algebra.module.submodule.lattice ⟷ Mathlib.Algebra.Module.Submodule.Lattice

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

@@ -4,7 +4,7 @@ Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Johannes Hölzl, Mario Carneiro, Kevin Buzzard, Yury Kudryashov
 -/
 import Algebra.Module.Submodule.Basic
-import Algebra.PunitInstances
+import Algebra.PUnitInstances
 
 #align_import algebra.module.submodule.lattice from "leanprover-community/mathlib"@"68d1483e8a718ec63219f0e227ca3f0140361086"
 

mathlib commit https://github.com/leanprover-community/mathlib/commit/b1abe23ae96fef89ad30d9f4362c307f72a55010

@@ -123,7 +123,7 @@ protected theorem bot_ext (x y : (⊥ : Submodule R M)) : x = y :=
 
 #print Submodule.ne_bot_iff /-
 protected theorem ne_bot_iff (p : Submodule R M) : p ≠ ⊥ ↔ ∃ x ∈ p, x ≠ (0 : M) := by
-  haveI := Classical.propDecidable; simp_rw [Ne.def, p.eq_bot_iff, not_forall]
+  haveI := Classical.propDecidable; simp_rw [Ne.def, p.eq_bot_iff, Classical.not_forall]
 #align submodule.ne_bot_iff Submodule.ne_bot_iff
 -/
 

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

@@ -3,8 +3,8 @@ Copyright (c) 2017 Johannes Hölzl. All rights reserved.
 Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Johannes Hölzl, Mario Carneiro, Kevin Buzzard, Yury Kudryashov
 -/
-import Mathbin.Algebra.Module.Submodule.Basic
-import Mathbin.Algebra.PunitInstances
+import Algebra.Module.Submodule.Basic
+import Algebra.PunitInstances
 
 #align_import algebra.module.submodule.lattice from "leanprover-community/mathlib"@"68d1483e8a718ec63219f0e227ca3f0140361086"
 

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

@@ -2,15 +2,12 @@
 Copyright (c) 2017 Johannes Hölzl. All rights reserved.
 Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Johannes Hölzl, Mario Carneiro, Kevin Buzzard, Yury Kudryashov
-
-! This file was ported from Lean 3 source module algebra.module.submodule.lattice
-! leanprover-community/mathlib commit 68d1483e8a718ec63219f0e227ca3f0140361086
-! Please do not edit these lines, except to modify the commit id
-! if you have ported upstream changes.
 -/
 import Mathbin.Algebra.Module.Submodule.Basic
 import Mathbin.Algebra.PunitInstances
 
+#align_import algebra.module.submodule.lattice from "leanprover-community/mathlib"@"68d1483e8a718ec63219f0e227ca3f0140361086"
+
 /-!
 # The lattice structure on `submodule`s
 

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

@@ -56,50 +56,65 @@ instance inhabited' : Inhabited (Submodule R M) :=
 #align submodule.inhabited' Submodule.inhabited'
 -/
 
+#print Submodule.bot_coe /-
 @[simp]
 theorem bot_coe : ((⊥ : Submodule R M) : Set M) = {0} :=
   rfl
 #align submodule.bot_coe Submodule.bot_coe
+-/
 
+#print Submodule.bot_toAddSubmonoid /-
 @[simp]
 theorem bot_toAddSubmonoid : (⊥ : Submodule R M).toAddSubmonoid = ⊥ :=
   rfl
 #align submodule.bot_to_add_submonoid Submodule.bot_toAddSubmonoid
+-/
 
 section
 
 variable (R)
 
+#print Submodule.restrictScalars_bot /-
 @[simp]
 theorem restrictScalars_bot : restrictScalars S (⊥ : Submodule R M) = ⊥ :=
   rfl
 #align submodule.restrict_scalars_bot Submodule.restrictScalars_bot
+-/
 
+#print Submodule.mem_bot /-
 @[simp]
 theorem mem_bot {x : M} : x ∈ (⊥ : Submodule R M) ↔ x = 0 :=
   Set.mem_singleton_iff
 #align submodule.mem_bot Submodule.mem_bot
+-/
 
 end
 
+#print Submodule.restrictScalars_eq_bot_iff /-
 @[simp]
 theorem restrictScalars_eq_bot_iff {p : Submodule R M} : restrictScalars S p = ⊥ ↔ p = ⊥ := by
   simp [SetLike.ext_iff]
 #align submodule.restrict_scalars_eq_bot_iff Submodule.restrictScalars_eq_bot_iff
+-/
 
+#print Submodule.uniqueBot /-
 instance uniqueBot : Unique (⊥ : Submodule R M) :=
   ⟨inferInstance, fun x => Subtype.ext <| (mem_bot R).1 x.Mem⟩
 #align submodule.unique_bot Submodule.uniqueBot
+-/
 
 instance : OrderBot (Submodule R M) where
   bot := ⊥
   bot_le p x := by simp (config := { contextual := true }) [zero_mem]
 
+#print Submodule.eq_bot_iff /-
 protected theorem eq_bot_iff (p : Submodule R M) : p = ⊥ ↔ ∀ x ∈ p, x = (0 : M) :=
   ⟨fun h => h.symm ▸ fun x hx => (mem_bot R).mp hx, fun h =>
     eq_bot_iff.mpr fun x hx => (mem_bot R).mpr (h x hx)⟩
 #align submodule.eq_bot_iff Submodule.eq_bot_iff
+-/
 
