup.{u1} R _inst_1)) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (Module.Baer.ExtensionOfMaxAdjoin.ideal.{u1, u2} R _inst_1 Q _inst_2 _inst_3 M N _inst_4 _inst_5 _inst_6 _inst_7 i f _inst_8 y)))) Q (AddCommGroup.toAddCommMonoid.{u1} (ModuleCat.carrier.{u1, u1} R _inst_1 (ModuleCat.of.{u1, u1} R _inst_1 (Subtype.{succ u1} R (fun (x : R) => Membership.mem.{u1, u1} R (Submodule.{u1, u1} R R (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} R (Ring.toAddCommGroup.{u1} R _inst_1)) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (SetLike.instMembership.{u1, u1} (Submodule.{u1, u1} R R (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} R (Ring.toAddCommGroup.{u1} R _inst_1)) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R _inst_1))) R (Submodule.setLike.{u1, u1} R R (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} R (Ring.toAddCommGroup.{u1} R _inst_1)) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R _inst_1)))) x (Module.Baer.ExtensionOfMaxAdjoin.ideal.{u1, u2} R _inst_1 Q _inst_2 _inst_3 M N _inst_4 _inst_5 _inst_6 _inst_7 i f _inst_8 y))) (Submodule.addCommGroup.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R _inst_1) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (Module.Baer.ExtensionOfMaxAdjoin.ideal.{u1, u2} R _inst_1 Q _inst_2 _inst_3 M N _inst_4 _inst_5 _inst_6 _inst_7 i f _inst_8 y)) (Submodule.module.{u1, u1} R R (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} R (Ring.toAddCommGroup.{u1} R _inst_1)) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (Module.Baer.ExtensionOfMaxAdjoin.ideal.{u1, u2} R _inst_1 Q _inst_2 _inst_3 M N _inst_4 _inst_5 _inst_6 _inst_7 i f _inst_8 y)))) (ModuleCat.isAddCommGroup.{u1, u1} R _inst_1 (ModuleCat.of.{u1, u1} R _inst_1 (Subtype.{succ u1} R (fun (x : R) => Membership.mem.{u1, u1} R (Submodule.{u1, u1} R R (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} R (Ring.toAddCommGroup.{u1} R _inst_1)) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (SetLike.instMembership.{u1, u1} (Submodule.{u1, u1} R R (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} R (Ring.toAddCommGroup.{u1} R _inst_1)) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R _inst_1))) R (Submodule.setLike.{u1, u1} R R (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} R (Ring.toAddCommGroup.{u1} R _inst_1)) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R _inst_1)))) x (Module.Baer.ExtensionOfMaxAdjoin.ideal.{u1, u2} R _inst_1 Q _inst_2 _inst_3 M N _inst_4 _inst_5 _inst_6 _inst_7 i f _inst_8 y))) (Submodule.addCommGroup.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R _inst_1) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (Module.Baer.ExtensionOfMaxAdjoin.ideal.{u1, u2} R _inst_1 Q _inst_2 _inst_3 M N _inst_4 _inst_5 _inst_6 _inst_7 i f _inst_8 y)) (Submodule.module.{u1, u1} R R (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} R (Ring.toAddCommGroup.{u1} R _inst_1)) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (Module.Baer.ExtensionOfMaxAdjoin.ideal.{u1, u2} R _inst_1 Q _inst_2 _inst_3 M N _inst_4 _inst_5 _inst_6 _inst_7 i f _inst_8 y))))) (AddCommGroup.toAddCommMonoid.{max u1 u2} Q _inst_2) (ModuleCat.isModule.{u1, u1} R _inst_1 (ModuleCat.of.{u1, u1} R _inst_1 (Subtype.{succ u1} R (fun (x : R) => Membership.mem.{u1, u1} R (Submodule.{u1, u1} R R (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} R (Ring.toAddCommGroup.{u1} R _inst_1)) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (SetLike.instMembership.{u1, u1} (Submodule.{u1, u1} R R (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} R (Ring.toAddCommGroup.{u1} R _inst_1)) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R _inst_1))) R (Submodule.setLike.{u1, u1} R R (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} R (Ring.toAddCommGroup.{u1} R _inst_1)) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R _inst_1)))) x (Module.Baer.ExtensionOfMaxAdjoin.ideal.{u1, u2} R _inst_1 Q _inst_2 _inst_3 M N _inst_4 _inst_5 _inst_6 _inst_7 i f _inst_8 y))) (Submodule.addCommGroup.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R _inst_1) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (Module.Baer.ExtensionOfMaxAdjoin.ideal.{u1, u2} R _inst_1 Q _inst_2 _inst_3 M N _inst_4 _inst_5 _inst_6 _inst_7 i f _inst_8 y)) (Submodule.module.{u1, u1} R R (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} R (Ring.toAddCommGroup.{u1} R _inst_1)) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (Module.Baer.ExtensionOfMaxAdjoin.ideal.{u1, u2} R _inst_1 Q _inst_2 _inst_3 M N _inst_4 _inst_5 _inst_6 _inst_7 i f _inst_8 y)))) _inst_3
 Case conversion may be inaccurate. Consider using '#align module.Baer.extension_of_max_adjoin.ideal_to Module.Baer.ExtensionOfMaxAdjoin.idealToₓ'. -/
 /-- A linear map `I ⟶ Q` by `x ↦ f' (x • y)` where `f'` is the maximal extension-/
 def ExtensionOfMaxAdjoin.idealTo (y : N) : ExtensionOfMaxAdjoin.ideal i f y →ₗ[R] Q
@@ -381,7 +381,7 @@ def ExtensionOfMaxAdjoin.idealTo (y : N) : ExtensionOfMaxAdjoin.ideal i f y →
 lean 3 declaration is
   forall {R : Type.{u1}} [_inst_1 : Ring.{u1} R] {Q : Type.{max u1 u2}} [_inst_2 : AddCommGroup.{max u1 u2} Q] [_inst_3 : Module.{u1, max u1 u2} R Q (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{max u1 u2} Q _inst_2)] {M : Type.{max u1 u2}} {N : Type.{max u1 u2}} [_inst_4 : AddCommGroup.{max u1 u2} M] [_inst_5 : AddCommGroup.{max u1 u2} N] [_inst_6 : Module.{u1, max u1 u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{max u1 u2} M _inst_4)] [_inst_7 : Module.{u1, max u1 u2} R N (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{max u1 u2} N _inst_5)] (i : LinearMap.{u1, u1, max u1 u2, max u1 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 N (AddCommGroup.toAddCommMonoid.{max u1 u2} M _inst_4) (AddCommGroup.toAddCommMonoid.{max u1 u2} N _inst_5) _inst_6 _inst_7), (LinearMap.{u1, u1, max u1 u2, max u1 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 Q (AddCommGroup.toAddCommMonoid.{max u1 u2} M _inst_4) (AddCommGroup.toAddCommMonoid.{max u1 u2} Q _inst_2) _inst_6 _inst_3) -> (forall [_inst_8 : Fact (Function.Injective.{succ (max u1 u2), succ (max u1 u2)} M N (coeFn.{succ (max u1 u2), succ (max u1 u2)} (LinearMap.{u1, u1, max u1 u2, max u1 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 N (AddCommGroup.toAddCommMonoid.{max u1 u2} M _inst_4) (AddCommGroup.toAddCommMonoid.{max u1 u2} N _inst_5) _inst_6 _inst_7) (fun (_x : LinearMap.{u1, u1, max u1 u2, max u1 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 N (AddCommGroup.toAddCommMonoid.{max u1 u2} M _inst_4) (AddCommGroup.toAddCommMonoid.{max u1 u2} N _inst_5) _inst_6 _inst_7) => M -> N) (LinearMap.hasCoeToFun.{u1, u1, max u1 u2, max u1 u2} R R M N (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{max u1 u2} M _inst_4) (AddCommGroup.toAddCommMonoid.{max u1 u2} N _inst_5) _inst_6 _inst_7 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1)))) i))], (Module.Baer.{u1, u2} R _inst_1 Q _inst_2 _inst_3) -> N -> (LinearMap.{u1, u1, u1, max u1 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))) R Q (AddCommGroup.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toAddCommGroup.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R _inst_1)))) (AddCommGroup.toAddCommMonoid.{max u1 u2} Q _inst_2) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R _inst_1)) _inst_3))
 but is expected to have type
-  forall {R : Type.{u1}} [_inst_1 : Ring.{u1} R] {Q : TypeMax.{u2, u1}} [_inst_2 : AddCommGroup.{max u1 u2} Q] [_inst_3 : Module.{u1, max u1 u2} R Q (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{max u1 u2} Q _inst_2)] {M : Type.{max u1 u2}} {N : Type.{max u1 u2}} [_inst_4 : AddCommGroup.{max u1 u2} M] [_inst_5 : AddCommGroup.{max u1 u2} N] [_inst_6 : Module.{u1, max u1 u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{max u1 u2} M _inst_4)] [_inst_7 : Module.{u1, max u1 u2} R N (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{max u1 u2} N _inst_5)] (i : LinearMap.{u1, u1, max u1 u2, max u1 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 N (AddCommGroup.toAddCommMonoid.{max u1 u2} M _inst_4) (AddCommGroup.toAddCommMonoid.{max u1 u2} N _inst_5) _inst_6 _inst_7), (LinearMap.{u1, u1, max u1 u2, max u1 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 Q (AddCommGroup.toAddCommMonoid.{max u1 u2} M _inst_4) (AddCommGroup.toAddCommMonoid.{max u1 u2} Q _inst_2) _inst_6 _inst_3) -> (forall [_inst_8 : Fact (Function.Injective.{max (succ u1) (succ u2), max (succ u1) (succ u2)} M N (FunLike.coe.{max (succ u1) (succ u2), max (succ u1) (succ u2), max (succ u1) (succ u2)} (LinearMap.{u1, u1, max u1 u2, max u1 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 N (AddCommGroup.toAddCommMonoid.{max u1 u2} M _inst_4) (AddCommGroup.toAddCommMonoid.{max u1 u2} N _inst_5) _inst_6 _inst_7) M (fun (_x : M) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : M) => N) _x) (LinearMap.instFunLikeLinearMap.{u1, u1, max u1 u2, max u1 u2} R R M N (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{max u1 u2} M _inst_4) (AddCommGroup.toAddCommMonoid.{max u1 u2} N _inst_5) _inst_6 _inst_7 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1)))) i))], (Module.Baer.{u1, u2} R _inst_1 Q _inst_2 _inst_3) -> N -> (LinearMap.{u1, u1, u1, max u1 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))) R Q (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R _inst_1)))) (AddCommGroup.toAddCommMonoid.{max u1 u2} Q _inst_2) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R _inst_1)) _inst_3))
+  forall {R : Type.{u1}} [_inst_1 : Ring.{u1} R] {Q : TypeMax.{u2, u1}} [_inst_2 : AddCommGroup.{max u1 u2} Q] [_inst_3 : Module.{u1, max u1 u2} R Q (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{max u1 u2} Q _inst_2)] {M : Type.{max u1 u2}} {N : Type.{max u1 u2}} [_inst_4 : AddCommGroup.{max u1 u2} M] [_inst_5 : AddCommGroup.{max u1 u2} N] [_inst_6 : Module.{u1, max u1 u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{max u1 u2} M _inst_4)] [_inst_7 : Module.{u1, max u1 u2} R N (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{max u1 u2} N _inst_5)] (i : LinearMap.{u1, u1, max u1 u2, max u1 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 N (AddCommGroup.toAddCommMonoid.{max u1 u2} M _inst_4) (AddCommGroup.toAddCommMonoid.{max u1 u2} N _inst_5) _inst_6 _inst_7), (LinearMap.{u1, u1, max u1 u2, max u1 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 Q (AddCommGroup.toAddCommMonoid.{max u1 u2} M _inst_4) (AddCommGroup.toAddCommMonoid.{max u1 u2} Q _inst_2) _inst_6 _inst_3) -> (forall [_inst_8 : Fact (Function.Injective.{max (succ u1) (succ u2), max (succ u1) (succ u2)} M N (FunLike.coe.{max (succ u1) (succ u2), max (succ u1) (succ u2), max (succ u1) (succ u2)} (LinearMap.{u1, u1, max u1 u2, max u1 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 N (AddCommGroup.toAddCommMonoid.{max u1 u2} M _inst_4) (AddCommGroup.toAddCommMonoid.{max u1 u2} N _inst_5) _inst_6 _inst_7) M (fun (_x : M) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : M) => N) _x) (LinearMap.instFunLikeLinearMap.{u1, u1, max u1 u2, max u1 u2} R R M N (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{max u1 u2} M _inst_4) (AddCommGroup.toAddCommMonoid.{max u1 u2} N _inst_5) _inst_6 _inst_7 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1)))) i))], (Module.Baer.{u1, u2} R _inst_1 Q _inst_2 _inst_3) -> N -> (LinearMap.{u1, u1, u1, max u1 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))) R Q (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R _inst_1)))) (AddCommGroup.toAddCommMonoid.{max u1 u2} Q _inst_2) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R _inst_1)) _inst_3))
 Case conversion may be inaccurate. Consider using '#align module.Baer.extension_of_max_adjoin.extend_ideal_to Module.Baer.ExtensionOfMaxAdjoin.extendIdealToₓ'. -/
 /-- Since we assumed `Q` being Baer, the linear map `x ↦ f' (x • y) : I ⟶ Q` extends to `R ⟶ Q`,
 call this extended map `φ`-/
@@ -393,7 +393,7 @@ def ExtensionOfMaxAdjoin.extendIdealTo (h : Module.Baer R Q) (y : N) : R →ₗ[
 lean 3 declaration is
   forall {R : Type.{u1}} [_inst_1 : Ring.{u1} R] {Q : Type.{max u1 u2}} [_inst_2 : AddCommGroup.{max u1 u2} Q] [_inst_3 : Module.{u1, max u1 u2} R Q (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{max u1 u2} Q _inst_2)] {M : Type.{max u1 u2}} {N : Type.{max u1 u2}} [_inst_4 : AddCommGroup.{max u1 u2} M] [_inst_5 : AddCommGroup.{max u1 u2} N] [_inst_6 : Module.{u1, max u1 u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{max u1 u2} M _inst_4)] [_inst_7 : Module.{u1, max u1 u2} R N (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{max u1 u2} N _inst_5)] (i : LinearMap.{u1, u1, max u1 u2, max u1 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 N (AddCommGroup.toAddCommMonoid.{max u1 u2} M _inst_4) (AddCommGroup.toAddCommMonoid.{max u1 u2} N _inst_5) _inst_6 _inst_7) (f : LinearMap.{u1, u1, max u1 u2, max u1 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 Q (AddCommGroup.toAddCommMonoid.{max u1 u2} M _inst_4) (AddCommGroup.toAddCommMonoid.{max u1 u2} Q _inst_2) _inst_6 _inst_3) [_inst_8 : Fact (Function.Injective.{succ (max u1 u2), succ (max u1 u2)} M N (coeFn.{succ (max u1 u2), succ (max u1 u2)} (LinearMap.{u1, u1, max u1 u2, max u1 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 N (AddCommGroup.toAddCommMonoid.{max u1 u2} M _inst_4) (AddCommGroup.toAddCommMonoid.{max u1 u2} N _inst_5) _inst_6 _inst_7) (fun (_x : LinearMap.{u1, u1, max u1 u2, max u1 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 N (AddCommGroup.toAddCommMonoid.{max u1 u2} M _inst_4) (AddCommGroup.toAddCommMonoid.{max u1 u2} N _inst_5) _inst_6 _inst_7) => M -> N) (LinearMap.hasCoeToFun.{u1, u1, max u1 u2, max u1 u2} R R M N (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{max u1 u2} M _inst_4) (AddCommGroup.toAddCommMonoid.{max u1 u2} N _inst_5) _inst_6 _inst_7 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1)))) i))] (h : Module.Baer.{u1, u2} R _inst_1 Q _inst_2 _inst_3) (y : N) (x : R) (mem : Membership.Mem.{u1, u1} R (Ideal.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (SetLike.hasMem.{u1, u1} (Ideal.{u1} R (Ring.toSemiring.{u1} R _inst_1)) R (Submodule.setLike.{u1, u1} R R (Ring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R _inst_1)))) x (Module.Baer.ExtensionOfMaxAdjoin.ideal.{u1, u2} R _inst_1 Q _inst_2 _inst_3 M N _inst_4 _inst_5 _inst_6 _inst_7 i f _inst_8 y)), Eq.{succ (max u1 u2)} Q (coeFn.{max (succ u1) (succ (max u1 u2)), max (succ u1) (succ (max u1 u2))} (LinearMap.{u1, u1, u1, max u1 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))) R Q (AddCommGroup.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toAddCommGroup.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R _inst_1)))) (AddCommGroup.toAddCommMonoid.{max u1 u2} Q _inst_2) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R _inst_1)) _inst_3) (fun (_x : LinearMap.{u1, u1, u1, max u1 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))) R Q (AddCommGroup.toAddCommMonoid.{u1} R 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 but is expected to have type
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+  forall {R : Type.{u1}} [_inst_1 : Ring.{u1} R] {Q : TypeMax.{u2, u1}} [_inst_2 : AddCommGroup.{max u1 u2} Q] [_inst_3 : Module.{u1, max u1 u2} R Q (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{max u1 u2} Q _inst_2)] {M : Type.{max u1 u2}} {N : Type.{max u1 u2}} [_inst_4 : AddCommGroup.{max u1 u2} M] [_inst_5 : AddCommGroup.{max u1 u2} N] [_inst_6 : Module.{u1, max u1 u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{max u1 u2} M _inst_4)] [_inst_7 : Module.{u1, max u1 u2} R N (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{max u1 u2} N _inst_5)] (i : LinearMap.{u1, u1, max u1 u2, max u1 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 N (AddCommGroup.toAddCommMonoid.{max u1 u2} M _inst_4) (AddCommGroup.toAddCommMonoid.{max u1 u2} N _inst_5) _inst_6 _inst_7) (f : LinearMap.{u1, u1, max u1 u2, max u1 u2} R R 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_inst_1 (Ring.toAddCommGroup.{u1} R _inst_1) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (Module.Baer.ExtensionOfMaxAdjoin.ideal.{u1, u2} R _inst_1 Q _inst_2 _inst_3 M N _inst_4 _inst_5 _inst_6 _inst_7 i f _inst_8 y)) (Submodule.module.{u1, u1} R R (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} R (Ring.toAddCommGroup.{u1} R _inst_1)) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (Module.Baer.ExtensionOfMaxAdjoin.ideal.{u1, u2} R _inst_1 Q _inst_2 _inst_3 M N _inst_4 _inst_5 _inst_6 _inst_7 i f _inst_8 y)))) (ModuleCat.isAddCommGroup.{u1, u1} R _inst_1 (ModuleCat.of.{u1, u1} R _inst_1 (Subtype.{succ u1} R (fun (x : R) => Membership.mem.{u1, u1} R (Submodule.{u1, u1} R R (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} R (Ring.toAddCommGroup.{u1} R _inst_1)) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (SetLike.instMembership.{u1, u1} (Submodule.{u1, u1} R R (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} R (Ring.toAddCommGroup.{u1} R _inst_1)) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R _inst_1))) R (Submodule.setLike.{u1, u1} R R (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} R (Ring.toAddCommGroup.{u1} R _inst_1)) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R _inst_1)))) x (Module.Baer.ExtensionOfMaxAdjoin.ideal.{u1, u2} R _inst_1 Q _inst_2 _inst_3 M N _inst_4 _inst_5 _inst_6 _inst_7 i f _inst_8 y))) (Submodule.addCommGroup.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R _inst_1) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (Module.Baer.ExtensionOfMaxAdjoin.ideal.{u1, u2} R _inst_1 Q _inst_2 _inst_3 M N _inst_4 _inst_5 _inst_6 _inst_7 i f _inst_8 y)) (Submodule.module.{u1, u1} R R (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} R (Ring.toAddCommGroup.{u1} R _inst_1)) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (Module.Baer.ExtensionOfMaxAdjoin.ideal.{u1, u2} R _inst_1 Q _inst_2 _inst_3 M N _inst_4 _inst_5 _inst_6 _inst_7 i f _inst_8 y))))) (AddCommGroup.toAddCommMonoid.{max u1 u2} Q _inst_2) (ModuleCat.isModule.{u1, u1} R _inst_1 (ModuleCat.of.{u1, u1} R _inst_1 (Subtype.{succ u1} R (fun (x : R) => Membership.mem.{u1, u1} R (Submodule.{u1, u1} R R (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} R (Ring.toAddCommGroup.{u1} R _inst_1)) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (SetLike.instMembership.{u1, u1} (Submodule.{u1, u1} R R (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} R (Ring.toAddCommGroup.{u1} R _inst_1)) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R _inst_1))) R (Submodule.setLike.{u1, u1} R R (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} R (Ring.toAddCommGroup.{u1} R _inst_1)) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R _inst_1)))) x (Module.Baer.ExtensionOfMaxAdjoin.ideal.{u1, u2} R _inst_1 Q _inst_2 _inst_3 M N _inst_4 _inst_5 _inst_6 _inst_7 i f _inst_8 y))) (Submodule.addCommGroup.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R _inst_1) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (Module.Baer.ExtensionOfMaxAdjoin.ideal.{u1, u2} R _inst_1 Q _inst_2 _inst_3 M N _inst_4 _inst_5 _inst_6 _inst_7 i f _inst_8 y)) (Submodule.module.{u1, u1} R R (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} R (Ring.toAddCommGroup.{u1} R _inst_1)) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (Module.Baer.ExtensionOfMaxAdjoin.ideal.{u1, u2} R _inst_1 Q _inst_2 _inst_3 M N _inst_4 _inst_5 _inst_6 _inst_7 i f _inst_8 y)))) _inst_3 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1)))) (Module.Baer.ExtensionOfMaxAdjoin.idealTo.{u1, u2} R _inst_1 Q _inst_2 _inst_3 M N _inst_4 _inst_5 _inst_6 _inst_7 i f _inst_8 y) (Subtype.mk.{succ u1} R (fun (x : R) => Membership.mem.{u1, u1} R (Submodule.{u1, u1} R R (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} R (Ring.toAddCommGroup.{u1} R _inst_1)) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (SetLike.instMembership.{u1, u1} (Submodule.{u1, u1} R R (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} R (Ring.toAddCommGroup.{u1} R _inst_1)) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R _inst_1))) R (Submodule.setLike.{u1, u1} R R (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} R (Ring.toAddCommGroup.{u1} R _inst_1)) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R _inst_1)))) x (Module.Baer.ExtensionOfMaxAdjoin.ideal.{u1, u2} R _inst_1 Q _inst_2 _inst_3 M N _inst_4 _inst_5 _inst_6 _inst_7 i f _inst_8 y)) x mem))
 Case conversion may be inaccurate. Consider using '#align module.Baer.extension_of_max_adjoin.extend_ideal_to_is_extension Module.Baer.ExtensionOfMaxAdjoin.extendIdealTo_is_extensionₓ'. -/
 theorem ExtensionOfMaxAdjoin.extendIdealTo_is_extension (h : Module.Baer R Q) (y : N) :
     ∀ (x : R) (mem : x ∈ ExtensionOfMaxAdjoin.ideal i f y),
@@ -405,7 +405,7 @@ theorem ExtensionOfMaxAdjoin.extendIdealTo_is_extension (h : Module.Baer R Q) (y
 lean 3 declaration is
   forall {R : Type.{u1}} [_inst_1 : Ring.{u1} R] {Q : Type.{max u1 u2}} [_inst_2 : AddCommGroup.{max u1 u2} Q] [_inst_3 : Module.{u1, max u1 u2} R Q (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{max u1 u2} Q _inst_2)] {M : Type.{max u1 u2}} {N : Type.{max u1 u2}} [_inst_4 : AddCommGroup.{max u1 u2} M] [_inst_5 : AddCommGroup.{max u1 u2} N] [_inst_6 : Module.{u1, max u1 u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{max u1 u2} M _inst_4)] [_inst_7 : Module.{u1, max u1 u2} R N (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{max u1 u2} N _inst_5)] (i : LinearMap.{u1, u1, max u1 u2, max u1 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 N (AddCommGroup.toAddCommMonoid.{max u1 u2} M _inst_4) (AddCommGroup.toAddCommMonoid.{max u1 u2} N _inst_5) _inst_6 _inst_7) (f : LinearMap.{u1, u1, max u1 u2, max u1 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 Q (AddCommGroup.toAddCommMonoid.{max u1 u2} M _inst_4) (AddCommGroup.toAddCommMonoid.{max u1 u2} Q _inst_2) _inst_6 _inst_3) [_inst_8 : Fact (Function.Injective.{succ (max u1 u2), succ (max u1 u2)} M N (coeFn.{succ (max u1 u2), succ (max u1 u2)} (LinearMap.{u1, u1, max u1 u2, max u1 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 N (AddCommGroup.toAddCommMonoid.{max u1 u2} M _inst_4) (AddCommGroup.toAddCommMonoid.{max u1 u2} N _inst_5) _inst_6 _inst_7) (fun (_x : LinearMap.{u1, u1, max u1 u2, max u1 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 N (AddCommGroup.toAddCommMonoid.{max u1 u2} M _inst_4) (AddCommGroup.toAddCommMonoid.{max u1 u2} N _inst_5) _inst_6 _inst_7) => M -> N) (LinearMap.hasCoeToFun.{u1, u1, max u1 u2, max u1 u2} R R M N (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{max u1 u2} M _inst_4) (AddCommGroup.toAddCommMonoid.{max u1 u2} N _inst_5) _inst_6 _inst_7 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1)))) i))] (h : Module.Baer.{u1, u2} R _inst_1 Q _inst_2 _inst_3) {y : N} (r : R), (Eq.{succ (max u1 u2)} N (SMul.smul.{u1, max u1 u2} R N (SMulZeroClass.toHasSmul.{u1, max u1 u2} R N (AddZeroClass.toHasZero.{max u1 u2} N (AddMonoid.toAddZeroClass.{max u1 u2} N (AddCommMonoid.toAddMonoid.{max u1 u2} N (AddCommGroup.toAddCommMonoid.{max u1 u2} N _inst_5)))) (SMulWithZero.toSmulZeroClass.{u1, max u1 u2} R N (MulZeroClass.toHasZero.{u1} R (MulZeroOneClass.toMulZeroClass.{u1} R (MonoidWithZero.toMulZeroOneClass.{u1} R (Semiring.toMonoidWithZero.{u1} R (Ring.toSemiring.{u1} R _inst_1))))) (AddZeroClass.toHasZero.{max u1 u2} N (AddMonoid.toAddZeroClass.{max u1 u2} N (AddCommMonoid.toAddMonoid.{max u1 u2} N (AddCommGroup.toAddCommMonoid.{max u1 u2} N _inst_5)))) (MulActionWithZero.toSMulWithZero.{u1, max u1 u2} R N (Semiring.toMonoidWithZero.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (AddZeroClass.toHasZero.{max u1 u2} N (AddMonoid.toAddZeroClass.{max u1 u2} N (AddCommMonoid.toAddMonoid.{max u1 u2} N (AddCommGroup.toAddCommMonoid.{max u1 u2} N _inst_5)))) (Module.toMulActionWithZero.{u1, max u1 u2} R N (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{max u1 u2} N _inst_5) _inst_7)))) r y) (OfNat.ofNat.{max u1 u2} N 0 (OfNat.mk.{max u1 u2} N 0 (Zero.zero.{max u1 u2} N (AddZeroClass.toHasZero.{max u1 u2} N (AddMonoid.toAddZeroClass.{max u1 u2} N (SubNegMonoid.toAddMonoid.{max u1 u2} N (AddGroup.toSubNegMonoid.{max u1 u2} N (AddCommGroup.toAddGroup.{max u1 u2} N _inst_5))))))))) -> (Eq.{succ (max u1 u2)} Q (coeFn.{max (succ u1) (succ (max u1 u2)), max (succ u1) (succ (max u1 u2))} (LinearMap.{u1, u1, u1, max u1 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))) R Q (AddCommGroup.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toAddCommGroup.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R _inst_1)))) (AddCommGroup.toAddCommMonoid.{max u1 u2} Q _inst_2) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R _inst_1)) _inst_3) (fun (_x : LinearMap.{u1, u1, u1, max u1 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))) R Q (AddCommGroup.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toAddCommGroup.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R _inst_1)))) (AddCommGroup.toAddCommMonoid.{max u1 u2} Q _inst_2) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R _inst_1)) _inst_3) => R -> Q) (LinearMap.hasCoeToFun.{u1, u1, u1, max u1 u2} R R R Q (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toAddCommGroup.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R _inst_1)))) (AddCommGroup.toAddCommMonoid.{max u1 u2} Q _inst_2) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R _inst_1)) _inst_3 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1)))) (Module.Baer.ExtensionOfMaxAdjoin.extendIdealTo.{u1, u2} R _inst_1 Q _inst_2 _inst_3 M N _inst_4 _inst_5 _inst_6 _inst_7 i f _inst_8 h y) r) (OfNat.ofNat.{max u1 u2} Q 0 (OfNat.mk.{max u1 u2} Q 0 (Zero.zero.{max u1 u2} Q (AddZeroClass.toHasZero.{max u1 u2} Q (AddMonoid.toAddZeroClass.{max u1 u2} Q (SubNegMonoid.toAddMonoid.{max u1 u2} Q (AddGroup.toSubNegMonoid.{max u1 u2} Q (AddCommGroup.toAddGroup.{max u1 u2} Q _inst_2)))))))))
 but is expected to have type
-  forall {R : Type.{u1}} [_inst_1 : Ring.{u1} R] {Q : TypeMax.{u2, u1}} [_inst_2 : AddCommGroup.{max u1 u2} Q] [_inst_3 : Module.{u1, max u1 u2} R Q (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{max u1 u2} Q _inst_2)] {M : Type.{max u1 u2}} {N : Type.{max u1 u2}} [_inst_4 : AddCommGroup.{max u1 u2} M] [_inst_5 : AddCommGroup.{max u1 u2} N] [_inst_6 : Module.{u1, max u1 u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{max u1 u2} M _inst_4)] [_inst_7 : Module.{u1, max u1 u2} R N (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{max u1 u2} N _inst_5)] (i : LinearMap.{u1, u1, max u1 u2, max u1 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 N (AddCommGroup.toAddCommMonoid.{max u1 u2} M _inst_4) (AddCommGroup.toAddCommMonoid.{max u1 u2} N _inst_5) _inst_6 _inst_7) (f : LinearMap.{u1, u1, max u1 u2, max u1 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 Q (AddCommGroup.toAddCommMonoid.{max u1 u2} M _inst_4) (AddCommGroup.toAddCommMonoid.{max u1 u2} Q _inst_2) _inst_6 _inst_3) [_inst_8 : Fact (Function.Injective.{max (succ u1) (succ u2), max (succ u1) (succ u2)} M N (FunLike.coe.{max (succ u1) (succ u2), max (succ u1) (succ u2), max (succ u1) (succ u2)} (LinearMap.{u1, u1, max u1 u2, max u1 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 N (AddCommGroup.toAddCommMonoid.{max u1 u2} M _inst_4) (AddCommGroup.toAddCommMonoid.{max u1 u2} N _inst_5) _inst_6 _inst_7) M (fun (_x : M) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : M) => N) _x) (LinearMap.instFunLikeLinearMap.{u1, u1, max u1 u2, max u1 u2} R R M N (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{max u1 u2} M _inst_4) (AddCommGroup.toAddCommMonoid.{max u1 u2} N _inst_5) _inst_6 _inst_7 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1)))) i))] (h : Module.Baer.{u1, u2} R _inst_1 Q _inst_2 _inst_3) {y : N} (r : R), (Eq.{max (succ u1) (succ u2)} N (HSMul.hSMul.{u1, max u1 u2, max u1 u2} R N N (instHSMul.{u1, max u1 u2} R N (SMulZeroClass.toSMul.{u1, max u1 u2} R N (NegZeroClass.toZero.{max u1 u2} N (SubNegZeroMonoid.toNegZeroClass.{max u1 u2} N (SubtractionMonoid.toSubNegZeroMonoid.{max u1 u2} N (SubtractionCommMonoid.toSubtractionMonoid.{max u1 u2} N (AddCommGroup.toDivisionAddCommMonoid.{max u1 u2} N _inst_5))))) (SMulWithZero.toSMulZeroClass.{u1, max u1 u2} R N (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (NegZeroClass.toZero.{max u1 u2} N (SubNegZeroMonoid.toNegZeroClass.{max u1 u2} N (SubtractionMonoid.toSubNegZeroMonoid.{max u1 u2} N (SubtractionCommMonoid.toSubtractionMonoid.{max u1 u2} N (AddCommGroup.toDivisionAddCommMonoid.{max u1 u2} N _inst_5))))) (MulActionWithZero.toSMulWithZero.{u1, max u1 u2} R N (Semiring.toMonoidWithZero.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (NegZeroClass.toZero.{max u1 u2} N (SubNegZeroMonoid.toNegZeroClass.{max u1 u2} N (SubtractionMonoid.toSubNegZeroMonoid.{max u1 u2} N (SubtractionCommMonoid.toSubtractionMonoid.{max u1 u2} N (AddCommGroup.toDivisionAddCommMonoid.{max u1 u2} N _inst_5))))) (Module.toMulActionWithZero.{u1, max u1 u2} R N (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{max u1 u2} N _inst_5) _inst_7))))) r y) (OfNat.ofNat.{max u1 u2} N 0 (Zero.toOfNat0.{max u1 u2} N (NegZeroClass.toZero.{max u1 u2} N (SubNegZeroMonoid.toNegZeroClass.{max u1 u2} N (SubtractionMonoid.toSubNegZeroMonoid.{max u1 u2} N (SubtractionCommMonoid.toSubtractionMonoid.{max u1 u2} N (AddCommGroup.toDivisionAddCommMonoid.{max u1 u2} N _inst_5)))))))) -> (Eq.{max (succ u1) (succ u2)} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : R) => Q) r) (FunLike.coe.{max (succ u1) (succ u2), succ u1, max (succ u1) (succ u2)} (LinearMap.{u1, u1, u1, max u1 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))) R Q (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R _inst_1)))) (AddCommGroup.toAddCommMonoid.{max u1 u2} Q _inst_2) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R _inst_1)) _inst_3) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : R) => Q) _x) (LinearMap.instFunLikeLinearMap.{u1, u1, u1, max u1 u2} R R R Q (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R _inst_1)))) (AddCommGroup.toAddCommMonoid.{max u1 u2} Q _inst_2) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R _inst_1)) _inst_3 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1)))) (Module.Baer.ExtensionOfMaxAdjoin.extendIdealTo.{u1, u2} R _inst_1 Q _inst_2 _inst_3 M N _inst_4 _inst_5 _inst_6 _inst_7 i f _inst_8 h y) r) (OfNat.ofNat.{max u1 u2} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : R) => Q) r) 0 (Zero.toOfNat0.{max u1 u2} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : R) => Q) r) (NegZeroClass.toZero.{max u1 u2} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : R) => Q) r) (SubNegZeroMonoid.toNegZeroClass.{max u1 u2} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : R) => Q) r) (SubtractionMonoid.toSubNegZeroMonoid.{max u1 u2} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : R) => Q) r) (SubtractionCommMonoid.toSubtractionMonoid.{max u1 u2} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : R) => Q) r) (AddCommGroup.toDivisionAddCommMonoid.{max u1 u2} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : R) => Q) r) _inst_2))))))))
+  forall {R : Type.{u1}} [_inst_1 : Ring.{u1} R] {Q : TypeMax.{u2, u1}} [_inst_2 : AddCommGroup.{max u1 u2} Q] [_inst_3 : Module.{u1, max u1 u2} R Q (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{max u1 u2} Q _inst_2)] {M : Type.{max u1 u2}} {N : Type.{max u1 u2}} [_inst_4 : AddCommGroup.{max u1 u2} M] [_inst_5 : AddCommGroup.{max u1 u2} N] [_inst_6 : Module.{u1, max u1 u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{max u1 u2} M _inst_4)] [_inst_7 : Module.{u1, max u1 u2} R N (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{max u1 u2} N _inst_5)] (i : LinearMap.{u1, u1, max u1 u2, max u1 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 N (AddCommGroup.toAddCommMonoid.{max u1 u2} M _inst_4) (AddCommGroup.toAddCommMonoid.{max u1 u2} N _inst_5) _inst_6 _inst_7) (f : LinearMap.{u1, u1, max u1 u2, max u1 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 Q (AddCommGroup.toAddCommMonoid.{max u1 u2} M _inst_4) (AddCommGroup.toAddCommMonoid.{max u1 u2} Q _inst_2) _inst_6 _inst_3) [_inst_8 : Fact (Function.Injective.{max (succ u1) (succ u2), max (succ u1) (succ u2)} M N (FunLike.coe.{max (succ u1) (succ u2), max (succ u1) (succ u2), max (succ u1) (succ u2)} (LinearMap.{u1, u1, max u1 u2, max u1 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 N (AddCommGroup.toAddCommMonoid.{max u1 u2} M _inst_4) (AddCommGroup.toAddCommMonoid.{max u1 u2} N _inst_5) _inst_6 _inst_7) M (fun (_x : M) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : M) => N) _x) (LinearMap.instFunLikeLinearMap.{u1, u1, max u1 u2, max u1 u2} R R M N (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{max u1 u2} M _inst_4) (AddCommGroup.toAddCommMonoid.{max u1 u2} N _inst_5) _inst_6 _inst_7 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1)))) i))] (h : Module.Baer.{u1, u2} R _inst_1 Q _inst_2 _inst_3) {y : N} (r : R), (Eq.{max (succ u1) (succ u2)} N (HSMul.hSMul.{u1, max u1 u2, max u1 u2} R N N (instHSMul.{u1, max u1 u2} R N (SMulZeroClass.toSMul.{u1, max u1 u2} R N (NegZeroClass.toZero.{max u1 u2} N (SubNegZeroMonoid.toNegZeroClass.{max u1 u2} N (SubtractionMonoid.toSubNegZeroMonoid.{max u1 u2} N (SubtractionCommMonoid.toSubtractionMonoid.{max u1 u2} N (AddCommGroup.toDivisionAddCommMonoid.{max u1 u2} N _inst_5))))) (SMulWithZero.toSMulZeroClass.{u1, max u1 u2} R N (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (NegZeroClass.toZero.{max u1 u2} N (SubNegZeroMonoid.toNegZeroClass.{max u1 u2} N (SubtractionMonoid.toSubNegZeroMonoid.{max u1 u2} N (SubtractionCommMonoid.toSubtractionMonoid.{max u1 u2} N (AddCommGroup.toDivisionAddCommMonoid.{max u1 u2} N _inst_5))))) (MulActionWithZero.toSMulWithZero.{u1, max u1 u2} R N (Semiring.toMonoidWithZero.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (NegZeroClass.toZero.{max u1 u2} N (SubNegZeroMonoid.toNegZeroClass.{max u1 u2} N (SubtractionMonoid.toSubNegZeroMonoid.{max u1 u2} N (SubtractionCommMonoid.toSubtractionMonoid.{max u1 u2} N (AddCommGroup.toDivisionAddCommMonoid.{max u1 u2} N _inst_5))))) (Module.toMulActionWithZero.{u1, max u1 u2} R N (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{max u1 u2} N _inst_5) _inst_7))))) r y) (OfNat.ofNat.{max u1 u2} N 0 (Zero.toOfNat0.{max u1 u2} N (NegZeroClass.toZero.{max u1 u2} N (SubNegZeroMonoid.toNegZeroClass.{max u1 u2} N (SubtractionMonoid.toSubNegZeroMonoid.{max u1 u2} N (SubtractionCommMonoid.toSubtractionMonoid.{max u1 u2} N (AddCommGroup.toDivisionAddCommMonoid.{max u1 u2} N _inst_5)))))))) -> (Eq.{max (succ u1) (succ u2)} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : R) => Q) r) (FunLike.coe.{max (succ u1) (succ u2), succ u1, max (succ u1) (succ u2)} (LinearMap.{u1, u1, u1, max u1 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))) R Q (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R _inst_1)))) (AddCommGroup.toAddCommMonoid.{max u1 u2} Q _inst_2) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R _inst_1)) _inst_3) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : R) => Q) _x) (LinearMap.instFunLikeLinearMap.{u1, u1, u1, max u1 u2} R R R Q (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R _inst_1)))) (AddCommGroup.toAddCommMonoid.{max u1 u2} Q _inst_2) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R _inst_1)) _inst_3 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1)))) (Module.Baer.ExtensionOfMaxAdjoin.extendIdealTo.{u1, u2} R _inst_1 Q _inst_2 _inst_3 M N _inst_4 _inst_5 _inst_6 _inst_7 i f _inst_8 h y) r) (OfNat.ofNat.{max u1 u2} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : R) => Q) r) 0 (Zero.toOfNat0.{max u1 u2} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : R) => Q) r) (NegZeroClass.toZero.{max u1 u2} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : R) => Q) r) (SubNegZeroMonoid.toNegZeroClass.{max u1 u2} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : R) => Q) r) (SubtractionMonoid.toSubNegZeroMonoid.{max u1 u2} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : R) => Q) r) (SubtractionCommMonoid.toSubtractionMonoid.{max u1 u2} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : R) => Q) r) (AddCommGroup.toDivisionAddCommMonoid.{max u1 u2} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : R) => Q) r) _inst_2))))))))
 Case conversion may be inaccurate. Consider using '#align module.Baer.extension_of_max_adjoin.extend_ideal_to_wd' Module.Baer.ExtensionOfMaxAdjoin.extendIdealTo_wd'ₓ'. -/
 theorem ExtensionOfMaxAdjoin.extendIdealTo_wd' (h : Module.Baer R Q) {y : N} (r : R)
     (eq1 : r • y = 0) : ExtensionOfMaxAdjoin.extendIdealTo i f h y r = 0 :=
@@ -420,7 +420,7 @@ theorem ExtensionOfMaxAdjoin.extendIdealTo_wd' (h : Module.Baer R Q) {y : N} (r
 lean 3 declaration is
   forall {R : Type.{u1}} [_inst_1 : Ring.{u1} R] {Q : Type.{max u1 u2}} [_inst_2 : AddCommGroup.{max u1 u2} Q] [_inst_3 : Module.{u1, max u1 u2} R Q (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{max u1 u2} Q _inst_2)] {M : Type.{max u1 u2}} {N : Type.{max u1 u2}} [_inst_4 : AddCommGroup.{max u1 u2} M] [_inst_5 : AddCommGroup.{max u1 u2} N] [_inst_6 : Module.{u1, max u1 u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{max u1 u2} M _inst_4)] [_inst_7 : Module.{u1, max u1 u2} R N (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{max u1 u2} N _inst_5)] (i : LinearMap.{u1, u1, max u1 u2, max u1 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 N (AddCommGroup.toAddCommMonoid.{max u1 u2} M _inst_4) (AddCommGroup.toAddCommMonoid.{max u1 u2} N _inst_5) _inst_6 _inst_7) (f : LinearMap.{u1, u1, max u1 u2, max u1 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 Q (AddCommGroup.toAddCommMonoid.{max u1 u2} M _inst_4) (AddCommGroup.toAddCommMonoid.{max u1 u2} Q _inst_2) _inst_6 _inst_3) [_inst_8 : Fact (Function.Injective.{succ (max u1 u2), succ (max u1 u2)} M N (coeFn.{succ (max u1 u2), succ (max u1 u2)} (LinearMap.{u1, u1, max u1 u2, max u1 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 N (AddCommGroup.toAddCommMonoid.{max u1 u2} M _inst_4) (AddCommGroup.toAddCommMonoid.{max u1 u2} N _inst_5) _inst_6 _inst_7) (fun (_x : LinearMap.{u1, u1, max u1 u2, max u1 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 N (AddCommGroup.toAddCommMonoid.{max u1 u2} M _inst_4) (AddCommGroup.toAddCommMonoid.{max u1 u2} N _inst_5) _inst_6 _inst_7) => M -> N) (LinearMap.hasCoeToFun.{u1, u1, max u1 u2, max u1 u2} R R M N (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{max u1 u2} M _inst_4) (AddCommGroup.toAddCommMonoid.{max u1 u2} N _inst_5) _inst_6 _inst_7 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1)))) i))] (h : Module.Baer.{u1, u2} R _inst_1 Q _inst_2 _inst_3) {y : N} (r : R) (r' : R), (Eq.{succ (max u1 u2)} N (SMul.smul.{u1, max u1 u2} R N (SMulZeroClass.toHasSmul.{u1, max u1 u2} R N (AddZeroClass.toHasZero.{max u1 u2} N (AddMonoid.toAddZeroClass.{max u1 u2} N (AddCommMonoid.toAddMonoid.{max u1 u2} N (AddCommGroup.toAddCommMonoid.{max u1 u2} N _inst_5)))) (SMulWithZero.toSmulZeroClass.{u1, max u1 u2} R N (MulZeroClass.toHasZero.{u1} R (MulZeroOneClass.toMulZeroClass.{u1} R (MonoidWithZero.toMulZeroOneClass.{u1} R (Semiring.toMonoidWithZero.{u1} R 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(MulZeroOneClass.toMulZeroClass.{u1} R (MonoidWithZero.toMulZeroOneClass.{u1} R (Semiring.toMonoidWithZero.{u1} R (Ring.toSemiring.{u1} R _inst_1))))) (AddZeroClass.toHasZero.{max u1 u2} N (AddMonoid.toAddZeroClass.{max u1 u2} N (AddCommMonoid.toAddMonoid.{max u1 u2} N (AddCommGroup.toAddCommMonoid.{max u1 u2} N _inst_5)))) (MulActionWithZero.toSMulWithZero.{u1, max u1 u2} R N (Semiring.toMonoidWithZero.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (AddZeroClass.toHasZero.{max u1 u2} N (AddMonoid.toAddZeroClass.{max u1 u2} N (AddCommMonoid.toAddMonoid.{max u1 u2} N (AddCommGroup.toAddCommMonoid.{max u1 u2} N _inst_5)))) (Module.toMulActionWithZero.{u1, max u1 u2} R N (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{max u1 u2} N _inst_5) _inst_7)))) r' y)) -> (Eq.{succ (max u1 u2)} Q (coeFn.{max (succ u1) (succ (max u1 u2)), max (succ u1) (succ (max u1 u2))} (LinearMap.{u1, u1, u1, max u1 u2} R R (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) 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(AddCommGroup.toAddCommMonoid.{max u1 u2} Q _inst_2) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R _inst_1)) _inst_3) (fun (_x : LinearMap.{u1, u1, u1, max u1 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))) R Q (AddCommGroup.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toAddCommGroup.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R _inst_1)))) (AddCommGroup.toAddCommMonoid.{max u1 u2} Q _inst_2) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R _inst_1)) _inst_3) => R -> Q) (LinearMap.hasCoeToFun.{u1, u1, u1, max u1 u2} R R R Q (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toAddCommGroup.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R _inst_1)))) (AddCommGroup.toAddCommMonoid.{max u1 u2} Q _inst_2) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R _inst_1)) _inst_3 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1)))) (Module.Baer.ExtensionOfMaxAdjoin.extendIdealTo.{u1, u2} R _inst_1 Q _inst_2 _inst_3 M N _inst_4 _inst_5 _inst_6 _inst_7 i f _inst_8 h y) r'))
 but is expected to have type
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(Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{max u1 u2} M _inst_4) (AddCommGroup.toAddCommMonoid.{max u1 u2} N _inst_5) _inst_6 _inst_7 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1)))) i))] (h : Module.Baer.{u1, u2} R _inst_1 Q _inst_2 _inst_3) {y : N} (r : R) (r' : R), (Eq.{max (succ u1) (succ u2)} N (HSMul.hSMul.{u1, max u1 u2, max u1 u2} R N N (instHSMul.{u1, max u1 u2} R N (SMulZeroClass.toSMul.{u1, max u1 u2} R N (NegZeroClass.toZero.{max u1 u2} N (SubNegZeroMonoid.toNegZeroClass.{max u1 u2} N (SubtractionMonoid.toSubNegZeroMonoid.{max u1 u2} N (SubtractionCommMonoid.toSubtractionMonoid.{max u1 u2} N (AddCommGroup.toDivisionAddCommMonoid.{max u1 u2} N _inst_5))))) (SMulWithZero.toSMulZeroClass.{u1, max u1 u2} R N (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (NegZeroClass.toZero.{max u1 u2} N (SubNegZeroMonoid.toNegZeroClass.{max u1 u2} N 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(SubtractionCommMonoid.toSubtractionMonoid.{max u1 u2} N (AddCommGroup.toDivisionAddCommMonoid.{max u1 u2} N _inst_5))))) (SMulWithZero.toSMulZeroClass.{u1, max u1 u2} R N (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (NegZeroClass.toZero.{max u1 u2} N (SubNegZeroMonoid.toNegZeroClass.{max u1 u2} N (SubtractionMonoid.toSubNegZeroMonoid.{max u1 u2} N (SubtractionCommMonoid.toSubtractionMonoid.{max u1 u2} N (AddCommGroup.toDivisionAddCommMonoid.{max u1 u2} N _inst_5))))) (MulActionWithZero.toSMulWithZero.{u1, max u1 u2} R N (Semiring.toMonoidWithZero.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (NegZeroClass.toZero.{max u1 u2} N (SubNegZeroMonoid.toNegZeroClass.{max u1 u2} N (SubtractionMonoid.toSubNegZeroMonoid.{max u1 u2} N (SubtractionCommMonoid.toSubtractionMonoid.{max u1 u2} N (AddCommGroup.toDivisionAddCommMonoid.{max u1 u2} N _inst_5))))) (Module.toMulActionWithZero.{u1, max u1 u2} R N (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{max u1 u2} N _inst_5) _inst_7))))) r' y)) -> (Eq.{max (succ u1) (succ u2)} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : R) => Q) r) (FunLike.coe.{max (succ u1) (succ u2), succ u1, max (succ u1) (succ u2)} (LinearMap.{u1, u1, u1, max u1 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))) R Q (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R _inst_1)))) (AddCommGroup.toAddCommMonoid.{max u1 u2} Q _inst_2) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R _inst_1)) _inst_3) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : R) => Q) _x) (LinearMap.instFunLikeLinearMap.{u1, u1, u1, max u1 u2} R R R Q (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R _inst_1)))) (AddCommGroup.toAddCommMonoid.{max u1 u2} Q _inst_2) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R _inst_1)) _inst_3 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1)))) (Module.Baer.ExtensionOfMaxAdjoin.extendIdealTo.{u1, u2} R _inst_1 Q _inst_2 _inst_3 M N _inst_4 _inst_5 _inst_6 _inst_7 i f _inst_8 h y) r) (FunLike.coe.{max (succ u1) (succ u2), succ u1, max (succ u1) (succ u2)} (LinearMap.{u1, u1, u1, max u1 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))) R Q (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R _inst_1)))) (AddCommGroup.toAddCommMonoid.{max u1 u2} Q _inst_2) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R _inst_1)) _inst_3) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : R) => Q) _x) (LinearMap.instFunLikeLinearMap.{u1, u1, u1, max u1 u2} R R R Q (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R _inst_1)))) (AddCommGroup.toAddCommMonoid.{max u1 u2} Q _inst_2) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R _inst_1)) _inst_3 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1)))) (Module.Baer.ExtensionOfMaxAdjoin.extendIdealTo.{u1, u2} R _inst_1 Q _inst_2 _inst_3 M N _inst_4 _inst_5 _inst_6 _inst_7 i f _inst_8 h y) r'))
+  forall {R : Type.{u1}} [_inst_1 : Ring.{u1} R] {Q : TypeMax.{u2, u1}} [_inst_2 : AddCommGroup.{max u1 u2} Q] [_inst_3 : Module.{u1, max u1 u2} R Q (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{max u1 u2} Q _inst_2)] {M : Type.{max u1 u2}} {N : Type.{max u1 u2}} [_inst_4 : AddCommGroup.{max u1 u2} M] [_inst_5 : AddCommGroup.{max u1 u2} N] [_inst_6 : Module.{u1, max u1 u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{max u1 u2} M _inst_4)] [_inst_7 : Module.{u1, max u1 u2} R N (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{max u1 u2} N _inst_5)] (i : LinearMap.{u1, u1, max u1 u2, max u1 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 N (AddCommGroup.toAddCommMonoid.{max u1 u2} M _inst_4) (AddCommGroup.toAddCommMonoid.{max u1 u2} N _inst_5) _inst_6 _inst_7) (f : LinearMap.{u1, u1, max u1 u2, max u1 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 Q (AddCommGroup.toAddCommMonoid.{max u1 u2} M _inst_4) (AddCommGroup.toAddCommMonoid.{max u1 u2} Q _inst_2) _inst_6 _inst_3) [_inst_8 : Fact (Function.Injective.{max (succ u1) (succ u2), max (succ u1) (succ u2)} M N (FunLike.coe.{max (succ u1) (succ u2), max (succ u1) (succ u2), max (succ u1) (succ u2)} (LinearMap.{u1, u1, max u1 u2, max u1 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 N (AddCommGroup.toAddCommMonoid.{max u1 u2} M _inst_4) (AddCommGroup.toAddCommMonoid.{max u1 u2} N _inst_5) _inst_6 _inst_7) M (fun (_x : M) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : M) => N) _x) (LinearMap.instFunLikeLinearMap.{u1, u1, max u1 u2, max u1 u2} R R M N (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{max u1 u2} M _inst_4) (AddCommGroup.toAddCommMonoid.{max u1 u2} N _inst_5) _inst_6 _inst_7 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1)))) i))] (h : Module.Baer.{u1, u2} R _inst_1 Q _inst_2 _inst_3) {y : N} (r : R) (r' : R), (Eq.{max (succ u1) (succ u2)} N (HSMul.hSMul.{u1, max u1 u2, max u1 u2} R N N (instHSMul.{u1, max u1 u2} R N (SMulZeroClass.toSMul.{u1, max u1 u2} R N (NegZeroClass.toZero.{max u1 u2} N (SubNegZeroMonoid.toNegZeroClass.{max u1 u2} N (SubtractionMonoid.toSubNegZeroMonoid.{max u1 u2} N (SubtractionCommMonoid.toSubtractionMonoid.{max u1 u2} N (AddCommGroup.toDivisionAddCommMonoid.{max u1 u2} N _inst_5))))) (SMulWithZero.toSMulZeroClass.{u1, max u1 u2} R N (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (NegZeroClass.toZero.{max u1 u2} N (SubNegZeroMonoid.toNegZeroClass.{max u1 u2} N (SubtractionMonoid.toSubNegZeroMonoid.{max u1 u2} N (SubtractionCommMonoid.toSubtractionMonoid.{max u1 u2} N (AddCommGroup.toDivisionAddCommMonoid.{max u1 u2} N _inst_5))))) (MulActionWithZero.toSMulWithZero.{u1, max u1 u2} R N (Semiring.toMonoidWithZero.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (NegZeroClass.toZero.{max u1 u2} N (SubNegZeroMonoid.toNegZeroClass.{max u1 u2} N (SubtractionMonoid.toSubNegZeroMonoid.{max u1 u2} N (SubtractionCommMonoid.toSubtractionMonoid.{max u1 u2} N (AddCommGroup.toDivisionAddCommMonoid.{max u1 u2} N _inst_5))))) (Module.toMulActionWithZero.{u1, max u1 u2} R N (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{max u1 u2} N _inst_5) _inst_7))))) r y) (HSMul.hSMul.{u1, max u1 u2, max u1 u2} R N N (instHSMul.{u1, max u1 u2} R N (SMulZeroClass.toSMul.{u1, max u1 u2} R N (NegZeroClass.toZero.{max u1 u2} N (SubNegZeroMonoid.toNegZeroClass.{max u1 u2} N (SubtractionMonoid.toSubNegZeroMonoid.{max u1 u2} N (SubtractionCommMonoid.toSubtractionMonoid.{max u1 u2} N (AddCommGroup.toDivisionAddCommMonoid.{max u1 u2} N _inst_5))))) (SMulWithZero.toSMulZeroClass.{u1, max u1 u2} R N (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (NegZeroClass.toZero.{max u1 u2} N (SubNegZeroMonoid.toNegZeroClass.{max u1 u2} N (SubtractionMonoid.toSubNegZeroMonoid.{max u1 u2} N (SubtractionCommMonoid.toSubtractionMonoid.{max u1 u2} N (AddCommGroup.toDivisionAddCommMonoid.{max u1 u2} N _inst_5))))) (MulActionWithZero.toSMulWithZero.{u1, max u1 u2} R N (Semiring.toMonoidWithZero.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (NegZeroClass.toZero.{max u1 u2} N (SubNegZeroMonoid.toNegZeroClass.{max u1 u2} N (SubtractionMonoid.toSubNegZeroMonoid.{max u1 u2} N (SubtractionCommMonoid.toSubtractionMonoid.{max u1 u2} N (AddCommGroup.toDivisionAddCommMonoid.{max u1 u2} N _inst_5))))) (Module.toMulActionWithZero.{u1, max u1 u2} R N (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{max u1 u2} N _inst_5) _inst_7))))) r' y)) -> (Eq.{max (succ u1) (succ u2)} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : R) => Q) r) (FunLike.coe.{max (succ u1) (succ u2), succ u1, max (succ u1) (succ u2)} (LinearMap.{u1, u1, u1, max u1 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))) R Q (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R _inst_1)))) (AddCommGroup.toAddCommMonoid.{max u1 u2} Q _inst_2) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R _inst_1)) _inst_3) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : R) => Q) _x) (LinearMap.instFunLikeLinearMap.{u1, u1, u1, max u1 u2} R R R Q (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R _inst_1)))) (AddCommGroup.toAddCommMonoid.{max u1 u2} Q _inst_2) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R _inst_1)) _inst_3 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1)))) (Module.Baer.ExtensionOfMaxAdjoin.extendIdealTo.{u1, u2} R _inst_1 Q _inst_2 _inst_3 M N _inst_4 _inst_5 _inst_6 _inst_7 i f _inst_8 h y) r) (FunLike.coe.{max (succ u1) (succ u2), succ u1, max (succ u1) (succ u2)} (LinearMap.{u1, u1, u1, max u1 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))) R Q (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R _inst_1)))) (AddCommGroup.toAddCommMonoid.{max u1 u2} Q _inst_2) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R _inst_1)) _inst_3) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : R) => Q) _x) (LinearMap.instFunLikeLinearMap.{u1, u1, u1, max u1 u2} R R R Q (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R _inst_1)))) (AddCommGroup.toAddCommMonoid.{max u1 u2} Q _inst_2) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R _inst_1)) _inst_3 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1)))) (Module.Baer.ExtensionOfMaxAdjoin.extendIdealTo.{u1, u2} R _inst_1 Q _inst_2 _inst_3 M N _inst_4 _inst_5 _inst_6 _inst_7 i f _inst_8 h y) r'))
 Case conversion may be inaccurate. Consider using '#align module.Baer.extension_of_max_adjoin.extend_ideal_to_wd Module.Baer.ExtensionOfMaxAdjoin.extendIdealTo_wdₓ'. -/
 theorem ExtensionOfMaxAdjoin.extendIdealTo_wd (h : Module.Baer R Q) {y : N} (r r' : R)
     (eq1 : r • y = r' • y) :
@@ -435,7 +435,7 @@ theorem ExtensionOfMaxAdjoin.extendIdealTo_wd (h : Module.Baer R Q) {y : N} (r r
 lean 3 declaration is
   forall {R : Type.{u1}} [_inst_1 : Ring.{u1} R] {Q : Type.{max u1 u2}} [_inst_2 : AddCommGroup.{max u1 u2} Q] [_inst_3 : Module.{u1, max u1 u2} R Q (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{max u1 u2} Q _inst_2)] {M : Type.{max u1 u2}} {N : Type.{max u1 u2}} [_inst_4 : AddCommGroup.{max u1 u2} M] [_inst_5 : AddCommGroup.{max u1 u2} N] [_inst_6 : Module.{u1, max u1 u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{max u1 u2} M _inst_4)] [_inst_7 : Module.{u1, max u1 u2} R N (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{max u1 u2} N _inst_5)] (i : LinearMap.{u1, u1, max u1 u2, max u1 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 N (AddCommGroup.toAddCommMonoid.{max u1 u2} M _inst_4) (AddCommGroup.toAddCommMonoid.{max u1 u2} N _inst_5) _inst_6 _inst_7) (f : LinearMap.{u1, u1, max u1 u2, max u1 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 Q (AddCommGroup.toAddCommMonoid.{max u1 u2} M _inst_4) (AddCommGroup.toAddCommMonoid.{max u1 u2} Q _inst_2) _inst_6 _inst_3) [_inst_8 : Fact (Function.Injective.{succ (max u1 u2), succ (max u1 u2)} M N (coeFn.{succ (max u1 u2), succ (max u1 u2)} (LinearMap.{u1, u1, max u1 u2, max u1 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 N (AddCommGroup.toAddCommMonoid.{max u1 u2} M _inst_4) (AddCommGroup.toAddCommMonoid.{max u1 u2} N _inst_5) _inst_6 _inst_7) (fun (_x : LinearMap.{u1, u1, max u1 u2, max u1 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 N (AddCommGroup.toAddCommMonoid.{max u1 u2} M _inst_4) (AddCommGroup.toAddCommMonoid.{max u1 u2} N _inst_5) _inst_6 _inst_7) => M -> N) (LinearMap.hasCoeToFun.{u1, u1, max u1 u2, max u1 u2} R R M N (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{max u1 u2} M _inst_4) (AddCommGroup.toAddCommMonoid.{max u1 u2} N _inst_5) _inst_6 _inst_7 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1)))) i))] (h : Module.Baer.{u1, u2} R _inst_1 Q _inst_2 _inst_3) {y : N} (r : R) (hr : Membership.Mem.{max u1 u2, max u1 u2} N (Submodule.{u1, max u1 u2} R N (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{max u1 u2} N _inst_5) _inst_7) (SetLike.hasMem.{max u1 u2, max u1 u2} (Submodule.{u1, max u1 u2} R N (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{max u1 u2} N _inst_5) _inst_7) N (Submodule.setLike.{u1, max u1 u2} R N (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{max u1 u2} N _inst_5) _inst_7)) (SMul.smul.{u1, max u1 u2} R N (SMulZeroClass.toHasSmul.{u1, max u1 u2} R N (AddZeroClass.toHasZero.{max u1 u2} N (AddMonoid.toAddZeroClass.{max u1 u2} N (AddCommMonoid.toAddMonoid.{max u1 u2} N (AddCommGroup.toAddCommMonoid.{max u1 u2} N _inst_5)))) (SMulWithZero.toSmulZeroClass.{u1, max u1 u2} R N (MulZeroClass.toHasZero.{u1} R (MulZeroOneClass.toMulZeroClass.{u1} R (MonoidWithZero.toMulZeroOneClass.{u1} R (Semiring.toMonoidWithZero.{u1} R (Ring.toSemiring.{u1} R _inst_1))))) (AddZeroClass.toHasZero.{max u1 u2} N (AddMonoid.toAddZeroClass.{max u1 u2} N (AddCommMonoid.toAddMonoid.{max u1 u2} N (AddCommGroup.toAddCommMonoid.{max u1 u2} N _inst_5)))) (MulActionWithZero.toSMulWithZero.{u1, max u1 u2} R N (Semiring.toMonoidWithZero.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (AddZeroClass.toHasZero.{max u1 u2} N (AddMonoid.toAddZeroClass.{max u1 u2} N (AddCommMonoid.toAddMonoid.{max u1 u2} N (AddCommGroup.toAddCommMonoid.{max u1 u2} N _inst_5)))) (Module.toMulActionWithZero.{u1, max u1 u2} R N (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{max u1 u2} N _inst_5) _inst_7)))) r y) (LinearPMap.domain.{u1, max u1 u2, max u1 u2} R _inst_1 N _inst_5 _inst_7 Q _inst_2 _inst_3 (Module.Baer.ExtensionOf.toLinearPmap.{u1, u2} R _inst_1 Q _inst_2 _inst_3 M N _inst_4 _inst_5 _inst_6 _inst_7 i f (Module.Baer.extensionOfMax.{u1, u2} R _inst_1 Q _inst_2 _inst_3 M N _inst_4 _inst_5 _inst_6 _inst_7 i f _inst_8)))), Eq.{succ (max u1 u2)} Q (coeFn.{max (succ u1) (succ (max u1 u2)), max (succ u1) (succ (max u1 u2))} (LinearMap.{u1, u1, u1, max u1 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))) R Q (AddCommGroup.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toAddCommGroup.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R _inst_1)))) (AddCommGroup.toAddCommMonoid.{max u1 u2} Q _inst_2) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R _inst_1)) _inst_3) (fun (_x : LinearMap.{u1, u1, u1, max u1 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))) R Q (AddCommGroup.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toAddCommGroup.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R _inst_1)))) (AddCommGroup.toAddCommMonoid.{max u1 u2} Q _inst_2) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R _inst_1)) _inst_3) => R -> Q) (LinearMap.hasCoeToFun.{u1, u1, u1, max u1 u2} R R R Q (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toAddCommGroup.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R _inst_1)))) (AddCommGroup.toAddCommMonoid.{max u1 u2} Q _inst_2) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R _inst_1)) _inst_3 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1)))) (Module.Baer.ExtensionOfMaxAdjoin.extendIdealTo.{u1, u2} R _inst_1 Q _inst_2 _inst_3 M N _inst_4 _inst_5 _inst_6 _inst_7 i f _inst_8 h y) r) (coeFn.{succ (max u1 u2), succ (max u1 u2)} (LinearPMap.{u1, max u1 u2, max u1 u2} R _inst_1 N _inst_5 _inst_7 Q _inst_2 _inst_3) (fun (f : LinearPMap.{u1, max u1 u2, max u1 u2} R _inst_1 N _inst_5 _inst_7 Q _inst_2 _inst_3) => (coeSort.{succ (max u1 u2), succ (succ (max u1 u2))} (Submodule.{u1, max u1 u2} R N (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{max u1 u2} N _inst_5) _inst_7) Type.{max u1 u2} (SetLike.hasCoeToSort.{max u1 u2, max u1 u2} (Submodule.{u1, max u1 u2} R N (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{max u1 u2} N _inst_5) _inst_7) N (Submodule.setLike.{u1, max u1 u2} R N (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{max u1 u2} N _inst_5) _inst_7)) (LinearPMap.domain.{u1, max u1 u2, max u1 u2} R _inst_1 N _inst_5 _inst_7 Q _inst_2 _inst_3 f)) -> Q) (LinearPMap.hasCoeToFun.{u1, max u1 u2, max u1 u2} R _inst_1 N _inst_5 _inst_7 Q _inst_2 _inst_3) (Module.Baer.ExtensionOf.toLinearPmap.{u1, u2} R _inst_1 Q _inst_2 _inst_3 M N _inst_4 _inst_5 _inst_6 _inst_7 i f (Module.Baer.extensionOfMax.{u1, u2} R _inst_1 Q _inst_2 _inst_3 M N _inst_4 _inst_5 _inst_6 _inst_7 i f _inst_8)) (Subtype.mk.{succ (max u1 u2)} N (fun (x : N) => Membership.Mem.{max u1 u2, max u1 u2} N (Submodule.{u1, max u1 u2} R N (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{max u1 u2} N _inst_5) _inst_7) (SetLike.hasMem.{max u1 u2, max u1 u2} (Submodule.{u1, max u1 u2} R N (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{max u1 u2} N _inst_5) _inst_7) N (Submodule.setLike.{u1, max u1 u2} R N (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{max u1 u2} N _inst_5) _inst_7)) x (LinearPMap.domain.{u1, max u1 u2, max u1 u2} R _inst_1 N _inst_5 _inst_7 Q _inst_2 _inst_3 (Module.Baer.ExtensionOf.toLinearPmap.{u1, u2} R _inst_1 Q _inst_2 _inst_3 M N _inst_4 _inst_5 _inst_6 _inst_7 i f (Module.Baer.extensionOfMax.{u1, u2} R _inst_1 Q _inst_2 _inst_3 M N _inst_4 _inst_5 _inst_6 _inst_7 i f _inst_8)))) (SMul.smul.{u1, max u1 u2} R N (SMulZeroClass.toHasSmul.{u1, max u1 u2} R N (AddZeroClass.toHasZero.{max u1 u2} N (AddMonoid.toAddZeroClass.{max u1 u2} N (AddCommMonoid.toAddMonoid.{max u1 u2} N (AddCommGroup.toAddCommMonoid.{max u1 u2} N _inst_5)))) (SMulWithZero.toSmulZeroClass.{u1, max u1 u2} R N (MulZeroClass.toHasZero.{u1} R (MulZeroOneClass.toMulZeroClass.{u1} R (MonoidWithZero.toMulZeroOneClass.{u1} R (Semiring.toMonoidWithZero.{u1} R (Ring.toSemiring.{u1} R _inst_1))))) (AddZeroClass.toHasZero.{max u1 u2} N (AddMonoid.toAddZeroClass.{max u1 u2} N (AddCommMonoid.toAddMonoid.{max u1 u2} N (AddCommGroup.toAddCommMonoid.{max u1 u2} N _inst_5)))) (MulActionWithZero.toSMulWithZero.{u1, max u1 u2} R N (Semiring.toMonoidWithZero.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (AddZeroClass.toHasZero.{max u1 u2} N (AddMonoid.toAddZeroClass.{max u1 u2} N (AddCommMonoid.toAddMonoid.{max u1 u2} N (AddCommGroup.toAddCommMonoid.{max u1 u2} N _inst_5)))) (Module.toMulActionWithZero.{u1, max u1 u2} R N (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{max u1 u2} N _inst_5) _inst_7)))) r y) hr))
 but is expected to have type
-  forall {R : Type.{u1}} [_inst_1 : Ring.{u1} R] {Q : TypeMax.{u2, u1}} [_inst_2 : AddCommGroup.{max u1 u2} Q] [_inst_3 : Module.{u1, max u1 u2} R Q (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{max u1 u2} Q _inst_2)] {M : Type.{max u1 u2}} {N : Type.{max u1 u2}} [_inst_4 : AddCommGroup.{max u1 u2} M] [_inst_5 : AddCommGroup.{max u1 u2} N] [_inst_6 : Module.{u1, max u1 u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{max u1 u2} M _inst_4)] [_inst_7 : Module.{u1, max u1 u2} R N (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{max u1 u2} N _inst_5)] (i : LinearMap.{u1, u1, max u1 u2, max u1 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 N (AddCommGroup.toAddCommMonoid.{max u1 u2} M _inst_4) (AddCommGroup.toAddCommMonoid.{max u1 u2} N _inst_5) _inst_6 _inst_7) (f : LinearMap.{u1, u1, max u1 u2, max u1 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 Q (AddCommGroup.toAddCommMonoid.{max u1 u2} M _inst_4) (AddCommGroup.toAddCommMonoid.{max u1 u2} Q _inst_2) _inst_6 _inst_3) [_inst_8 : Fact (Function.Injective.{max (succ u1) (succ u2), max (succ u1) (succ u2)} M N (FunLike.coe.{max (succ u1) (succ u2), max (succ u1) (succ u2), max (succ u1) (succ u2)} (LinearMap.{u1, u1, max u1 u2, max u1 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 N (AddCommGroup.toAddCommMonoid.{max u1 u2} M _inst_4) (AddCommGroup.toAddCommMonoid.{max u1 u2} N _inst_5) _inst_6 _inst_7) M (fun (_x : M) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : M) => N) _x) (LinearMap.instFunLikeLinearMap.{u1, u1, max u1 u2, max u1 u2} R R M N (Ring.toSemiring.{u1} R _inst_1) 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_inst_1)))) (AddCommGroup.toAddCommMonoid.{max u1 u2} Q _inst_2) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R _inst_1)) _inst_3) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : R) => Q) _x) (LinearMap.instFunLikeLinearMap.{u1, u1, u1, max u1 u2} R R R Q (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R _inst_1)))) (AddCommGroup.toAddCommMonoid.{max u1 u2} Q _inst_2) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R _inst_1)) _inst_3 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1)))) (Module.Baer.ExtensionOfMaxAdjoin.extendIdealTo.{u1, u2} R _inst_1 Q _inst_2 _inst_3 M N _inst_4 _inst_5 _inst_6 _inst_7 i f _inst_8 h y) r) (LinearPMap.toFun'.{u1, max u1 u2, max u1 u2} R _inst_1 N _inst_5 _inst_7 Q _inst_2 _inst_3 (Module.Baer.ExtensionOf.toLinearPMap.{u1, u2} R _inst_1 Q _inst_2 _inst_3 M N _inst_4 _inst_5 _inst_6 _inst_7 i f (Module.Baer.extensionOfMax.{u1, u2} R _inst_1 Q _inst_2 _inst_3 M N _inst_4 _inst_5 _inst_6 _inst_7 i f _inst_8)) (Subtype.mk.{max (succ u1) (succ u2)} N (fun (x : N) => Membership.mem.{max u1 u2, max u1 u2} N (Submodule.{u1, max u1 u2} R N (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{max u1 u2} N _inst_5) _inst_7) (SetLike.instMembership.{max u1 u2, max u1 u2} (Submodule.{u1, max u1 u2} R N (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{max u1 u2} N _inst_5) _inst_7) N (Submodule.setLike.{u1, max u1 u2} R N (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{max u1 u2} N _inst_5) _inst_7)) x (LinearPMap.domain.{u1, max u1 u2, max u1 u2} R _inst_1 N _inst_5 _inst_7 Q _inst_2 _inst_3 (Module.Baer.ExtensionOf.toLinearPMap.{u1, u2} R _inst_1 Q _inst_2 _inst_3 M N _inst_4 _inst_5 _inst_6 _inst_7 i f 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(Ring.toSemiring.{u1} R _inst_1)) (NegZeroClass.toZero.{max u1 u2} N (SubNegZeroMonoid.toNegZeroClass.{max u1 u2} N (SubtractionMonoid.toSubNegZeroMonoid.{max u1 u2} N (SubtractionCommMonoid.toSubtractionMonoid.{max u1 u2} N (AddCommGroup.toDivisionAddCommMonoid.{max u1 u2} N _inst_5))))) (Module.toMulActionWithZero.{u1, max u1 u2} R N (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{max u1 u2} N _inst_5) _inst_7))))) r y) hr))
+  forall {R : Type.{u1}} [_inst_1 : Ring.{u1} R] {Q : TypeMax.{u2, u1}} [_inst_2 : AddCommGroup.{max u1 u2} Q] [_inst_3 : Module.{u1, max u1 u2} R Q (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{max u1 u2} Q _inst_2)] {M : Type.{max u1 u2}} {N : Type.{max u1 u2}} [_inst_4 : AddCommGroup.{max u1 u2} M] [_inst_5 : AddCommGroup.{max u1 u2} N] [_inst_6 : Module.{u1, max u1 u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{max u1 u2} M _inst_4)] [_inst_7 : Module.{u1, max u1 u2} R N (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{max u1 u2} N _inst_5)] (i : LinearMap.{u1, u1, max u1 u2, max u1 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 N (AddCommGroup.toAddCommMonoid.{max u1 u2} M _inst_4) (AddCommGroup.toAddCommMonoid.{max u1 u2} N _inst_5) _inst_6 _inst_7) (f : LinearMap.{u1, u1, max u1 u2, max u1 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 Q (AddCommGroup.toAddCommMonoid.{max u1 u2} M _inst_4) (AddCommGroup.toAddCommMonoid.{max u1 u2} Q _inst_2) _inst_6 _inst_3) [_inst_8 : Fact (Function.Injective.{max (succ u1) (succ u2), max (succ u1) (succ u2)} M N (FunLike.coe.{max (succ u1) (succ u2), max (succ u1) (succ u2), max (succ u1) (succ u2)} (LinearMap.{u1, u1, max u1 u2, max u1 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 N (AddCommGroup.toAddCommMonoid.{max u1 u2} M _inst_4) (AddCommGroup.toAddCommMonoid.{max u1 u2} N _inst_5) _inst_6 _inst_7) M (fun (_x : M) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : M) => N) _x) (LinearMap.instFunLikeLinearMap.{u1, u1, max u1 u2, max u1 u2} R R M N (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{max u1 u2} M _inst_4) (AddCommGroup.toAddCommMonoid.{max u1 u2} N _inst_5) _inst_6 _inst_7 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1)))) i))] (h : Module.Baer.{u1, u2} R _inst_1 Q _inst_2 _inst_3) {y : N} (r : R) (hr : Membership.mem.{max u1 u2, max u1 u2} N (Submodule.{u1, max u1 u2} R N (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{max u1 u2} N _inst_5) _inst_7) (SetLike.instMembership.{max u1 u2, max u1 u2} (Submodule.{u1, max u1 u2} R N (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{max u1 u2} N _inst_5) _inst_7) N (Submodule.setLike.{u1, max u1 u2} R N (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{max u1 u2} N _inst_5) _inst_7)) (HSMul.hSMul.{u1, max u1 u2, max u1 u2} R N N (instHSMul.{u1, max u1 u2} R N (SMulZeroClass.toSMul.{u1, max u1 u2} R N (NegZeroClass.toZero.{max u1 u2} N (SubNegZeroMonoid.toNegZeroClass.{max u1 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_inst_1)))) (AddCommGroup.toAddCommMonoid.{max u1 u2} Q _inst_2) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R _inst_1)) _inst_3) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : R) => Q) _x) (LinearMap.instFunLikeLinearMap.{u1, u1, u1, max u1 u2} R R R Q (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R _inst_1)))) (AddCommGroup.toAddCommMonoid.{max u1 u2} Q _inst_2) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R _inst_1)) _inst_3 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1)))) (Module.Baer.ExtensionOfMaxAdjoin.extendIdealTo.{u1, u2} R _inst_1 Q _inst_2 _inst_3 M N _inst_4 _inst_5 _inst_6 _inst_7 i f _inst_8 h y) r) (LinearPMap.toFun'.{u1, max u1 u2, max u1 u2} R _inst_1 N _inst_5 _inst_7 Q _inst_2 _inst_3 (Module.Baer.ExtensionOf.toLinearPMap.{u1, u2} R _inst_1 Q _inst_2 _inst_3 M N _inst_4 _inst_5 _inst_6 _inst_7 i f (Module.Baer.extensionOfMax.{u1, u2} R _inst_1 Q _inst_2 _inst_3 M N _inst_4 _inst_5 _inst_6 _inst_7 i f _inst_8)) (Subtype.mk.{max (succ u1) (succ u2)} N (fun (x : N) => Membership.mem.{max u1 u2, max u1 u2} N (Submodule.{u1, max u1 u2} R N (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{max u1 u2} N _inst_5) _inst_7) (SetLike.instMembership.{max u1 u2, max u1 u2} (Submodule.{u1, max u1 u2} R N (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{max u1 u2} N _inst_5) _inst_7) N (Submodule.setLike.{u1, max u1 u2} R N (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{max u1 u2} N _inst_5) _inst_7)) x (LinearPMap.domain.{u1, max u1 u2, max u1 u2} R _inst_1 N _inst_5 _inst_7 Q _inst_2 _inst_3 (Module.Baer.ExtensionOf.toLinearPMap.{u1, u2} R _inst_1 Q _inst_2 _inst_3 M N _inst_4 _inst_5 _inst_6 _inst_7 i f 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(Ring.toSemiring.{u1} R _inst_1)) (NegZeroClass.toZero.{max u1 u2} N (SubNegZeroMonoid.toNegZeroClass.{max u1 u2} N (SubtractionMonoid.toSubNegZeroMonoid.{max u1 u2} N (SubtractionCommMonoid.toSubtractionMonoid.{max u1 u2} N (AddCommGroup.toDivisionAddCommMonoid.{max u1 u2} N _inst_5))))) (Module.toMulActionWithZero.{u1, max u1 u2} R N (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{max u1 u2} N _inst_5) _inst_7))))) r y) hr))
 Case conversion may be inaccurate. Consider using '#align module.Baer.extension_of_max_adjoin.extend_ideal_to_eq Module.Baer.ExtensionOfMaxAdjoin.extendIdealTo_eqₓ'. -/
 theorem ExtensionOfMaxAdjoin.extendIdealTo_eq (h : Module.Baer R Q) {y : N} (r : R)
     (hr : r • y ∈ (extensionOfMax i f).domain) :
@@ -449,7 +449,7 @@ theorem ExtensionOfMaxAdjoin.extendIdealTo_eq (h : Module.Baer R Q) {y : N} (r :
 lean 3 declaration is
   forall {R : Type.{u1}} [_inst_1 : Ring.{u1} R] {Q : Type.{max u1 u2}} [_inst_2 : AddCommGroup.{max u1 u2} Q] [_inst_3 : Module.{u1, max u1 u2} R Q (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{max u1 u2} Q _inst_2)] {M : Type.{max u1 u2}} {N : Type.{max u1 u2}} [_inst_4 : AddCommGroup.{max u1 u2} M] [_inst_5 : AddCommGroup.{max u1 u2} N] [_inst_6 : Module.{u1, max u1 u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{max u1 u2} M _inst_4)] [_inst_7 : Module.{u1, max u1 u2} R N (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{max u1 u2} N _inst_5)] (i : LinearMap.{u1, u1, max u1 u2, max u1 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 N (AddCommGroup.toAddCommMonoid.{max u1 u2} M _inst_4) (AddCommGroup.toAddCommMonoid.{max u1 u2} N _inst_5) _inst_6 _inst_7) (f : LinearMap.{u1, u1, max u1 u2, max u1 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 Q (AddCommGroup.toAddCommMonoid.{max u1 u2} M _inst_4) (AddCommGroup.toAddCommMonoid.{max u1 u2} Q _inst_2) _inst_6 _inst_3) [_inst_8 : Fact (Function.Injective.{succ (max u1 u2), succ (max u1 u2)} M N (coeFn.{succ (max u1 u2), succ (max u1 u2)} (LinearMap.{u1, u1, max u1 u2, max u1 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 N (AddCommGroup.toAddCommMonoid.{max u1 u2} M _inst_4) (AddCommGroup.toAddCommMonoid.{max u1 u2} N _inst_5) _inst_6 _inst_7) (fun (_x : LinearMap.{u1, u1, max u1 u2, max u1 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 N (AddCommGroup.toAddCommMonoid.{max u1 u2} M _inst_4) (AddCommGroup.toAddCommMonoid.{max u1 u2} N _inst_5) _inst_6 _inst_7) => M -> N) (LinearMap.hasCoeToFun.{u1, u1, max u1 u2, max u1 u2} R R M N (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{max u1 u2} M _inst_4) (AddCommGroup.toAddCommMonoid.{max u1 u2} N _inst_5) _inst_6 _inst_7 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1)))) i))], (Module.Baer.{u1, u2} R _inst_1 Q _inst_2 _inst_3) -> (forall {y : N}, (coeSort.{succ (max u1 u2), succ (succ (max u1 u2))} (Submodule.{u1, max u1 u2} R N (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{max u1 u2} N _inst_5) _inst_7) Type.{max u1 u2} (SetLike.hasCoeToSort.{max u1 u2, max u1 u2} (Submodule.{u1, max u1 u2} R N (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{max u1 u2} N _inst_5) _inst_7) N (Submodule.setLike.{u1, max u1 u2} R N (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{max u1 u2} N _inst_5) _inst_7)) (Sup.sup.{max u1 u2} (Submodule.{u1, max u1 u2} R N (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{max u1 u2} N _inst_5) _inst_7) (SemilatticeSup.toHasSup.{max u1 u2} (Submodule.{u1, max u1 u2} R N (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{max u1 u2} N _inst_5) _inst_7) (Lattice.toSemilatticeSup.{max u1 u2} (Submodule.{u1, max u1 u2} R N (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{max u1 u2} N _inst_5) _inst_7) (ConditionallyCompleteLattice.toLattice.{max u1 u2} (Submodule.{u1, max u1 u2} R N (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{max u1 u2} N _inst_5) _inst_7) (CompleteLattice.toConditionallyCompleteLattice.{max u1 u2} (Submodule.{u1, max u1 u2} R N (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{max u1 u2} N _inst_5) _inst_7) (Submodule.completeLattice.{u1, max u1 u2} R N (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{max u1 u2} N _inst_5) _inst_7))))) (LinearPMap.domain.{u1, max u1 u2, max u1 u2} R _inst_1 N _inst_5 _inst_7 Q _inst_2 _inst_3 (Module.Baer.ExtensionOf.toLinearPmap.{u1, u2} R _inst_1 Q _inst_2 _inst_3 M N _inst_4 _inst_5 _inst_6 _inst_7 i f (Module.Baer.extensionOfMax.{u1, u2} R _inst_1 Q _inst_2 _inst_3 M N _inst_4 _inst_5 _inst_6 _inst_7 i f _inst_8))) (Submodule.span.{u1, max u1 u2} R N (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{max u1 u2} N _inst_5) _inst_7 (Singleton.singleton.{max u1 u2, max u1 u2} N (Set.{max u1 u2} N) (Set.hasSingleton.{max u1 u2} N) y)))) -> Q)
 but is expected to have type
-  forall {R : Type.{u1}} [_inst_1 : Ring.{u1} R] {Q : TypeMax.{u2, u1}} [_inst_2 : AddCommGroup.{max u1 u2} Q] [_inst_3 : Module.{u1, max u1 u2} R Q (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{max u1 u2} Q _inst_2)] {M : Type.{max u1 u2}} {N : Type.{max u1 u2}} [_inst_4 : AddCommGroup.{max u1 u2} M] [_inst_5 : AddCommGroup.{max u1 u2} N] [_inst_6 : Module.{u1, max u1 u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{max u1 u2} M _inst_4)] [_inst_7 : Module.{u1, max u1 u2} R N (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{max u1 u2} N _inst_5)] (i : LinearMap.{u1, u1, max u1 u2, max u1 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 N (AddCommGroup.toAddCommMonoid.{max u1 u2} M _inst_4) (AddCommGroup.toAddCommMonoid.{max u1 u2} N _inst_5) _inst_6 _inst_7) (f : LinearMap.{u1, u1, max u1 u2, max u1 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 Q (AddCommGroup.toAddCommMonoid.{max u1 u2} M _inst_4) (AddCommGroup.toAddCommMonoid.{max u1 u2} Q _inst_2) _inst_6 _inst_3) [_inst_8 : Fact (Function.Injective.{max (succ u1) (succ u2), max (succ u1) (succ u2)} M N (FunLike.coe.{max (succ u1) (succ u2), max (succ u1) (succ u2), max (succ u1) (succ u2)} (LinearMap.{u1, u1, max u1 u2, max u1 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 N (AddCommGroup.toAddCommMonoid.{max u1 u2} M _inst_4) (AddCommGroup.toAddCommMonoid.{max u1 u2} N _inst_5) _inst_6 _inst_7) M (fun (_x : M) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : M) => N) _x) (LinearMap.instFunLikeLinearMap.{u1, u1, max u1 u2, max u1 u2} R R M N (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{max u1 u2} M _inst_4) (AddCommGroup.toAddCommMonoid.{max u1 u2} N _inst_5) _inst_6 _inst_7 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1)))) i))], (Module.Baer.{u1, u2} R _inst_1 Q _inst_2 _inst_3) -> (forall {y : N}, (Subtype.{succ (max u1 u2)} N (fun (x : N) => Membership.mem.{max u1 u2, max u1 u2} N (Submodule.{u1, max u1 u2} R N (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{max u1 u2} N _inst_5) _inst_7) (SetLike.instMembership.{max u1 u2, max u1 u2} (Submodule.{u1, max u1 u2} R N (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{max u1 u2} N _inst_5) _inst_7) N (Submodule.setLike.{u1, max u1 u2} R N (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{max u1 u2} N _inst_5) _inst_7)) x (Module.Baer.supExtensionOfMaxSingleton.{u1, u2} R _inst_1 Q _inst_2 _inst_3 M N _inst_4 _inst_5 _inst_6 _inst_7 i f _inst_8 y))) -> Q)
+  forall {R : Type.{u1}} [_inst_1 : Ring.{u1} R] {Q : TypeMax.{u2, u1}} [_inst_2 : AddCommGroup.{max u1 u2} Q] [_inst_3 : Module.{u1, max u1 u2} R Q (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{max u1 u2} Q _inst_2)] {M : Type.{max u1 u2}} {N : Type.{max u1 u2}} [_inst_4 : AddCommGroup.{max u1 u2} M] [_inst_5 : AddCommGroup.{max u1 u2} N] [_inst_6 : Module.{u1, max u1 u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{max u1 u2} M _inst_4)] [_inst_7 : Module.{u1, max u1 u2} R N (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{max u1 u2} N _inst_5)] (i : LinearMap.{u1, u1, max u1 u2, max u1 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 N (AddCommGroup.toAddCommMonoid.{max u1 u2} M _inst_4) (AddCommGroup.toAddCommMonoid.{max u1 u2} N _inst_5) _inst_6 _inst_7) (f : LinearMap.{u1, u1, max u1 u2, max u1 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 Q (AddCommGroup.toAddCommMonoid.{max u1 u2} M _inst_4) (AddCommGroup.toAddCommMonoid.{max u1 u2} Q _inst_2) _inst_6 _inst_3) [_inst_8 : Fact (Function.Injective.{max (succ u1) (succ u2), max (succ u1) (succ u2)} M N (FunLike.coe.{max (succ u1) (succ u2), max (succ u1) (succ u2), max (succ u1) (succ u2)} (LinearMap.{u1, u1, max u1 u2, max u1 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 N (AddCommGroup.toAddCommMonoid.{max u1 u2} M _inst_4) (AddCommGroup.toAddCommMonoid.{max u1 u2} N _inst_5) _inst_6 _inst_7) M (fun (_x : M) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : M) => N) _x) (LinearMap.instFunLikeLinearMap.{u1, u1, max u1 u2, max u1 u2} R R M N (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{max u1 u2} M _inst_4) (AddCommGroup.toAddCommMonoid.{max u1 u2} N _inst_5) _inst_6 _inst_7 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1)))) i))], (Module.Baer.{u1, u2} R _inst_1 Q _inst_2 _inst_3) -> (forall {y : N}, (Subtype.{succ (max u1 u2)} N (fun (x : N) => Membership.mem.{max u1 u2, max u1 u2} N (Submodule.{u1, max u1 u2} R N (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{max u1 u2} N _inst_5) _inst_7) (SetLike.instMembership.{max u1 u2, max u1 u2} (Submodule.{u1, max u1 u2} R N (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{max u1 u2} N _inst_5) _inst_7) N (Submodule.setLike.{u1, max u1 u2} R N (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{max u1 u2} N _inst_5) _inst_7)) x (Module.Baer.supExtensionOfMaxSingleton.{u1, u2} R _inst_1 Q _inst_2 _inst_3 M N _inst_4 _inst_5 _inst_6 _inst_7 i f _inst_8 y))) -> Q)
 Case conversion may be inaccurate. Consider using '#align module.Baer.extension_of_max_adjoin.extension_to_fun Module.Baer.ExtensionOfMaxAdjoin.extensionToFunₓ'. -/
 /-- We can finally define a linear map `M ⊔ ⟨y⟩ ⟶ Q` by `x + r • y ↦ f x + φ r`
 -/
@@ -463,7 +463,7 @@ def ExtensionOfMaxAdjoin.extensionToFun (h : Module.Baer R Q) {y : N} :
 lean 3 declaration is
   forall {R : Type.{u1}} [_inst_1 : Ring.{u1} R] {Q : Type.{max u1 u2}} [_inst_2 : AddCommGroup.{max u1 u2} Q] [_inst_3 : Module.{u1, max u1 u2} R Q (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{max u1 u2} Q _inst_2)] {M : Type.{max u1 u2}} {N : Type.{max u1 u2}} [_inst_4 : AddCommGroup.{max u1 u2} M] [_inst_5 : AddCommGroup.{max u1 u2} N] [_inst_6 : Module.{u1, max u1 u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{max u1 u2} M _inst_4)] [_inst_7 : Module.{u1, max u1 u2} R N (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{max u1 u2} N _inst_5)] (i : LinearMap.{u1, u1, max u1 u2, max u1 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 N (AddCommGroup.toAddCommMonoid.{max u1 u2} M _inst_4) (AddCommGroup.toAddCommMonoid.{max u1 u2} N _inst_5) _inst_6 _inst_7) (f : LinearMap.{u1, u1, max u1 u2, max u1 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 Q (AddCommGroup.toAddCommMonoid.{max u1 u2} M _inst_4) (AddCommGroup.toAddCommMonoid.{max u1 u2} Q _inst_2) _inst_6 _inst_3) [_inst_8 : Fact (Function.Injective.{succ (max u1 u2), succ (max u1 u2)} M N (coeFn.{succ (max u1 u2), succ (max u1 u2)} (LinearMap.{u1, u1, max u1 u2, max u1 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 N (AddCommGroup.toAddCommMonoid.{max u1 u2} M _inst_4) (AddCommGroup.toAddCommMonoid.{max u1 u2} N _inst_5) _inst_6 _inst_7) (fun (_x : LinearMap.{u1, u1, max u1 u2, max u1 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 N (AddCommGroup.toAddCommMonoid.{max u1 u2} M _inst_4) (AddCommGroup.toAddCommMonoid.{max u1 u2} N _inst_5) _inst_6 _inst_7) => M -> N) (LinearMap.hasCoeToFun.{u1, u1, max u1 u2, max u1 u2} R R M N (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{max u1 u2} M _inst_4) (AddCommGroup.toAddCommMonoid.{max u1 u2} N _inst_5) _inst_6 _inst_7 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1)))) i))] (h : Module.Baer.{u1, u2} R _inst_1 Q _inst_2 _inst_3) {y : N} (x : coeSort.{succ (max u1 u2), succ (succ (max u1 u2))} (Submodule.{u1, max u1 u2} R N (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{max u1 u2} N _inst_5) _inst_7) Type.{max u1 u2} (SetLike.hasCoeToSort.{max u1 u2, max u1 u2} (Submodule.{u1, max u1 u2} R N (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{max u1 u2} N _inst_5) _inst_7) N (Submodule.setLike.{u1, max u1 u2} R N (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{max u1 u2} N _inst_5) _inst_7)) (Sup.sup.{max u1 u2} (Submodule.{u1, max u1 u2} R N (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{max u1 u2} N _inst_5) _inst_7) (SemilatticeSup.toHasSup.{max u1 u2} (Submodule.{u1, max u1 u2} R N (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{max u1 u2} N _inst_5) _inst_7) (Lattice.toSemilatticeSup.{max u1 u2} (Submodule.{u1, max u1 u2} R N (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{max u1 u2} N _inst_5) _inst_7) (ConditionallyCompleteLattice.toLattice.{max u1 u2} (Submodule.{u1, max u1 u2} R N (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{max u1 u2} N _inst_5) _inst_7) (CompleteLattice.toConditionallyCompleteLattice.{max u1 u2} (Submodule.{u1, max u1 u2} R N (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{max u1 u2} N _inst_5) _inst_7) (Submodule.completeLattice.{u1, max u1 u2} R N (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{max u1 u2} N _inst_5) _inst_7))))) 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 but is expected to have type
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_inst_1 Q _inst_2 _inst_3 M N _inst_4 _inst_5 _inst_6 _inst_7 i f _inst_8 h y) r)))
+  forall {R : Type.{u1}} [_inst_1 : Ring.{u1} R] {Q : TypeMax.{u2, u1}} [_inst_2 : AddCommGroup.{max u1 u2} Q] [_inst_3 : Module.{u1, max u1 u2} R Q (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{max u1 u2} Q _inst_2)] {M : Type.{max u1 u2}} {N : Type.{max u1 u2}} [_inst_4 : AddCommGroup.{max u1 u2} M] [_inst_5 : AddCommGroup.{max u1 u2} N] [_inst_6 : Module.{u1, max u1 u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{max u1 u2} M _inst_4)] [_inst_7 : Module.{u1, max u1 u2} R N (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{max u1 u2} N _inst_5)] (i : LinearMap.{u1, u1, max u1 u2, max u1 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 N (AddCommGroup.toAddCommMonoid.{max u1 u2} M _inst_4) (AddCommGroup.toAddCommMonoid.{max u1 u2} N _inst_5) _inst_6 _inst_7) (f : LinearMap.{u1, u1, max u1 u2, max u1 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 Q (AddCommGroup.toAddCommMonoid.{max u1 u2} M _inst_4) (AddCommGroup.toAddCommMonoid.{max u1 u2} Q _inst_2) _inst_6 _inst_3) [_inst_8 : Fact (Function.Injective.{max (succ u1) (succ u2), max (succ u1) (succ u2)} M N (FunLike.coe.{max (succ u1) (succ u2), max (succ u1) (succ u2), max (succ u1) (succ u2)} (LinearMap.{u1, u1, max u1 u2, max u1 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 N (AddCommGroup.toAddCommMonoid.{max u1 u2} M _inst_4) (AddCommGroup.toAddCommMonoid.{max u1 u2} N _inst_5) _inst_6 _inst_7) M (fun (_x : M) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : M) => N) _x) (LinearMap.instFunLikeLinearMap.{u1, u1, max u1 u2, max u1 u2} R R M N (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{max u1 u2} M _inst_4) (AddCommGroup.toAddCommMonoid.{max u1 u2} N _inst_5) _inst_6 _inst_7 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1)))) i))] (h : Module.Baer.{u1, u2} R _inst_1 Q _inst_2 _inst_3) {y : N} (x : Subtype.{succ (max u1 u2)} N (fun (x : N) => Membership.mem.{max u1 u2, max u1 u2} N (Submodule.{u1, max u1 u2} R N (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{max u1 u2} N _inst_5) _inst_7) (SetLike.instMembership.{max u1 u2, max u1 u2} (Submodule.{u1, max u1 u2} R N (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{max u1 u2} N _inst_5) _inst_7) N (Submodule.setLike.{u1, max u1 u2} R N (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{max u1 u2} N _inst_5) _inst_7)) x (Module.Baer.supExtensionOfMaxSingleton.{u1, u2} R _inst_1 Q _inst_2 _inst_3 M N _inst_4 _inst_5 _inst_6 _inst_7 i f _inst_8 y))) (a : Subtype.{succ (max u1 u2)} N (fun (x : N) => Membership.mem.{max u1 u2, max u1 u2} N (Submodule.{u1, max u1 u2} R N (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{max u1 u2} N _inst_5) _inst_7) (SetLike.instMembership.{max u1 u2, max u1 u2} (Submodule.{u1, max u1 u2} R N (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{max u1 u2} N _inst_5) _inst_7) N (Submodule.setLike.{u1, max u1 u2} R N (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{max u1 u2} N _inst_5) _inst_7)) x (LinearPMap.domain.{u1, max u1 u2, max u1 u2} R _inst_1 N _inst_5 _inst_7 Q _inst_2 _inst_3 (Module.Baer.ExtensionOf.toLinearPMap.{u1, u2} R _inst_1 Q _inst_2 _inst_3 M N _inst_4 _inst_5 _inst_6 _inst_7 i f (Module.Baer.extensionOfMax.{u1, u2} R _inst_1 Q _inst_2 _inst_3 M N _inst_4 _inst_5 _inst_6 _inst_7 i f _inst_8))))) (r : R), (Eq.{max (succ u1) (succ u2)} N (Subtype.val.{succ (max u1 u2)} N (fun (x : N) => Membership.mem.{max u1 u2, max u1 u2} N (Set.{max u1 u2} N) (Set.instMembershipSet.{max u1 u2} N) x (SetLike.coe.{max u1 u2, max u1 u2} (Submodule.{u1, max u1 u2} R N (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{max u1 u2} N _inst_5) _inst_7) N (Submodule.setLike.{u1, max u1 u2} R N (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{max u1 u2} N _inst_5) _inst_7) (Module.Baer.supExtensionOfMaxSingleton.{u1, u2} R _inst_1 Q _inst_2 _inst_3 M N _inst_4 _inst_5 _inst_6 _inst_7 i f _inst_8 y))) x) (HAdd.hAdd.{max u1 u2, max u1 u2, max u1 u2} N N N (instHAdd.{max u1 u2} N (AddZeroClass.toAdd.{max u1 u2} N (AddMonoid.toAddZeroClass.{max u1 u2} N (SubNegMonoid.toAddMonoid.{max u1 u2} N (AddGroup.toSubNegMonoid.{max u1 u2} N (AddCommGroup.toAddGroup.{max u1 u2} N _inst_5)))))) (Subtype.val.{succ (max u1 u2)} N (fun (x : N) => Membership.mem.{max u1 u2, max u1 u2} N (Set.{max u1 u2} N) (Set.instMembershipSet.{max u1 u2} N) x (SetLike.coe.{max u1 u2, max u1 u2} (Submodule.{u1, max u1 u2} R N (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{max u1 u2} N _inst_5) _inst_7) N (Submodule.setLike.{u1, max u1 u2} R N (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{max u1 u2} N _inst_5) _inst_7) (LinearPMap.domain.{u1, max u1 u2, max u1 u2} R _inst_1 N _inst_5 _inst_7 Q _inst_2 _inst_3 (Module.Baer.ExtensionOf.toLinearPMap.{u1, u2} R _inst_1 Q _inst_2 _inst_3 M N _inst_4 _inst_5 _inst_6 _inst_7 i f (Module.Baer.extensionOfMax.{u1, u2} R _inst_1 Q _inst_2 _inst_3 M N _inst_4 _inst_5 _inst_6 _inst_7 i f _inst_8))))) a) (HSMul.hSMul.{u1, max u1 u2, max u1 u2} R N N (instHSMul.{u1, max u1 u2} R N (SMulZeroClass.toSMul.{u1, max u1 u2} R N (NegZeroClass.toZero.{max u1 u2} N (SubNegZeroMonoid.toNegZeroClass.{max u1 u2} N (SubtractionMonoid.toSubNegZeroMonoid.{max u1 u2} N (SubtractionCommMonoid.toSubtractionMonoid.{max u1 u2} N (AddCommGroup.toDivisionAddCommMonoid.{max u1 u2} N _inst_5))))) (SMulWithZero.toSMulZeroClass.{u1, max u1 u2} R N (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (NegZeroClass.toZero.{max u1 u2} N (SubNegZeroMonoid.toNegZeroClass.{max u1 u2} N (SubtractionMonoid.toSubNegZeroMonoid.{max u1 u2} N (SubtractionCommMonoid.toSubtractionMonoid.{max u1 u2} N (AddCommGroup.toDivisionAddCommMonoid.{max u1 u2} N _inst_5))))) (MulActionWithZero.toSMulWithZero.{u1, max u1 u2} R N (Semiring.toMonoidWithZero.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (NegZeroClass.toZero.{max u1 u2} N (SubNegZeroMonoid.toNegZeroClass.{max u1 u2} N (SubtractionMonoid.toSubNegZeroMonoid.{max u1 u2} N (SubtractionCommMonoid.toSubtractionMonoid.{max u1 u2} N (AddCommGroup.toDivisionAddCommMonoid.{max u1 u2} N _inst_5))))) (Module.toMulActionWithZero.{u1, max u1 u2} R N (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{max u1 u2} N _inst_5) _inst_7))))) r y))) -> (Eq.{max (succ u1) (succ u2)} Q (Module.Baer.ExtensionOfMaxAdjoin.extensionToFun.{u1, u2} R _inst_1 Q _inst_2 _inst_3 M N _inst_4 _inst_5 _inst_6 _inst_7 i f _inst_8 h y x) (HAdd.hAdd.{max u1 u2, max u1 u2, max u1 u2} Q ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : R) => Q) r) Q (instHAdd.{max u1 u2} Q (AddZeroClass.toAdd.{max u1 u2} Q (AddMonoid.toAddZeroClass.{max u1 u2} Q (SubNegMonoid.toAddMonoid.{max u1 u2} Q (AddGroup.toSubNegMonoid.{max u1 u2} Q (AddCommGroup.toAddGroup.{max u1 u2} Q _inst_2)))))) (LinearPMap.toFun'.{u1, max u1 u2, max u1 u2} R _inst_1 N _inst_5 _inst_7 Q _inst_2 _inst_3 (Module.Baer.ExtensionOf.toLinearPMap.{u1, u2} R _inst_1 Q _inst_2 _inst_3 M N _inst_4 _inst_5 _inst_6 _inst_7 i f (Module.Baer.extensionOfMax.{u1, u2} R _inst_1 Q _inst_2 _inst_3 M N _inst_4 _inst_5 _inst_6 _inst_7 i f _inst_8)) a) (FunLike.coe.{max (succ u1) (succ u2), succ u1, max (succ u1) (succ u2)} (LinearMap.{u1, u1, u1, max u1 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))) R Q (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R _inst_1)))) (AddCommGroup.toAddCommMonoid.{max u1 u2} Q _inst_2) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R _inst_1)) _inst_3) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : R) => Q) _x) (LinearMap.instFunLikeLinearMap.{u1, u1, u1, max u1 u2} R R R Q (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R _inst_1)))) (AddCommGroup.toAddCommMonoid.{max u1 u2} Q _inst_2) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R _inst_1)) _inst_3 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1)))) (Module.Baer.ExtensionOfMaxAdjoin.extendIdealTo.{u1, u2} R _inst_1 Q _inst_2 _inst_3 M N _inst_4 _inst_5 _inst_6 _inst_7 i f _inst_8 h y) r)))
 Case conversion may be inaccurate. Consider using '#align module.Baer.extension_of_max_adjoin.extension_to_fun_wd Module.Baer.ExtensionOfMaxAdjoin.extensionToFun_wdₓ'. -/
 theorem ExtensionOfMaxAdjoin.extensionToFun_wd (h : Module.Baer R Q) {y : N}
     (x : (extensionOfMax i f).domain ⊔ Submodule.span R {y}) (a : (extensionOfMax i f).domain)
@@ -493,7 +493,7 @@ theorem ExtensionOfMaxAdjoin.extensionToFun_wd (h : Module.Baer R Q) {y : N}
 lean 3 declaration is
   forall {R : Type.{u1}} [_inst_1 : Ring.{u1} R] {Q : Type.{max u1 u2}} [_inst_2 : AddCommGroup.{max u1 u2} Q] [_inst_3 : Module.{u1, max u1 u2} R Q (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{max u1 u2} Q _inst_2)] {M : Type.{max u1 u2}} {N : Type.{max u1 u2}} [_inst_4 : AddCommGroup.{max u1 u2} M] [_inst_5 : AddCommGroup.{max u1 u2} N] [_inst_6 : Module.{u1, max u1 u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{max u1 u2} M _inst_4)] [_inst_7 : Module.{u1, max u1 u2} R N (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{max u1 u2} N _inst_5)] (i : LinearMap.{u1, u1, max u1 u2, max u1 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 N (AddCommGroup.toAddCommMonoid.{max u1 u2} M _inst_4) (AddCommGroup.toAddCommMonoid.{max u1 u2} N _inst_5) _inst_6 _inst_7) (f : LinearMap.{u1, u1, max u1 u2, max u1 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 Q (AddCommGroup.toAddCommMonoid.{max u1 u2} M _inst_4) (AddCommGroup.toAddCommMonoid.{max u1 u2} Q _inst_2) _inst_6 _inst_3) [_inst_8 : Fact (Function.Injective.{succ (max u1 u2), succ (max u1 u2)} M N (coeFn.{succ (max u1 u2), succ (max u1 u2)} (LinearMap.{u1, u1, max u1 u2, max u1 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 N (AddCommGroup.toAddCommMonoid.{max u1 u2} M _inst_4) (AddCommGroup.toAddCommMonoid.{max u1 u2} N _inst_5) _inst_6 _inst_7) (fun (_x : LinearMap.{u1, u1, max u1 u2, max u1 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 N (AddCommGroup.toAddCommMonoid.{max u1 u2} M _inst_4) (AddCommGroup.toAddCommMonoid.{max u1 u2} N _inst_5) _inst_6 _inst_7) => M -> N) (LinearMap.hasCoeToFun.{u1, u1, max u1 u2, max u1 u2} R R M N (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{max u1 u2} M _inst_4) (AddCommGroup.toAddCommMonoid.{max u1 u2} N _inst_5) _inst_6 _inst_7 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1)))) i))], (Module.Baer.{u1, u2} R _inst_1 Q _inst_2 _inst_3) -> N -> (Module.Baer.ExtensionOf.{u1, u2} R _inst_1 Q _inst_2 _inst_3 M N _inst_4 _inst_5 _inst_6 _inst_7 i f)
 but is expected to have type
-  forall {R : Type.{u1}} [_inst_1 : Ring.{u1} R] {Q : TypeMax.{u2, u1}} [_inst_2 : AddCommGroup.{max u1 u2} Q] [_inst_3 : Module.{u1, max u1 u2} R Q (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{max u1 u2} Q _inst_2)] {M : Type.{max u1 u2}} {N : Type.{max u1 u2}} [_inst_4 : AddCommGroup.{max u1 u2} M] [_inst_5 : AddCommGroup.{max u1 u2} N] [_inst_6 : Module.{u1, max u1 u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{max u1 u2} M _inst_4)] [_inst_7 : Module.{u1, max u1 u2} R N (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{max u1 u2} N _inst_5)] (i : LinearMap.{u1, u1, max u1 u2, max u1 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 N (AddCommGroup.toAddCommMonoid.{max u1 u2} M _inst_4) (AddCommGroup.toAddCommMonoid.{max u1 u2} N _inst_5) _inst_6 _inst_7) (f : LinearMap.{u1, u1, max u1 u2, max u1 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 Q (AddCommGroup.toAddCommMonoid.{max u1 u2} M _inst_4) (AddCommGroup.toAddCommMonoid.{max u1 u2} Q _inst_2) _inst_6 _inst_3) [_inst_8 : Fact (Function.Injective.{max (succ u1) (succ u2), max (succ u1) (succ u2)} M N (FunLike.coe.{max (succ u1) (succ u2), max (succ u1) (succ u2), max (succ u1) (succ u2)} (LinearMap.{u1, u1, max u1 u2, max u1 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 N (AddCommGroup.toAddCommMonoid.{max u1 u2} M _inst_4) (AddCommGroup.toAddCommMonoid.{max u1 u2} N _inst_5) _inst_6 _inst_7) M (fun (_x : M) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : M) => N) _x) (LinearMap.instFunLikeLinearMap.{u1, u1, max u1 u2, max u1 u2} R R M N (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{max u1 u2} M _inst_4) (AddCommGroup.toAddCommMonoid.{max u1 u2} N _inst_5) _inst_6 _inst_7 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1)))) i))], (Module.Baer.{u1, u2} R _inst_1 Q _inst_2 _inst_3) -> N -> (Module.Baer.ExtensionOf.{u1, u2} R _inst_1 Q _inst_2 _inst_3 M N _inst_4 _inst_5 _inst_6 _inst_7 i f)
+  forall {R : Type.{u1}} [_inst_1 : Ring.{u1} R] {Q : TypeMax.{u2, u1}} [_inst_2 : AddCommGroup.{max u1 u2} Q] [_inst_3 : Module.{u1, max u1 u2} R Q (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{max u1 u2} Q _inst_2)] {M : Type.{max u1 u2}} {N : Type.{max u1 u2}} [_inst_4 : AddCommGroup.{max u1 u2} M] [_inst_5 : AddCommGroup.{max u1 u2} N] [_inst_6 : Module.{u1, max u1 u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{max u1 u2} M _inst_4)] [_inst_7 : Module.{u1, max u1 u2} R N (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{max u1 u2} N _inst_5)] (i : LinearMap.{u1, u1, max u1 u2, max u1 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 N (AddCommGroup.toAddCommMonoid.{max u1 u2} M _inst_4) (AddCommGroup.toAddCommMonoid.{max u1 u2} N _inst_5) _inst_6 _inst_7) (f : LinearMap.{u1, u1, max u1 u2, max u1 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 Q (AddCommGroup.toAddCommMonoid.{max u1 u2} M _inst_4) (AddCommGroup.toAddCommMonoid.{max u1 u2} Q _inst_2) _inst_6 _inst_3) [_inst_8 : Fact (Function.Injective.{max (succ u1) (succ u2), max (succ u1) (succ u2)} M N (FunLike.coe.{max (succ u1) (succ u2), max (succ u1) (succ u2), max (succ u1) (succ u2)} (LinearMap.{u1, u1, max u1 u2, max u1 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 N (AddCommGroup.toAddCommMonoid.{max u1 u2} M _inst_4) (AddCommGroup.toAddCommMonoid.{max u1 u2} N _inst_5) _inst_6 _inst_7) M (fun (_x : M) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : M) => N) _x) (LinearMap.instFunLikeLinearMap.{u1, u1, max u1 u2, max u1 u2} R R M N (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{max u1 u2} M _inst_4) (AddCommGroup.toAddCommMonoid.{max u1 u2} N _inst_5) _inst_6 _inst_7 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1)))) i))], (Module.Baer.{u1, u2} R _inst_1 Q _inst_2 _inst_3) -> N -> (Module.Baer.ExtensionOf.{u1, u2} R _inst_1 Q _inst_2 _inst_3 M N _inst_4 _inst_5 _inst_6 _inst_7 i f)
 Case conversion may be inaccurate. Consider using '#align module.Baer.extension_of_max_adjoin Module.Baer.extensionOfMaxAdjoinₓ'. -/
 /-- The linear map `M ⊔ ⟨y⟩ ⟶ Q` by `x + r • y ↦ f x + φ r` is an extension of `f`-/
 def extensionOfMaxAdjoin (h : Module.Baer R Q) (y : N) : ExtensionOf i f
@@ -537,7 +537,7 @@ def extensionOfMaxAdjoin (h : Module.Baer R Q) (y : N) : ExtensionOf i f
 lean 3 declaration is
   forall {R : Type.{u1}} [_inst_1 : Ring.{u1} R] {Q : Type.{max u1 u2}} [_inst_2 : AddCommGroup.{max u1 u2} Q] [_inst_3 : Module.{u1, max u1 u2} R Q (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{max u1 u2} Q _inst_2)] {M : Type.{max u1 u2}} {N : Type.{max u1 u2}} [_inst_4 : AddCommGroup.{max u1 u2} M] [_inst_5 : AddCommGroup.{max u1 u2} N] [_inst_6 : Module.{u1, max u1 u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{max u1 u2} M _inst_4)] [_inst_7 : Module.{u1, max u1 u2} R N (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{max u1 u2} N _inst_5)] (i : LinearMap.{u1, u1, max u1 u2, max u1 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 N (AddCommGroup.toAddCommMonoid.{max u1 u2} M _inst_4) (AddCommGroup.toAddCommMonoid.{max u1 u2} N _inst_5) _inst_6 _inst_7) (f : LinearMap.{u1, u1, max u1 u2, max u1 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 Q (AddCommGroup.toAddCommMonoid.{max u1 u2} M _inst_4) (AddCommGroup.toAddCommMonoid.{max u1 u2} Q _inst_2) _inst_6 _inst_3) [_inst_8 : Fact (Function.Injective.{succ (max u1 u2), succ (max u1 u2)} M N (coeFn.{succ (max u1 u2), succ (max u1 u2)} (LinearMap.{u1, u1, max u1 u2, max u1 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 N (AddCommGroup.toAddCommMonoid.{max u1 u2} M _inst_4) (AddCommGroup.toAddCommMonoid.{max u1 u2} N _inst_5) _inst_6 _inst_7) (fun (_x : LinearMap.{u1, u1, max u1 u2, max u1 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 N (AddCommGroup.toAddCommMonoid.{max u1 u2} M _inst_4) (AddCommGroup.toAddCommMonoid.{max u1 u2} N _inst_5) _inst_6 _inst_7) => M -> N) (LinearMap.hasCoeToFun.{u1, u1, max u1 u2, max u1 u2} R R M N (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{max u1 u2} M _inst_4) (AddCommGroup.toAddCommMonoid.{max u1 u2} N _inst_5) _inst_6 _inst_7 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1)))) i))] (h : Module.Baer.{u1, u2} R _inst_1 Q _inst_2 _inst_3) {y : N}, LE.le.{max u1 u2} (Module.Baer.ExtensionOf.{u1, u2} R _inst_1 Q _inst_2 _inst_3 M N _inst_4 _inst_5 _inst_6 _inst_7 i f) (Preorder.toHasLe.{max u1 u2} (Module.Baer.ExtensionOf.{u1, u2} R _inst_1 Q _inst_2 _inst_3 M N _inst_4 _inst_5 _inst_6 _inst_7 i f) (PartialOrder.toPreorder.{max u1 u2} (Module.Baer.ExtensionOf.{u1, u2} R _inst_1 Q _inst_2 _inst_3 M N _inst_4 _inst_5 _inst_6 _inst_7 i f) (SemilatticeInf.toPartialOrder.{max u1 u2} (Module.Baer.ExtensionOf.{u1, u2} R _inst_1 Q _inst_2 _inst_3 M N _inst_4 _inst_5 _inst_6 _inst_7 i f) (Module.Baer.ExtensionOf.semilatticeInf.{u1, u2} R _inst_1 Q _inst_2 _inst_3 M N _inst_4 _inst_5 _inst_6 _inst_7 i f)))) (Module.Baer.extensionOfMax.{u1, u2} R _inst_1 Q _inst_2 _inst_3 M N _inst_4 _inst_5 _inst_6 _inst_7 i f _inst_8) (Module.Baer.extensionOfMaxAdjoin.{u1, u2} R _inst_1 Q _inst_2 _inst_3 M N _inst_4 _inst_5 _inst_6 _inst_7 i f _inst_8 h y)
 but is expected to have type
-  forall {R : Type.{u1}} [_inst_1 : Ring.{u1} R] {Q : TypeMax.{u2, u1}} [_inst_2 : AddCommGroup.{max u1 u2} Q] [_inst_3 : Module.{u1, max u1 u2} R Q (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{max u1 u2} Q _inst_2)] {M : Type.{max u1 u2}} {N : Type.{max u1 u2}} [_inst_4 : AddCommGroup.{max u1 u2} M] [_inst_5 : AddCommGroup.{max u1 u2} N] [_inst_6 : Module.{u1, max u1 u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{max u1 u2} M _inst_4)] [_inst_7 : Module.{u1, max u1 u2} R N (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{max u1 u2} N _inst_5)] (i : LinearMap.{u1, u1, max u1 u2, max u1 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 N (AddCommGroup.toAddCommMonoid.{max u1 u2} M _inst_4) (AddCommGroup.toAddCommMonoid.{max u1 u2} N _inst_5) _inst_6 _inst_7) (f : LinearMap.{u1, u1, max u1 u2, max u1 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 Q (AddCommGroup.toAddCommMonoid.{max u1 u2} M _inst_4) (AddCommGroup.toAddCommMonoid.{max u1 u2} Q _inst_2) _inst_6 _inst_3) [_inst_8 : Fact (Function.Injective.{max (succ u1) (succ u2), max (succ u1) (succ u2)} M N (FunLike.coe.{max (succ u1) (succ u2), max (succ u1) (succ u2), max (succ u1) (succ u2)} (LinearMap.{u1, u1, max u1 u2, max u1 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 N (AddCommGroup.toAddCommMonoid.{max u1 u2} M _inst_4) (AddCommGroup.toAddCommMonoid.{max u1 u2} N _inst_5) _inst_6 _inst_7) M (fun (_x : M) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : M) => N) _x) (LinearMap.instFunLikeLinearMap.{u1, u1, max u1 u2, max u1 u2} R R M N (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{max u1 u2} M _inst_4) (AddCommGroup.toAddCommMonoid.{max u1 u2} N _inst_5) _inst_6 _inst_7 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1)))) i))] (h : Module.Baer.{u1, u2} R _inst_1 Q _inst_2 _inst_3) {y : N}, LE.le.{max u1 u2} (Module.Baer.ExtensionOf.{u1, u2} R _inst_1 Q _inst_2 _inst_3 M N _inst_4 _inst_5 _inst_6 _inst_7 i f) (Preorder.toLE.{max u1 u2} (Module.Baer.ExtensionOf.{u1, u2} R _inst_1 Q _inst_2 _inst_3 M N _inst_4 _inst_5 _inst_6 _inst_7 i f) (PartialOrder.toPreorder.{max u1 u2} (Module.Baer.ExtensionOf.{u1, u2} R _inst_1 Q _inst_2 _inst_3 M N _inst_4 _inst_5 _inst_6 _inst_7 i f) (SemilatticeInf.toPartialOrder.{max u1 u2} (Module.Baer.ExtensionOf.{u1, u2} R _inst_1 Q _inst_2 _inst_3 M N _inst_4 _inst_5 _inst_6 _inst_7 i f) (Module.Baer.instSemilatticeInfExtensionOf.{u1, u2} R _inst_1 Q _inst_2 _inst_3 M N _inst_4 _inst_5 _inst_6 _inst_7 i f)))) (Module.Baer.extensionOfMax.{u1, u2} R _inst_1 Q _inst_2 _inst_3 M N _inst_4 _inst_5 _inst_6 _inst_7 i f _inst_8) (Module.Baer.extensionOfMaxAdjoin.{u1, u2} R _inst_1 Q _inst_2 _inst_3 M N _inst_4 _inst_5 _inst_6 _inst_7 i f _inst_8 h y)
+  forall {R : Type.{u1}} [_inst_1 : Ring.{u1} R] {Q : TypeMax.{u2, u1}} [_inst_2 : AddCommGroup.{max u1 u2} Q] [_inst_3 : Module.{u1, max u1 u2} R Q (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{max u1 u2} Q _inst_2)] {M : Type.{max u1 u2}} {N : Type.{max u1 u2}} [_inst_4 : AddCommGroup.{max u1 u2} M] [_inst_5 : AddCommGroup.{max u1 u2} N] [_inst_6 : Module.{u1, max u1 u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{max u1 u2} M _inst_4)] [_inst_7 : Module.{u1, max u1 u2} R N (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{max u1 u2} N _inst_5)] (i : LinearMap.{u1, u1, max u1 u2, max u1 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 N (AddCommGroup.toAddCommMonoid.{max u1 u2} M _inst_4) (AddCommGroup.toAddCommMonoid.{max u1 u2} N _inst_5) _inst_6 _inst_7) (f : LinearMap.{u1, u1, max u1 u2, max u1 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 Q (AddCommGroup.toAddCommMonoid.{max u1 u2} M _inst_4) (AddCommGroup.toAddCommMonoid.{max u1 u2} Q _inst_2) _inst_6 _inst_3) [_inst_8 : Fact (Function.Injective.{max (succ u1) (succ u2), max (succ u1) (succ u2)} M N (FunLike.coe.{max (succ u1) (succ u2), max (succ u1) (succ u2), max (succ u1) (succ u2)} (LinearMap.{u1, u1, max u1 u2, max u1 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 N (AddCommGroup.toAddCommMonoid.{max u1 u2} M _inst_4) (AddCommGroup.toAddCommMonoid.{max u1 u2} N _inst_5) _inst_6 _inst_7) M (fun (_x : M) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : M) => N) _x) (LinearMap.instFunLikeLinearMap.{u1, u1, max u1 u2, max u1 u2} R R M N (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{max u1 u2} M _inst_4) (AddCommGroup.toAddCommMonoid.{max u1 u2} N _inst_5) _inst_6 _inst_7 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1)))) i))] (h : Module.Baer.{u1, u2} R _inst_1 Q _inst_2 _inst_3) {y : N}, LE.le.{max u1 u2} (Module.Baer.ExtensionOf.{u1, u2} R _inst_1 Q _inst_2 _inst_3 M N _inst_4 _inst_5 _inst_6 _inst_7 i f) (Preorder.toLE.{max u1 u2} (Module.Baer.ExtensionOf.{u1, u2} R _inst_1 Q _inst_2 _inst_3 M N _inst_4 _inst_5 _inst_6 _inst_7 i f) (PartialOrder.toPreorder.{max u1 u2} (Module.Baer.ExtensionOf.{u1, u2} R _inst_1 Q _inst_2 _inst_3 M N _inst_4 _inst_5 _inst_6 _inst_7 i f) (SemilatticeInf.toPartialOrder.{max u1 u2} (Module.Baer.ExtensionOf.{u1, u2} R _inst_1 Q _inst_2 _inst_3 M N _inst_4 _inst_5 _inst_6 _inst_7 i f) (Module.Baer.instSemilatticeInfExtensionOf.{u1, u2} R _inst_1 Q _inst_2 _inst_3 M N _inst_4 _inst_5 _inst_6 _inst_7 i f)))) (Module.Baer.extensionOfMax.{u1, u2} R _inst_1 Q _inst_2 _inst_3 M N _inst_4 _inst_5 _inst_6 _inst_7 i f _inst_8) (Module.Baer.extensionOfMaxAdjoin.{u1, u2} R _inst_1 Q _inst_2 _inst_3 M N _inst_4 _inst_5 _inst_6 _inst_7 i f _inst_8 h y)
 Case conversion may be inaccurate. Consider using '#align module.Baer.extension_of_max_le Module.Baer.extensionOfMax_leₓ'. -/
 theorem extensionOfMax_le (h : Module.Baer R Q) {y : N} :
     extensionOfMax i f ≤ extensionOfMaxAdjoin i f h y :=
@@ -552,7 +552,7 @@ theorem extensionOfMax_le (h : Module.Baer R Q) {y : N} :
 lean 3 declaration is
   forall {R : Type.{u1}} [_inst_1 : Ring.{u1} R] {Q : Type.{max u1 u2}} [_inst_2 : AddCommGroup.{max u1 u2} Q] [_inst_3 : Module.{u1, max u1 u2} R Q (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{max u1 u2} Q _inst_2)] {M : Type.{max u1 u2}} {N : Type.{max u1 u2}} [_inst_4 : AddCommGroup.{max u1 u2} M] [_inst_5 : AddCommGroup.{max u1 u2} N] [_inst_6 : Module.{u1, max u1 u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{max u1 u2} M _inst_4)] [_inst_7 : Module.{u1, max u1 u2} R N (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{max u1 u2} N _inst_5)] (i : LinearMap.{u1, u1, max u1 u2, max u1 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 N (AddCommGroup.toAddCommMonoid.{max u1 u2} M _inst_4) (AddCommGroup.toAddCommMonoid.{max u1 u2} N _inst_5) _inst_6 _inst_7) (f : LinearMap.{u1, u1, max u1 u2, max u1 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 Q (AddCommGroup.toAddCommMonoid.{max u1 u2} M _inst_4) (AddCommGroup.toAddCommMonoid.{max u1 u2} Q _inst_2) _inst_6 _inst_3) [_inst_8 : Fact (Function.Injective.{succ (max u1 u2), succ (max u1 u2)} M N (coeFn.{succ (max u1 u2), succ (max u1 u2)} (LinearMap.{u1, u1, max u1 u2, max u1 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 N (AddCommGroup.toAddCommMonoid.{max u1 u2} M _inst_4) (AddCommGroup.toAddCommMonoid.{max u1 u2} N _inst_5) _inst_6 _inst_7) (fun (_x : LinearMap.{u1, u1, max u1 u2, max u1 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 N (AddCommGroup.toAddCommMonoid.{max u1 u2} M _inst_4) (AddCommGroup.toAddCommMonoid.{max u1 u2} N _inst_5) _inst_6 _inst_7) => M -> N) (LinearMap.hasCoeToFun.{u1, u1, max u1 u2, max u1 u2} R R M N (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{max u1 u2} M _inst_4) (AddCommGroup.toAddCommMonoid.{max u1 u2} N _inst_5) _inst_6 _inst_7 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1)))) i))], (Module.Baer.{u1, u2} R _inst_1 Q _inst_2 _inst_3) -> (Eq.{succ (max u1 u2)} (Submodule.{u1, max u1 u2} R N (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{max u1 u2} N _inst_5) _inst_7) (LinearPMap.domain.{u1, max u1 u2, max u1 u2} R _inst_1 N _inst_5 _inst_7 Q _inst_2 _inst_3 (Module.Baer.ExtensionOf.toLinearPmap.{u1, u2} R _inst_1 Q _inst_2 _inst_3 M N _inst_4 _inst_5 _inst_6 _inst_7 i f (Module.Baer.extensionOfMax.{u1, u2} R _inst_1 Q _inst_2 _inst_3 M N _inst_4 _inst_5 _inst_6 _inst_7 i f _inst_8))) (Top.top.{max u1 u2} (Submodule.{u1, max u1 u2} R N (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{max u1 u2} N _inst_5) _inst_7) (Submodule.hasTop.{u1, max u1 u2} R N (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{max u1 u2} N _inst_5) _inst_7)))
 but is expected to have type
-  forall {R : Type.{u1}} [_inst_1 : Ring.{u1} R] {Q : TypeMax.{u2, u1}} [_inst_2 : AddCommGroup.{max u1 u2} Q] [_inst_3 : Module.{u1, max u1 u2} R Q (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{max u1 u2} Q _inst_2)] {M : Type.{max u1 u2}} {N : Type.{max u1 u2}} [_inst_4 : AddCommGroup.{max u1 u2} M] [_inst_5 : AddCommGroup.{max u1 u2} N] [_inst_6 : Module.{u1, max u1 u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{max u1 u2} M _inst_4)] [_inst_7 : Module.{u1, max u1 u2} R N (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{max u1 u2} N _inst_5)] (i : LinearMap.{u1, u1, max u1 u2, max u1 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 N (AddCommGroup.toAddCommMonoid.{max u1 u2} M _inst_4) (AddCommGroup.toAddCommMonoid.{max u1 u2} N _inst_5) _inst_6 _inst_7) (f : LinearMap.{u1, u1, max u1 u2, max u1 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 Q (AddCommGroup.toAddCommMonoid.{max u1 u2} M _inst_4) (AddCommGroup.toAddCommMonoid.{max u1 u2} Q _inst_2) _inst_6 _inst_3) [_inst_8 : Fact (Function.Injective.{max (succ u1) (succ u2), max (succ u1) (succ u2)} M N (FunLike.coe.{max (succ u1) (succ u2), max (succ u1) (succ u2), max (succ u1) (succ u2)} (LinearMap.{u1, u1, max u1 u2, max u1 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 N (AddCommGroup.toAddCommMonoid.{max u1 u2} M _inst_4) (AddCommGroup.toAddCommMonoid.{max u1 u2} N _inst_5) _inst_6 _inst_7) M (fun (_x : M) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : M) => N) _x) (LinearMap.instFunLikeLinearMap.{u1, u1, max u1 u2, max u1 u2} R R M N (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{max u1 u2} M _inst_4) (AddCommGroup.toAddCommMonoid.{max u1 u2} N _inst_5) _inst_6 _inst_7 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1)))) i))], (Module.Baer.{u1, u2} R _inst_1 Q _inst_2 _inst_3) -> (Eq.{max (succ u1) (succ u2)} (Submodule.{u1, max u1 u2} R N (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{max u1 u2} N _inst_5) _inst_7) (LinearPMap.domain.{u1, max u1 u2, max u1 u2} R _inst_1 N _inst_5 _inst_7 Q _inst_2 _inst_3 (Module.Baer.ExtensionOf.toLinearPMap.{u1, u2} R _inst_1 Q _inst_2 _inst_3 M N _inst_4 _inst_5 _inst_6 _inst_7 i f (Module.Baer.extensionOfMax.{u1, u2} R _inst_1 Q _inst_2 _inst_3 M N _inst_4 _inst_5 _inst_6 _inst_7 i f _inst_8))) (Top.top.{max u1 u2} (Submodule.{u1, max u1 u2} R N (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{max u1 u2} N _inst_5) _inst_7) (Submodule.instTopSubmodule.{u1, max u1 u2} R N (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{max u1 u2} N _inst_5) _inst_7)))
+  forall {R : Type.{u1}} [_inst_1 : Ring.{u1} R] {Q : TypeMax.{u2, u1}} [_inst_2 : AddCommGroup.{max u1 u2} Q] [_inst_3 : Module.{u1, max u1 u2} R Q (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{max u1 u2} Q _inst_2)] {M : Type.{max u1 u2}} {N : Type.{max u1 u2}} [_inst_4 : AddCommGroup.{max u1 u2} M] [_inst_5 : AddCommGroup.{max u1 u2} N] [_inst_6 : Module.{u1, max u1 u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{max u1 u2} M _inst_4)] [_inst_7 : Module.{u1, max u1 u2} R N (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{max u1 u2} N _inst_5)] (i : LinearMap.{u1, u1, max u1 u2, max u1 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 N (AddCommGroup.toAddCommMonoid.{max u1 u2} M _inst_4) (AddCommGroup.toAddCommMonoid.{max u1 u2} N _inst_5) _inst_6 _inst_7) (f : LinearMap.{u1, u1, max u1 u2, max u1 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 Q (AddCommGroup.toAddCommMonoid.{max u1 u2} M _inst_4) (AddCommGroup.toAddCommMonoid.{max u1 u2} Q _inst_2) _inst_6 _inst_3) [_inst_8 : Fact (Function.Injective.{max (succ u1) (succ u2), max (succ u1) (succ u2)} M N (FunLike.coe.{max (succ u1) (succ u2), max (succ u1) (succ u2), max (succ u1) (succ u2)} (LinearMap.{u1, u1, max u1 u2, max u1 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 N (AddCommGroup.toAddCommMonoid.{max u1 u2} M _inst_4) (AddCommGroup.toAddCommMonoid.{max u1 u2} N _inst_5) _inst_6 _inst_7) M (fun (_x : M) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : M) => N) _x) (LinearMap.instFunLikeLinearMap.{u1, u1, max u1 u2, max u1 u2} R R M N (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{max u1 u2} M _inst_4) (AddCommGroup.toAddCommMonoid.{max u1 u2} N _inst_5) _inst_6 _inst_7 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1)))) i))], (Module.Baer.{u1, u2} R _inst_1 Q _inst_2 _inst_3) -> (Eq.{max (succ u1) (succ u2)} (Submodule.{u1, max u1 u2} R N (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{max u1 u2} N _inst_5) _inst_7) (LinearPMap.domain.{u1, max u1 u2, max u1 u2} R _inst_1 N _inst_5 _inst_7 Q _inst_2 _inst_3 (Module.Baer.ExtensionOf.toLinearPMap.{u1, u2} R _inst_1 Q _inst_2 _inst_3 M N _inst_4 _inst_5 _inst_6 _inst_7 i f (Module.Baer.extensionOfMax.{u1, u2} R _inst_1 Q _inst_2 _inst_3 M N _inst_4 _inst_5 _inst_6 _inst_7 i f _inst_8))) (Top.top.{max u1 u2} (Submodule.{u1, max u1 u2} R N (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{max u1 u2} N _inst_5) _inst_7) (Submodule.instTopSubmodule.{u1, max u1 u2} R N (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{max u1 u2} N _inst_5) _inst_7)))
 Case conversion may be inaccurate. Consider using '#align module.Baer.extension_of_max_to_submodule_eq_top Module.Baer.extensionOfMax_to_submodule_eq_topₓ'. -/
 theorem extensionOfMax_to_submodule_eq_top (h : Module.Baer R Q) :
     (extensionOfMax i f).domain = ⊤ :=