+#print Submodule.bot_ext /-
 @[ext]
 protected theorem bot_ext (x y : (⊥ : Submodule R M)) : x = y :=
   by
@@ -107,21 +122,29 @@ protected theorem bot_ext (x y : (⊥ : Submodule R M)) : x = y :=
   rw [(Submodule.eq_bot_iff _).mp rfl x xm]
   rw [(Submodule.eq_bot_iff _).mp rfl y ym]
 #align submodule.bot_ext Submodule.bot_ext
+-/
 
+#print Submodule.ne_bot_iff /-
 protected theorem ne_bot_iff (p : Submodule R M) : p ≠ ⊥ ↔ ∃ x ∈ p, x ≠ (0 : M) := by
   haveI := Classical.propDecidable; simp_rw [Ne.def, p.eq_bot_iff, not_forall]
 #align submodule.ne_bot_iff Submodule.ne_bot_iff
+-/
 
+#print Submodule.nonzero_mem_of_bot_lt /-
 theorem nonzero_mem_of_bot_lt {p : Submodule R M} (bot_lt : ⊥ < p) : ∃ a : p, a ≠ 0 :=
   let ⟨b, hb₁, hb₂⟩ := p.ne_bot_iff.mp bot_lt.ne'
   ⟨⟨b, hb₁⟩, hb₂ ∘ congr_arg coe⟩
 #align submodule.nonzero_mem_of_bot_lt Submodule.nonzero_mem_of_bot_lt
+-/
 
+#print Submodule.exists_mem_ne_zero_of_ne_bot /-
 theorem exists_mem_ne_zero_of_ne_bot {p : Submodule R M} (h : p ≠ ⊥) : ∃ b : M, b ∈ p ∧ b ≠ 0 :=
   let ⟨b, hb₁, hb₂⟩ := p.ne_bot_iff.mp h
   ⟨b, hb₁, hb₂⟩
 #align submodule.exists_mem_ne_zero_of_ne_bot Submodule.exists_mem_ne_zero_of_ne_bot
+-/
 
+#print Submodule.botEquivPUnit /-
 /-- The bottom submodule is linearly equivalent to punit as an `R`-module. -/
 @[simps]
 def botEquivPUnit : (⊥ : Submodule R M) ≃ₗ[R] PUnit
@@ -133,13 +156,16 @@ def botEquivPUnit : (⊥ : Submodule R M) ≃ₗ[R] PUnit
   left_inv := by intro x; ext
   right_inv := by intro x; ext
 #align submodule.bot_equiv_punit Submodule.botEquivPUnit
+-/
 
+#print Submodule.eq_bot_of_subsingleton /-
 theorem eq_bot_of_subsingleton (p : Submodule R M) [Subsingleton p] : p = ⊥ :=
   by
   rw [eq_bot_iff]
   intro v hv
   exact congr_arg coe (Subsingleton.elim (⟨v, hv⟩ : p) 0)
 #align submodule.eq_bot_of_subsingleton Submodule.eq_bot_of_subsingleton
+-/
 
 /-- The universal set is the top element of the lattice of submodules. -/
 instance : Top (Submodule R M) :=
@@ -147,45 +173,58 @@ instance : Top (Submodule R M) :=
       carrier := Set.univ
       smul_mem' := fun _ _ _ => trivial }⟩
 
+#print Submodule.top_coe /-
 @[simp]
 theorem top_coe : ((⊤ : Submodule R M) : Set M) = Set.univ :=
   rfl
 #align submodule.top_coe Submodule.top_coe
+-/
 
+#print Submodule.top_toAddSubmonoid /-
 @[simp]
 theorem top_toAddSubmonoid : (⊤ : Submodule R M).toAddSubmonoid = ⊤ :=
   rfl
 #align submodule.top_to_add_submonoid Submodule.top_toAddSubmonoid
+-/
 
+#print Submodule.mem_top /-
 @[simp]
 theorem mem_top {x : M} : x ∈ (⊤ : Submodule R M) :=
   trivial
 #align submodule.mem_top Submodule.mem_top
+-/
 
 section
 
 variable (R)
 
+#print Submodule.restrictScalars_top /-
 @[simp]
 theorem restrictScalars_top : restrictScalars S (⊤ : Submodule R M) = ⊤ :=
   rfl
 #align submodule.restrict_scalars_top Submodule.restrictScalars_top
+-/
 
 end
 
+#print Submodule.restrictScalars_eq_top_iff /-
 @[simp]
 theorem restrictScalars_eq_top_iff {p : Submodule R M} : restrictScalars S p = ⊤ ↔ p = ⊤ := by
   simp [SetLike.ext_iff]
 #align submodule.restrict_scalars_eq_top_iff Submodule.restrictScalars_eq_top_iff
+-/
 
 instance : OrderTop (Submodule R M) where
   top := ⊤
   le_top p x _ := trivial
 
+#print Submodule.eq_top_iff' /-
 theorem eq_top_iff' {p : Submodule R M} : p = ⊤ ↔ ∀ x, x ∈ p :=
   eq_top_iff.trans ⟨fun h x => h trivial, fun h x _ => h x⟩
 #align submodule.eq_top_iff' Submodule.eq_top_iff'
+-/
 
+#print Submodule.topEquiv /-
 /-- The top submodule is linearly equivalent to the module.
 
 This is the module version of `add_submonoid.top_equiv`. -/
@@ -199,6 +238,7 @@ def topEquiv : (⊤ : Submodule R M) ≃ₗ[R] M
   left_inv := by intro x; ext; rfl
   right_inv := by intro x; rfl
 #align submodule.top_equiv Submodule.topEquiv
+-/
 
 instance : InfSet (Submodule R M) :=
   ⟨fun S =>
@@ -238,21 +278,28 @@ instance : CompleteLattice (Submodule R M) :=
     le_inf := fun s a => le_Inf'
     inf_le := fun s a => sInf_le' }
 
+#print Submodule.inf_coe /-
 @[simp]
 theorem inf_coe : ↑(p ⊓ q) = (p ∩ q : Set M) :=
   rfl
 #align submodule.inf_coe Submodule.inf_coe
+-/
 
+#print Submodule.mem_inf /-
 @[simp]
 theorem mem_inf {p q : Submodule R M} {x : M} : x ∈ p ⊓ q ↔ x ∈ p ∧ x ∈ q :=
   Iff.rfl
 #align submodule.mem_inf Submodule.mem_inf
+-/
 
+#print Submodule.sInf_coe /-
 @[simp]
 theorem sInf_coe (P : Set (Submodule R M)) : (↑(sInf P) : Set M) = ⋂ p ∈ P, ↑p :=
   rfl
 #align submodule.Inf_coe Submodule.sInf_coe
+-/
 
+#print Submodule.finset_inf_coe /-
 @[simp]
 theorem finset_inf_coe {ι} (s : Finset ι) (p : ι → Submodule R M) :
     (↑(s.inf p) : Set M) = ⋂ i ∈ s, ↑(p i) :=
@@ -263,91 +310,123 @@ theorem finset_inf_coe {ι} (s : Finset ι) (p : ι → Submodule R M) :
   · rw [Finset.inf_insert, inf_coe, ih]
     simp
 #align submodule.finset_inf_coe Submodule.finset_inf_coe
+-/
 
+#print Submodule.iInf_coe /-
 @[simp]
 theorem iInf_coe {ι} (p : ι → Submodule R M) : (↑(⨅ i, p i) : Set M) = ⋂ i, ↑(p i) := by
   rw [iInf, Inf_coe] <;> ext a <;> simp <;> exact ⟨fun h i => h _ i rfl, fun h i x e => e ▸ h _⟩
 #align submodule.infi_coe Submodule.iInf_coe
+-/
 
+#print Submodule.mem_sInf /-
 @[simp]
 theorem mem_sInf {S : Set (Submodule R M)} {x : M} : x ∈ sInf S ↔ ∀ p ∈ S, x ∈ p :=
   Set.mem_iInter₂
 #align submodule.mem_Inf Submodule.mem_sInf
+-/
 
+#print Submodule.mem_iInf /-
 @[simp]
 theorem mem_iInf {ι} (p : ι → Submodule R M) {x} : (x ∈ ⨅ i, p i) ↔ ∀ i, x ∈ p i := by
   rw [← SetLike.mem_coe, infi_coe, Set.mem_iInter] <;> rfl
 #align submodule.mem_infi Submodule.mem_iInf
+-/
 
+#print Submodule.mem_finset_inf /-
 @[simp]
 theorem mem_finset_inf {ι} {s : Finset ι} {p : ι → Submodule R M} {x : M} :
     x ∈ s.inf p ↔ ∀ i ∈ s, x ∈ p i := by
   simp only [← SetLike.mem_coe, finset_inf_coe, Set.mem_iInter]
 #align submodule.mem_finset_inf Submodule.mem_finset_inf
+-/
 
+#print Submodule.mem_sup_left /-
 theorem mem_sup_left {S T : Submodule R M} : ∀ {x : M}, x ∈ S → x ∈ S ⊔ T :=
   show S ≤ S ⊔ T from le_sup_left
 #align submodule.mem_sup_left Submodule.mem_sup_left
+-/
 
+#print Submodule.mem_sup_right /-
 theorem mem_sup_right {S T : Submodule R M} : ∀ {x : M}, x ∈ T → x ∈ S ⊔ T :=
   show T ≤ S ⊔ T from le_sup_right
 #align submodule.mem_sup_right Submodule.mem_sup_right
+-/
 
+#print Submodule.add_mem_sup /-
 theorem add_mem_sup {S T : Submodule R M} {s t : M} (hs : s ∈ S) (ht : t ∈ T) : s + t ∈ S ⊔ T :=
   add_mem (mem_sup_left hs) (mem_sup_right ht)
 #align submodule.add_mem_sup Submodule.add_mem_sup
+-/
 
+#print Submodule.sub_mem_sup /-
 theorem sub_mem_sup {R' M' : Type _} [Ring R'] [AddCommGroup M'] [Module R' M']
     {S T : Submodule R' M'} {s t : M'} (hs : s ∈ S) (ht : t ∈ T) : s - t ∈ S ⊔ T :=
   by
   rw [sub_eq_add_neg]
   exact add_mem_sup hs (neg_mem ht)
 #align submodule.sub_mem_sup Submodule.sub_mem_sup
+-/
 