mathlib commit https://github.com/leanprover-community/mathlib/commit/c89fe2d59ae06402c3f55f978016d1ada444f57e

@@ -252,7 +252,7 @@ variable (i f) [Fact <| Function.Injective i]
 lean 3 declaration is
   forall {R : Type.{u1}} [_inst_1 : Ring.{u1} R] {Q : Type.{max u1 u2}} [_inst_2 : AddCommGroup.{max u1 u2} Q] [_inst_3 : Module.{u1, max u1 u2} R Q (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{max u1 u2} Q _inst_2)] {M : Type.{max u1 u2}} {N : Type.{max u1 u2}} [_inst_4 : AddCommGroup.{max u1 u2} M] [_inst_5 : AddCommGroup.{max u1 u2} N] [_inst_6 : Module.{u1, max u1 u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{max u1 u2} M _inst_4)] [_inst_7 : Module.{u1, max u1 u2} R N (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{max u1 u2} N _inst_5)] (i : LinearMap.{u1, u1, max u1 u2, max u1 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 N (AddCommGroup.toAddCommMonoid.{max u1 u2} M _inst_4) (AddCommGroup.toAddCommMonoid.{max u1 u2} N _inst_5) _inst_6 _inst_7) (f : LinearMap.{u1, u1, max u1 u2, max u1 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 Q (AddCommGroup.toAddCommMonoid.{max u1 u2} M _inst_4) (AddCommGroup.toAddCommMonoid.{max u1 u2} Q _inst_2) _inst_6 _inst_3) [_inst_8 : Fact (Function.Injective.{succ (max u1 u2), succ (max u1 u2)} M N (coeFn.{succ (max u1 u2), succ (max u1 u2)} (LinearMap.{u1, u1, max u1 u2, max u1 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 N (AddCommGroup.toAddCommMonoid.{max u1 u2} M _inst_4) (AddCommGroup.toAddCommMonoid.{max u1 u2} N _inst_5) _inst_6 _inst_7) (fun (_x : LinearMap.{u1, u1, max u1 u2, max u1 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 N (AddCommGroup.toAddCommMonoid.{max u1 u2} M _inst_4) (AddCommGroup.toAddCommMonoid.{max u1 u2} N _inst_5) _inst_6 _inst_7) => M -> N) (LinearMap.hasCoeToFun.{u1, u1, max u1 u2, max u1 u2} R R M N (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{max u1 u2} M _inst_4) (AddCommGroup.toAddCommMonoid.{max u1 u2} N _inst_5) _inst_6 _inst_7 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1)))) i))], Inhabited.{max (succ u1) (succ u2)} (Module.Baer.ExtensionOf.{u1, u2} R _inst_1 Q _inst_2 _inst_3 M N _inst_4 _inst_5 _inst_6 _inst_7 i f)
 but is expected to have type
-  forall {R : Type.{u1}} [_inst_1 : Ring.{u1} R] {Q : TypeMax.{u2, u1}} [_inst_2 : AddCommGroup.{max u1 u2} Q] [_inst_3 : Module.{u1, max u1 u2} R Q (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{max u1 u2} Q _inst_2)] {M : Type.{max u1 u2}} {N : Type.{max u1 u2}} [_inst_4 : AddCommGroup.{max u1 u2} M] [_inst_5 : AddCommGroup.{max u1 u2} N] [_inst_6 : Module.{u1, max u1 u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{max u1 u2} M _inst_4)] [_inst_7 : Module.{u1, max u1 u2} R N (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{max u1 u2} N _inst_5)] (i : LinearMap.{u1, u1, max u1 u2, max u1 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 N (AddCommGroup.toAddCommMonoid.{max u1 u2} M _inst_4) (AddCommGroup.toAddCommMonoid.{max u1 u2} N _inst_5) _inst_6 _inst_7) (f : LinearMap.{u1, u1, max u1 u2, max u1 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 Q (AddCommGroup.toAddCommMonoid.{max u1 u2} M _inst_4) (AddCommGroup.toAddCommMonoid.{max u1 u2} Q _inst_2) _inst_6 _inst_3) [_inst_8 : Fact (Function.Injective.{max (succ u1) (succ u2), max (succ u1) (succ u2)} M N (FunLike.coe.{max (succ u1) (succ u2), max (succ u1) (succ u2), max (succ u1) (succ u2)} (LinearMap.{u1, u1, max u1 u2, max u1 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 N (AddCommGroup.toAddCommMonoid.{max u1 u2} M _inst_4) (AddCommGroup.toAddCommMonoid.{max u1 u2} N _inst_5) _inst_6 _inst_7) M (fun (_x : M) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : M) => N) _x) (LinearMap.instFunLikeLinearMap.{u1, u1, max u1 u2, max u1 u2} R R M N (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{max u1 u2} M _inst_4) (AddCommGroup.toAddCommMonoid.{max u1 u2} N _inst_5) _inst_6 _inst_7 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1)))) i))], Inhabited.{max (succ u2) (succ u1)} (Module.Baer.ExtensionOf.{u1, u2} R _inst_1 Q _inst_2 _inst_3 M N _inst_4 _inst_5 _inst_6 _inst_7 i f)
+  forall {R : Type.{u1}} [_inst_1 : Ring.{u1} R] {Q : TypeMax.{u2, u1}} [_inst_2 : AddCommGroup.{max u1 u2} Q] [_inst_3 : Module.{u1, max u1 u2} R Q (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{max u1 u2} Q _inst_2)] {M : Type.{max u1 u2}} {N : Type.{max u1 u2}} [_inst_4 : AddCommGroup.{max u1 u2} M] [_inst_5 : AddCommGroup.{max u1 u2} N] [_inst_6 : Module.{u1, max u1 u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{max u1 u2} M _inst_4)] [_inst_7 : Module.{u1, max u1 u2} R N (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{max u1 u2} N _inst_5)] (i : LinearMap.{u1, u1, max u1 u2, max u1 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 N (AddCommGroup.toAddCommMonoid.{max u1 u2} M _inst_4) (AddCommGroup.toAddCommMonoid.{max u1 u2} N _inst_5) _inst_6 _inst_7) (f : LinearMap.{u1, u1, max u1 u2, max u1 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 Q (AddCommGroup.toAddCommMonoid.{max u1 u2} M _inst_4) (AddCommGroup.toAddCommMonoid.{max u1 u2} Q _inst_2) _inst_6 _inst_3) [_inst_8 : Fact (Function.Injective.{max (succ u1) (succ u2), max (succ u1) (succ u2)} M N (FunLike.coe.{max (succ u1) (succ u2), max (succ u1) (succ u2), max (succ u1) (succ u2)} (LinearMap.{u1, u1, max u1 u2, max u1 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 N (AddCommGroup.toAddCommMonoid.{max u1 u2} M _inst_4) (AddCommGroup.toAddCommMonoid.{max u1 u2} N _inst_5) _inst_6 _inst_7) M (fun (_x : M) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : M) => N) _x) (LinearMap.instFunLikeLinearMap.{u1, u1, max u1 u2, max u1 u2} R R M N (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{max u1 u2} M _inst_4) (AddCommGroup.toAddCommMonoid.{max u1 u2} N _inst_5) _inst_6 _inst_7 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1)))) i))], Inhabited.{max (succ u2) (succ u1)} (Module.Baer.ExtensionOf.{u1, u2} R _inst_1 Q _inst_2 _inst_3 M N _inst_4 _inst_5 _inst_6 _inst_7 i f)
 Case conversion may be inaccurate. Consider using '#align module.Baer.extension_of.inhabited Module.Baer.ExtensionOf.inhabitedₓ'. -/
 instance ExtensionOf.inhabited : Inhabited (ExtensionOf i f)
     where default :=
@@ -281,7 +281,7 @@ instance ExtensionOf.inhabited : Inhabited (ExtensionOf i f)
 lean 3 declaration is
   forall {R : Type.{u1}} [_inst_1 : Ring.{u1} R] {Q : Type.{max u1 u2}} [_inst_2 : AddCommGroup.{max u1 u2} Q] [_inst_3 : Module.{u1, max u1 u2} R Q (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{max u1 u2} Q _inst_2)] {M : Type.{max u1 u2}} {N : Type.{max u1 u2}} [_inst_4 : AddCommGroup.{max u1 u2} M] [_inst_5 : AddCommGroup.{max u1 u2} N] [_inst_6 : Module.{u1, max u1 u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{max u1 u2} M _inst_4)] [_inst_7 : Module.{u1, max u1 u2} R N (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{max u1 u2} N _inst_5)] (i : LinearMap.{u1, u1, max u1 u2, max u1 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 N (AddCommGroup.toAddCommMonoid.{max u1 u2} M _inst_4) (AddCommGroup.toAddCommMonoid.{max u1 u2} N _inst_5) _inst_6 _inst_7) (f : LinearMap.{u1, u1, max u1 u2, max u1 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 Q (AddCommGroup.toAddCommMonoid.{max u1 u2} M _inst_4) (AddCommGroup.toAddCommMonoid.{max u1 u2} Q _inst_2) _inst_6 _inst_3) [_inst_8 : Fact (Function.Injective.{succ (max u1 u2), succ (max u1 u2)} M N (coeFn.{succ (max u1 u2), succ (max u1 u2)} (LinearMap.{u1, u1, max u1 u2, max u1 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 N (AddCommGroup.toAddCommMonoid.{max u1 u2} M _inst_4) (AddCommGroup.toAddCommMonoid.{max u1 u2} N _inst_5) _inst_6 _inst_7) (fun (_x : LinearMap.{u1, u1, max u1 u2, max u1 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 N (AddCommGroup.toAddCommMonoid.{max u1 u2} M _inst_4) (AddCommGroup.toAddCommMonoid.{max u1 u2} N _inst_5) _inst_6 _inst_7) => M -> N) (LinearMap.hasCoeToFun.{u1, u1, max u1 u2, max u1 u2} R R M N (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{max u1 u2} M _inst_4) (AddCommGroup.toAddCommMonoid.{max u1 u2} N _inst_5) _inst_6 _inst_7 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1)))) i))], Module.Baer.ExtensionOf.{u1, u2} R _inst_1 Q _inst_2 _inst_3 M N _inst_4 _inst_5 _inst_6 _inst_7 i f
 but is expected to have type
-  forall {R : Type.{u1}} [_inst_1 : Ring.{u1} R] {Q : TypeMax.{u2, u1}} [_inst_2 : AddCommGroup.{max u1 u2} Q] [_inst_3 : Module.{u1, max u1 u2} R Q (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{max u1 u2} Q _inst_2)] {M : Type.{max u1 u2}} {N : Type.{max u1 u2}} [_inst_4 : AddCommGroup.{max u1 u2} M] [_inst_5 : AddCommGroup.{max u1 u2} N] [_inst_6 : Module.{u1, max u1 u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{max u1 u2} M _inst_4)] [_inst_7 : Module.{u1, max u1 u2} R N (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{max u1 u2} N _inst_5)] (i : LinearMap.{u1, u1, max u1 u2, max u1 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 N (AddCommGroup.toAddCommMonoid.{max u1 u2} M _inst_4) (AddCommGroup.toAddCommMonoid.{max u1 u2} N _inst_5) _inst_6 _inst_7) (f : LinearMap.{u1, u1, max u1 u2, max u1 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 Q (AddCommGroup.toAddCommMonoid.{max u1 u2} M _inst_4) (AddCommGroup.toAddCommMonoid.{max u1 u2} Q _inst_2) _inst_6 _inst_3) [_inst_8 : Fact (Function.Injective.{max (succ u1) (succ u2), max (succ u1) (succ u2)} M N (FunLike.coe.{max (succ u1) (succ u2), max (succ u1) (succ u2), max (succ u1) (succ u2)} (LinearMap.{u1, u1, max u1 u2, max u1 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 N (AddCommGroup.toAddCommMonoid.{max u1 u2} M _inst_4) (AddCommGroup.toAddCommMonoid.{max u1 u2} N _inst_5) _inst_6 _inst_7) M (fun (_x : M) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : M) => N) _x) (LinearMap.instFunLikeLinearMap.{u1, u1, max u1 u2, max u1 u2} R R M N (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{max u1 u2} M _inst_4) (AddCommGroup.toAddCommMonoid.{max u1 u2} N _inst_5) _inst_6 _inst_7 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1)))) i))], Module.Baer.ExtensionOf.{u1, u2} R _inst_1 Q _inst_2 _inst_3 M N _inst_4 _inst_5 _inst_6 _inst_7 i f
+  forall {R : Type.{u1}} [_inst_1 : Ring.{u1} R] {Q : TypeMax.{u2, u1}} [_inst_2 : AddCommGroup.{max u1 u2} Q] [_inst_3 : Module.{u1, max u1 u2} R Q (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{max u1 u2} Q _inst_2)] {M : Type.{max u1 u2}} {N : Type.{max u1 u2}} [_inst_4 : AddCommGroup.{max u1 u2} M] [_inst_5 : AddCommGroup.{max u1 u2} N] [_inst_6 : Module.{u1, max u1 u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{max u1 u2} M _inst_4)] [_inst_7 : Module.{u1, max u1 u2} R N (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{max u1 u2} N _inst_5)] (i : LinearMap.{u1, u1, max u1 u2, max u1 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 N (AddCommGroup.toAddCommMonoid.{max u1 u2} M _inst_4) (AddCommGroup.toAddCommMonoid.{max u1 u2} N _inst_5) _inst_6 _inst_7) (f : LinearMap.{u1, u1, max u1 u2, max u1 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 Q (AddCommGroup.toAddCommMonoid.{max u1 u2} M _inst_4) (AddCommGroup.toAddCommMonoid.{max u1 u2} Q _inst_2) _inst_6 _inst_3) [_inst_8 : Fact (Function.Injective.{max (succ u1) (succ u2), max (succ u1) (succ u2)} M N (FunLike.coe.{max (succ u1) (succ u2), max (succ u1) (succ u2), max (succ u1) (succ u2)} (LinearMap.{u1, u1, max u1 u2, max u1 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 N (AddCommGroup.toAddCommMonoid.{max u1 u2} M _inst_4) (AddCommGroup.toAddCommMonoid.{max u1 u2} N _inst_5) _inst_6 _inst_7) M (fun (_x : M) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : M) => N) _x) (LinearMap.instFunLikeLinearMap.{u1, u1, max u1 u2, max u1 u2} R R M N (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{max u1 u2} M _inst_4) (AddCommGroup.toAddCommMonoid.{max u1 u2} N _inst_5) _inst_6 _inst_7 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1)))) i))], Module.Baer.ExtensionOf.{u1, u2} R _inst_1 Q _inst_2 _inst_3 M N _inst_4 _inst_5 _inst_6 _inst_7 i f
 Case conversion may be inaccurate. Consider using '#align module.Baer.extension_of_max Module.Baer.extensionOfMaxₓ'. -/
 /-- Since every nonempty chain has a maximal element, by Zorn's lemma, there is a maximal
 `extension_of i f`. -/
@@ -294,7 +294,7 @@ def extensionOfMax : ExtensionOf i f :=
 lean 3 declaration is
   forall {R : Type.{u1}} [_inst_1 : Ring.{u1} R] {Q : Type.{max u1 u2}} [_inst_2 : AddCommGroup.{max u1 u2} Q] [_inst_3 : Module.{u1, max u1 u2} R Q (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{max u1 u2} Q _inst_2)] {M : Type.{max u1 u2}} {N : Type.{max u1 u2}} [_inst_4 : AddCommGroup.{max u1 u2} M] [_inst_5 : AddCommGroup.{max u1 u2} N] [_inst_6 : Module.{u1, max u1 u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{max u1 u2} M _inst_4)] [_inst_7 : Module.{u1, max u1 u2} R N (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{max u1 u2} N _inst_5)] (i : LinearMap.{u1, u1, max u1 u2, max u1 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 N (AddCommGroup.toAddCommMonoid.{max u1 u2} M _inst_4) (AddCommGroup.toAddCommMonoid.{max u1 u2} N _inst_5) _inst_6 _inst_7) (f : LinearMap.{u1, u1, max u1 u2, max u1 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 Q (AddCommGroup.toAddCommMonoid.{max u1 u2} M _inst_4) (AddCommGroup.toAddCommMonoid.{max u1 u2} Q _inst_2) _inst_6 _inst_3) [_inst_8 : Fact (Function.Injective.{succ (max u1 u2), succ (max u1 u2)} M N (coeFn.{succ (max u1 u2), succ (max u1 u2)} (LinearMap.{u1, u1, max u1 u2, max u1 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 N (AddCommGroup.toAddCommMonoid.{max u1 u2} M _inst_4) (AddCommGroup.toAddCommMonoid.{max u1 u2} N _inst_5) _inst_6 _inst_7) (fun (_x : LinearMap.{u1, u1, max u1 u2, max u1 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 N (AddCommGroup.toAddCommMonoid.{max u1 u2} M _inst_4) (AddCommGroup.toAddCommMonoid.{max u1 u2} N _inst_5) _inst_6 _inst_7) => M -> N) (LinearMap.hasCoeToFun.{u1, u1, max u1 u2, max u1 u2} R R M N (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{max u1 u2} M _inst_4) (AddCommGroup.toAddCommMonoid.{max u1 u2} N _inst_5) _inst_6 _inst_7 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1)))) i))] (a : Module.Baer.ExtensionOf.{u1, u2} R _inst_1 Q _inst_2 _inst_3 M N _inst_4 _inst_5 _inst_6 _inst_7 i f), (LE.le.{max u1 u2} (Module.Baer.ExtensionOf.{u1, u2} R _inst_1 Q _inst_2 _inst_3 M N _inst_4 _inst_5 _inst_6 _inst_7 i f) (Preorder.toHasLe.{max u1 u2} (Module.Baer.ExtensionOf.{u1, u2} R _inst_1 Q _inst_2 _inst_3 M N _inst_4 _inst_5 _inst_6 _inst_7 i f) (PartialOrder.toPreorder.{max u1 u2} (Module.Baer.ExtensionOf.{u1, u2} R _inst_1 Q _inst_2 _inst_3 M N _inst_4 _inst_5 _inst_6 _inst_7 i f) (SemilatticeInf.toPartialOrder.{max u1 u2} (Module.Baer.ExtensionOf.{u1, u2} R _inst_1 Q _inst_2 _inst_3 M N _inst_4 _inst_5 _inst_6 _inst_7 i f) (Module.Baer.ExtensionOf.semilatticeInf.{u1, u2} R _inst_1 Q _inst_2 _inst_3 M N _inst_4 _inst_5 _inst_6 _inst_7 i f)))) (Module.Baer.extensionOfMax.{u1, u2} R _inst_1 Q _inst_2 _inst_3 M N _inst_4 _inst_5 _inst_6 _inst_7 i f _inst_8) a) -> (Eq.{max (succ u1) (succ u2)} (Module.Baer.ExtensionOf.{u1, u2} R _inst_1 Q _inst_2 _inst_3 M N _inst_4 _inst_5 _inst_6 _inst_7 i f) a (Module.Baer.extensionOfMax.{u1, u2} R _inst_1 Q _inst_2 _inst_3 M N _inst_4 _inst_5 _inst_6 _inst_7 i f _inst_8))
 but is expected to have type
-  forall {R : Type.{u1}} [_inst_1 : Ring.{u1} R] {Q : TypeMax.{u2, u1}} [_inst_2 : AddCommGroup.{max u1 u2} Q] [_inst_3 : Module.{u1, max u1 u2} R Q (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{max u1 u2} Q _inst_2)] {M : Type.{max u1 u2}} {N : Type.{max u1 u2}} [_inst_4 : AddCommGroup.{max u1 u2} M] [_inst_5 : AddCommGroup.{max u1 u2} N] [_inst_6 : Module.{u1, max u1 u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{max u1 u2} M _inst_4)] [_inst_7 : Module.{u1, max u1 u2} R N (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{max u1 u2} N _inst_5)] (i : LinearMap.{u1, u1, max u1 u2, max u1 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 N (AddCommGroup.toAddCommMonoid.{max u1 u2} M _inst_4) (AddCommGroup.toAddCommMonoid.{max u1 u2} N _inst_5) _inst_6 _inst_7) (f : LinearMap.{u1, u1, max u1 u2, max u1 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 Q (AddCommGroup.toAddCommMonoid.{max u1 u2} M _inst_4) (AddCommGroup.toAddCommMonoid.{max u1 u2} Q _inst_2) _inst_6 _inst_3) [_inst_8 : Fact (Function.Injective.{max (succ u1) (succ u2), max (succ u1) (succ u2)} M N (FunLike.coe.{max (succ u1) (succ u2), max (succ u1) (succ u2), max (succ u1) (succ u2)} (LinearMap.{u1, u1, max u1 u2, max u1 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 N (AddCommGroup.toAddCommMonoid.{max u1 u2} M _inst_4) (AddCommGroup.toAddCommMonoid.{max u1 u2} N _inst_5) _inst_6 _inst_7) M (fun (_x : M) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : M) => N) _x) (LinearMap.instFunLikeLinearMap.{u1, u1, max u1 u2, max u1 u2} R R M N (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{max u1 u2} M _inst_4) (AddCommGroup.toAddCommMonoid.{max u1 u2} N _inst_5) _inst_6 _inst_7 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1)))) i))] (a : Module.Baer.ExtensionOf.{u1, u2} R _inst_1 Q _inst_2 _inst_3 M N _inst_4 _inst_5 _inst_6 _inst_7 i f), (LE.le.{max u1 u2} (Module.Baer.ExtensionOf.{u1, u2} R _inst_1 Q _inst_2 _inst_3 M N _inst_4 _inst_5 _inst_6 _inst_7 i f) (Preorder.toLE.{max u1 u2} (Module.Baer.ExtensionOf.{u1, u2} R _inst_1 Q _inst_2 _inst_3 M N _inst_4 _inst_5 _inst_6 _inst_7 i f) (PartialOrder.toPreorder.{max u1 u2} (Module.Baer.ExtensionOf.{u1, u2} R _inst_1 Q _inst_2 _inst_3 M N _inst_4 _inst_5 _inst_6 _inst_7 i f) (SemilatticeInf.toPartialOrder.{max u1 u2} (Module.Baer.ExtensionOf.{u1, u2} R _inst_1 Q _inst_2 _inst_3 M N _inst_4 _inst_5 _inst_6 _inst_7 i f) (Module.Baer.instSemilatticeInfExtensionOf.{u1, u2} R _inst_1 Q _inst_2 _inst_3 M N _inst_4 _inst_5 _inst_6 _inst_7 i f)))) (Module.Baer.extensionOfMax.{u1, u2} R _inst_1 Q _inst_2 _inst_3 M N _inst_4 _inst_5 _inst_6 _inst_7 i f _inst_8) a) -> (Eq.{max (succ u1) (succ u2)} (Module.Baer.ExtensionOf.{u1, u2} R _inst_1 Q _inst_2 _inst_3 M N _inst_4 _inst_5 _inst_6 _inst_7 i f) a (Module.Baer.extensionOfMax.{u1, u2} R _inst_1 Q _inst_2 _inst_3 M N _inst_4 _inst_5 _inst_6 _inst_7 i f _inst_8))
+  forall {R : Type.{u1}} [_inst_1 : Ring.{u1} R] {Q : TypeMax.{u2, u1}} [_inst_2 : AddCommGroup.{max u1 u2} Q] [_inst_3 : Module.{u1, max u1 u2} R Q (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{max u1 u2} Q _inst_2)] {M : Type.{max u1 u2}} {N : Type.{max u1 u2}} [_inst_4 : AddCommGroup.{max u1 u2} M] [_inst_5 : AddCommGroup.{max u1 u2} N] [_inst_6 : Module.{u1, max u1 u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{max u1 u2} M _inst_4)] [_inst_7 : Module.{u1, max u1 u2} R N (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{max u1 u2} N _inst_5)] (i : LinearMap.{u1, u1, max u1 u2, max u1 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 N (AddCommGroup.toAddCommMonoid.{max u1 u2} M _inst_4) (AddCommGroup.toAddCommMonoid.{max u1 u2} N _inst_5) _inst_6 _inst_7) (f : LinearMap.{u1, u1, max u1 u2, max u1 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 Q (AddCommGroup.toAddCommMonoid.{max u1 u2} M _inst_4) (AddCommGroup.toAddCommMonoid.{max u1 u2} Q _inst_2) _inst_6 _inst_3) [_inst_8 : Fact (Function.Injective.{max (succ u1) (succ u2), max (succ u1) (succ u2)} M N (FunLike.coe.{max (succ u1) (succ u2), max (succ u1) (succ u2), max (succ u1) (succ u2)} (LinearMap.{u1, u1, max u1 u2, max u1 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 N (AddCommGroup.toAddCommMonoid.{max u1 u2} M _inst_4) (AddCommGroup.toAddCommMonoid.{max u1 u2} N _inst_5) _inst_6 _inst_7) M (fun (_x : M) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : M) => N) _x) (LinearMap.instFunLikeLinearMap.{u1, u1, max u1 u2, max u1 u2} R R M N (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{max u1 u2} M _inst_4) (AddCommGroup.toAddCommMonoid.{max u1 u2} N _inst_5) _inst_6 _inst_7 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1)))) i))] (a : Module.Baer.ExtensionOf.{u1, u2} R _inst_1 Q _inst_2 _inst_3 M N _inst_4 _inst_5 _inst_6 _inst_7 i f), (LE.le.{max u1 u2} (Module.Baer.ExtensionOf.{u1, u2} R _inst_1 Q _inst_2 _inst_3 M N _inst_4 _inst_5 _inst_6 _inst_7 i f) (Preorder.toLE.{max u1 u2} (Module.Baer.ExtensionOf.{u1, u2} R _inst_1 Q _inst_2 _inst_3 M N _inst_4 _inst_5 _inst_6 _inst_7 i f) (PartialOrder.toPreorder.{max u1 u2} (Module.Baer.ExtensionOf.{u1, u2} R _inst_1 Q _inst_2 _inst_3 M N _inst_4 _inst_5 _inst_6 _inst_7 i f) (SemilatticeInf.toPartialOrder.{max u1 u2} (Module.Baer.ExtensionOf.{u1, u2} R _inst_1 Q _inst_2 _inst_3 M N _inst_4 _inst_5 _inst_6 _inst_7 i f) (Module.Baer.instSemilatticeInfExtensionOf.{u1, u2} R _inst_1 Q _inst_2 _inst_3 M N _inst_4 _inst_5 _inst_6 _inst_7 i f)))) (Module.Baer.extensionOfMax.{u1, u2} R _inst_1 Q _inst_2 _inst_3 M N _inst_4 _inst_5 _inst_6 _inst_7 i f _inst_8) a) -> (Eq.{max (succ u1) (succ u2)} (Module.Baer.ExtensionOf.{u1, u2} R _inst_1 Q _inst_2 _inst_3 M N _inst_4 _inst_5 _inst_6 _inst_7 i f) a (Module.Baer.extensionOfMax.{u1, u2} R _inst_1 Q _inst_2 _inst_3 M N _inst_4 _inst_5 _inst_6 _inst_7 i f _inst_8))
 Case conversion may be inaccurate. Consider using '#align module.Baer.extension_of_max_is_max Module.Baer.extensionOfMax_is_maxₓ'. -/
 theorem extensionOfMax_is_max :
     ∀ a : ExtensionOf i f, extensionOfMax i f ≤ a → a = extensionOfMax i f :=
@@ -320,7 +320,7 @@ private theorem extensionOfMax_adjoin.aux1 {y : N}
 lean 3 declaration is
   forall {R : Type.{u1}} [_inst_1 : Ring.{u1} R] {Q : Type.{max u1 u2}} [_inst_2 : AddCommGroup.{max u1 u2} Q] [_inst_3 : Module.{u1, max u1 u2} R Q (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{max u1 u2} Q _inst_2)] {M : Type.{max u1 u2}} {N : Type.{max u1 u2}} [_inst_4 : AddCommGroup.{max u1 u2} M] [_inst_5 : AddCommGroup.{max u1 u2} N] [_inst_6 : Module.{u1, max u1 u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{max u1 u2} M _inst_4)] [_inst_7 : Module.{u1, max u1 u2} R N (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{max u1 u2} N _inst_5)] (i : LinearMap.{u1, u1, max u1 u2, max u1 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 N (AddCommGroup.toAddCommMonoid.{max u1 u2} M _inst_4) (AddCommGroup.toAddCommMonoid.{max u1 u2} N _inst_5) _inst_6 _inst_7) {f : LinearMap.{u1, u1, max u1 u2, max u1 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 Q (AddCommGroup.toAddCommMonoid.{max u1 u2} M _inst_4) (AddCommGroup.toAddCommMonoid.{max u1 u2} Q _inst_2) _inst_6 _inst_3} [_inst_8 : Fact (Function.Injective.{succ (max u1 u2), succ (max u1 u2)} M N (coeFn.{succ (max u1 u2), succ (max u1 u2)} (LinearMap.{u1, u1, max u1 u2, max u1 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 N (AddCommGroup.toAddCommMonoid.{max u1 u2} M _inst_4) (AddCommGroup.toAddCommMonoid.{max u1 u2} N _inst_5) _inst_6 _inst_7) (fun (_x : LinearMap.{u1, u1, max u1 u2, max u1 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 N (AddCommGroup.toAddCommMonoid.{max u1 u2} M _inst_4) (AddCommGroup.toAddCommMonoid.{max u1 u2} N _inst_5) _inst_6 _inst_7) => M -> N) (LinearMap.hasCoeToFun.{u1, u1, max u1 u2, max u1 u2} R R M N (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{max u1 u2} M _inst_4) (AddCommGroup.toAddCommMonoid.{max u1 u2} N _inst_5) _inst_6 _inst_7 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1)))) i))] {y : N}, (coeSort.{succ (max u1 u2), succ (succ (max u1 u2))} (Submodule.{u1, max u1 u2} R N (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{max u1 u2} N _inst_5) _inst_7) Type.{max u1 u2} (SetLike.hasCoeToSort.{max u1 u2, max u1 u2} (Submodule.{u1, max u1 u2} R N (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{max u1 u2} N _inst_5) _inst_7) N (Submodule.setLike.{u1, max u1 u2} R N (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{max u1 u2} N _inst_5) _inst_7)) (Sup.sup.{max u1 u2} (Submodule.{u1, max u1 u2} R N (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{max u1 u2} N _inst_5) _inst_7) (SemilatticeSup.toHasSup.{max u1 u2} (Submodule.{u1, max u1 u2} R N (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{max u1 u2} N _inst_5) _inst_7) (Lattice.toSemilatticeSup.{max u1 u2} (Submodule.{u1, max u1 u2} R N (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{max u1 u2} N _inst_5) _inst_7) (ConditionallyCompleteLattice.toLattice.{max u1 u2} (Submodule.{u1, max u1 u2} R N (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{max u1 u2} N _inst_5) _inst_7) (CompleteLattice.toConditionallyCompleteLattice.{max u1 u2} (Submodule.{u1, max u1 u2} R N (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{max u1 u2} N _inst_5) _inst_7) (Submodule.completeLattice.{u1, max u1 u2} R N (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{max u1 u2} N _inst_5) _inst_7))))) (LinearPMap.domain.{u1, max u1 u2, max u1 u2} R _inst_1 N _inst_5 _inst_7 Q _inst_2 _inst_3 (Module.Baer.ExtensionOf.toLinearPmap.{u1, u2} R _inst_1 Q _inst_2 _inst_3 M N _inst_4 _inst_5 _inst_6 _inst_7 i f (Module.Baer.extensionOfMax.{u1, u2} R _inst_1 Q _inst_2 _inst_3 M N _inst_4 _inst_5 _inst_6 _inst_7 i f _inst_8))) (Submodule.span.{u1, max u1 u2} R N (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{max u1 u2} N _inst_5) _inst_7 (Singleton.singleton.{max u1 u2, max u1 u2} N (Set.{max u1 u2} N) (Set.hasSingleton.{max u1 u2} N) y)))) -> (coeSort.{succ (max u1 u2), succ (succ (max u1 u2))} (Submodule.{u1, max u1 u2} R N (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{max u1 u2} N _inst_5) _inst_7) Type.{max u1 u2} (SetLike.hasCoeToSort.{max u1 u2, max u1 u2} (Submodule.{u1, max u1 u2} R N (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{max u1 u2} N _inst_5) _inst_7) N (Submodule.setLike.{u1, max u1 u2} R N (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{max u1 u2} N _inst_5) _inst_7)) (LinearPMap.domain.{u1, max u1 u2, max u1 u2} R _inst_1 N _inst_5 _inst_7 Q _inst_2 _inst_3 (Module.Baer.ExtensionOf.toLinearPmap.{u1, u2} R _inst_1 Q _inst_2 _inst_3 M N _inst_4 _inst_5 _inst_6 _inst_7 i f (Module.Baer.extensionOfMax.{u1, u2} R _inst_1 Q _inst_2 _inst_3 M N _inst_4 _inst_5 _inst_6 _inst_7 i f _inst_8))))
 but is expected to have type
-  forall {R : Type.{u1}} [_inst_1 : Ring.{u1} R] {Q : TypeMax.{u2, u1}} [_inst_2 : AddCommGroup.{max u1 u2} Q] [_inst_3 : Module.{u1, max u1 u2} R Q (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{max u1 u2} Q _inst_2)] {M : Type.{max u1 u2}} {N : Type.{max u1 u2}} [_inst_4 : AddCommGroup.{max u1 u2} M] [_inst_5 : AddCommGroup.{max u1 u2} N] [_inst_6 : Module.{u1, max u1 u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{max u1 u2} M _inst_4)] [_inst_7 : Module.{u1, max u1 u2} R N (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{max u1 u2} N _inst_5)] (i : LinearMap.{u1, u1, max u1 u2, max u1 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 N (AddCommGroup.toAddCommMonoid.{max u1 u2} M _inst_4) (AddCommGroup.toAddCommMonoid.{max u1 u2} N _inst_5) _inst_6 _inst_7) {f : LinearMap.{u1, u1, max u1 u2, max u1 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 Q (AddCommGroup.toAddCommMonoid.{max u1 u2} M _inst_4) (AddCommGroup.toAddCommMonoid.{max u1 u2} Q _inst_2) _inst_6 _inst_3} [_inst_8 : Fact (Function.Injective.{max (succ u1) (succ u2), max (succ u1) (succ u2)} M N (FunLike.coe.{max (succ u1) (succ u2), max (succ u1) (succ u2), max (succ u1) (succ u2)} (LinearMap.{u1, u1, max u1 u2, max u1 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 N (AddCommGroup.toAddCommMonoid.{max u1 u2} M _inst_4) (AddCommGroup.toAddCommMonoid.{max u1 u2} N _inst_5) _inst_6 _inst_7) M (fun (_x : M) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : M) => N) _x) (LinearMap.instFunLikeLinearMap.{u1, u1, max u1 u2, max u1 u2} R R M N (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{max u1 u2} M _inst_4) (AddCommGroup.toAddCommMonoid.{max u1 u2} N _inst_5) _inst_6 _inst_7 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1)))) i))] {y : N}, (Subtype.{succ (max u1 u2)} N (fun (x : N) => Membership.mem.{max u1 u2, max u1 u2} N (Submodule.{u1, max u1 u2} R N (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{max u1 u2} N _inst_5) _inst_7) (SetLike.instMembership.{max u1 u2, max u1 u2} (Submodule.{u1, max u1 u2} R N (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{max u1 u2} N _inst_5) _inst_7) N (Submodule.setLike.{u1, max u1 u2} R N (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{max u1 u2} N _inst_5) _inst_7)) x (Module.Baer.supExtensionOfMaxSingleton.{u1, u2} R _inst_1 Q _inst_2 _inst_3 M N _inst_4 _inst_5 _inst_6 _inst_7 i f _inst_8 y))) -> (Subtype.{succ (max u1 u2)} N (fun (x : N) => Membership.mem.{max u1 u2, max u1 u2} N (Submodule.{u1, max u1 u2} R N (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{max u1 u2} N _inst_5) _inst_7) (SetLike.instMembership.{max u1 u2, max u1 u2} (Submodule.{u1, max u1 u2} R N (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{max u1 u2} N _inst_5) _inst_7) N (Submodule.setLike.{u1, max u1 u2} R N (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{max u1 u2} N _inst_5) _inst_7)) x (LinearPMap.domain.{u1, max u1 u2, max u1 u2} R _inst_1 N _inst_5 _inst_7 Q _inst_2 _inst_3 (Module.Baer.ExtensionOf.toLinearPMap.{u1, u2} R _inst_1 Q _inst_2 _inst_3 M N _inst_4 _inst_5 _inst_6 _inst_7 i f (Module.Baer.extensionOfMax.{u1, u2} R _inst_1 Q _inst_2 _inst_3 M N _inst_4 _inst_5 _inst_6 _inst_7 i f _inst_8)))))
+  forall {R : Type.{u1}} [_inst_1 : Ring.{u1} R] {Q : TypeMax.{u2, u1}} [_inst_2 : AddCommGroup.{max u1 u2} Q] [_inst_3 : Module.{u1, max u1 u2} R Q (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{max u1 u2} Q _inst_2)] {M : Type.{max u1 u2}} {N : Type.{max u1 u2}} [_inst_4 : AddCommGroup.{max u1 u2} M] [_inst_5 : AddCommGroup.{max u1 u2} N] [_inst_6 : Module.{u1, max u1 u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{max u1 u2} M _inst_4)] [_inst_7 : Module.{u1, max u1 u2} R N (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{max u1 u2} N _inst_5)] (i : LinearMap.{u1, u1, max u1 u2, max u1 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 N (AddCommGroup.toAddCommMonoid.{max u1 u2} M _inst_4) (AddCommGroup.toAddCommMonoid.{max u1 u2} N _inst_5) _inst_6 _inst_7) {f : LinearMap.{u1, u1, max u1 u2, max u1 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 Q (AddCommGroup.toAddCommMonoid.{max u1 u2} M _inst_4) (AddCommGroup.toAddCommMonoid.{max u1 u2} Q _inst_2) _inst_6 _inst_3} [_inst_8 : Fact (Function.Injective.{max (succ u1) (succ u2), max (succ u1) (succ u2)} M N (FunLike.coe.{max (succ u1) (succ u2), max (succ u1) (succ u2), max (succ u1) (succ u2)} (LinearMap.{u1, u1, max u1 u2, max u1 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 N (AddCommGroup.toAddCommMonoid.{max u1 u2} M _inst_4) (AddCommGroup.toAddCommMonoid.{max u1 u2} N _inst_5) _inst_6 _inst_7) M (fun (_x : M) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : M) => N) _x) (LinearMap.instFunLikeLinearMap.{u1, u1, max u1 u2, max u1 u2} R R M N (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{max u1 u2} M _inst_4) (AddCommGroup.toAddCommMonoid.{max u1 u2} N _inst_5) _inst_6 _inst_7 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1)))) i))] {y : N}, (Subtype.{succ (max u1 u2)} N (fun (x : N) => Membership.mem.{max u1 u2, max u1 u2} N (Submodule.{u1, max u1 u2} R N (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{max u1 u2} N _inst_5) _inst_7) (SetLike.instMembership.{max u1 u2, max u1 u2} (Submodule.{u1, max u1 u2} R N (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{max u1 u2} N _inst_5) _inst_7) N (Submodule.setLike.{u1, max u1 u2} R N (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{max u1 u2} N _inst_5) _inst_7)) x (Module.Baer.supExtensionOfMaxSingleton.{u1, u2} R _inst_1 Q _inst_2 _inst_3 M N _inst_4 _inst_5 _inst_6 _inst_7 i f _inst_8 y))) -> (Subtype.{succ (max u1 u2)} N (fun (x : N) => Membership.mem.{max u1 u2, max u1 u2} N (Submodule.{u1, max u1 u2} R N (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{max u1 u2} N _inst_5) _inst_7) (SetLike.instMembership.{max u1 u2, max u1 u2} (Submodule.{u1, max u1 u2} R N (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{max u1 u2} N _inst_5) _inst_7) N (Submodule.setLike.{u1, max u1 u2} R N (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{max u1 u2} N _inst_5) _inst_7)) x (LinearPMap.domain.{u1, max u1 u2, max u1 u2} R _inst_1 N _inst_5 _inst_7 Q _inst_2 _inst_3 (Module.Baer.ExtensionOf.toLinearPMap.{u1, u2} R _inst_1 Q _inst_2 _inst_3 M N _inst_4 _inst_5 _inst_6 _inst_7 i f (Module.Baer.extensionOfMax.{u1, u2} R _inst_1 Q _inst_2 _inst_3 M N _inst_4 _inst_5 _inst_6 _inst_7 i f _inst_8)))))
 Case conversion may be inaccurate. Consider using '#align module.Baer.extension_of_max_adjoin.fst Module.Baer.ExtensionOfMaxAdjoin.fstₓ'. -/
 /-- If `x ∈ M ⊔ ⟨y⟩`, then `x = m + r • y`, `fst` pick an arbitrary such `m`.-/
 def ExtensionOfMaxAdjoin.fst {y : N} (x : (extensionOfMax i f).domain ⊔ Submodule.span R {y}) :
@@ -332,7 +332,7 @@ def ExtensionOfMaxAdjoin.fst {y : N} (x : (extensionOfMax i f).domain ⊔ Submod
 lean 3 declaration is
   forall {R : Type.{u1}} [_inst_1 : Ring.{u1} R] {Q : Type.{max u1 u2}} [_inst_2 : AddCommGroup.{max u1 u2} Q] [_inst_3 : Module.{u1, max u1 u2} R Q (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{max u1 u2} Q _inst_2)] {M : Type.{max u1 u2}} {N : Type.{max u1 u2}} [_inst_4 : AddCommGroup.{max u1 u2} M] [_inst_5 : AddCommGroup.{max u1 u2} N] [_inst_6 : Module.{u1, max u1 u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{max u1 u2} M _inst_4)] [_inst_7 : Module.{u1, max u1 u2} R N (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{max u1 u2} N _inst_5)] (i : LinearMap.{u1, u1, max u1 u2, max u1 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 N (AddCommGroup.toAddCommMonoid.{max u1 u2} M _inst_4) (AddCommGroup.toAddCommMonoid.{max u1 u2} N _inst_5) _inst_6 _inst_7) {f : LinearMap.{u1, u1, max u1 u2, max u1 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 Q (AddCommGroup.toAddCommMonoid.{max u1 u2} M _inst_4) (AddCommGroup.toAddCommMonoid.{max u1 u2} Q _inst_2) _inst_6 _inst_3} [_inst_8 : Fact (Function.Injective.{succ (max u1 u2), succ (max u1 u2)} M N (coeFn.{succ (max u1 u2), succ (max u1 u2)} (LinearMap.{u1, u1, max u1 u2, max u1 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 N (AddCommGroup.toAddCommMonoid.{max u1 u2} M _inst_4) (AddCommGroup.toAddCommMonoid.{max u1 u2} N _inst_5) _inst_6 _inst_7) (fun (_x : LinearMap.{u1, u1, max u1 u2, max u1 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 N (AddCommGroup.toAddCommMonoid.{max u1 u2} M _inst_4) (AddCommGroup.toAddCommMonoid.{max u1 u2} N _inst_5) _inst_6 _inst_7) => M -> N) (LinearMap.hasCoeToFun.{u1, u1, max u1 u2, max u1 u2} R R M N (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{max u1 u2} M _inst_4) (AddCommGroup.toAddCommMonoid.{max u1 u2} N _inst_5) _inst_6 _inst_7 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1)))) i))] {y : N}, (coeSort.{succ (max u1 u2), succ (succ (max u1 u2))} (Submodule.{u1, max u1 u2} R N (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{max u1 u2} N _inst_5) _inst_7) Type.{max u1 u2} (SetLike.hasCoeToSort.{max u1 u2, max u1 u2} (Submodule.{u1, max u1 u2} R N (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{max u1 u2} N _inst_5) _inst_7) N (Submodule.setLike.{u1, max u1 u2} R N (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{max u1 u2} N _inst_5) _inst_7)) (Sup.sup.{max u1 u2} (Submodule.{u1, max u1 u2} R N (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{max u1 u2} N _inst_5) _inst_7) (SemilatticeSup.toHasSup.{max u1 u2} (Submodule.{u1, max u1 u2} R N (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{max u1 u2} N _inst_5) _inst_7) (Lattice.toSemilatticeSup.{max u1 u2} (Submodule.{u1, max u1 u2} R N (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{max u1 u2} N _inst_5) _inst_7) (ConditionallyCompleteLattice.toLattice.{max u1 u2} (Submodule.{u1, max u1 u2} R N (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{max u1 u2} N _inst_5) _inst_7) (CompleteLattice.toConditionallyCompleteLattice.{max u1 u2} (Submodule.{u1, max u1 u2} R N (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{max u1 u2} N _inst_5) _inst_7) (Submodule.completeLattice.{u1, max u1 u2} R N (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{max u1 u2} N _inst_5) _inst_7))))) (LinearPMap.domain.{u1, max u1 u2, max u1 u2} R _inst_1 N _inst_5 _inst_7 Q _inst_2 _inst_3 (Module.Baer.ExtensionOf.toLinearPmap.{u1, u2} R _inst_1 Q _inst_2 _inst_3 M N _inst_4 _inst_5 _inst_6 _inst_7 i f (Module.Baer.extensionOfMax.{u1, u2} R _inst_1 Q _inst_2 _inst_3 M N _inst_4 _inst_5 _inst_6 _inst_7 i f _inst_8))) (Submodule.span.{u1, max u1 u2} R N (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{max u1 u2} N _inst_5) _inst_7 (Singleton.singleton.{max u1 u2, max u1 u2} N (Set.{max u1 u2} N) (Set.hasSingleton.{max u1 u2} N) y)))) -> R
 but is expected to have type
-  forall {R : Type.{u1}} [_inst_1 : Ring.{u1} R] {Q : TypeMax.{u2, u1}} [_inst_2 : AddCommGroup.{max u1 u2} Q] [_inst_3 : Module.{u1, max u1 u2} R Q (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{max u1 u2} Q _inst_2)] {M : Type.{max u1 u2}} {N : Type.{max u1 u2}} [_inst_4 : AddCommGroup.{max u1 u2} M] [_inst_5 : AddCommGroup.{max u1 u2} N] [_inst_6 : Module.{u1, max u1 u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{max u1 u2} M _inst_4)] [_inst_7 : Module.{u1, max u1 u2} R N (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{max u1 u2} N _inst_5)] (i : LinearMap.{u1, u1, max u1 u2, max u1 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 N (AddCommGroup.toAddCommMonoid.{max u1 u2} M _inst_4) (AddCommGroup.toAddCommMonoid.{max u1 u2} N _inst_5) _inst_6 _inst_7) {f : LinearMap.{u1, u1, max u1 u2, max u1 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 Q (AddCommGroup.toAddCommMonoid.{max u1 u2} M _inst_4) (AddCommGroup.toAddCommMonoid.{max u1 u2} Q _inst_2) _inst_6 _inst_3} [_inst_8 : Fact (Function.Injective.{max (succ u1) (succ u2), max (succ u1) (succ u2)} M N (FunLike.coe.{max (succ u1) (succ u2), max (succ u1) (succ u2), max (succ u1) (succ u2)} (LinearMap.{u1, u1, max u1 u2, max u1 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 N (AddCommGroup.toAddCommMonoid.{max u1 u2} M _inst_4) (AddCommGroup.toAddCommMonoid.{max u1 u2} N _inst_5) _inst_6 _inst_7) M (fun (_x : M) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : M) => N) _x) (LinearMap.instFunLikeLinearMap.{u1, u1, max u1 u2, max u1 u2} R R M N (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{max u1 u2} M _inst_4) (AddCommGroup.toAddCommMonoid.{max u1 u2} N _inst_5) _inst_6 _inst_7 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1)))) i))] {y : N}, (Subtype.{succ (max u1 u2)} N (fun (x : N) => Membership.mem.{max u1 u2, max u1 u2} N (Submodule.{u1, max u1 u2} R N (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{max u1 u2} N _inst_5) _inst_7) (SetLike.instMembership.{max u1 u2, max u1 u2} (Submodule.{u1, max u1 u2} R N (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{max u1 u2} N _inst_5) _inst_7) N (Submodule.setLike.{u1, max u1 u2} R N (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{max u1 u2} N _inst_5) _inst_7)) x (Module.Baer.supExtensionOfMaxSingleton.{u1, u2} R _inst_1 Q _inst_2 _inst_3 M N _inst_4 _inst_5 _inst_6 _inst_7 i f _inst_8 y))) -> R
+  forall {R : Type.{u1}} [_inst_1 : Ring.{u1} R] {Q : TypeMax.{u2, u1}} [_inst_2 : AddCommGroup.{max u1 u2} Q] [_inst_3 : Module.{u1, max u1 u2} R Q (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{max u1 u2} Q _inst_2)] {M : Type.{max u1 u2}} {N : Type.{max u1 u2}} [_inst_4 : AddCommGroup.{max u1 u2} M] [_inst_5 : AddCommGroup.{max u1 u2} N] [_inst_6 : Module.{u1, max u1 u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{max u1 u2} M _inst_4)] [_inst_7 : Module.{u1, max u1 u2} R N (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{max u1 u2} N _inst_5)] (i : LinearMap.{u1, u1, max u1 u2, max u1 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 N (AddCommGroup.toAddCommMonoid.{max u1 u2} M _inst_4) (AddCommGroup.toAddCommMonoid.{max u1 u2} N _inst_5) _inst_6 _inst_7) {f : LinearMap.{u1, u1, max u1 u2, max u1 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 Q (AddCommGroup.toAddCommMonoid.{max u1 u2} M _inst_4) (AddCommGroup.toAddCommMonoid.{max u1 u2} Q _inst_2) _inst_6 _inst_3} [_inst_8 : Fact (Function.Injective.{max (succ u1) (succ u2), max (succ u1) (succ u2)} M N (FunLike.coe.{max (succ u1) (succ u2), max (succ u1) (succ u2), max (succ u1) (succ u2)} (LinearMap.{u1, u1, max u1 u2, max u1 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 N (AddCommGroup.toAddCommMonoid.{max u1 u2} M _inst_4) (AddCommGroup.toAddCommMonoid.{max u1 u2} N _inst_5) _inst_6 _inst_7) M (fun (_x : M) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : M) => N) _x) (LinearMap.instFunLikeLinearMap.{u1, u1, max u1 u2, max u1 u2} R R M N (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{max u1 u2} M _inst_4) (AddCommGroup.toAddCommMonoid.{max u1 u2} N _inst_5) _inst_6 _inst_7 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1)))) i))] {y : N}, (Subtype.{succ (max u1 u2)} N (fun (x : N) => Membership.mem.{max u1 u2, max u1 u2} N (Submodule.{u1, max u1 u2} R N (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{max u1 u2} N _inst_5) _inst_7) (SetLike.instMembership.{max u1 u2, max u1 u2} (Submodule.{u1, max u1 u2} R N (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{max u1 u2} N _inst_5) _inst_7) N (Submodule.setLike.{u1, max u1 u2} R N (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{max u1 u2} N _inst_5) _inst_7)) x (Module.Baer.supExtensionOfMaxSingleton.{u1, u2} R _inst_1 Q _inst_2 _inst_3 M N _inst_4 _inst_5 _inst_6 _inst_7 i f _inst_8 y))) -> R
 Case conversion may be inaccurate. Consider using '#align module.Baer.extension_of_max_adjoin.snd Module.Baer.ExtensionOfMaxAdjoin.sndₓ'. -/
 /-- If `x ∈ M ⊔ ⟨y⟩`, then `x = m + r • y`, `snd` pick an arbitrary such `r`.-/
 def ExtensionOfMaxAdjoin.snd {y : N} (x : (extensionOfMax i f).domain ⊔ Submodule.span R {y}) : R :=
@@ -343,7 +343,7 @@ def ExtensionOfMaxAdjoin.snd {y : N} (x : (extensionOfMax i f).domain ⊔ Submod
 lean 3 declaration is
   forall {R : Type.{u1}} [_inst_1 : Ring.{u1} R] {Q : Type.{max u1 u2}} [_inst_2 : AddCommGroup.{max u1 u2} Q] [_inst_3 : Module.{u1, max u1 u2} R Q (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{max u1 u2} Q _inst_2)] {M : Type.{max u1 u2}} {N : Type.{max u1 u2}} [_inst_4 : AddCommGroup.{max u1 u2} M] [_inst_5 : AddCommGroup.{max u1 u2} N] [_inst_6 : Module.{u1, max u1 u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{max u1 u2} M _inst_4)] [_inst_7 : Module.{u1, max u1 u2} R N (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{max u1 u2} N _inst_5)] (i : LinearMap.{u1, u1, max u1 u2, max u1 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 N (AddCommGroup.toAddCommMonoid.{max u1 u2} M _inst_4) (AddCommGroup.toAddCommMonoid.{max u1 u2} N _inst_5) _inst_6 _inst_7) {f : LinearMap.{u1, u1, max u1 u2, max u1 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 Q (AddCommGroup.toAddCommMonoid.{max u1 u2} M _inst_4) (AddCommGroup.toAddCommMonoid.{max u1 u2} Q _inst_2) _inst_6 _inst_3} [_inst_8 : Fact (Function.Injective.{succ (max u1 u2), succ (max u1 u2)} M N (coeFn.{succ (max u1 u2), succ (max u1 u2)} (LinearMap.{u1, u1, max u1 u2, max u1 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 N (AddCommGroup.toAddCommMonoid.{max u1 u2} M _inst_4) (AddCommGroup.toAddCommMonoid.{max u1 u2} N _inst_5) _inst_6 _inst_7) (fun (_x : LinearMap.{u1, u1, max u1 u2, max u1 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 N (AddCommGroup.toAddCommMonoid.{max u1 u2} M _inst_4) (AddCommGroup.toAddCommMonoid.{max u1 u2} N _inst_5) _inst_6 _inst_7) => M -> N) (LinearMap.hasCoeToFun.{u1, u1, max u1 u2, max u1 u2} R R M N (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{max u1 u2} M _inst_4) (AddCommGroup.toAddCommMonoid.{max u1 u2} N _inst_5) _inst_6 _inst_7 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1)))) i))] {y : N} (x : coeSort.{succ (max u1 u2), succ (succ (max u1 u2))} (Submodule.{u1, max u1 u2} R N (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{max u1 u2} N _inst_5) _inst_7) Type.{max u1 u2} (SetLike.hasCoeToSort.{max u1 u2, max u1 u2} (Submodule.{u1, max u1 u2} R N (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{max u1 u2} N _inst_5) _inst_7) N (Submodule.setLike.{u1, max u1 u2} R N (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{max u1 u2} N _inst_5) _inst_7)) (Sup.sup.{max u1 u2} (Submodule.{u1, max u1 u2} 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_inst_5 _inst_7 Q _inst_2 _inst_3 (Module.Baer.ExtensionOf.toLinearPmap.{u1, u2} R _inst_1 Q _inst_2 _inst_3 M N _inst_4 _inst_5 _inst_6 _inst_7 i f (Module.Baer.extensionOfMax.{u1, u2} R _inst_1 Q _inst_2 _inst_3 M N _inst_4 _inst_5 _inst_6 _inst_7 i f _inst_8))) (Submodule.span.{u1, max u1 u2} R N (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{max u1 u2} N _inst_5) _inst_7 (Singleton.singleton.{max u1 u2, max u1 u2} N (Set.{max u1 u2} N) (Set.hasSingleton.{max u1 u2} N) y)))), Eq.{succ (max u1 u2)} N ((fun (a : Type.{max u1 u2}) (b : Type.{max u1 u2}) [self : HasLiftT.{succ (max u1 u2), succ (max u1 u2)} a b] => self.0) (coeSort.{succ (max u1 u2), succ (succ (max u1 u2))} (Submodule.{u1, max u1 u2} R N (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{max u1 u2} N _inst_5) _inst_7) Type.{max u1 u2} (SetLike.hasCoeToSort.{max u1 u2, max u1 u2} (Submodule.{u1, max u1 u2} R N (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{max u1 u2} N 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_inst_5 _inst_7 Q _inst_2 _inst_3 (Module.Baer.ExtensionOf.toLinearPmap.{u1, u2} R _inst_1 Q _inst_2 _inst_3 M N _inst_4 _inst_5 _inst_6 _inst_7 i f (Module.Baer.extensionOfMax.{u1, u2} R _inst_1 Q _inst_2 _inst_3 M N _inst_4 _inst_5 _inst_6 _inst_7 i f _inst_8)))) N (CoeTCₓ.coe.{succ (max u1 u2), succ (max u1 u2)} (coeSort.{succ (max u1 u2), succ (succ (max u1 u2))} (Submodule.{u1, max u1 u2} R N (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{max u1 u2} N _inst_5) _inst_7) Type.{max u1 u2} (SetLike.hasCoeToSort.{max u1 u2, max u1 u2} (Submodule.{u1, max u1 u2} R N (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{max u1 u2} N _inst_5) _inst_7) N (Submodule.setLike.{u1, max u1 u2} R N (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{max u1 u2} N _inst_5) _inst_7)) (LinearPMap.domain.{u1, max u1 u2, max u1 u2} R _inst_1 N _inst_5 _inst_7 Q _inst_2 _inst_3 (Module.Baer.ExtensionOf.toLinearPmap.{u1, u2} R _inst_1 Q _inst_2 _inst_3 M N _inst_4 _inst_5 _inst_6 _inst_7 i f (Module.Baer.extensionOfMax.{u1, u2} R _inst_1 Q _inst_2 _inst_3 M N _inst_4 _inst_5 _inst_6 _inst_7 i f _inst_8)))) N (coeBase.{succ (max u1 u2), succ (max u1 u2)} (coeSort.{succ (max u1 u2), succ (succ (max u1 u2))} (Submodule.{u1, max u1 u2} R N (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{max u1 u2} N _inst_5) _inst_7) Type.{max u1 u2} (SetLike.hasCoeToSort.{max u1 u2, max u1 u2} (Submodule.{u1, max u1 u2} R N (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{max u1 u2} N _inst_5) _inst_7) N (Submodule.setLike.{u1, max u1 u2} R N (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{max u1 u2} N _inst_5) _inst_7)) (LinearPMap.domain.{u1, max u1 u2, max u1 u2} R _inst_1 N _inst_5 _inst_7 Q _inst_2 _inst_3 (Module.Baer.ExtensionOf.toLinearPmap.{u1, u2} R _inst_1 Q _inst_2 _inst_3 M N _inst_4 _inst_5 _inst_6 _inst_7 i f (Module.Baer.extensionOfMax.{u1, u2} R _inst_1 Q _inst_2 _inst_3 M N _inst_4 _inst_5 _inst_6 _inst_7 i f _inst_8)))) N (coeSubtype.{succ (max u1 u2)} N (fun (x : N) => Membership.Mem.{max u1 u2, max u1 u2} N (Submodule.{u1, max u1 u2} R N (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{max u1 u2} N _inst_5) _inst_7) (SetLike.hasMem.{max u1 u2, max u1 u2} (Submodule.{u1, max u1 u2} R N (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{max u1 u2} N _inst_5) _inst_7) N (Submodule.setLike.{u1, max u1 u2} R N (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{max u1 u2} N _inst_5) _inst_7)) x (LinearPMap.domain.{u1, max u1 u2, max u1 u2} R _inst_1 N _inst_5 _inst_7 Q _inst_2 _inst_3 (Module.Baer.ExtensionOf.toLinearPmap.{u1, u2} R _inst_1 Q _inst_2 _inst_3 M N _inst_4 _inst_5 _inst_6 _inst_7 i f (Module.Baer.extensionOfMax.{u1, u2} R _inst_1 Q _inst_2 _inst_3 M N _inst_4 _inst_5 _inst_6 _inst_7 i f _inst_8)))))))) (Module.Baer.ExtensionOfMaxAdjoin.fst.{u1, u2} R _inst_1 Q _inst_2 _inst_3 M N _inst_4 _inst_5 _inst_6 _inst_7 i f _inst_8 y x)) (SMul.smul.{u1, max u1 u2} R N (SMulZeroClass.toHasSmul.{u1, max u1 u2} R N (AddZeroClass.toHasZero.{max u1 u2} N (AddMonoid.toAddZeroClass.{max u1 u2} N (AddCommMonoid.toAddMonoid.{max u1 u2} N (AddCommGroup.toAddCommMonoid.{max u1 u2} N _inst_5)))) (SMulWithZero.toSmulZeroClass.{u1, max u1 u2} R N (MulZeroClass.toHasZero.{u1} R (MulZeroOneClass.toMulZeroClass.{u1} R (MonoidWithZero.toMulZeroOneClass.{u1} R (Semiring.toMonoidWithZero.{u1} R (Ring.toSemiring.{u1} R _inst_1))))) (AddZeroClass.toHasZero.{max u1 u2} N (AddMonoid.toAddZeroClass.{max u1 u2} N (AddCommMonoid.toAddMonoid.{max u1 u2} N (AddCommGroup.toAddCommMonoid.{max u1 u2} N _inst_5)))) (MulActionWithZero.toSMulWithZero.{u1, max u1 u2} R N (Semiring.toMonoidWithZero.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (AddZeroClass.toHasZero.{max u1 u2} N (AddMonoid.toAddZeroClass.{max u1 u2} N (AddCommMonoid.toAddMonoid.{max u1 u2} N (AddCommGroup.toAddCommMonoid.{max u1 u2} N _inst_5)))) (Module.toMulActionWithZero.{u1, max u1 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 but is expected to have type
-  forall {R : Type.{u1}} [_inst_1 : Ring.{u1} R] {Q : TypeMax.{u2, u1}} [_inst_2 : AddCommGroup.{max u1 u2} Q] [_inst_3 : Module.{u1, max u1 u2} R Q (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{max u1 u2} Q _inst_2)] {M : Type.{max u1 u2}} {N : Type.{max u1 u2}} [_inst_4 : AddCommGroup.{max u1 u2} M] [_inst_5 : AddCommGroup.{max u1 u2} N] [_inst_6 : Module.{u1, max u1 u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{max u1 u2} M _inst_4)] [_inst_7 : Module.{u1, max u1 u2} R N (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{max u1 u2} N _inst_5)] (i : LinearMap.{u1, u1, max u1 u2, max u1 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 N (AddCommGroup.toAddCommMonoid.{max u1 u2} M _inst_4) (AddCommGroup.toAddCommMonoid.{max u1 u2} N _inst_5) _inst_6 _inst_7) {f : LinearMap.{u1, u1, max u1 u2, max u1 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 Q (AddCommGroup.toAddCommMonoid.{max u1 u2} M _inst_4) (AddCommGroup.toAddCommMonoid.{max u1 u2} Q _inst_2) _inst_6 _inst_3} [_inst_8 : Fact (Function.Injective.{max (succ u1) (succ u2), max (succ u1) (succ u2)} M N (FunLike.coe.{max (succ u1) (succ u2), max (succ u1) (succ u2), max (succ u1) (succ u2)} (LinearMap.{u1, u1, max u1 u2, max u1 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 N (AddCommGroup.toAddCommMonoid.{max u1 u2} M _inst_4) (AddCommGroup.toAddCommMonoid.{max u1 u2} N _inst_5) _inst_6 _inst_7) M (fun (_x : M) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : M) => N) _x) (LinearMap.instFunLikeLinearMap.{u1, u1, max u1 u2, max u1 u2} R R M N (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{max u1 u2} M _inst_4) (AddCommGroup.toAddCommMonoid.{max u1 u2} N _inst_5) _inst_6 _inst_7 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1)))) i))] {y : N} (x : Subtype.{succ (max u1 u2)} N (fun (x : N) => Membership.mem.{max u1 u2, max u1 u2} N (Submodule.{u1, max u1 u2} R N (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{max u1 u2} N _inst_5) _inst_7) (SetLike.instMembership.{max u1 u2, max u1 u2} (Submodule.{u1, max u1 u2} R N (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{max u1 u2} N _inst_5) _inst_7) N (Submodule.setLike.{u1, max u1 u2} R N (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{max u1 u2} N _inst_5) _inst_7)) x (Module.Baer.supExtensionOfMaxSingleton.{u1, u2} R _inst_1 Q _inst_2 _inst_3 M N _inst_4 _inst_5 _inst_6 _inst_7 i f _inst_8 y))), Eq.{max (succ u1) (succ u2)} N (Subtype.val.{succ (max u1 u2)} N (fun (x : N) => 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(Submodule.{u1, max u1 u2} R N (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{max u1 u2} N _inst_5) _inst_7) N (Submodule.setLike.{u1, max u1 u2} R N (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{max u1 u2} N _inst_5) _inst_7) (LinearPMap.domain.{u1, max u1 u2, max u1 u2} R _inst_1 N _inst_5 _inst_7 Q _inst_2 _inst_3 (Module.Baer.ExtensionOf.toLinearPMap.{u1, u2} R _inst_1 Q _inst_2 _inst_3 M N _inst_4 _inst_5 _inst_6 _inst_7 i f (Module.Baer.extensionOfMax.{u1, u2} R _inst_1 Q _inst_2 _inst_3 M N _inst_4 _inst_5 _inst_6 _inst_7 i f _inst_8))))) (Module.Baer.ExtensionOfMaxAdjoin.fst.{u1, u2} R _inst_1 Q _inst_2 _inst_3 M N _inst_4 _inst_5 _inst_6 _inst_7 i f _inst_8 y x)) (HSMul.hSMul.{u1, max u1 u2, max u1 u2} R N N (instHSMul.{u1, max u1 u2} R N (SMulZeroClass.toSMul.{u1, max u1 u2} R N (NegZeroClass.toZero.{max u1 u2} N (SubNegZeroMonoid.toNegZeroClass.{max u1 u2} N (SubtractionMonoid.toSubNegZeroMonoid.{max u1 u2} N (SubtractionCommMonoid.toSubtractionMonoid.{max u1 u2} N (AddCommGroup.toDivisionAddCommMonoid.{max u1 u2} N _inst_5))))) (SMulWithZero.toSMulZeroClass.{u1, max u1 u2} R N (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (NegZeroClass.toZero.{max u1 u2} N (SubNegZeroMonoid.toNegZeroClass.{max u1 u2} N (SubtractionMonoid.toSubNegZeroMonoid.{max u1 u2} N (SubtractionCommMonoid.toSubtractionMonoid.{max u1 u2} N (AddCommGroup.toDivisionAddCommMonoid.{max u1 u2} N _inst_5))))) (MulActionWithZero.toSMulWithZero.{u1, max u1 u2} R N (Semiring.toMonoidWithZero.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (NegZeroClass.toZero.{max u1 u2} N (SubNegZeroMonoid.toNegZeroClass.{max u1 u2} N (SubtractionMonoid.toSubNegZeroMonoid.{max u1 u2} N (SubtractionCommMonoid.toSubtractionMonoid.{max u1 u2} N (AddCommGroup.toDivisionAddCommMonoid.{max u1 u2} N _inst_5))))) (Module.toMulActionWithZero.{u1, max u1 u2} R N (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{max u1 u2} N _inst_5) _inst_7))))) (Module.Baer.ExtensionOfMaxAdjoin.snd.{u1, u2} R _inst_1 Q _inst_2 _inst_3 M N _inst_4 _inst_5 _inst_6 _inst_7 i f _inst_8 y x) y))
+  forall {R : Type.{u1}} [_inst_1 : Ring.{u1} R] {Q : TypeMax.{u2, u1}} [_inst_2 : AddCommGroup.{max u1 u2} Q] [_inst_3 : Module.{u1, max u1 u2} R Q (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{max u1 u2} Q _inst_2)] {M : Type.{max u1 u2}} {N : Type.{max u1 u2}} [_inst_4 : AddCommGroup.{max u1 u2} M] [_inst_5 : AddCommGroup.{max u1 u2} N] [_inst_6 : Module.{u1, max u1 u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{max u1 u2} M _inst_4)] [_inst_7 : Module.{u1, max u1 u2} R N (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{max u1 u2} N _inst_5)] (i : LinearMap.{u1, u1, max u1 u2, max u1 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 N (AddCommGroup.toAddCommMonoid.{max u1 u2} M _inst_4) (AddCommGroup.toAddCommMonoid.{max u1 u2} N _inst_5) _inst_6 _inst_7) {f : LinearMap.{u1, u1, max u1 u2, max u1 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 Q (AddCommGroup.toAddCommMonoid.{max u1 u2} M _inst_4) (AddCommGroup.toAddCommMonoid.{max u1 u2} Q _inst_2) _inst_6 _inst_3} [_inst_8 : Fact (Function.Injective.{max (succ u1) (succ u2), max (succ u1) (succ u2)} M N (FunLike.coe.{max (succ u1) (succ u2), max (succ u1) (succ u2), max (succ u1) (succ u2)} (LinearMap.{u1, u1, max u1 u2, max u1 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 N (AddCommGroup.toAddCommMonoid.{max u1 u2} M _inst_4) (AddCommGroup.toAddCommMonoid.{max u1 u2} N _inst_5) _inst_6 _inst_7) M (fun (_x : M) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : M) => N) _x) (LinearMap.instFunLikeLinearMap.{u1, u1, max u1 u2, max u1 u2} R R M N (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{max u1 u2} M _inst_4) (AddCommGroup.toAddCommMonoid.{max u1 u2} N _inst_5) _inst_6 _inst_7 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1)))) i))] {y : N} (x : Subtype.{succ (max u1 u2)} N (fun (x : N) => Membership.mem.{max u1 u2, max u1 u2} N (Submodule.{u1, max u1 u2} R N (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{max u1 u2} N _inst_5) _inst_7) (SetLike.instMembership.{max u1 u2, max u1 u2} (Submodule.{u1, max u1 u2} R N (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{max u1 u2} N _inst_5) _inst_7) N (Submodule.setLike.{u1, max u1 u2} R N (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{max u1 u2} N _inst_5) _inst_7)) x (Module.Baer.supExtensionOfMaxSingleton.{u1, u2} R _inst_1 Q _inst_2 _inst_3 M N _inst_4 _inst_5 _inst_6 _inst_7 i f _inst_8 y))), Eq.{max (succ u1) (succ u2)} N (Subtype.val.{succ (max u1 u2)} N (fun (x : N) => 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(Submodule.{u1, max u1 u2} R N (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{max u1 u2} N _inst_5) _inst_7) N (Submodule.setLike.{u1, max u1 u2} R N (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{max u1 u2} N _inst_5) _inst_7) (LinearPMap.domain.{u1, max u1 u2, max u1 u2} R _inst_1 N _inst_5 _inst_7 Q _inst_2 _inst_3 (Module.Baer.ExtensionOf.toLinearPMap.{u1, u2} R _inst_1 Q _inst_2 _inst_3 M N _inst_4 _inst_5 _inst_6 _inst_7 i f (Module.Baer.extensionOfMax.{u1, u2} R _inst_1 Q _inst_2 _inst_3 M N _inst_4 _inst_5 _inst_6 _inst_7 i f _inst_8))))) (Module.Baer.ExtensionOfMaxAdjoin.fst.{u1, u2} R _inst_1 Q _inst_2 _inst_3 M N _inst_4 _inst_5 _inst_6 _inst_7 i f _inst_8 y x)) (HSMul.hSMul.{u1, max u1 u2, max u1 u2} R N N (instHSMul.{u1, max u1 u2} R N (SMulZeroClass.toSMul.{u1, max u1 u2} R N (NegZeroClass.toZero.{max u1 u2} N (SubNegZeroMonoid.toNegZeroClass.{max u1 u2} N (SubtractionMonoid.toSubNegZeroMonoid.{max u1 u2} N (SubtractionCommMonoid.toSubtractionMonoid.{max u1 u2} N (AddCommGroup.toDivisionAddCommMonoid.{max u1 u2} N _inst_5))))) (SMulWithZero.toSMulZeroClass.{u1, max u1 u2} R N (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (NegZeroClass.toZero.{max u1 u2} N (SubNegZeroMonoid.toNegZeroClass.{max u1 u2} N (SubtractionMonoid.toSubNegZeroMonoid.{max u1 u2} N (SubtractionCommMonoid.toSubtractionMonoid.{max u1 u2} N (AddCommGroup.toDivisionAddCommMonoid.{max u1 u2} N _inst_5))))) (MulActionWithZero.toSMulWithZero.{u1, max u1 u2} R N (Semiring.toMonoidWithZero.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (NegZeroClass.toZero.{max u1 u2} N (SubNegZeroMonoid.toNegZeroClass.{max u1 u2} N (SubtractionMonoid.toSubNegZeroMonoid.{max u1 u2} N (SubtractionCommMonoid.toSubtractionMonoid.{max u1 u2} N (AddCommGroup.toDivisionAddCommMonoid.{max u1 u2} N _inst_5))))) (Module.toMulActionWithZero.{u1, max u1 u2} R N (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{max u1 u2} N _inst_5) _inst_7))))) (Module.Baer.ExtensionOfMaxAdjoin.snd.{u1, u2} R _inst_1 Q _inst_2 _inst_3 M N _inst_4 _inst_5 _inst_6 _inst_7 i f _inst_8 y x) y))
 Case conversion may be inaccurate. Consider using '#align module.Baer.extension_of_max_adjoin.eqn Module.Baer.ExtensionOfMaxAdjoin.eqnₓ'. -/
 theorem ExtensionOfMaxAdjoin.eqn {y : N} (x : (extensionOfMax i f).domain ⊔ Submodule.span R {y}) :
     ↑x = ↑(ExtensionOfMaxAdjoin.fst i x) + ExtensionOfMaxAdjoin.snd i x • y :=
@@ -356,7 +356,7 @@ variable (f)
 lean 3 declaration is
   forall {R : Type.{u1}} [_inst_1 : Ring.{u1} R] {Q : Type.{max u1 u2}} [_inst_2 : AddCommGroup.{max u1 u2} Q] [_inst_3 : Module.{u1, max u1 u2} R Q (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{max u1 u2} Q _inst_2)] {M : Type.{max u1 u2}} {N : Type.{max u1 u2}} [_inst_4 : AddCommGroup.{max u1 u2} M] [_inst_5 : AddCommGroup.{max u1 u2} N] [_inst_6 : Module.{u1, max u1 u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{max u1 u2} M _inst_4)] [_inst_7 : Module.{u1, max u1 u2} R N (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{max u1 u2} N _inst_5)] (i : LinearMap.{u1, u1, max u1 u2, max u1 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 N (AddCommGroup.toAddCommMonoid.{max u1 u2} M _inst_4) (AddCommGroup.toAddCommMonoid.{max u1 u2} N _inst_5) _inst_6 _inst_7), (LinearMap.{u1, u1, max u1 u2, max u1 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 Q (AddCommGroup.toAddCommMonoid.{max u1 u2} M _inst_4) (AddCommGroup.toAddCommMonoid.{max u1 u2} Q _inst_2) _inst_6 _inst_3) -> (forall [_inst_8 : Fact (Function.Injective.{succ (max u1 u2), succ (max u1 u2)} M N (coeFn.{succ (max u1 u2), succ (max u1 u2)} (LinearMap.{u1, u1, max u1 u2, max u1 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 N (AddCommGroup.toAddCommMonoid.{max u1 u2} M _inst_4) (AddCommGroup.toAddCommMonoid.{max u1 u2} N _inst_5) _inst_6 _inst_7) (fun (_x : LinearMap.{u1, u1, max u1 u2, max u1 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 N (AddCommGroup.toAddCommMonoid.{max u1 u2} M _inst_4) (AddCommGroup.toAddCommMonoid.{max u1 u2} N _inst_5) _inst_6 _inst_7) => M -> N) (LinearMap.hasCoeToFun.{u1, u1, max u1 u2, max u1 u2} R R M N (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{max u1 u2} M _inst_4) (AddCommGroup.toAddCommMonoid.{max u1 u2} N _inst_5) _inst_6 _inst_7 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1)))) i))], N -> (Ideal.{u1} R (Ring.toSemiring.{u1} R _inst_1)))
 but is expected to have type
-  forall {R : Type.{u1}} [_inst_1 : Ring.{u1} R] {Q : TypeMax.{u2, u1}} [_inst_2 : AddCommGroup.{max u1 u2} Q] [_inst_3 : Module.{u1, max u1 u2} R Q (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{max u1 u2} Q _inst_2)] {M : Type.{max u1 u2}} {N : Type.{max u1 u2}} [_inst_4 : AddCommGroup.{max u1 u2} M] [_inst_5 : AddCommGroup.{max u1 u2} N] [_inst_6 : Module.{u1, max u1 u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{max u1 u2} M _inst_4)] [_inst_7 : Module.{u1, max u1 u2} R N (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{max u1 u2} N _inst_5)] (i : LinearMap.{u1, u1, max u1 u2, max u1 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 N (AddCommGroup.toAddCommMonoid.{max u1 u2} M _inst_4) (AddCommGroup.toAddCommMonoid.{max u1 u2} N _inst_5) _inst_6 _inst_7), (LinearMap.{u1, u1, max u1 u2, max u1 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 Q (AddCommGroup.toAddCommMonoid.{max u1 u2} M _inst_4) (AddCommGroup.toAddCommMonoid.{max u1 u2} Q _inst_2) _inst_6 _inst_3) -> (forall [_inst_8 : Fact (Function.Injective.{max (succ u1) (succ u2), max (succ u1) (succ u2)} M N (FunLike.coe.{max (succ u1) (succ u2), max (succ u1) (succ u2), max (succ u1) (succ u2)} (LinearMap.{u1, u1, max u1 u2, max u1 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 N (AddCommGroup.toAddCommMonoid.{max u1 u2} M _inst_4) (AddCommGroup.toAddCommMonoid.{max u1 u2} N _inst_5) _inst_6 _inst_7) M (fun (_x : M) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : M) => N) _x) (LinearMap.instFunLikeLinearMap.{u1, u1, max u1 u2, max u1 u2} R R M N (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{max u1 u2} M _inst_4) (AddCommGroup.toAddCommMonoid.{max u1 u2} N _inst_5) _inst_6 _inst_7 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1)))) i))], N -> (Ideal.{u1} R (Ring.toSemiring.{u1} R _inst_1)))
+  forall {R : Type.{u1}} [_inst_1 : Ring.{u1} R] {Q : TypeMax.{u2, u1}} [_inst_2 : AddCommGroup.{max u1 u2} Q] [_inst_3 : Module.{u1, max u1 u2} R Q (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{max u1 u2} Q _inst_2)] {M : Type.{max u1 u2}} {N : Type.{max u1 u2}} [_inst_4 : AddCommGroup.{max u1 u2} M] [_inst_5 : AddCommGroup.{max u1 u2} N] [_inst_6 : Module.{u1, max u1 u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{max u1 u2} M _inst_4)] [_inst_7 : Module.{u1, max u1 u2} R N (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{max u1 u2} N _inst_5)] (i : LinearMap.{u1, u1, max u1 u2, max u1 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 N (AddCommGroup.toAddCommMonoid.{max u1 u2} M _inst_4) (AddCommGroup.toAddCommMonoid.{max u1 u2} N _inst_5) _inst_6 _inst_7), (LinearMap.{u1, u1, max u1 u2, max u1 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 Q (AddCommGroup.toAddCommMonoid.{max u1 u2} M _inst_4) (AddCommGroup.toAddCommMonoid.{max u1 u2} Q _inst_2) _inst_6 _inst_3) -> (forall [_inst_8 : Fact (Function.Injective.{max (succ u1) (succ u2), max (succ u1) (succ u2)} M N (FunLike.coe.{max (succ u1) (succ u2), max (succ u1) (succ u2), max (succ u1) (succ u2)} (LinearMap.{u1, u1, max u1 u2, max u1 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 N (AddCommGroup.toAddCommMonoid.{max u1 u2} M _inst_4) (AddCommGroup.toAddCommMonoid.{max u1 u2} N _inst_5) _inst_6 _inst_7) M (fun (_x : M) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : M) => N) _x) (LinearMap.instFunLikeLinearMap.{u1, u1, max u1 u2, max u1 u2} R R M N (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{max u1 u2} M _inst_4) (AddCommGroup.toAddCommMonoid.{max u1 u2} N _inst_5) _inst_6 _inst_7 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1)))) i))], N -> (Ideal.{u1} R (Ring.toSemiring.{u1} R _inst_1)))
 Case conversion may be inaccurate. Consider using '#align module.Baer.extension_of_max_adjoin.ideal Module.Baer.ExtensionOfMaxAdjoin.idealₓ'. -/
 /-- the ideal `I = {r | r • y ∈ N}`-/
 def ExtensionOfMaxAdjoin.ideal (y : N) : Ideal R :=
@@ -367,7 +367,7 @@ def ExtensionOfMaxAdjoin.ideal (y : N) : Ideal R :=
 lean 3 declaration is
   forall {R : Type.{u1}} [_inst_1 : Ring.{u1} R] {Q : Type.{max u1 u2}} [_inst_2 : AddCommGroup.{max u1 u2} Q] [_inst_3 : Module.{u1, max u1 u2} R Q (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{max u1 u2} Q _inst_2)] {M : Type.{max u1 u2}} {N : Type.{max u1 u2}} [_inst_4 : AddCommGroup.{max u1 u2} M] [_inst_5 : AddCommGroup.{max u1 u2} N] [_inst_6 : Module.{u1, max u1 u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{max u1 u2} M _inst_4)] [_inst_7 : Module.{u1, max u1 u2} R N (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{max u1 u2} N _inst_5)] (i : LinearMap.{u1, u1, max u1 u2, max u1 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 N (AddCommGroup.toAddCommMonoid.{max u1 u2} M _inst_4) (AddCommGroup.toAddCommMonoid.{max u1 u2} N _inst_5) _inst_6 _inst_7) (f : LinearMap.{u1, u1, max u1 u2, max u1 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 Q (AddCommGroup.toAddCommMonoid.{max u1 u2} M _inst_4) (AddCommGroup.toAddCommMonoid.{max u1 u2} Q _inst_2) _inst_6 _inst_3) [_inst_8 : Fact (Function.Injective.{succ (max u1 u2), succ (max u1 u2)} M N (coeFn.{succ (max u1 u2), succ (max u1 u2)} (LinearMap.{u1, u1, max u1 u2, max u1 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 N (AddCommGroup.toAddCommMonoid.{max u1 u2} M _inst_4) (AddCommGroup.toAddCommMonoid.{max u1 u2} N _inst_5) _inst_6 _inst_7) (fun (_x : LinearMap.{u1, u1, max u1 u2, max u1 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 N (AddCommGroup.toAddCommMonoid.{max u1 u2} M _inst_4) (AddCommGroup.toAddCommMonoid.{max u1 u2} N _inst_5) _inst_6 _inst_7) => M -> N) (LinearMap.hasCoeToFun.{u1, u1, max u1 u2, max u1 u2} R R M N (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{max u1 u2} M _inst_4) (AddCommGroup.toAddCommMonoid.{max u1 u2} N _inst_5) _inst_6 _inst_7 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1)))) i))] (y : N), LinearMap.{u1, u1, u1, max u1 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))) (coeSort.{succ u1, succ (succ u1)} (Ideal.{u1} R (Ring.toSemiring.{u1} R _inst_1)) Type.{u1} (SetLike.hasCoeToSort.{u1, u1} (Ideal.{u1} R (Ring.toSemiring.{u1} R _inst_1)) R (Submodule.setLike.{u1, u1} R R (Ring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R _inst_1)))) (Module.Baer.ExtensionOfMaxAdjoin.ideal.{u1, u2} R _inst_1 Q _inst_2 _inst_3 M N _inst_4 _inst_5 _inst_6 _inst_7 i f _inst_8 y)) Q (Submodule.addCommMonoid.{u1, u1} R R (Ring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (Module.Baer.ExtensionOfMaxAdjoin.ideal.{u1, u2} R _inst_1 Q _inst_2 _inst_3 M N _inst_4 _inst_5 _inst_6 _inst_7 i f _inst_8 y)) (AddCommGroup.toAddCommMonoid.{max u1 u2} Q _inst_2) (Submodule.module.{u1, u1} R R (Ring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (Module.Baer.ExtensionOfMaxAdjoin.ideal.{u1, u2} R _inst_1 Q _inst_2 _inst_3 M N _inst_4 _inst_5 _inst_6 _inst_7 i f _inst_8 y)) _inst_3
 but is expected to have type
-  forall {R : Type.{u1}} [_inst_1 : Ring.{u1} R] {Q : TypeMax.{u2, u1}} [_inst_2 : AddCommGroup.{max u1 u2} Q] [_inst_3 : Module.{u1, max u1 u2} R Q (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{max u1 u2} Q _inst_2)] {M : Type.{max u1 u2}} {N : Type.{max u1 u2}} [_inst_4 : AddCommGroup.{max u1 u2} M] [_inst_5 : AddCommGroup.{max u1 u2} N] [_inst_6 : Module.{u1, max u1 u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{max u1 u2} M _inst_4)] [_inst_7 : Module.{u1, max u1 u2} R N (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{max u1 u2} N _inst_5)] (i : LinearMap.{u1, u1, max u1 u2, max u1 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 N (AddCommGroup.toAddCommMonoid.{max u1 u2} M _inst_4) (AddCommGroup.toAddCommMonoid.{max u1 u2} N _inst_5) _inst_6 _inst_7) (f : LinearMap.{u1, u1, max u1 u2, max u1 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 Q (AddCommGroup.toAddCommMonoid.{max u1 u2} M _inst_4) (AddCommGroup.toAddCommMonoid.{max u1 u2} Q _inst_2) _inst_6 _inst_3) [_inst_8 : Fact (Function.Injective.{max (succ u1) (succ u2), max (succ u1) (succ u2)} M N (FunLike.coe.{max (succ u1) (succ u2), max (succ u1) (succ u2), max (succ u1) (succ u2)} (LinearMap.{u1, u1, max u1 u2, max u1 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 N (AddCommGroup.toAddCommMonoid.{max u1 u2} M _inst_4) (AddCommGroup.toAddCommMonoid.{max u1 u2} N _inst_5) _inst_6 _inst_7) M (fun (_x : M) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : M) => N) _x) (LinearMap.instFunLikeLinearMap.{u1, u1, max u1 u2, max u1 u2} R R M N (Ring.toSemiring.{u1} R _inst_1) 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(Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R _inst_1))) R (Submodule.setLike.{u1, u1} R R (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} R (Ring.toAddCommGroup.{u1} R _inst_1)) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R _inst_1)))) x (Module.Baer.ExtensionOfMaxAdjoin.ideal.{u1, u2} R _inst_1 Q _inst_2 _inst_3 M N _inst_4 _inst_5 _inst_6 _inst_7 i f _inst_8 y))) (Submodule.addCommGroup.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R _inst_1) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (Module.Baer.ExtensionOfMaxAdjoin.ideal.{u1, u2} R _inst_1 Q _inst_2 _inst_3 M N _inst_4 _inst_5 _inst_6 _inst_7 i f _inst_8 y)) (Submodule.module.{u1, u1} R R (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} R (Ring.toAddCommGroup.{u1} R _inst_1)) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (Module.Baer.ExtensionOfMaxAdjoin.ideal.{u1, u2} R _inst_1 Q _inst_2 _inst_3 M N _inst_4 _inst_5 _inst_6 _inst_7 i f _inst_8 y))))) (AddCommGroup.toAddCommMonoid.{max u1 u2} Q _inst_2) (ModuleCat.isModule.{u1, u1} R _inst_1 (ModuleCat.of.{u1, u1} R _inst_1 (Subtype.{succ u1} R (fun (x : R) => Membership.mem.{u1, u1} R (Submodule.{u1, u1} R R (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} R (Ring.toAddCommGroup.{u1} R _inst_1)) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (SetLike.instMembership.{u1, u1} (Submodule.{u1, u1} R R (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} R (Ring.toAddCommGroup.{u1} R _inst_1)) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R _inst_1))) R (Submodule.setLike.{u1, u1} R R (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} R (Ring.toAddCommGroup.{u1} R _inst_1)) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R _inst_1)))) x (Module.Baer.ExtensionOfMaxAdjoin.ideal.{u1, u2} R _inst_1 Q _inst_2 _inst_3 M N _inst_4 _inst_5 _inst_6 _inst_7 i f _inst_8 y))) (Submodule.addCommGroup.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R _inst_1) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (Module.Baer.ExtensionOfMaxAdjoin.ideal.{u1, u2} R _inst_1 Q _inst_2 _inst_3 M N _inst_4 _inst_5 _inst_6 _inst_7 i f _inst_8 y)) (Submodule.module.{u1, u1} R R (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} R (Ring.toAddCommGroup.{u1} R _inst_1)) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (Module.Baer.ExtensionOfMaxAdjoin.ideal.{u1, u2} R _inst_1 Q _inst_2 _inst_3 M N _inst_4 _inst_5 _inst_6 _inst_7 i f _inst_8 y)))) _inst_3
+  forall {R : Type.{u1}} [_inst_1 : Ring.{u1} R] {Q : TypeMax.{u2, u1}} [_inst_2 : AddCommGroup.{max u1 u2} Q] [_inst_3 : Module.{u1, max u1 u2} R Q (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{max u1 u2} Q _inst_2)] {M : Type.{max u1 u2}} {N : Type.{max u1 u2}} [_inst_4 : AddCommGroup.{max u1 u2} M] [_inst_5 : AddCommGroup.{max u1 u2} N] [_inst_6 : Module.{u1, max u1 u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{max u1 u2} M _inst_4)] [_inst_7 : Module.{u1, max u1 u2} R N (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{max u1 u2} N _inst_5)] (i : LinearMap.{u1, u1, max u1 u2, max u1 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 N (AddCommGroup.toAddCommMonoid.{max u1 u2} M _inst_4) (AddCommGroup.toAddCommMonoid.{max u1 u2} N _inst_5) _inst_6 _inst_7) (f : LinearMap.{u1, u1, max u1 u2, max u1 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 Q (AddCommGroup.toAddCommMonoid.{max u1 u2} M _inst_4) (AddCommGroup.toAddCommMonoid.{max u1 u2} Q _inst_2) _inst_6 _inst_3) [_inst_8 : Fact (Function.Injective.{max (succ u1) (succ u2), max (succ u1) (succ u2)} M N (FunLike.coe.{max (succ u1) (succ u2), max (succ u1) (succ u2), max (succ u1) (succ u2)} (LinearMap.{u1, u1, max u1 u2, max u1 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 N (AddCommGroup.toAddCommMonoid.{max u1 u2} M _inst_4) (AddCommGroup.toAddCommMonoid.{max u1 u2} N _inst_5) _inst_6 _inst_7) M (fun (_x : M) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : M) => N) _x) (LinearMap.instFunLikeLinearMap.{u1, u1, max u1 u2, max u1 u2} R R M N (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{max u1 u2} M _inst_4) (AddCommGroup.toAddCommMonoid.{max u1 u2} N _inst_5) _inst_6 _inst_7 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1)))) i))] (y : N), LinearMap.{u1, u1, u1, max u1 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))) (ModuleCat.carrier.{u1, u1} R _inst_1 (ModuleCat.of.{u1, u1} R _inst_1 (Subtype.{succ u1} R (fun (x : R) => Membership.mem.{u1, u1} R (Submodule.{u1, u1} R R (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} R (Ring.toAddCommGroup.{u1} R _inst_1)) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (SetLike.instMembership.{u1, u1} (Submodule.{u1, u1} R R (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} R (Ring.toAddCommGroup.{u1} R _inst_1)) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R _inst_1))) R (Submodule.setLike.{u1, u1} R R (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} R (Ring.toAddCommGroup.{u1} R _inst_1)) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R _inst_1)))) x (Module.Baer.ExtensionOfMaxAdjoin.ideal.{u1, u2} R _inst_1 Q _inst_2 _inst_3 M N _inst_4 _inst_5 _inst_6 _inst_7 i f _inst_8 y))) (Submodule.addCommGroup.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R _inst_1) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (Module.Baer.ExtensionOfMaxAdjoin.ideal.{u1, u2} R _inst_1 Q _inst_2 _inst_3 M N _inst_4 _inst_5 _inst_6 _inst_7 i f _inst_8 y)) (Submodule.module.{u1, u1} R R (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} R (Ring.toAddCommGroup.{u1} R _inst_1)) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (Module.Baer.ExtensionOfMaxAdjoin.ideal.{u1, u2} R _inst_1 Q _inst_2 _inst_3 M N _inst_4 _inst_5 _inst_6 _inst_7 i f _inst_8 y)))) Q (AddCommGroup.toAddCommMonoid.{u1} (ModuleCat.carrier.{u1, u1} R _inst_1 (ModuleCat.of.{u1, u1} R _inst_1 (Subtype.{succ u1} R (fun (x : R) => Membership.mem.{u1, u1} R (Submodule.{u1, u1} R R (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} R (Ring.toAddCommGroup.{u1} R _inst_1)) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (SetLike.instMembership.{u1, u1} (Submodule.{u1, u1} R R (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} R (Ring.toAddCommGroup.{u1} R _inst_1)) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R _inst_1))) R (Submodule.setLike.{u1, u1} R R (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} R (Ring.toAddCommGroup.{u1} R _inst_1)) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R _inst_1)))) x (Module.Baer.ExtensionOfMaxAdjoin.ideal.{u1, u2} R _inst_1 Q _inst_2 _inst_3 M N _inst_4 _inst_5 _inst_6 _inst_7 i f _inst_8 y))) (Submodule.addCommGroup.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R _inst_1) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (Module.Baer.ExtensionOfMaxAdjoin.ideal.{u1, u2} R _inst_1 Q _inst_2 _inst_3 M N _inst_4 _inst_5 _inst_6 _inst_7 i f _inst_8 y)) (Submodule.module.{u1, u1} R R (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} R (Ring.toAddCommGroup.{u1} R _inst_1)) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (Module.Baer.ExtensionOfMaxAdjoin.ideal.{u1, u2} R _inst_1 Q _inst_2 _inst_3 M N _inst_4 _inst_5 _inst_6 _inst_7 i f _inst_8 y)))) (ModuleCat.isAddCommGroup.{u1, u1} R _inst_1 (ModuleCat.of.{u1, u1} R _inst_1 (Subtype.{succ u1} R (fun (x : R) => Membership.mem.{u1, u1} R (Submodule.{u1, u1} R R (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} R (Ring.toAddCommGroup.{u1} R _inst_1)) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (SetLike.instMembership.{u1, u1} (Submodule.{u1, u1} R R (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} R (Ring.toAddCommGroup.{u1} R _inst_1)) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R _inst_1))) R (Submodule.setLike.{u1, u1} R R (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} R (Ring.toAddCommGroup.{u1} R _inst_1)) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R _inst_1)))) x (Module.Baer.ExtensionOfMaxAdjoin.ideal.{u1, u2} R _inst_1 Q _inst_2 _inst_3 M N _inst_4 _inst_5 _inst_6 _inst_7 i f _inst_8 y))) (Submodule.addCommGroup.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R _inst_1) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (Module.Baer.ExtensionOfMaxAdjoin.ideal.{u1, u2} R _inst_1 Q _inst_2 _inst_3 M N _inst_4 _inst_5 _inst_6 _inst_7 i f _inst_8 y)) (Submodule.module.{u1, u1} R R (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} R (Ring.toAddCommGroup.{u1} R _inst_1)) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (Module.Baer.ExtensionOfMaxAdjoin.ideal.{u1, u2} R _inst_1 Q _inst_2 _inst_3 M N _inst_4 _inst_5 _inst_6 _inst_7 i f _inst_8 y))))) (AddCommGroup.toAddCommMonoid.{max u1 u2} Q _inst_2) (ModuleCat.isModule.{u1, u1} R _inst_1 (ModuleCat.of.{u1, u1} R _inst_1 (Subtype.{succ u1} R (fun (x : R) => Membership.mem.{u1, u1} R (Submodule.{u1, u1} R R (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} R (Ring.toAddCommGroup.{u1} R _inst_1)) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (SetLike.instMembership.{u1, u1} (Submodule.{u1, u1} R R (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} R (Ring.toAddCommGroup.{u1} R _inst_1)) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R _inst_1))) R (Submodule.setLike.{u1, u1} R R (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} R (Ring.toAddCommGroup.{u1} R _inst_1)) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R _inst_1)))) x (Module.Baer.ExtensionOfMaxAdjoin.ideal.{u1, u2} R _inst_1 Q _inst_2 _inst_3 M N _inst_4 _inst_5 _inst_6 _inst_7 i f _inst_8 y))) (Submodule.addCommGroup.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R _inst_1) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (Module.Baer.ExtensionOfMaxAdjoin.ideal.{u1, u2} R _inst_1 Q _inst_2 _inst_3 M N _inst_4 _inst_5 _inst_6 _inst_7 i f _inst_8 y)) (Submodule.module.{u1, u1} R R (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} R (Ring.toAddCommGroup.{u1} R _inst_1)) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (Module.Baer.ExtensionOfMaxAdjoin.ideal.{u1, u2} R _inst_1 Q _inst_2 _inst_3 M N _inst_4 _inst_5 _inst_6 _inst_7 i f _inst_8 y)))) _inst_3
 Case conversion may be inaccurate. Consider using '#align module.Baer.extension_of_max_adjoin.ideal_to Module.Baer.ExtensionOfMaxAdjoin.idealToₓ'. -/
 /-- A linear map `I ⟶ Q` by `x ↦ f' (x • y)` where `f'` is the maximal extension-/
 def ExtensionOfMaxAdjoin.idealTo (y : N) : ExtensionOfMaxAdjoin.ideal i f y →ₗ[R] Q
@@ -381,7 +381,7 @@ def ExtensionOfMaxAdjoin.idealTo (y : N) : ExtensionOfMaxAdjoin.ideal i f y →
 lean 3 declaration is
   forall {R : Type.{u1}} [_inst_1 : Ring.{u1} R] {Q : Type.{max u1 u2}} [_inst_2 : AddCommGroup.{max u1 u2} Q] [_inst_3 : Module.{u1, max u1 u2} R Q (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{max u1 u2} Q _inst_2)] {M : Type.{max u1 u2}} {N : Type.{max u1 u2}} [_inst_4 : AddCommGroup.{max u1 u2} M] [_inst_5 : AddCommGroup.{max u1 u2} N] [_inst_6 : Module.{u1, max u1 u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{max u1 u2} M _inst_4)] [_inst_7 : Module.{u1, max u1 u2} R N (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{max u1 u2} N _inst_5)] (i : LinearMap.{u1, u1, max u1 u2, max u1 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 N (AddCommGroup.toAddCommMonoid.{max u1 u2} M _inst_4) (AddCommGroup.toAddCommMonoid.{max u1 u2} N _inst_5) _inst_6 _inst_7), (LinearMap.{u1, u1, max u1 u2, max u1 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 Q (AddCommGroup.toAddCommMonoid.{max u1 u2} M _inst_4) (AddCommGroup.toAddCommMonoid.{max u1 u2} Q _inst_2) _inst_6 _inst_3) -> (forall [_inst_8 : Fact (Function.Injective.{succ (max u1 u2), succ (max u1 u2)} M N (coeFn.{succ (max u1 u2), succ (max u1 u2)} (LinearMap.{u1, u1, max u1 u2, max u1 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 N (AddCommGroup.toAddCommMonoid.{max u1 u2} M _inst_4) (AddCommGroup.toAddCommMonoid.{max u1 u2} N _inst_5) _inst_6 _inst_7) (fun (_x : LinearMap.{u1, u1, max u1 u2, max u1 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 N (AddCommGroup.toAddCommMonoid.{max u1 u2} M _inst_4) (AddCommGroup.toAddCommMonoid.{max u1 u2} N _inst_5) _inst_6 _inst_7) => M -> N) (LinearMap.hasCoeToFun.{u1, u1, max u1 u2, max u1 u2} R R M N (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{max u1 u2} M _inst_4) (AddCommGroup.toAddCommMonoid.{max u1 u2} N _inst_5) _inst_6 _inst_7 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1)))) i))], (Module.Baer.{u1, u2} R _inst_1 Q _inst_2 _inst_3) -> N -> (LinearMap.{u1, u1, u1, max u1 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))) R Q (AddCommGroup.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toAddCommGroup.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R _inst_1)))) (AddCommGroup.toAddCommMonoid.{max u1 u2} Q _inst_2) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R _inst_1)) _inst_3))
 but is expected to have type
-  forall {R : Type.{u1}} [_inst_1 : Ring.{u1} R] {Q : TypeMax.{u2, u1}} [_inst_2 : AddCommGroup.{max u1 u2} Q] [_inst_3 : Module.{u1, max u1 u2} R Q (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{max u1 u2} Q _inst_2)] {M : Type.{max u1 u2}} {N : Type.{max u1 u2}} [_inst_4 : AddCommGroup.{max u1 u2} M] [_inst_5 : AddCommGroup.{max u1 u2} N] [_inst_6 : Module.{u1, max u1 u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{max u1 u2} M _inst_4)] [_inst_7 : Module.{u1, max u1 u2} R N (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{max u1 u2} N _inst_5)] (i : LinearMap.{u1, u1, max u1 u2, max u1 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 N (AddCommGroup.toAddCommMonoid.{max u1 u2} M _inst_4) (AddCommGroup.toAddCommMonoid.{max u1 u2} N _inst_5) _inst_6 _inst_7), (LinearMap.{u1, u1, max u1 u2, max u1 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 Q (AddCommGroup.toAddCommMonoid.{max u1 u2} M _inst_4) (AddCommGroup.toAddCommMonoid.{max u1 u2} Q _inst_2) _inst_6 _inst_3) -> (forall [_inst_8 : Fact (Function.Injective.{max (succ u1) (succ u2), max (succ u1) (succ u2)} M N (FunLike.coe.{max (succ u1) (succ u2), max (succ u1) (succ u2), max (succ u1) (succ u2)} (LinearMap.{u1, u1, max u1 u2, max u1 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 N (AddCommGroup.toAddCommMonoid.{max u1 u2} M _inst_4) (AddCommGroup.toAddCommMonoid.{max u1 u2} N _inst_5) _inst_6 _inst_7) M (fun (_x : M) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : M) => N) _x) (LinearMap.instFunLikeLinearMap.{u1, u1, max u1 u2, max u1 u2} R R M N (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{max u1 u2} M _inst_4) (AddCommGroup.toAddCommMonoid.{max u1 u2} N _inst_5) _inst_6 _inst_7 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1)))) i))], (Module.Baer.{u1, u2} R _inst_1 Q _inst_2 _inst_3) -> N -> (LinearMap.{u1, u1, u1, max u1 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))) R Q (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R _inst_1)))) (AddCommGroup.toAddCommMonoid.{max u1 u2} Q _inst_2) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R _inst_1)) _inst_3))
+  forall {R : Type.{u1}} [_inst_1 : Ring.{u1} R] {Q : TypeMax.{u2, u1}} [_inst_2 : AddCommGroup.{max u1 u2} Q] [_inst_3 : Module.{u1, max u1 u2} R Q (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{max u1 u2} Q _inst_2)] {M : Type.{max u1 u2}} {N : Type.{max u1 u2}} [_inst_4 : AddCommGroup.{max u1 u2} M] [_inst_5 : AddCommGroup.{max u1 u2} N] [_inst_6 : Module.{u1, max u1 u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{max u1 u2} M _inst_4)] [_inst_7 : Module.{u1, max u1 u2} R N (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{max u1 u2} N _inst_5)] (i : LinearMap.{u1, u1, max u1 u2, max u1 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 N (AddCommGroup.toAddCommMonoid.{max u1 u2} M _inst_4) (AddCommGroup.toAddCommMonoid.{max u1 u2} N _inst_5) _inst_6 _inst_7), (LinearMap.{u1, u1, max u1 u2, max u1 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 Q (AddCommGroup.toAddCommMonoid.{max u1 u2} M _inst_4) (AddCommGroup.toAddCommMonoid.{max u1 u2} Q _inst_2) _inst_6 _inst_3) -> (forall [_inst_8 : Fact (Function.Injective.{max (succ u1) (succ u2), max (succ u1) (succ u2)} M N (FunLike.coe.{max (succ u1) (succ u2), max (succ u1) (succ u2), max (succ u1) (succ u2)} (LinearMap.{u1, u1, max u1 u2, max u1 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 N (AddCommGroup.toAddCommMonoid.{max u1 u2} M _inst_4) (AddCommGroup.toAddCommMonoid.{max u1 u2} N _inst_5) _inst_6 _inst_7) M (fun (_x : M) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : M) => N) _x) (LinearMap.instFunLikeLinearMap.{u1, u1, max u1 u2, max u1 u2} R R M N (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{max u1 u2} M _inst_4) (AddCommGroup.toAddCommMonoid.{max u1 u2} N _inst_5) _inst_6 _inst_7 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1)))) i))], (Module.Baer.{u1, u2} R _inst_1 Q _inst_2 _inst_3) -> N -> (LinearMap.{u1, u1, u1, max u1 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))) R Q (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R _inst_1)))) (AddCommGroup.toAddCommMonoid.{max u1 u2} Q _inst_2) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R _inst_1)) _inst_3))
 Case conversion may be inaccurate. Consider using '#align module.Baer.extension_of_max_adjoin.extend_ideal_to Module.Baer.ExtensionOfMaxAdjoin.extendIdealToₓ'. -/
 /-- Since we assumed `Q` being Baer, the linear map `x ↦ f' (x • y) : I ⟶ Q` extends to `R ⟶ Q`,
 call this extended map `φ`-/
@@ -393,7 +393,7 @@ def ExtensionOfMaxAdjoin.extendIdealTo (h : Module.Baer R Q) (y : N) : R →ₗ[
 lean 3 declaration is
   forall {R : Type.{u1}} [_inst_1 : Ring.{u1} R] {Q : Type.{max u1 u2}} [_inst_2 : AddCommGroup.{max u1 u2} Q] [_inst_3 : Module.{u1, max u1 u2} R Q (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{max u1 u2} Q _inst_2)] {M : Type.{max u1 u2}} {N : Type.{max u1 u2}} [_inst_4 : AddCommGroup.{max u1 u2} M] [_inst_5 : AddCommGroup.{max u1 u2} N] [_inst_6 : Module.{u1, max u1 u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{max u1 u2} M _inst_4)] [_inst_7 : Module.{u1, max u1 u2} R N (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{max u1 u2} N _inst_5)] (i : LinearMap.{u1, u1, max u1 u2, max u1 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 N (AddCommGroup.toAddCommMonoid.{max u1 u2} M _inst_4) (AddCommGroup.toAddCommMonoid.{max u1 u2} N _inst_5) _inst_6 _inst_7) (f : LinearMap.{u1, u1, max u1 u2, max u1 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 Q (AddCommGroup.toAddCommMonoid.{max u1 u2} M _inst_4) (AddCommGroup.toAddCommMonoid.{max u1 u2} Q _inst_2) _inst_6 _inst_3) [_inst_8 : Fact (Function.Injective.{succ (max u1 u2), succ (max u1 u2)} M N (coeFn.{succ (max u1 u2), succ (max u1 u2)} (LinearMap.{u1, u1, max u1 u2, max u1 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 N (AddCommGroup.toAddCommMonoid.{max u1 u2} M _inst_4) (AddCommGroup.toAddCommMonoid.{max u1 u2} N _inst_5) _inst_6 _inst_7) (fun (_x : LinearMap.{u1, u1, max u1 u2, max u1 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 N (AddCommGroup.toAddCommMonoid.{max u1 u2} M _inst_4) (AddCommGroup.toAddCommMonoid.{max u1 u2} N _inst_5) _inst_6 _inst_7) => M -> N) (LinearMap.hasCoeToFun.{u1, u1, max u1 u2, max u1 u2} R R M N (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{max u1 u2} M _inst_4) (AddCommGroup.toAddCommMonoid.{max u1 u2} N _inst_5) _inst_6 _inst_7 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1)))) i))] (h : Module.Baer.{u1, u2} R _inst_1 Q _inst_2 _inst_3) (y : N) (x : R) (mem : Membership.Mem.{u1, u1} R (Ideal.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (SetLike.hasMem.{u1, u1} (Ideal.{u1} R (Ring.toSemiring.{u1} R _inst_1)) R (Submodule.setLike.{u1, u1} R R (Ring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R _inst_1)))) x (Module.Baer.ExtensionOfMaxAdjoin.ideal.{u1, u2} R _inst_1 Q _inst_2 _inst_3 M N _inst_4 _inst_5 _inst_6 _inst_7 i f _inst_8 y)), Eq.{succ (max u1 u2)} Q (coeFn.{max (succ u1) (succ (max u1 u2)), max (succ u1) (succ (max u1 u2))} (LinearMap.{u1, u1, u1, max u1 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))) R Q (AddCommGroup.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toAddCommGroup.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R _inst_1)))) (AddCommGroup.toAddCommMonoid.{max u1 u2} Q _inst_2) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R _inst_1)) _inst_3) (fun (_x : LinearMap.{u1, u1, u1, max u1 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))) R Q (AddCommGroup.toAddCommMonoid.{u1} R 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 but is expected to have type
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+  forall {R : Type.{u1}} [_inst_1 : Ring.{u1} R] {Q : TypeMax.{u2, u1}} [_inst_2 : AddCommGroup.{max u1 u2} Q] [_inst_3 : Module.{u1, max u1 u2} R Q (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{max u1 u2} Q _inst_2)] {M : Type.{max u1 u2}} {N : Type.{max u1 u2}} [_inst_4 : AddCommGroup.{max u1 u2} M] [_inst_5 : AddCommGroup.{max u1 u2} N] [_inst_6 : Module.{u1, max u1 u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{max u1 u2} M _inst_4)] [_inst_7 : Module.{u1, max u1 u2} R N (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{max u1 u2} N _inst_5)] (i : LinearMap.{u1, u1, max u1 u2, max u1 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 N (AddCommGroup.toAddCommMonoid.{max u1 u2} M _inst_4) (AddCommGroup.toAddCommMonoid.{max u1 u2} N _inst_5) _inst_6 _inst_7) (f : LinearMap.{u1, u1, max u1 u2, max u1 u2} R R 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_inst_1 (Ring.toAddCommGroup.{u1} R _inst_1) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (Module.Baer.ExtensionOfMaxAdjoin.ideal.{u1, u2} R _inst_1 Q _inst_2 _inst_3 M N _inst_4 _inst_5 _inst_6 _inst_7 i f _inst_8 y)) (Submodule.module.{u1, u1} R R (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} R (Ring.toAddCommGroup.{u1} R _inst_1)) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (Module.Baer.ExtensionOfMaxAdjoin.ideal.{u1, u2} R _inst_1 Q _inst_2 _inst_3 M N _inst_4 _inst_5 _inst_6 _inst_7 i f _inst_8 y)))) (ModuleCat.isAddCommGroup.{u1, u1} R _inst_1 (ModuleCat.of.{u1, u1} R _inst_1 (Subtype.{succ u1} R (fun (x : R) => Membership.mem.{u1, u1} R (Submodule.{u1, u1} R R (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} R (Ring.toAddCommGroup.{u1} R _inst_1)) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (SetLike.instMembership.{u1, u1} (Submodule.{u1, u1} R R (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} R (Ring.toAddCommGroup.{u1} R _inst_1)) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R _inst_1))) R (Submodule.setLike.{u1, u1} R R (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} R (Ring.toAddCommGroup.{u1} R _inst_1)) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R _inst_1)))) x (Module.Baer.ExtensionOfMaxAdjoin.ideal.{u1, u2} R _inst_1 Q _inst_2 _inst_3 M N _inst_4 _inst_5 _inst_6 _inst_7 i f _inst_8 y))) (Submodule.addCommGroup.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R _inst_1) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (Module.Baer.ExtensionOfMaxAdjoin.ideal.{u1, u2} R _inst_1 Q _inst_2 _inst_3 M N _inst_4 _inst_5 _inst_6 _inst_7 i f _inst_8 y)) (Submodule.module.{u1, u1} R R (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} R (Ring.toAddCommGroup.{u1} R _inst_1)) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (Module.Baer.ExtensionOfMaxAdjoin.ideal.{u1, u2} R _inst_1 Q _inst_2 _inst_3 M N _inst_4 _inst_5 _inst_6 _inst_7 i f _inst_8 y))))) (AddCommGroup.toAddCommMonoid.{max u1 u2} Q _inst_2) (ModuleCat.isModule.{u1, u1} R _inst_1 (ModuleCat.of.{u1, u1} R _inst_1 (Subtype.{succ u1} R (fun (x : R) => Membership.mem.{u1, u1} R (Submodule.{u1, u1} R R (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} R (Ring.toAddCommGroup.{u1} R _inst_1)) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (SetLike.instMembership.{u1, u1} (Submodule.{u1, u1} R R (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} R (Ring.toAddCommGroup.{u1} R _inst_1)) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R _inst_1))) R (Submodule.setLike.{u1, u1} R R (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} R (Ring.toAddCommGroup.{u1} R _inst_1)) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R _inst_1)))) x (Module.Baer.ExtensionOfMaxAdjoin.ideal.{u1, u2} R _inst_1 Q _inst_2 _inst_3 M N _inst_4 _inst_5 _inst_6 _inst_7 i f _inst_8 y))) (Submodule.addCommGroup.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R _inst_1) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (Module.Baer.ExtensionOfMaxAdjoin.ideal.{u1, u2} R _inst_1 Q _inst_2 _inst_3 M N _inst_4 _inst_5 _inst_6 _inst_7 i f _inst_8 y)) (Submodule.module.{u1, u1} R R (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} R (Ring.toAddCommGroup.{u1} R _inst_1)) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (Module.Baer.ExtensionOfMaxAdjoin.ideal.{u1, u2} R _inst_1 Q _inst_2 _inst_3 M N _inst_4 _inst_5 _inst_6 _inst_7 i f _inst_8 y)))) _inst_3 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1)))) (Module.Baer.ExtensionOfMaxAdjoin.idealTo.{u1, u2} R _inst_1 Q _inst_2 _inst_3 M N _inst_4 _inst_5 _inst_6 _inst_7 i f _inst_8 y) (Subtype.mk.{succ u1} R (fun (x : R) => Membership.mem.{u1, u1} R (Submodule.{u1, u1} R R (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} R (Ring.toAddCommGroup.{u1} R _inst_1)) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (SetLike.instMembership.{u1, u1} (Submodule.{u1, u1} R R (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} R (Ring.toAddCommGroup.{u1} R _inst_1)) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R _inst_1))) R (Submodule.setLike.{u1, u1} R R (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} R (Ring.toAddCommGroup.{u1} R _inst_1)) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R _inst_1)))) x (Module.Baer.ExtensionOfMaxAdjoin.ideal.{u1, u2} R _inst_1 Q _inst_2 _inst_3 M N _inst_4 _inst_5 _inst_6 _inst_7 i f _inst_8 y)) x mem))
 Case conversion may be inaccurate. Consider using '#align module.Baer.extension_of_max_adjoin.extend_ideal_to_is_extension Module.Baer.ExtensionOfMaxAdjoin.extendIdealTo_is_extensionₓ'. -/
 theorem ExtensionOfMaxAdjoin.extendIdealTo_is_extension (h : Module.Baer R Q) (y : N) :
     ∀ (x : R) (mem : x ∈ ExtensionOfMaxAdjoin.ideal i f y),
@@ -405,7 +405,7 @@ theorem ExtensionOfMaxAdjoin.extendIdealTo_is_extension (h : Module.Baer R Q) (y
 lean 3 declaration is
   forall {R : Type.{u1}} [_inst_1 : Ring.{u1} R] {Q : Type.{max u1 u2}} [_inst_2 : AddCommGroup.{max u1 u2} Q] [_inst_3 : Module.{u1, max u1 u2} R Q (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{max u1 u2} Q _inst_2)] {M : Type.{max u1 u2}} {N : Type.{max u1 u2}} [_inst_4 : AddCommGroup.{max u1 u2} M] [_inst_5 : AddCommGroup.{max u1 u2} N] [_inst_6 : Module.{u1, max u1 u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{max u1 u2} M _inst_4)] [_inst_7 : Module.{u1, max u1 u2} R N (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{max u1 u2} N _inst_5)] (i : LinearMap.{u1, u1, max u1 u2, max u1 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 N (AddCommGroup.toAddCommMonoid.{max u1 u2} M _inst_4) (AddCommGroup.toAddCommMonoid.{max u1 u2} N _inst_5) _inst_6 _inst_7) (f : LinearMap.{u1, u1, max u1 u2, max u1 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 Q (AddCommGroup.toAddCommMonoid.{max u1 u2} M _inst_4) (AddCommGroup.toAddCommMonoid.{max u1 u2} Q _inst_2) _inst_6 _inst_3) [_inst_8 : Fact (Function.Injective.{succ (max u1 u2), succ (max u1 u2)} M N (coeFn.{succ (max u1 u2), succ (max u1 u2)} (LinearMap.{u1, u1, max u1 u2, max u1 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 N (AddCommGroup.toAddCommMonoid.{max u1 u2} M _inst_4) (AddCommGroup.toAddCommMonoid.{max u1 u2} N _inst_5) _inst_6 _inst_7) (fun (_x : LinearMap.{u1, u1, max u1 u2, max u1 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 N (AddCommGroup.toAddCommMonoid.{max u1 u2} M _inst_4) (AddCommGroup.toAddCommMonoid.{max u1 u2} N _inst_5) _inst_6 _inst_7) => M -> N) (LinearMap.hasCoeToFun.{u1, u1, max u1 u2, max u1 u2} R R M N (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{max u1 u2} M _inst_4) (AddCommGroup.toAddCommMonoid.{max u1 u2} N _inst_5) _inst_6 _inst_7 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1)))) i))] (h : Module.Baer.{u1, u2} R _inst_1 Q _inst_2 _inst_3) {y : N} (r : R), (Eq.{succ (max u1 u2)} N (SMul.smul.{u1, max u1 u2} R N (SMulZeroClass.toHasSmul.{u1, max u1 u2} R N (AddZeroClass.toHasZero.{max u1 u2} N (AddMonoid.toAddZeroClass.{max u1 u2} N (AddCommMonoid.toAddMonoid.{max u1 u2} N (AddCommGroup.toAddCommMonoid.{max u1 u2} N _inst_5)))) (SMulWithZero.toSmulZeroClass.{u1, max u1 u2} R N (MulZeroClass.toHasZero.{u1} R (MulZeroOneClass.toMulZeroClass.{u1} R (MonoidWithZero.toMulZeroOneClass.{u1} R (Semiring.toMonoidWithZero.{u1} R (Ring.toSemiring.{u1} R _inst_1))))) (AddZeroClass.toHasZero.{max u1 u2} N (AddMonoid.toAddZeroClass.{max u1 u2} N (AddCommMonoid.toAddMonoid.{max u1 u2} N (AddCommGroup.toAddCommMonoid.{max u1 u2} N _inst_5)))) (MulActionWithZero.toSMulWithZero.{u1, max u1 u2} R N (Semiring.toMonoidWithZero.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (AddZeroClass.toHasZero.{max u1 u2} N (AddMonoid.toAddZeroClass.{max u1 u2} N (AddCommMonoid.toAddMonoid.{max u1 u2} N (AddCommGroup.toAddCommMonoid.{max u1 u2} N _inst_5)))) (Module.toMulActionWithZero.{u1, max u1 u2} R N (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{max u1 u2} N _inst_5) _inst_7)))) r y) (OfNat.ofNat.{max u1 u2} N 0 (OfNat.mk.{max u1 u2} N 0 (Zero.zero.{max u1 u2} N (AddZeroClass.toHasZero.{max u1 u2} N (AddMonoid.toAddZeroClass.{max u1 u2} N (SubNegMonoid.toAddMonoid.{max u1 u2} N (AddGroup.toSubNegMonoid.{max u1 u2} N (AddCommGroup.toAddGroup.{max u1 u2} N _inst_5))))))))) -> (Eq.{succ (max u1 u2)} Q (coeFn.{max (succ u1) (succ (max u1 u2)), max (succ u1) (succ (max u1 u2))} (LinearMap.{u1, u1, u1, max u1 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))) R Q (AddCommGroup.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toAddCommGroup.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R _inst_1)))) (AddCommGroup.toAddCommMonoid.{max u1 u2} Q _inst_2) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R _inst_1)) _inst_3) (fun (_x : LinearMap.{u1, u1, u1, max u1 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))) R Q (AddCommGroup.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toAddCommGroup.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R _inst_1)))) (AddCommGroup.toAddCommMonoid.{max u1 u2} Q _inst_2) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R _inst_1)) _inst_3) => R -> Q) (LinearMap.hasCoeToFun.{u1, u1, u1, max u1 u2} R R R Q (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toAddCommGroup.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R _inst_1)))) (AddCommGroup.toAddCommMonoid.{max u1 u2} Q _inst_2) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R _inst_1)) _inst_3 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1)))) (Module.Baer.ExtensionOfMaxAdjoin.extendIdealTo.{u1, u2} R _inst_1 Q _inst_2 _inst_3 M N _inst_4 _inst_5 _inst_6 _inst_7 i f _inst_8 h y) r) (OfNat.ofNat.{max u1 u2} Q 0 (OfNat.mk.{max u1 u2} Q 0 (Zero.zero.{max u1 u2} Q (AddZeroClass.toHasZero.{max u1 u2} Q (AddMonoid.toAddZeroClass.{max u1 u2} Q (SubNegMonoid.toAddMonoid.{max u1 u2} Q (AddGroup.toSubNegMonoid.{max u1 u2} Q (AddCommGroup.toAddGroup.{max u1 u2} Q _inst_2)))))))))
 but is expected to have type
-  forall {R : Type.{u1}} [_inst_1 : Ring.{u1} R] {Q : TypeMax.{u2, u1}} [_inst_2 : AddCommGroup.{max u1 u2} Q] [_inst_3 : Module.{u1, max u1 u2} R Q (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{max u1 u2} Q _inst_2)] {M : Type.{max u1 u2}} {N : Type.{max u1 u2}} [_inst_4 : AddCommGroup.{max u1 u2} M] [_inst_5 : AddCommGroup.{max u1 u2} N] [_inst_6 : Module.{u1, max u1 u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{max u1 u2} M _inst_4)] [_inst_7 : Module.{u1, max u1 u2} R N (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{max u1 u2} N _inst_5)] (i : LinearMap.{u1, u1, max u1 u2, max u1 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 N (AddCommGroup.toAddCommMonoid.{max u1 u2} M _inst_4) (AddCommGroup.toAddCommMonoid.{max u1 u2} N _inst_5) _inst_6 _inst_7) (f : LinearMap.{u1, u1, max u1 u2, max u1 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 Q (AddCommGroup.toAddCommMonoid.{max u1 u2} M _inst_4) (AddCommGroup.toAddCommMonoid.{max u1 u2} Q _inst_2) _inst_6 _inst_3) [_inst_8 : Fact (Function.Injective.{max (succ u1) (succ u2), max (succ u1) (succ u2)} M N (FunLike.coe.{max (succ u1) (succ u2), max (succ u1) (succ u2), max (succ u1) (succ u2)} (LinearMap.{u1, u1, max u1 u2, max u1 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 N (AddCommGroup.toAddCommMonoid.{max u1 u2} M _inst_4) (AddCommGroup.toAddCommMonoid.{max u1 u2} N _inst_5) _inst_6 _inst_7) M (fun (_x : M) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : M) => N) _x) (LinearMap.instFunLikeLinearMap.{u1, u1, max u1 u2, max u1 u2} R R M N (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{max u1 u2} M _inst_4) (AddCommGroup.toAddCommMonoid.{max u1 u2} N _inst_5) _inst_6 _inst_7 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1)))) i))] (h : Module.Baer.{u1, u2} R _inst_1 Q _inst_2 _inst_3) {y : N} (r : R), (Eq.{max (succ u1) (succ u2)} N (HSMul.hSMul.{u1, max u1 u2, max u1 u2} R N N (instHSMul.{u1, max u1 u2} R N (SMulZeroClass.toSMul.{u1, max u1 u2} R N (NegZeroClass.toZero.{max u1 u2} N (SubNegZeroMonoid.toNegZeroClass.{max u1 u2} N (SubtractionMonoid.toSubNegZeroMonoid.{max u1 u2} N (SubtractionCommMonoid.toSubtractionMonoid.{max u1 u2} N (AddCommGroup.toDivisionAddCommMonoid.{max u1 u2} N _inst_5))))) (SMulWithZero.toSMulZeroClass.{u1, max u1 u2} R N (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (NegZeroClass.toZero.{max u1 u2} N (SubNegZeroMonoid.toNegZeroClass.{max u1 u2} N (SubtractionMonoid.toSubNegZeroMonoid.{max u1 u2} N (SubtractionCommMonoid.toSubtractionMonoid.{max u1 u2} N (AddCommGroup.toDivisionAddCommMonoid.{max u1 u2} N _inst_5))))) (MulActionWithZero.toSMulWithZero.{u1, max u1 u2} R N (Semiring.toMonoidWithZero.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (NegZeroClass.toZero.{max u1 u2} N (SubNegZeroMonoid.toNegZeroClass.{max u1 u2} N (SubtractionMonoid.toSubNegZeroMonoid.{max u1 u2} N (SubtractionCommMonoid.toSubtractionMonoid.{max u1 u2} N (AddCommGroup.toDivisionAddCommMonoid.{max u1 u2} N _inst_5))))) (Module.toMulActionWithZero.{u1, max u1 u2} R N (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{max u1 u2} N _inst_5) _inst_7))))) r y) (OfNat.ofNat.{max u1 u2} N 0 (Zero.toOfNat0.{max u1 u2} N (NegZeroClass.toZero.{max u1 u2} N (SubNegZeroMonoid.toNegZeroClass.{max u1 u2} N (SubtractionMonoid.toSubNegZeroMonoid.{max u1 u2} N (SubtractionCommMonoid.toSubtractionMonoid.{max u1 u2} N (AddCommGroup.toDivisionAddCommMonoid.{max u1 u2} N _inst_5)))))))) -> (Eq.{max (succ u1) (succ u2)} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : R) => Q) r) (FunLike.coe.{max (succ u1) (succ u2), succ u1, max (succ u1) (succ u2)} (LinearMap.{u1, u1, u1, max u1 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))) R Q (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R _inst_1)))) (AddCommGroup.toAddCommMonoid.{max u1 u2} Q _inst_2) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R _inst_1)) _inst_3) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : R) => Q) _x) (LinearMap.instFunLikeLinearMap.{u1, u1, u1, max u1 u2} R R R Q (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R _inst_1)))) (AddCommGroup.toAddCommMonoid.{max u1 u2} Q _inst_2) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R _inst_1)) _inst_3 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1)))) (Module.Baer.ExtensionOfMaxAdjoin.extendIdealTo.{u1, u2} R _inst_1 Q _inst_2 _inst_3 M N _inst_4 _inst_5 _inst_6 _inst_7 i f _inst_8 h y) r) (OfNat.ofNat.{max u1 u2} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : R) => Q) r) 0 (Zero.toOfNat0.{max u1 u2} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : R) => Q) r) (NegZeroClass.toZero.{max u1 u2} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : R) => Q) r) (SubNegZeroMonoid.toNegZeroClass.{max u1 u2} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : R) => Q) r) (SubtractionMonoid.toSubNegZeroMonoid.{max u1 u2} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : R) => Q) r) (SubtractionCommMonoid.toSubtractionMonoid.{max u1 u2} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : R) => Q) r) (AddCommGroup.toDivisionAddCommMonoid.{max u1 u2} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : R) => Q) r) _inst_2))))))))
+  forall {R : Type.{u1}} [_inst_1 : Ring.{u1} R] {Q : TypeMax.{u2, u1}} [_inst_2 : AddCommGroup.{max u1 u2} Q] [_inst_3 : Module.{u1, max u1 u2} R Q (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{max u1 u2} Q _inst_2)] {M : Type.{max u1 u2}} {N : Type.{max u1 u2}} [_inst_4 : AddCommGroup.{max u1 u2} M] [_inst_5 : AddCommGroup.{max u1 u2} N] [_inst_6 : Module.{u1, max u1 u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{max u1 u2} M _inst_4)] [_inst_7 : Module.{u1, max u1 u2} R N (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{max u1 u2} N _inst_5)] (i : LinearMap.{u1, u1, max u1 u2, max u1 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 N (AddCommGroup.toAddCommMonoid.{max u1 u2} M _inst_4) (AddCommGroup.toAddCommMonoid.{max u1 u2} N _inst_5) _inst_6 _inst_7) (f : LinearMap.{u1, u1, max u1 u2, max u1 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 Q (AddCommGroup.toAddCommMonoid.{max u1 u2} M _inst_4) (AddCommGroup.toAddCommMonoid.{max u1 u2} Q _inst_2) _inst_6 _inst_3) [_inst_8 : Fact (Function.Injective.{max (succ u1) (succ u2), max (succ u1) (succ u2)} M N (FunLike.coe.{max (succ u1) (succ u2), max (succ u1) (succ u2), max (succ u1) (succ u2)} (LinearMap.{u1, u1, max u1 u2, max u1 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 N (AddCommGroup.toAddCommMonoid.{max u1 u2} M _inst_4) (AddCommGroup.toAddCommMonoid.{max u1 u2} N _inst_5) _inst_6 _inst_7) M (fun (_x : M) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : M) => N) _x) (LinearMap.instFunLikeLinearMap.{u1, u1, max u1 u2, max u1 u2} R R M N (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{max u1 u2} M _inst_4) (AddCommGroup.toAddCommMonoid.{max u1 u2} N _inst_5) _inst_6 _inst_7 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1)))) i))] (h : Module.Baer.{u1, u2} R _inst_1 Q _inst_2 _inst_3) {y : N} (r : R), (Eq.{max (succ u1) (succ u2)} N (HSMul.hSMul.{u1, max u1 u2, max u1 u2} R N N (instHSMul.{u1, max u1 u2} R N (SMulZeroClass.toSMul.{u1, max u1 u2} R N (NegZeroClass.toZero.{max u1 u2} N (SubNegZeroMonoid.toNegZeroClass.{max u1 u2} N (SubtractionMonoid.toSubNegZeroMonoid.{max u1 u2} N (SubtractionCommMonoid.toSubtractionMonoid.{max u1 u2} N (AddCommGroup.toDivisionAddCommMonoid.{max u1 u2} N _inst_5))))) (SMulWithZero.toSMulZeroClass.{u1, max u1 u2} R N (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (NegZeroClass.toZero.{max u1 u2} N (SubNegZeroMonoid.toNegZeroClass.{max u1 u2} N (SubtractionMonoid.toSubNegZeroMonoid.{max u1 u2} N (SubtractionCommMonoid.toSubtractionMonoid.{max u1 u2} N (AddCommGroup.toDivisionAddCommMonoid.{max u1 u2} N _inst_5))))) (MulActionWithZero.toSMulWithZero.{u1, max u1 u2} R N (Semiring.toMonoidWithZero.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (NegZeroClass.toZero.{max u1 u2} N (SubNegZeroMonoid.toNegZeroClass.{max u1 u2} N (SubtractionMonoid.toSubNegZeroMonoid.{max u1 u2} N (SubtractionCommMonoid.toSubtractionMonoid.{max u1 u2} N (AddCommGroup.toDivisionAddCommMonoid.{max u1 u2} N _inst_5))))) (Module.toMulActionWithZero.{u1, max u1 u2} R N (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{max u1 u2} N _inst_5) _inst_7))))) r y) (OfNat.ofNat.{max u1 u2} N 0 (Zero.toOfNat0.{max u1 u2} N (NegZeroClass.toZero.{max u1 u2} N (SubNegZeroMonoid.toNegZeroClass.{max u1 u2} N (SubtractionMonoid.toSubNegZeroMonoid.{max u1 u2} N (SubtractionCommMonoid.toSubtractionMonoid.{max u1 u2} N (AddCommGroup.toDivisionAddCommMonoid.{max u1 u2} N _inst_5)))))))) -> (Eq.{max (succ u1) (succ u2)} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : R) => Q) r) (FunLike.coe.{max (succ u1) (succ u2), succ u1, max (succ u1) (succ u2)} (LinearMap.{u1, u1, u1, max u1 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))) R Q (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R _inst_1)))) (AddCommGroup.toAddCommMonoid.{max u1 u2} Q _inst_2) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R _inst_1)) _inst_3) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : R) => Q) _x) (LinearMap.instFunLikeLinearMap.{u1, u1, u1, max u1 u2} R R R Q (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R _inst_1)))) (AddCommGroup.toAddCommMonoid.{max u1 u2} Q _inst_2) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R _inst_1)) _inst_3 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1)))) (Module.Baer.ExtensionOfMaxAdjoin.extendIdealTo.{u1, u2} R _inst_1 Q _inst_2 _inst_3 M N _inst_4 _inst_5 _inst_6 _inst_7 i f _inst_8 h y) r) (OfNat.ofNat.{max u1 u2} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : R) => Q) r) 0 (Zero.toOfNat0.{max u1 u2} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : R) => Q) r) (NegZeroClass.toZero.{max u1 u2} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : R) => Q) r) (SubNegZeroMonoid.toNegZeroClass.{max u1 u2} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : R) => Q) r) (SubtractionMonoid.toSubNegZeroMonoid.{max u1 u2} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : R) => Q) r) (SubtractionCommMonoid.toSubtractionMonoid.{max u1 u2} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : R) => Q) r) (AddCommGroup.toDivisionAddCommMonoid.{max u1 u2} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : R) => Q) r) _inst_2))))))))
 Case conversion may be inaccurate. Consider using '#align module.Baer.extension_of_max_adjoin.extend_ideal_to_wd' Module.Baer.ExtensionOfMaxAdjoin.extendIdealTo_wd'ₓ'. -/
 theorem ExtensionOfMaxAdjoin.extendIdealTo_wd' (h : Module.Baer R Q) {y : N} (r : R)
     (eq1 : r • y = 0) : ExtensionOfMaxAdjoin.extendIdealTo i f h y r = 0 :=
@@ -420,7 +420,7 @@ theorem ExtensionOfMaxAdjoin.extendIdealTo_wd' (h : Module.Baer R Q) {y : N} (r
 lean 3 declaration is
   forall {R : Type.{u1}} [_inst_1 : Ring.{u1} R] {Q : Type.{max u1 u2}} [_inst_2 : AddCommGroup.{max u1 u2} Q] [_inst_3 : Module.{u1, max u1 u2} R Q (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{max u1 u2} Q _inst_2)] {M : Type.{max u1 u2}} {N : Type.{max u1 u2}} [_inst_4 : AddCommGroup.{max u1 u2} M] [_inst_5 : AddCommGroup.{max u1 u2} N] [_inst_6 : Module.{u1, max u1 u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{max u1 u2} M _inst_4)] [_inst_7 : Module.{u1, max u1 u2} R N (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{max u1 u2} N _inst_5)] (i : LinearMap.{u1, u1, max u1 u2, max u1 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 N (AddCommGroup.toAddCommMonoid.{max u1 u2} M _inst_4) (AddCommGroup.toAddCommMonoid.{max u1 u2} N _inst_5) _inst_6 _inst_7) (f : LinearMap.{u1, u1, max u1 u2, max u1 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 Q (AddCommGroup.toAddCommMonoid.{max u1 u2} M _inst_4) (AddCommGroup.toAddCommMonoid.{max u1 u2} Q _inst_2) _inst_6 _inst_3) [_inst_8 : Fact (Function.Injective.{succ (max u1 u2), succ (max u1 u2)} M N (coeFn.{succ (max u1 u2), succ (max u1 u2)} (LinearMap.{u1, u1, max u1 u2, max u1 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 N (AddCommGroup.toAddCommMonoid.{max u1 u2} M _inst_4) (AddCommGroup.toAddCommMonoid.{max u1 u2} N _inst_5) _inst_6 _inst_7) (fun (_x : LinearMap.{u1, u1, max u1 u2, max u1 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 N (AddCommGroup.toAddCommMonoid.{max u1 u2} M _inst_4) (AddCommGroup.toAddCommMonoid.{max u1 u2} N _inst_5) _inst_6 _inst_7) => M -> N) (LinearMap.hasCoeToFun.{u1, u1, max u1 u2, max u1 u2} R R M N (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{max u1 u2} M _inst_4) (AddCommGroup.toAddCommMonoid.{max u1 u2} N _inst_5) _inst_6 _inst_7 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1)))) i))] (h : Module.Baer.{u1, u2} R _inst_1 Q _inst_2 _inst_3) {y : N} (r : R) (r' : R), (Eq.{succ (max u1 u2)} N (SMul.smul.{u1, max u1 u2} R N (SMulZeroClass.toHasSmul.{u1, max u1 u2} R N (AddZeroClass.toHasZero.{max u1 u2} N (AddMonoid.toAddZeroClass.{max u1 u2} N (AddCommMonoid.toAddMonoid.{max u1 u2} N (AddCommGroup.toAddCommMonoid.{max u1 u2} N _inst_5)))) (SMulWithZero.toSmulZeroClass.{u1, max u1 u2} R N (MulZeroClass.toHasZero.{u1} R (MulZeroOneClass.toMulZeroClass.{u1} R (MonoidWithZero.toMulZeroOneClass.{u1} R (Semiring.toMonoidWithZero.{u1} R 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(MulZeroOneClass.toMulZeroClass.{u1} R (MonoidWithZero.toMulZeroOneClass.{u1} R (Semiring.toMonoidWithZero.{u1} R (Ring.toSemiring.{u1} R _inst_1))))) (AddZeroClass.toHasZero.{max u1 u2} N (AddMonoid.toAddZeroClass.{max u1 u2} N (AddCommMonoid.toAddMonoid.{max u1 u2} N (AddCommGroup.toAddCommMonoid.{max u1 u2} N _inst_5)))) (MulActionWithZero.toSMulWithZero.{u1, max u1 u2} R N (Semiring.toMonoidWithZero.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (AddZeroClass.toHasZero.{max u1 u2} N (AddMonoid.toAddZeroClass.{max u1 u2} N (AddCommMonoid.toAddMonoid.{max u1 u2} N (AddCommGroup.toAddCommMonoid.{max u1 u2} N _inst_5)))) (Module.toMulActionWithZero.{u1, max u1 u2} R N (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{max u1 u2} N _inst_5) _inst_7)))) r' y)) -> (Eq.{succ (max u1 u2)} Q (coeFn.{max (succ u1) (succ (max u1 u2)), max (succ u1) (succ (max u1 u2))} (LinearMap.{u1, u1, u1, max u1 u2} R R (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) 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(AddCommGroup.toAddCommMonoid.{max u1 u2} Q _inst_2) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R _inst_1)) _inst_3) (fun (_x : LinearMap.{u1, u1, u1, max u1 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))) R Q (AddCommGroup.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toAddCommGroup.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R _inst_1)))) (AddCommGroup.toAddCommMonoid.{max u1 u2} Q _inst_2) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R _inst_1)) _inst_3) => R -> Q) (LinearMap.hasCoeToFun.{u1, u1, u1, max u1 u2} R R R Q (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toAddCommGroup.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R _inst_1)))) (AddCommGroup.toAddCommMonoid.{max u1 u2} Q _inst_2) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R _inst_1)) _inst_3 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1)))) (Module.Baer.ExtensionOfMaxAdjoin.extendIdealTo.{u1, u2} R _inst_1 Q _inst_2 _inst_3 M N _inst_4 _inst_5 _inst_6 _inst_7 i f _inst_8 h y) r'))
 but is expected to have type
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(Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{max u1 u2} M _inst_4) (AddCommGroup.toAddCommMonoid.{max u1 u2} N _inst_5) _inst_6 _inst_7 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1)))) i))] (h : Module.Baer.{u1, u2} R _inst_1 Q _inst_2 _inst_3) {y : N} (r : R) (r' : R), (Eq.{max (succ u1) (succ u2)} N (HSMul.hSMul.{u1, max u1 u2, max u1 u2} R N N (instHSMul.{u1, max u1 u2} R N (SMulZeroClass.toSMul.{u1, max u1 u2} R N (NegZeroClass.toZero.{max u1 u2} N (SubNegZeroMonoid.toNegZeroClass.{max u1 u2} N (SubtractionMonoid.toSubNegZeroMonoid.{max u1 u2} N (SubtractionCommMonoid.toSubtractionMonoid.{max u1 u2} N (AddCommGroup.toDivisionAddCommMonoid.{max u1 u2} N _inst_5))))) (SMulWithZero.toSMulZeroClass.{u1, max u1 u2} R N (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (NegZeroClass.toZero.{max u1 u2} N (SubNegZeroMonoid.toNegZeroClass.{max u1 u2} N 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(SubtractionCommMonoid.toSubtractionMonoid.{max u1 u2} N (AddCommGroup.toDivisionAddCommMonoid.{max u1 u2} N _inst_5))))) (SMulWithZero.toSMulZeroClass.{u1, max u1 u2} R N (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (NegZeroClass.toZero.{max u1 u2} N (SubNegZeroMonoid.toNegZeroClass.{max u1 u2} N (SubtractionMonoid.toSubNegZeroMonoid.{max u1 u2} N (SubtractionCommMonoid.toSubtractionMonoid.{max u1 u2} N (AddCommGroup.toDivisionAddCommMonoid.{max u1 u2} N _inst_5))))) (MulActionWithZero.toSMulWithZero.{u1, max u1 u2} R N (Semiring.toMonoidWithZero.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (NegZeroClass.toZero.{max u1 u2} N (SubNegZeroMonoid.toNegZeroClass.{max u1 u2} N (SubtractionMonoid.toSubNegZeroMonoid.{max u1 u2} N (SubtractionCommMonoid.toSubtractionMonoid.{max u1 u2} N (AddCommGroup.toDivisionAddCommMonoid.{max u1 u2} N _inst_5))))) (Module.toMulActionWithZero.{u1, max u1 u2} R N (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{max u1 u2} N _inst_5) _inst_7))))) r' y)) -> (Eq.{max (succ u1) (succ u2)} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : R) => Q) r) (FunLike.coe.{max (succ u1) (succ u2), succ u1, max (succ u1) (succ u2)} (LinearMap.{u1, u1, u1, max u1 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))) R Q (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R _inst_1)))) (AddCommGroup.toAddCommMonoid.{max u1 u2} Q _inst_2) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R _inst_1)) _inst_3) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : R) => Q) _x) (LinearMap.instFunLikeLinearMap.{u1, u1, u1, max u1 u2} R R R Q (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R _inst_1)))) (AddCommGroup.toAddCommMonoid.{max u1 u2} Q _inst_2) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R _inst_1)) _inst_3 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1)))) (Module.Baer.ExtensionOfMaxAdjoin.extendIdealTo.{u1, u2} R _inst_1 Q _inst_2 _inst_3 M N _inst_4 _inst_5 _inst_6 _inst_7 i f _inst_8 h y) r) (FunLike.coe.{max (succ u1) (succ u2), succ u1, max (succ u1) (succ u2)} (LinearMap.{u1, u1, u1, max u1 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))) R Q (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R _inst_1)))) (AddCommGroup.toAddCommMonoid.{max u1 u2} Q _inst_2) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R _inst_1)) _inst_3) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : R) => Q) _x) (LinearMap.instFunLikeLinearMap.{u1, u1, u1, max u1 u2} R R R Q (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R _inst_1)))) (AddCommGroup.toAddCommMonoid.{max u1 u2} Q _inst_2) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R _inst_1)) _inst_3 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1)))) (Module.Baer.ExtensionOfMaxAdjoin.extendIdealTo.{u1, u2} R _inst_1 Q _inst_2 _inst_3 M N _inst_4 _inst_5 _inst_6 _inst_7 i f _inst_8 h y) r'))
+  forall {R : Type.{u1}} [_inst_1 : Ring.{u1} R] {Q : TypeMax.{u2, u1}} [_inst_2 : AddCommGroup.{max u1 u2} Q] [_inst_3 : Module.{u1, max u1 u2} R Q (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{max u1 u2} Q _inst_2)] {M : Type.{max u1 u2}} {N : Type.{max u1 u2}} [_inst_4 : AddCommGroup.{max u1 u2} M] [_inst_5 : AddCommGroup.{max u1 u2} N] [_inst_6 : Module.{u1, max u1 u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{max u1 u2} M _inst_4)] [_inst_7 : Module.{u1, max u1 u2} R N (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{max u1 u2} N _inst_5)] (i : LinearMap.{u1, u1, max u1 u2, max u1 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 N (AddCommGroup.toAddCommMonoid.{max u1 u2} M _inst_4) (AddCommGroup.toAddCommMonoid.{max u1 u2} N _inst_5) _inst_6 _inst_7) (f : LinearMap.{u1, u1, max u1 u2, max u1 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 Q (AddCommGroup.toAddCommMonoid.{max u1 u2} M _inst_4) (AddCommGroup.toAddCommMonoid.{max u1 u2} Q _inst_2) _inst_6 _inst_3) [_inst_8 : Fact (Function.Injective.{max (succ u1) (succ u2), max (succ u1) (succ u2)} M N (FunLike.coe.{max (succ u1) (succ u2), max (succ u1) (succ u2), max (succ u1) (succ u2)} (LinearMap.{u1, u1, max u1 u2, max u1 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 N (AddCommGroup.toAddCommMonoid.{max u1 u2} M _inst_4) (AddCommGroup.toAddCommMonoid.{max u1 u2} N _inst_5) _inst_6 _inst_7) M (fun (_x : M) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : M) => N) _x) (LinearMap.instFunLikeLinearMap.{u1, u1, max u1 u2, max u1 u2} R R M N (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{max u1 u2} M _inst_4) (AddCommGroup.toAddCommMonoid.{max u1 u2} N _inst_5) _inst_6 _inst_7 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1)))) i))] (h : Module.Baer.{u1, u2} R _inst_1 Q _inst_2 _inst_3) {y : N} (r : R) (r' : R), (Eq.{max (succ u1) (succ u2)} N (HSMul.hSMul.{u1, max u1 u2, max u1 u2} R N N (instHSMul.{u1, max u1 u2} R N (SMulZeroClass.toSMul.{u1, max u1 u2} R N (NegZeroClass.toZero.{max u1 u2} N (SubNegZeroMonoid.toNegZeroClass.{max u1 u2} N (SubtractionMonoid.toSubNegZeroMonoid.{max u1 u2} N (SubtractionCommMonoid.toSubtractionMonoid.{max u1 u2} N (AddCommGroup.toDivisionAddCommMonoid.{max u1 u2} N _inst_5))))) (SMulWithZero.toSMulZeroClass.{u1, max u1 u2} R N (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (NegZeroClass.toZero.{max u1 u2} N (SubNegZeroMonoid.toNegZeroClass.{max u1 u2} N (SubtractionMonoid.toSubNegZeroMonoid.{max u1 u2} N (SubtractionCommMonoid.toSubtractionMonoid.{max u1 u2} N (AddCommGroup.toDivisionAddCommMonoid.{max u1 u2} N _inst_5))))) (MulActionWithZero.toSMulWithZero.{u1, max u1 u2} R N (Semiring.toMonoidWithZero.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (NegZeroClass.toZero.{max u1 u2} N (SubNegZeroMonoid.toNegZeroClass.{max u1 u2} N (SubtractionMonoid.toSubNegZeroMonoid.{max u1 u2} N (SubtractionCommMonoid.toSubtractionMonoid.{max u1 u2} N (AddCommGroup.toDivisionAddCommMonoid.{max u1 u2} N _inst_5))))) (Module.toMulActionWithZero.{u1, max u1 u2} R N (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{max u1 u2} N _inst_5) _inst_7))))) r y) (HSMul.hSMul.{u1, max u1 u2, max u1 u2} R N N (instHSMul.{u1, max u1 u2} R N (SMulZeroClass.toSMul.{u1, max u1 u2} R N (NegZeroClass.toZero.{max u1 u2} N (SubNegZeroMonoid.toNegZeroClass.{max u1 u2} N (SubtractionMonoid.toSubNegZeroMonoid.{max u1 u2} N (SubtractionCommMonoid.toSubtractionMonoid.{max u1 u2} N (AddCommGroup.toDivisionAddCommMonoid.{max u1 u2} N _inst_5))))) (SMulWithZero.toSMulZeroClass.{u1, max u1 u2} R N (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (NegZeroClass.toZero.{max u1 u2} N (SubNegZeroMonoid.toNegZeroClass.{max u1 u2} N (SubtractionMonoid.toSubNegZeroMonoid.{max u1 u2} N (SubtractionCommMonoid.toSubtractionMonoid.{max u1 u2} N (AddCommGroup.toDivisionAddCommMonoid.{max u1 u2} N _inst_5))))) (MulActionWithZero.toSMulWithZero.{u1, max u1 u2} R N (Semiring.toMonoidWithZero.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (NegZeroClass.toZero.{max u1 u2} N (SubNegZeroMonoid.toNegZeroClass.{max u1 u2} N (SubtractionMonoid.toSubNegZeroMonoid.{max u1 u2} N (SubtractionCommMonoid.toSubtractionMonoid.{max u1 u2} N (AddCommGroup.toDivisionAddCommMonoid.{max u1 u2} N _inst_5))))) (Module.toMulActionWithZero.{u1, max u1 u2} R N (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{max u1 u2} N _inst_5) _inst_7))))) r' y)) -> (Eq.{max (succ u1) (succ u2)} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : R) => Q) r) (FunLike.coe.{max (succ u1) (succ u2), succ u1, max (succ u1) (succ u2)} (LinearMap.{u1, u1, u1, max u1 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))) R Q (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R _inst_1)))) (AddCommGroup.toAddCommMonoid.{max u1 u2} Q _inst_2) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R _inst_1)) _inst_3) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : R) => Q) _x) (LinearMap.instFunLikeLinearMap.{u1, u1, u1, max u1 u2} R R R Q (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R _inst_1)))) (AddCommGroup.toAddCommMonoid.{max u1 u2} Q _inst_2) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R _inst_1)) _inst_3 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1)))) (Module.Baer.ExtensionOfMaxAdjoin.extendIdealTo.{u1, u2} R _inst_1 Q _inst_2 _inst_3 M N _inst_4 _inst_5 _inst_6 _inst_7 i f _inst_8 h y) r) (FunLike.coe.{max (succ u1) (succ u2), succ u1, max (succ u1) (succ u2)} (LinearMap.{u1, u1, u1, max u1 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))) R Q (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R _inst_1)))) (AddCommGroup.toAddCommMonoid.{max u1 u2} Q _inst_2) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R _inst_1)) _inst_3) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : R) => Q) _x) (LinearMap.instFunLikeLinearMap.{u1, u1, u1, max u1 u2} R R R Q (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R _inst_1)))) (AddCommGroup.toAddCommMonoid.{max u1 u2} Q _inst_2) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R _inst_1)) _inst_3 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1)))) (Module.Baer.ExtensionOfMaxAdjoin.extendIdealTo.{u1, u2} R _inst_1 Q _inst_2 _inst_3 M N _inst_4 _inst_5 _inst_6 _inst_7 i f _inst_8 h y) r'))