+#print Submodule.mem_iSup_of_mem /-
 theorem mem_iSup_of_mem {ι : Sort _} {b : M} {p : ι → Submodule R M} (i : ι) (h : b ∈ p i) :
     b ∈ ⨆ i, p i :=
   have : p i ≤ ⨆ i, p i := le_iSup p i
   @this b h
 #align submodule.mem_supr_of_mem Submodule.mem_iSup_of_mem
+-/
 
 open scoped BigOperators
 
+#print Submodule.sum_mem_iSup /-
 theorem sum_mem_iSup {ι : Type _} [Fintype ι] {f : ι → M} {p : ι → Submodule R M}
     (h : ∀ i, f i ∈ p i) : ∑ i, f i ∈ ⨆ i, p i :=
   sum_mem fun i hi => mem_iSup_of_mem i (h i)
 #align submodule.sum_mem_supr Submodule.sum_mem_iSup
+-/
 
+#print Submodule.sum_mem_biSup /-
 theorem sum_mem_biSup {ι : Type _} {s : Finset ι} {f : ι → M} {p : ι → Submodule R M}
     (h : ∀ i ∈ s, f i ∈ p i) : ∑ i in s, f i ∈ ⨆ i ∈ s, p i :=
   sum_mem fun i hi => mem_iSup_of_mem i <| mem_iSup_of_mem hi (h i hi)
 #align submodule.sum_mem_bsupr Submodule.sum_mem_biSup
+-/
 
 /-! Note that `submodule.mem_supr` is provided in `linear_algebra/basic.lean`. -/
 
 
+#print Submodule.mem_sSup_of_mem /-
 theorem mem_sSup_of_mem {S : Set (Submodule R M)} {s : Submodule R M} (hs : s ∈ S) :
     ∀ {x : M}, x ∈ s → x ∈ sSup S :=
   show s ≤ sSup S from le_sSup hs
 #align submodule.mem_Sup_of_mem Submodule.mem_sSup_of_mem
+-/
 
+#print Submodule.disjoint_def /-
 theorem disjoint_def {p p' : Submodule R M} : Disjoint p p' ↔ ∀ x ∈ p, x ∈ p' → x = (0 : M) :=
   disjoint_iff_inf_le.trans <| show (∀ x, x ∈ p ∧ x ∈ p' → x ∈ ({0} : Set M)) ↔ _ by simp
 #align submodule.disjoint_def Submodule.disjoint_def
+-/
 
+#print Submodule.disjoint_def' /-
 theorem disjoint_def' {p p' : Submodule R M} :
     Disjoint p p' ↔ ∀ x ∈ p, ∀ y ∈ p', x = y → x = (0 : M) :=
   disjoint_def.trans
     ⟨fun h x hx y hy hxy => h x hx <| hxy.symm ▸ hy, fun h x hx hx' => h _ hx x hx' rfl⟩
 #align submodule.disjoint_def' Submodule.disjoint_def'
+-/
 
+#print Submodule.eq_zero_of_coe_mem_of_disjoint /-
 theorem eq_zero_of_coe_mem_of_disjoint (hpq : Disjoint p q) {a : p} (ha : (a : M) ∈ q) : a = 0 := by
   exact_mod_cast disjoint_def.mp hpq a (coe_mem a) ha
 #align submodule.eq_zero_of_coe_mem_of_disjoint Submodule.eq_zero_of_coe_mem_of_disjoint
+-/
 
 end Submodule
 
 section NatSubmodule
 
+#print AddSubmonoid.toNatSubmodule /-
 /-- An additive submonoid is equivalent to a ℕ-submodule. -/
 def AddSubmonoid.toNatSubmodule : AddSubmonoid M ≃o Submodule ℕ M
     where
@@ -357,29 +436,38 @@ def AddSubmonoid.toNatSubmodule : AddSubmonoid M ≃o Submodule ℕ M
   right_inv := fun ⟨S, _, _, _⟩ => rfl
   map_rel_iff' a b := Iff.rfl
 #align add_submonoid.to_nat_submodule AddSubmonoid.toNatSubmodule
+-/
 
+#print AddSubmonoid.toNatSubmodule_symm /-
 @[simp]
 theorem AddSubmonoid.toNatSubmodule_symm :
     ⇑(AddSubmonoid.toNatSubmodule.symm : _ ≃o AddSubmonoid M) = Submodule.toAddSubmonoid :=
   rfl
 #align add_submonoid.to_nat_submodule_symm AddSubmonoid.toNatSubmodule_symm
+-/
 
+#print AddSubmonoid.coe_toNatSubmodule /-
 @[simp]
 theorem AddSubmonoid.coe_toNatSubmodule (S : AddSubmonoid M) : (S.toNatSubmodule : Set M) = S :=
   rfl
 #align add_submonoid.coe_to_nat_submodule AddSubmonoid.coe_toNatSubmodule
+-/
 