 Case conversion may be inaccurate. Consider using '#align module.Baer.extension_of_max_adjoin.extend_ideal_to_wd Module.Baer.ExtensionOfMaxAdjoin.extendIdealTo_wdₓ'. -/
 theorem ExtensionOfMaxAdjoin.extendIdealTo_wd (h : Module.Baer R Q) {y : N} (r r' : R)
     (eq1 : r • y = r' • y) :
@@ -435,7 +435,7 @@ theorem ExtensionOfMaxAdjoin.extendIdealTo_wd (h : Module.Baer R Q) {y : N} (r r
 lean 3 declaration is
   forall {R : Type.{u1}} [_inst_1 : Ring.{u1} R] {Q : Type.{max u1 u2}} [_inst_2 : AddCommGroup.{max u1 u2} Q] [_inst_3 : Module.{u1, max u1 u2} R Q (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{max u1 u2} Q _inst_2)] {M : Type.{max u1 u2}} {N : Type.{max u1 u2}} [_inst_4 : AddCommGroup.{max u1 u2} M] [_inst_5 : AddCommGroup.{max u1 u2} N] [_inst_6 : Module.{u1, max u1 u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{max u1 u2} M _inst_4)] [_inst_7 : Module.{u1, max u1 u2} R N (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{max u1 u2} N _inst_5)] (i : LinearMap.{u1, u1, max u1 u2, max u1 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 N (AddCommGroup.toAddCommMonoid.{max u1 u2} M _inst_4) (AddCommGroup.toAddCommMonoid.{max u1 u2} N _inst_5) _inst_6 _inst_7) (f : LinearMap.{u1, u1, max u1 u2, max u1 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 Q (AddCommGroup.toAddCommMonoid.{max u1 u2} M _inst_4) (AddCommGroup.toAddCommMonoid.{max u1 u2} Q _inst_2) _inst_6 _inst_3) [_inst_8 : Fact (Function.Injective.{succ (max u1 u2), succ (max u1 u2)} M N (coeFn.{succ (max u1 u2), succ (max u1 u2)} (LinearMap.{u1, u1, max u1 u2, max u1 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 N (AddCommGroup.toAddCommMonoid.{max u1 u2} M _inst_4) (AddCommGroup.toAddCommMonoid.{max u1 u2} N _inst_5) _inst_6 _inst_7) (fun (_x : LinearMap.{u1, u1, max u1 u2, max u1 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 N (AddCommGroup.toAddCommMonoid.{max u1 u2} M _inst_4) (AddCommGroup.toAddCommMonoid.{max u1 u2} N _inst_5) _inst_6 _inst_7) => M -> N) (LinearMap.hasCoeToFun.{u1, u1, max u1 u2, max u1 u2} R R M N (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{max u1 u2} M _inst_4) (AddCommGroup.toAddCommMonoid.{max u1 u2} N _inst_5) _inst_6 _inst_7 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1)))) i))] (h : Module.Baer.{u1, u2} R _inst_1 Q _inst_2 _inst_3) {y : N} (r : R) (hr : Membership.Mem.{max u1 u2, max u1 u2} N (Submodule.{u1, max u1 u2} R N (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{max u1 u2} N _inst_5) _inst_7) (SetLike.hasMem.{max u1 u2, max u1 u2} (Submodule.{u1, max u1 u2} R N (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{max u1 u2} N _inst_5) _inst_7) N (Submodule.setLike.{u1, max u1 u2} R N (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{max u1 u2} N _inst_5) _inst_7)) (SMul.smul.{u1, max u1 u2} R N (SMulZeroClass.toHasSmul.{u1, max u1 u2} R N (AddZeroClass.toHasZero.{max u1 u2} N (AddMonoid.toAddZeroClass.{max u1 u2} N (AddCommMonoid.toAddMonoid.{max u1 u2} N (AddCommGroup.toAddCommMonoid.{max u1 u2} N _inst_5)))) (SMulWithZero.toSmulZeroClass.{u1, max u1 u2} R N (MulZeroClass.toHasZero.{u1} R (MulZeroOneClass.toMulZeroClass.{u1} R (MonoidWithZero.toMulZeroOneClass.{u1} R (Semiring.toMonoidWithZero.{u1} R (Ring.toSemiring.{u1} R _inst_1))))) (AddZeroClass.toHasZero.{max u1 u2} N (AddMonoid.toAddZeroClass.{max u1 u2} N (AddCommMonoid.toAddMonoid.{max u1 u2} N (AddCommGroup.toAddCommMonoid.{max u1 u2} N _inst_5)))) (MulActionWithZero.toSMulWithZero.{u1, max u1 u2} R N (Semiring.toMonoidWithZero.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (AddZeroClass.toHasZero.{max u1 u2} N (AddMonoid.toAddZeroClass.{max u1 u2} N (AddCommMonoid.toAddMonoid.{max u1 u2} N (AddCommGroup.toAddCommMonoid.{max u1 u2} N _inst_5)))) (Module.toMulActionWithZero.{u1, max u1 u2} R N (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{max u1 u2} N _inst_5) _inst_7)))) r y) (LinearPMap.domain.{u1, max u1 u2, max u1 u2} R _inst_1 N _inst_5 _inst_7 Q _inst_2 _inst_3 (Module.Baer.ExtensionOf.toLinearPmap.{u1, u2} R _inst_1 Q _inst_2 _inst_3 M N _inst_4 _inst_5 _inst_6 _inst_7 i f (Module.Baer.extensionOfMax.{u1, u2} R _inst_1 Q _inst_2 _inst_3 M N _inst_4 _inst_5 _inst_6 _inst_7 i f _inst_8)))), Eq.{succ (max u1 u2)} Q (coeFn.{max (succ u1) (succ (max u1 u2)), max (succ u1) (succ (max u1 u2))} (LinearMap.{u1, u1, u1, max u1 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))) R Q (AddCommGroup.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toAddCommGroup.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R _inst_1)))) (AddCommGroup.toAddCommMonoid.{max u1 u2} Q _inst_2) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R _inst_1)) _inst_3) (fun (_x : LinearMap.{u1, u1, u1, max u1 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))) R Q (AddCommGroup.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toAddCommGroup.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R _inst_1)))) (AddCommGroup.toAddCommMonoid.{max u1 u2} Q _inst_2) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R _inst_1)) _inst_3) => R -> Q) (LinearMap.hasCoeToFun.{u1, u1, u1, max u1 u2} R R R Q (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toAddCommGroup.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R _inst_1)))) (AddCommGroup.toAddCommMonoid.{max u1 u2} Q _inst_2) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R _inst_1)) _inst_3 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1)))) (Module.Baer.ExtensionOfMaxAdjoin.extendIdealTo.{u1, u2} R _inst_1 Q _inst_2 _inst_3 M N _inst_4 _inst_5 _inst_6 _inst_7 i f _inst_8 h y) r) (coeFn.{succ (max u1 u2), succ (max u1 u2)} (LinearPMap.{u1, max u1 u2, max u1 u2} R _inst_1 N _inst_5 _inst_7 Q _inst_2 _inst_3) (fun (f : LinearPMap.{u1, max u1 u2, max u1 u2} R _inst_1 N _inst_5 _inst_7 Q _inst_2 _inst_3) => (coeSort.{succ (max u1 u2), succ (succ (max u1 u2))} (Submodule.{u1, max u1 u2} R N (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{max u1 u2} N _inst_5) _inst_7) Type.{max u1 u2} (SetLike.hasCoeToSort.{max u1 u2, max u1 u2} (Submodule.{u1, max u1 u2} R N (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{max u1 u2} N _inst_5) _inst_7) N (Submodule.setLike.{u1, max u1 u2} R N (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{max u1 u2} N _inst_5) _inst_7)) (LinearPMap.domain.{u1, max u1 u2, max u1 u2} R _inst_1 N _inst_5 _inst_7 Q _inst_2 _inst_3 f)) -> Q) (LinearPMap.hasCoeToFun.{u1, max u1 u2, max u1 u2} R _inst_1 N _inst_5 _inst_7 Q _inst_2 _inst_3) (Module.Baer.ExtensionOf.toLinearPmap.{u1, u2} R _inst_1 Q _inst_2 _inst_3 M N _inst_4 _inst_5 _inst_6 _inst_7 i f (Module.Baer.extensionOfMax.{u1, u2} R _inst_1 Q _inst_2 _inst_3 M N _inst_4 _inst_5 _inst_6 _inst_7 i f _inst_8)) (Subtype.mk.{succ (max u1 u2)} N (fun (x : N) => Membership.Mem.{max u1 u2, max u1 u2} N (Submodule.{u1, max u1 u2} R N (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{max u1 u2} N _inst_5) _inst_7) (SetLike.hasMem.{max u1 u2, max u1 u2} (Submodule.{u1, max u1 u2} R N (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{max u1 u2} N _inst_5) _inst_7) N (Submodule.setLike.{u1, max u1 u2} R N (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{max u1 u2} N _inst_5) _inst_7)) x (LinearPMap.domain.{u1, max u1 u2, max u1 u2} R _inst_1 N _inst_5 _inst_7 Q _inst_2 _inst_3 (Module.Baer.ExtensionOf.toLinearPmap.{u1, u2} R _inst_1 Q _inst_2 _inst_3 M N _inst_4 _inst_5 _inst_6 _inst_7 i f (Module.Baer.extensionOfMax.{u1, u2} R _inst_1 Q _inst_2 _inst_3 M N _inst_4 _inst_5 _inst_6 _inst_7 i f _inst_8)))) (SMul.smul.{u1, max u1 u2} R N (SMulZeroClass.toHasSmul.{u1, max u1 u2} R N (AddZeroClass.toHasZero.{max u1 u2} N (AddMonoid.toAddZeroClass.{max u1 u2} N (AddCommMonoid.toAddMonoid.{max u1 u2} N (AddCommGroup.toAddCommMonoid.{max u1 u2} N _inst_5)))) (SMulWithZero.toSmulZeroClass.{u1, max u1 u2} R N (MulZeroClass.toHasZero.{u1} R (MulZeroOneClass.toMulZeroClass.{u1} R (MonoidWithZero.toMulZeroOneClass.{u1} R (Semiring.toMonoidWithZero.{u1} R (Ring.toSemiring.{u1} R _inst_1))))) (AddZeroClass.toHasZero.{max u1 u2} N (AddMonoid.toAddZeroClass.{max u1 u2} N (AddCommMonoid.toAddMonoid.{max u1 u2} N (AddCommGroup.toAddCommMonoid.{max u1 u2} N _inst_5)))) (MulActionWithZero.toSMulWithZero.{u1, max u1 u2} R N (Semiring.toMonoidWithZero.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (AddZeroClass.toHasZero.{max u1 u2} N (AddMonoid.toAddZeroClass.{max u1 u2} N (AddCommMonoid.toAddMonoid.{max u1 u2} N (AddCommGroup.toAddCommMonoid.{max u1 u2} N _inst_5)))) (Module.toMulActionWithZero.{u1, max u1 u2} R N (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{max u1 u2} N _inst_5) _inst_7)))) r y) hr))
 but is expected to have type
-  forall {R : Type.{u1}} [_inst_1 : Ring.{u1} R] {Q : TypeMax.{u2, u1}} [_inst_2 : AddCommGroup.{max u1 u2} Q] [_inst_3 : Module.{u1, max u1 u2} R Q (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{max u1 u2} Q _inst_2)] {M : Type.{max u1 u2}} {N : Type.{max u1 u2}} [_inst_4 : AddCommGroup.{max u1 u2} M] [_inst_5 : AddCommGroup.{max u1 u2} N] [_inst_6 : Module.{u1, max u1 u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{max u1 u2} M _inst_4)] [_inst_7 : Module.{u1, max u1 u2} R N (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{max u1 u2} N _inst_5)] (i : LinearMap.{u1, u1, max u1 u2, max u1 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 N (AddCommGroup.toAddCommMonoid.{max u1 u2} M _inst_4) (AddCommGroup.toAddCommMonoid.{max u1 u2} N _inst_5) _inst_6 _inst_7) (f : LinearMap.{u1, u1, max u1 u2, max u1 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 Q (AddCommGroup.toAddCommMonoid.{max u1 u2} M _inst_4) (AddCommGroup.toAddCommMonoid.{max u1 u2} Q _inst_2) _inst_6 _inst_3) [_inst_8 : Fact (Function.Injective.{max (succ u1) (succ u2), max (succ u1) (succ u2)} M N (FunLike.coe.{max (succ u1) (succ u2), max (succ u1) (succ u2), max (succ u1) (succ u2)} (LinearMap.{u1, u1, max u1 u2, max u1 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 N (AddCommGroup.toAddCommMonoid.{max u1 u2} M _inst_4) (AddCommGroup.toAddCommMonoid.{max u1 u2} N _inst_5) _inst_6 _inst_7) M (fun (_x : M) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : M) => N) _x) (LinearMap.instFunLikeLinearMap.{u1, u1, max u1 u2, max u1 u2} R R M N (Ring.toSemiring.{u1} R _inst_1) 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_inst_1)))) (AddCommGroup.toAddCommMonoid.{max u1 u2} Q _inst_2) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R _inst_1)) _inst_3) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : R) => Q) _x) (LinearMap.instFunLikeLinearMap.{u1, u1, u1, max u1 u2} R R R Q (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R _inst_1)))) (AddCommGroup.toAddCommMonoid.{max u1 u2} Q _inst_2) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R _inst_1)) _inst_3 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1)))) (Module.Baer.ExtensionOfMaxAdjoin.extendIdealTo.{u1, u2} R _inst_1 Q _inst_2 _inst_3 M N _inst_4 _inst_5 _inst_6 _inst_7 i f _inst_8 h y) r) (LinearPMap.toFun'.{u1, max u1 u2, max u1 u2} R _inst_1 N _inst_5 _inst_7 Q _inst_2 _inst_3 (Module.Baer.ExtensionOf.toLinearPMap.{u1, u2} R _inst_1 Q _inst_2 _inst_3 M N _inst_4 _inst_5 _inst_6 _inst_7 i f (Module.Baer.extensionOfMax.{u1, u2} R _inst_1 Q _inst_2 _inst_3 M N _inst_4 _inst_5 _inst_6 _inst_7 i f _inst_8)) (Subtype.mk.{max (succ u1) (succ u2)} N (fun (x : N) => Membership.mem.{max u1 u2, max u1 u2} N (Submodule.{u1, max u1 u2} R N (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{max u1 u2} N _inst_5) _inst_7) (SetLike.instMembership.{max u1 u2, max u1 u2} (Submodule.{u1, max u1 u2} R N (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{max u1 u2} N _inst_5) _inst_7) N (Submodule.setLike.{u1, max u1 u2} R N (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{max u1 u2} N _inst_5) _inst_7)) x (LinearPMap.domain.{u1, max u1 u2, max u1 u2} R _inst_1 N _inst_5 _inst_7 Q _inst_2 _inst_3 (Module.Baer.ExtensionOf.toLinearPMap.{u1, u2} R _inst_1 Q _inst_2 _inst_3 M N _inst_4 _inst_5 _inst_6 _inst_7 i f 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(Ring.toSemiring.{u1} R _inst_1)) (NegZeroClass.toZero.{max u1 u2} N (SubNegZeroMonoid.toNegZeroClass.{max u1 u2} N (SubtractionMonoid.toSubNegZeroMonoid.{max u1 u2} N (SubtractionCommMonoid.toSubtractionMonoid.{max u1 u2} N (AddCommGroup.toDivisionAddCommMonoid.{max u1 u2} N _inst_5))))) (Module.toMulActionWithZero.{u1, max u1 u2} R N (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{max u1 u2} N _inst_5) _inst_7))))) r y) hr))
+  forall {R : Type.{u1}} [_inst_1 : Ring.{u1} R] {Q : TypeMax.{u2, u1}} [_inst_2 : AddCommGroup.{max u1 u2} Q] [_inst_3 : Module.{u1, max u1 u2} R Q (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{max u1 u2} Q _inst_2)] {M : Type.{max u1 u2}} {N : Type.{max u1 u2}} [_inst_4 : AddCommGroup.{max u1 u2} M] [_inst_5 : AddCommGroup.{max u1 u2} N] [_inst_6 : Module.{u1, max u1 u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{max u1 u2} M _inst_4)] [_inst_7 : Module.{u1, max u1 u2} R N (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{max u1 u2} N _inst_5)] (i : LinearMap.{u1, u1, max u1 u2, max u1 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 N (AddCommGroup.toAddCommMonoid.{max u1 u2} M _inst_4) (AddCommGroup.toAddCommMonoid.{max u1 u2} N _inst_5) _inst_6 _inst_7) (f : LinearMap.{u1, u1, max u1 u2, max u1 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 Q (AddCommGroup.toAddCommMonoid.{max u1 u2} M _inst_4) (AddCommGroup.toAddCommMonoid.{max u1 u2} Q _inst_2) _inst_6 _inst_3) [_inst_8 : Fact (Function.Injective.{max (succ u1) (succ u2), max (succ u1) (succ u2)} M N (FunLike.coe.{max (succ u1) (succ u2), max (succ u1) (succ u2), max (succ u1) (succ u2)} (LinearMap.{u1, u1, max u1 u2, max u1 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 N (AddCommGroup.toAddCommMonoid.{max u1 u2} M _inst_4) (AddCommGroup.toAddCommMonoid.{max u1 u2} N _inst_5) _inst_6 _inst_7) M (fun (_x : M) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : M) => N) _x) (LinearMap.instFunLikeLinearMap.{u1, u1, max u1 u2, max u1 u2} R R M N (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{max u1 u2} M _inst_4) (AddCommGroup.toAddCommMonoid.{max u1 u2} N _inst_5) _inst_6 _inst_7 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1)))) i))] (h : Module.Baer.{u1, u2} R _inst_1 Q _inst_2 _inst_3) {y : N} (r : R) (hr : Membership.mem.{max u1 u2, max u1 u2} N (Submodule.{u1, max u1 u2} R N (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{max u1 u2} N _inst_5) _inst_7) (SetLike.instMembership.{max u1 u2, max u1 u2} (Submodule.{u1, max u1 u2} R N (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{max u1 u2} N _inst_5) _inst_7) N (Submodule.setLike.{u1, max u1 u2} R N (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{max u1 u2} N _inst_5) _inst_7)) (HSMul.hSMul.{u1, max u1 u2, max u1 u2} R N N (instHSMul.{u1, max u1 u2} R N (SMulZeroClass.toSMul.{u1, max u1 u2} R N (NegZeroClass.toZero.{max u1 u2} N (SubNegZeroMonoid.toNegZeroClass.{max u1 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_inst_1)))) (AddCommGroup.toAddCommMonoid.{max u1 u2} Q _inst_2) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R _inst_1)) _inst_3) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : R) => Q) _x) (LinearMap.instFunLikeLinearMap.{u1, u1, u1, max u1 u2} R R R Q (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R _inst_1)))) (AddCommGroup.toAddCommMonoid.{max u1 u2} Q _inst_2) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R _inst_1)) _inst_3 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1)))) (Module.Baer.ExtensionOfMaxAdjoin.extendIdealTo.{u1, u2} R _inst_1 Q _inst_2 _inst_3 M N _inst_4 _inst_5 _inst_6 _inst_7 i f _inst_8 h y) r) (LinearPMap.toFun'.{u1, max u1 u2, max u1 u2} R _inst_1 N _inst_5 _inst_7 Q _inst_2 _inst_3 (Module.Baer.ExtensionOf.toLinearPMap.{u1, u2} R _inst_1 Q _inst_2 _inst_3 M N _inst_4 _inst_5 _inst_6 _inst_7 i f (Module.Baer.extensionOfMax.{u1, u2} R _inst_1 Q _inst_2 _inst_3 M N _inst_4 _inst_5 _inst_6 _inst_7 i f _inst_8)) (Subtype.mk.{max (succ u1) (succ u2)} N (fun (x : N) => Membership.mem.{max u1 u2, max u1 u2} N (Submodule.{u1, max u1 u2} R N (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{max u1 u2} N _inst_5) _inst_7) (SetLike.instMembership.{max u1 u2, max u1 u2} (Submodule.{u1, max u1 u2} R N (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{max u1 u2} N _inst_5) _inst_7) N (Submodule.setLike.{u1, max u1 u2} R N (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{max u1 u2} N _inst_5) _inst_7)) x (LinearPMap.domain.{u1, max u1 u2, max u1 u2} R _inst_1 N _inst_5 _inst_7 Q _inst_2 _inst_3 (Module.Baer.ExtensionOf.toLinearPMap.{u1, u2} R _inst_1 Q _inst_2 _inst_3 M N _inst_4 _inst_5 _inst_6 _inst_7 i f 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(Ring.toSemiring.{u1} R _inst_1)) (NegZeroClass.toZero.{max u1 u2} N (SubNegZeroMonoid.toNegZeroClass.{max u1 u2} N (SubtractionMonoid.toSubNegZeroMonoid.{max u1 u2} N (SubtractionCommMonoid.toSubtractionMonoid.{max u1 u2} N (AddCommGroup.toDivisionAddCommMonoid.{max u1 u2} N _inst_5))))) (Module.toMulActionWithZero.{u1, max u1 u2} R N (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{max u1 u2} N _inst_5) _inst_7))))) r y) hr))
 Case conversion may be inaccurate. Consider using '#align module.Baer.extension_of_max_adjoin.extend_ideal_to_eq Module.Baer.ExtensionOfMaxAdjoin.extendIdealTo_eqₓ'. -/
 theorem ExtensionOfMaxAdjoin.extendIdealTo_eq (h : Module.Baer R Q) {y : N} (r : R)
     (hr : r • y ∈ (extensionOfMax i f).domain) :
@@ -449,7 +449,7 @@ theorem ExtensionOfMaxAdjoin.extendIdealTo_eq (h : Module.Baer R Q) {y : N} (r :
 lean 3 declaration is
   forall {R : Type.{u1}} [_inst_1 : Ring.{u1} R] {Q : Type.{max u1 u2}} [_inst_2 : AddCommGroup.{max u1 u2} Q] [_inst_3 : Module.{u1, max u1 u2} R Q (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{max u1 u2} Q _inst_2)] {M : Type.{max u1 u2}} {N : Type.{max u1 u2}} [_inst_4 : AddCommGroup.{max u1 u2} M] [_inst_5 : AddCommGroup.{max u1 u2} N] [_inst_6 : Module.{u1, max u1 u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{max u1 u2} M _inst_4)] [_inst_7 : Module.{u1, max u1 u2} R N (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{max u1 u2} N _inst_5)] (i : LinearMap.{u1, u1, max u1 u2, max u1 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 N (AddCommGroup.toAddCommMonoid.{max u1 u2} M _inst_4) (AddCommGroup.toAddCommMonoid.{max u1 u2} N _inst_5) _inst_6 _inst_7) (f : LinearMap.{u1, u1, max u1 u2, max u1 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 Q (AddCommGroup.toAddCommMonoid.{max u1 u2} M _inst_4) (AddCommGroup.toAddCommMonoid.{max u1 u2} Q _inst_2) _inst_6 _inst_3) [_inst_8 : Fact (Function.Injective.{succ (max u1 u2), succ (max u1 u2)} M N (coeFn.{succ (max u1 u2), succ (max u1 u2)} (LinearMap.{u1, u1, max u1 u2, max u1 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 N (AddCommGroup.toAddCommMonoid.{max u1 u2} M _inst_4) (AddCommGroup.toAddCommMonoid.{max u1 u2} N _inst_5) _inst_6 _inst_7) (fun (_x : LinearMap.{u1, u1, max u1 u2, max u1 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 N (AddCommGroup.toAddCommMonoid.{max u1 u2} M _inst_4) (AddCommGroup.toAddCommMonoid.{max u1 u2} N _inst_5) _inst_6 _inst_7) => M -> N) (LinearMap.hasCoeToFun.{u1, u1, max u1 u2, max u1 u2} R R M N (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{max u1 u2} M _inst_4) (AddCommGroup.toAddCommMonoid.{max u1 u2} N _inst_5) _inst_6 _inst_7 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1)))) i))], (Module.Baer.{u1, u2} R _inst_1 Q _inst_2 _inst_3) -> (forall {y : N}, (coeSort.{succ (max u1 u2), succ (succ (max u1 u2))} (Submodule.{u1, max u1 u2} R N (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{max u1 u2} N _inst_5) _inst_7) Type.{max u1 u2} (SetLike.hasCoeToSort.{max u1 u2, max u1 u2} (Submodule.{u1, max u1 u2} R N (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{max u1 u2} N _inst_5) _inst_7) N (Submodule.setLike.{u1, max u1 u2} R N (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{max u1 u2} N _inst_5) _inst_7)) (Sup.sup.{max u1 u2} (Submodule.{u1, max u1 u2} R N (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{max u1 u2} N _inst_5) _inst_7) (SemilatticeSup.toHasSup.{max u1 u2} (Submodule.{u1, max u1 u2} R N (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{max u1 u2} N _inst_5) _inst_7) (Lattice.toSemilatticeSup.{max u1 u2} (Submodule.{u1, max u1 u2} R N (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{max u1 u2} N _inst_5) _inst_7) (ConditionallyCompleteLattice.toLattice.{max u1 u2} (Submodule.{u1, max u1 u2} R N (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{max u1 u2} N _inst_5) _inst_7) (CompleteLattice.toConditionallyCompleteLattice.{max u1 u2} (Submodule.{u1, max u1 u2} R N (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{max u1 u2} N _inst_5) _inst_7) (Submodule.completeLattice.{u1, max u1 u2} R N (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{max u1 u2} N _inst_5) _inst_7))))) (LinearPMap.domain.{u1, max u1 u2, max u1 u2} R _inst_1 N _inst_5 _inst_7 Q _inst_2 _inst_3 (Module.Baer.ExtensionOf.toLinearPmap.{u1, u2} R _inst_1 Q _inst_2 _inst_3 M N _inst_4 _inst_5 _inst_6 _inst_7 i f (Module.Baer.extensionOfMax.{u1, u2} R _inst_1 Q _inst_2 _inst_3 M N _inst_4 _inst_5 _inst_6 _inst_7 i f _inst_8))) (Submodule.span.{u1, max u1 u2} R N (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{max u1 u2} N _inst_5) _inst_7 (Singleton.singleton.{max u1 u2, max u1 u2} N (Set.{max u1 u2} N) (Set.hasSingleton.{max u1 u2} N) y)))) -> Q)
 but is expected to have type
-  forall {R : Type.{u1}} [_inst_1 : Ring.{u1} R] {Q : TypeMax.{u2, u1}} [_inst_2 : AddCommGroup.{max u1 u2} Q] [_inst_3 : Module.{u1, max u1 u2} R Q (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{max u1 u2} Q _inst_2)] {M : Type.{max u1 u2}} {N : Type.{max u1 u2}} [_inst_4 : AddCommGroup.{max u1 u2} M] [_inst_5 : AddCommGroup.{max u1 u2} N] [_inst_6 : Module.{u1, max u1 u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{max u1 u2} M _inst_4)] [_inst_7 : Module.{u1, max u1 u2} R N (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{max u1 u2} N _inst_5)] (i : LinearMap.{u1, u1, max u1 u2, max u1 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 N (AddCommGroup.toAddCommMonoid.{max u1 u2} M _inst_4) (AddCommGroup.toAddCommMonoid.{max u1 u2} N _inst_5) _inst_6 _inst_7) (f : LinearMap.{u1, u1, max u1 u2, max u1 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 Q (AddCommGroup.toAddCommMonoid.{max u1 u2} M _inst_4) (AddCommGroup.toAddCommMonoid.{max u1 u2} Q _inst_2) _inst_6 _inst_3) [_inst_8 : Fact (Function.Injective.{max (succ u1) (succ u2), max (succ u1) (succ u2)} M N (FunLike.coe.{max (succ u1) (succ u2), max (succ u1) (succ u2), max (succ u1) (succ u2)} (LinearMap.{u1, u1, max u1 u2, max u1 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 N (AddCommGroup.toAddCommMonoid.{max u1 u2} M _inst_4) (AddCommGroup.toAddCommMonoid.{max u1 u2} N _inst_5) _inst_6 _inst_7) M (fun (_x : M) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : M) => N) _x) (LinearMap.instFunLikeLinearMap.{u1, u1, max u1 u2, max u1 u2} R R M N (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{max u1 u2} M _inst_4) (AddCommGroup.toAddCommMonoid.{max u1 u2} N _inst_5) _inst_6 _inst_7 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1)))) i))], (Module.Baer.{u1, u2} R _inst_1 Q _inst_2 _inst_3) -> (forall {y : N}, (Subtype.{succ (max u1 u2)} N (fun (x : N) => Membership.mem.{max u1 u2, max u1 u2} N (Submodule.{u1, max u1 u2} R N (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{max u1 u2} N _inst_5) _inst_7) (SetLike.instMembership.{max u1 u2, max u1 u2} (Submodule.{u1, max u1 u2} R N (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{max u1 u2} N _inst_5) _inst_7) N (Submodule.setLike.{u1, max u1 u2} R N (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{max u1 u2} N _inst_5) _inst_7)) x (Module.Baer.supExtensionOfMaxSingleton.{u1, u2} R _inst_1 Q _inst_2 _inst_3 M N _inst_4 _inst_5 _inst_6 _inst_7 i f _inst_8 y))) -> Q)
+  forall {R : Type.{u1}} [_inst_1 : Ring.{u1} R] {Q : TypeMax.{u2, u1}} [_inst_2 : AddCommGroup.{max u1 u2} Q] [_inst_3 : Module.{u1, max u1 u2} R Q (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{max u1 u2} Q _inst_2)] {M : Type.{max u1 u2}} {N : Type.{max u1 u2}} [_inst_4 : AddCommGroup.{max u1 u2} M] [_inst_5 : AddCommGroup.{max u1 u2} N] [_inst_6 : Module.{u1, max u1 u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{max u1 u2} M _inst_4)] [_inst_7 : Module.{u1, max u1 u2} R N (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{max u1 u2} N _inst_5)] (i : LinearMap.{u1, u1, max u1 u2, max u1 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 N (AddCommGroup.toAddCommMonoid.{max u1 u2} M _inst_4) (AddCommGroup.toAddCommMonoid.{max u1 u2} N _inst_5) _inst_6 _inst_7) (f : LinearMap.{u1, u1, max u1 u2, max u1 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 Q (AddCommGroup.toAddCommMonoid.{max u1 u2} M _inst_4) (AddCommGroup.toAddCommMonoid.{max u1 u2} Q _inst_2) _inst_6 _inst_3) [_inst_8 : Fact (Function.Injective.{max (succ u1) (succ u2), max (succ u1) (succ u2)} M N (FunLike.coe.{max (succ u1) (succ u2), max (succ u1) (succ u2), max (succ u1) (succ u2)} (LinearMap.{u1, u1, max u1 u2, max u1 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 N (AddCommGroup.toAddCommMonoid.{max u1 u2} M _inst_4) (AddCommGroup.toAddCommMonoid.{max u1 u2} N _inst_5) _inst_6 _inst_7) M (fun (_x : M) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : M) => N) _x) (LinearMap.instFunLikeLinearMap.{u1, u1, max u1 u2, max u1 u2} R R M N (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{max u1 u2} M _inst_4) (AddCommGroup.toAddCommMonoid.{max u1 u2} N _inst_5) _inst_6 _inst_7 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1)))) i))], (Module.Baer.{u1, u2} R _inst_1 Q _inst_2 _inst_3) -> (forall {y : N}, (Subtype.{succ (max u1 u2)} N (fun (x : N) => Membership.mem.{max u1 u2, max u1 u2} N (Submodule.{u1, max u1 u2} R N (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{max u1 u2} N _inst_5) _inst_7) (SetLike.instMembership.{max u1 u2, max u1 u2} (Submodule.{u1, max u1 u2} R N (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{max u1 u2} N _inst_5) _inst_7) N (Submodule.setLike.{u1, max u1 u2} R N (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{max u1 u2} N _inst_5) _inst_7)) x (Module.Baer.supExtensionOfMaxSingleton.{u1, u2} R _inst_1 Q _inst_2 _inst_3 M N _inst_4 _inst_5 _inst_6 _inst_7 i f _inst_8 y))) -> Q)
 Case conversion may be inaccurate. Consider using '#align module.Baer.extension_of_max_adjoin.extension_to_fun Module.Baer.ExtensionOfMaxAdjoin.extensionToFunₓ'. -/
 /-- We can finally define a linear map `M ⊔ ⟨y⟩ ⟶ Q` by `x + r • y ↦ f x + φ r`
 -/
@@ -463,7 +463,7 @@ def ExtensionOfMaxAdjoin.extensionToFun (h : Module.Baer R Q) {y : N} :
 lean 3 declaration is
   forall {R : Type.{u1}} [_inst_1 : Ring.{u1} R] {Q : Type.{max u1 u2}} [_inst_2 : AddCommGroup.{max u1 u2} Q] [_inst_3 : Module.{u1, max u1 u2} R Q (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{max u1 u2} Q _inst_2)] {M : Type.{max u1 u2}} {N : Type.{max u1 u2}} [_inst_4 : AddCommGroup.{max u1 u2} M] [_inst_5 : AddCommGroup.{max u1 u2} N] [_inst_6 : Module.{u1, max u1 u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{max u1 u2} M _inst_4)] [_inst_7 : Module.{u1, max u1 u2} R N (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{max u1 u2} N _inst_5)] (i : LinearMap.{u1, u1, max u1 u2, max u1 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 N (AddCommGroup.toAddCommMonoid.{max u1 u2} M _inst_4) (AddCommGroup.toAddCommMonoid.{max u1 u2} N _inst_5) _inst_6 _inst_7) (f : LinearMap.{u1, u1, max u1 u2, max u1 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 Q (AddCommGroup.toAddCommMonoid.{max u1 u2} M _inst_4) (AddCommGroup.toAddCommMonoid.{max u1 u2} Q _inst_2) _inst_6 _inst_3) [_inst_8 : Fact (Function.Injective.{succ (max u1 u2), succ (max u1 u2)} M N (coeFn.{succ (max u1 u2), succ (max u1 u2)} (LinearMap.{u1, u1, max u1 u2, max u1 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 N (AddCommGroup.toAddCommMonoid.{max u1 u2} M _inst_4) (AddCommGroup.toAddCommMonoid.{max u1 u2} N _inst_5) _inst_6 _inst_7) (fun (_x : LinearMap.{u1, u1, max u1 u2, max u1 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 N (AddCommGroup.toAddCommMonoid.{max u1 u2} M _inst_4) (AddCommGroup.toAddCommMonoid.{max u1 u2} N _inst_5) _inst_6 _inst_7) => M -> N) (LinearMap.hasCoeToFun.{u1, u1, max u1 u2, max u1 u2} R R M N (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{max u1 u2} M _inst_4) (AddCommGroup.toAddCommMonoid.{max u1 u2} N _inst_5) _inst_6 _inst_7 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1)))) i))] (h : Module.Baer.{u1, u2} R _inst_1 Q _inst_2 _inst_3) {y : N} (x : coeSort.{succ (max u1 u2), succ (succ (max u1 u2))} (Submodule.{u1, max u1 u2} R N (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{max u1 u2} N _inst_5) _inst_7) Type.{max u1 u2} (SetLike.hasCoeToSort.{max u1 u2, max u1 u2} (Submodule.{u1, max u1 u2} R N (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{max u1 u2} N _inst_5) _inst_7) N (Submodule.setLike.{u1, max u1 u2} R N (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{max u1 u2} N _inst_5) _inst_7)) (Sup.sup.{max u1 u2} (Submodule.{u1, max u1 u2} R N (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{max u1 u2} N _inst_5) _inst_7) (SemilatticeSup.toHasSup.{max u1 u2} (Submodule.{u1, max u1 u2} R N (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{max u1 u2} N _inst_5) _inst_7) (Lattice.toSemilatticeSup.{max u1 u2} (Submodule.{u1, max u1 u2} R N (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{max u1 u2} N _inst_5) _inst_7) (ConditionallyCompleteLattice.toLattice.{max u1 u2} (Submodule.{u1, max u1 u2} R N (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{max u1 u2} N _inst_5) _inst_7) (CompleteLattice.toConditionallyCompleteLattice.{max u1 u2} (Submodule.{u1, max u1 u2} R N (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{max u1 u2} N _inst_5) _inst_7) (Submodule.completeLattice.{u1, max u1 u2} R N (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{max u1 u2} N _inst_5) _inst_7))))) 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 but is expected to have type
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_inst_1 Q _inst_2 _inst_3 M N _inst_4 _inst_5 _inst_6 _inst_7 i f _inst_8 h y) r)))
+  forall {R : Type.{u1}} [_inst_1 : Ring.{u1} R] {Q : TypeMax.{u2, u1}} [_inst_2 : AddCommGroup.{max u1 u2} Q] [_inst_3 : Module.{u1, max u1 u2} R Q (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{max u1 u2} Q _inst_2)] {M : Type.{max u1 u2}} {N : Type.{max u1 u2}} [_inst_4 : AddCommGroup.{max u1 u2} M] [_inst_5 : AddCommGroup.{max u1 u2} N] [_inst_6 : Module.{u1, max u1 u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{max u1 u2} M _inst_4)] [_inst_7 : Module.{u1, max u1 u2} R N (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{max u1 u2} N _inst_5)] (i : LinearMap.{u1, u1, max u1 u2, max u1 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 N (AddCommGroup.toAddCommMonoid.{max u1 u2} M _inst_4) (AddCommGroup.toAddCommMonoid.{max u1 u2} N _inst_5) _inst_6 _inst_7) (f : LinearMap.{u1, u1, max u1 u2, max u1 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 Q (AddCommGroup.toAddCommMonoid.{max u1 u2} M _inst_4) (AddCommGroup.toAddCommMonoid.{max u1 u2} Q _inst_2) _inst_6 _inst_3) [_inst_8 : Fact (Function.Injective.{max (succ u1) (succ u2), max (succ u1) (succ u2)} M N (FunLike.coe.{max (succ u1) (succ u2), max (succ u1) (succ u2), max (succ u1) (succ u2)} (LinearMap.{u1, u1, max u1 u2, max u1 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 N (AddCommGroup.toAddCommMonoid.{max u1 u2} M _inst_4) (AddCommGroup.toAddCommMonoid.{max u1 u2} N _inst_5) _inst_6 _inst_7) M (fun (_x : M) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : M) => N) _x) (LinearMap.instFunLikeLinearMap.{u1, u1, max u1 u2, max u1 u2} R R M N (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{max u1 u2} M _inst_4) (AddCommGroup.toAddCommMonoid.{max u1 u2} N _inst_5) _inst_6 _inst_7 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1)))) i))] (h : Module.Baer.{u1, u2} R _inst_1 Q _inst_2 _inst_3) {y : N} (x : Subtype.{succ (max u1 u2)} N (fun (x : N) => Membership.mem.{max u1 u2, max u1 u2} N (Submodule.{u1, max u1 u2} R N (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{max u1 u2} N _inst_5) _inst_7) (SetLike.instMembership.{max u1 u2, max u1 u2} (Submodule.{u1, max u1 u2} R N (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{max u1 u2} N _inst_5) _inst_7) N (Submodule.setLike.{u1, max u1 u2} R N (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{max u1 u2} N _inst_5) _inst_7)) x (Module.Baer.supExtensionOfMaxSingleton.{u1, u2} R _inst_1 Q _inst_2 _inst_3 M N _inst_4 _inst_5 _inst_6 _inst_7 i f _inst_8 y))) (a : Subtype.{succ (max u1 u2)} N (fun (x : N) => Membership.mem.{max u1 u2, max u1 u2} N (Submodule.{u1, max u1 u2} R N (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{max u1 u2} N _inst_5) _inst_7) (SetLike.instMembership.{max u1 u2, max u1 u2} (Submodule.{u1, max u1 u2} R N (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{max u1 u2} N _inst_5) _inst_7) N (Submodule.setLike.{u1, max u1 u2} R N (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{max u1 u2} N _inst_5) _inst_7)) x (LinearPMap.domain.{u1, max u1 u2, max u1 u2} R _inst_1 N _inst_5 _inst_7 Q _inst_2 _inst_3 (Module.Baer.ExtensionOf.toLinearPMap.{u1, u2} R _inst_1 Q _inst_2 _inst_3 M N _inst_4 _inst_5 _inst_6 _inst_7 i f (Module.Baer.extensionOfMax.{u1, u2} R _inst_1 Q _inst_2 _inst_3 M N _inst_4 _inst_5 _inst_6 _inst_7 i f _inst_8))))) (r : R), (Eq.{max (succ u1) (succ u2)} N (Subtype.val.{succ (max u1 u2)} N (fun (x : N) => Membership.mem.{max u1 u2, max u1 u2} N (Set.{max u1 u2} N) (Set.instMembershipSet.{max u1 u2} N) x (SetLike.coe.{max u1 u2, max u1 u2} (Submodule.{u1, max u1 u2} R N (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{max u1 u2} N _inst_5) _inst_7) N (Submodule.setLike.{u1, max u1 u2} R N (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{max u1 u2} N _inst_5) _inst_7) (Module.Baer.supExtensionOfMaxSingleton.{u1, u2} R _inst_1 Q _inst_2 _inst_3 M N _inst_4 _inst_5 _inst_6 _inst_7 i f _inst_8 y))) x) (HAdd.hAdd.{max u1 u2, max u1 u2, max u1 u2} N N N (instHAdd.{max u1 u2} N (AddZeroClass.toAdd.{max u1 u2} N (AddMonoid.toAddZeroClass.{max u1 u2} N (SubNegMonoid.toAddMonoid.{max u1 u2} N (AddGroup.toSubNegMonoid.{max u1 u2} N (AddCommGroup.toAddGroup.{max u1 u2} N _inst_5)))))) (Subtype.val.{succ (max u1 u2)} N (fun (x : N) => Membership.mem.{max u1 u2, max u1 u2} N (Set.{max u1 u2} N) (Set.instMembershipSet.{max u1 u2} N) x (SetLike.coe.{max u1 u2, max u1 u2} (Submodule.{u1, max u1 u2} R N (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{max u1 u2} N _inst_5) _inst_7) N (Submodule.setLike.{u1, max u1 u2} R N (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{max u1 u2} N _inst_5) _inst_7) (LinearPMap.domain.{u1, max u1 u2, max u1 u2} R _inst_1 N _inst_5 _inst_7 Q _inst_2 _inst_3 (Module.Baer.ExtensionOf.toLinearPMap.{u1, u2} R _inst_1 Q _inst_2 _inst_3 M N _inst_4 _inst_5 _inst_6 _inst_7 i f (Module.Baer.extensionOfMax.{u1, u2} R _inst_1 Q _inst_2 _inst_3 M N _inst_4 _inst_5 _inst_6 _inst_7 i f _inst_8))))) a) (HSMul.hSMul.{u1, max u1 u2, max u1 u2} R N N (instHSMul.{u1, max u1 u2} R N (SMulZeroClass.toSMul.{u1, max u1 u2} R N (NegZeroClass.toZero.{max u1 u2} N (SubNegZeroMonoid.toNegZeroClass.{max u1 u2} N (SubtractionMonoid.toSubNegZeroMonoid.{max u1 u2} N (SubtractionCommMonoid.toSubtractionMonoid.{max u1 u2} N (AddCommGroup.toDivisionAddCommMonoid.{max u1 u2} N _inst_5))))) (SMulWithZero.toSMulZeroClass.{u1, max u1 u2} R N (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (NegZeroClass.toZero.{max u1 u2} N (SubNegZeroMonoid.toNegZeroClass.{max u1 u2} N (SubtractionMonoid.toSubNegZeroMonoid.{max u1 u2} N (SubtractionCommMonoid.toSubtractionMonoid.{max u1 u2} N (AddCommGroup.toDivisionAddCommMonoid.{max u1 u2} N _inst_5))))) (MulActionWithZero.toSMulWithZero.{u1, max u1 u2} R N (Semiring.toMonoidWithZero.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (NegZeroClass.toZero.{max u1 u2} N (SubNegZeroMonoid.toNegZeroClass.{max u1 u2} N (SubtractionMonoid.toSubNegZeroMonoid.{max u1 u2} N (SubtractionCommMonoid.toSubtractionMonoid.{max u1 u2} N (AddCommGroup.toDivisionAddCommMonoid.{max u1 u2} N _inst_5))))) (Module.toMulActionWithZero.{u1, max u1 u2} R N (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{max u1 u2} N _inst_5) _inst_7))))) r y))) -> (Eq.{max (succ u1) (succ u2)} Q (Module.Baer.ExtensionOfMaxAdjoin.extensionToFun.{u1, u2} R _inst_1 Q _inst_2 _inst_3 M N _inst_4 _inst_5 _inst_6 _inst_7 i f _inst_8 h y x) (HAdd.hAdd.{max u1 u2, max u1 u2, max u1 u2} Q ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : R) => Q) r) Q (instHAdd.{max u1 u2} Q (AddZeroClass.toAdd.{max u1 u2} Q (AddMonoid.toAddZeroClass.{max u1 u2} Q (SubNegMonoid.toAddMonoid.{max u1 u2} Q (AddGroup.toSubNegMonoid.{max u1 u2} Q (AddCommGroup.toAddGroup.{max u1 u2} Q _inst_2)))))) (LinearPMap.toFun'.{u1, max u1 u2, max u1 u2} R _inst_1 N _inst_5 _inst_7 Q _inst_2 _inst_3 (Module.Baer.ExtensionOf.toLinearPMap.{u1, u2} R _inst_1 Q _inst_2 _inst_3 M N _inst_4 _inst_5 _inst_6 _inst_7 i f (Module.Baer.extensionOfMax.{u1, u2} R _inst_1 Q _inst_2 _inst_3 M N _inst_4 _inst_5 _inst_6 _inst_7 i f _inst_8)) a) (FunLike.coe.{max (succ u1) (succ u2), succ u1, max (succ u1) (succ u2)} (LinearMap.{u1, u1, u1, max u1 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))) R Q (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R _inst_1)))) (AddCommGroup.toAddCommMonoid.{max u1 u2} Q _inst_2) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R _inst_1)) _inst_3) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : R) => Q) _x) (LinearMap.instFunLikeLinearMap.{u1, u1, u1, max u1 u2} R R R Q (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R _inst_1)))) (AddCommGroup.toAddCommMonoid.{max u1 u2} Q _inst_2) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R _inst_1)) _inst_3 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1)))) (Module.Baer.ExtensionOfMaxAdjoin.extendIdealTo.{u1, u2} R _inst_1 Q _inst_2 _inst_3 M N _inst_4 _inst_5 _inst_6 _inst_7 i f _inst_8 h y) r)))
 Case conversion may be inaccurate. Consider using '#align module.Baer.extension_of_max_adjoin.extension_to_fun_wd Module.Baer.ExtensionOfMaxAdjoin.extensionToFun_wdₓ'. -/
 theorem ExtensionOfMaxAdjoin.extensionToFun_wd (h : Module.Baer R Q) {y : N}
     (x : (extensionOfMax i f).domain ⊔ Submodule.span R {y}) (a : (extensionOfMax i f).domain)
@@ -493,7 +493,7 @@ theorem ExtensionOfMaxAdjoin.extensionToFun_wd (h : Module.Baer R Q) {y : N}
 lean 3 declaration is
   forall {R : Type.{u1}} [_inst_1 : Ring.{u1} R] {Q : Type.{max u1 u2}} [_inst_2 : AddCommGroup.{max u1 u2} Q] [_inst_3 : Module.{u1, max u1 u2} R Q (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{max u1 u2} Q _inst_2)] {M : Type.{max u1 u2}} {N : Type.{max u1 u2}} [_inst_4 : AddCommGroup.{max u1 u2} M] [_inst_5 : AddCommGroup.{max u1 u2} N] [_inst_6 : Module.{u1, max u1 u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{max u1 u2} M _inst_4)] [_inst_7 : Module.{u1, max u1 u2} R N (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{max u1 u2} N _inst_5)] (i : LinearMap.{u1, u1, max u1 u2, max u1 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 N (AddCommGroup.toAddCommMonoid.{max u1 u2} M _inst_4) (AddCommGroup.toAddCommMonoid.{max u1 u2} N _inst_5) _inst_6 _inst_7) (f : LinearMap.{u1, u1, max u1 u2, max u1 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 Q (AddCommGroup.toAddCommMonoid.{max u1 u2} M _inst_4) (AddCommGroup.toAddCommMonoid.{max u1 u2} Q _inst_2) _inst_6 _inst_3) [_inst_8 : Fact (Function.Injective.{succ (max u1 u2), succ (max u1 u2)} M N (coeFn.{succ (max u1 u2), succ (max u1 u2)} (LinearMap.{u1, u1, max u1 u2, max u1 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 N (AddCommGroup.toAddCommMonoid.{max u1 u2} M _inst_4) (AddCommGroup.toAddCommMonoid.{max u1 u2} N _inst_5) _inst_6 _inst_7) (fun (_x : LinearMap.{u1, u1, max u1 u2, max u1 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 N (AddCommGroup.toAddCommMonoid.{max u1 u2} M _inst_4) (AddCommGroup.toAddCommMonoid.{max u1 u2} N _inst_5) _inst_6 _inst_7) => M -> N) (LinearMap.hasCoeToFun.{u1, u1, max u1 u2, max u1 u2} R R M N (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{max u1 u2} M _inst_4) (AddCommGroup.toAddCommMonoid.{max u1 u2} N _inst_5) _inst_6 _inst_7 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1)))) i))], (Module.Baer.{u1, u2} R _inst_1 Q _inst_2 _inst_3) -> N -> (Module.Baer.ExtensionOf.{u1, u2} R _inst_1 Q _inst_2 _inst_3 M N _inst_4 _inst_5 _inst_6 _inst_7 i f)
 but is expected to have type
-  forall {R : Type.{u1}} [_inst_1 : Ring.{u1} R] {Q : TypeMax.{u2, u1}} [_inst_2 : AddCommGroup.{max u1 u2} Q] [_inst_3 : Module.{u1, max u1 u2} R Q (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{max u1 u2} Q _inst_2)] {M : Type.{max u1 u2}} {N : Type.{max u1 u2}} [_inst_4 : AddCommGroup.{max u1 u2} M] [_inst_5 : AddCommGroup.{max u1 u2} N] [_inst_6 : Module.{u1, max u1 u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{max u1 u2} M _inst_4)] [_inst_7 : Module.{u1, max u1 u2} R N (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{max u1 u2} N _inst_5)] (i : LinearMap.{u1, u1, max u1 u2, max u1 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 N (AddCommGroup.toAddCommMonoid.{max u1 u2} M _inst_4) (AddCommGroup.toAddCommMonoid.{max u1 u2} N _inst_5) _inst_6 _inst_7) (f : LinearMap.{u1, u1, max u1 u2, max u1 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 Q (AddCommGroup.toAddCommMonoid.{max u1 u2} M _inst_4) (AddCommGroup.toAddCommMonoid.{max u1 u2} Q _inst_2) _inst_6 _inst_3) [_inst_8 : Fact (Function.Injective.{max (succ u1) (succ u2), max (succ u1) (succ u2)} M N (FunLike.coe.{max (succ u1) (succ u2), max (succ u1) (succ u2), max (succ u1) (succ u2)} (LinearMap.{u1, u1, max u1 u2, max u1 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 N (AddCommGroup.toAddCommMonoid.{max u1 u2} M _inst_4) (AddCommGroup.toAddCommMonoid.{max u1 u2} N _inst_5) _inst_6 _inst_7) M (fun (_x : M) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : M) => N) _x) (LinearMap.instFunLikeLinearMap.{u1, u1, max u1 u2, max u1 u2} R R M N (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{max u1 u2} M _inst_4) (AddCommGroup.toAddCommMonoid.{max u1 u2} N _inst_5) _inst_6 _inst_7 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1)))) i))], (Module.Baer.{u1, u2} R _inst_1 Q _inst_2 _inst_3) -> N -> (Module.Baer.ExtensionOf.{u1, u2} R _inst_1 Q _inst_2 _inst_3 M N _inst_4 _inst_5 _inst_6 _inst_7 i f)
+  forall {R : Type.{u1}} [_inst_1 : Ring.{u1} R] {Q : TypeMax.{u2, u1}} [_inst_2 : AddCommGroup.{max u1 u2} Q] [_inst_3 : Module.{u1, max u1 u2} R Q (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{max u1 u2} Q _inst_2)] {M : Type.{max u1 u2}} {N : Type.{max u1 u2}} [_inst_4 : AddCommGroup.{max u1 u2} M] [_inst_5 : AddCommGroup.{max u1 u2} N] [_inst_6 : Module.{u1, max u1 u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{max u1 u2} M _inst_4)] [_inst_7 : Module.{u1, max u1 u2} R N (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{max u1 u2} N _inst_5)] (i : LinearMap.{u1, u1, max u1 u2, max u1 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 N (AddCommGroup.toAddCommMonoid.{max u1 u2} M _inst_4) (AddCommGroup.toAddCommMonoid.{max u1 u2} N _inst_5) _inst_6 _inst_7) (f : LinearMap.{u1, u1, max u1 u2, max u1 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 Q (AddCommGroup.toAddCommMonoid.{max u1 u2} M _inst_4) (AddCommGroup.toAddCommMonoid.{max u1 u2} Q _inst_2) _inst_6 _inst_3) [_inst_8 : Fact (Function.Injective.{max (succ u1) (succ u2), max (succ u1) (succ u2)} M N (FunLike.coe.{max (succ u1) (succ u2), max (succ u1) (succ u2), max (succ u1) (succ u2)} (LinearMap.{u1, u1, max u1 u2, max u1 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 N (AddCommGroup.toAddCommMonoid.{max u1 u2} M _inst_4) (AddCommGroup.toAddCommMonoid.{max u1 u2} N _inst_5) _inst_6 _inst_7) M (fun (_x : M) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : M) => N) _x) (LinearMap.instFunLikeLinearMap.{u1, u1, max u1 u2, max u1 u2} R R M N (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{max u1 u2} M _inst_4) (AddCommGroup.toAddCommMonoid.{max u1 u2} N _inst_5) _inst_6 _inst_7 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1)))) i))], (Module.Baer.{u1, u2} R _inst_1 Q _inst_2 _inst_3) -> N -> (Module.Baer.ExtensionOf.{u1, u2} R _inst_1 Q _inst_2 _inst_3 M N _inst_4 _inst_5 _inst_6 _inst_7 i f)
 Case conversion may be inaccurate. Consider using '#align module.Baer.extension_of_max_adjoin Module.Baer.extensionOfMaxAdjoinₓ'. -/
 /-- The linear map `M ⊔ ⟨y⟩ ⟶ Q` by `x + r • y ↦ f x + φ r` is an extension of `f`-/
 def extensionOfMaxAdjoin (h : Module.Baer R Q) (y : N) : ExtensionOf i f
@@ -537,7 +537,7 @@ def extensionOfMaxAdjoin (h : Module.Baer R Q) (y : N) : ExtensionOf i f
 lean 3 declaration is
   forall {R : Type.{u1}} [_inst_1 : Ring.{u1} R] {Q : Type.{max u1 u2}} [_inst_2 : AddCommGroup.{max u1 u2} Q] [_inst_3 : Module.{u1, max u1 u2} R Q (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{max u1 u2} Q _inst_2)] {M : Type.{max u1 u2}} {N : Type.{max u1 u2}} [_inst_4 : AddCommGroup.{max u1 u2} M] [_inst_5 : AddCommGroup.{max u1 u2} N] [_inst_6 : Module.{u1, max u1 u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{max u1 u2} M _inst_4)] [_inst_7 : Module.{u1, max u1 u2} R N (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{max u1 u2} N _inst_5)] (i : LinearMap.{u1, u1, max u1 u2, max u1 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 N (AddCommGroup.toAddCommMonoid.{max u1 u2} M _inst_4) (AddCommGroup.toAddCommMonoid.{max u1 u2} N _inst_5) _inst_6 _inst_7) (f : LinearMap.{u1, u1, max u1 u2, max u1 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 Q (AddCommGroup.toAddCommMonoid.{max u1 u2} M _inst_4) (AddCommGroup.toAddCommMonoid.{max u1 u2} Q _inst_2) _inst_6 _inst_3) [_inst_8 : Fact (Function.Injective.{succ (max u1 u2), succ (max u1 u2)} M N (coeFn.{succ (max u1 u2), succ (max u1 u2)} (LinearMap.{u1, u1, max u1 u2, max u1 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 N (AddCommGroup.toAddCommMonoid.{max u1 u2} M _inst_4) (AddCommGroup.toAddCommMonoid.{max u1 u2} N _inst_5) _inst_6 _inst_7) (fun (_x : LinearMap.{u1, u1, max u1 u2, max u1 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 N (AddCommGroup.toAddCommMonoid.{max u1 u2} M _inst_4) (AddCommGroup.toAddCommMonoid.{max u1 u2} N _inst_5) _inst_6 _inst_7) => M -> N) (LinearMap.hasCoeToFun.{u1, u1, max u1 u2, max u1 u2} R R M N (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{max u1 u2} M _inst_4) (AddCommGroup.toAddCommMonoid.{max u1 u2} N _inst_5) _inst_6 _inst_7 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1)))) i))] (h : Module.Baer.{u1, u2} R _inst_1 Q _inst_2 _inst_3) {y : N}, LE.le.{max u1 u2} (Module.Baer.ExtensionOf.{u1, u2} R _inst_1 Q _inst_2 _inst_3 M N _inst_4 _inst_5 _inst_6 _inst_7 i f) (Preorder.toHasLe.{max u1 u2} (Module.Baer.ExtensionOf.{u1, u2} R _inst_1 Q _inst_2 _inst_3 M N _inst_4 _inst_5 _inst_6 _inst_7 i f) (PartialOrder.toPreorder.{max u1 u2} (Module.Baer.ExtensionOf.{u1, u2} R _inst_1 Q _inst_2 _inst_3 M N _inst_4 _inst_5 _inst_6 _inst_7 i f) (SemilatticeInf.toPartialOrder.{max u1 u2} (Module.Baer.ExtensionOf.{u1, u2} R _inst_1 Q _inst_2 _inst_3 M N _inst_4 _inst_5 _inst_6 _inst_7 i f) (Module.Baer.ExtensionOf.semilatticeInf.{u1, u2} R _inst_1 Q _inst_2 _inst_3 M N _inst_4 _inst_5 _inst_6 _inst_7 i f)))) (Module.Baer.extensionOfMax.{u1, u2} R _inst_1 Q _inst_2 _inst_3 M N _inst_4 _inst_5 _inst_6 _inst_7 i f _inst_8) (Module.Baer.extensionOfMaxAdjoin.{u1, u2} R _inst_1 Q _inst_2 _inst_3 M N _inst_4 _inst_5 _inst_6 _inst_7 i f _inst_8 h y)
 but is expected to have type
-  forall {R : Type.{u1}} [_inst_1 : Ring.{u1} R] {Q : TypeMax.{u2, u1}} [_inst_2 : AddCommGroup.{max u1 u2} Q] [_inst_3 : Module.{u1, max u1 u2} R Q (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{max u1 u2} Q _inst_2)] {M : Type.{max u1 u2}} {N : Type.{max u1 u2}} [_inst_4 : AddCommGroup.{max u1 u2} M] [_inst_5 : AddCommGroup.{max u1 u2} N] [_inst_6 : Module.{u1, max u1 u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{max u1 u2} M _inst_4)] [_inst_7 : Module.{u1, max u1 u2} R N (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{max u1 u2} N _inst_5)] (i : LinearMap.{u1, u1, max u1 u2, max u1 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 N (AddCommGroup.toAddCommMonoid.{max u1 u2} M _inst_4) (AddCommGroup.toAddCommMonoid.{max u1 u2} N _inst_5) _inst_6 _inst_7) (f : LinearMap.{u1, u1, max u1 u2, max u1 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 Q (AddCommGroup.toAddCommMonoid.{max u1 u2} M _inst_4) (AddCommGroup.toAddCommMonoid.{max u1 u2} Q _inst_2) _inst_6 _inst_3) [_inst_8 : Fact (Function.Injective.{max (succ u1) (succ u2), max (succ u1) (succ u2)} M N (FunLike.coe.{max (succ u1) (succ u2), max (succ u1) (succ u2), max (succ u1) (succ u2)} (LinearMap.{u1, u1, max u1 u2, max u1 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 N (AddCommGroup.toAddCommMonoid.{max u1 u2} M _inst_4) (AddCommGroup.toAddCommMonoid.{max u1 u2} N _inst_5) _inst_6 _inst_7) M (fun (_x : M) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : M) => N) _x) (LinearMap.instFunLikeLinearMap.{u1, u1, max u1 u2, max u1 u2} R R M N (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{max u1 u2} M _inst_4) (AddCommGroup.toAddCommMonoid.{max u1 u2} N _inst_5) _inst_6 _inst_7 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1)))) i))] (h : Module.Baer.{u1, u2} R _inst_1 Q _inst_2 _inst_3) {y : N}, LE.le.{max u1 u2} (Module.Baer.ExtensionOf.{u1, u2} R _inst_1 Q _inst_2 _inst_3 M N _inst_4 _inst_5 _inst_6 _inst_7 i f) (Preorder.toLE.{max u1 u2} (Module.Baer.ExtensionOf.{u1, u2} R _inst_1 Q _inst_2 _inst_3 M N _inst_4 _inst_5 _inst_6 _inst_7 i f) (PartialOrder.toPreorder.{max u1 u2} (Module.Baer.ExtensionOf.{u1, u2} R _inst_1 Q _inst_2 _inst_3 M N _inst_4 _inst_5 _inst_6 _inst_7 i f) (SemilatticeInf.toPartialOrder.{max u1 u2} (Module.Baer.ExtensionOf.{u1, u2} R _inst_1 Q _inst_2 _inst_3 M N _inst_4 _inst_5 _inst_6 _inst_7 i f) (Module.Baer.instSemilatticeInfExtensionOf.{u1, u2} R _inst_1 Q _inst_2 _inst_3 M N _inst_4 _inst_5 _inst_6 _inst_7 i f)))) (Module.Baer.extensionOfMax.{u1, u2} R _inst_1 Q _inst_2 _inst_3 M N _inst_4 _inst_5 _inst_6 _inst_7 i f _inst_8) (Module.Baer.extensionOfMaxAdjoin.{u1, u2} R _inst_1 Q _inst_2 _inst_3 M N _inst_4 _inst_5 _inst_6 _inst_7 i f _inst_8 h y)
+  forall {R : Type.{u1}} [_inst_1 : Ring.{u1} R] {Q : TypeMax.{u2, u1}} [_inst_2 : AddCommGroup.{max u1 u2} Q] [_inst_3 : Module.{u1, max u1 u2} R Q (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{max u1 u2} Q _inst_2)] {M : Type.{max u1 u2}} {N : Type.{max u1 u2}} [_inst_4 : AddCommGroup.{max u1 u2} M] [_inst_5 : AddCommGroup.{max u1 u2} N] [_inst_6 : Module.{u1, max u1 u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{max u1 u2} M _inst_4)] [_inst_7 : Module.{u1, max u1 u2} R N (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{max u1 u2} N _inst_5)] (i : LinearMap.{u1, u1, max u1 u2, max u1 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 N (AddCommGroup.toAddCommMonoid.{max u1 u2} M _inst_4) (AddCommGroup.toAddCommMonoid.{max u1 u2} N _inst_5) _inst_6 _inst_7) (f : LinearMap.{u1, u1, max u1 u2, max u1 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 Q (AddCommGroup.toAddCommMonoid.{max u1 u2} M _inst_4) (AddCommGroup.toAddCommMonoid.{max u1 u2} Q _inst_2) _inst_6 _inst_3) [_inst_8 : Fact (Function.Injective.{max (succ u1) (succ u2), max (succ u1) (succ u2)} M N (FunLike.coe.{max (succ u1) (succ u2), max (succ u1) (succ u2), max (succ u1) (succ u2)} (LinearMap.{u1, u1, max u1 u2, max u1 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 N (AddCommGroup.toAddCommMonoid.{max u1 u2} M _inst_4) (AddCommGroup.toAddCommMonoid.{max u1 u2} N _inst_5) _inst_6 _inst_7) M (fun (_x : M) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : M) => N) _x) (LinearMap.instFunLikeLinearMap.{u1, u1, max u1 u2, max u1 u2} R R M N (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{max u1 u2} M _inst_4) (AddCommGroup.toAddCommMonoid.{max u1 u2} N _inst_5) _inst_6 _inst_7 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1)))) i))] (h : Module.Baer.{u1, u2} R _inst_1 Q _inst_2 _inst_3) {y : N}, LE.le.{max u1 u2} (Module.Baer.ExtensionOf.{u1, u2} R _inst_1 Q _inst_2 _inst_3 M N _inst_4 _inst_5 _inst_6 _inst_7 i f) (Preorder.toLE.{max u1 u2} (Module.Baer.ExtensionOf.{u1, u2} R _inst_1 Q _inst_2 _inst_3 M N _inst_4 _inst_5 _inst_6 _inst_7 i f) (PartialOrder.toPreorder.{max u1 u2} (Module.Baer.ExtensionOf.{u1, u2} R _inst_1 Q _inst_2 _inst_3 M N _inst_4 _inst_5 _inst_6 _inst_7 i f) (SemilatticeInf.toPartialOrder.{max u1 u2} (Module.Baer.ExtensionOf.{u1, u2} R _inst_1 Q _inst_2 _inst_3 M N _inst_4 _inst_5 _inst_6 _inst_7 i f) (Module.Baer.instSemilatticeInfExtensionOf.{u1, u2} R _inst_1 Q _inst_2 _inst_3 M N _inst_4 _inst_5 _inst_6 _inst_7 i f)))) (Module.Baer.extensionOfMax.{u1, u2} R _inst_1 Q _inst_2 _inst_3 M N _inst_4 _inst_5 _inst_6 _inst_7 i f _inst_8) (Module.Baer.extensionOfMaxAdjoin.{u1, u2} R _inst_1 Q _inst_2 _inst_3 M N _inst_4 _inst_5 _inst_6 _inst_7 i f _inst_8 h y)
 Case conversion may be inaccurate. Consider using '#align module.Baer.extension_of_max_le Module.Baer.extensionOfMax_leₓ'. -/
 theorem extensionOfMax_le (h : Module.Baer R Q) {y : N} :
     extensionOfMax i f ≤ extensionOfMaxAdjoin i f h y :=
@@ -552,7 +552,7 @@ theorem extensionOfMax_le (h : Module.Baer R Q) {y : N} :
 lean 3 declaration is
   forall {R : Type.{u1}} [_inst_1 : Ring.{u1} R] {Q : Type.{max u1 u2}} [_inst_2 : AddCommGroup.{max u1 u2} Q] [_inst_3 : Module.{u1, max u1 u2} R Q (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{max u1 u2} Q _inst_2)] {M : Type.{max u1 u2}} {N : Type.{max u1 u2}} [_inst_4 : AddCommGroup.{max u1 u2} M] [_inst_5 : AddCommGroup.{max u1 u2} N] [_inst_6 : Module.{u1, max u1 u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{max u1 u2} M _inst_4)] [_inst_7 : Module.{u1, max u1 u2} R N (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{max u1 u2} N _inst_5)] (i : LinearMap.{u1, u1, max u1 u2, max u1 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 N (AddCommGroup.toAddCommMonoid.{max u1 u2} M _inst_4) (AddCommGroup.toAddCommMonoid.{max u1 u2} N _inst_5) _inst_6 _inst_7) (f : LinearMap.{u1, u1, max u1 u2, max u1 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 Q (AddCommGroup.toAddCommMonoid.{max u1 u2} M _inst_4) (AddCommGroup.toAddCommMonoid.{max u1 u2} Q _inst_2) _inst_6 _inst_3) [_inst_8 : Fact (Function.Injective.{succ (max u1 u2), succ (max u1 u2)} M N (coeFn.{succ (max u1 u2), succ (max u1 u2)} (LinearMap.{u1, u1, max u1 u2, max u1 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 N (AddCommGroup.toAddCommMonoid.{max u1 u2} M _inst_4) (AddCommGroup.toAddCommMonoid.{max u1 u2} N _inst_5) _inst_6 _inst_7) (fun (_x : LinearMap.{u1, u1, max u1 u2, max u1 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 N (AddCommGroup.toAddCommMonoid.{max u1 u2} M _inst_4) (AddCommGroup.toAddCommMonoid.{max u1 u2} N _inst_5) _inst_6 _inst_7) => M -> N) (LinearMap.hasCoeToFun.{u1, u1, max u1 u2, max u1 u2} R R M N (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{max u1 u2} M _inst_4) (AddCommGroup.toAddCommMonoid.{max u1 u2} N _inst_5) _inst_6 _inst_7 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1)))) i))], (Module.Baer.{u1, u2} R _inst_1 Q _inst_2 _inst_3) -> (Eq.{succ (max u1 u2)} (Submodule.{u1, max u1 u2} R N (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{max u1 u2} N _inst_5) _inst_7) (LinearPMap.domain.{u1, max u1 u2, max u1 u2} R _inst_1 N _inst_5 _inst_7 Q _inst_2 _inst_3 (Module.Baer.ExtensionOf.toLinearPmap.{u1, u2} R _inst_1 Q _inst_2 _inst_3 M N _inst_4 _inst_5 _inst_6 _inst_7 i f (Module.Baer.extensionOfMax.{u1, u2} R _inst_1 Q _inst_2 _inst_3 M N _inst_4 _inst_5 _inst_6 _inst_7 i f _inst_8))) (Top.top.{max u1 u2} (Submodule.{u1, max u1 u2} R N (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{max u1 u2} N _inst_5) _inst_7) (Submodule.hasTop.{u1, max u1 u2} R N (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{max u1 u2} N _inst_5) _inst_7)))
 but is expected to have type
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+  forall {R : Type.{u1}} [_inst_1 : Ring.{u1} R] {Q : TypeMax.{u2, u1}} [_inst_2 : AddCommGroup.{max u1 u2} Q] [_inst_3 : Module.{u1, max u1 u2} R Q (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{max u1 u2} Q _inst_2)] {M : Type.{max u1 u2}} {N : Type.{max u1 u2}} [_inst_4 : AddCommGroup.{max u1 u2} M] [_inst_5 : AddCommGroup.{max u1 u2} N] [_inst_6 : Module.{u1, max u1 u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{max u1 u2} M _inst_4)] [_inst_7 : Module.{u1, max u1 u2} R N (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{max u1 u2} N _inst_5)] (i : LinearMap.{u1, u1, max u1 u2, max u1 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 N (AddCommGroup.toAddCommMonoid.{max u1 u2} M _inst_4) (AddCommGroup.toAddCommMonoid.{max u1 u2} N _inst_5) _inst_6 _inst_7) (f : LinearMap.{u1, u1, max u1 u2, max u1 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 Q (AddCommGroup.toAddCommMonoid.{max u1 u2} M _inst_4) (AddCommGroup.toAddCommMonoid.{max u1 u2} Q _inst_2) _inst_6 _inst_3) [_inst_8 : Fact (Function.Injective.{max (succ u1) (succ u2), max (succ u1) (succ u2)} M N (FunLike.coe.{max (succ u1) (succ u2), max (succ u1) (succ u2), max (succ u1) (succ u2)} (LinearMap.{u1, u1, max u1 u2, max u1 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 N (AddCommGroup.toAddCommMonoid.{max u1 u2} M _inst_4) (AddCommGroup.toAddCommMonoid.{max u1 u2} N _inst_5) _inst_6 _inst_7) M (fun (_x : M) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : M) => N) _x) (LinearMap.instFunLikeLinearMap.{u1, u1, max u1 u2, max u1 u2} R R M N (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{max u1 u2} M _inst_4) (AddCommGroup.toAddCommMonoid.{max u1 u2} N _inst_5) _inst_6 _inst_7 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1)))) i))], (Module.Baer.{u1, u2} R _inst_1 Q _inst_2 _inst_3) -> (Eq.{max (succ u1) (succ u2)} (Submodule.{u1, max u1 u2} R N (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{max u1 u2} N _inst_5) _inst_7) (LinearPMap.domain.{u1, max u1 u2, max u1 u2} R _inst_1 N _inst_5 _inst_7 Q _inst_2 _inst_3 (Module.Baer.ExtensionOf.toLinearPMap.{u1, u2} R _inst_1 Q _inst_2 _inst_3 M N _inst_4 _inst_5 _inst_6 _inst_7 i f (Module.Baer.extensionOfMax.{u1, u2} R _inst_1 Q _inst_2 _inst_3 M N _inst_4 _inst_5 _inst_6 _inst_7 i f _inst_8))) (Top.top.{max u1 u2} (Submodule.{u1, max u1 u2} R N (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{max u1 u2} N _inst_5) _inst_7) (Submodule.instTopSubmodule.{u1, max u1 u2} R N (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{max u1 u2} N _inst_5) _inst_7)))
 Case conversion may be inaccurate. Consider using '#align module.Baer.extension_of_max_to_submodule_eq_top Module.Baer.extensionOfMax_to_submodule_eq_topₓ'. -/
 theorem extensionOfMax_to_submodule_eq_top (h : Module.Baer R Q) :
     (extensionOfMax i f).domain = ⊤ :=

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

@@ -193,7 +193,7 @@ variable {R i f}
 
 /- warning: module.Baer.chain_linear_pmap_of_chain_extension_of -> Module.Baer.chain_linearPMap_of_chain_extensionOf is a dubious translation:
 lean 3 declaration is
-  forall {R : Type.{u1}} [_inst_1 : Ring.{u1} R] {Q : Type.{max u1 u2}} [_inst_2 : AddCommGroup.{max u1 u2} Q] [_inst_3 : Module.{u1, max u1 u2} R Q (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{max u1 u2} Q _inst_2)] {M : Type.{max u1 u2}} {N : Type.{max u1 u2}} [_inst_4 : AddCommGroup.{max u1 u2} M] [_inst_5 : AddCommGroup.{max u1 u2} N] [_inst_6 : Module.{u1, max u1 u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{max u1 u2} M _inst_4)] [_inst_7 : Module.{u1, max u1 u2} R N (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{max u1 u2} N _inst_5)] {i : LinearMap.{u1, u1, max u1 u2, max u1 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 N (AddCommGroup.toAddCommMonoid.{max u1 u2} M _inst_4) (AddCommGroup.toAddCommMonoid.{max u1 u2} N _inst_5) _inst_6 _inst_7} {f : LinearMap.{u1, u1, max u1 u2, max u1 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 Q (AddCommGroup.toAddCommMonoid.{max u1 u2} M _inst_4) (AddCommGroup.toAddCommMonoid.{max u1 u2} Q _inst_2) _inst_6 _inst_3} {c : Set.{max u1 u2} (Module.Baer.ExtensionOf.{u1, u2} R _inst_1 Q _inst_2 _inst_3 M N _inst_4 _inst_5 _inst_6 _inst_7 i f)}, (IsChain.{max u1 u2} (Module.Baer.ExtensionOf.{u1, u2} R _inst_1 Q _inst_2 _inst_3 M N _inst_4 _inst_5 _inst_6 _inst_7 i f) (LE.le.{max u1 u2} (Module.Baer.ExtensionOf.{u1, u2} R _inst_1 Q _inst_2 _inst_3 M N _inst_4 _inst_5 _inst_6 _inst_7 i f) (Preorder.toLE.{max u1 u2} (Module.Baer.ExtensionOf.{u1, u2} R _inst_1 Q _inst_2 _inst_3 M N _inst_4 _inst_5 _inst_6 _inst_7 i f) (PartialOrder.toPreorder.{max u1 u2} (Module.Baer.ExtensionOf.{u1, u2} R _inst_1 Q _inst_2 _inst_3 M N _inst_4 _inst_5 _inst_6 _inst_7 i f) (SemilatticeInf.toPartialOrder.{max u1 u2} (Module.Baer.ExtensionOf.{u1, u2} R _inst_1 Q _inst_2 _inst_3 M N _inst_4 _inst_5 _inst_6 _inst_7 i f) (Module.Baer.ExtensionOf.semilatticeInf.{u1, u2} R _inst_1 Q _inst_2 _inst_3 M N _inst_4 _inst_5 _inst_6 _inst_7 i f))))) c) -> (IsChain.{max u1 u2} (LinearPMap.{u1, max u1 u2, max u1 u2} R _inst_1 N _inst_5 _inst_7 Q _inst_2 _inst_3) (LE.le.{max u1 u2} (LinearPMap.{u1, max u1 u2, max u1 u2} R _inst_1 N _inst_5 _inst_7 Q _inst_2 _inst_3) (LinearPMap.le.{u1, max u1 u2, max u1 u2} R _inst_1 N _inst_5 _inst_7 Q _inst_2 _inst_3)) (Set.image.{max u1 u2, max u1 u2} (Module.Baer.ExtensionOf.{u1, u2} R _inst_1 Q _inst_2 _inst_3 M N _inst_4 _inst_5 _inst_6 _inst_7 i f) (LinearPMap.{u1, max u1 u2, max u1 u2} R _inst_1 N _inst_5 _inst_7 Q _inst_2 _inst_3) (fun (x : Module.Baer.ExtensionOf.{u1, u2} R _inst_1 Q _inst_2 _inst_3 M N _inst_4 _inst_5 _inst_6 _inst_7 i f) => Module.Baer.ExtensionOf.toLinearPmap.{u1, u2} R _inst_1 Q _inst_2 _inst_3 M N _inst_4 _inst_5 _inst_6 _inst_7 i f x) c))
+  forall {R : Type.{u1}} [_inst_1 : Ring.{u1} R] {Q : Type.{max u1 u2}} [_inst_2 : AddCommGroup.{max u1 u2} Q] [_inst_3 : Module.{u1, max u1 u2} R Q (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{max u1 u2} Q _inst_2)] {M : Type.{max u1 u2}} {N : Type.{max u1 u2}} [_inst_4 : AddCommGroup.{max u1 u2} M] [_inst_5 : AddCommGroup.{max u1 u2} N] [_inst_6 : Module.{u1, max u1 u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{max u1 u2} M _inst_4)] [_inst_7 : Module.{u1, max u1 u2} R N (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{max u1 u2} N _inst_5)] {i : LinearMap.{u1, u1, max u1 u2, max u1 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 N (AddCommGroup.toAddCommMonoid.{max u1 u2} M _inst_4) (AddCommGroup.toAddCommMonoid.{max u1 u2} N _inst_5) _inst_6 _inst_7} {f : LinearMap.{u1, u1, max u1 u2, max u1 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 Q (AddCommGroup.toAddCommMonoid.{max u1 u2} M _inst_4) (AddCommGroup.toAddCommMonoid.{max u1 u2} Q _inst_2) _inst_6 _inst_3} {c : Set.{max u1 u2} (Module.Baer.ExtensionOf.{u1, u2} R _inst_1 Q _inst_2 _inst_3 M N _inst_4 _inst_5 _inst_6 _inst_7 i f)}, (IsChain.{max u1 u2} (Module.Baer.ExtensionOf.{u1, u2} R _inst_1 Q _inst_2 _inst_3 M N _inst_4 _inst_5 _inst_6 _inst_7 i f) (LE.le.{max u1 u2} (Module.Baer.ExtensionOf.{u1, u2} R _inst_1 Q _inst_2 _inst_3 M N _inst_4 _inst_5 _inst_6 _inst_7 i f) (Preorder.toHasLe.{max u1 u2} (Module.Baer.ExtensionOf.{u1, u2} R _inst_1 Q _inst_2 _inst_3 M N _inst_4 _inst_5 _inst_6 _inst_7 i f) (PartialOrder.toPreorder.{max u1 u2} (Module.Baer.ExtensionOf.{u1, u2} R _inst_1 Q _inst_2 _inst_3 M N _inst_4 _inst_5 _inst_6 _inst_7 i f) (SemilatticeInf.toPartialOrder.{max u1 u2} (Module.Baer.ExtensionOf.{u1, u2} R _inst_1 Q _inst_2 _inst_3 M N _inst_4 _inst_5 _inst_6 _inst_7 i f) (Module.Baer.ExtensionOf.semilatticeInf.{u1, u2} R _inst_1 Q _inst_2 _inst_3 M N _inst_4 _inst_5 _inst_6 _inst_7 i f))))) c) -> (IsChain.{max u1 u2} (LinearPMap.{u1, max u1 u2, max u1 u2} R _inst_1 N _inst_5 _inst_7 Q _inst_2 _inst_3) (LE.le.{max u1 u2} (LinearPMap.{u1, max u1 u2, max u1 u2} R _inst_1 N _inst_5 _inst_7 Q _inst_2 _inst_3) (LinearPMap.le.{u1, max u1 u2, max u1 u2} R _inst_1 N _inst_5 _inst_7 Q _inst_2 _inst_3)) (Set.image.{max u1 u2, max u1 u2} (Module.Baer.ExtensionOf.{u1, u2} R _inst_1 Q _inst_2 _inst_3 M N _inst_4 _inst_5 _inst_6 _inst_7 i f) (LinearPMap.{u1, max u1 u2, max u1 u2} R _inst_1 N _inst_5 _inst_7 Q _inst_2 _inst_3) (fun (x : Module.Baer.ExtensionOf.{u1, u2} R _inst_1 Q _inst_2 _inst_3 M N _inst_4 _inst_5 _inst_6 _inst_7 i f) => Module.Baer.ExtensionOf.toLinearPmap.{u1, u2} R _inst_1 Q _inst_2 _inst_3 M N _inst_4 _inst_5 _inst_6 _inst_7 i f x) c))
 but is expected to have type
   forall {R : Type.{u1}} [_inst_1 : Ring.{u1} R] {Q : TypeMax.{u2, u1}} [_inst_2 : AddCommGroup.{max u1 u2} Q] [_inst_3 : Module.{u1, max u1 u2} R Q (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{max u1 u2} Q _inst_2)] {M : Type.{max u1 u2}} {N : Type.{max u1 u2}} [_inst_4 : AddCommGroup.{max u1 u2} M] [_inst_5 : AddCommGroup.{max u1 u2} N] [_inst_6 : Module.{u1, max u1 u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{max u1 u2} M _inst_4)] [_inst_7 : Module.{u1, max u1 u2} R N (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{max u1 u2} N _inst_5)] {i : LinearMap.{u1, u1, max u1 u2, max u1 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 N (AddCommGroup.toAddCommMonoid.{max u1 u2} M _inst_4) (AddCommGroup.toAddCommMonoid.{max u1 u2} N _inst_5) _inst_6 _inst_7} {f : LinearMap.{u1, u1, max u1 u2, max u1 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 Q (AddCommGroup.toAddCommMonoid.{max u1 u2} M _inst_4) (AddCommGroup.toAddCommMonoid.{max u1 u2} Q _inst_2) _inst_6 _inst_3} {c : Set.{max u2 u1} (Module.Baer.ExtensionOf.{u1, u2} R _inst_1 Q _inst_2 _inst_3 M N _inst_4 _inst_5 _inst_6 _inst_7 i f)}, (IsChain.{max u1 u2} (Module.Baer.ExtensionOf.{u1, u2} R _inst_1 Q _inst_2 _inst_3 M N _inst_4 _inst_5 _inst_6 _inst_7 i f) (fun (x._@.Mathlib.Algebra.Module.Injective._hyg.1521 : Module.Baer.ExtensionOf.{u1, u2} R _inst_1 Q _inst_2 _inst_3 M N _inst_4 _inst_5 _inst_6 _inst_7 i f) (x._@.Mathlib.Algebra.Module.Injective._hyg.1523 : Module.Baer.ExtensionOf.{u1, u2} R _inst_1 Q _inst_2 _inst_3 M N _inst_4 _inst_5 _inst_6 _inst_7 i f) => LE.le.{max u1 u2} (Module.Baer.ExtensionOf.{u1, u2} R _inst_1 Q _inst_2 _inst_3 M N _inst_4 _inst_5 _inst_6 _inst_7 i f) (Preorder.toLE.{max u1 u2} (Module.Baer.ExtensionOf.{u1, u2} R _inst_1 Q _inst_2 _inst_3 M N _inst_4 _inst_5 _inst_6 _inst_7 i f) (PartialOrder.toPreorder.{max u1 u2} (Module.Baer.ExtensionOf.{u1, u2} R _inst_1 Q _inst_2 _inst_3 M N _inst_4 _inst_5 _inst_6 _inst_7 i f) (SemilatticeInf.toPartialOrder.{max u1 u2} (Module.Baer.ExtensionOf.{u1, u2} R _inst_1 Q _inst_2 _inst_3 M N _inst_4 _inst_5 _inst_6 _inst_7 i f) (Module.Baer.instSemilatticeInfExtensionOf.{u1, u2} R _inst_1 Q _inst_2 _inst_3 M N _inst_4 _inst_5 _inst_6 _inst_7 i f)))) x._@.Mathlib.Algebra.Module.Injective._hyg.1521 x._@.Mathlib.Algebra.Module.Injective._hyg.1523) c) -> (IsChain.{max u1 u2} (LinearPMap.{u1, max u1 u2, max u1 u2} R _inst_1 N _inst_5 _inst_7 Q _inst_2 _inst_3) (fun (x._@.Mathlib.Algebra.Module.Injective._hyg.1540 : LinearPMap.{u1, max u1 u2, max u1 u2} R _inst_1 N _inst_5 _inst_7 Q _inst_2 _inst_3) (x._@.Mathlib.Algebra.Module.Injective._hyg.1542 : LinearPMap.{u1, max u1 u2, max u1 u2} R _inst_1 N _inst_5 _inst_7 Q _inst_2 _inst_3) => LE.le.{max u1 u2} (LinearPMap.{u1, max u1 u2, max u1 u2} R _inst_1 N _inst_5 _inst_7 Q _inst_2 _inst_3) (LinearPMap.le.{u1, max u1 u2, max u1 u2} R _inst_1 N _inst_5 _inst_7 Q _inst_2 _inst_3) x._@.Mathlib.Algebra.Module.Injective._hyg.1540 x._@.Mathlib.Algebra.Module.Injective._hyg.1542) (Set.image.{max u1 u2, max u1 u2} (Module.Baer.ExtensionOf.{u1, u2} R _inst_1 Q _inst_2 _inst_3 M N _inst_4 _inst_5 _inst_6 _inst_7 i f) (LinearPMap.{u1, max u1 u2, max u1 u2} R _inst_1 N _inst_5 _inst_7 Q _inst_2 _inst_3) (fun (x : Module.Baer.ExtensionOf.{u1, u2} R _inst_1 Q _inst_2 _inst_3 M N _inst_4 _inst_5 _inst_6 _inst_7 i f) => Module.Baer.ExtensionOf.toLinearPMap.{u1, u2} R _inst_1 Q _inst_2 _inst_3 M N _inst_4 _inst_5 _inst_6 _inst_7 i f x) c))
 Case conversion may be inaccurate. Consider using '#align module.Baer.chain_linear_pmap_of_chain_extension_of Module.Baer.chain_linearPMap_of_chain_extensionOfₓ'. -/
@@ -207,7 +207,7 @@ theorem chain_linearPMap_of_chain_extensionOf {c : Set (ExtensionOf i f)}
 
 /- warning: module.Baer.extension_of.max -> Module.Baer.ExtensionOf.max is a dubious translation:
 lean 3 declaration is
-  forall {R : Type.{u1}} [_inst_1 : Ring.{u1} R] {Q : Type.{max u1 u2}} [_inst_2 : AddCommGroup.{max u1 u2} Q] [_inst_3 : Module.{u1, max u1 u2} R Q (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{max u1 u2} Q _inst_2)] {M : Type.{max u1 u2}} {N : Type.{max u1 u2}} [_inst_4 : AddCommGroup.{max u1 u2} M] [_inst_5 : AddCommGroup.{max u1 u2} N] [_inst_6 : Module.{u1, max u1 u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{max u1 u2} M _inst_4)] [_inst_7 : Module.{u1, max u1 u2} R N (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{max u1 u2} N _inst_5)] {i : LinearMap.{u1, u1, max u1 u2, max u1 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 N (AddCommGroup.toAddCommMonoid.{max u1 u2} M _inst_4) (AddCommGroup.toAddCommMonoid.{max u1 u2} N _inst_5) _inst_6 _inst_7} {f : LinearMap.{u1, u1, max u1 u2, max u1 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 Q (AddCommGroup.toAddCommMonoid.{max u1 u2} M _inst_4) (AddCommGroup.toAddCommMonoid.{max u1 u2} Q _inst_2) _inst_6 _inst_3} {c : Set.{max u1 u2} (Module.Baer.ExtensionOf.{u1, u2} R _inst_1 Q _inst_2 _inst_3 M N _inst_4 _inst_5 _inst_6 _inst_7 i f)}, (IsChain.{max u1 u2} (Module.Baer.ExtensionOf.{u1, u2} R _inst_1 Q _inst_2 _inst_3 M N _inst_4 _inst_5 _inst_6 _inst_7 i f) (LE.le.{max u1 u2} (Module.Baer.ExtensionOf.{u1, u2} R _inst_1 Q _inst_2 _inst_3 M N _inst_4 _inst_5 _inst_6 _inst_7 i f) (Preorder.toLE.{max u1 u2} (Module.Baer.ExtensionOf.{u1, u2} R _inst_1 Q _inst_2 _inst_3 M N _inst_4 _inst_5 _inst_6 _inst_7 i f) (PartialOrder.toPreorder.{max u1 u2} (Module.Baer.ExtensionOf.{u1, u2} R _inst_1 Q _inst_2 _inst_3 M N _inst_4 _inst_5 _inst_6 _inst_7 i f) (SemilatticeInf.toPartialOrder.{max u1 u2} (Module.Baer.ExtensionOf.{u1, u2} R _inst_1 Q _inst_2 _inst_3 M N _inst_4 _inst_5 _inst_6 _inst_7 i f) (Module.Baer.ExtensionOf.semilatticeInf.{u1, u2} R _inst_1 Q _inst_2 _inst_3 M N _inst_4 _inst_5 _inst_6 _inst_7 i f))))) c) -> (Set.Nonempty.{max u1 u2} (Module.Baer.ExtensionOf.{u1, u2} R _inst_1 Q _inst_2 _inst_3 M N _inst_4 _inst_5 _inst_6 _inst_7 i f) c) -> (Module.Baer.ExtensionOf.{u1, u2} R _inst_1 Q _inst_2 _inst_3 M N _inst_4 _inst_5 _inst_6 _inst_7 i f)
+  forall {R : Type.{u1}} [_inst_1 : Ring.{u1} R] {Q : Type.{max u1 u2}} [_inst_2 : AddCommGroup.{max u1 u2} Q] [_inst_3 : Module.{u1, max u1 u2} R Q (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{max u1 u2} Q _inst_2)] {M : Type.{max u1 u2}} {N : Type.{max u1 u2}} [_inst_4 : AddCommGroup.{max u1 u2} M] [_inst_5 : AddCommGroup.{max u1 u2} N] [_inst_6 : Module.{u1, max u1 u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{max u1 u2} M _inst_4)] [_inst_7 : Module.{u1, max u1 u2} R N (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{max u1 u2} N _inst_5)] {i : LinearMap.{u1, u1, max u1 u2, max u1 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 N (AddCommGroup.toAddCommMonoid.{max u1 u2} M _inst_4) (AddCommGroup.toAddCommMonoid.{max u1 u2} N _inst_5) _inst_6 _inst_7} {f : LinearMap.{u1, u1, max u1 u2, max u1 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 Q (AddCommGroup.toAddCommMonoid.{max u1 u2} M _inst_4) (AddCommGroup.toAddCommMonoid.{max u1 u2} Q _inst_2) _inst_6 _inst_3} {c : Set.{max u1 u2} (Module.Baer.ExtensionOf.{u1, u2} R _inst_1 Q _inst_2 _inst_3 M N _inst_4 _inst_5 _inst_6 _inst_7 i f)}, (IsChain.{max u1 u2} (Module.Baer.ExtensionOf.{u1, u2} R _inst_1 Q _inst_2 _inst_3 M N _inst_4 _inst_5 _inst_6 _inst_7 i f) (LE.le.{max u1 u2} (Module.Baer.ExtensionOf.{u1, u2} R _inst_1 Q _inst_2 _inst_3 M N _inst_4 _inst_5 _inst_6 _inst_7 i f) (Preorder.toHasLe.{max u1 u2} (Module.Baer.ExtensionOf.{u1, u2} R _inst_1 Q _inst_2 _inst_3 M N _inst_4 _inst_5 _inst_6 _inst_7 i f) (PartialOrder.toPreorder.{max u1 u2} (Module.Baer.ExtensionOf.{u1, u2} R _inst_1 Q _inst_2 _inst_3 M N _inst_4 _inst_5 _inst_6 _inst_7 i f) (SemilatticeInf.toPartialOrder.{max u1 u2} (Module.Baer.ExtensionOf.{u1, u2} R _inst_1 Q _inst_2 _inst_3 M N _inst_4 _inst_5 _inst_6 _inst_7 i f) (Module.Baer.ExtensionOf.semilatticeInf.{u1, u2} R _inst_1 Q _inst_2 _inst_3 M N _inst_4 _inst_5 _inst_6 _inst_7 i f))))) c) -> (Set.Nonempty.{max u1 u2} (Module.Baer.ExtensionOf.{u1, u2} R _inst_1 Q _inst_2 _inst_3 M N _inst_4 _inst_5 _inst_6 _inst_7 i f) c) -> (Module.Baer.ExtensionOf.{u1, u2} R _inst_1 Q _inst_2 _inst_3 M N _inst_4 _inst_5 _inst_6 _inst_7 i f)
 but is expected to have type
   forall {R : Type.{u1}} [_inst_1 : Ring.{u1} R] {Q : TypeMax.{u2, u1}} [_inst_2 : AddCommGroup.{max u1 u2} Q] [_inst_3 : Module.{u1, max u1 u2} R Q (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{max u1 u2} Q _inst_2)] {M : Type.{max u1 u2}} {N : Type.{max u1 u2}} [_inst_4 : AddCommGroup.{max u1 u2} M] [_inst_5 : AddCommGroup.{max u1 u2} N] [_inst_6 : Module.{u1, max u1 u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{max u1 u2} M _inst_4)] [_inst_7 : Module.{u1, max u1 u2} R N (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{max u1 u2} N _inst_5)] {i : LinearMap.{u1, u1, max u1 u2, max u1 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 N (AddCommGroup.toAddCommMonoid.{max u1 u2} M _inst_4) (AddCommGroup.toAddCommMonoid.{max u1 u2} N _inst_5) _inst_6 _inst_7} {f : LinearMap.{u1, u1, max u1 u2, max u1 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 Q (AddCommGroup.toAddCommMonoid.{max u1 u2} M _inst_4) (AddCommGroup.toAddCommMonoid.{max u1 u2} Q _inst_2) _inst_6 _inst_3} {c : Set.{max u2 u1} (Module.Baer.ExtensionOf.{u1, u2} R _inst_1 Q _inst_2 _inst_3 M N _inst_4 _inst_5 _inst_6 _inst_7 i f)}, (IsChain.{max u1 u2} (Module.Baer.ExtensionOf.{u1, u2} R _inst_1 Q _inst_2 _inst_3 M N _inst_4 _inst_5 _inst_6 _inst_7 i f) (fun (x._@.Mathlib.Algebra.Module.Injective._hyg.1654 : Module.Baer.ExtensionOf.{u1, u2} R _inst_1 Q _inst_2 _inst_3 M N _inst_4 _inst_5 _inst_6 _inst_7 i f) (x._@.Mathlib.Algebra.Module.Injective._hyg.1656 : Module.Baer.ExtensionOf.{u1, u2} R _inst_1 Q _inst_2 _inst_3 M N _inst_4 _inst_5 _inst_6 _inst_7 i f) => LE.le.{max u1 u2} (Module.Baer.ExtensionOf.{u1, u2} R _inst_1 Q _inst_2 _inst_3 M N _inst_4 _inst_5 _inst_6 _inst_7 i f) (Preorder.toLE.{max u1 u2} (Module.Baer.ExtensionOf.{u1, u2} R _inst_1 Q _inst_2 _inst_3 M N _inst_4 _inst_5 _inst_6 _inst_7 i f) (PartialOrder.toPreorder.{max u1 u2} (Module.Baer.ExtensionOf.{u1, u2} R _inst_1 Q _inst_2 _inst_3 M N _inst_4 _inst_5 _inst_6 _inst_7 i f) (SemilatticeInf.toPartialOrder.{max u1 u2} (Module.Baer.ExtensionOf.{u1, u2} R _inst_1 Q _inst_2 _inst_3 M N _inst_4 _inst_5 _inst_6 _inst_7 i f) (Module.Baer.instSemilatticeInfExtensionOf.{u1, u2} R _inst_1 Q _inst_2 _inst_3 M N _inst_4 _inst_5 _inst_6 _inst_7 i f)))) x._@.Mathlib.Algebra.Module.Injective._hyg.1654 x._@.Mathlib.Algebra.Module.Injective._hyg.1656) c) -> (Set.Nonempty.{max u1 u2} (Module.Baer.ExtensionOf.{u1, u2} R _inst_1 Q _inst_2 _inst_3 M N _inst_4 _inst_5 _inst_6 _inst_7 i f) c) -> (Module.Baer.ExtensionOf.{u1, u2} R _inst_1 Q _inst_2 _inst_3 M N _inst_4 _inst_5 _inst_6 _inst_7 i f)
 Case conversion may be inaccurate. Consider using '#align module.Baer.extension_of.max Module.Baer.ExtensionOf.maxₓ'. -/
@@ -235,7 +235,7 @@ def ExtensionOf.max {c : Set (ExtensionOf i f)} (hchain : IsChain (· ≤ ·) c)
 
 /- warning: module.Baer.extension_of.le_max -> Module.Baer.ExtensionOf.le_max is a dubious translation:
 lean 3 declaration is
-  forall {R : Type.{u1}} [_inst_1 : Ring.{u1} R] {Q : Type.{max u1 u2}} [_inst_2 : AddCommGroup.{max u1 u2} Q] [_inst_3 : Module.{u1, max u1 u2} R Q (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{max u1 u2} Q _inst_2)] {M : Type.{max u1 u2}} {N : Type.{max u1 u2}} [_inst_4 : AddCommGroup.{max u1 u2} M] [_inst_5 : AddCommGroup.{max u1 u2} N] [_inst_6 : Module.{u1, max u1 u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{max u1 u2} M _inst_4)] [_inst_7 : Module.{u1, max u1 u2} R N (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{max u1 u2} N _inst_5)] {i : LinearMap.{u1, u1, max u1 u2, max u1 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 N (AddCommGroup.toAddCommMonoid.{max u1 u2} M _inst_4) (AddCommGroup.toAddCommMonoid.{max u1 u2} N _inst_5) _inst_6 _inst_7} {f : LinearMap.{u1, u1, max u1 u2, max u1 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 Q (AddCommGroup.toAddCommMonoid.{max u1 u2} M _inst_4) (AddCommGroup.toAddCommMonoid.{max u1 u2} Q _inst_2) _inst_6 _inst_3} {c : Set.{max u1 u2} (Module.Baer.ExtensionOf.{u1, u2} R _inst_1 Q _inst_2 _inst_3 M N _inst_4 _inst_5 _inst_6 _inst_7 i f)} (hchain : IsChain.{max u1 u2} (Module.Baer.ExtensionOf.{u1, u2} R _inst_1 Q _inst_2 _inst_3 M N _inst_4 _inst_5 _inst_6 _inst_7 i f) (LE.le.{max u1 u2} (Module.Baer.ExtensionOf.{u1, u2} R _inst_1 Q _inst_2 _inst_3 M N _inst_4 _inst_5 _inst_6 _inst_7 i f) (Preorder.toLE.{max u1 u2} (Module.Baer.ExtensionOf.{u1, u2} R _inst_1 Q _inst_2 _inst_3 M N _inst_4 _inst_5 _inst_6 _inst_7 i f) (PartialOrder.toPreorder.{max u1 u2} (Module.Baer.ExtensionOf.{u1, u2} R _inst_1 Q _inst_2 _inst_3 M N _inst_4 _inst_5 _inst_6 _inst_7 i f) (SemilatticeInf.toPartialOrder.{max u1 u2} (Module.Baer.ExtensionOf.{u1, u2} R _inst_1 Q _inst_2 _inst_3 M N _inst_4 _inst_5 _inst_6 _inst_7 i f) (Module.Baer.ExtensionOf.semilatticeInf.{u1, u2} R _inst_1 Q _inst_2 _inst_3 M N _inst_4 _inst_5 _inst_6 _inst_7 i f))))) c) (hnonempty : Set.Nonempty.{max u1 u2} (Module.Baer.ExtensionOf.{u1, u2} R _inst_1 Q _inst_2 _inst_3 M N _inst_4 _inst_5 _inst_6 _inst_7 i f) c) (a : Module.Baer.ExtensionOf.{u1, u2} R _inst_1 Q _inst_2 _inst_3 M N _inst_4 _inst_5 _inst_6 _inst_7 i f), (Membership.Mem.{max u1 u2, max u1 u2} (Module.Baer.ExtensionOf.{u1, u2} R _inst_1 Q _inst_2 _inst_3 M N _inst_4 _inst_5 _inst_6 _inst_7 i f) (Set.{max u1 u2} (Module.Baer.ExtensionOf.{u1, u2} R _inst_1 Q _inst_2 _inst_3 M N _inst_4 _inst_5 _inst_6 _inst_7 i f)) (Set.hasMem.{max u1 u2} (Module.Baer.ExtensionOf.{u1, u2} R _inst_1 Q _inst_2 _inst_3 M N _inst_4 _inst_5 _inst_6 _inst_7 i f)) a c) -> (LE.le.{max u1 u2} (Module.Baer.ExtensionOf.{u1, u2} R _inst_1 Q _inst_2 _inst_3 M N _inst_4 _inst_5 _inst_6 _inst_7 i f) (Preorder.toLE.{max u1 u2} (Module.Baer.ExtensionOf.{u1, u2} R _inst_1 Q _inst_2 _inst_3 M N _inst_4 _inst_5 _inst_6 _inst_7 i f) (PartialOrder.toPreorder.{max u1 u2} (Module.Baer.ExtensionOf.{u1, u2} R _inst_1 Q _inst_2 _inst_3 M N _inst_4 _inst_5 _inst_6 _inst_7 i f) (SemilatticeInf.toPartialOrder.{max u1 u2} (Module.Baer.ExtensionOf.{u1, u2} R _inst_1 Q _inst_2 _inst_3 M N _inst_4 _inst_5 _inst_6 _inst_7 i f) (Module.Baer.ExtensionOf.semilatticeInf.{u1, u2} R _inst_1 Q _inst_2 _inst_3 M N _inst_4 _inst_5 _inst_6 _inst_7 i f)))) a (Module.Baer.ExtensionOf.max.{u1, u2} R _inst_1 Q _inst_2 _inst_3 M N _inst_4 _inst_5 _inst_6 _inst_7 i f c hchain hnonempty))
+  forall {R : Type.{u1}} [_inst_1 : Ring.{u1} R] {Q : Type.{max u1 u2}} [_inst_2 : AddCommGroup.{max u1 u2} Q] [_inst_3 : Module.{u1, max u1 u2} R Q (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{max u1 u2} Q _inst_2)] {M : Type.{max u1 u2}} {N : Type.{max u1 u2}} [_inst_4 : AddCommGroup.{max u1 u2} M] [_inst_5 : AddCommGroup.{max u1 u2} N] [_inst_6 : Module.{u1, max u1 u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{max u1 u2} M _inst_4)] [_inst_7 : Module.{u1, max u1 u2} R N (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{max u1 u2} N _inst_5)] {i : LinearMap.{u1, u1, max u1 u2, max u1 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 N (AddCommGroup.toAddCommMonoid.{max u1 u2} M _inst_4) (AddCommGroup.toAddCommMonoid.{max u1 u2} N _inst_5) _inst_6 _inst_7} {f : LinearMap.{u1, u1, max u1 u2, max u1 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 Q (AddCommGroup.toAddCommMonoid.{max u1 u2} M _inst_4) (AddCommGroup.toAddCommMonoid.{max u1 u2} Q _inst_2) _inst_6 _inst_3} {c : Set.{max u1 u2} (Module.Baer.ExtensionOf.{u1, u2} R _inst_1 Q _inst_2 _inst_3 M N _inst_4 _inst_5 _inst_6 _inst_7 i f)} (hchain : IsChain.{max u1 u2} (Module.Baer.ExtensionOf.{u1, u2} R _inst_1 Q _inst_2 _inst_3 M N _inst_4 _inst_5 _inst_6 _inst_7 i f) (LE.le.{max u1 u2} (Module.Baer.ExtensionOf.{u1, u2} R _inst_1 Q _inst_2 _inst_3 M N _inst_4 _inst_5 _inst_6 _inst_7 i f) (Preorder.toHasLe.{max u1 u2} (Module.Baer.ExtensionOf.{u1, u2} R _inst_1 Q _inst_2 _inst_3 M N _inst_4 _inst_5 _inst_6 _inst_7 i f) (PartialOrder.toPreorder.{max u1 u2} (Module.Baer.ExtensionOf.{u1, u2} R _inst_1 Q _inst_2 _inst_3 M N _inst_4 _inst_5 _inst_6 _inst_7 i f) (SemilatticeInf.toPartialOrder.{max u1 u2} (Module.Baer.ExtensionOf.{u1, u2} R _inst_1 Q _inst_2 _inst_3 M N _inst_4 _inst_5 _inst_6 _inst_7 i f) (Module.Baer.ExtensionOf.semilatticeInf.{u1, u2} R _inst_1 Q _inst_2 _inst_3 M N _inst_4 _inst_5 _inst_6 _inst_7 i f))))) c) (hnonempty : Set.Nonempty.{max u1 u2} (Module.Baer.ExtensionOf.{u1, u2} R _inst_1 Q _inst_2 _inst_3 M N _inst_4 _inst_5 _inst_6 _inst_7 i f) c) (a : Module.Baer.ExtensionOf.{u1, u2} R _inst_1 Q _inst_2 _inst_3 M N _inst_4 _inst_5 _inst_6 _inst_7 i f), (Membership.Mem.{max u1 u2, max u1 u2} (Module.Baer.ExtensionOf.{u1, u2} R _inst_1 Q _inst_2 _inst_3 M N _inst_4 _inst_5 _inst_6 _inst_7 i f) (Set.{max u1 u2} (Module.Baer.ExtensionOf.{u1, u2} R _inst_1 Q _inst_2 _inst_3 M N _inst_4 _inst_5 _inst_6 _inst_7 i f)) (Set.hasMem.{max u1 u2} (Module.Baer.ExtensionOf.{u1, u2} R _inst_1 Q _inst_2 _inst_3 M N _inst_4 _inst_5 _inst_6 _inst_7 i f)) a c) -> (LE.le.{max u1 u2} (Module.Baer.ExtensionOf.{u1, u2} R _inst_1 Q _inst_2 _inst_3 M N _inst_4 _inst_5 _inst_6 _inst_7 i f) (Preorder.toHasLe.{max u1 u2} (Module.Baer.ExtensionOf.{u1, u2} R _inst_1 Q _inst_2 _inst_3 M N _inst_4 _inst_5 _inst_6 _inst_7 i f) (PartialOrder.toPreorder.{max u1 u2} (Module.Baer.ExtensionOf.{u1, u2} R _inst_1 Q _inst_2 _inst_3 M N _inst_4 _inst_5 _inst_6 _inst_7 i f) (SemilatticeInf.toPartialOrder.{max u1 u2} (Module.Baer.ExtensionOf.{u1, u2} R _inst_1 Q _inst_2 _inst_3 M N _inst_4 _inst_5 _inst_6 _inst_7 i f) (Module.Baer.ExtensionOf.semilatticeInf.{u1, u2} R _inst_1 Q _inst_2 _inst_3 M N _inst_4 _inst_5 _inst_6 _inst_7 i f)))) a (Module.Baer.ExtensionOf.max.{u1, u2} R _inst_1 Q _inst_2 _inst_3 M N _inst_4 _inst_5 _inst_6 _inst_7 i f c hchain hnonempty))
 but is expected to have type
   forall {R : Type.{u1}} [_inst_1 : Ring.{u1} R] {Q : TypeMax.{u2, u1}} [_inst_2 : AddCommGroup.{max u1 u2} Q] [_inst_3 : Module.{u1, max u1 u2} R Q (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{max u1 u2} Q _inst_2)] {M : Type.{max u1 u2}} {N : Type.{max u1 u2}} [_inst_4 : AddCommGroup.{max u1 u2} M] [_inst_5 : AddCommGroup.{max u1 u2} N] [_inst_6 : Module.{u1, max u1 u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{max u1 u2} M _inst_4)] [_inst_7 : Module.{u1, max u1 u2} R N (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{max u1 u2} N _inst_5)] {i : LinearMap.{u1, u1, max u1 u2, max u1 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 N (AddCommGroup.toAddCommMonoid.{max u1 u2} M _inst_4) (AddCommGroup.toAddCommMonoid.{max u1 u2} N _inst_5) _inst_6 _inst_7} {f : LinearMap.{u1, u1, max u1 u2, max u1 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 Q (AddCommGroup.toAddCommMonoid.{max u1 u2} M _inst_4) (AddCommGroup.toAddCommMonoid.{max u1 u2} Q _inst_2) _inst_6 _inst_3} {c : Set.{max u2 u1} (Module.Baer.ExtensionOf.{u1, u2} R _inst_1 Q _inst_2 _inst_3 M N _inst_4 _inst_5 _inst_6 _inst_7 i f)} (hchain : IsChain.{max u1 u2} (Module.Baer.ExtensionOf.{u1, u2} R _inst_1 Q _inst_2 _inst_3 M N _inst_4 _inst_5 _inst_6 _inst_7 i f) (fun (x._@.Mathlib.Algebra.Module.Injective._hyg.1845 : Module.Baer.ExtensionOf.{u1, u2} R _inst_1 Q _inst_2 _inst_3 M N _inst_4 _inst_5 _inst_6 _inst_7 i f) (x._@.Mathlib.Algebra.Module.Injective._hyg.1847 : Module.Baer.ExtensionOf.{u1, u2} R _inst_1 Q _inst_2 _inst_3 M N _inst_4 _inst_5 _inst_6 _inst_7 i f) => LE.le.{max u1 u2} (Module.Baer.ExtensionOf.{u1, u2} R _inst_1 Q _inst_2 _inst_3 M N _inst_4 _inst_5 _inst_6 _inst_7 i f) (Preorder.toLE.{max u1 u2} (Module.Baer.ExtensionOf.{u1, u2} R _inst_1 Q _inst_2 _inst_3 M N _inst_4 _inst_5 _inst_6 _inst_7 i f) (PartialOrder.toPreorder.{max u1 u2} (Module.Baer.ExtensionOf.{u1, u2} R _inst_1 Q _inst_2 _inst_3 M N _inst_4 _inst_5 _inst_6 _inst_7 i f) (SemilatticeInf.toPartialOrder.{max u1 u2} (Module.Baer.ExtensionOf.{u1, u2} R _inst_1 Q _inst_2 _inst_3 M N _inst_4 _inst_5 _inst_6 _inst_7 i f) (Module.Baer.instSemilatticeInfExtensionOf.{u1, u2} R _inst_1 Q _inst_2 _inst_3 M N _inst_4 _inst_5 _inst_6 _inst_7 i f)))) x._@.Mathlib.Algebra.Module.Injective._hyg.1845 x._@.Mathlib.Algebra.Module.Injective._hyg.1847) c) (hnonempty : Set.Nonempty.{max u1 u2} (Module.Baer.ExtensionOf.{u1, u2} R _inst_1 Q _inst_2 _inst_3 M N _inst_4 _inst_5 _inst_6 _inst_7 i f) c) (a : Module.Baer.ExtensionOf.{u1, u2} R _inst_1 Q _inst_2 _inst_3 M N _inst_4 _inst_5 _inst_6 _inst_7 i f), (Membership.mem.{max u1 u2, max u1 u2} (Module.Baer.ExtensionOf.{u1, u2} R _inst_1 Q _inst_2 _inst_3 M N _inst_4 _inst_5 _inst_6 _inst_7 i f) (Set.{max u2 u1} (Module.Baer.ExtensionOf.{u1, u2} R _inst_1 Q _inst_2 _inst_3 M N _inst_4 _inst_5 _inst_6 _inst_7 i f)) (Set.instMembershipSet.{max u1 u2} (Module.Baer.ExtensionOf.{u1, u2} R _inst_1 Q _inst_2 _inst_3 M N _inst_4 _inst_5 _inst_6 _inst_7 i f)) a c) -> (LE.le.{max u1 u2} (Module.Baer.ExtensionOf.{u1, u2} R _inst_1 Q _inst_2 _inst_3 M N _inst_4 _inst_5 _inst_6 _inst_7 i f) (Preorder.toLE.{max u1 u2} (Module.Baer.ExtensionOf.{u1, u2} R _inst_1 Q _inst_2 _inst_3 M N _inst_4 _inst_5 _inst_6 _inst_7 i f) (PartialOrder.toPreorder.{max u1 u2} (Module.Baer.ExtensionOf.{u1, u2} R _inst_1 Q _inst_2 _inst_3 M N _inst_4 _inst_5 _inst_6 _inst_7 i f) (SemilatticeInf.toPartialOrder.{max u1 u2} (Module.Baer.ExtensionOf.{u1, u2} R _inst_1 Q _inst_2 _inst_3 M N _inst_4 _inst_5 _inst_6 _inst_7 i f) (Module.Baer.instSemilatticeInfExtensionOf.{u1, u2} R _inst_1 Q _inst_2 _inst_3 M N _inst_4 _inst_5 _inst_6 _inst_7 i f)))) a (Module.Baer.ExtensionOf.max.{u1, u2} R _inst_1 Q _inst_2 _inst_3 M N _inst_4 _inst_5 _inst_6 _inst_7 i f c hchain hnonempty))
 Case conversion may be inaccurate. Consider using '#align module.Baer.extension_of.le_max Module.Baer.ExtensionOf.le_maxₓ'. -/
@@ -292,7 +292,7 @@ def extensionOfMax : ExtensionOf i f :=
 