+#print AddSubmonoid.toNatSubmodule_toAddSubmonoid /-
 @[simp]
 theorem AddSubmonoid.toNatSubmodule_toAddSubmonoid (S : AddSubmonoid M) :
     S.toNatSubmodule.toAddSubmonoid = S :=
   AddSubmonoid.toNatSubmodule.symm_apply_apply S
 #align add_submonoid.to_nat_submodule_to_add_submonoid AddSubmonoid.toNatSubmodule_toAddSubmonoid
+-/
 
+#print Submodule.toAddSubmonoid_toNatSubmodule /-
 @[simp]
 theorem Submodule.toAddSubmonoid_toNatSubmodule (S : Submodule ℕ M) :
     S.toAddSubmonoid.toNatSubmodule = S :=
   AddSubmonoid.toNatSubmodule.apply_symm_apply S
 #align submodule.to_add_submonoid_to_nat_submodule Submodule.toAddSubmonoid_toNatSubmodule
+-/
 
 end NatSubmodule
 
@@ -389,6 +477,7 @@ section IntSubmodule
 
 variable [AddCommGroup M]
 
+#print AddSubgroup.toIntSubmodule /-
 /-- An additive subgroup is equivalent to a ℤ-submodule. -/
 def AddSubgroup.toIntSubmodule : AddSubgroup M ≃o Submodule ℤ M
     where
@@ -398,29 +487,38 @@ def AddSubgroup.toIntSubmodule : AddSubgroup M ≃o Submodule ℤ M
   right_inv := fun ⟨S, _, _, _⟩ => rfl
   map_rel_iff' a b := Iff.rfl
 #align add_subgroup.to_int_submodule AddSubgroup.toIntSubmodule
+-/
 
+#print AddSubgroup.toIntSubmodule_symm /-
 @[simp]
 theorem AddSubgroup.toIntSubmodule_symm :
     ⇑(AddSubgroup.toIntSubmodule.symm : _ ≃o AddSubgroup M) = Submodule.toAddSubgroup :=
   rfl
 #align add_subgroup.to_int_submodule_symm AddSubgroup.toIntSubmodule_symm
+-/
 
+#print AddSubgroup.coe_toIntSubmodule /-
 @[simp]
 theorem AddSubgroup.coe_toIntSubmodule (S : AddSubgroup M) : (S.toIntSubmodule : Set M) = S :=
   rfl
 #align add_subgroup.coe_to_int_submodule AddSubgroup.coe_toIntSubmodule
+-/
 
+#print AddSubgroup.toIntSubmodule_toAddSubgroup /-
 @[simp]
 theorem AddSubgroup.toIntSubmodule_toAddSubgroup (S : AddSubgroup M) :
     S.toIntSubmodule.toAddSubgroup = S :=
   AddSubgroup.toIntSubmodule.symm_apply_apply S
 #align add_subgroup.to_int_submodule_to_add_subgroup AddSubgroup.toIntSubmodule_toAddSubgroup
+-/
 
+#print Submodule.toAddSubgroup_toIntSubmodule /-
 @[simp]
 theorem Submodule.toAddSubgroup_toIntSubmodule (S : Submodule ℤ M) :
     S.toAddSubgroup.toIntSubmodule = S :=
   AddSubgroup.toIntSubmodule.apply_symm_apply S
 #align submodule.to_add_subgroup_to_int_submodule Submodule.toAddSubgroup_toIntSubmodule
+-/
 
 end IntSubmodule
 

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

@@ -313,12 +313,12 @@ theorem mem_iSup_of_mem {ι : Sort _} {b : M} {p : ι → Submodule R M} (i : ι
 open scoped BigOperators
 
 theorem sum_mem_iSup {ι : Type _} [Fintype ι] {f : ι → M} {p : ι → Submodule R M}
-    (h : ∀ i, f i ∈ p i) : (∑ i, f i) ∈ ⨆ i, p i :=
+    (h : ∀ i, f i ∈ p i) : ∑ i, f i ∈ ⨆ i, p i :=
   sum_mem fun i hi => mem_iSup_of_mem i (h i)
 #align submodule.sum_mem_supr Submodule.sum_mem_iSup
 
 theorem sum_mem_biSup {ι : Type _} {s : Finset ι} {f : ι → M} {p : ι → Submodule R M}
-    (h : ∀ i ∈ s, f i ∈ p i) : (∑ i in s, f i) ∈ ⨆ i ∈ s, p i :=
+    (h : ∀ i ∈ s, f i ∈ p i) : ∑ i in s, f i ∈ ⨆ i ∈ s, p i :=
   sum_mem fun i hi => mem_iSup_of_mem i <| mem_iSup_of_mem hi (h i hi)
 #align submodule.sum_mem_bsupr Submodule.sum_mem_biSup
 