 /- warning: module.Baer.extension_of_max_is_max -> Module.Baer.extensionOfMax_is_max is a dubious translation:
 lean 3 declaration is
-  forall {R : Type.{u1}} [_inst_1 : Ring.{u1} R] {Q : Type.{max u1 u2}} [_inst_2 : AddCommGroup.{max u1 u2} Q] [_inst_3 : Module.{u1, max u1 u2} R Q (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{max u1 u2} Q _inst_2)] {M : Type.{max u1 u2}} {N : Type.{max u1 u2}} [_inst_4 : AddCommGroup.{max u1 u2} M] [_inst_5 : AddCommGroup.{max u1 u2} N] [_inst_6 : Module.{u1, max u1 u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{max u1 u2} M _inst_4)] [_inst_7 : Module.{u1, max u1 u2} R N (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{max u1 u2} N _inst_5)] (i : LinearMap.{u1, u1, max u1 u2, max u1 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 N (AddCommGroup.toAddCommMonoid.{max u1 u2} M _inst_4) (AddCommGroup.toAddCommMonoid.{max u1 u2} N _inst_5) _inst_6 _inst_7) (f : LinearMap.{u1, u1, max u1 u2, max u1 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 Q (AddCommGroup.toAddCommMonoid.{max u1 u2} M _inst_4) (AddCommGroup.toAddCommMonoid.{max u1 u2} Q _inst_2) _inst_6 _inst_3) [_inst_8 : Fact (Function.Injective.{succ (max u1 u2), succ (max u1 u2)} M N (coeFn.{succ (max u1 u2), succ (max u1 u2)} (LinearMap.{u1, u1, max u1 u2, max u1 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 N (AddCommGroup.toAddCommMonoid.{max u1 u2} M _inst_4) (AddCommGroup.toAddCommMonoid.{max u1 u2} N _inst_5) _inst_6 _inst_7) (fun (_x : LinearMap.{u1, u1, max u1 u2, max u1 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 N (AddCommGroup.toAddCommMonoid.{max u1 u2} M _inst_4) (AddCommGroup.toAddCommMonoid.{max u1 u2} N _inst_5) _inst_6 _inst_7) => M -> N) (LinearMap.hasCoeToFun.{u1, u1, max u1 u2, max u1 u2} R R M N (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{max u1 u2} M _inst_4) (AddCommGroup.toAddCommMonoid.{max u1 u2} N _inst_5) _inst_6 _inst_7 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1)))) i))] (a : Module.Baer.ExtensionOf.{u1, u2} R _inst_1 Q _inst_2 _inst_3 M N _inst_4 _inst_5 _inst_6 _inst_7 i f), (LE.le.{max u1 u2} (Module.Baer.ExtensionOf.{u1, u2} R _inst_1 Q _inst_2 _inst_3 M N _inst_4 _inst_5 _inst_6 _inst_7 i f) (Preorder.toLE.{max u1 u2} (Module.Baer.ExtensionOf.{u1, u2} R _inst_1 Q _inst_2 _inst_3 M N _inst_4 _inst_5 _inst_6 _inst_7 i f) (PartialOrder.toPreorder.{max u1 u2} (Module.Baer.ExtensionOf.{u1, u2} R _inst_1 Q _inst_2 _inst_3 M N _inst_4 _inst_5 _inst_6 _inst_7 i f) (SemilatticeInf.toPartialOrder.{max u1 u2} (Module.Baer.ExtensionOf.{u1, u2} R _inst_1 Q _inst_2 _inst_3 M N _inst_4 _inst_5 _inst_6 _inst_7 i f) (Module.Baer.ExtensionOf.semilatticeInf.{u1, u2} R _inst_1 Q _inst_2 _inst_3 M N _inst_4 _inst_5 _inst_6 _inst_7 i f)))) (Module.Baer.extensionOfMax.{u1, u2} R _inst_1 Q _inst_2 _inst_3 M N _inst_4 _inst_5 _inst_6 _inst_7 i f _inst_8) a) -> (Eq.{max (succ u1) (succ u2)} (Module.Baer.ExtensionOf.{u1, u2} R _inst_1 Q _inst_2 _inst_3 M N _inst_4 _inst_5 _inst_6 _inst_7 i f) a (Module.Baer.extensionOfMax.{u1, u2} R _inst_1 Q _inst_2 _inst_3 M N _inst_4 _inst_5 _inst_6 _inst_7 i f _inst_8))
+  forall {R : Type.{u1}} [_inst_1 : Ring.{u1} R] {Q : Type.{max u1 u2}} [_inst_2 : AddCommGroup.{max u1 u2} Q] [_inst_3 : Module.{u1, max u1 u2} R Q (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{max u1 u2} Q _inst_2)] {M : Type.{max u1 u2}} {N : Type.{max u1 u2}} [_inst_4 : AddCommGroup.{max u1 u2} M] [_inst_5 : AddCommGroup.{max u1 u2} N] [_inst_6 : Module.{u1, max u1 u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{max u1 u2} M _inst_4)] [_inst_7 : Module.{u1, max u1 u2} R N (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{max u1 u2} N _inst_5)] (i : LinearMap.{u1, u1, max u1 u2, max u1 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 N (AddCommGroup.toAddCommMonoid.{max u1 u2} M _inst_4) (AddCommGroup.toAddCommMonoid.{max u1 u2} N _inst_5) _inst_6 _inst_7) (f : LinearMap.{u1, u1, max u1 u2, max u1 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 Q (AddCommGroup.toAddCommMonoid.{max u1 u2} M _inst_4) (AddCommGroup.toAddCommMonoid.{max u1 u2} Q _inst_2) _inst_6 _inst_3) [_inst_8 : Fact (Function.Injective.{succ (max u1 u2), succ (max u1 u2)} M N (coeFn.{succ (max u1 u2), succ (max u1 u2)} (LinearMap.{u1, u1, max u1 u2, max u1 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 N (AddCommGroup.toAddCommMonoid.{max u1 u2} M _inst_4) (AddCommGroup.toAddCommMonoid.{max u1 u2} N _inst_5) _inst_6 _inst_7) (fun (_x : LinearMap.{u1, u1, max u1 u2, max u1 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 N (AddCommGroup.toAddCommMonoid.{max u1 u2} M _inst_4) (AddCommGroup.toAddCommMonoid.{max u1 u2} N _inst_5) _inst_6 _inst_7) => M -> N) (LinearMap.hasCoeToFun.{u1, u1, max u1 u2, max u1 u2} R R M N (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{max u1 u2} M _inst_4) (AddCommGroup.toAddCommMonoid.{max u1 u2} N _inst_5) _inst_6 _inst_7 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1)))) i))] (a : Module.Baer.ExtensionOf.{u1, u2} R _inst_1 Q _inst_2 _inst_3 M N _inst_4 _inst_5 _inst_6 _inst_7 i f), (LE.le.{max u1 u2} (Module.Baer.ExtensionOf.{u1, u2} R _inst_1 Q _inst_2 _inst_3 M N _inst_4 _inst_5 _inst_6 _inst_7 i f) (Preorder.toHasLe.{max u1 u2} (Module.Baer.ExtensionOf.{u1, u2} R _inst_1 Q _inst_2 _inst_3 M N _inst_4 _inst_5 _inst_6 _inst_7 i f) (PartialOrder.toPreorder.{max u1 u2} (Module.Baer.ExtensionOf.{u1, u2} R _inst_1 Q _inst_2 _inst_3 M N _inst_4 _inst_5 _inst_6 _inst_7 i f) (SemilatticeInf.toPartialOrder.{max u1 u2} (Module.Baer.ExtensionOf.{u1, u2} R _inst_1 Q _inst_2 _inst_3 M N _inst_4 _inst_5 _inst_6 _inst_7 i f) (Module.Baer.ExtensionOf.semilatticeInf.{u1, u2} R _inst_1 Q _inst_2 _inst_3 M N _inst_4 _inst_5 _inst_6 _inst_7 i f)))) (Module.Baer.extensionOfMax.{u1, u2} R _inst_1 Q _inst_2 _inst_3 M N _inst_4 _inst_5 _inst_6 _inst_7 i f _inst_8) a) -> (Eq.{max (succ u1) (succ u2)} (Module.Baer.ExtensionOf.{u1, u2} R _inst_1 Q _inst_2 _inst_3 M N _inst_4 _inst_5 _inst_6 _inst_7 i f) a (Module.Baer.extensionOfMax.{u1, u2} R _inst_1 Q _inst_2 _inst_3 M N _inst_4 _inst_5 _inst_6 _inst_7 i f _inst_8))
 but is expected to have type
   forall {R : Type.{u1}} [_inst_1 : Ring.{u1} R] {Q : TypeMax.{u2, u1}} [_inst_2 : AddCommGroup.{max u1 u2} Q] [_inst_3 : Module.{u1, max u1 u2} R Q (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{max u1 u2} Q _inst_2)] {M : Type.{max u1 u2}} {N : Type.{max u1 u2}} [_inst_4 : AddCommGroup.{max u1 u2} M] [_inst_5 : AddCommGroup.{max u1 u2} N] [_inst_6 : Module.{u1, max u1 u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{max u1 u2} M _inst_4)] [_inst_7 : Module.{u1, max u1 u2} R N (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{max u1 u2} N _inst_5)] (i : LinearMap.{u1, u1, max u1 u2, max u1 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 N (AddCommGroup.toAddCommMonoid.{max u1 u2} M _inst_4) (AddCommGroup.toAddCommMonoid.{max u1 u2} N _inst_5) _inst_6 _inst_7) (f : LinearMap.{u1, u1, max u1 u2, max u1 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 Q (AddCommGroup.toAddCommMonoid.{max u1 u2} M _inst_4) (AddCommGroup.toAddCommMonoid.{max u1 u2} Q _inst_2) _inst_6 _inst_3) [_inst_8 : Fact (Function.Injective.{max (succ u1) (succ u2), max (succ u1) (succ u2)} M N (FunLike.coe.{max (succ u1) (succ u2), max (succ u1) (succ u2), max (succ u1) (succ u2)} (LinearMap.{u1, u1, max u1 u2, max u1 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 N (AddCommGroup.toAddCommMonoid.{max u1 u2} M _inst_4) (AddCommGroup.toAddCommMonoid.{max u1 u2} N _inst_5) _inst_6 _inst_7) M (fun (_x : M) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : M) => N) _x) (LinearMap.instFunLikeLinearMap.{u1, u1, max u1 u2, max u1 u2} R R M N (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{max u1 u2} M _inst_4) (AddCommGroup.toAddCommMonoid.{max u1 u2} N _inst_5) _inst_6 _inst_7 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1)))) i))] (a : Module.Baer.ExtensionOf.{u1, u2} R _inst_1 Q _inst_2 _inst_3 M N _inst_4 _inst_5 _inst_6 _inst_7 i f), (LE.le.{max u1 u2} (Module.Baer.ExtensionOf.{u1, u2} R _inst_1 Q _inst_2 _inst_3 M N _inst_4 _inst_5 _inst_6 _inst_7 i f) (Preorder.toLE.{max u1 u2} (Module.Baer.ExtensionOf.{u1, u2} R _inst_1 Q _inst_2 _inst_3 M N _inst_4 _inst_5 _inst_6 _inst_7 i f) (PartialOrder.toPreorder.{max u1 u2} (Module.Baer.ExtensionOf.{u1, u2} R _inst_1 Q _inst_2 _inst_3 M N _inst_4 _inst_5 _inst_6 _inst_7 i f) (SemilatticeInf.toPartialOrder.{max u1 u2} (Module.Baer.ExtensionOf.{u1, u2} R _inst_1 Q _inst_2 _inst_3 M N _inst_4 _inst_5 _inst_6 _inst_7 i f) (Module.Baer.instSemilatticeInfExtensionOf.{u1, u2} R _inst_1 Q _inst_2 _inst_3 M N _inst_4 _inst_5 _inst_6 _inst_7 i f)))) (Module.Baer.extensionOfMax.{u1, u2} R _inst_1 Q _inst_2 _inst_3 M N _inst_4 _inst_5 _inst_6 _inst_7 i f _inst_8) a) -> (Eq.{max (succ u1) (succ u2)} (Module.Baer.ExtensionOf.{u1, u2} R _inst_1 Q _inst_2 _inst_3 M N _inst_4 _inst_5 _inst_6 _inst_7 i f) a (Module.Baer.extensionOfMax.{u1, u2} R _inst_1 Q _inst_2 _inst_3 M N _inst_4 _inst_5 _inst_6 _inst_7 i f _inst_8))
 Case conversion may be inaccurate. Consider using '#align module.Baer.extension_of_max_is_max Module.Baer.extensionOfMax_is_maxₓ'. -/
@@ -535,7 +535,7 @@ def extensionOfMaxAdjoin (h : Module.Baer R Q) (y : N) : ExtensionOf i f
 
 /- warning: module.Baer.extension_of_max_le -> Module.Baer.extensionOfMax_le is a dubious translation:
 lean 3 declaration is
-  forall {R : Type.{u1}} [_inst_1 : Ring.{u1} R] {Q : Type.{max u1 u2}} [_inst_2 : AddCommGroup.{max u1 u2} Q] [_inst_3 : Module.{u1, max u1 u2} R Q (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{max u1 u2} Q _inst_2)] {M : Type.{max u1 u2}} {N : Type.{max u1 u2}} [_inst_4 : AddCommGroup.{max u1 u2} M] [_inst_5 : AddCommGroup.{max u1 u2} N] [_inst_6 : Module.{u1, max u1 u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{max u1 u2} M _inst_4)] [_inst_7 : Module.{u1, max u1 u2} R N (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{max u1 u2} N _inst_5)] (i : LinearMap.{u1, u1, max u1 u2, max u1 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 N (AddCommGroup.toAddCommMonoid.{max u1 u2} M _inst_4) (AddCommGroup.toAddCommMonoid.{max u1 u2} N _inst_5) _inst_6 _inst_7) (f : LinearMap.{u1, u1, max u1 u2, max u1 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 Q (AddCommGroup.toAddCommMonoid.{max u1 u2} M _inst_4) (AddCommGroup.toAddCommMonoid.{max u1 u2} Q _inst_2) _inst_6 _inst_3) [_inst_8 : Fact (Function.Injective.{succ (max u1 u2), succ (max u1 u2)} M N (coeFn.{succ (max u1 u2), succ (max u1 u2)} (LinearMap.{u1, u1, max u1 u2, max u1 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 N (AddCommGroup.toAddCommMonoid.{max u1 u2} M _inst_4) (AddCommGroup.toAddCommMonoid.{max u1 u2} N _inst_5) _inst_6 _inst_7) (fun (_x : LinearMap.{u1, u1, max u1 u2, max u1 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 N (AddCommGroup.toAddCommMonoid.{max u1 u2} M _inst_4) (AddCommGroup.toAddCommMonoid.{max u1 u2} N _inst_5) _inst_6 _inst_7) => M -> N) (LinearMap.hasCoeToFun.{u1, u1, max u1 u2, max u1 u2} R R M N (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{max u1 u2} M _inst_4) (AddCommGroup.toAddCommMonoid.{max u1 u2} N _inst_5) _inst_6 _inst_7 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1)))) i))] (h : Module.Baer.{u1, u2} R _inst_1 Q _inst_2 _inst_3) {y : N}, LE.le.{max u1 u2} (Module.Baer.ExtensionOf.{u1, u2} R _inst_1 Q _inst_2 _inst_3 M N _inst_4 _inst_5 _inst_6 _inst_7 i f) (Preorder.toLE.{max u1 u2} (Module.Baer.ExtensionOf.{u1, u2} R _inst_1 Q _inst_2 _inst_3 M N _inst_4 _inst_5 _inst_6 _inst_7 i f) (PartialOrder.toPreorder.{max u1 u2} (Module.Baer.ExtensionOf.{u1, u2} R _inst_1 Q _inst_2 _inst_3 M N _inst_4 _inst_5 _inst_6 _inst_7 i f) (SemilatticeInf.toPartialOrder.{max u1 u2} (Module.Baer.ExtensionOf.{u1, u2} R _inst_1 Q _inst_2 _inst_3 M N _inst_4 _inst_5 _inst_6 _inst_7 i f) (Module.Baer.ExtensionOf.semilatticeInf.{u1, u2} R _inst_1 Q _inst_2 _inst_3 M N _inst_4 _inst_5 _inst_6 _inst_7 i f)))) (Module.Baer.extensionOfMax.{u1, u2} R _inst_1 Q _inst_2 _inst_3 M N _inst_4 _inst_5 _inst_6 _inst_7 i f _inst_8) (Module.Baer.extensionOfMaxAdjoin.{u1, u2} R _inst_1 Q _inst_2 _inst_3 M N _inst_4 _inst_5 _inst_6 _inst_7 i f _inst_8 h y)
+  forall {R : Type.{u1}} [_inst_1 : Ring.{u1} R] {Q : Type.{max u1 u2}} [_inst_2 : AddCommGroup.{max u1 u2} Q] [_inst_3 : Module.{u1, max u1 u2} R Q (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{max u1 u2} Q _inst_2)] {M : Type.{max u1 u2}} {N : Type.{max u1 u2}} [_inst_4 : AddCommGroup.{max u1 u2} M] [_inst_5 : AddCommGroup.{max u1 u2} N] [_inst_6 : Module.{u1, max u1 u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{max u1 u2} M _inst_4)] [_inst_7 : Module.{u1, max u1 u2} R N (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{max u1 u2} N _inst_5)] (i : LinearMap.{u1, u1, max u1 u2, max u1 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 N (AddCommGroup.toAddCommMonoid.{max u1 u2} M _inst_4) (AddCommGroup.toAddCommMonoid.{max u1 u2} N _inst_5) _inst_6 _inst_7) (f : LinearMap.{u1, u1, max u1 u2, max u1 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 Q (AddCommGroup.toAddCommMonoid.{max u1 u2} M _inst_4) (AddCommGroup.toAddCommMonoid.{max u1 u2} Q _inst_2) _inst_6 _inst_3) [_inst_8 : Fact (Function.Injective.{succ (max u1 u2), succ (max u1 u2)} M N (coeFn.{succ (max u1 u2), succ (max u1 u2)} (LinearMap.{u1, u1, max u1 u2, max u1 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 N (AddCommGroup.toAddCommMonoid.{max u1 u2} M _inst_4) (AddCommGroup.toAddCommMonoid.{max u1 u2} N _inst_5) _inst_6 _inst_7) (fun (_x : LinearMap.{u1, u1, max u1 u2, max u1 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 N (AddCommGroup.toAddCommMonoid.{max u1 u2} M _inst_4) (AddCommGroup.toAddCommMonoid.{max u1 u2} N _inst_5) _inst_6 _inst_7) => M -> N) (LinearMap.hasCoeToFun.{u1, u1, max u1 u2, max u1 u2} R R M N (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{max u1 u2} M _inst_4) (AddCommGroup.toAddCommMonoid.{max u1 u2} N _inst_5) _inst_6 _inst_7 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1)))) i))] (h : Module.Baer.{u1, u2} R _inst_1 Q _inst_2 _inst_3) {y : N}, LE.le.{max u1 u2} (Module.Baer.ExtensionOf.{u1, u2} R _inst_1 Q _inst_2 _inst_3 M N _inst_4 _inst_5 _inst_6 _inst_7 i f) (Preorder.toHasLe.{max u1 u2} (Module.Baer.ExtensionOf.{u1, u2} R _inst_1 Q _inst_2 _inst_3 M N _inst_4 _inst_5 _inst_6 _inst_7 i f) (PartialOrder.toPreorder.{max u1 u2} (Module.Baer.ExtensionOf.{u1, u2} R _inst_1 Q _inst_2 _inst_3 M N _inst_4 _inst_5 _inst_6 _inst_7 i f) (SemilatticeInf.toPartialOrder.{max u1 u2} (Module.Baer.ExtensionOf.{u1, u2} R _inst_1 Q _inst_2 _inst_3 M N _inst_4 _inst_5 _inst_6 _inst_7 i f) (Module.Baer.ExtensionOf.semilatticeInf.{u1, u2} R _inst_1 Q _inst_2 _inst_3 M N _inst_4 _inst_5 _inst_6 _inst_7 i f)))) (Module.Baer.extensionOfMax.{u1, u2} R _inst_1 Q _inst_2 _inst_3 M N _inst_4 _inst_5 _inst_6 _inst_7 i f _inst_8) (Module.Baer.extensionOfMaxAdjoin.{u1, u2} R _inst_1 Q _inst_2 _inst_3 M N _inst_4 _inst_5 _inst_6 _inst_7 i f _inst_8 h y)
 but is expected to have type
   forall {R : Type.{u1}} [_inst_1 : Ring.{u1} R] {Q : TypeMax.{u2, u1}} [_inst_2 : AddCommGroup.{max u1 u2} Q] [_inst_3 : Module.{u1, max u1 u2} R Q (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{max u1 u2} Q _inst_2)] {M : Type.{max u1 u2}} {N : Type.{max u1 u2}} [_inst_4 : AddCommGroup.{max u1 u2} M] [_inst_5 : AddCommGroup.{max u1 u2} N] [_inst_6 : Module.{u1, max u1 u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{max u1 u2} M _inst_4)] [_inst_7 : Module.{u1, max u1 u2} R N (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{max u1 u2} N _inst_5)] (i : LinearMap.{u1, u1, max u1 u2, max u1 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 N (AddCommGroup.toAddCommMonoid.{max u1 u2} M _inst_4) (AddCommGroup.toAddCommMonoid.{max u1 u2} N _inst_5) _inst_6 _inst_7) (f : LinearMap.{u1, u1, max u1 u2, max u1 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 Q (AddCommGroup.toAddCommMonoid.{max u1 u2} M _inst_4) (AddCommGroup.toAddCommMonoid.{max u1 u2} Q _inst_2) _inst_6 _inst_3) [_inst_8 : Fact (Function.Injective.{max (succ u1) (succ u2), max (succ u1) (succ u2)} M N (FunLike.coe.{max (succ u1) (succ u2), max (succ u1) (succ u2), max (succ u1) (succ u2)} (LinearMap.{u1, u1, max u1 u2, max u1 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 N (AddCommGroup.toAddCommMonoid.{max u1 u2} M _inst_4) (AddCommGroup.toAddCommMonoid.{max u1 u2} N _inst_5) _inst_6 _inst_7) M (fun (_x : M) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : M) => N) _x) (LinearMap.instFunLikeLinearMap.{u1, u1, max u1 u2, max u1 u2} R R M N (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{max u1 u2} M _inst_4) (AddCommGroup.toAddCommMonoid.{max u1 u2} N _inst_5) _inst_6 _inst_7 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1)))) i))] (h : Module.Baer.{u1, u2} R _inst_1 Q _inst_2 _inst_3) {y : N}, LE.le.{max u1 u2} (Module.Baer.ExtensionOf.{u1, u2} R _inst_1 Q _inst_2 _inst_3 M N _inst_4 _inst_5 _inst_6 _inst_7 i f) (Preorder.toLE.{max u1 u2} (Module.Baer.ExtensionOf.{u1, u2} R _inst_1 Q _inst_2 _inst_3 M N _inst_4 _inst_5 _inst_6 _inst_7 i f) (PartialOrder.toPreorder.{max u1 u2} (Module.Baer.ExtensionOf.{u1, u2} R _inst_1 Q _inst_2 _inst_3 M N _inst_4 _inst_5 _inst_6 _inst_7 i f) (SemilatticeInf.toPartialOrder.{max u1 u2} (Module.Baer.ExtensionOf.{u1, u2} R _inst_1 Q _inst_2 _inst_3 M N _inst_4 _inst_5 _inst_6 _inst_7 i f) (Module.Baer.instSemilatticeInfExtensionOf.{u1, u2} R _inst_1 Q _inst_2 _inst_3 M N _inst_4 _inst_5 _inst_6 _inst_7 i f)))) (Module.Baer.extensionOfMax.{u1, u2} R _inst_1 Q _inst_2 _inst_3 M N _inst_4 _inst_5 _inst_6 _inst_7 i f _inst_8) (Module.Baer.extensionOfMaxAdjoin.{u1, u2} R _inst_1 Q _inst_2 _inst_3 M N _inst_4 _inst_5 _inst_6 _inst_7 i f _inst_8 h y)
 Case conversion may be inaccurate. Consider using '#align module.Baer.extension_of_max_le Module.Baer.extensionOfMax_leₓ'. -/

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

@@ -195,7 +195,7 @@ variable {R i f}
 lean 3 declaration is
   forall {R : Type.{u1}} [_inst_1 : Ring.{u1} R] {Q : Type.{max u1 u2}} [_inst_2 : AddCommGroup.{max u1 u2} Q] [_inst_3 : Module.{u1, max u1 u2} R Q (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{max u1 u2} Q _inst_2)] {M : Type.{max u1 u2}} {N : Type.{max u1 u2}} [_inst_4 : AddCommGroup.{max u1 u2} M] [_inst_5 : AddCommGroup.{max u1 u2} N] [_inst_6 : Module.{u1, max u1 u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{max u1 u2} M _inst_4)] [_inst_7 : Module.{u1, max u1 u2} R N (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{max u1 u2} N _inst_5)] {i : LinearMap.{u1, u1, max u1 u2, max u1 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 N (AddCommGroup.toAddCommMonoid.{max u1 u2} M _inst_4) (AddCommGroup.toAddCommMonoid.{max u1 u2} N _inst_5) _inst_6 _inst_7} {f : LinearMap.{u1, u1, max u1 u2, max u1 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 Q (AddCommGroup.toAddCommMonoid.{max u1 u2} M _inst_4) (AddCommGroup.toAddCommMonoid.{max u1 u2} Q _inst_2) _inst_6 _inst_3} {c : Set.{max u1 u2} (Module.Baer.ExtensionOf.{u1, u2} R _inst_1 Q _inst_2 _inst_3 M N _inst_4 _inst_5 _inst_6 _inst_7 i f)}, (IsChain.{max u1 u2} (Module.Baer.ExtensionOf.{u1, u2} R _inst_1 Q _inst_2 _inst_3 M N _inst_4 _inst_5 _inst_6 _inst_7 i f) (LE.le.{max u1 u2} (Module.Baer.ExtensionOf.{u1, u2} R _inst_1 Q _inst_2 _inst_3 M N _inst_4 _inst_5 _inst_6 _inst_7 i f) (Preorder.toLE.{max u1 u2} (Module.Baer.ExtensionOf.{u1, u2} R _inst_1 Q _inst_2 _inst_3 M N _inst_4 _inst_5 _inst_6 _inst_7 i f) (PartialOrder.toPreorder.{max u1 u2} (Module.Baer.ExtensionOf.{u1, u2} R _inst_1 Q _inst_2 _inst_3 M N _inst_4 _inst_5 _inst_6 _inst_7 i f) (SemilatticeInf.toPartialOrder.{max u1 u2} (Module.Baer.ExtensionOf.{u1, u2} R _inst_1 Q _inst_2 _inst_3 M N _inst_4 _inst_5 _inst_6 _inst_7 i f) (Module.Baer.ExtensionOf.semilatticeInf.{u1, u2} R _inst_1 Q _inst_2 _inst_3 M N _inst_4 _inst_5 _inst_6 _inst_7 i f))))) c) -> (IsChain.{max u1 u2} (LinearPMap.{u1, max u1 u2, max u1 u2} R _inst_1 N _inst_5 _inst_7 Q _inst_2 _inst_3) (LE.le.{max u1 u2} (LinearPMap.{u1, max u1 u2, max u1 u2} R _inst_1 N _inst_5 _inst_7 Q _inst_2 _inst_3) (LinearPMap.le.{u1, max u1 u2, max u1 u2} R _inst_1 N _inst_5 _inst_7 Q _inst_2 _inst_3)) (Set.image.{max u1 u2, max u1 u2} (Module.Baer.ExtensionOf.{u1, u2} R _inst_1 Q _inst_2 _inst_3 M N _inst_4 _inst_5 _inst_6 _inst_7 i f) (LinearPMap.{u1, max u1 u2, max u1 u2} R _inst_1 N _inst_5 _inst_7 Q _inst_2 _inst_3) (fun (x : Module.Baer.ExtensionOf.{u1, u2} R _inst_1 Q _inst_2 _inst_3 M N _inst_4 _inst_5 _inst_6 _inst_7 i f) => Module.Baer.ExtensionOf.toLinearPmap.{u1, u2} R _inst_1 Q _inst_2 _inst_3 M N _inst_4 _inst_5 _inst_6 _inst_7 i f x) c))
 but is expected to have type
-  forall {R : Type.{u1}} [_inst_1 : Ring.{u1} R] {Q : TypeMax.{u2, u1}} [_inst_2 : AddCommGroup.{max u1 u2} Q] [_inst_3 : Module.{u1, max u1 u2} R Q (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{max u1 u2} Q _inst_2)] {M : Type.{max u1 u2}} {N : Type.{max u1 u2}} [_inst_4 : AddCommGroup.{max u1 u2} M] [_inst_5 : AddCommGroup.{max u1 u2} N] [_inst_6 : Module.{u1, max u1 u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{max u1 u2} M _inst_4)] [_inst_7 : Module.{u1, max u1 u2} R N (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{max u1 u2} N _inst_5)] {i : LinearMap.{u1, u1, max u1 u2, max u1 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 N (AddCommGroup.toAddCommMonoid.{max u1 u2} M _inst_4) (AddCommGroup.toAddCommMonoid.{max u1 u2} N _inst_5) _inst_6 _inst_7} {f : LinearMap.{u1, u1, max u1 u2, max u1 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 Q (AddCommGroup.toAddCommMonoid.{max u1 u2} M _inst_4) (AddCommGroup.toAddCommMonoid.{max u1 u2} Q _inst_2) _inst_6 _inst_3} {c : Set.{max u2 u1} (Module.Baer.ExtensionOf.{u1, u2} R _inst_1 Q _inst_2 _inst_3 M N _inst_4 _inst_5 _inst_6 _inst_7 i f)}, (IsChain.{max u1 u2} (Module.Baer.ExtensionOf.{u1, u2} R _inst_1 Q _inst_2 _inst_3 M N _inst_4 _inst_5 _inst_6 _inst_7 i f) (fun (x._@.Mathlib.Algebra.Module.Injective._hyg.1527 : Module.Baer.ExtensionOf.{u1, u2} R _inst_1 Q _inst_2 _inst_3 M N _inst_4 _inst_5 _inst_6 _inst_7 i f) (x._@.Mathlib.Algebra.Module.Injective._hyg.1529 : Module.Baer.ExtensionOf.{u1, u2} R _inst_1 Q _inst_2 _inst_3 M N _inst_4 _inst_5 _inst_6 _inst_7 i f) => LE.le.{max u1 u2} (Module.Baer.ExtensionOf.{u1, u2} R _inst_1 Q _inst_2 _inst_3 M N _inst_4 _inst_5 _inst_6 _inst_7 i f) (Preorder.toLE.{max u1 u2} (Module.Baer.ExtensionOf.{u1, u2} R _inst_1 Q _inst_2 _inst_3 M N _inst_4 _inst_5 _inst_6 _inst_7 i f) (PartialOrder.toPreorder.{max u1 u2} (Module.Baer.ExtensionOf.{u1, u2} R _inst_1 Q _inst_2 _inst_3 M N _inst_4 _inst_5 _inst_6 _inst_7 i f) (SemilatticeInf.toPartialOrder.{max u1 u2} (Module.Baer.ExtensionOf.{u1, u2} R _inst_1 Q _inst_2 _inst_3 M N _inst_4 _inst_5 _inst_6 _inst_7 i f) (Module.Baer.instSemilatticeInfExtensionOf.{u1, u2} R _inst_1 Q _inst_2 _inst_3 M N _inst_4 _inst_5 _inst_6 _inst_7 i f)))) x._@.Mathlib.Algebra.Module.Injective._hyg.1527 x._@.Mathlib.Algebra.Module.Injective._hyg.1529) c) -> (IsChain.{max u1 u2} (LinearPMap.{u1, max u1 u2, max u1 u2} R _inst_1 N _inst_5 _inst_7 Q _inst_2 _inst_3) (fun (x._@.Mathlib.Algebra.Module.Injective._hyg.1546 : LinearPMap.{u1, max u1 u2, max u1 u2} R _inst_1 N _inst_5 _inst_7 Q _inst_2 _inst_3) (x._@.Mathlib.Algebra.Module.Injective._hyg.1548 : LinearPMap.{u1, max u1 u2, max u1 u2} R _inst_1 N _inst_5 _inst_7 Q _inst_2 _inst_3) => LE.le.{max u1 u2} (LinearPMap.{u1, max u1 u2, max u1 u2} R _inst_1 N _inst_5 _inst_7 Q _inst_2 _inst_3) (LinearPMap.le.{u1, max u1 u2, max u1 u2} R _inst_1 N _inst_5 _inst_7 Q _inst_2 _inst_3) x._@.Mathlib.Algebra.Module.Injective._hyg.1546 x._@.Mathlib.Algebra.Module.Injective._hyg.1548) (Set.image.{max u1 u2, max u1 u2} (Module.Baer.ExtensionOf.{u1, u2} R _inst_1 Q _inst_2 _inst_3 M N _inst_4 _inst_5 _inst_6 _inst_7 i f) (LinearPMap.{u1, max u1 u2, max u1 u2} R _inst_1 N _inst_5 _inst_7 Q _inst_2 _inst_3) (fun (x : Module.Baer.ExtensionOf.{u1, u2} R _inst_1 Q _inst_2 _inst_3 M N _inst_4 _inst_5 _inst_6 _inst_7 i f) => Module.Baer.ExtensionOf.toLinearPMap.{u1, u2} R _inst_1 Q _inst_2 _inst_3 M N _inst_4 _inst_5 _inst_6 _inst_7 i f x) c))
+  forall {R : Type.{u1}} [_inst_1 : Ring.{u1} R] {Q : TypeMax.{u2, u1}} [_inst_2 : AddCommGroup.{max u1 u2} Q] [_inst_3 : Module.{u1, max u1 u2} R Q (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{max u1 u2} Q _inst_2)] {M : Type.{max u1 u2}} {N : Type.{max u1 u2}} [_inst_4 : AddCommGroup.{max u1 u2} M] [_inst_5 : AddCommGroup.{max u1 u2} N] [_inst_6 : Module.{u1, max u1 u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{max u1 u2} M _inst_4)] [_inst_7 : Module.{u1, max u1 u2} R N (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{max u1 u2} N _inst_5)] {i : LinearMap.{u1, u1, max u1 u2, max u1 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 N (AddCommGroup.toAddCommMonoid.{max u1 u2} M _inst_4) (AddCommGroup.toAddCommMonoid.{max u1 u2} N _inst_5) _inst_6 _inst_7} {f : LinearMap.{u1, u1, max u1 u2, max u1 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 Q (AddCommGroup.toAddCommMonoid.{max u1 u2} M _inst_4) (AddCommGroup.toAddCommMonoid.{max u1 u2} Q _inst_2) _inst_6 _inst_3} {c : Set.{max u2 u1} (Module.Baer.ExtensionOf.{u1, u2} R _inst_1 Q _inst_2 _inst_3 M N _inst_4 _inst_5 _inst_6 _inst_7 i f)}, (IsChain.{max u1 u2} (Module.Baer.ExtensionOf.{u1, u2} R _inst_1 Q _inst_2 _inst_3 M N _inst_4 _inst_5 _inst_6 _inst_7 i f) (fun (x._@.Mathlib.Algebra.Module.Injective._hyg.1521 : Module.Baer.ExtensionOf.{u1, u2} R _inst_1 Q _inst_2 _inst_3 M N _inst_4 _inst_5 _inst_6 _inst_7 i f) (x._@.Mathlib.Algebra.Module.Injective._hyg.1523 : Module.Baer.ExtensionOf.{u1, u2} R _inst_1 Q _inst_2 _inst_3 M N _inst_4 _inst_5 _inst_6 _inst_7 i f) => LE.le.{max u1 u2} (Module.Baer.ExtensionOf.{u1, u2} R _inst_1 Q _inst_2 _inst_3 M N _inst_4 _inst_5 _inst_6 _inst_7 i f) (Preorder.toLE.{max u1 u2} (Module.Baer.ExtensionOf.{u1, u2} R _inst_1 Q _inst_2 _inst_3 M N _inst_4 _inst_5 _inst_6 _inst_7 i f) (PartialOrder.toPreorder.{max u1 u2} (Module.Baer.ExtensionOf.{u1, u2} R _inst_1 Q _inst_2 _inst_3 M N _inst_4 _inst_5 _inst_6 _inst_7 i f) (SemilatticeInf.toPartialOrder.{max u1 u2} (Module.Baer.ExtensionOf.{u1, u2} R _inst_1 Q _inst_2 _inst_3 M N _inst_4 _inst_5 _inst_6 _inst_7 i f) (Module.Baer.instSemilatticeInfExtensionOf.{u1, u2} R _inst_1 Q _inst_2 _inst_3 M N _inst_4 _inst_5 _inst_6 _inst_7 i f)))) x._@.Mathlib.Algebra.Module.Injective._hyg.1521 x._@.Mathlib.Algebra.Module.Injective._hyg.1523) c) -> (IsChain.{max u1 u2} (LinearPMap.{u1, max u1 u2, max u1 u2} R _inst_1 N _inst_5 _inst_7 Q _inst_2 _inst_3) (fun (x._@.Mathlib.Algebra.Module.Injective._hyg.1540 : LinearPMap.{u1, max u1 u2, max u1 u2} R _inst_1 N _inst_5 _inst_7 Q _inst_2 _inst_3) (x._@.Mathlib.Algebra.Module.Injective._hyg.1542 : LinearPMap.{u1, max u1 u2, max u1 u2} R _inst_1 N _inst_5 _inst_7 Q _inst_2 _inst_3) => LE.le.{max u1 u2} (LinearPMap.{u1, max u1 u2, max u1 u2} R _inst_1 N _inst_5 _inst_7 Q _inst_2 _inst_3) (LinearPMap.le.{u1, max u1 u2, max u1 u2} R _inst_1 N _inst_5 _inst_7 Q _inst_2 _inst_3) x._@.Mathlib.Algebra.Module.Injective._hyg.1540 x._@.Mathlib.Algebra.Module.Injective._hyg.1542) (Set.image.{max u1 u2, max u1 u2} (Module.Baer.ExtensionOf.{u1, u2} R _inst_1 Q _inst_2 _inst_3 M N _inst_4 _inst_5 _inst_6 _inst_7 i f) (LinearPMap.{u1, max u1 u2, max u1 u2} R _inst_1 N _inst_5 _inst_7 Q _inst_2 _inst_3) (fun (x : Module.Baer.ExtensionOf.{u1, u2} R _inst_1 Q _inst_2 _inst_3 M N _inst_4 _inst_5 _inst_6 _inst_7 i f) => Module.Baer.ExtensionOf.toLinearPMap.{u1, u2} R _inst_1 Q _inst_2 _inst_3 M N _inst_4 _inst_5 _inst_6 _inst_7 i f x) c))
 Case conversion may be inaccurate. Consider using '#align module.Baer.chain_linear_pmap_of_chain_extension_of Module.Baer.chain_linearPMap_of_chain_extensionOfₓ'. -/
 theorem chain_linearPMap_of_chain_extensionOf {c : Set (ExtensionOf i f)}
     (hchain : IsChain (· ≤ ·) c) :
@@ -209,7 +209,7 @@ theorem chain_linearPMap_of_chain_extensionOf {c : Set (ExtensionOf i f)}
 lean 3 declaration is
   forall {R : Type.{u1}} [_inst_1 : Ring.{u1} R] {Q : Type.{max u1 u2}} [_inst_2 : AddCommGroup.{max u1 u2} Q] [_inst_3 : Module.{u1, max u1 u2} R Q (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{max u1 u2} Q _inst_2)] {M : Type.{max u1 u2}} {N : Type.{max u1 u2}} [_inst_4 : AddCommGroup.{max u1 u2} M] [_inst_5 : AddCommGroup.{max u1 u2} N] [_inst_6 : Module.{u1, max u1 u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{max u1 u2} M _inst_4)] [_inst_7 : Module.{u1, max u1 u2} R N (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{max u1 u2} N _inst_5)] {i : LinearMap.{u1, u1, max u1 u2, max u1 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 N (AddCommGroup.toAddCommMonoid.{max u1 u2} M _inst_4) (AddCommGroup.toAddCommMonoid.{max u1 u2} N _inst_5) _inst_6 _inst_7} {f : LinearMap.{u1, u1, max u1 u2, max u1 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 Q (AddCommGroup.toAddCommMonoid.{max u1 u2} M _inst_4) (AddCommGroup.toAddCommMonoid.{max u1 u2} Q _inst_2) _inst_6 _inst_3} {c : Set.{max u1 u2} (Module.Baer.ExtensionOf.{u1, u2} R _inst_1 Q _inst_2 _inst_3 M N _inst_4 _inst_5 _inst_6 _inst_7 i f)}, (IsChain.{max u1 u2} (Module.Baer.ExtensionOf.{u1, u2} R _inst_1 Q _inst_2 _inst_3 M N _inst_4 _inst_5 _inst_6 _inst_7 i f) (LE.le.{max u1 u2} (Module.Baer.ExtensionOf.{u1, u2} R _inst_1 Q _inst_2 _inst_3 M N _inst_4 _inst_5 _inst_6 _inst_7 i f) (Preorder.toLE.{max u1 u2} (Module.Baer.ExtensionOf.{u1, u2} R _inst_1 Q _inst_2 _inst_3 M N _inst_4 _inst_5 _inst_6 _inst_7 i f) (PartialOrder.toPreorder.{max u1 u2} (Module.Baer.ExtensionOf.{u1, u2} R _inst_1 Q _inst_2 _inst_3 M N _inst_4 _inst_5 _inst_6 _inst_7 i f) (SemilatticeInf.toPartialOrder.{max u1 u2} (Module.Baer.ExtensionOf.{u1, u2} R _inst_1 Q _inst_2 _inst_3 M N _inst_4 _inst_5 _inst_6 _inst_7 i f) (Module.Baer.ExtensionOf.semilatticeInf.{u1, u2} R _inst_1 Q _inst_2 _inst_3 M N _inst_4 _inst_5 _inst_6 _inst_7 i f))))) c) -> (Set.Nonempty.{max u1 u2} (Module.Baer.ExtensionOf.{u1, u2} R _inst_1 Q _inst_2 _inst_3 M N _inst_4 _inst_5 _inst_6 _inst_7 i f) c) -> (Module.Baer.ExtensionOf.{u1, u2} R _inst_1 Q _inst_2 _inst_3 M N _inst_4 _inst_5 _inst_6 _inst_7 i f)
 but is expected to have type
-  forall {R : Type.{u1}} [_inst_1 : Ring.{u1} R] {Q : TypeMax.{u2, u1}} [_inst_2 : AddCommGroup.{max u1 u2} Q] [_inst_3 : Module.{u1, max u1 u2} R Q (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{max u1 u2} Q _inst_2)] {M : Type.{max u1 u2}} {N : Type.{max u1 u2}} [_inst_4 : AddCommGroup.{max u1 u2} M] [_inst_5 : AddCommGroup.{max u1 u2} N] [_inst_6 : Module.{u1, max u1 u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{max u1 u2} M _inst_4)] [_inst_7 : Module.{u1, max u1 u2} R N (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{max u1 u2} N _inst_5)] {i : LinearMap.{u1, u1, max u1 u2, max u1 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 N (AddCommGroup.toAddCommMonoid.{max u1 u2} M _inst_4) (AddCommGroup.toAddCommMonoid.{max u1 u2} N _inst_5) _inst_6 _inst_7} {f : LinearMap.{u1, u1, max u1 u2, max u1 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 Q (AddCommGroup.toAddCommMonoid.{max u1 u2} M _inst_4) (AddCommGroup.toAddCommMonoid.{max u1 u2} Q _inst_2) _inst_6 _inst_3} {c : Set.{max u2 u1} (Module.Baer.ExtensionOf.{u1, u2} R _inst_1 Q _inst_2 _inst_3 M N _inst_4 _inst_5 _inst_6 _inst_7 i f)}, (IsChain.{max u1 u2} (Module.Baer.ExtensionOf.{u1, u2} R _inst_1 Q _inst_2 _inst_3 M N _inst_4 _inst_5 _inst_6 _inst_7 i f) (fun (x._@.Mathlib.Algebra.Module.Injective._hyg.1660 : Module.Baer.ExtensionOf.{u1, u2} R _inst_1 Q _inst_2 _inst_3 M N _inst_4 _inst_5 _inst_6 _inst_7 i f) (x._@.Mathlib.Algebra.Module.Injective._hyg.1662 : Module.Baer.ExtensionOf.{u1, u2} R _inst_1 Q _inst_2 _inst_3 M N _inst_4 _inst_5 _inst_6 _inst_7 i f) => LE.le.{max u1 u2} (Module.Baer.ExtensionOf.{u1, u2} R _inst_1 Q _inst_2 _inst_3 M N _inst_4 _inst_5 _inst_6 _inst_7 i f) (Preorder.toLE.{max u1 u2} (Module.Baer.ExtensionOf.{u1, u2} R _inst_1 Q _inst_2 _inst_3 M N _inst_4 _inst_5 _inst_6 _inst_7 i f) (PartialOrder.toPreorder.{max u1 u2} (Module.Baer.ExtensionOf.{u1, u2} R _inst_1 Q _inst_2 _inst_3 M N _inst_4 _inst_5 _inst_6 _inst_7 i f) (SemilatticeInf.toPartialOrder.{max u1 u2} (Module.Baer.ExtensionOf.{u1, u2} R _inst_1 Q _inst_2 _inst_3 M N _inst_4 _inst_5 _inst_6 _inst_7 i f) (Module.Baer.instSemilatticeInfExtensionOf.{u1, u2} R _inst_1 Q _inst_2 _inst_3 M N _inst_4 _inst_5 _inst_6 _inst_7 i f)))) x._@.Mathlib.Algebra.Module.Injective._hyg.1660 x._@.Mathlib.Algebra.Module.Injective._hyg.1662) c) -> (Set.Nonempty.{max u1 u2} (Module.Baer.ExtensionOf.{u1, u2} R _inst_1 Q _inst_2 _inst_3 M N _inst_4 _inst_5 _inst_6 _inst_7 i f) c) -> (Module.Baer.ExtensionOf.{u1, u2} R _inst_1 Q _inst_2 _inst_3 M N _inst_4 _inst_5 _inst_6 _inst_7 i f)
+  forall {R : Type.{u1}} [_inst_1 : Ring.{u1} R] {Q : TypeMax.{u2, u1}} [_inst_2 : AddCommGroup.{max u1 u2} Q] [_inst_3 : Module.{u1, max u1 u2} R Q (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{max u1 u2} Q _inst_2)] {M : Type.{max u1 u2}} {N : Type.{max u1 u2}} [_inst_4 : AddCommGroup.{max u1 u2} M] [_inst_5 : AddCommGroup.{max u1 u2} N] [_inst_6 : Module.{u1, max u1 u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{max u1 u2} M _inst_4)] [_inst_7 : Module.{u1, max u1 u2} R N (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{max u1 u2} N _inst_5)] {i : LinearMap.{u1, u1, max u1 u2, max u1 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 N (AddCommGroup.toAddCommMonoid.{max u1 u2} M _inst_4) (AddCommGroup.toAddCommMonoid.{max u1 u2} N _inst_5) _inst_6 _inst_7} {f : LinearMap.{u1, u1, max u1 u2, max u1 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 Q (AddCommGroup.toAddCommMonoid.{max u1 u2} M _inst_4) (AddCommGroup.toAddCommMonoid.{max u1 u2} Q _inst_2) _inst_6 _inst_3} {c : Set.{max u2 u1} (Module.Baer.ExtensionOf.{u1, u2} R _inst_1 Q _inst_2 _inst_3 M N _inst_4 _inst_5 _inst_6 _inst_7 i f)}, (IsChain.{max u1 u2} (Module.Baer.ExtensionOf.{u1, u2} R _inst_1 Q _inst_2 _inst_3 M N _inst_4 _inst_5 _inst_6 _inst_7 i f) (fun (x._@.Mathlib.Algebra.Module.Injective._hyg.1654 : Module.Baer.ExtensionOf.{u1, u2} R _inst_1 Q _inst_2 _inst_3 M N _inst_4 _inst_5 _inst_6 _inst_7 i f) (x._@.Mathlib.Algebra.Module.Injective._hyg.1656 : Module.Baer.ExtensionOf.{u1, u2} R _inst_1 Q _inst_2 _inst_3 M N _inst_4 _inst_5 _inst_6 _inst_7 i f) => LE.le.{max u1 u2} (Module.Baer.ExtensionOf.{u1, u2} R _inst_1 Q _inst_2 _inst_3 M N _inst_4 _inst_5 _inst_6 _inst_7 i f) (Preorder.toLE.{max u1 u2} (Module.Baer.ExtensionOf.{u1, u2} R _inst_1 Q _inst_2 _inst_3 M N _inst_4 _inst_5 _inst_6 _inst_7 i f) (PartialOrder.toPreorder.{max u1 u2} (Module.Baer.ExtensionOf.{u1, u2} R _inst_1 Q _inst_2 _inst_3 M N _inst_4 _inst_5 _inst_6 _inst_7 i f) (SemilatticeInf.toPartialOrder.{max u1 u2} (Module.Baer.ExtensionOf.{u1, u2} R _inst_1 Q _inst_2 _inst_3 M N _inst_4 _inst_5 _inst_6 _inst_7 i f) (Module.Baer.instSemilatticeInfExtensionOf.{u1, u2} R _inst_1 Q _inst_2 _inst_3 M N _inst_4 _inst_5 _inst_6 _inst_7 i f)))) x._@.Mathlib.Algebra.Module.Injective._hyg.1654 x._@.Mathlib.Algebra.Module.Injective._hyg.1656) c) -> (Set.Nonempty.{max u1 u2} (Module.Baer.ExtensionOf.{u1, u2} R _inst_1 Q _inst_2 _inst_3 M N _inst_4 _inst_5 _inst_6 _inst_7 i f) c) -> (Module.Baer.ExtensionOf.{u1, u2} R _inst_1 Q _inst_2 _inst_3 M N _inst_4 _inst_5 _inst_6 _inst_7 i f)
 Case conversion may be inaccurate. Consider using '#align module.Baer.extension_of.max Module.Baer.ExtensionOf.maxₓ'. -/
 /-- The maximal element of every nonempty chain of `extension_of i f`. -/
 def ExtensionOf.max {c : Set (ExtensionOf i f)} (hchain : IsChain (· ≤ ·) c)
@@ -237,7 +237,7 @@ def ExtensionOf.max {c : Set (ExtensionOf i f)} (hchain : IsChain (· ≤ ·) c)
 lean 3 declaration is
   forall {R : Type.{u1}} [_inst_1 : Ring.{u1} R] {Q : Type.{max u1 u2}} [_inst_2 : AddCommGroup.{max u1 u2} Q] [_inst_3 : Module.{u1, max u1 u2} R Q (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{max u1 u2} Q _inst_2)] {M : Type.{max u1 u2}} {N : Type.{max u1 u2}} [_inst_4 : AddCommGroup.{max u1 u2} M] [_inst_5 : AddCommGroup.{max u1 u2} N] [_inst_6 : Module.{u1, max u1 u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{max u1 u2} M _inst_4)] [_inst_7 : Module.{u1, max u1 u2} R N (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{max u1 u2} N _inst_5)] {i : LinearMap.{u1, u1, max u1 u2, max u1 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 N (AddCommGroup.toAddCommMonoid.{max u1 u2} M _inst_4) (AddCommGroup.toAddCommMonoid.{max u1 u2} N _inst_5) _inst_6 _inst_7} {f : LinearMap.{u1, u1, max u1 u2, max u1 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 Q (AddCommGroup.toAddCommMonoid.{max u1 u2} M _inst_4) (AddCommGroup.toAddCommMonoid.{max u1 u2} Q _inst_2) _inst_6 _inst_3} {c : Set.{max u1 u2} (Module.Baer.ExtensionOf.{u1, u2} R _inst_1 Q _inst_2 _inst_3 M N _inst_4 _inst_5 _inst_6 _inst_7 i f)} (hchain : IsChain.{max u1 u2} (Module.Baer.ExtensionOf.{u1, u2} R _inst_1 Q _inst_2 _inst_3 M N _inst_4 _inst_5 _inst_6 _inst_7 i f) (LE.le.{max u1 u2} (Module.Baer.ExtensionOf.{u1, u2} R _inst_1 Q _inst_2 _inst_3 M N _inst_4 _inst_5 _inst_6 _inst_7 i f) (Preorder.toLE.{max u1 u2} (Module.Baer.ExtensionOf.{u1, u2} R _inst_1 Q _inst_2 _inst_3 M N _inst_4 _inst_5 _inst_6 _inst_7 i f) (PartialOrder.toPreorder.{max u1 u2} (Module.Baer.ExtensionOf.{u1, u2} R _inst_1 Q _inst_2 _inst_3 M N _inst_4 _inst_5 _inst_6 _inst_7 i f) (SemilatticeInf.toPartialOrder.{max u1 u2} (Module.Baer.ExtensionOf.{u1, u2} R _inst_1 Q _inst_2 _inst_3 M N _inst_4 _inst_5 _inst_6 _inst_7 i f) (Module.Baer.ExtensionOf.semilatticeInf.{u1, u2} R _inst_1 Q _inst_2 _inst_3 M N _inst_4 _inst_5 _inst_6 _inst_7 i f))))) c) (hnonempty : Set.Nonempty.{max u1 u2} (Module.Baer.ExtensionOf.{u1, u2} R _inst_1 Q _inst_2 _inst_3 M N _inst_4 _inst_5 _inst_6 _inst_7 i f) c) (a : Module.Baer.ExtensionOf.{u1, u2} R _inst_1 Q _inst_2 _inst_3 M N _inst_4 _inst_5 _inst_6 _inst_7 i f), (Membership.Mem.{max u1 u2, max u1 u2} (Module.Baer.ExtensionOf.{u1, u2} R _inst_1 Q _inst_2 _inst_3 M N _inst_4 _inst_5 _inst_6 _inst_7 i f) (Set.{max u1 u2} (Module.Baer.ExtensionOf.{u1, u2} R _inst_1 Q _inst_2 _inst_3 M N _inst_4 _inst_5 _inst_6 _inst_7 i f)) (Set.hasMem.{max u1 u2} (Module.Baer.ExtensionOf.{u1, u2} R _inst_1 Q _inst_2 _inst_3 M N _inst_4 _inst_5 _inst_6 _inst_7 i f)) a c) -> (LE.le.{max u1 u2} (Module.Baer.ExtensionOf.{u1, u2} R _inst_1 Q _inst_2 _inst_3 M N _inst_4 _inst_5 _inst_6 _inst_7 i f) (Preorder.toLE.{max u1 u2} (Module.Baer.ExtensionOf.{u1, u2} R _inst_1 Q _inst_2 _inst_3 M N _inst_4 _inst_5 _inst_6 _inst_7 i f) (PartialOrder.toPreorder.{max u1 u2} (Module.Baer.ExtensionOf.{u1, u2} R _inst_1 Q _inst_2 _inst_3 M N _inst_4 _inst_5 _inst_6 _inst_7 i f) (SemilatticeInf.toPartialOrder.{max u1 u2} (Module.Baer.ExtensionOf.{u1, u2} R _inst_1 Q _inst_2 _inst_3 M N _inst_4 _inst_5 _inst_6 _inst_7 i f) (Module.Baer.ExtensionOf.semilatticeInf.{u1, u2} R _inst_1 Q _inst_2 _inst_3 M N _inst_4 _inst_5 _inst_6 _inst_7 i f)))) a (Module.Baer.ExtensionOf.max.{u1, u2} R _inst_1 Q _inst_2 _inst_3 M N _inst_4 _inst_5 _inst_6 _inst_7 i f c hchain hnonempty))
 but is expected to have type
-  forall {R : Type.{u1}} [_inst_1 : Ring.{u1} R] {Q : TypeMax.{u2, u1}} [_inst_2 : AddCommGroup.{max u1 u2} Q] [_inst_3 : Module.{u1, max u1 u2} R Q (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{max u1 u2} Q _inst_2)] {M : Type.{max u1 u2}} {N : Type.{max u1 u2}} [_inst_4 : AddCommGroup.{max u1 u2} M] [_inst_5 : AddCommGroup.{max u1 u2} N] [_inst_6 : Module.{u1, max u1 u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{max u1 u2} M _inst_4)] [_inst_7 : Module.{u1, max u1 u2} R N (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{max u1 u2} N _inst_5)] {i : LinearMap.{u1, u1, max u1 u2, max u1 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 N (AddCommGroup.toAddCommMonoid.{max u1 u2} M _inst_4) (AddCommGroup.toAddCommMonoid.{max u1 u2} N _inst_5) _inst_6 _inst_7} {f : LinearMap.{u1, u1, max u1 u2, max u1 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 Q (AddCommGroup.toAddCommMonoid.{max u1 u2} M _inst_4) (AddCommGroup.toAddCommMonoid.{max u1 u2} Q _inst_2) _inst_6 _inst_3} {c : Set.{max u2 u1} (Module.Baer.ExtensionOf.{u1, u2} R _inst_1 Q _inst_2 _inst_3 M N _inst_4 _inst_5 _inst_6 _inst_7 i f)} (hchain : IsChain.{max u1 u2} (Module.Baer.ExtensionOf.{u1, u2} R _inst_1 Q _inst_2 _inst_3 M N _inst_4 _inst_5 _inst_6 _inst_7 i f) (fun (x._@.Mathlib.Algebra.Module.Injective._hyg.1839 : Module.Baer.ExtensionOf.{u1, u2} R _inst_1 Q _inst_2 _inst_3 M N _inst_4 _inst_5 _inst_6 _inst_7 i f) (x._@.Mathlib.Algebra.Module.Injective._hyg.1841 : Module.Baer.ExtensionOf.{u1, u2} R _inst_1 Q _inst_2 _inst_3 M N _inst_4 _inst_5 _inst_6 _inst_7 i f) => LE.le.{max u1 u2} (Module.Baer.ExtensionOf.{u1, u2} R _inst_1 Q _inst_2 _inst_3 M N _inst_4 _inst_5 _inst_6 _inst_7 i f) (Preorder.toLE.{max u1 u2} (Module.Baer.ExtensionOf.{u1, u2} R _inst_1 Q _inst_2 _inst_3 M N _inst_4 _inst_5 _inst_6 _inst_7 i f) (PartialOrder.toPreorder.{max u1 u2} (Module.Baer.ExtensionOf.{u1, u2} R _inst_1 Q _inst_2 _inst_3 M N _inst_4 _inst_5 _inst_6 _inst_7 i f) (SemilatticeInf.toPartialOrder.{max u1 u2} (Module.Baer.ExtensionOf.{u1, u2} R _inst_1 Q _inst_2 _inst_3 M N _inst_4 _inst_5 _inst_6 _inst_7 i f) (Module.Baer.instSemilatticeInfExtensionOf.{u1, u2} R _inst_1 Q _inst_2 _inst_3 M N _inst_4 _inst_5 _inst_6 _inst_7 i f)))) x._@.Mathlib.Algebra.Module.Injective._hyg.1839 x._@.Mathlib.Algebra.Module.Injective._hyg.1841) c) (hnonempty : Set.Nonempty.{max u1 u2} (Module.Baer.ExtensionOf.{u1, u2} R _inst_1 Q _inst_2 _inst_3 M N _inst_4 _inst_5 _inst_6 _inst_7 i f) c) (a : Module.Baer.ExtensionOf.{u1, u2} R _inst_1 Q _inst_2 _inst_3 M N _inst_4 _inst_5 _inst_6 _inst_7 i f), (Membership.mem.{max u1 u2, max u1 u2} (Module.Baer.ExtensionOf.{u1, u2} R _inst_1 Q _inst_2 _inst_3 M N _inst_4 _inst_5 _inst_6 _inst_7 i f) (Set.{max u2 u1} (Module.Baer.ExtensionOf.{u1, u2} R _inst_1 Q _inst_2 _inst_3 M N _inst_4 _inst_5 _inst_6 _inst_7 i f)) (Set.instMembershipSet.{max u1 u2} (Module.Baer.ExtensionOf.{u1, u2} R _inst_1 Q _inst_2 _inst_3 M N _inst_4 _inst_5 _inst_6 _inst_7 i f)) a c) -> (LE.le.{max u1 u2} (Module.Baer.ExtensionOf.{u1, u2} R _inst_1 Q _inst_2 _inst_3 M N _inst_4 _inst_5 _inst_6 _inst_7 i f) (Preorder.toLE.{max u1 u2} (Module.Baer.ExtensionOf.{u1, u2} R _inst_1 Q _inst_2 _inst_3 M N _inst_4 _inst_5 _inst_6 _inst_7 i f) (PartialOrder.toPreorder.{max u1 u2} (Module.Baer.ExtensionOf.{u1, u2} R _inst_1 Q _inst_2 _inst_3 M N _inst_4 _inst_5 _inst_6 _inst_7 i f) (SemilatticeInf.toPartialOrder.{max u1 u2} (Module.Baer.ExtensionOf.{u1, u2} R _inst_1 Q _inst_2 _inst_3 M N _inst_4 _inst_5 _inst_6 _inst_7 i f) (Module.Baer.instSemilatticeInfExtensionOf.{u1, u2} R _inst_1 Q _inst_2 _inst_3 M N _inst_4 _inst_5 _inst_6 _inst_7 i f)))) a (Module.Baer.ExtensionOf.max.{u1, u2} R _inst_1 Q _inst_2 _inst_3 M N _inst_4 _inst_5 _inst_6 _inst_7 i f c hchain hnonempty))
+  forall {R : Type.{u1}} [_inst_1 : Ring.{u1} R] {Q : TypeMax.{u2, u1}} [_inst_2 : AddCommGroup.{max u1 u2} Q] [_inst_3 : Module.{u1, max u1 u2} R Q (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{max u1 u2} Q _inst_2)] {M : Type.{max u1 u2}} {N : Type.{max u1 u2}} [_inst_4 : AddCommGroup.{max u1 u2} M] [_inst_5 : AddCommGroup.{max u1 u2} N] [_inst_6 : Module.{u1, max u1 u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{max u1 u2} M _inst_4)] [_inst_7 : Module.{u1, max u1 u2} R N (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{max u1 u2} N _inst_5)] {i : LinearMap.{u1, u1, max u1 u2, max u1 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 N (AddCommGroup.toAddCommMonoid.{max u1 u2} M _inst_4) (AddCommGroup.toAddCommMonoid.{max u1 u2} N _inst_5) _inst_6 _inst_7} {f : LinearMap.{u1, u1, max u1 u2, max u1 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 Q (AddCommGroup.toAddCommMonoid.{max u1 u2} M _inst_4) (AddCommGroup.toAddCommMonoid.{max u1 u2} Q _inst_2) _inst_6 _inst_3} {c : Set.{max u2 u1} (Module.Baer.ExtensionOf.{u1, u2} R _inst_1 Q _inst_2 _inst_3 M N _inst_4 _inst_5 _inst_6 _inst_7 i f)} (hchain : IsChain.{max u1 u2} (Module.Baer.ExtensionOf.{u1, u2} R _inst_1 Q _inst_2 _inst_3 M N _inst_4 _inst_5 _inst_6 _inst_7 i f) (fun (x._@.Mathlib.Algebra.Module.Injective._hyg.1845 : Module.Baer.ExtensionOf.{u1, u2} R _inst_1 Q _inst_2 _inst_3 M N _inst_4 _inst_5 _inst_6 _inst_7 i f) (x._@.Mathlib.Algebra.Module.Injective._hyg.1847 : Module.Baer.ExtensionOf.{u1, u2} R _inst_1 Q _inst_2 _inst_3 M N _inst_4 _inst_5 _inst_6 _inst_7 i f) => LE.le.{max u1 u2} (Module.Baer.ExtensionOf.{u1, u2} R _inst_1 Q _inst_2 _inst_3 M N _inst_4 _inst_5 _inst_6 _inst_7 i f) (Preorder.toLE.{max u1 u2} (Module.Baer.ExtensionOf.{u1, u2} R _inst_1 Q _inst_2 _inst_3 M N _inst_4 _inst_5 _inst_6 _inst_7 i f) (PartialOrder.toPreorder.{max u1 u2} (Module.Baer.ExtensionOf.{u1, u2} R _inst_1 Q _inst_2 _inst_3 M N _inst_4 _inst_5 _inst_6 _inst_7 i f) (SemilatticeInf.toPartialOrder.{max u1 u2} (Module.Baer.ExtensionOf.{u1, u2} R _inst_1 Q _inst_2 _inst_3 M N _inst_4 _inst_5 _inst_6 _inst_7 i f) (Module.Baer.instSemilatticeInfExtensionOf.{u1, u2} R _inst_1 Q _inst_2 _inst_3 M N _inst_4 _inst_5 _inst_6 _inst_7 i f)))) x._@.Mathlib.Algebra.Module.Injective._hyg.1845 x._@.Mathlib.Algebra.Module.Injective._hyg.1847) c) (hnonempty : Set.Nonempty.{max u1 u2} (Module.Baer.ExtensionOf.{u1, u2} R _inst_1 Q _inst_2 _inst_3 M N _inst_4 _inst_5 _inst_6 _inst_7 i f) c) (a : Module.Baer.ExtensionOf.{u1, u2} R _inst_1 Q _inst_2 _inst_3 M N _inst_4 _inst_5 _inst_6 _inst_7 i f), (Membership.mem.{max u1 u2, max u1 u2} (Module.Baer.ExtensionOf.{u1, u2} R _inst_1 Q _inst_2 _inst_3 M N _inst_4 _inst_5 _inst_6 _inst_7 i f) (Set.{max u2 u1} (Module.Baer.ExtensionOf.{u1, u2} R _inst_1 Q _inst_2 _inst_3 M N _inst_4 _inst_5 _inst_6 _inst_7 i f)) (Set.instMembershipSet.{max u1 u2} (Module.Baer.ExtensionOf.{u1, u2} R _inst_1 Q _inst_2 _inst_3 M N _inst_4 _inst_5 _inst_6 _inst_7 i f)) a c) -> (LE.le.{max u1 u2} (Module.Baer.ExtensionOf.{u1, u2} R _inst_1 Q _inst_2 _inst_3 M N _inst_4 _inst_5 _inst_6 _inst_7 i f) (Preorder.toLE.{max u1 u2} (Module.Baer.ExtensionOf.{u1, u2} R _inst_1 Q _inst_2 _inst_3 M N _inst_4 _inst_5 _inst_6 _inst_7 i f) (PartialOrder.toPreorder.{max u1 u2} (Module.Baer.ExtensionOf.{u1, u2} R _inst_1 Q _inst_2 _inst_3 M N _inst_4 _inst_5 _inst_6 _inst_7 i f) (SemilatticeInf.toPartialOrder.{max u1 u2} (Module.Baer.ExtensionOf.{u1, u2} R _inst_1 Q _inst_2 _inst_3 M N _inst_4 _inst_5 _inst_6 _inst_7 i f) (Module.Baer.instSemilatticeInfExtensionOf.{u1, u2} R _inst_1 Q _inst_2 _inst_3 M N _inst_4 _inst_5 _inst_6 _inst_7 i f)))) a (Module.Baer.ExtensionOf.max.{u1, u2} R _inst_1 Q _inst_2 _inst_3 M N _inst_4 _inst_5 _inst_6 _inst_7 i f c hchain hnonempty))
 Case conversion may be inaccurate. Consider using '#align module.Baer.extension_of.le_max Module.Baer.ExtensionOf.le_maxₓ'. -/
 theorem ExtensionOf.le_max {c : Set (ExtensionOf i f)} (hchain : IsChain (· ≤ ·) c)
     (hnonempty : c.Nonempty) (a : ExtensionOf i f) (ha : a ∈ c) :
@@ -367,7 +367,7 @@ def ExtensionOfMaxAdjoin.ideal (y : N) : Ideal R :=
 lean 3 declaration is
   forall {R : Type.{u1}} [_inst_1 : Ring.{u1} R] {Q : Type.{max u1 u2}} [_inst_2 : AddCommGroup.{max u1 u2} Q] [_inst_3 : Module.{u1, max u1 u2} R Q (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{max u1 u2} Q _inst_2)] {M : Type.{max u1 u2}} {N : Type.{max u1 u2}} [_inst_4 : AddCommGroup.{max u1 u2} M] [_inst_5 : AddCommGroup.{max u1 u2} N] [_inst_6 : Module.{u1, max u1 u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{max u1 u2} M _inst_4)] [_inst_7 : Module.{u1, max u1 u2} R N (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{max u1 u2} N _inst_5)] (i : LinearMap.{u1, u1, max u1 u2, max u1 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 N (AddCommGroup.toAddCommMonoid.{max u1 u2} M _inst_4) (AddCommGroup.toAddCommMonoid.{max u1 u2} N _inst_5) _inst_6 _inst_7) (f : LinearMap.{u1, u1, max u1 u2, max u1 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 Q (AddCommGroup.toAddCommMonoid.{max u1 u2} M _inst_4) (AddCommGroup.toAddCommMonoid.{max u1 u2} Q _inst_2) _inst_6 _inst_3) [_inst_8 : Fact (Function.Injective.{succ (max u1 u2), succ (max u1 u2)} M N (coeFn.{succ (max u1 u2), succ (max u1 u2)} (LinearMap.{u1, u1, max u1 u2, max u1 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 N (AddCommGroup.toAddCommMonoid.{max u1 u2} M _inst_4) (AddCommGroup.toAddCommMonoid.{max u1 u2} N _inst_5) _inst_6 _inst_7) (fun (_x : LinearMap.{u1, u1, max u1 u2, max u1 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 N (AddCommGroup.toAddCommMonoid.{max u1 u2} M _inst_4) (AddCommGroup.toAddCommMonoid.{max u1 u2} N _inst_5) _inst_6 _inst_7) => M -> N) (LinearMap.hasCoeToFun.{u1, u1, max u1 u2, max u1 u2} R R M N (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{max u1 u2} M _inst_4) (AddCommGroup.toAddCommMonoid.{max u1 u2} N _inst_5) _inst_6 _inst_7 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1)))) i))] (y : N), LinearMap.{u1, u1, u1, max u1 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))) (coeSort.{succ u1, succ (succ u1)} (Ideal.{u1} R (Ring.toSemiring.{u1} R _inst_1)) Type.{u1} (SetLike.hasCoeToSort.{u1, u1} (Ideal.{u1} R (Ring.toSemiring.{u1} R _inst_1)) R (Submodule.setLike.{u1, u1} R R (Ring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R _inst_1)))) (Module.Baer.ExtensionOfMaxAdjoin.ideal.{u1, u2} R _inst_1 Q _inst_2 _inst_3 M N _inst_4 _inst_5 _inst_6 _inst_7 i f _inst_8 y)) Q (Submodule.addCommMonoid.{u1, u1} R R (Ring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (Module.Baer.ExtensionOfMaxAdjoin.ideal.{u1, u2} R _inst_1 Q _inst_2 _inst_3 M N _inst_4 _inst_5 _inst_6 _inst_7 i f _inst_8 y)) (AddCommGroup.toAddCommMonoid.{max u1 u2} Q _inst_2) (Submodule.module.{u1, u1} R R (Ring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (Module.Baer.ExtensionOfMaxAdjoin.ideal.{u1, u2} R _inst_1 Q _inst_2 _inst_3 M N _inst_4 _inst_5 _inst_6 _inst_7 i f _inst_8 y)) _inst_3
 but is expected to have type
-  forall {R : Type.{u1}} [_inst_1 : Ring.{u1} R] {Q : TypeMax.{u2, u1}} [_inst_2 : AddCommGroup.{max u1 u2} Q] [_inst_3 : Module.{u1, max u1 u2} R Q (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{max u1 u2} Q _inst_2)] {M : Type.{max u1 u2}} {N : Type.{max u1 u2}} [_inst_4 : AddCommGroup.{max u1 u2} M] [_inst_5 : AddCommGroup.{max u1 u2} N] [_inst_6 : Module.{u1, max u1 u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{max u1 u2} M _inst_4)] [_inst_7 : Module.{u1, max u1 u2} R N (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{max u1 u2} N _inst_5)] (i : LinearMap.{u1, u1, max u1 u2, max u1 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 N (AddCommGroup.toAddCommMonoid.{max u1 u2} M _inst_4) (AddCommGroup.toAddCommMonoid.{max u1 u2} N _inst_5) _inst_6 _inst_7) (f : LinearMap.{u1, u1, max u1 u2, max u1 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 Q (AddCommGroup.toAddCommMonoid.{max u1 u2} M _inst_4) (AddCommGroup.toAddCommMonoid.{max u1 u2} Q _inst_2) _inst_6 _inst_3) [_inst_8 : Fact (Function.Injective.{max (succ u1) (succ u2), max (succ u1) (succ u2)} M N (FunLike.coe.{max (succ u1) (succ u2), max (succ u1) (succ u2), max (succ u1) (succ u2)} (LinearMap.{u1, u1, max u1 u2, max u1 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 N (AddCommGroup.toAddCommMonoid.{max u1 u2} M _inst_4) (AddCommGroup.toAddCommMonoid.{max u1 u2} N _inst_5) _inst_6 _inst_7) M (fun (_x : M) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : M) => N) _x) (LinearMap.instFunLikeLinearMap.{u1, u1, max u1 u2, max u1 u2} R R M N (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{max u1 u2} M _inst_4) (AddCommGroup.toAddCommMonoid.{max u1 u2} N _inst_5) _inst_6 _inst_7 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1)))) i))] (y : N), LinearMap.{u1, u1, u1, max u1 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))) (Subtype.{succ u1} R (fun (x : R) => Membership.mem.{u1, u1} R (Ideal.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (SetLike.instMembership.{u1, u1} (Ideal.{u1} R (Ring.toSemiring.{u1} R _inst_1)) R (Submodule.setLike.{u1, u1} R R (Ring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R _inst_1)))) x (Module.Baer.ExtensionOfMaxAdjoin.ideal.{u1, u2} R _inst_1 Q _inst_2 _inst_3 M N _inst_4 _inst_5 _inst_6 _inst_7 i f _inst_8 y))) Q (Submodule.addCommMonoid.{u1, u1} R R (Ring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (Module.Baer.ExtensionOfMaxAdjoin.ideal.{u1, u2} R _inst_1 Q _inst_2 _inst_3 M N _inst_4 _inst_5 _inst_6 _inst_7 i f _inst_8 y)) (AddCommGroup.toAddCommMonoid.{max u1 u2} Q _inst_2) (Submodule.module.{u1, u1} R R (Ring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (Module.Baer.ExtensionOfMaxAdjoin.ideal.{u1, u2} R _inst_1 Q _inst_2 _inst_3 M N _inst_4 _inst_5 _inst_6 _inst_7 i f _inst_8 y)) _inst_3
+  forall {R : Type.{u1}} [_inst_1 : Ring.{u1} R] {Q : TypeMax.{u2, u1}} [_inst_2 : AddCommGroup.{max u1 u2} Q] [_inst_3 : Module.{u1, max u1 u2} R Q (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{max u1 u2} Q _inst_2)] {M : Type.{max u1 u2}} {N : Type.{max u1 u2}} [_inst_4 : AddCommGroup.{max u1 u2} M] [_inst_5 : AddCommGroup.{max u1 u2} N] [_inst_6 : Module.{u1, max u1 u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{max u1 u2} M _inst_4)] [_inst_7 : Module.{u1, max u1 u2} R N (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{max u1 u2} N _inst_5)] (i : LinearMap.{u1, u1, max u1 u2, max u1 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 N (AddCommGroup.toAddCommMonoid.{max u1 u2} M _inst_4) (AddCommGroup.toAddCommMonoid.{max u1 u2} N _inst_5) _inst_6 _inst_7) (f : LinearMap.{u1, u1, max u1 u2, max u1 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 Q (AddCommGroup.toAddCommMonoid.{max u1 u2} M _inst_4) (AddCommGroup.toAddCommMonoid.{max u1 u2} Q _inst_2) _inst_6 _inst_3) [_inst_8 : Fact (Function.Injective.{max (succ u1) (succ u2), max (succ u1) (succ u2)} M N (FunLike.coe.{max (succ u1) (succ u2), max (succ u1) (succ u2), max (succ u1) (succ u2)} (LinearMap.{u1, u1, max u1 u2, max u1 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 N (AddCommGroup.toAddCommMonoid.{max u1 u2} M _inst_4) (AddCommGroup.toAddCommMonoid.{max u1 u2} N _inst_5) _inst_6 _inst_7) M (fun (_x : M) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : M) => N) _x) (LinearMap.instFunLikeLinearMap.{u1, u1, max u1 u2, max u1 u2} R R M N (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{max u1 u2} M _inst_4) (AddCommGroup.toAddCommMonoid.{max u1 u2} N _inst_5) _inst_6 _inst_7 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1)))) i))] (y : N), LinearMap.{u1, u1, u1, max u1 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))) (ModuleCat.carrier.{u1, u1} R _inst_1 (ModuleCat.of.{u1, u1} R _inst_1 (Subtype.{succ u1} R (fun (x : R) => Membership.mem.{u1, u1} R (Submodule.{u1, u1} R R (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} R (Ring.toAddCommGroup.{u1} R _inst_1)) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (SetLike.instMembership.{u1, u1} (Submodule.{u1, u1} R R (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} R (Ring.toAddCommGroup.{u1} R _inst_1)) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R _inst_1))) R (Submodule.setLike.{u1, u1} R R (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} R (Ring.toAddCommGroup.{u1} R _inst_1)) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R _inst_1)))) x (Module.Baer.ExtensionOfMaxAdjoin.ideal.{u1, u2} R _inst_1 Q _inst_2 _inst_3 M N _inst_4 _inst_5 _inst_6 _inst_7 i f _inst_8 y))) (Submodule.addCommGroup.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R _inst_1) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (Module.Baer.ExtensionOfMaxAdjoin.ideal.{u1, u2} R _inst_1 Q _inst_2 _inst_3 M N _inst_4 _inst_5 _inst_6 _inst_7 i f _inst_8 y)) (Submodule.module.{u1, u1} R R (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} R (Ring.toAddCommGroup.{u1} R _inst_1)) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (Module.Baer.ExtensionOfMaxAdjoin.ideal.{u1, u2} R _inst_1 Q _inst_2 _inst_3 M N _inst_4 _inst_5 _inst_6 _inst_7 i f _inst_8 y)))) Q (AddCommGroup.toAddCommMonoid.{u1} 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(AddCommGroup.toAddCommMonoid.{max u1 u2} Q _inst_2) (ModuleCat.isModule.{u1, u1} R _inst_1 (ModuleCat.of.{u1, u1} R _inst_1 (Subtype.{succ u1} R (fun (x : R) => Membership.mem.{u1, u1} R (Submodule.{u1, u1} R R (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} R (Ring.toAddCommGroup.{u1} R _inst_1)) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (SetLike.instMembership.{u1, u1} (Submodule.{u1, u1} R R (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} R (Ring.toAddCommGroup.{u1} R _inst_1)) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R _inst_1))) R (Submodule.setLike.{u1, u1} R R (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} R (Ring.toAddCommGroup.{u1} R _inst_1)) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R _inst_1)))) x (Module.Baer.ExtensionOfMaxAdjoin.ideal.{u1, u2} R _inst_1 Q _inst_2 _inst_3 M N _inst_4 _inst_5 _inst_6 _inst_7 i f _inst_8 y))) (Submodule.addCommGroup.{u1, u1} R R _inst_1 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 Case conversion may be inaccurate. Consider using '#align module.Baer.extension_of_max_adjoin.ideal_to Module.Baer.ExtensionOfMaxAdjoin.idealToₓ'. -/
 /-- A linear map `I ⟶ Q` by `x ↦ f' (x • y)` where `f'` is the maximal extension-/
 def ExtensionOfMaxAdjoin.idealTo (y : N) : ExtensionOfMaxAdjoin.ideal i f y →ₗ[R] Q
@@ -393,7 +393,7 @@ def ExtensionOfMaxAdjoin.extendIdealTo (h : Module.Baer R Q) (y : N) : R →ₗ[
 lean 3 declaration is
   forall {R : Type.{u1}} [_inst_1 : Ring.{u1} R] {Q : Type.{max u1 u2}} [_inst_2 : AddCommGroup.{max u1 u2} Q] [_inst_3 : Module.{u1, max u1 u2} R Q (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{max u1 u2} Q _inst_2)] {M : Type.{max u1 u2}} {N : Type.{max u1 u2}} [_inst_4 : AddCommGroup.{max u1 u2} M] [_inst_5 : AddCommGroup.{max u1 u2} N] [_inst_6 : Module.{u1, max u1 u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{max u1 u2} M _inst_4)] [_inst_7 : Module.{u1, max u1 u2} R N (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{max u1 u2} N _inst_5)] (i : LinearMap.{u1, u1, max u1 u2, max u1 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 N (AddCommGroup.toAddCommMonoid.{max u1 u2} M _inst_4) (AddCommGroup.toAddCommMonoid.{max u1 u2} N _inst_5) _inst_6 _inst_7) (f : LinearMap.{u1, u1, max u1 u2, max u1 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 Q (AddCommGroup.toAddCommMonoid.{max u1 u2} M _inst_4) (AddCommGroup.toAddCommMonoid.{max u1 u2} Q _inst_2) _inst_6 _inst_3) [_inst_8 : Fact (Function.Injective.{succ (max u1 u2), succ (max u1 u2)} M N (coeFn.{succ (max u1 u2), succ (max u1 u2)} (LinearMap.{u1, u1, max u1 u2, max u1 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 N (AddCommGroup.toAddCommMonoid.{max u1 u2} M _inst_4) (AddCommGroup.toAddCommMonoid.{max u1 u2} N _inst_5) _inst_6 _inst_7) (fun (_x : LinearMap.{u1, u1, max u1 u2, max u1 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 N (AddCommGroup.toAddCommMonoid.{max u1 u2} M 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 but is expected to have type
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Membership.mem.{u1, u1} R (Submodule.{u1, u1} R R (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} R (Ring.toAddCommGroup.{u1} R _inst_1)) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (SetLike.instMembership.{u1, u1} (Submodule.{u1, u1} R R (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} R (Ring.toAddCommGroup.{u1} R _inst_1)) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R _inst_1))) R (Submodule.setLike.{u1, u1} R R (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} R (Ring.toAddCommGroup.{u1} R _inst_1)) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R _inst_1)))) x (Module.Baer.ExtensionOfMaxAdjoin.ideal.{u1, u2} R _inst_1 Q _inst_2 _inst_3 M N _inst_4 _inst_5 _inst_6 _inst_7 i f _inst_8 y))) (Submodule.addCommGroup.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R _inst_1) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (Module.Baer.ExtensionOfMaxAdjoin.ideal.{u1, u2} R _inst_1 Q _inst_2 _inst_3 M N _inst_4 _inst_5 _inst_6 _inst_7 i f _inst_8 y)) (Submodule.module.{u1, u1} R R (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} R (Ring.toAddCommGroup.{u1} R _inst_1)) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (Module.Baer.ExtensionOfMaxAdjoin.ideal.{u1, u2} R _inst_1 Q _inst_2 _inst_3 M N _inst_4 _inst_5 _inst_6 _inst_7 i f _inst_8 y)))) => Q) _x) (LinearMap.instFunLikeLinearMap.{u1, u1, u1, max u1 u2} R R (ModuleCat.carrier.{u1, u1} R _inst_1 (ModuleCat.of.{u1, u1} R _inst_1 (Subtype.{succ u1} R (fun (x : R) => Membership.mem.{u1, u1} R (Submodule.{u1, u1} R R (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} R (Ring.toAddCommGroup.{u1} R _inst_1)) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (SetLike.instMembership.{u1, u1} (Submodule.{u1, u1} R R (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} R (Ring.toAddCommGroup.{u1} R _inst_1)) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R 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Q _inst_2 _inst_3 M N _inst_4 _inst_5 _inst_6 _inst_7 i f _inst_8 y))))) (AddCommGroup.toAddCommMonoid.{max u1 u2} Q _inst_2) (ModuleCat.isModule.{u1, u1} R _inst_1 (ModuleCat.of.{u1, u1} R _inst_1 (Subtype.{succ u1} R (fun (x : R) => Membership.mem.{u1, u1} R (Submodule.{u1, u1} R R (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} R (Ring.toAddCommGroup.{u1} R _inst_1)) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (SetLike.instMembership.{u1, u1} (Submodule.{u1, u1} R R (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} R (Ring.toAddCommGroup.{u1} R _inst_1)) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R _inst_1))) R (Submodule.setLike.{u1, u1} R R (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} R (Ring.toAddCommGroup.{u1} R _inst_1)) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R _inst_1)))) x (Module.Baer.ExtensionOfMaxAdjoin.ideal.{u1, u2} R _inst_1 Q _inst_2 _inst_3 M N _inst_4 _inst_5 _inst_6 _inst_7 i f _inst_8 y))) (Submodule.addCommGroup.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R _inst_1) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (Module.Baer.ExtensionOfMaxAdjoin.ideal.{u1, u2} R _inst_1 Q _inst_2 _inst_3 M N _inst_4 _inst_5 _inst_6 _inst_7 i f _inst_8 y)) (Submodule.module.{u1, u1} R R (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} R (Ring.toAddCommGroup.{u1} R _inst_1)) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (Module.Baer.ExtensionOfMaxAdjoin.ideal.{u1, u2} R _inst_1 Q _inst_2 _inst_3 M N _inst_4 _inst_5 _inst_6 _inst_7 i f _inst_8 y)))) _inst_3 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1)))) (Module.Baer.ExtensionOfMaxAdjoin.idealTo.{u1, u2} R _inst_1 Q _inst_2 _inst_3 M N _inst_4 _inst_5 _inst_6 _inst_7 i f _inst_8 y) (Subtype.mk.{succ u1} R (fun (x : R) => Membership.mem.{u1, u1} R (Submodule.{u1, u1} R R (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} R (Ring.toAddCommGroup.{u1} R _inst_1)) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (SetLike.instMembership.{u1, u1} (Submodule.{u1, u1} R R (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} R (Ring.toAddCommGroup.{u1} R _inst_1)) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R _inst_1))) R (Submodule.setLike.{u1, u1} R R (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} R (Ring.toAddCommGroup.{u1} R _inst_1)) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R _inst_1)))) x (Module.Baer.ExtensionOfMaxAdjoin.ideal.{u1, u2} R _inst_1 Q _inst_2 _inst_3 M N _inst_4 _inst_5 _inst_6 _inst_7 i f _inst_8 y)) x mem))
 Case conversion may be inaccurate. Consider using '#align module.Baer.extension_of_max_adjoin.extend_ideal_to_is_extension Module.Baer.ExtensionOfMaxAdjoin.extendIdealTo_is_extensionₓ'. -/
 theorem ExtensionOfMaxAdjoin.extendIdealTo_is_extension (h : Module.Baer R Q) (y : N) :
     ∀ (x : R) (mem : x ∈ ExtensionOfMaxAdjoin.ideal i f y),

mathlib commit https://github.com/leanprover-community/mathlib/commit/e3fb84046afd187b710170887195d50bada934ee

@@ -215,13 +215,13 @@ Case conversion may be inaccurate. Consider using '#align module.Baer.extension_
 def ExtensionOf.max {c : Set (ExtensionOf i f)} (hchain : IsChain (· ≤ ·) c)
     (hnonempty : c.Nonempty) : ExtensionOf i f :=
   {
-    LinearPMap.supₛ _
+    LinearPMap.sSup _
       (IsChain.directedOn <|
         chain_linearPMap_of_chain_extensionOf
           hchain) with
     le :=
       le_trans hnonempty.some.le <|
-        (LinearPMap.le_supₛ _ <|
+        (LinearPMap.le_sSup _ <|
             (Set.mem_image _ _ _).mpr ⟨hnonempty.some, hnonempty.choose_spec, rfl⟩).1
     is_extension := fun m =>
       by
@@ -229,7 +229,7 @@ def ExtensionOf.max {c : Set (ExtensionOf i f)} (hchain : IsChain (· ≤ ·) c)
       symm
       generalize_proofs _ h0 h1
       exact
-        LinearPMap.supₛ_apply (IsChain.directedOn <| chain_linear_pmap_of_chain_extension_of hchain)
+        LinearPMap.sSup_apply (IsChain.directedOn <| chain_linear_pmap_of_chain_extension_of hchain)
           ((Set.mem_image _ _ _).mpr ⟨hnonempty.some, hnonempty.some_spec, rfl⟩) ⟨i m, h1⟩ }
 #align module.Baer.extension_of.max Module.Baer.ExtensionOf.max
 
@@ -242,7 +242,7 @@ Case conversion may be inaccurate. Consider using '#align module.Baer.extension_
 theorem ExtensionOf.le_max {c : Set (ExtensionOf i f)} (hchain : IsChain (· ≤ ·) c)
     (hnonempty : c.Nonempty) (a : ExtensionOf i f) (ha : a ∈ c) :
     a ≤ ExtensionOf.max hchain hnonempty :=
-  LinearPMap.le_supₛ (IsChain.directedOn <| chain_linearPMap_of_chain_extensionOf hchain) <|
+  LinearPMap.le_sSup (IsChain.directedOn <| chain_linearPMap_of_chain_extensionOf hchain) <|
     (Set.mem_image _ _ _).mpr ⟨a, ha, rfl⟩
 #align module.Baer.extension_of.le_max Module.Baer.ExtensionOf.le_max
 

mathlib commit https://github.com/leanprover-community/mathlib/commit/403190b5419b3f03f1a2893ad9352ca7f7d8bff6

@@ -4,7 +4,7 @@ Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Jujian Zhang
 
 ! This file was ported from Lean 3 source module algebra.module.injective
-! leanprover-community/mathlib commit f8d8465c3c392a93b9ed226956e26dee00975946
+! leanprover-community/mathlib commit bd15ff41b70f5e2cc210f26f25a8d5c53b20d3de
 ! Please do not edit these lines, except to modify the commit id
 ! if you have ported upstream changes.
 -/
@@ -16,6 +16,9 @@ import Mathbin.LinearAlgebra.LinearPmap
 /-!
 # Injective modules
 
+> THIS FILE IS SYNCHRONIZED WITH MATHLIB4.
+> Any changes to this file require a corresponding PR to mathlib4.
+
 ## Main definitions
 
 * `module.injective`: an `R`-module `Q` is injective if and only if every injective `R`-linear

mathlib commit https://github.com/leanprover-community/mathlib/commit/28b2a92f2996d28e580450863c130955de0ed398

@@ -44,6 +44,7 @@ universe u v
 
 variable (R : Type u) [Ring R] (Q : Type max u v) [AddCommGroup Q] [Module R Q]
 
+#print Module.Injective /-
 /--
 An `R`-module `Q` is injective if and only if every injective `R`-linear map descends to a linear
 map to `Q`, i.e. in the following diagram, if `f` is injective then there is an `R`-linear map
@@ -62,7 +63,9 @@ class Module.Injective : Prop where
       (f : X →ₗ[R] Y) (hf : Function.Injective f) (g : X →ₗ[R] Q),
       ∃ h : Y →ₗ[R] Q, ∀ x, h (f x) = g x
 #align module.injective Module.Injective
+-/
 
+#print Module.injective_object_of_injective_module /-
 theorem Module.injective_object_of_injective_module [Module.Injective.{u, v} R Q] :
     CategoryTheory.Injective.{max u v} (⟨Q⟩ : ModuleCat.{max u v} R) :=
   {
@@ -71,7 +74,9 @@ theorem Module.injective_object_of_injective_module [Module.Injective.{u, v} R Q
       rcases Module.Injective.out X Y f ((ModuleCat.mono_iff_injective f).mp mn) g with ⟨h, eq1⟩
       exact ⟨h, LinearMap.ext eq1⟩ }
 #align module.injective_object_of_injective_module Module.injective_object_of_injective_module
+-/
 
+#print Module.injective_module_of_injective_object /-
 theorem Module.injective_module_of_injective_object
     [CategoryTheory.Injective.{max u v} (⟨Q⟩ : ModuleCat.{max u v} R)] :
     Module.Injective.{u, v} R Q :=
@@ -83,19 +88,24 @@ theorem Module.injective_module_of_injective_object
         ⟨h, rfl⟩
       exact ⟨h, fun x => rfl⟩ }
 #align module.injective_module_of_injective_object Module.injective_module_of_injective_object
+-/
 
+#print Module.injective_iff_injective_object /-
 theorem Module.injective_iff_injective_object :
     Module.Injective.{u, v} R Q ↔
       CategoryTheory.Injective.{max u v} (⟨Q⟩ : ModuleCat.{max u v} R) :=
   ⟨fun h => @Module.injective_object_of_injective_module R _ Q _ _ h, fun h =>
     @Module.injective_module_of_injective_object R _ Q _ _ h⟩
 #align module.injective_iff_injective_object Module.injective_iff_injective_object
+-/
 
+#print Module.Baer /-
 /-- An `R`-module `Q` satisfies Baer's criterion if any `R`-linear map from an `ideal R` extends to
 an `R`-linear map `R ⟶ Q`-/
 def Module.Baer : Prop :=
   ∀ (I : Ideal R) (g : I →ₗ[R] Q), ∃ g' : R →ₗ[R] Q, ∀ (x : R) (mem : x ∈ I), g' x = g ⟨x, mem⟩
 #align module.Baer Module.Baer
+-/
 
 namespace Module.Baer
 
@@ -103,6 +113,7 @@ variable {R Q} {M N : Type max u v} [AddCommGroup M] [AddCommGroup N]
 
 variable [Module R M] [Module R N] (i : M →ₗ[R] N) (f : M →ₗ[R] Q)
 
+#print Module.Baer.ExtensionOf /-
 /-- If we view `M` as a submodule of `N` via the injective linear map `i : M ↪ N`, then a submodule
 between `M` and `N` is a submodule `N'` of `N`. To prove Baer's criterion, we need to consider
 pairs of `(N', f')` such that `M ≤ N' ≤ N` and `f'` extends `f`. -/
@@ -110,11 +121,18 @@ structure ExtensionOf extends LinearPMap R N Q where
   le : i.range ≤ domain
   is_extension : ∀ m : M, f m = to_linear_pmap ⟨i m, le ⟨m, rfl⟩⟩
 #align module.Baer.extension_of Module.Baer.ExtensionOf
+-/
 
 section Ext
 
 variable {i f}
 
+/- warning: module.Baer.extension_of.ext -> Module.Baer.ExtensionOf.ext is a dubious translation:
+lean 3 declaration is
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+Case conversion may be inaccurate. Consider using '#align module.Baer.extension_of.ext Module.Baer.ExtensionOf.extₓ'. -/
 @[ext]
 theorem ExtensionOf.ext {a b : ExtensionOf i f} (domain_eq : a.domain = b.domain)
     (to_fun_eq :
@@ -126,6 +144,12 @@ theorem ExtensionOf.ext {a b : ExtensionOf i f} (domain_eq : a.domain = b.domain
   exact LinearPMap.ext domain_eq to_fun_eq
 #align module.Baer.extension_of.ext Module.Baer.ExtensionOf.ext
 
+/- warning: module.Baer.extension_of.ext_iff -> Module.Baer.ExtensionOf.ext_iff is a dubious translation:
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+Case conversion may be inaccurate. Consider using '#align module.Baer.extension_of.ext_iff Module.Baer.ExtensionOf.ext_iffₓ'. -/
 theorem ExtensionOf.ext_iff {a b : ExtensionOf i f} :
     a = b ↔
       ∃ domain_eq : a.domain = b.domain,
@@ -164,6 +188,12 @@ instance : SemilatticeInf (ExtensionOf i f) :=
 
 variable {R i f}
 
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+  forall {R : Type.{u1}} [_inst_1 : Ring.{u1} R] {Q : Type.{max u1 u2}} [_inst_2 : AddCommGroup.{max u1 u2} Q] [_inst_3 : Module.{u1, max u1 u2} R Q (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{max u1 u2} Q _inst_2)] {M : Type.{max u1 u2}} {N : Type.{max u1 u2}} [_inst_4 : AddCommGroup.{max u1 u2} M] [_inst_5 : AddCommGroup.{max u1 u2} N] [_inst_6 : Module.{u1, max u1 u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{max u1 u2} M _inst_4)] [_inst_7 : Module.{u1, max u1 u2} R N (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{max u1 u2} N _inst_5)] {i : LinearMap.{u1, u1, max u1 u2, max u1 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 N (AddCommGroup.toAddCommMonoid.{max u1 u2} M _inst_4) (AddCommGroup.toAddCommMonoid.{max u1 u2} N _inst_5) _inst_6 _inst_7} {f : LinearMap.{u1, u1, max u1 u2, max u1 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 Q (AddCommGroup.toAddCommMonoid.{max u1 u2} M _inst_4) (AddCommGroup.toAddCommMonoid.{max u1 u2} Q _inst_2) _inst_6 _inst_3} {c : Set.{max u1 u2} (Module.Baer.ExtensionOf.{u1, u2} R _inst_1 Q _inst_2 _inst_3 M N _inst_4 _inst_5 _inst_6 _inst_7 i f)}, (IsChain.{max u1 u2} (Module.Baer.ExtensionOf.{u1, u2} R _inst_1 Q _inst_2 _inst_3 M N _inst_4 _inst_5 _inst_6 _inst_7 i f) (LE.le.{max u1 u2} (Module.Baer.ExtensionOf.{u1, u2} R _inst_1 Q _inst_2 _inst_3 M N _inst_4 _inst_5 _inst_6 _inst_7 i f) (Preorder.toLE.{max u1 u2} (Module.Baer.ExtensionOf.{u1, u2} R _inst_1 Q _inst_2 _inst_3 M N _inst_4 _inst_5 _inst_6 _inst_7 i f) (PartialOrder.toPreorder.{max u1 u2} (Module.Baer.ExtensionOf.{u1, u2} R _inst_1 Q _inst_2 _inst_3 M N _inst_4 _inst_5 _inst_6 _inst_7 i f) (SemilatticeInf.toPartialOrder.{max u1 u2} (Module.Baer.ExtensionOf.{u1, u2} R _inst_1 Q _inst_2 _inst_3 M N _inst_4 _inst_5 _inst_6 _inst_7 i f) (Module.Baer.ExtensionOf.semilatticeInf.{u1, u2} R _inst_1 Q _inst_2 _inst_3 M N _inst_4 _inst_5 _inst_6 _inst_7 i f))))) c) -> (IsChain.{max u1 u2} (LinearPMap.{u1, max u1 u2, max u1 u2} R _inst_1 N _inst_5 _inst_7 Q _inst_2 _inst_3) (LE.le.{max u1 u2} (LinearPMap.{u1, max u1 u2, max u1 u2} R _inst_1 N _inst_5 _inst_7 Q _inst_2 _inst_3) (LinearPMap.le.{u1, max u1 u2, max u1 u2} R _inst_1 N _inst_5 _inst_7 Q _inst_2 _inst_3)) (Set.image.{max u1 u2, max u1 u2} (Module.Baer.ExtensionOf.{u1, u2} R _inst_1 Q _inst_2 _inst_3 M N _inst_4 _inst_5 _inst_6 _inst_7 i f) (LinearPMap.{u1, max u1 u2, max u1 u2} R _inst_1 N _inst_5 _inst_7 Q _inst_2 _inst_3) (fun (x : Module.Baer.ExtensionOf.{u1, u2} R _inst_1 Q _inst_2 _inst_3 M N _inst_4 _inst_5 _inst_6 _inst_7 i f) => Module.Baer.ExtensionOf.toLinearPmap.{u1, u2} R _inst_1 Q _inst_2 _inst_3 M N _inst_4 _inst_5 _inst_6 _inst_7 i f x) c))
+but is expected to have type
+  forall {R : Type.{u1}} [_inst_1 : Ring.{u1} R] {Q : TypeMax.{u2, u1}} [_inst_2 : AddCommGroup.{max u1 u2} Q] [_inst_3 : Module.{u1, max u1 u2} R Q (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{max u1 u2} Q _inst_2)] {M : Type.{max u1 u2}} {N : Type.{max u1 u2}} [_inst_4 : AddCommGroup.{max u1 u2} M] [_inst_5 : AddCommGroup.{max u1 u2} N] [_inst_6 : Module.{u1, max u1 u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{max u1 u2} M _inst_4)] [_inst_7 : Module.{u1, max u1 u2} R N (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{max u1 u2} N _inst_5)] {i : LinearMap.{u1, u1, max u1 u2, max u1 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 N (AddCommGroup.toAddCommMonoid.{max u1 u2} M _inst_4) (AddCommGroup.toAddCommMonoid.{max u1 u2} N _inst_5) _inst_6 _inst_7} {f : LinearMap.{u1, u1, max u1 u2, max u1 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 Q (AddCommGroup.toAddCommMonoid.{max u1 u2} M _inst_4) (AddCommGroup.toAddCommMonoid.{max u1 u2} Q _inst_2) _inst_6 _inst_3} {c : Set.{max u2 u1} (Module.Baer.ExtensionOf.{u1, u2} R _inst_1 Q _inst_2 _inst_3 M N _inst_4 _inst_5 _inst_6 _inst_7 i f)}, (IsChain.{max u1 u2} (Module.Baer.ExtensionOf.{u1, u2} R _inst_1 Q _inst_2 _inst_3 M N _inst_4 _inst_5 _inst_6 _inst_7 i f) (fun (x._@.Mathlib.Algebra.Module.Injective._hyg.1527 : Module.Baer.ExtensionOf.{u1, u2} R _inst_1 Q _inst_2 _inst_3 M N _inst_4 _inst_5 _inst_6 _inst_7 i f) (x._@.Mathlib.Algebra.Module.Injective._hyg.1529 : Module.Baer.ExtensionOf.{u1, u2} R _inst_1 Q _inst_2 _inst_3 M N _inst_4 _inst_5 _inst_6 _inst_7 i f) => LE.le.{max u1 u2} (Module.Baer.ExtensionOf.{u1, u2} R _inst_1 Q _inst_2 _inst_3 M N _inst_4 _inst_5 _inst_6 _inst_7 i f) (Preorder.toLE.{max u1 u2} (Module.Baer.ExtensionOf.{u1, u2} R _inst_1 Q _inst_2 _inst_3 M N _inst_4 _inst_5 _inst_6 _inst_7 i f) (PartialOrder.toPreorder.{max u1 u2} (Module.Baer.ExtensionOf.{u1, u2} R _inst_1 Q _inst_2 _inst_3 M N _inst_4 _inst_5 _inst_6 _inst_7 i f) (SemilatticeInf.toPartialOrder.{max u1 u2} (Module.Baer.ExtensionOf.{u1, u2} R _inst_1 Q _inst_2 _inst_3 M N _inst_4 _inst_5 _inst_6 _inst_7 i f) (Module.Baer.instSemilatticeInfExtensionOf.{u1, u2} R _inst_1 Q _inst_2 _inst_3 M N _inst_4 _inst_5 _inst_6 _inst_7 i f)))) x._@.Mathlib.Algebra.Module.Injective._hyg.1527 x._@.Mathlib.Algebra.Module.Injective._hyg.1529) c) -> (IsChain.{max u1 u2} (LinearPMap.{u1, max u1 u2, max u1 u2} R _inst_1 N _inst_5 _inst_7 Q _inst_2 _inst_3) (fun (x._@.Mathlib.Algebra.Module.Injective._hyg.1546 : LinearPMap.{u1, max u1 u2, max u1 u2} R _inst_1 N _inst_5 _inst_7 Q _inst_2 _inst_3) (x._@.Mathlib.Algebra.Module.Injective._hyg.1548 : LinearPMap.{u1, max u1 u2, max u1 u2} R _inst_1 N _inst_5 _inst_7 Q _inst_2 _inst_3) => LE.le.{max u1 u2} (LinearPMap.{u1, max u1 u2, max u1 u2} R _inst_1 N _inst_5 _inst_7 Q _inst_2 _inst_3) (LinearPMap.le.{u1, max u1 u2, max u1 u2} R _inst_1 N _inst_5 _inst_7 Q _inst_2 _inst_3) x._@.Mathlib.Algebra.Module.Injective._hyg.1546 x._@.Mathlib.Algebra.Module.Injective._hyg.1548) (Set.image.{max u1 u2, max u1 u2} (Module.Baer.ExtensionOf.{u1, u2} R _inst_1 Q _inst_2 _inst_3 M N _inst_4 _inst_5 _inst_6 _inst_7 i f) (LinearPMap.{u1, max u1 u2, max u1 u2} R _inst_1 N _inst_5 _inst_7 Q _inst_2 _inst_3) (fun (x : Module.Baer.ExtensionOf.{u1, u2} R _inst_1 Q _inst_2 _inst_3 M N _inst_4 _inst_5 _inst_6 _inst_7 i f) => Module.Baer.ExtensionOf.toLinearPMap.{u1, u2} R _inst_1 Q _inst_2 _inst_3 M N _inst_4 _inst_5 _inst_6 _inst_7 i f x) c))
+Case conversion may be inaccurate. Consider using '#align module.Baer.chain_linear_pmap_of_chain_extension_of Module.Baer.chain_linearPMap_of_chain_extensionOfₓ'. -/
 theorem chain_linearPMap_of_chain_extensionOf {c : Set (ExtensionOf i f)}
     (hchain : IsChain (· ≤ ·) c) :
     IsChain (· ≤ ·) <| (fun x : ExtensionOf i f => x.toLinearPMap) '' c :=
@@ -172,6 +202,12 @@ theorem chain_linearPMap_of_chain_extensionOf {c : Set (ExtensionOf i f)}
   exact hchain a_mem b_mem (ne_of_apply_ne _ neq)
 #align module.Baer.chain_linear_pmap_of_chain_extension_of Module.Baer.chain_linearPMap_of_chain_extensionOf
 
+/- warning: module.Baer.extension_of.max -> Module.Baer.ExtensionOf.max is a dubious translation:
+lean 3 declaration is
+  forall {R : Type.{u1}} [_inst_1 : Ring.{u1} R] {Q : Type.{max u1 u2}} [_inst_2 : AddCommGroup.{max u1 u2} Q] [_inst_3 : Module.{u1, max u1 u2} R Q (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{max u1 u2} Q _inst_2)] {M : Type.{max u1 u2}} {N : Type.{max u1 u2}} [_inst_4 : AddCommGroup.{max u1 u2} M] [_inst_5 : AddCommGroup.{max u1 u2} N] [_inst_6 : Module.{u1, max u1 u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{max u1 u2} M _inst_4)] [_inst_7 : Module.{u1, max u1 u2} R N (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{max u1 u2} N _inst_5)] {i : LinearMap.{u1, u1, max u1 u2, max u1 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 N (AddCommGroup.toAddCommMonoid.{max u1 u2} M _inst_4) (AddCommGroup.toAddCommMonoid.{max u1 u2} N _inst_5) _inst_6 _inst_7} {f : LinearMap.{u1, u1, max u1 u2, max u1 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 Q (AddCommGroup.toAddCommMonoid.{max u1 u2} M _inst_4) (AddCommGroup.toAddCommMonoid.{max u1 u2} Q _inst_2) _inst_6 _inst_3} {c : Set.{max u1 u2} (Module.Baer.ExtensionOf.{u1, u2} R _inst_1 Q _inst_2 _inst_3 M N _inst_4 _inst_5 _inst_6 _inst_7 i f)}, (IsChain.{max u1 u2} (Module.Baer.ExtensionOf.{u1, u2} R _inst_1 Q _inst_2 _inst_3 M N _inst_4 _inst_5 _inst_6 _inst_7 i f) (LE.le.{max u1 u2} (Module.Baer.ExtensionOf.{u1, u2} R _inst_1 Q _inst_2 _inst_3 M N _inst_4 _inst_5 _inst_6 _inst_7 i f) (Preorder.toLE.{max u1 u2} (Module.Baer.ExtensionOf.{u1, u2} R _inst_1 Q _inst_2 _inst_3 M N _inst_4 _inst_5 _inst_6 _inst_7 i f) (PartialOrder.toPreorder.{max u1 u2} (Module.Baer.ExtensionOf.{u1, u2} R _inst_1 Q _inst_2 _inst_3 M N _inst_4 _inst_5 _inst_6 _inst_7 i f) (SemilatticeInf.toPartialOrder.{max u1 u2} (Module.Baer.ExtensionOf.{u1, u2} R _inst_1 Q _inst_2 _inst_3 M N _inst_4 _inst_5 _inst_6 _inst_7 i f) (Module.Baer.ExtensionOf.semilatticeInf.{u1, u2} R _inst_1 Q _inst_2 _inst_3 M N _inst_4 _inst_5 _inst_6 _inst_7 i f))))) c) -> (Set.Nonempty.{max u1 u2} (Module.Baer.ExtensionOf.{u1, u2} R _inst_1 Q _inst_2 _inst_3 M N _inst_4 _inst_5 _inst_6 _inst_7 i f) c) -> (Module.Baer.ExtensionOf.{u1, u2} R _inst_1 Q _inst_2 _inst_3 M N _inst_4 _inst_5 _inst_6 _inst_7 i f)
+but is expected to have type
+  forall {R : Type.{u1}} [_inst_1 : Ring.{u1} R] {Q : TypeMax.{u2, u1}} [_inst_2 : AddCommGroup.{max u1 u2} Q] [_inst_3 : Module.{u1, max u1 u2} R Q (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{max u1 u2} Q _inst_2)] {M : Type.{max u1 u2}} {N : Type.{max u1 u2}} [_inst_4 : AddCommGroup.{max u1 u2} M] [_inst_5 : AddCommGroup.{max u1 u2} N] [_inst_6 : Module.{u1, max u1 u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{max u1 u2} M _inst_4)] [_inst_7 : Module.{u1, max u1 u2} R N (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{max u1 u2} N _inst_5)] {i : LinearMap.{u1, u1, max u1 u2, max u1 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 N (AddCommGroup.toAddCommMonoid.{max u1 u2} M _inst_4) (AddCommGroup.toAddCommMonoid.{max u1 u2} N _inst_5) _inst_6 _inst_7} {f : LinearMap.{u1, u1, max u1 u2, max u1 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 Q (AddCommGroup.toAddCommMonoid.{max u1 u2} M _inst_4) (AddCommGroup.toAddCommMonoid.{max u1 u2} Q _inst_2) _inst_6 _inst_3} {c : Set.{max u2 u1} (Module.Baer.ExtensionOf.{u1, u2} R _inst_1 Q _inst_2 _inst_3 M N _inst_4 _inst_5 _inst_6 _inst_7 i f)}, (IsChain.{max u1 u2} (Module.Baer.ExtensionOf.{u1, u2} R _inst_1 Q _inst_2 _inst_3 M N _inst_4 _inst_5 _inst_6 _inst_7 i f) (fun (x._@.Mathlib.Algebra.Module.Injective._hyg.1660 : Module.Baer.ExtensionOf.{u1, u2} R _inst_1 Q _inst_2 _inst_3 M N _inst_4 _inst_5 _inst_6 _inst_7 i f) (x._@.Mathlib.Algebra.Module.Injective._hyg.1662 : Module.Baer.ExtensionOf.{u1, u2} R _inst_1 Q _inst_2 _inst_3 M N _inst_4 _inst_5 _inst_6 _inst_7 i f) => LE.le.{max u1 u2} (Module.Baer.ExtensionOf.{u1, u2} R _inst_1 Q _inst_2 _inst_3 M N _inst_4 _inst_5 _inst_6 _inst_7 i f) (Preorder.toLE.{max u1 u2} (Module.Baer.ExtensionOf.{u1, u2} R _inst_1 Q _inst_2 _inst_3 M N _inst_4 _inst_5 _inst_6 _inst_7 i f) (PartialOrder.toPreorder.{max u1 u2} (Module.Baer.ExtensionOf.{u1, u2} R _inst_1 Q _inst_2 _inst_3 M N _inst_4 _inst_5 _inst_6 _inst_7 i f) (SemilatticeInf.toPartialOrder.{max u1 u2} (Module.Baer.ExtensionOf.{u1, u2} R _inst_1 Q _inst_2 _inst_3 M N _inst_4 _inst_5 _inst_6 _inst_7 i f) (Module.Baer.instSemilatticeInfExtensionOf.{u1, u2} R _inst_1 Q _inst_2 _inst_3 M N _inst_4 _inst_5 _inst_6 _inst_7 i f)))) x._@.Mathlib.Algebra.Module.Injective._hyg.1660 x._@.Mathlib.Algebra.Module.Injective._hyg.1662) c) -> (Set.Nonempty.{max u1 u2} (Module.Baer.ExtensionOf.{u1, u2} R _inst_1 Q _inst_2 _inst_3 M N _inst_4 _inst_5 _inst_6 _inst_7 i f) c) -> (Module.Baer.ExtensionOf.{u1, u2} R _inst_1 Q _inst_2 _inst_3 M N _inst_4 _inst_5 _inst_6 _inst_7 i f)
+Case conversion may be inaccurate. Consider using '#align module.Baer.extension_of.max Module.Baer.ExtensionOf.maxₓ'. -/
 /-- The maximal element of every nonempty chain of `extension_of i f`. -/
 def ExtensionOf.max {c : Set (ExtensionOf i f)} (hchain : IsChain (· ≤ ·) c)
     (hnonempty : c.Nonempty) : ExtensionOf i f :=
@@ -194,6 +230,12 @@ def ExtensionOf.max {c : Set (ExtensionOf i f)} (hchain : IsChain (· ≤ ·) c)
           ((Set.mem_image _ _ _).mpr ⟨hnonempty.some, hnonempty.some_spec, rfl⟩) ⟨i m, h1⟩ }
 #align module.Baer.extension_of.max Module.Baer.ExtensionOf.max
 
+/- warning: module.Baer.extension_of.le_max -> Module.Baer.ExtensionOf.le_max is a dubious translation:
+lean 3 declaration is
+  forall {R : Type.{u1}} [_inst_1 : Ring.{u1} R] {Q : Type.{max u1 u2}} [_inst_2 : AddCommGroup.{max u1 u2} Q] [_inst_3 : Module.{u1, max u1 u2} R Q (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{max u1 u2} Q _inst_2)] {M : Type.{max u1 u2}} {N : Type.{max u1 u2}} [_inst_4 : AddCommGroup.{max u1 u2} M] [_inst_5 : AddCommGroup.{max u1 u2} N] [_inst_6 : Module.{u1, max u1 u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{max u1 u2} M _inst_4)] [_inst_7 : Module.{u1, max u1 u2} R N (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{max u1 u2} N _inst_5)] {i : LinearMap.{u1, u1, max u1 u2, max u1 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 N (AddCommGroup.toAddCommMonoid.{max u1 u2} M _inst_4) (AddCommGroup.toAddCommMonoid.{max u1 u2} N _inst_5) _inst_6 _inst_7} {f : LinearMap.{u1, u1, max u1 u2, max u1 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 Q (AddCommGroup.toAddCommMonoid.{max u1 u2} M _inst_4) (AddCommGroup.toAddCommMonoid.{max u1 u2} Q _inst_2) _inst_6 _inst_3} {c : Set.{max u1 u2} (Module.Baer.ExtensionOf.{u1, u2} R _inst_1 Q _inst_2 _inst_3 M N _inst_4 _inst_5 _inst_6 _inst_7 i f)} (hchain : IsChain.{max u1 u2} (Module.Baer.ExtensionOf.{u1, u2} R _inst_1 Q _inst_2 _inst_3 M N _inst_4 _inst_5 _inst_6 _inst_7 i f) (LE.le.{max u1 u2} (Module.Baer.ExtensionOf.{u1, u2} R _inst_1 Q _inst_2 _inst_3 M N _inst_4 _inst_5 _inst_6 _inst_7 i f) (Preorder.toLE.{max u1 u2} (Module.Baer.ExtensionOf.{u1, u2} R _inst_1 Q _inst_2 _inst_3 M N _inst_4 _inst_5 _inst_6 _inst_7 i f) (PartialOrder.toPreorder.{max u1 u2} (Module.Baer.ExtensionOf.{u1, u2} R _inst_1 Q _inst_2 _inst_3 M N _inst_4 _inst_5 _inst_6 _inst_7 i f) (SemilatticeInf.toPartialOrder.{max u1 u2} (Module.Baer.ExtensionOf.{u1, u2} R _inst_1 Q _inst_2 _inst_3 M N _inst_4 _inst_5 _inst_6 _inst_7 i f) (Module.Baer.ExtensionOf.semilatticeInf.{u1, u2} R _inst_1 Q _inst_2 _inst_3 M N _inst_4 _inst_5 _inst_6 _inst_7 i f))))) c) (hnonempty : Set.Nonempty.{max u1 u2} (Module.Baer.ExtensionOf.{u1, u2} R _inst_1 Q _inst_2 _inst_3 M N _inst_4 _inst_5 _inst_6 _inst_7 i f) c) (a : Module.Baer.ExtensionOf.{u1, u2} R _inst_1 Q _inst_2 _inst_3 M N _inst_4 _inst_5 _inst_6 _inst_7 i f), (Membership.Mem.{max u1 u2, max u1 u2} (Module.Baer.ExtensionOf.{u1, u2} R _inst_1 Q _inst_2 _inst_3 M N _inst_4 _inst_5 _inst_6 _inst_7 i f) (Set.{max u1 u2} (Module.Baer.ExtensionOf.{u1, u2} R _inst_1 Q _inst_2 _inst_3 M N _inst_4 _inst_5 _inst_6 _inst_7 i f)) (Set.hasMem.{max u1 u2} (Module.Baer.ExtensionOf.{u1, u2} R _inst_1 Q _inst_2 _inst_3 M N _inst_4 _inst_5 _inst_6 _inst_7 i f)) a c) -> (LE.le.{max u1 u2} (Module.Baer.ExtensionOf.{u1, u2} R _inst_1 Q _inst_2 _inst_3 M N _inst_4 _inst_5 _inst_6 _inst_7 i f) (Preorder.toLE.{max u1 u2} (Module.Baer.ExtensionOf.{u1, u2} R _inst_1 Q _inst_2 _inst_3 M N _inst_4 _inst_5 _inst_6 _inst_7 i f) (PartialOrder.toPreorder.{max u1 u2} (Module.Baer.ExtensionOf.{u1, u2} R _inst_1 Q _inst_2 _inst_3 M N _inst_4 _inst_5 _inst_6 _inst_7 i f) (SemilatticeInf.toPartialOrder.{max u1 u2} (Module.Baer.ExtensionOf.{u1, u2} R _inst_1 Q _inst_2 _inst_3 M N _inst_4 _inst_5 _inst_6 _inst_7 i f) (Module.Baer.ExtensionOf.semilatticeInf.{u1, u2} R _inst_1 Q _inst_2 _inst_3 M N _inst_4 _inst_5 _inst_6 _inst_7 i f)))) a (Module.Baer.ExtensionOf.max.{u1, u2} R _inst_1 Q _inst_2 _inst_3 M N _inst_4 _inst_5 _inst_6 _inst_7 i f c hchain hnonempty))
+but is expected to have type
+  forall {R : Type.{u1}} [_inst_1 : Ring.{u1} R] {Q : TypeMax.{u2, u1}} [_inst_2 : AddCommGroup.{max u1 u2} Q] [_inst_3 : Module.{u1, max u1 u2} R Q (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{max u1 u2} Q _inst_2)] {M : Type.{max u1 u2}} {N : Type.{max u1 u2}} [_inst_4 : AddCommGroup.{max u1 u2} M] [_inst_5 : AddCommGroup.{max u1 u2} N] [_inst_6 : Module.{u1, max u1 u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{max u1 u2} M _inst_4)] [_inst_7 : Module.{u1, max u1 u2} R N (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{max u1 u2} N _inst_5)] {i : LinearMap.{u1, u1, max u1 u2, max u1 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 N (AddCommGroup.toAddCommMonoid.{max u1 u2} M _inst_4) (AddCommGroup.toAddCommMonoid.{max u1 u2} N _inst_5) _inst_6 _inst_7} {f : LinearMap.{u1, u1, max u1 u2, max u1 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 Q (AddCommGroup.toAddCommMonoid.{max u1 u2} M _inst_4) (AddCommGroup.toAddCommMonoid.{max u1 u2} Q _inst_2) _inst_6 _inst_3} {c : Set.{max u2 u1} (Module.Baer.ExtensionOf.{u1, u2} R _inst_1 Q _inst_2 _inst_3 M N _inst_4 _inst_5 _inst_6 _inst_7 i f)} (hchain : IsChain.{max u1 u2} (Module.Baer.ExtensionOf.{u1, u2} R _inst_1 Q _inst_2 _inst_3 M N _inst_4 _inst_5 _inst_6 _inst_7 i f) (fun (x._@.Mathlib.Algebra.Module.Injective._hyg.1839 : Module.Baer.ExtensionOf.{u1, u2} R _inst_1 Q _inst_2 _inst_3 M N _inst_4 _inst_5 _inst_6 _inst_7 i f) (x._@.Mathlib.Algebra.Module.Injective._hyg.1841 : Module.Baer.ExtensionOf.{u1, u2} R _inst_1 Q _inst_2 _inst_3 M N _inst_4 _inst_5 _inst_6 _inst_7 i f) => LE.le.{max u1 u2} (Module.Baer.ExtensionOf.{u1, u2} R _inst_1 Q _inst_2 _inst_3 M N _inst_4 _inst_5 _inst_6 _inst_7 i f) (Preorder.toLE.{max u1 u2} (Module.Baer.ExtensionOf.{u1, u2} R _inst_1 Q _inst_2 _inst_3 M N _inst_4 _inst_5 _inst_6 _inst_7 i f) (PartialOrder.toPreorder.{max u1 u2} (Module.Baer.ExtensionOf.{u1, u2} R _inst_1 Q _inst_2 _inst_3 M N _inst_4 _inst_5 _inst_6 _inst_7 i f) (SemilatticeInf.toPartialOrder.{max u1 u2} (Module.Baer.ExtensionOf.{u1, u2} R _inst_1 Q _inst_2 _inst_3 M N _inst_4 _inst_5 _inst_6 _inst_7 i f) (Module.Baer.instSemilatticeInfExtensionOf.{u1, u2} R _inst_1 Q _inst_2 _inst_3 M N _inst_4 _inst_5 _inst_6 _inst_7 i f)))) x._@.Mathlib.Algebra.Module.Injective._hyg.1839 x._@.Mathlib.Algebra.Module.Injective._hyg.1841) c) (hnonempty : Set.Nonempty.{max u1 u2} (Module.Baer.ExtensionOf.{u1, u2} R _inst_1 Q _inst_2 _inst_3 M N _inst_4 _inst_5 _inst_6 _inst_7 i f) c) (a : Module.Baer.ExtensionOf.{u1, u2} R _inst_1 Q _inst_2 _inst_3 M N _inst_4 _inst_5 _inst_6 _inst_7 i f), (Membership.mem.{max u1 u2, max u1 u2} (Module.Baer.ExtensionOf.{u1, u2} R _inst_1 Q _inst_2 _inst_3 M N _inst_4 _inst_5 _inst_6 _inst_7 i f) (Set.{max u2 u1} (Module.Baer.ExtensionOf.{u1, u2} R _inst_1 Q _inst_2 _inst_3 M N _inst_4 _inst_5 _inst_6 _inst_7 i f)) (Set.instMembershipSet.{max u1 u2} (Module.Baer.ExtensionOf.{u1, u2} R _inst_1 Q _inst_2 _inst_3 M N _inst_4 _inst_5 _inst_6 _inst_7 i f)) a c) -> (LE.le.{max u1 u2} (Module.Baer.ExtensionOf.{u1, u2} R _inst_1 Q _inst_2 _inst_3 M N _inst_4 _inst_5 _inst_6 _inst_7 i f) (Preorder.toLE.{max u1 u2} (Module.Baer.ExtensionOf.{u1, u2} R _inst_1 Q _inst_2 _inst_3 M N _inst_4 _inst_5 _inst_6 _inst_7 i f) (PartialOrder.toPreorder.{max u1 u2} (Module.Baer.ExtensionOf.{u1, u2} R _inst_1 Q _inst_2 _inst_3 M N _inst_4 _inst_5 _inst_6 _inst_7 i f) (SemilatticeInf.toPartialOrder.{max u1 u2} (Module.Baer.ExtensionOf.{u1, u2} R _inst_1 Q _inst_2 _inst_3 M N _inst_4 _inst_5 _inst_6 _inst_7 i f) (Module.Baer.instSemilatticeInfExtensionOf.{u1, u2} R _inst_1 Q _inst_2 _inst_3 M N _inst_4 _inst_5 _inst_6 _inst_7 i f)))) a (Module.Baer.ExtensionOf.max.{u1, u2} R _inst_1 Q _inst_2 _inst_3 M N _inst_4 _inst_5 _inst_6 _inst_7 i f c hchain hnonempty))
+Case conversion may be inaccurate. Consider using '#align module.Baer.extension_of.le_max Module.Baer.ExtensionOf.le_maxₓ'. -/
 theorem ExtensionOf.le_max {c : Set (ExtensionOf i f)} (hchain : IsChain (· ≤ ·) c)
     (hnonempty : c.Nonempty) (a : ExtensionOf i f) (ha : a ∈ c) :
     a ≤ ExtensionOf.max hchain hnonempty :=
@@ -203,6 +245,12 @@ theorem ExtensionOf.le_max {c : Set (ExtensionOf i f)} (hchain : IsChain (· ≤
 
 variable (i f) [Fact <| Function.Injective i]
 
+/- warning: module.Baer.extension_of.inhabited -> Module.Baer.ExtensionOf.inhabited is a dubious translation:
+lean 3 declaration is
+  forall {R : Type.{u1}} [_inst_1 : Ring.{u1} R] {Q : Type.{max u1 u2}} [_inst_2 : AddCommGroup.{max u1 u2} Q] [_inst_3 : Module.{u1, max u1 u2} R Q (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{max u1 u2} Q _inst_2)] {M : Type.{max u1 u2}} {N : Type.{max u1 u2}} [_inst_4 : AddCommGroup.{max u1 u2} M] [_inst_5 : AddCommGroup.{max u1 u2} N] [_inst_6 : Module.{u1, max u1 u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{max u1 u2} M _inst_4)] [_inst_7 : Module.{u1, max u1 u2} R N (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{max u1 u2} N _inst_5)] (i : LinearMap.{u1, u1, max u1 u2, max u1 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 N (AddCommGroup.toAddCommMonoid.{max u1 u2} M _inst_4) (AddCommGroup.toAddCommMonoid.{max u1 u2} N _inst_5) _inst_6 _inst_7) (f : LinearMap.{u1, u1, max u1 u2, max u1 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 Q (AddCommGroup.toAddCommMonoid.{max u1 u2} M _inst_4) (AddCommGroup.toAddCommMonoid.{max u1 u2} Q _inst_2) _inst_6 _inst_3) [_inst_8 : Fact (Function.Injective.{succ (max u1 u2), succ (max u1 u2)} M N (coeFn.{succ (max u1 u2), succ (max u1 u2)} (LinearMap.{u1, u1, max u1 u2, max u1 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 N (AddCommGroup.toAddCommMonoid.{max u1 u2} M _inst_4) (AddCommGroup.toAddCommMonoid.{max u1 u2} N _inst_5) _inst_6 _inst_7) (fun (_x : LinearMap.{u1, u1, max u1 u2, max u1 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 N (AddCommGroup.toAddCommMonoid.{max u1 u2} M _inst_4) (AddCommGroup.toAddCommMonoid.{max u1 u2} N _inst_5) _inst_6 _inst_7) => M -> N) (LinearMap.hasCoeToFun.{u1, u1, max u1 u2, max u1 u2} R R M N (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{max u1 u2} M _inst_4) (AddCommGroup.toAddCommMonoid.{max u1 u2} N _inst_5) _inst_6 _inst_7 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1)))) i))], Inhabited.{max (succ u1) (succ u2)} (Module.Baer.ExtensionOf.{u1, u2} R _inst_1 Q _inst_2 _inst_3 M N _inst_4 _inst_5 _inst_6 _inst_7 i f)
+but is expected to have type
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+Case conversion may be inaccurate. Consider using '#align module.Baer.extension_of.inhabited Module.Baer.ExtensionOf.inhabitedₓ'. -/
 instance ExtensionOf.inhabited : Inhabited (ExtensionOf i f)
     where default :=
     { domain := i.range
@@ -226,6 +274,12 @@ instance ExtensionOf.inhabited : Inhabited (ExtensionOf i f)
         exact Fact.out (Function.Injective i) (⟨i m, ⟨_, rfl⟩⟩ : i.range).2.choose_spec.symm }
 #align module.Baer.extension_of.inhabited Module.Baer.ExtensionOf.inhabited
 
+/- warning: module.Baer.extension_of_max -> Module.Baer.extensionOfMax is a dubious translation:
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+Case conversion may be inaccurate. Consider using '#align module.Baer.extension_of_max Module.Baer.extensionOfMaxₓ'. -/
 /-- Since every nonempty chain has a maximal element, by Zorn's lemma, there is a maximal
 `extension_of i f`. -/
 def extensionOfMax : ExtensionOf i f :=
@@ -233,6 +287,12 @@ def extensionOfMax : ExtensionOf i f :=
       ⟨ExtensionOf.max hchain hnonempty, ExtensionOf.le_max hchain hnonempty⟩).some
 #align module.Baer.extension_of_max Module.Baer.extensionOfMax
 
+/- warning: module.Baer.extension_of_max_is_max -> Module.Baer.extensionOfMax_is_max is a dubious translation:
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+Case conversion may be inaccurate. Consider using '#align module.Baer.extension_of_max_is_max Module.Baer.extensionOfMax_is_maxₓ'. -/
 theorem extensionOfMax_is_max :
     ∀ a : ExtensionOf i f, extensionOfMax i f ≤ a → a = extensionOfMax i f :=
   (@zorn_nonempty_partialOrder (ExtensionOf i f) _ ⟨Inhabited.default⟩ fun c hchain hnonempty =>
@@ -241,7 +301,7 @@ theorem extensionOfMax_is_max :
 
 variable {f}
 
-private theorem extension_of_max_adjoin.aux1 {y : N}
+private theorem extensionOfMax_adjoin.aux1 {y : N}
     (x : (extensionOfMax i f).domain ⊔ Submodule.span R {y}) :
     ∃ (a : (extensionOfMax i f).domain)(b : R), x.1 = a.1 + b • y :=
   by
@@ -251,19 +311,37 @@ private theorem extension_of_max_adjoin.aux1 {y : N}
   rw [Submodule.mem_span_singleton] at b_mem
   rcases b_mem with ⟨z, eq2⟩
   exact ⟨⟨a, a_mem⟩, z, by rw [← eq1, ← eq2]⟩
-#align module.Baer.extension_of_max_adjoin.aux1 module.Baer.extension_of_max_adjoin.aux1
-
+#align module.Baer.extension_of_max_adjoin.aux1 Module.Baer.extensionOfMax_adjoin.aux1
+
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 /-- If `x ∈ M ⊔ ⟨y⟩`, then `x = m + r • y`, `fst` pick an arbitrary such `m`.-/
 def ExtensionOfMaxAdjoin.fst {y : N} (x : (extensionOfMax i f).domain ⊔ Submodule.span R {y}) :
     (extensionOfMax i f).domain :=
   (ExtensionOfMaxAdjoin.aux1 i x).some
 #align module.Baer.extension_of_max_adjoin.fst Module.Baer.ExtensionOfMaxAdjoin.fst
 
+/- warning: module.Baer.extension_of_max_adjoin.snd -> Module.Baer.ExtensionOfMaxAdjoin.snd is a dubious translation:
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 /-- If `x ∈ M ⊔ ⟨y⟩`, then `x = m + r • y`, `snd` pick an arbitrary such `r`.-/
 def ExtensionOfMaxAdjoin.snd {y : N} (x : (extensionOfMax i f).domain ⊔ Submodule.span R {y}) : R :=
   (ExtensionOfMaxAdjoin.aux1 i x).choose_spec.some
 #align module.Baer.extension_of_max_adjoin.snd Module.Baer.ExtensionOfMaxAdjoin.snd
 
+/- warning: module.Baer.extension_of_max_adjoin.eqn -> Module.Baer.ExtensionOfMaxAdjoin.eqn is a dubious translation:
+lean 3 declaration is
+  forall {R : Type.{u1}} [_inst_1 : Ring.{u1} R] {Q : Type.{max u1 u2}} [_inst_2 : AddCommGroup.{max u1 u2} Q] [_inst_3 : Module.{u1, max u1 u2} R Q (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{max u1 u2} Q _inst_2)] {M : Type.{max u1 u2}} {N : Type.{max u1 u2}} [_inst_4 : AddCommGroup.{max u1 u2} M] [_inst_5 : AddCommGroup.{max u1 u2} N] [_inst_6 : Module.{u1, max u1 u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{max u1 u2} M _inst_4)] [_inst_7 : Module.{u1, max u1 u2} R N (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{max u1 u2} N _inst_5)] (i : LinearMap.{u1, u1, max u1 u2, max u1 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 N (AddCommGroup.toAddCommMonoid.{max u1 u2} M _inst_4) (AddCommGroup.toAddCommMonoid.{max u1 u2} N _inst_5) _inst_6 _inst_7) {f : LinearMap.{u1, u1, max u1 u2, max u1 u2} R R 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+but is expected to have type
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(AddCommGroup.toAddCommMonoid.{max u1 u2} N _inst_5) _inst_7))))) (Module.Baer.ExtensionOfMaxAdjoin.snd.{u1, u2} R _inst_1 Q _inst_2 _inst_3 M N _inst_4 _inst_5 _inst_6 _inst_7 i f _inst_8 y x) y))
+Case conversion may be inaccurate. Consider using '#align module.Baer.extension_of_max_adjoin.eqn Module.Baer.ExtensionOfMaxAdjoin.eqnₓ'. -/
 theorem ExtensionOfMaxAdjoin.eqn {y : N} (x : (extensionOfMax i f).domain ⊔ Submodule.span R {y}) :
     ↑x = ↑(ExtensionOfMaxAdjoin.fst i x) + ExtensionOfMaxAdjoin.snd i x • y :=
   (ExtensionOfMaxAdjoin.aux1 i x).choose_spec.choose_spec
@@ -271,11 +349,23 @@ theorem ExtensionOfMaxAdjoin.eqn {y : N} (x : (extensionOfMax i f).domain ⊔ Su
 
 variable (f)
 
+/- warning: module.Baer.extension_of_max_adjoin.ideal -> Module.Baer.ExtensionOfMaxAdjoin.ideal is a dubious translation:
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 /-- the ideal `I = {r | r • y ∈ N}`-/
 def ExtensionOfMaxAdjoin.ideal (y : N) : Ideal R :=
   (extensionOfMax i f).domain.comap ((LinearMap.id : R →ₗ[R] R).smul_right y)
 #align module.Baer.extension_of_max_adjoin.ideal Module.Baer.ExtensionOfMaxAdjoin.ideal
 
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+Case conversion may be inaccurate. Consider using '#align module.Baer.extension_of_max_adjoin.ideal_to Module.Baer.ExtensionOfMaxAdjoin.idealToₓ'. -/
 /-- A linear map `I ⟶ Q` by `x ↦ f' (x • y)` where `f'` is the maximal extension-/
 def ExtensionOfMaxAdjoin.idealTo (y : N) : ExtensionOfMaxAdjoin.ideal i f y →ₗ[R] Q
     where
@@ -284,18 +374,36 @@ def ExtensionOfMaxAdjoin.idealTo (y : N) : ExtensionOfMaxAdjoin.ideal i f y →
   map_smul' z1 z2 := by simp [← (extension_of_max i f).toLinearPMap.map_smul, mul_smul] <;> rfl
 #align module.Baer.extension_of_max_adjoin.ideal_to Module.Baer.ExtensionOfMaxAdjoin.idealTo
 
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+but is expected to have type
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+Case conversion may be inaccurate. Consider using '#align module.Baer.extension_of_max_adjoin.extend_ideal_to Module.Baer.ExtensionOfMaxAdjoin.extendIdealToₓ'. -/
 /-- Since we assumed `Q` being Baer, the linear map `x ↦ f' (x • y) : I ⟶ Q` extends to `R ⟶ Q`,
 call this extended map `φ`-/
 def ExtensionOfMaxAdjoin.extendIdealTo (h : Module.Baer R Q) (y : N) : R →ₗ[R] Q :=
   (h (ExtensionOfMaxAdjoin.ideal i f y) (ExtensionOfMaxAdjoin.idealTo i f y)).some
 #align module.Baer.extension_of_max_adjoin.extend_ideal_to Module.Baer.ExtensionOfMaxAdjoin.extendIdealTo
 
+/- warning: module.Baer.extension_of_max_adjoin.extend_ideal_to_is_extension -> Module.Baer.ExtensionOfMaxAdjoin.extendIdealTo_is_extension is a dubious translation:
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+Case conversion may be inaccurate. Consider using '#align module.Baer.extension_of_max_adjoin.extend_ideal_to_is_extension Module.Baer.ExtensionOfMaxAdjoin.extendIdealTo_is_extensionₓ'. -/
 theorem ExtensionOfMaxAdjoin.extendIdealTo_is_extension (h : Module.Baer R Q) (y : N) :
     ∀ (x : R) (mem : x ∈ ExtensionOfMaxAdjoin.ideal i f y),
       ExtensionOfMaxAdjoin.extendIdealTo i f h y x = ExtensionOfMaxAdjoin.idealTo i f y ⟨x, mem⟩ :=
   (h (ExtensionOfMaxAdjoin.ideal i f y) (ExtensionOfMaxAdjoin.idealTo i f y)).choose_spec
 #align module.Baer.extension_of_max_adjoin.extend_ideal_to_is_extension Module.Baer.ExtensionOfMaxAdjoin.extendIdealTo_is_extension
 
+/- warning: module.Baer.extension_of_max_adjoin.extend_ideal_to_wd' -> Module.Baer.ExtensionOfMaxAdjoin.extendIdealTo_wd' is a dubious translation:
+lean 3 declaration is
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_inst_1)) _inst_3) => R -> Q) (LinearMap.hasCoeToFun.{u1, u1, u1, max u1 u2} R R R Q (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toAddCommGroup.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R _inst_1)))) (AddCommGroup.toAddCommMonoid.{max u1 u2} Q _inst_2) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R _inst_1)) _inst_3 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1)))) (Module.Baer.ExtensionOfMaxAdjoin.extendIdealTo.{u1, u2} R _inst_1 Q _inst_2 _inst_3 M N _inst_4 _inst_5 _inst_6 _inst_7 i f _inst_8 h y) r) (OfNat.ofNat.{max u1 u2} Q 0 (OfNat.mk.{max u1 u2} Q 0 (Zero.zero.{max u1 u2} Q (AddZeroClass.toHasZero.{max u1 u2} Q (AddMonoid.toAddZeroClass.{max u1 u2} Q (SubNegMonoid.toAddMonoid.{max u1 u2} Q (AddGroup.toSubNegMonoid.{max u1 u2} Q (AddCommGroup.toAddGroup.{max u1 u2} Q _inst_2)))))))))
+but is expected to have type
+  forall {R : Type.{u1}} [_inst_1 : Ring.{u1} R] {Q : TypeMax.{u2, u1}} [_inst_2 : AddCommGroup.{max u1 u2} Q] [_inst_3 : Module.{u1, max u1 u2} R Q (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{max u1 u2} Q _inst_2)] {M : Type.{max u1 u2}} {N : Type.{max u1 u2}} [_inst_4 : AddCommGroup.{max u1 u2} M] [_inst_5 : AddCommGroup.{max u1 u2} N] [_inst_6 : Module.{u1, max u1 u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{max u1 u2} M _inst_4)] [_inst_7 : Module.{u1, max u1 u2} R N (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{max u1 u2} N _inst_5)] (i : LinearMap.{u1, u1, max u1 u2, max u1 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 N (AddCommGroup.toAddCommMonoid.{max u1 u2} M _inst_4) (AddCommGroup.toAddCommMonoid.{max u1 u2} N _inst_5) _inst_6 _inst_7) (f : LinearMap.{u1, u1, max u1 u2, max u1 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 Q (AddCommGroup.toAddCommMonoid.{max u1 u2} M _inst_4) (AddCommGroup.toAddCommMonoid.{max u1 u2} Q _inst_2) _inst_6 _inst_3) [_inst_8 : Fact (Function.Injective.{max (succ u1) (succ u2), max (succ u1) (succ u2)} M N (FunLike.coe.{max (succ u1) (succ u2), max (succ u1) (succ u2), max (succ u1) (succ u2)} (LinearMap.{u1, u1, max u1 u2, max u1 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 N (AddCommGroup.toAddCommMonoid.{max u1 u2} M _inst_4) (AddCommGroup.toAddCommMonoid.{max u1 u2} N _inst_5) _inst_6 _inst_7) M (fun (_x : M) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : M) => N) _x) (LinearMap.instFunLikeLinearMap.{u1, u1, max u1 u2, max u1 u2} R R M N (Ring.toSemiring.{u1} R _inst_1) 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(x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : R) => Q) r) (SubtractionCommMonoid.toSubtractionMonoid.{max u1 u2} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : R) => Q) r) (AddCommGroup.toDivisionAddCommMonoid.{max u1 u2} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : R) => Q) r) _inst_2))))))))
+Case conversion may be inaccurate. Consider using '#align module.Baer.extension_of_max_adjoin.extend_ideal_to_wd' Module.Baer.ExtensionOfMaxAdjoin.extendIdealTo_wd'ₓ'. -/
 theorem ExtensionOfMaxAdjoin.extendIdealTo_wd' (h : Module.Baer R Q) {y : N} (r : R)
     (eq1 : r • y = 0) : ExtensionOfMaxAdjoin.extendIdealTo i f h y r = 0 :=
   by
@@ -305,6 +413,12 @@ theorem ExtensionOfMaxAdjoin.extendIdealTo_wd' (h : Module.Baer R Q) {y : N} (r
     ZeroMemClass.zero_def, (extension_of_max i f).toLinearPMap.map_zero]
 #align module.Baer.extension_of_max_adjoin.extend_ideal_to_wd' Module.Baer.ExtensionOfMaxAdjoin.extendIdealTo_wd'
 
+/- warning: module.Baer.extension_of_max_adjoin.extend_ideal_to_wd -> Module.Baer.ExtensionOfMaxAdjoin.extendIdealTo_wd is a dubious translation:
+lean 3 declaration is
+  forall {R : Type.{u1}} [_inst_1 : Ring.{u1} R] {Q : Type.{max u1 u2}} [_inst_2 : AddCommGroup.{max u1 u2} Q] [_inst_3 : Module.{u1, max u1 u2} R Q (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{max u1 u2} Q _inst_2)] {M : Type.{max u1 u2}} {N : Type.{max u1 u2}} [_inst_4 : AddCommGroup.{max u1 u2} M] [_inst_5 : AddCommGroup.{max u1 u2} N] [_inst_6 : Module.{u1, max u1 u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{max u1 u2} M _inst_4)] [_inst_7 : Module.{u1, max u1 u2} R N (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{max u1 u2} N _inst_5)] (i : LinearMap.{u1, u1, max u1 u2, max u1 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 N (AddCommGroup.toAddCommMonoid.{max u1 u2} M _inst_4) (AddCommGroup.toAddCommMonoid.{max u1 u2} N _inst_5) _inst_6 _inst_7) (f : LinearMap.{u1, u1, max u1 u2, max u1 u2} R R 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+but is expected to have type
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+Case conversion may be inaccurate. Consider using '#align module.Baer.extension_of_max_adjoin.extend_ideal_to_wd Module.Baer.ExtensionOfMaxAdjoin.extendIdealTo_wdₓ'. -/
 theorem ExtensionOfMaxAdjoin.extendIdealTo_wd (h : Module.Baer R Q) {y : N} (r r' : R)
     (eq1 : r • y = r' • y) :
     ExtensionOfMaxAdjoin.extendIdealTo i f h y r = ExtensionOfMaxAdjoin.extendIdealTo i f h y r' :=
@@ -314,6 +428,12 @@ theorem ExtensionOfMaxAdjoin.extendIdealTo_wd (h : Module.Baer R Q) {y : N} (r r
   rw [sub_smul, sub_eq_zero, eq1]
 #align module.Baer.extension_of_max_adjoin.extend_ideal_to_wd Module.Baer.ExtensionOfMaxAdjoin.extendIdealTo_wd
 
+/- warning: module.Baer.extension_of_max_adjoin.extend_ideal_to_eq -> Module.Baer.ExtensionOfMaxAdjoin.extendIdealTo_eq is a dubious translation:
+lean 3 declaration is
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_inst_4) (AddCommGroup.toAddCommMonoid.{max u1 u2} N _inst_5) _inst_6 _inst_7) => M -> N) (LinearMap.hasCoeToFun.{u1, u1, max u1 u2, max u1 u2} R R M N (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{max u1 u2} M _inst_4) (AddCommGroup.toAddCommMonoid.{max u1 u2} N _inst_5) _inst_6 _inst_7 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1)))) i))] (h : Module.Baer.{u1, u2} R _inst_1 Q _inst_2 _inst_3) {y : N} (r : R) (hr : Membership.Mem.{max u1 u2, max u1 u2} N (Submodule.{u1, max u1 u2} R N (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{max u1 u2} N _inst_5) _inst_7) (SetLike.hasMem.{max u1 u2, max u1 u2} (Submodule.{u1, max u1 u2} R N (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{max u1 u2} N _inst_5) _inst_7) N (Submodule.setLike.{u1, max u1 u2} R N (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{max u1 u2} N _inst_5) _inst_7)) (SMul.smul.{u1, max 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_inst_1 Q _inst_2 _inst_3 M N _inst_4 _inst_5 _inst_6 _inst_7 i f (Module.Baer.extensionOfMax.{u1, u2} R _inst_1 Q _inst_2 _inst_3 M N _inst_4 _inst_5 _inst_6 _inst_7 i f _inst_8)))) (SMul.smul.{u1, max u1 u2} R N (SMulZeroClass.toHasSmul.{u1, max u1 u2} R N (AddZeroClass.toHasZero.{max u1 u2} N (AddMonoid.toAddZeroClass.{max u1 u2} N (AddCommMonoid.toAddMonoid.{max u1 u2} N (AddCommGroup.toAddCommMonoid.{max u1 u2} N _inst_5)))) (SMulWithZero.toSmulZeroClass.{u1, max u1 u2} R N (MulZeroClass.toHasZero.{u1} R (MulZeroOneClass.toMulZeroClass.{u1} R (MonoidWithZero.toMulZeroOneClass.{u1} R (Semiring.toMonoidWithZero.{u1} R (Ring.toSemiring.{u1} R _inst_1))))) (AddZeroClass.toHasZero.{max u1 u2} N (AddMonoid.toAddZeroClass.{max u1 u2} N (AddCommMonoid.toAddMonoid.{max u1 u2} N (AddCommGroup.toAddCommMonoid.{max u1 u2} N _inst_5)))) (MulActionWithZero.toSMulWithZero.{u1, max u1 u2} R N (Semiring.toMonoidWithZero.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (AddZeroClass.toHasZero.{max u1 u2} N (AddMonoid.toAddZeroClass.{max u1 u2} N (AddCommMonoid.toAddMonoid.{max u1 u2} N (AddCommGroup.toAddCommMonoid.{max u1 u2} N _inst_5)))) (Module.toMulActionWithZero.{u1, max u1 u2} R N (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{max u1 u2} N _inst_5) _inst_7)))) r y) hr))
+but is expected to have type
+  forall {R : Type.{u1}} [_inst_1 : Ring.{u1} R] {Q : TypeMax.{u2, u1}} [_inst_2 : AddCommGroup.{max u1 u2} Q] [_inst_3 : Module.{u1, max u1 u2} R Q (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{max u1 u2} Q _inst_2)] {M : Type.{max u1 u2}} {N : Type.{max u1 u2}} [_inst_4 : AddCommGroup.{max u1 u2} M] [_inst_5 : AddCommGroup.{max u1 u2} N] [_inst_6 : Module.{u1, max u1 u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{max u1 u2} M _inst_4)] [_inst_7 : Module.{u1, max u1 u2} R N (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{max u1 u2} N _inst_5)] (i : LinearMap.{u1, u1, max u1 u2, max u1 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 N (AddCommGroup.toAddCommMonoid.{max u1 u2} M _inst_4) (AddCommGroup.toAddCommMonoid.{max u1 u2} N _inst_5) _inst_6 _inst_7) (f : LinearMap.{u1, u1, max u1 u2, max u1 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 Q (AddCommGroup.toAddCommMonoid.{max u1 u2} M _inst_4) (AddCommGroup.toAddCommMonoid.{max u1 u2} Q _inst_2) _inst_6 _inst_3) [_inst_8 : Fact (Function.Injective.{max (succ u1) (succ u2), max (succ u1) (succ u2)} M N (FunLike.coe.{max (succ u1) (succ u2), max (succ u1) (succ u2), max (succ u1) (succ u2)} (LinearMap.{u1, u1, max u1 u2, max u1 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 N (AddCommGroup.toAddCommMonoid.{max u1 u2} M _inst_4) (AddCommGroup.toAddCommMonoid.{max u1 u2} N _inst_5) _inst_6 _inst_7) M (fun (_x : M) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : M) => N) _x) (LinearMap.instFunLikeLinearMap.{u1, u1, max u1 u2, max u1 u2} R R M N (Ring.toSemiring.{u1} R _inst_1) 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(Ring.toSemiring.{u1} R _inst_1)) (NegZeroClass.toZero.{max u1 u2} N (SubNegZeroMonoid.toNegZeroClass.{max u1 u2} N (SubtractionMonoid.toSubNegZeroMonoid.{max u1 u2} N (SubtractionCommMonoid.toSubtractionMonoid.{max u1 u2} N (AddCommGroup.toDivisionAddCommMonoid.{max u1 u2} N _inst_5))))) (Module.toMulActionWithZero.{u1, max u1 u2} R N (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{max u1 u2} N _inst_5) _inst_7))))) r y) hr))
+Case conversion may be inaccurate. Consider using '#align module.Baer.extension_of_max_adjoin.extend_ideal_to_eq Module.Baer.ExtensionOfMaxAdjoin.extendIdealTo_eqₓ'. -/
 theorem ExtensionOfMaxAdjoin.extendIdealTo_eq (h : Module.Baer R Q) {y : N} (r : R)
     (hr : r • y ∈ (extensionOfMax i f).domain) :
     ExtensionOfMaxAdjoin.extendIdealTo i f h y r = (extensionOfMax i f).toLinearPMap ⟨r • y, hr⟩ :=
@@ -322,6 +442,12 @@ theorem ExtensionOfMaxAdjoin.extendIdealTo_eq (h : Module.Baer R Q) {y : N} (r :
     extension_of_max_adjoin.ideal_to, LinearMap.coe_mk, Subtype.coe_mk]
 #align module.Baer.extension_of_max_adjoin.extend_ideal_to_eq Module.Baer.ExtensionOfMaxAdjoin.extendIdealTo_eq
 
+/- warning: module.Baer.extension_of_max_adjoin.extension_to_fun -> Module.Baer.ExtensionOfMaxAdjoin.extensionToFun is a dubious translation:
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+Case conversion may be inaccurate. Consider using '#align module.Baer.extension_of_max_adjoin.extension_to_fun Module.Baer.ExtensionOfMaxAdjoin.extensionToFunₓ'. -/
 /-- We can finally define a linear map `M ⊔ ⟨y⟩ ⟶ Q` by `x + r • y ↦ f x + φ r`
 -/
 def ExtensionOfMaxAdjoin.extensionToFun (h : Module.Baer R Q) {y : N} :
@@ -330,6 +456,12 @@ def ExtensionOfMaxAdjoin.extensionToFun (h : Module.Baer R Q) {y : N} :
     ExtensionOfMaxAdjoin.extendIdealTo i f h y (ExtensionOfMaxAdjoin.snd i x)
 #align module.Baer.extension_of_max_adjoin.extension_to_fun Module.Baer.ExtensionOfMaxAdjoin.extensionToFun
 