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

@@ -223,7 +223,7 @@ instance : Inf (Submodule R M) :=
 instance : CompleteLattice (Submodule R M) :=
   { Submodule.orderTop, Submodule.orderBot,
     SetLike.partialOrder with
-    sup := fun a b => sInf { x | a ≤ x ∧ b ≤ x }
+    sup := fun a b => sInf {x | a ≤ x ∧ b ≤ x}
     le_sup_left := fun a b => le_Inf' fun x ⟨ha, hb⟩ => ha
     le_sup_right := fun a b => le_Inf' fun x ⟨ha, hb⟩ => hb
     sup_le := fun a b c h₁ h₂ => sInf_le' ⟨h₁, h₂⟩
@@ -231,7 +231,7 @@ instance : CompleteLattice (Submodule R M) :=
     le_inf := fun a b c => Set.subset_inter
     inf_le_left := fun a b => Set.inter_subset_left _ _
     inf_le_right := fun a b => Set.inter_subset_right _ _
-    sSup := fun tt => sInf { t | ∀ t' ∈ tt, t' ≤ t }
+    sSup := fun tt => sInf {t | ∀ t' ∈ tt, t' ≤ t}
     le_sup := fun s p hs => le_Inf' fun q hq => hq _ hs
     sup_le := fun s p hs => sInf_le' hs
     sInf := sInf

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

@@ -128,8 +128,8 @@ def botEquivPUnit : (⊥ : Submodule R M) ≃ₗ[R] PUnit
     where
   toFun x := PUnit.unit
   invFun x := 0
-  map_add' := by intros ; ext
-  map_smul' := by intros ; ext
+  map_add' := by intros; ext
+  map_smul' := by intros; ext
   left_inv := by intro x; ext
   right_inv := by intro x; ext
 #align submodule.bot_equiv_punit Submodule.botEquivPUnit
@@ -194,8 +194,8 @@ def topEquiv : (⊤ : Submodule R M) ≃ₗ[R] M
     where
   toFun x := x
   invFun x := ⟨x, by simp⟩
-  map_add' := by intros ; rfl
-  map_smul' := by intros ; rfl
+  map_add' := by intros; rfl
+  map_smul' := by intros; rfl
   left_inv := by intro x; ext; rfl
   right_inv := by intro x; rfl
 #align submodule.top_equiv Submodule.topEquiv

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

@@ -310,7 +310,7 @@ theorem mem_iSup_of_mem {ι : Sort _} {b : M} {p : ι → Submodule R M} (i : ι
   @this b h
 #align submodule.mem_supr_of_mem Submodule.mem_iSup_of_mem
 
-open BigOperators
+open scoped BigOperators
 
 theorem sum_mem_iSup {ι : Type _} [Fintype ι] {f : ι → M} {p : ι → Submodule R M}
     (h : ∀ i, f i ∈ p i) : (∑ i, f i) ∈ ⨆ i, p i :=

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

@@ -56,23 +56,11 @@ instance inhabited' : Inhabited (Submodule R M) :=
 #align submodule.inhabited' Submodule.inhabited'
 -/
 
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 @[simp]
 theorem bot_coe : ((⊥ : Submodule R M) : Set M) = {0} :=
   rfl
 #align submodule.bot_coe Submodule.bot_coe
 
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 @[simp]
 theorem bot_toAddSubmonoid : (⊥ : Submodule R M).toAddSubmonoid = ⊥ :=
   rfl
@@ -82,23 +70,11 @@ section
 
 variable (R)
 
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 @[simp]
 theorem restrictScalars_bot : restrictScalars S (⊥ : Submodule R M) = ⊥ :=
   rfl
 #align submodule.restrict_scalars_bot Submodule.restrictScalars_bot
 
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 @[simp]
 theorem mem_bot {x : M} : x ∈ (⊥ : Submodule R M) ↔ x = 0 :=
   Set.mem_singleton_iff
@@ -106,23 +82,11 @@ theorem mem_bot {x : M} : x ∈ (⊥ : Submodule R M) ↔ x = 0 :=
 
 end
 
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 @[simp]
 theorem restrictScalars_eq_bot_iff {p : Submodule R M} : restrictScalars S p = ⊥ ↔ p = ⊥ := by
   simp [SetLike.ext_iff]
 #align submodule.restrict_scalars_eq_bot_iff Submodule.restrictScalars_eq_bot_iff
 
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 instance uniqueBot : Unique (⊥ : Submodule R M) :=
   ⟨inferInstance, fun x => Subtype.ext <| (mem_bot R).1 x.Mem⟩
 #align submodule.unique_bot Submodule.uniqueBot
@@ -131,23 +95,11 @@ instance : OrderBot (Submodule R M) where
   bot := ⊥
   bot_le p x := by simp (config := { contextual := true }) [zero_mem]
 
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 protected theorem eq_bot_iff (p : Submodule R M) : p = ⊥ ↔ ∀ x ∈ p, x = (0 : M) :=
   ⟨fun h => h.symm ▸ fun x hx => (mem_bot R).mp hx, fun h =>
     eq_bot_iff.mpr fun x hx => (mem_bot R).mpr (h x hx)⟩
 #align submodule.eq_bot_iff Submodule.eq_bot_iff
 
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 @[ext]
 protected theorem bot_ext (x y : (⊥ : Submodule R M)) : x = y :=
   by
@@ -156,44 +108,20 @@ protected theorem bot_ext (x y : (⊥ : Submodule R M)) : x = y :=
   rw [(Submodule.eq_bot_iff _).mp rfl y ym]
 #align submodule.bot_ext Submodule.bot_ext
 
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 protected theorem ne_bot_iff (p : Submodule R M) : p ≠ ⊥ ↔ ∃ x ∈ p, x ≠ (0 : M) := by
   haveI := Classical.propDecidable; simp_rw [Ne.def, p.eq_bot_iff, not_forall]
 #align submodule.ne_bot_iff Submodule.ne_bot_iff
 