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_inst_1 Q _inst_2 _inst_3 M N _inst_4 _inst_5 _inst_6 _inst_7 i f _inst_8 h y) r)))
+Case conversion may be inaccurate. Consider using '#align module.Baer.extension_of_max_adjoin.extension_to_fun_wd Module.Baer.ExtensionOfMaxAdjoin.extensionToFun_wdₓ'. -/
 theorem ExtensionOfMaxAdjoin.extensionToFun_wd (h : Module.Baer R Q) {y : N}
     (x : (extensionOfMax i f).domain ⊔ Submodule.span R {y}) (a : (extensionOfMax i f).domain)
     (r : R) (eq1 : ↑x = ↑a + r • y) :
@@ -354,6 +486,12 @@ theorem ExtensionOfMaxAdjoin.extensionToFun_wd (h : Module.Baer R Q) {y : N}
   exact eq_sub_of_add_eq (extension_of_max_adjoin.eqn _ _).symm
 #align module.Baer.extension_of_max_adjoin.extension_to_fun_wd Module.Baer.ExtensionOfMaxAdjoin.extensionToFun_wd
 
+/- warning: module.Baer.extension_of_max_adjoin -> Module.Baer.extensionOfMaxAdjoin is a dubious translation:
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+Case conversion may be inaccurate. Consider using '#align module.Baer.extension_of_max_adjoin Module.Baer.extensionOfMaxAdjoinₓ'. -/
 /-- The linear map `M ⊔ ⟨y⟩ ⟶ Q` by `x + r • y ↦ f x + φ r` is an extension of `f`-/
 def extensionOfMaxAdjoin (h : Module.Baer R Q) (y : N) : ExtensionOf i f
     where
@@ -392,6 +530,12 @@ def extensionOfMaxAdjoin (h : Module.Baer R Q) (y : N) : ExtensionOf i f
     simp
 #align module.Baer.extension_of_max_adjoin Module.Baer.extensionOfMaxAdjoin
 
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+Case conversion may be inaccurate. Consider using '#align module.Baer.extension_of_max_le Module.Baer.extensionOfMax_leₓ'. -/
 theorem extensionOfMax_le (h : Module.Baer R Q) {y : N} :
     extensionOfMax i f ≤ extensionOfMaxAdjoin i f h y :=
   ⟨le_sup_left, fun x x' EQ => by
@@ -401,6 +545,12 @@ theorem extensionOfMax_le (h : Module.Baer R Q) {y : N} :
       add_zero]⟩
 #align module.Baer.extension_of_max_le Module.Baer.extensionOfMax_le
 
+/- warning: module.Baer.extension_of_max_to_submodule_eq_top -> Module.Baer.extensionOfMax_to_submodule_eq_top is a dubious translation:
+lean 3 declaration is
+  forall {R : Type.{u1}} [_inst_1 : Ring.{u1} R] {Q : Type.{max u1 u2}} [_inst_2 : AddCommGroup.{max u1 u2} Q] [_inst_3 : Module.{u1, max u1 u2} R Q (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{max u1 u2} Q _inst_2)] {M : Type.{max u1 u2}} {N : Type.{max u1 u2}} [_inst_4 : AddCommGroup.{max u1 u2} M] [_inst_5 : AddCommGroup.{max u1 u2} N] [_inst_6 : Module.{u1, max u1 u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{max u1 u2} M _inst_4)] [_inst_7 : Module.{u1, max u1 u2} R N (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{max u1 u2} N _inst_5)] (i : LinearMap.{u1, u1, max u1 u2, max u1 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 N (AddCommGroup.toAddCommMonoid.{max u1 u2} M _inst_4) (AddCommGroup.toAddCommMonoid.{max u1 u2} N _inst_5) _inst_6 _inst_7) (f : LinearMap.{u1, u1, max u1 u2, max u1 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 Q (AddCommGroup.toAddCommMonoid.{max u1 u2} M _inst_4) (AddCommGroup.toAddCommMonoid.{max u1 u2} Q _inst_2) _inst_6 _inst_3) [_inst_8 : Fact (Function.Injective.{succ (max u1 u2), succ (max u1 u2)} M N (coeFn.{succ (max u1 u2), succ (max u1 u2)} (LinearMap.{u1, u1, max u1 u2, max u1 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 N (AddCommGroup.toAddCommMonoid.{max u1 u2} M _inst_4) (AddCommGroup.toAddCommMonoid.{max u1 u2} N _inst_5) _inst_6 _inst_7) (fun (_x : LinearMap.{u1, u1, max u1 u2, max u1 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 N (AddCommGroup.toAddCommMonoid.{max u1 u2} M _inst_4) (AddCommGroup.toAddCommMonoid.{max u1 u2} N _inst_5) _inst_6 _inst_7) => M -> N) (LinearMap.hasCoeToFun.{u1, u1, max u1 u2, max u1 u2} R R M N (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{max u1 u2} M _inst_4) (AddCommGroup.toAddCommMonoid.{max u1 u2} N _inst_5) _inst_6 _inst_7 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1)))) i))], (Module.Baer.{u1, u2} R _inst_1 Q _inst_2 _inst_3) -> (Eq.{succ (max u1 u2)} (Submodule.{u1, max u1 u2} R N (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{max u1 u2} N _inst_5) _inst_7) (LinearPMap.domain.{u1, max u1 u2, max u1 u2} R _inst_1 N _inst_5 _inst_7 Q _inst_2 _inst_3 (Module.Baer.ExtensionOf.toLinearPmap.{u1, u2} R _inst_1 Q _inst_2 _inst_3 M N _inst_4 _inst_5 _inst_6 _inst_7 i f (Module.Baer.extensionOfMax.{u1, u2} R _inst_1 Q _inst_2 _inst_3 M N _inst_4 _inst_5 _inst_6 _inst_7 i f _inst_8))) (Top.top.{max u1 u2} (Submodule.{u1, max u1 u2} R N (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{max u1 u2} N _inst_5) _inst_7) (Submodule.hasTop.{u1, max u1 u2} R N (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{max u1 u2} N _inst_5) _inst_7)))
+but is expected to have type
+  forall {R : Type.{u1}} [_inst_1 : Ring.{u1} R] {Q : TypeMax.{u2, u1}} [_inst_2 : AddCommGroup.{max u1 u2} Q] [_inst_3 : Module.{u1, max u1 u2} R Q (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{max u1 u2} Q _inst_2)] {M : Type.{max u1 u2}} {N : Type.{max u1 u2}} [_inst_4 : AddCommGroup.{max u1 u2} M] [_inst_5 : AddCommGroup.{max u1 u2} N] [_inst_6 : Module.{u1, max u1 u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{max u1 u2} M _inst_4)] [_inst_7 : Module.{u1, max u1 u2} R N (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{max u1 u2} N _inst_5)] (i : LinearMap.{u1, u1, max u1 u2, max u1 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 N (AddCommGroup.toAddCommMonoid.{max u1 u2} M _inst_4) (AddCommGroup.toAddCommMonoid.{max u1 u2} N _inst_5) _inst_6 _inst_7) (f : LinearMap.{u1, u1, max u1 u2, max u1 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 Q (AddCommGroup.toAddCommMonoid.{max u1 u2} M _inst_4) (AddCommGroup.toAddCommMonoid.{max u1 u2} Q _inst_2) _inst_6 _inst_3) [_inst_8 : Fact (Function.Injective.{max (succ u1) (succ u2), max (succ u1) (succ u2)} M N (FunLike.coe.{max (succ u1) (succ u2), max (succ u1) (succ u2), max (succ u1) (succ u2)} (LinearMap.{u1, u1, max u1 u2, max u1 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 N (AddCommGroup.toAddCommMonoid.{max u1 u2} M _inst_4) (AddCommGroup.toAddCommMonoid.{max u1 u2} N _inst_5) _inst_6 _inst_7) M (fun (_x : M) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : M) => N) _x) (LinearMap.instFunLikeLinearMap.{u1, u1, max u1 u2, max u1 u2} R R M N (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{max u1 u2} M _inst_4) (AddCommGroup.toAddCommMonoid.{max u1 u2} N _inst_5) _inst_6 _inst_7 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1)))) i))], (Module.Baer.{u1, u2} R _inst_1 Q _inst_2 _inst_3) -> (Eq.{max (succ u1) (succ u2)} (Submodule.{u1, max u1 u2} R N (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{max u1 u2} N _inst_5) _inst_7) (LinearPMap.domain.{u1, max u1 u2, max u1 u2} R _inst_1 N _inst_5 _inst_7 Q _inst_2 _inst_3 (Module.Baer.ExtensionOf.toLinearPMap.{u1, u2} R _inst_1 Q _inst_2 _inst_3 M N _inst_4 _inst_5 _inst_6 _inst_7 i f (Module.Baer.extensionOfMax.{u1, u2} R _inst_1 Q _inst_2 _inst_3 M N _inst_4 _inst_5 _inst_6 _inst_7 i f _inst_8))) (Top.top.{max u1 u2} (Submodule.{u1, max u1 u2} R N (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{max u1 u2} N _inst_5) _inst_7) (Submodule.instTopSubmodule.{u1, max u1 u2} R N (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{max u1 u2} N _inst_5) _inst_7)))
+Case conversion may be inaccurate. Consider using '#align module.Baer.extension_of_max_to_submodule_eq_top Module.Baer.extensionOfMax_to_submodule_eq_topₓ'. -/
 theorem extensionOfMax_to_submodule_eq_top (h : Module.Baer R Q) :
     (extensionOfMax i f).domain = ⊤ :=
   by
@@ -410,6 +560,7 @@ theorem extensionOfMax_to_submodule_eq_top (h : Module.Baer R Q) :
   exact ⟨0, Submodule.zero_mem _, y, Submodule.mem_span_singleton_self _, zero_add _⟩
 #align module.Baer.extension_of_max_to_submodule_eq_top Module.Baer.extensionOfMax_to_submodule_eq_top
 
+#print Module.Baer.injective /-
 /-- **Baer's criterion** for injective module : a Baer module is an injective module, i.e. if every
 linear map from an ideal can be extended, then the module is injective.-/
 protected theorem injective (h : Module.Baer R Q) : Module.Injective R Q :=
@@ -427,6 +578,7 @@ protected theorem injective (h : Module.Baer R Q) : Module.Injective R Q :=
             congr },
         fun x => ((extension_of_max i f).is_extension x).symm⟩ }
 #align module.Baer.injective Module.Baer.injective
+-/
 
 end Module.Baer
 

mathlib commit https://github.com/leanprover-community/mathlib/commit/ce11c3c2a285bbe6937e26d9792fda4e51f3fe1a

@@ -4,12 +4,14 @@ Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Jujian Zhang
 
 ! This file was ported from Lean 3 source module algebra.module.injective
-! leanprover-community/mathlib commit 70fd9563a21e7b963887c9360bd29b2393e6225a
+! leanprover-community/mathlib commit f8d8465c3c392a93b9ed226956e26dee00975946
 ! Please do not edit these lines, except to modify the commit id
 ! if you have ported upstream changes.
 -/
 import Mathbin.CategoryTheory.Preadditive.Injective
+import Mathbin.Algebra.Category.Module.EpiMono
 import Mathbin.RingTheory.Ideal.Basic
+import Mathbin.LinearAlgebra.LinearPmap
 
 /-!
 # Injective modules

mathlib commit https://github.com/leanprover-community/mathlib/commit/9da1b3534b65d9661eb8f42443598a92bbb49211

@@ -134,7 +134,7 @@ theorem ExtensionOf.ext_iff {a b : ExtensionOf i f} :
 
 end Ext
 
-instance : HasInf (ExtensionOf i f)
+instance : Inf (ExtensionOf i f)
     where inf X1 X2 :=
     {
       X1.toLinearPMap ⊓

mathlib commit https://github.com/leanprover-community/mathlib/commit/22131150f88a2d125713ffa0f4693e3355b1eb49

@@ -104,7 +104,7 @@ variable [Module R M] [Module R N] (i : M →ₗ[R] N) (f : M →ₗ[R] Q)
 /-- If we view `M` as a submodule of `N` via the injective linear map `i : M ↪ N`, then a submodule
 between `M` and `N` is a submodule `N'` of `N`. To prove Baer's criterion, we need to consider
 pairs of `(N', f')` such that `M ≤ N' ≤ N` and `f'` extends `f`. -/
-structure ExtensionOf extends LinearPmap R N Q where
+structure ExtensionOf extends LinearPMap R N Q where
   le : i.range ≤ domain
   is_extension : ∀ m : M, f m = to_linear_pmap ⟨i m, le ⟨m, rfl⟩⟩
 #align module.Baer.extension_of Module.Baer.ExtensionOf
@@ -116,18 +116,18 @@ variable {i f}
 @[ext]
 theorem ExtensionOf.ext {a b : ExtensionOf i f} (domain_eq : a.domain = b.domain)
     (to_fun_eq :
-      ∀ ⦃x : a.domain⦄ ⦃y : b.domain⦄, (x : N) = y → a.toLinearPmap x = b.toLinearPmap y) :
+      ∀ ⦃x : a.domain⦄ ⦃y : b.domain⦄, (x : N) = y → a.toLinearPMap x = b.toLinearPMap y) :
     a = b := by
   rcases a with ⟨a, a_le, e1⟩
   rcases b with ⟨b, b_le, e2⟩
   congr
-  exact LinearPmap.ext domain_eq to_fun_eq
+  exact LinearPMap.ext domain_eq to_fun_eq
 #align module.Baer.extension_of.ext Module.Baer.ExtensionOf.ext
 
 theorem ExtensionOf.ext_iff {a b : ExtensionOf i f} :
     a = b ↔
       ∃ domain_eq : a.domain = b.domain,
-        ∀ ⦃x : a.domain⦄ ⦃y : b.domain⦄, (x : N) = y → a.toLinearPmap x = b.toLinearPmap y :=
+        ∀ ⦃x : a.domain⦄ ⦃y : b.domain⦄, (x : N) = y → a.toLinearPMap x = b.toLinearPMap y :=
   ⟨fun r => r ▸ ⟨rfl, fun x y h => congr_arg a.toFun <| by exact_mod_cast h⟩, fun ⟨h1, h2⟩ =>
     ExtensionOf.ext h1 h2⟩
 #align module.Baer.extension_of.ext_iff Module.Baer.ExtensionOf.ext_iff
@@ -137,14 +137,14 @@ end Ext
 instance : HasInf (ExtensionOf i f)
     where inf X1 X2 :=
     {
-      X1.toLinearPmap ⊓
-        X2.toLinearPmap with
+      X1.toLinearPMap ⊓
+        X2.toLinearPMap with
       le := fun x hx =>
         (by
           rcases hx with ⟨x, rfl⟩
           refine' ⟨X1.le (Set.mem_range_self _), X2.le (Set.mem_range_self _), _⟩
           rw [← X1.is_extension x, ← X2.is_extension x] :
-          x ∈ X1.toLinearPmap.eqLocus X2.toLinearPmap)
+          x ∈ X1.toLinearPMap.eqLocus X2.toLinearPMap)
       is_extension := fun m => X1.is_extension _ }
 
 instance : SemilatticeInf (ExtensionOf i f) :=
@@ -156,31 +156,31 @@ instance : SemilatticeInf (ExtensionOf i f) :=
         congr
         exact_mod_cast h')
     fun X Y =>
-    LinearPmap.ext rfl fun x y h => by
+    LinearPMap.ext rfl fun x y h => by
       congr
       exact_mod_cast h
 
 variable {R i f}
 
-theorem chain_linearPmap_of_chain_extensionOf {c : Set (ExtensionOf i f)}
+theorem chain_linearPMap_of_chain_extensionOf {c : Set (ExtensionOf i f)}
     (hchain : IsChain (· ≤ ·) c) :
-    IsChain (· ≤ ·) <| (fun x : ExtensionOf i f => x.toLinearPmap) '' c :=
+    IsChain (· ≤ ·) <| (fun x : ExtensionOf i f => x.toLinearPMap) '' c :=
   by
   rintro _ ⟨a, a_mem, rfl⟩ _ ⟨b, b_mem, rfl⟩ neq
   exact hchain a_mem b_mem (ne_of_apply_ne _ neq)
-#align module.Baer.chain_linear_pmap_of_chain_extension_of Module.Baer.chain_linearPmap_of_chain_extensionOf
+#align module.Baer.chain_linear_pmap_of_chain_extension_of Module.Baer.chain_linearPMap_of_chain_extensionOf
 
 /-- The maximal element of every nonempty chain of `extension_of i f`. -/
 def ExtensionOf.max {c : Set (ExtensionOf i f)} (hchain : IsChain (· ≤ ·) c)
     (hnonempty : c.Nonempty) : ExtensionOf i f :=
   {
-    LinearPmap.sup _
+    LinearPMap.supₛ _
       (IsChain.directedOn <|
-        chain_linearPmap_of_chain_extensionOf
+        chain_linearPMap_of_chain_extensionOf
           hchain) with
     le :=
       le_trans hnonempty.some.le <|
-        (LinearPmap.le_sup _ <|
+        (LinearPMap.le_supₛ _ <|
             (Set.mem_image _ _ _).mpr ⟨hnonempty.some, hnonempty.choose_spec, rfl⟩).1
     is_extension := fun m =>
       by
@@ -188,14 +188,14 @@ def ExtensionOf.max {c : Set (ExtensionOf i f)} (hchain : IsChain (· ≤ ·) c)
       symm
       generalize_proofs _ h0 h1
       exact
-        LinearPmap.sup_apply (IsChain.directedOn <| chain_linear_pmap_of_chain_extension_of hchain)
+        LinearPMap.supₛ_apply (IsChain.directedOn <| chain_linear_pmap_of_chain_extension_of hchain)
           ((Set.mem_image _ _ _).mpr ⟨hnonempty.some, hnonempty.some_spec, rfl⟩) ⟨i m, h1⟩ }
 #align module.Baer.extension_of.max Module.Baer.ExtensionOf.max
 
 theorem ExtensionOf.le_max {c : Set (ExtensionOf i f)} (hchain : IsChain (· ≤ ·) c)
     (hnonempty : c.Nonempty) (a : ExtensionOf i f) (ha : a ∈ c) :
     a ≤ ExtensionOf.max hchain hnonempty :=
-  LinearPmap.le_sup (IsChain.directedOn <| chain_linearPmap_of_chain_extensionOf hchain) <|
+  LinearPMap.le_supₛ (IsChain.directedOn <| chain_linearPMap_of_chain_extensionOf hchain) <|
     (Set.mem_image _ _ _).mpr ⟨a, ha, rfl⟩
 #align module.Baer.extension_of.le_max Module.Baer.ExtensionOf.le_max
 
@@ -219,7 +219,7 @@ instance ExtensionOf.inhabited : Inhabited (ExtensionOf i f)
       le := le_refl _
       is_extension := fun m =>
         by
-        simp only [LinearPmap.mk_apply, LinearMap.coe_mk]
+        simp only [LinearPMap.mk_apply, LinearMap.coe_mk]
         congr
         exact Fact.out (Function.Injective i) (⟨i m, ⟨_, rfl⟩⟩ : i.range).2.choose_spec.symm }
 #align module.Baer.extension_of.inhabited Module.Baer.ExtensionOf.inhabited
@@ -277,9 +277,9 @@ def ExtensionOfMaxAdjoin.ideal (y : N) : Ideal R :=
 /-- A linear map `I ⟶ Q` by `x ↦ f' (x • y)` where `f'` is the maximal extension-/
 def ExtensionOfMaxAdjoin.idealTo (y : N) : ExtensionOfMaxAdjoin.ideal i f y →ₗ[R] Q
     where
-  toFun z := (extensionOfMax i f).toLinearPmap ⟨(↑z : R) • y, z.Prop⟩
-  map_add' z1 z2 := by simp [← (extension_of_max i f).toLinearPmap.map_add, add_smul]
-  map_smul' z1 z2 := by simp [← (extension_of_max i f).toLinearPmap.map_smul, mul_smul] <;> rfl
+  toFun z := (extensionOfMax i f).toLinearPMap ⟨(↑z : R) • y, z.Prop⟩
+  map_add' z1 z2 := by simp [← (extension_of_max i f).toLinearPMap.map_add, add_smul]
+  map_smul' z1 z2 := by simp [← (extension_of_max i f).toLinearPMap.map_smul, mul_smul] <;> rfl
 #align module.Baer.extension_of_max_adjoin.ideal_to Module.Baer.ExtensionOfMaxAdjoin.idealTo
 
 /-- Since we assumed `Q` being Baer, the linear map `x ↦ f' (x • y) : I ⟶ Q` extends to `R ⟶ Q`,
@@ -300,7 +300,7 @@ theorem ExtensionOfMaxAdjoin.extendIdealTo_wd' (h : Module.Baer R Q) {y : N} (r
   rw [extension_of_max_adjoin.extend_ideal_to_is_extension i f h y r
       (by rw [eq1] <;> exact Submodule.zero_mem _ : r • y ∈ _)]
   simp only [extension_of_max_adjoin.ideal_to, LinearMap.coe_mk, eq1, Subtype.coe_mk, ←
-    ZeroMemClass.zero_def, (extension_of_max i f).toLinearPmap.map_zero]
+    ZeroMemClass.zero_def, (extension_of_max i f).toLinearPMap.map_zero]
 #align module.Baer.extension_of_max_adjoin.extend_ideal_to_wd' Module.Baer.ExtensionOfMaxAdjoin.extendIdealTo_wd'
 
 theorem ExtensionOfMaxAdjoin.extendIdealTo_wd (h : Module.Baer R Q) {y : N} (r r' : R)
@@ -314,7 +314,7 @@ theorem ExtensionOfMaxAdjoin.extendIdealTo_wd (h : Module.Baer R Q) {y : N} (r r
 
 theorem ExtensionOfMaxAdjoin.extendIdealTo_eq (h : Module.Baer R Q) {y : N} (r : R)
     (hr : r • y ∈ (extensionOfMax i f).domain) :
-    ExtensionOfMaxAdjoin.extendIdealTo i f h y r = (extensionOfMax i f).toLinearPmap ⟨r • y, hr⟩ :=
+    ExtensionOfMaxAdjoin.extendIdealTo i f h y r = (extensionOfMax i f).toLinearPMap ⟨r • y, hr⟩ :=
   by
   simp only [extension_of_max_adjoin.extend_ideal_to_is_extension i f h _ _ hr,
     extension_of_max_adjoin.ideal_to, LinearMap.coe_mk, Subtype.coe_mk]
@@ -324,7 +324,7 @@ theorem ExtensionOfMaxAdjoin.extendIdealTo_eq (h : Module.Baer R Q) {y : N} (r :
 -/
 def ExtensionOfMaxAdjoin.extensionToFun (h : Module.Baer R Q) {y : N} :
     (extensionOfMax i f).domain ⊔ Submodule.span R {y} → Q := fun x =>
-  (extensionOfMax i f).toLinearPmap (ExtensionOfMaxAdjoin.fst i x) +
+  (extensionOfMax i f).toLinearPMap (ExtensionOfMaxAdjoin.fst i x) +
     ExtensionOfMaxAdjoin.extendIdealTo i f h y (ExtensionOfMaxAdjoin.snd i x)
 #align module.Baer.extension_of_max_adjoin.extension_to_fun Module.Baer.ExtensionOfMaxAdjoin.extensionToFun
 
@@ -332,7 +332,7 @@ theorem ExtensionOfMaxAdjoin.extensionToFun_wd (h : Module.Baer R Q) {y : N}
     (x : (extensionOfMax i f).domain ⊔ Submodule.span R {y}) (a : (extensionOfMax i f).domain)
     (r : R) (eq1 : ↑x = ↑a + r • y) :
     ExtensionOfMaxAdjoin.extensionToFun i f h x =
-      (extensionOfMax i f).toLinearPmap a + ExtensionOfMaxAdjoin.extendIdealTo i f h y r :=
+      (extensionOfMax i f).toLinearPMap a + ExtensionOfMaxAdjoin.extendIdealTo i f h y r :=
   by
   cases' a with a ha
   rw [Subtype.coe_mk] at eq1
@@ -345,7 +345,7 @@ theorem ExtensionOfMaxAdjoin.extensionToFun_wd (h : Module.Baer R Q) {y : N}
       (by rw [← eq2] <;> exact Submodule.sub_mem _ (extension_of_max_adjoin.fst i x).2 ha)
   simp only [map_sub, sub_smul, sub_eq_iff_eq_add] at eq3
   unfold extension_of_max_adjoin.extension_to_fun
-  rw [eq3, ← add_assoc, ← (extension_of_max i f).toLinearPmap.map_add, AddMemClass.mk_add_mk]
+  rw [eq3, ← add_assoc, ← (extension_of_max i f).toLinearPMap.map_add, AddMemClass.mk_add_mk]
   congr
   ext
   rw [Subtype.coe_mk, add_sub, ← eq1]
@@ -368,7 +368,7 @@ def extensionOfMaxAdjoin (h : Module.Baer R Q) (y : N) : ExtensionOf i f
           by
           rw [extension_of_max_adjoin.eqn, extension_of_max_adjoin.eqn, add_smul]
           abel
-        rw [extension_of_max_adjoin.extension_to_fun_wd i f h (a + b) _ _ eq1, LinearPmap.map_add,
+        rw [extension_of_max_adjoin.extension_to_fun_wd i f h (a + b) _ _ eq1, LinearPMap.map_add,
           map_add]
         unfold extension_of_max_adjoin.extension_to_fun
         abel
@@ -381,10 +381,10 @@ def extensionOfMaxAdjoin (h : Module.Baer R Q) (y : N) : ExtensionOf i f
           rw [extension_of_max_adjoin.eqn, smul_add, smul_eq_mul, mul_smul]
           rfl
         rw [extension_of_max_adjoin.extension_to_fun_wd i f h (r • a) _ _ eq1, LinearMap.map_smul,
-          LinearPmap.map_smul, ← smul_add]
+          LinearPMap.map_smul, ← smul_add]
         congr }
   is_extension m := by
-    simp only [LinearPmap.mk_apply, LinearMap.coe_mk]
+    simp only [LinearPMap.mk_apply, LinearMap.coe_mk]
     rw [(extension_of_max i f).is_extension,
       extension_of_max_adjoin.extension_to_fun_wd i f h _ ⟨i m, _⟩ 0 _, map_zero, add_zero]
     simp
@@ -415,13 +415,13 @@ protected theorem injective (h : Module.Baer R Q) : Module.Injective R Q :=
     out := fun X Y ins1 ins2 ins3 ins4 i hi f =>
       haveI : Fact (Function.Injective i) := ⟨hi⟩
       ⟨{  toFun := fun y =>
-            (extension_of_max i f).toLinearPmap
+            (extension_of_max i f).toLinearPMap
               ⟨y, (extension_of_max_to_submodule_eq_top i f h).symm ▸ trivial⟩
           map_add' := fun x y => by
-            rw [← LinearPmap.map_add]
+            rw [← LinearPMap.map_add]
             congr
           map_smul' := fun r x => by
-            rw [← LinearPmap.map_smul]
+            rw [← LinearPMap.map_smul]
             congr },
         fun x => ((extension_of_max i f).is_extension x).symm⟩ }
 #align module.Baer.injective Module.Baer.injective

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

Purely automatic replacement. If this is in any way controversial; I'm happy to just close this PR.

@@ -259,14 +259,14 @@ set_option align.precheck false in
 set_option linter.uppercaseLean3 false in
 #align module.Baer.extension_of_max_adjoin.aux1 Module.Baer.extensionOfMax_adjoin.aux1
 
-/-- If `x ∈ M ⊔ ⟨y⟩`, then `x = m + r • y`, `fst` pick an arbitrary such `m`.-/
+/-- If `x ∈ M ⊔ ⟨y⟩`, then `x = m + r • y`, `fst` pick an arbitrary such `m`. -/
 def ExtensionOfMaxAdjoin.fst {y : N} (x : supExtensionOfMaxSingleton i f y) :
     (extensionOfMax i f).domain :=
   (extensionOfMax_adjoin.aux1 i x).choose
 set_option linter.uppercaseLean3 false in
 #align module.Baer.extension_of_max_adjoin.fst Module.Baer.ExtensionOfMaxAdjoin.fst
 
-/-- If `x ∈ M ⊔ ⟨y⟩`, then `x = m + r • y`, `snd` pick an arbitrary such `r`.-/
+/-- If `x ∈ M ⊔ ⟨y⟩`, then `x = m + r • y`, `snd` pick an arbitrary such `r`. -/
 def ExtensionOfMaxAdjoin.snd {y : N} (x : supExtensionOfMaxSingleton i f y) : R :=
   (extensionOfMax_adjoin.aux1 i x).choose_spec.choose
 set_option linter.uppercaseLean3 false in
@@ -453,7 +453,7 @@ theorem extension_property_addMonoidHom (h : Module.Baer ℤ Q)
   ⟨g', congr(LinearMap.toAddMonoidHom $hg')⟩
 
 /-- **Baer's criterion** for injective module : a Baer module is an injective module, i.e. if every
-linear map from an ideal can be extended, then the module is injective.-/
+linear map from an ideal can be extended, then the module is injective. -/
 protected theorem injective (h : Module.Baer R Q) : Module.Injective R Q where
   out := fun X Y _ _ _ _ i hi f ↦ by
     obtain ⟨h, H⟩ := Module.Baer.extension_property h i hi f

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)

@@ -93,7 +93,6 @@ set_option linter.uppercaseLean3 false in
 namespace Module.Baer
 
 variable {R Q} {M N : Type*} [AddCommGroup M] [AddCommGroup N]
-
 variable [Module R M] [Module R N] (i : M →ₗ[R] N) (f : M →ₗ[R] Q)
 
 /-- If we view `M` as a submodule of `N` via the injective linear map `i : M ↪ N`, then a submodule

Per the style guidelines, λ is disallowed in mathlib. This is close to exhaustive; I left some tactic code alone when it seemed to me that tactic could be upstreamed soon.

Notes

• In lines I was modifying anyway, I also converted => to ↦.
• Also contains some mild in-passing indentation fixes in Mathlib/Order/SupClosed.
• Some doc comments still contained Lean 3 syntax λ x, , which I also replaced.

@@ -445,7 +445,7 @@ protected theorem extension_property (h : Module.Baer R Q)
     { toFun := ((extensionOfMax f g).toLinearPMap
         ⟨·, (extensionOfMax_to_submodule_eq_top f g h).symm ▸ ⟨⟩⟩)
       map_add' := fun x y ↦ by rw [← LinearPMap.map_add]; congr
-      map_smul' := fun r x ↦  by rw [← LinearPMap.map_smul]; dsimp } <|
+      map_smul' := fun r x ↦ by rw [← LinearPMap.map_smul]; dsimp } <|
     LinearMap.ext fun x ↦ ((extensionOfMax f g).is_extension x).symm
 
 theorem extension_property_addMonoidHom (h : Module.Baer ℤ Q)

Homogenises porting notes via capitalisation and addition of whitespace.

It makes the following changes:

• converts "--porting note" into "-- Porting note";
• converts "porting note" into "Porting note".

@@ -292,12 +292,12 @@ set_option linter.uppercaseLean3 false in
 def ExtensionOfMaxAdjoin.idealTo (y : N) : ExtensionOfMaxAdjoin.ideal i f y →ₗ[R] Q where
   toFun (z : { x // x ∈ ideal i f y }) := (extensionOfMax i f).toLinearPMap ⟨(↑z : R) • y, z.prop⟩
   map_add' (z1 z2 : { x // x ∈ ideal i f y }) := by
-    -- porting note: a single simp took care of the goal before reenableeta
+    -- Porting note: a single simp took care of the goal before reenableeta
     simp_rw [← (extensionOfMax i f).toLinearPMap.map_add]
     congr
     apply add_smul
   map_smul' z1 (z2 : {x // x ∈ ideal i f y}) := by
-    -- porting note: a single simp took care of the goal before reenableeta
+    -- Porting note: a single simp took care of the goal before reenableeta
     simp_rw [← (extensionOfMax i f).toLinearPMap.map_smul]
     congr 2
     apply mul_smul
@@ -343,7 +343,7 @@ set_option linter.uppercaseLean3 false in
 theorem ExtensionOfMaxAdjoin.extendIdealTo_eq (h : Module.Baer R Q) {y : N} (r : R)
     (hr : r • y ∈ (extensionOfMax i f).domain) : ExtensionOfMaxAdjoin.extendIdealTo i f h y r =
     (extensionOfMax i f).toLinearPMap ⟨r • y, hr⟩ := by
-    -- porting note: in mathlib3 `AddHom.coe_mk` was not needed
+    -- Porting note: in mathlib3 `AddHom.coe_mk` was not needed
   simp only [ExtensionOfMaxAdjoin.extendIdealTo_is_extension i f h _ _ hr,
     ExtensionOfMaxAdjoin.idealTo, LinearMap.coe_mk, Subtype.coe_mk, AddHom.coe_mk]
 set_option linter.uppercaseLean3 false in

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

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

@@ -54,7 +54,7 @@ map to `Q`, i.e. in the following diagram, if `f` is injective then there is an
   Q
   ```
 -/
-class Module.Injective : Prop where
+@[mk_iff] class Module.Injective : Prop where
   out : ∀ ⦃X Y : Type v⦄ [AddCommGroup X] [AddCommGroup Y] [Module R X] [Module R Y]
     (f : X →ₗ[R] Y) (_ : Function.Injective f) (g : X →ₗ[R] Q),
     ∃ h : Y →ₗ[R] Q, ∀ x, h (f x) = g x
@@ -462,7 +462,7 @@ protected theorem injective (h : Module.Baer R Q) : Module.Injective R Q where
 set_option linter.uppercaseLean3 false in
 #align module.Baer.injective Module.Baer.injective
 
-protected theorem of_injective [UnivLE.{u, v}] (inj : Module.Injective R Q) : Module.Baer R Q := by
+protected theorem of_injective [Small.{v} R] (inj : Module.Injective R Q) : Module.Baer R Q := by
   intro I g
   let eI := Shrink.linearEquiv I R
   let eR := Shrink.linearEquiv R R
@@ -470,7 +470,7 @@ protected theorem of_injective [UnivLE.{u, v}] (inj : Module.Injective R Q) : Mo
     (eR.symm.injective.comp <| Subtype.val_injective.comp eI.injective) (g ∘ₗ eI.toLinearMap)
   exact ⟨g' ∘ₗ eR.symm.toLinearMap, fun x mx ↦ by simpa [eI,eR] using hg' (equivShrink I ⟨x, mx⟩)⟩
 
-protected theorem iff_injective [UnivLE.{u, v}] : Module.Baer R Q ↔ Module.Injective R Q :=
+protected theorem iff_injective [Small.{v} R] : Module.Baer R Q ↔ Module.Injective R Q :=
   ⟨Module.Baer.injective, Module.Baer.of_injective⟩
 
 end Module.Baer
@@ -479,7 +479,7 @@ section ULift
 
 variable {M : Type v} [AddCommGroup M] [Module R M]
 
-lemma Module.ulift_injective_of_injective [UnivLE.{u, v}]
+lemma Module.ulift_injective_of_injective [Small.{v} R]
     (inj : Module.Injective R M) :
     Module.Injective R (ULift.{v'} M) := Module.Baer.injective fun I g ↦
   have ⟨g', hg'⟩ := Module.Baer.iff_injective.mpr inj I (ULift.moduleEquiv.toLinearMap ∘ₗ g)
@@ -496,7 +496,7 @@ lemma Module.injective_of_ulift_injective
     ⟨ULift.moduleEquiv.toLinearMap ∘ₗ g' ∘ₗ ULift.moduleEquiv.symm.toLinearMap,
       fun x ↦ by exact congr(ULift.down $(hg' ⟨x⟩))⟩
 
-variable (M) [UnivLE.{u, v}]
+variable (M) [Small.{v} R]
 
 lemma Module.injective_iff_ulift_injective :
     Module.Injective R M ↔ Module.Injective R (ULift.{v'} M) :=
@@ -516,8 +516,7 @@ section lifting_property
 
 universe uR uM uP uP'
 
-variable [UnivLE.{uR, uM}]
-variable (R : Type uR) [Ring R]
+variable (R : Type uR) [Ring R] [Small.{uM} R]
 variable (M : Type uM) [AddCommGroup M] [Module R M] [inj : Module.Injective R M]
 variable (P : Type uP) [AddCommGroup P] [Module R P]
 variable (P' : Type uP') [AddCommGroup P'] [Module R P']

Co-authored-by: Scott Morrison <scott.morrison@gmail.com>

@@ -468,7 +468,7 @@ protected theorem of_injective [UnivLE.{u, v}] (inj : Module.Injective R Q) : Mo
   let eR := Shrink.linearEquiv R R
   obtain ⟨g', hg'⟩ := Module.Injective.out (eR.symm.toLinearMap ∘ₗ I.subtype ∘ₗ eI.toLinearMap)
     (eR.symm.injective.comp <| Subtype.val_injective.comp eI.injective) (g ∘ₗ eI.toLinearMap)
-  exact ⟨g' ∘ₗ eR.symm.toLinearMap, fun x mx ↦ by simpa using hg' (equivShrink I ⟨x, mx⟩)⟩
+  exact ⟨g' ∘ₗ eR.symm.toLinearMap, fun x mx ↦ by simpa [eI,eR] using hg' (equivShrink I ⟨x, mx⟩)⟩
 
 protected theorem iff_injective [UnivLE.{u, v}] : Module.Baer R Q ↔ Module.Injective R Q :=
   ⟨Module.Baer.injective, Module.Baer.of_injective⟩

This is because injective modules are Baer, and Baer modules do not concern universe levels

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

@@ -7,9 +7,7 @@ import Mathlib.CategoryTheory.Preadditive.Injective
 import Mathlib.Algebra.Category.ModuleCat.EpiMono
 import Mathlib.RingTheory.Ideal.Basic
 import Mathlib.LinearAlgebra.LinearPMap
-import Mathlib.Data.TypeMax -- Porting note: added for universe issues
-import Mathlib.Algebra.Module.ULift
-import Mathlib.Data.Set.Basic
+import Mathlib.Logic.Equiv.TransferInstance
 
 #align_import algebra.module.injective from "leanprover-community/mathlib"@"f8d8465c3c392a93b9ed226956e26dee00975946"
 
@@ -40,9 +38,9 @@ import Mathlib.Data.Set.Basic
 
 noncomputable section
 
-universe u v
+universe u v v'
 
-variable (R : Type u) [Ring R] (Q : TypeMax.{v,u}) [AddCommGroup Q] [Module R Q]
+variable (R : Type u) [Ring R] (Q : Type v) [AddCommGroup Q] [Module R Q]
 
 /--
 An `R`-module `Q` is injective if and only if every injective `R`-linear map descends to a linear
@@ -57,35 +55,32 @@ map to `Q`, i.e. in the following diagram, if `f` is injective then there is an
   ```
 -/
 class Module.Injective : Prop where
-  out : ∀ (X Y : TypeMax.{v,u}) [AddCommGroup X] [AddCommGroup Y] [Module R X] [Module R Y]
+  out : ∀ ⦃X Y : Type v⦄ [AddCommGroup X] [AddCommGroup Y] [Module R X] [Module R Y]
     (f : X →ₗ[R] Y) (_ : Function.Injective f) (g : X →ₗ[R] Q),
     ∃ h : Y →ₗ[R] Q, ∀ x, h (f x) = g x
 #align module.injective Module.Injective
 
--- Porting note: egregious max u v abuse
-theorem Module.injective_object_of_injective_module [Module.Injective.{u, v} R Q] :
-    CategoryTheory.Injective.{max u v} (⟨Q⟩ : ModuleCat.{max u v} R) :=
-  { factors := fun g f mn => by
-      rcases Module.Injective.out _ _ f ((ModuleCat.mono_iff_injective f).mp mn) g with ⟨h, eq1⟩
-      exact ⟨h, LinearMap.ext eq1⟩ }
+theorem Module.injective_object_of_injective_module [inj : Module.Injective R Q] :
+    CategoryTheory.Injective (ModuleCat.of R Q) where
+  factors g f m :=
+    have ⟨l, h⟩ := inj.out f ((ModuleCat.mono_iff_injective f).mp m) g
+    ⟨l, LinearMap.ext h⟩
 #align module.injective_object_of_injective_module Module.injective_object_of_injective_module
 
 theorem Module.injective_module_of_injective_object
-    [CategoryTheory.Injective.{max u v} (⟨Q⟩ : ModuleCat.{max u v} R)] :
-    Module.Injective.{u, v} R Q :=
-  { out := fun X Y ins1 ins2 ins3 ins4 f hf g => by
-      skip
-      rcases@CategoryTheory.Injective.factors (ModuleCat R) _ ⟨Q⟩ _ ⟨X⟩ ⟨Y⟩ g f
-          ((ModuleCat.mono_iff_injective _).mpr hf) with
-        ⟨h, rfl⟩
-      exact ⟨h, fun x => rfl⟩ }
+    [inj : CategoryTheory.Injective <| ModuleCat.of R Q] :
+    Module.Injective R Q where
+  out X Y _ _ _ _ f hf g := by
+    have : CategoryTheory.Mono (ModuleCat.ofHom f) := (ModuleCat.mono_iff_injective _).mpr hf
+    obtain ⟨l, rfl⟩ := inj.factors (ModuleCat.ofHom g) (ModuleCat.ofHom f)
+    exact ⟨l, fun _ ↦ rfl⟩
 #align module.injective_module_of_injective_object Module.injective_module_of_injective_object
 
 theorem Module.injective_iff_injective_object :
-    Module.Injective.{u, v} R Q ↔
-      CategoryTheory.Injective.{max u v} (⟨Q⟩ : ModuleCat.{max u v} R) :=
-  ⟨fun h => @Module.injective_object_of_injective_module R _ Q _ _ h, fun h =>
-    @Module.injective_module_of_injective_object R _ Q _ _ h⟩
+    Module.Injective R Q ↔
+    CategoryTheory.Injective (ModuleCat.of R Q) :=
+  ⟨fun _ => injective_object_of_injective_module R Q,
+   fun _ => injective_module_of_injective_object R Q⟩
 #align module.injective_iff_injective_object Module.injective_iff_injective_object
 
 /-- An `R`-module `Q` satisfies Baer's criterion if any `R`-linear map from an `Ideal R` extends to
@@ -97,7 +92,7 @@ set_option linter.uppercaseLean3 false in
 
 namespace Module.Baer
 
-variable {R Q} {M N : Type max u v} [AddCommGroup M] [AddCommGroup N]
+variable {R Q} {M N : Type*} [AddCommGroup M] [AddCommGroup N]
 
 variable [Module R M] [Module R N] (i : M →ₗ[R] N) (f : M →ₗ[R] Q)
 
@@ -443,32 +438,93 @@ theorem extensionOfMax_to_submodule_eq_top (h : Module.Baer R Q) :
 set_option linter.uppercaseLean3 false in
 #align module.Baer.extension_of_max_to_submodule_eq_top Module.Baer.extensionOfMax_to_submodule_eq_top
 
+protected theorem extension_property (h : Module.Baer R Q)
+    (f : M →ₗ[R] N) (hf : Function.Injective f) (g : M →ₗ[R] Q) : ∃ h, h ∘ₗ f = g :=
+  haveI : Fact (Function.Injective f) := ⟨hf⟩
+  Exists.intro
+    { toFun := ((extensionOfMax f g).toLinearPMap
+        ⟨·, (extensionOfMax_to_submodule_eq_top f g h).symm ▸ ⟨⟩⟩)
+      map_add' := fun x y ↦ by rw [← LinearPMap.map_add]; congr
+      map_smul' := fun r x ↦  by rw [← LinearPMap.map_smul]; dsimp } <|
+    LinearMap.ext fun x ↦ ((extensionOfMax f g).is_extension x).symm
+
+theorem extension_property_addMonoidHom (h : Module.Baer ℤ Q)
+    (f : M →+ N) (hf : Function.Injective f) (g : M →+ Q) : ∃ h : N →+ Q, h.comp f = g :=
+  have ⟨g', hg'⟩ := h.extension_property f.toIntLinearMap hf g.toIntLinearMap
+  ⟨g', congr(LinearMap.toAddMonoidHom $hg')⟩
+
 /-- **Baer's criterion** for injective module : a Baer module is an injective module, i.e. if every
 linear map from an ideal can be extended, then the module is injective.-/
-protected theorem injective (h : Module.Baer R Q) : Module.Injective R Q :=
-  { out := fun X Y ins1 ins2 ins3 ins4 i hi f =>
-      haveI : Fact (Function.Injective i) := ⟨hi⟩
-      ⟨{  toFun := fun y =>
-            (extensionOfMax i f).toLinearPMap
-              ⟨y, (extensionOfMax_to_submodule_eq_top i f h).symm ▸ trivial⟩
-          map_add' := fun x y => by
-            rw [← LinearPMap.map_add]
-            congr
-          map_smul' := fun r x => by
-            rw [← LinearPMap.map_smul]
-            -- Porting note: used to be congr
-            dsimp },
-        fun x => ((extensionOfMax i f).is_extension x).symm⟩ }
+protected theorem injective (h : Module.Baer R Q) : Module.Injective R Q where
+  out := fun X Y _ _ _ _ i hi f ↦ by
+    obtain ⟨h, H⟩ := Module.Baer.extension_property h i hi f
+    exact ⟨h, DFunLike.congr_fun H⟩
 set_option linter.uppercaseLean3 false in
 #align module.Baer.injective Module.Baer.injective
 
-protected theorem of_injective (inj : Module.Injective R Q) : Module.Baer R Q := fun I g ↦
-  let ⟨g', hg'⟩ := inj.1 (ULift.{max u v} I) (ULift.{max u v} R)
-    (ULift.moduleEquiv.symm.toLinearMap ∘ₗ I.subtype ∘ₗ ULift.moduleEquiv.toLinearMap)
-    (fun a b h ↦ by aesop) (g ∘ₗ ULift.moduleEquiv.toLinearMap)
-  ⟨g' ∘ₗ ULift.moduleEquiv.symm.toLinearMap, by aesop⟩
+protected theorem of_injective [UnivLE.{u, v}] (inj : Module.Injective R Q) : Module.Baer R Q := by
+  intro I g
+  let eI := Shrink.linearEquiv I R
+  let eR := Shrink.linearEquiv R R
+  obtain ⟨g', hg'⟩ := Module.Injective.out (eR.symm.toLinearMap ∘ₗ I.subtype ∘ₗ eI.toLinearMap)
+    (eR.symm.injective.comp <| Subtype.val_injective.comp eI.injective) (g ∘ₗ eI.toLinearMap)
+  exact ⟨g' ∘ₗ eR.symm.toLinearMap, fun x mx ↦ by simpa using hg' (equivShrink I ⟨x, mx⟩)⟩
 
-protected theorem iff_injective : Module.Baer R Q ↔ Module.Injective R Q :=
+protected theorem iff_injective [UnivLE.{u, v}] : Module.Baer R Q ↔ Module.Injective R Q :=
   ⟨Module.Baer.injective, Module.Baer.of_injective⟩
 
 end Module.Baer
+
+section ULift
+
+variable {M : Type v} [AddCommGroup M] [Module R M]
+
+lemma Module.ulift_injective_of_injective [UnivLE.{u, v}]
+    (inj : Module.Injective R M) :
+    Module.Injective R (ULift.{v'} M) := Module.Baer.injective fun I g ↦
+  have ⟨g', hg'⟩ := Module.Baer.iff_injective.mpr inj I (ULift.moduleEquiv.toLinearMap ∘ₗ g)
+  ⟨ULift.moduleEquiv.symm.toLinearMap ∘ₗ g', fun r hr ↦ ULift.ext _ _ <| hg' r hr⟩
+
+lemma Module.injective_of_ulift_injective
+    (inj : Module.Injective R (ULift.{v'} M)) :
+    Module.Injective R M where
+  out X Y _ _ _ _ f hf g :=
+    let eX := ULift.moduleEquiv.{_,_,v'} (R := R) (M := X)
+    have ⟨g', hg'⟩ := inj.out (ULift.moduleEquiv.{_,_,v'}.symm.toLinearMap ∘ₗ f ∘ₗ eX.toLinearMap)
+      (by exact ULift.moduleEquiv.symm.injective.comp <| hf.comp eX.injective)
+      (ULift.moduleEquiv.symm.toLinearMap ∘ₗ g ∘ₗ eX.toLinearMap)
+    ⟨ULift.moduleEquiv.toLinearMap ∘ₗ g' ∘ₗ ULift.moduleEquiv.symm.toLinearMap,
+      fun x ↦ by exact congr(ULift.down $(hg' ⟨x⟩))⟩
+
+variable (M) [UnivLE.{u, v}]
+
+lemma Module.injective_iff_ulift_injective :
+    Module.Injective R M ↔ Module.Injective R (ULift.{v'} M) :=
+  ⟨Module.ulift_injective_of_injective R,
+   Module.injective_of_ulift_injective R⟩
+
+instance ModuleCat.ulift_injective_of_injective
+    [inj : CategoryTheory.Injective <| ModuleCat.of R M] :
+    CategoryTheory.Injective <| ModuleCat.of R (ULift.{v'} M) :=
+  Module.injective_object_of_injective_module
+    (inj := Module.ulift_injective_of_injective
+      (inj := Module.injective_module_of_injective_object (inj := inj)))
+
+end ULift
+
+section lifting_property
+
+universe uR uM uP uP'
+
+variable [UnivLE.{uR, uM}]
+variable (R : Type uR) [Ring R]
+variable (M : Type uM) [AddCommGroup M] [Module R M] [inj : Module.Injective R M]
+variable (P : Type uP) [AddCommGroup P] [Module R P]
+variable (P' : Type uP') [AddCommGroup P'] [Module R P']
+
+lemma Module.Injective.extension_property
+    (f : P →ₗ[R] P') (hf : Function.Injective f)
+    (g : P →ₗ[R] M) : ∃ h : P' →ₗ[R] M, h ∘ₗ f = g :=
+  (Module.Baer.of_injective inj).extension_property f hf g
+
+end lifting_property

• Remove Data.Set.Basic from scripts/noshake.json.
• Remove an exception that was used by examples only, move these examples to a new test file.
• Drop an exception for Order.Filter.Basic dependency on Control.Traversable.Instances, as the relevant parts were moved to Order.Filter.ListTraverse.
• Run lake exe shake --fix.

@@ -9,6 +9,7 @@ import Mathlib.RingTheory.Ideal.Basic
 import Mathlib.LinearAlgebra.LinearPMap
 import Mathlib.Data.TypeMax -- Porting note: added for universe issues
 import Mathlib.Algebra.Module.ULift
+import Mathlib.Data.Set.Basic
 
 #align_import algebra.module.injective from "leanprover-community/mathlib"@"f8d8465c3c392a93b9ed226956e26dee00975946"
 

Co-authored-by: Scott Morrison <scott.morrison@gmail.com> Co-authored-by: Eric Wieser <wieser.eric@gmail.com> Co-authored-by: Joachim Breitner <mail@joachim-breitner.de>

@@ -184,10 +184,6 @@ def ExtensionOf.max {c : Set (ExtensionOf i f)} (hchain : IsChain (· ≤ ·) c)
       refine' le_trans hnonempty.some.le <|
         (LinearPMap.le_sSup _ <|
             (Set.mem_image _ _ _).mpr ⟨hnonempty.some, hnonempty.choose_spec, rfl⟩).1
-      -- porting note: this subgoal didn't exist before the reenableeta branch
-      -- follow-up note: the subgoal was moved from after `refine'` in `is_extension` to here
-      -- after the behavior of `refine'` changed.
-      exact (IsChain.directedOn <| chain_linearPMap_of_chain_extensionOf hchain)
     is_extension := fun m => by
       refine' Eq.trans (hnonempty.some.is_extension m) _
       symm

• Redefine Set.image2 to use ∃ a ∈ s, ∃ b ∈ t, f a b = c instead of ∃ a b, a ∈ s ∧ b ∈ t ∧ f a b = c.
• Redefine Set.seq as Set.image2. The new definition is equal to the old one but rw [Set.seq] gives a different result.
• Redefine Filter.map₂ to use ∃ u ∈ f, ∃ v ∈ g, image2 m u v ⊆ s instead of ∃ u v, u ∈ f ∧ v ∈ g ∧ ...
• Update lemmas like Set.mem_image2, Finset.mem_image₂, Set.mem_mul, Finset.mem_div etc

The two reasons to make the change are:

• ∃ a ∈ s, ∃ b ∈ t, _ is a simp-normal form, and
• it looks a bit nicer.

@@ -260,7 +260,7 @@ private theorem extensionOfMax_adjoin.aux1 {y : N} (x : supExtensionOfMaxSinglet
     ∃ (a : (extensionOfMax i f).domain) (b : R), x.1 = a.1 + b • y := by
   have mem1 : x.1 ∈ (_ : Set _) := x.2
   rw [Submodule.coe_sup] at mem1
-  rcases mem1 with ⟨a, b, a_mem, b_mem : b ∈ (Submodule.span R _ : Submodule R N), eq1⟩
+  rcases mem1 with ⟨a, a_mem, b, b_mem : b ∈ (Submodule.span R _ : Submodule R N), eq1⟩
   rw [Submodule.mem_span_singleton] at b_mem
   rcases b_mem with ⟨z, eq2⟩
   exact ⟨⟨a, a_mem⟩, z, by rw [← eq1, ← eq2]⟩

I used the regex \(\(· (.) ·\) (.)\), replacing with ($2 $1 ·).

@@ -219,7 +219,7 @@ instance ExtensionOf.inhabited : Inhabited (ExtensionOf i f) where
             dsimp
             rw [← Fact.out (p := Function.Injective i) eq1, map_add]
           map_smul' := fun r x => by
-            have eq1 : r • _ = (r • x).1 := congr_arg ((· • ·) r) x.2.choose_spec
+            have eq1 : r • _ = (r • x).1 := congr_arg (r • ·) x.2.choose_spec
             rw [← LinearMap.map_smul, ← (r • x).2.choose_spec] at eq1
             dsimp
             rw [← Fact.out (p := Function.Injective i) eq1, LinearMap.map_smul] }

We already know that Baer modules are injective, the other direction is easier

@@ -8,6 +8,7 @@ import Mathlib.Algebra.Category.ModuleCat.EpiMono
 import Mathlib.RingTheory.Ideal.Basic
 import Mathlib.LinearAlgebra.LinearPMap
 import Mathlib.Data.TypeMax -- Porting note: added for universe issues
+import Mathlib.Algebra.Module.ULift
 
 #align_import algebra.module.injective from "leanprover-community/mathlib"@"f8d8465c3c392a93b9ed226956e26dee00975946"
 
@@ -464,4 +465,13 @@ protected theorem injective (h : Module.Baer R Q) : Module.Injective R Q :=
 set_option linter.uppercaseLean3 false in
 #align module.Baer.injective Module.Baer.injective
 
+protected theorem of_injective (inj : Module.Injective R Q) : Module.Baer R Q := fun I g ↦
+  let ⟨g', hg'⟩ := inj.1 (ULift.{max u v} I) (ULift.{max u v} R)
+    (ULift.moduleEquiv.symm.toLinearMap ∘ₗ I.subtype ∘ₗ ULift.moduleEquiv.toLinearMap)
+    (fun a b h ↦ by aesop) (g ∘ₗ ULift.moduleEquiv.toLinearMap)
+  ⟨g' ∘ₗ ULift.moduleEquiv.symm.toLinearMap, by aesop⟩
+
+protected theorem iff_injective : Module.Baer R Q ↔ Module.Injective R Q :=
+  ⟨Module.Baer.injective, Module.Baer.of_injective⟩
+
 end Module.Baer

The bracket position seems off

@@ -175,8 +175,7 @@ set_option linter.uppercaseLean3 false in
 /-- The maximal element of every nonempty chain of `extension_of i f`. -/
 def ExtensionOf.max {c : Set (ExtensionOf i f)} (hchain : IsChain (· ≤ ·) c)
     (hnonempty : c.Nonempty) : ExtensionOf i f :=
-  {
-    LinearPMap.sSup _
+  { LinearPMap.sSup _
       (IsChain.directedOn <|
         chain_linearPMap_of_chain_extensionOf
           hchain) with

We still have the exact_mod_cast tactic, used in a few places, which somehow (?) works a little bit harder to prevent the expected type influencing the elaboration of the term. I would like to get to the bottom of this, and it will be easier once the only usages of exact_mod_cast are the ones that don't work using the term elaborator by itself.

Co-authored-by: Scott Morrison <scott.morrison@gmail.com>

@@ -127,7 +127,7 @@ set_option linter.uppercaseLean3 false in
 theorem ExtensionOf.ext_iff {a b : ExtensionOf i f} :
     a = b ↔ ∃ _ : a.domain = b.domain, ∀ ⦃x : a.domain⦄ ⦃y : b.domain⦄,
     (x : N) = y → a.toLinearPMap x = b.toLinearPMap y :=
-  ⟨fun r => r ▸ ⟨rfl, fun x y h => congr_arg a.toFun <| by exact_mod_cast h⟩, fun ⟨h1, h2⟩ =>
+  ⟨fun r => r ▸ ⟨rfl, fun _ _ h => congr_arg a.toFun <| mod_cast h⟩, fun ⟨h1, h2⟩ =>
     ExtensionOf.ext h1 h2⟩
 set_option linter.uppercaseLean3 false in
 #align module.Baer.extension_of.ext_iff Module.Baer.ExtensionOf.ext_iff
@@ -160,7 +160,7 @@ instance : SemilatticeInf (ExtensionOf i f) :=
     fun X Y =>
     LinearPMap.ext rfl fun x y h => by
       congr
-      exact_mod_cast h
+      exact mod_cast h
 
 variable {i f}
 

PR contents

This is the supremum of

• #8284
• #8056
• #8023
• #8332
• #8226 (already approved)
• #7834 (already approved)

along with some minor fixes from failures on nightly-testing as Mathlib master is merged into it.

Note that some PRs for changes that are already compatible with the current toolchain and will be necessary have already been split out: #8380.

I am hopeful that in future we will be able to progressively merge adaptation PRs into a bump/v4.X.0 branch, so we never end up with a "big merge" like this. However one of these adaptation PRs (#8056) predates my new scheme for combined CI, and it wasn't possible to keep that PR viable in the meantime.

Lean PRs involved in this bump

In particular this includes adjustments for the Lean PRs

• leanprover/lean4#2778
• leanprover/lean4#2790
• leanprover/lean4#2783
• leanprover/lean4#2825
• leanprover/lean4#2722

leanprover/lean4#2778

We can get rid of all the

local macro_rules | `($x ^ $y) => `(HPow.hPow $x $y) -- Porting note: See issue [lean4#2220](https://github.com/leanprover/lean4/pull/2220)

macros across Mathlib (and in any projects that want to write natural number powers of reals).

leanprover/lean4#2722

Changes the default behaviour of simp to (config := {decide := false}). This makes simp (and consequentially norm_num) less powerful, but also more consistent, and less likely to blow up in long failures. This requires a variety of changes: changing some previously by simp or norm_num to decide or rfl, or adding (config := {decide := true}).

leanprover/lean4#2783

This changed the behaviour of simp so that simp [f] will only unfold "fully applied" occurrences of f. The old behaviour can be recovered with simp (config := { unfoldPartialApp := true }). We may in future add a syntax for this, e.g. simp [!f]; please provide feedback! In the meantime, we have made the following changes:

• switching to using explicit lemmas that have the intended level of application
• (config := { unfoldPartialApp := true }) in some places, to recover the old behaviour
• Using @[eqns] to manually adjust the equation lemmas for a particular definition, recovering the old behaviour just for that definition. See #8371, where we do this for Function.comp and Function.flip.

This change in Lean may require further changes down the line (e.g. adding the !f syntax, and/or upstreaming the special treatment for Function.comp and Function.flip, and/or removing this special treatment). Please keep an open and skeptical mind about these changes!

Co-authored-by: leanprover-community-mathlib4-bot <leanprover-community-mathlib4-bot@users.noreply.github.com> Co-authored-by: Scott Morrison <scott.morrison@gmail.com> Co-authored-by: Eric Wieser <wieser.eric@gmail.com> Co-authored-by: Mauricio Collares <mauricio@collares.org>

@@ -415,7 +415,7 @@ def extensionOfMaxAdjoin (h : Module.Baer R Q) (y : N) : ExtensionOf i f where
             ↑(r • ExtensionOfMaxAdjoin.fst i a) + (r • ExtensionOfMaxAdjoin.snd i a) • y := by
           rw [ExtensionOfMaxAdjoin.eqn, smul_add, smul_eq_mul, mul_smul]
           rfl
-        rw [ExtensionOfMaxAdjoin.extensionToFun_wd i f h (r • a) _ _ eq1, LinearMap.map_smul,
+        rw [ExtensionOfMaxAdjoin.extensionToFun_wd i f h (r • a :) _ _ eq1, LinearMap.map_smul,
           LinearPMap.map_smul, ← smul_add]
         congr }
   is_extension m := by

This rolls in the changed from #6928.

Co-authored-by: Thomas Murrills <thomasmurrills@gmail.com>

Co-authored-by: Scott Morrison <scott.morrison@gmail.com>

@@ -180,15 +180,16 @@ def ExtensionOf.max {c : Set (ExtensionOf i f)} (hchain : IsChain (· ≤ ·) c)
       (IsChain.directedOn <|
         chain_linearPMap_of_chain_extensionOf
           hchain) with
-    le :=
-      le_trans hnonempty.some.le <|
+    le := by
+      refine' le_trans hnonempty.some.le <|
         (LinearPMap.le_sSup _ <|
             (Set.mem_image _ _ _).mpr ⟨hnonempty.some, hnonempty.choose_spec, rfl⟩).1
+      -- porting note: this subgoal didn't exist before the reenableeta branch
+      -- follow-up note: the subgoal was moved from after `refine'` in `is_extension` to here
+      -- after the behavior of `refine'` changed.
+      exact (IsChain.directedOn <| chain_linearPMap_of_chain_extensionOf hchain)
     is_extension := fun m => by
       refine' Eq.trans (hnonempty.some.is_extension m) _
-      · -- porting note: this subgoal didn't exist before the reenableeta branch
-        intros c hchain _
-        exact (IsChain.directedOn <| chain_linearPMap_of_chain_extensionOf hchain)
       symm
       generalize_proofs _ h1
       exact

Co-authored-by: Eric Wieser <wieser.eric@gmail.com>

@@ -419,7 +419,6 @@ def extensionOfMaxAdjoin (h : Module.Baer R Q) (y : N) : ExtensionOf i f where
         congr }
   is_extension m := by
     dsimp
-    simp only [LinearPMap.mk_apply, LinearMap.coe_mk]
     rw [(extensionOfMax i f).is_extension,
       ExtensionOfMaxAdjoin.extensionToFun_wd i f h _ ⟨i m, _⟩ 0 _, map_zero, add_zero]
     simp

• depends on: #5966

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

@@ -2,11 +2,6 @@
 Copyright (c) 2022 Jujian Zhang. All rights reserved.
 Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Jujian Zhang
-
-! This file was ported from Lean 3 source module algebra.module.injective
-! leanprover-community/mathlib commit f8d8465c3c392a93b9ed226956e26dee00975946
-! Please do not edit these lines, except to modify the commit id
-! if you have ported upstream changes.
 -/
 import Mathlib.CategoryTheory.Preadditive.Injective
 import Mathlib.Algebra.Category.ModuleCat.EpiMono
@@ -14,6 +9,8 @@ import Mathlib.RingTheory.Ideal.Basic
 import Mathlib.LinearAlgebra.LinearPMap
 import Mathlib.Data.TypeMax -- Porting note: added for universe issues
 
+#align_import algebra.module.injective from "leanprover-community/mathlib"@"f8d8465c3c392a93b9ed226956e26dee00975946"
+
 /-!
 # Injective modules
 

Grepping for [^ .:{-] [^ :] and reviewing the results. Once I started I couldn't stop. :-)

Co-authored-by: Scott Morrison <scott.morrison@gmail.com>

@@ -21,7 +21,7 @@ import Mathlib.Data.TypeMax -- Porting note: added for universe issues
 
 * `Module.Injective`: an `R`-module `Q` is injective if and only if every injective `R`-linear
   map descends to a linear map to `Q`, i.e. in the following diagram, if `f` is injective then there
-  is an `R`-linear map `h : Y ⟶  Q` such that `g = h ∘ f`
+  is an `R`-linear map `h : Y ⟶ Q` such that `g = h ∘ f`
   ```
   X --- f ---> Y
   |
@@ -30,7 +30,7 @@ import Mathlib.Data.TypeMax -- Porting note: added for universe issues
   Q
   ```
 * `Module.Baer`: an `R`-module `Q` satisfies Baer's criterion if any `R`-linear map from an
-  `Ideal R` extends to an `R`-linear map `R ⟶  Q`
+  `Ideal R` extends to an `R`-linear map `R ⟶ Q`
 
 ## Main statements
 

• Run a non-interactive version of fix-comments.py on all files.
• Go through the diff and manually add/discard/edit chunks.

@@ -30,7 +30,7 @@ import Mathlib.Data.TypeMax -- Porting note: added for universe issues
   Q
   ```
 * `Module.Baer`: an `R`-module `Q` satisfies Baer's criterion if any `R`-linear map from an
-  `ideal R` extends to an `R`-linear map `R ⟶  Q`
+  `Ideal R` extends to an `R`-linear map `R ⟶  Q`
 
 ## Main statements
 
@@ -89,7 +89,7 @@ theorem Module.injective_iff_injective_object :
     @Module.injective_module_of_injective_object R _ Q _ _ h⟩
 #align module.injective_iff_injective_object Module.injective_iff_injective_object
 
-/-- An `R`-module `Q` satisfies Baer's criterion if any `R`-linear map from an `ideal R` extends to
+/-- An `R`-module `Q` satisfies Baer's criterion if any `R`-linear map from an `Ideal R` extends to
 an `R`-linear map `R ⟶ Q`-/
 def Module.Baer : Prop :=
   ∀ (I : Ideal R) (g : I →ₗ[R] Q), ∃ g' : R →ₗ[R] Q, ∀ (x : R) (mem : x ∈ I), g' x = g ⟨x, mem⟩

Now that leanprover/lean4#2210 has been merged, this PR:

• removes all the set_option synthInstance.etaExperiment true commands (and some etaExperiment% term elaborators)
• removes many but not quite all set_option maxHeartbeats commands
• makes various other changes required to cope with leanprover/lean4#2210.

Co-authored-by: Scott Morrison <scott.morrison@anu.edu.au> Co-authored-by: Scott Morrison <scott.morrison@gmail.com> Co-authored-by: Matthew Ballard <matt@mrb.email>

@@ -89,7 +89,6 @@ theorem Module.injective_iff_injective_object :
     @Module.injective_module_of_injective_object R _ Q _ _ h⟩
 #align module.injective_iff_injective_object Module.injective_iff_injective_object
 
-set_option synthInstance.etaExperiment true in
 /-- An `R`-module `Q` satisfies Baer's criterion if any `R`-linear map from an `ideal R` extends to
 an `R`-linear map `R ⟶ Q`-/
 def Module.Baer : Prop :=
@@ -190,6 +189,9 @@ def ExtensionOf.max {c : Set (ExtensionOf i f)} (hchain : IsChain (· ≤ ·) c)
             (Set.mem_image _ _ _).mpr ⟨hnonempty.some, hnonempty.choose_spec, rfl⟩).1
     is_extension := fun m => by
       refine' Eq.trans (hnonempty.some.is_extension m) _
+      · -- porting note: this subgoal didn't exist before the reenableeta branch
+        intros c hchain _
+        exact (IsChain.directedOn <| chain_linearPMap_of_chain_extensionOf hchain)
       symm
       generalize_proofs _ h1
       exact
@@ -289,7 +291,6 @@ set_option linter.uppercaseLean3 false in
 
 variable (f)
 
-set_option synthInstance.etaExperiment true in
 -- TODO: refactor to use colon ideals?
 /-- The ideal `I = {r | r • y ∈ N}`-/
 def ExtensionOfMaxAdjoin.ideal (y : N) : Ideal R :=
@@ -299,13 +300,20 @@ set_option linter.uppercaseLean3 false in
 
 /-- A linear map `I ⟶ Q` by `x ↦ f' (x • y)` where `f'` is the maximal extension-/
 def ExtensionOfMaxAdjoin.idealTo (y : N) : ExtensionOfMaxAdjoin.ideal i f y →ₗ[R] Q where
-  toFun z := (extensionOfMax i f).toLinearPMap ⟨(↑z : R) • y, z.prop⟩
-  map_add' z1 z2 := by simp [← (extensionOfMax i f).toLinearPMap.map_add, add_smul]
-  map_smul' z1 z2 := by simp [← (extensionOfMax i f).toLinearPMap.map_smul, mul_smul]; rfl
+  toFun (z : { x // x ∈ ideal i f y }) := (extensionOfMax i f).toLinearPMap ⟨(↑z : R) • y, z.prop⟩
+  map_add' (z1 z2 : { x // x ∈ ideal i f y }) := by
+    -- porting note: a single simp took care of the goal before reenableeta
+    simp_rw [← (extensionOfMax i f).toLinearPMap.map_add]
+    congr
+    apply add_smul
+  map_smul' z1 (z2 : {x // x ∈ ideal i f y}) := by
+    -- porting note: a single simp took care of the goal before reenableeta
+    simp_rw [← (extensionOfMax i f).toLinearPMap.map_smul]
+    congr 2
+    apply mul_smul
 set_option linter.uppercaseLean3 false in
 #align module.Baer.extension_of_max_adjoin.ideal_to Module.Baer.ExtensionOfMaxAdjoin.idealTo
 
-set_option synthInstance.etaExperiment true in
 /-- Since we assumed `Q` being Baer, the linear map `x ↦ f' (x • y) : I ⟶ Q` extends to `R ⟶ Q`,
 call this extended map `φ`-/
 def ExtensionOfMaxAdjoin.extendIdealTo (h : Module.Baer R Q) (y : N) : R →ₗ[R] Q :=
@@ -313,7 +321,6 @@ def ExtensionOfMaxAdjoin.extendIdealTo (h : Module.Baer R Q) (y : N) : R →ₗ[
 set_option linter.uppercaseLean3 false in
 #align module.Baer.extension_of_max_adjoin.extend_ideal_to Module.Baer.ExtensionOfMaxAdjoin.extendIdealTo
 
-set_option synthInstance.etaExperiment true in
 theorem ExtensionOfMaxAdjoin.extendIdealTo_is_extension (h : Module.Baer R Q) (y : N) :
     ∀ (x : R) (mem : x ∈ ExtensionOfMaxAdjoin.ideal i f y),
       ExtensionOfMaxAdjoin.extendIdealTo i f h y x = ExtensionOfMaxAdjoin.idealTo i f y ⟨x, mem⟩ :=
@@ -321,7 +328,6 @@ theorem ExtensionOfMaxAdjoin.extendIdealTo_is_extension (h : Module.Baer R Q) (y
 set_option linter.uppercaseLean3 false in
 #align module.Baer.extension_of_max_adjoin.extend_ideal_to_is_extension Module.Baer.ExtensionOfMaxAdjoin.extendIdealTo_is_extension
 
-set_option synthInstance.etaExperiment true in
 theorem ExtensionOfMaxAdjoin.extendIdealTo_wd' (h : Module.Baer R Q) {y : N} (r : R)
     (eq1 : r • y = 0) : ExtensionOfMaxAdjoin.extendIdealTo i f h y r = 0 := by
   have : r ∈ ideal i f y := by
@@ -335,7 +341,6 @@ theorem ExtensionOfMaxAdjoin.extendIdealTo_wd' (h : Module.Baer R Q) {y : N} (r
 set_option linter.uppercaseLean3 false in
 #align module.Baer.extension_of_max_adjoin.extend_ideal_to_wd' Module.Baer.ExtensionOfMaxAdjoin.extendIdealTo_wd'
 
-set_option synthInstance.etaExperiment true in
 theorem ExtensionOfMaxAdjoin.extendIdealTo_wd (h : Module.Baer R Q) {y : N} (r r' : R)
     (eq1 : r • y = r' • y) : ExtensionOfMaxAdjoin.extendIdealTo i f h y r =
     ExtensionOfMaxAdjoin.extendIdealTo i f h y r' := by
@@ -345,7 +350,6 @@ theorem ExtensionOfMaxAdjoin.extendIdealTo_wd (h : Module.Baer R Q) {y : N} (r r
 set_option linter.uppercaseLean3 false in
 #align module.Baer.extension_of_max_adjoin.extend_ideal_to_wd Module.Baer.ExtensionOfMaxAdjoin.extendIdealTo_wd
 
-set_option synthInstance.etaExperiment true in
 theorem ExtensionOfMaxAdjoin.extendIdealTo_eq (h : Module.Baer R Q) {y : N} (r : R)
     (hr : r • y ∈ (extensionOfMax i f).domain) : ExtensionOfMaxAdjoin.extendIdealTo i f h y r =
     (extensionOfMax i f).toLinearPMap ⟨r • y, hr⟩ := by
@@ -355,7 +359,6 @@ theorem ExtensionOfMaxAdjoin.extendIdealTo_eq (h : Module.Baer R Q) {y : N} (r :
 set_option linter.uppercaseLean3 false in
 #align module.Baer.extension_of_max_adjoin.extend_ideal_to_eq Module.Baer.ExtensionOfMaxAdjoin.extendIdealTo_eq
 
-set_option synthInstance.etaExperiment true in
 /-- We can finally define a linear map `M ⊔ ⟨y⟩ ⟶ Q` by `x + r • y ↦ f x + φ r`
 -/
 def ExtensionOfMaxAdjoin.extensionToFun (h : Module.Baer R Q) {y : N} :
@@ -365,7 +368,6 @@ def ExtensionOfMaxAdjoin.extensionToFun (h : Module.Baer R Q) {y : N} :
 set_option linter.uppercaseLean3 false in
 #align module.Baer.extension_of_max_adjoin.extension_to_fun Module.Baer.ExtensionOfMaxAdjoin.extensionToFun
 
-set_option synthInstance.etaExperiment true in
 theorem ExtensionOfMaxAdjoin.extensionToFun_wd (h : Module.Baer R Q) {y : N}
     (x : supExtensionOfMaxSingleton i f y) (a : (extensionOfMax i f).domain)
     (r : R) (eq1 : ↑x = ↑a + r • y) :
@@ -391,7 +393,6 @@ theorem ExtensionOfMaxAdjoin.extensionToFun_wd (h : Module.Baer R Q) {y : N}
 set_option linter.uppercaseLean3 false in
 #align module.Baer.extension_of_max_adjoin.extension_to_fun_wd Module.Baer.ExtensionOfMaxAdjoin.extensionToFun_wd
 
-set_option synthInstance.etaExperiment true in
 /-- The linear map `M ⊔ ⟨y⟩ ⟶ Q` by `x + r • y ↦ f x + φ r` is an extension of `f`-/
 def extensionOfMaxAdjoin (h : Module.Baer R Q) (y : N) : ExtensionOf i f where
   domain := supExtensionOfMaxSingleton i f y -- (extensionOfMax i f).domain ⊔ Submodule.span R {y}
@@ -428,7 +429,6 @@ def extensionOfMaxAdjoin (h : Module.Baer R Q) (y : N) : ExtensionOf i f where
 set_option linter.uppercaseLean3 false in
 #align module.Baer.extension_of_max_adjoin Module.Baer.extensionOfMaxAdjoin
 
-set_option synthInstance.etaExperiment true in
 theorem extensionOfMax_le (h : Module.Baer R Q) {y : N} :
     extensionOfMax i f ≤ extensionOfMaxAdjoin i f h y :=
   ⟨le_sup_left, fun x x' EQ => by

As discussed on Zulip

Renames

• supₛ → sSup
• infₛ → sInf
• supᵢ → iSup
• infᵢ → iInf
• bsupₛ → bsSup
• binfₛ → bsInf
• bsupᵢ → biSup
• binfᵢ → biInf
• csupₛ → csSup
• cinfₛ → csInf
• csupᵢ → ciSup
• cinfᵢ → ciInf
• unionₛ → sUnion
• interₛ → sInter
• unionᵢ → iUnion
• interᵢ → iInter
• bunionₛ → bsUnion
• binterₛ → bsInter
• bunionᵢ → biUnion
• binterᵢ → biInter

Co-authored-by: Parcly Taxel <reddeloostw@gmail.com>

@@ -180,20 +180,20 @@ set_option linter.uppercaseLean3 false in
 def ExtensionOf.max {c : Set (ExtensionOf i f)} (hchain : IsChain (· ≤ ·) c)
     (hnonempty : c.Nonempty) : ExtensionOf i f :=
   {
-    LinearPMap.supₛ _
+    LinearPMap.sSup _
       (IsChain.directedOn <|
         chain_linearPMap_of_chain_extensionOf
           hchain) with
     le :=
       le_trans hnonempty.some.le <|
-        (LinearPMap.le_supₛ _ <|
+        (LinearPMap.le_sSup _ <|
             (Set.mem_image _ _ _).mpr ⟨hnonempty.some, hnonempty.choose_spec, rfl⟩).1
     is_extension := fun m => by
       refine' Eq.trans (hnonempty.some.is_extension m) _
       symm
       generalize_proofs _ h1
       exact
-        LinearPMap.supₛ_apply (IsChain.directedOn <| chain_linearPMap_of_chain_extensionOf hchain)
+        LinearPMap.sSup_apply (IsChain.directedOn <| chain_linearPMap_of_chain_extensionOf hchain)
           ((Set.mem_image _ _ _).mpr ⟨hnonempty.some, hnonempty.choose_spec, rfl⟩) ⟨i m, h1⟩ }
 set_option linter.uppercaseLean3 false in
 #align module.Baer.extension_of.max Module.Baer.ExtensionOf.max
@@ -201,7 +201,7 @@ set_option linter.uppercaseLean3 false in
 theorem ExtensionOf.le_max {c : Set (ExtensionOf i f)} (hchain : IsChain (· ≤ ·) c)
     (hnonempty : c.Nonempty) (a : ExtensionOf i f) (ha : a ∈ c) :
     a ≤ ExtensionOf.max hchain hnonempty :=
-  LinearPMap.le_supₛ (IsChain.directedOn <| chain_linearPMap_of_chain_extensionOf hchain) <|
+  LinearPMap.le_sSup (IsChain.directedOn <| chain_linearPMap_of_chain_extensionOf hchain) <|
     (Set.mem_image _ _ _).mpr ⟨a, ha, rfl⟩
 set_option linter.uppercaseLean3 false in
 #align module.Baer.extension_of.le_max Module.Baer.ExtensionOf.le_max
@@ -469,4 +469,3 @@ set_option linter.uppercaseLean3 false in
 #align module.Baer.injective Module.Baer.injective
 
 end Module.Baer
-