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 theorem nonzero_mem_of_bot_lt {p : Submodule R M} (bot_lt : ⊥ < p) : ∃ a : p, a ≠ 0 :=
   let ⟨b, hb₁, hb₂⟩ := p.ne_bot_iff.mp bot_lt.ne'
   ⟨⟨b, hb₁⟩, hb₂ ∘ congr_arg coe⟩
 #align submodule.nonzero_mem_of_bot_lt Submodule.nonzero_mem_of_bot_lt
 
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 theorem exists_mem_ne_zero_of_ne_bot {p : Submodule R M} (h : p ≠ ⊥) : ∃ b : M, b ∈ p ∧ b ≠ 0 :=
   let ⟨b, hb₁, hb₂⟩ := p.ne_bot_iff.mp h
   ⟨b, hb₁, hb₂⟩
 #align submodule.exists_mem_ne_zero_of_ne_bot Submodule.exists_mem_ne_zero_of_ne_bot
 
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 /-- The bottom submodule is linearly equivalent to punit as an `R`-module. -/
 @[simps]
 def botEquivPUnit : (⊥ : Submodule R M) ≃ₗ[R] PUnit
@@ -206,12 +134,6 @@ def botEquivPUnit : (⊥ : Submodule R M) ≃ₗ[R] PUnit
   right_inv := by intro x; ext
 #align submodule.bot_equiv_punit Submodule.botEquivPUnit
 
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 theorem eq_bot_of_subsingleton (p : Submodule R M) [Subsingleton p] : p = ⊥ :=
   by
   rw [eq_bot_iff]
@@ -225,34 +147,16 @@ instance : Top (Submodule R M) :=
       carrier := Set.univ
       smul_mem' := fun _ _ _ => trivial }⟩
 
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 @[simp]
 theorem top_coe : ((⊤ : Submodule R M) : Set M) = Set.univ :=
   rfl
 #align submodule.top_coe Submodule.top_coe
 
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 @[simp]
 theorem top_toAddSubmonoid : (⊤ : Submodule R M).toAddSubmonoid = ⊤ :=
   rfl
 #align submodule.top_to_add_submonoid Submodule.top_toAddSubmonoid
 
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 @[simp]
 theorem mem_top {x : M} : x ∈ (⊤ : Submodule R M) :=
   trivial
@@ -262,12 +166,6 @@ section
 
 variable (R)
 
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 @[simp]
 theorem restrictScalars_top : restrictScalars S (⊤ : Submodule R M) = ⊤ :=
   rfl
@@ -275,12 +173,6 @@ theorem restrictScalars_top : restrictScalars S (⊤ : Submodule R M) = ⊤ :=
 
 end
 
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 @[simp]
 theorem restrictScalars_eq_top_iff {p : Submodule R M} : restrictScalars S p = ⊤ ↔ p = ⊤ := by
   simp [SetLike.ext_iff]
@@ -290,22 +182,10 @@ instance : OrderTop (Submodule R M) where
   top := ⊤
   le_top p x _ := trivial
 
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 theorem eq_top_iff' {p : Submodule R M} : p = ⊤ ↔ ∀ x, x ∈ p :=
   eq_top_iff.trans ⟨fun h x => h trivial, fun h x _ => h x⟩
 #align submodule.eq_top_iff' Submodule.eq_top_iff'
 
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 /-- The top submodule is linearly equivalent to the module.
 
 This is the module version of `add_submonoid.top_equiv`. -/
@@ -358,45 +238,21 @@ instance : CompleteLattice (Submodule R M) :=
     le_inf := fun s a => le_Inf'
     inf_le := fun s a => sInf_le' }
 
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 @[simp]
 theorem inf_coe : ↑(p ⊓ q) = (p ∩ q : Set M) :=
   rfl
 #align submodule.inf_coe Submodule.inf_coe
 
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 @[simp]
 theorem mem_inf {p q : Submodule R M} {x : M} : x ∈ p ⊓ q ↔ x ∈ p ∧ x ∈ q :=
   Iff.rfl
 #align submodule.mem_inf Submodule.mem_inf
 
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 @[simp]
 theorem sInf_coe (P : Set (Submodule R M)) : (↑(sInf P) : Set M) = ⋂ p ∈ P, ↑p :=
   rfl
 #align submodule.Inf_coe Submodule.sInf_coe
 
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 @[simp]
 theorem finset_inf_coe {ι} (s : Finset ι) (p : ι → Submodule R M) :
     (↑(s.inf p) : Set M) = ⋂ i ∈ s, ↑(p i) :=
@@ -408,87 +264,39 @@ theorem finset_inf_coe {ι} (s : Finset ι) (p : ι → Submodule R M) :
     simp
 #align submodule.finset_inf_coe Submodule.finset_inf_coe
 
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 @[simp]
 theorem iInf_coe {ι} (p : ι → Submodule R M) : (↑(⨅ i, p i) : Set M) = ⋂ i, ↑(p i) := by
   rw [iInf, Inf_coe] <;> ext a <;> simp <;> exact ⟨fun h i => h _ i rfl, fun h i x e => e ▸ h _⟩
 #align submodule.infi_coe Submodule.iInf_coe
 
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 @[simp]
 theorem mem_sInf {S : Set (Submodule R M)} {x : M} : x ∈ sInf S ↔ ∀ p ∈ S, x ∈ p :=
   Set.mem_iInter₂
 #align submodule.mem_Inf Submodule.mem_sInf
 
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 @[simp]
 theorem mem_iInf {ι} (p : ι → Submodule R M) {x} : (x ∈ ⨅ i, p i) ↔ ∀ i, x ∈ p i := by
   rw [← SetLike.mem_coe, infi_coe, Set.mem_iInter] <;> rfl
 #align submodule.mem_infi Submodule.mem_iInf
 
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 @[simp]
 theorem mem_finset_inf {ι} {s : Finset ι} {p : ι → Submodule R M} {x : M} :
     x ∈ s.inf p ↔ ∀ i ∈ s, x ∈ p i := by
   simp only [← SetLike.mem_coe, finset_inf_coe, Set.mem_iInter]
 #align submodule.mem_finset_inf Submodule.mem_finset_inf
 
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 theorem mem_sup_left {S T : Submodule R M} : ∀ {x : M}, x ∈ S → x ∈ S ⊔ T :=
   show S ≤ S ⊔ T from le_sup_left
 #align submodule.mem_sup_left Submodule.mem_sup_left
 
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 theorem mem_sup_right {S T : Submodule R M} : ∀ {x : M}, x ∈ T → x ∈ S ⊔ T :=
   show T ≤ S ⊔ T from le_sup_right
 #align submodule.mem_sup_right Submodule.mem_sup_right
 
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 theorem add_mem_sup {S T : Submodule R M} {s t : M} (hs : s ∈ S) (ht : t ∈ T) : s + t ∈ S ⊔ T :=
   add_mem (mem_sup_left hs) (mem_sup_right ht)
 #align submodule.add_mem_sup Submodule.add_mem_sup
 
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-Case conversion may be inaccurate. Consider using '#align submodule.sub_mem_sup Submodule.sub_mem_supₓ'. -/
 theorem sub_mem_sup {R' M' : Type _} [Ring R'] [AddCommGroup M'] [Module R' M']
     {S T : Submodule R' M'} {s t : M'} (hs : s ∈ S) (ht : t ∈ T) : s - t ∈ S ⊔ T :=
   by
@@ -496,12 +304,6 @@ theorem sub_mem_sup {R' M' : Type _} [Ring R'] [AddCommGroup M'] [Module R' M']
   exact add_mem_sup hs (neg_mem ht)
 #align submodule.sub_mem_sup Submodule.sub_mem_sup
 
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-Case conversion may be inaccurate. Consider using '#align submodule.mem_supr_of_mem Submodule.mem_iSup_of_memₓ'. -/
 theorem mem_iSup_of_mem {ι : Sort _} {b : M} {p : ι → Submodule R M} (i : ι) (h : b ∈ p i) :
     b ∈ ⨆ i, p i :=
   have : p i ≤ ⨆ i, p i := le_iSup p i
@@ -510,23 +312,11 @@ theorem mem_iSup_of_mem {ι : Sort _} {b : M} {p : ι → Submodule R M} (i : ι
 
 open BigOperators
 
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 theorem sum_mem_iSup {ι : Type _} [Fintype ι] {f : ι → M} {p : ι → Submodule R M}
     (h : ∀ i, f i ∈ p i) : (∑ i, f i) ∈ ⨆ i, p i :=
   sum_mem fun i hi => mem_iSup_of_mem i (h i)
 #align submodule.sum_mem_supr Submodule.sum_mem_iSup
 
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-Case conversion may be inaccurate. Consider using '#align submodule.sum_mem_bsupr Submodule.sum_mem_biSupₓ'. -/
 theorem sum_mem_biSup {ι : Type _} {s : Finset ι} {f : ι → M} {p : ι → Submodule R M}
     (h : ∀ i ∈ s, f i ∈ p i) : (∑ i in s, f i) ∈ ⨆ i ∈ s, p i :=
   sum_mem fun i hi => mem_iSup_of_mem i <| mem_iSup_of_mem hi (h i hi)
@@ -535,45 +325,21 @@ theorem sum_mem_biSup {ι : Type _} {s : Finset ι} {f : ι → M} {p : ι → S
 /-! Note that `submodule.mem_supr` is provided in `linear_algebra/basic.lean`. -/
 
 
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 theorem mem_sSup_of_mem {S : Set (Submodule R M)} {s : Submodule R M} (hs : s ∈ S) :
     ∀ {x : M}, x ∈ s → x ∈ sSup S :=
   show s ≤ sSup S from le_sSup hs
 #align submodule.mem_Sup_of_mem Submodule.mem_sSup_of_mem
 
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 theorem disjoint_def {p p' : Submodule R M} : Disjoint p p' ↔ ∀ x ∈ p, x ∈ p' → x = (0 : M) :=
   disjoint_iff_inf_le.trans <| show (∀ x, x ∈ p ∧ x ∈ p' → x ∈ ({0} : Set M)) ↔ _ by simp
 #align submodule.disjoint_def Submodule.disjoint_def
 
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 theorem disjoint_def' {p p' : Submodule R M} :
     Disjoint p p' ↔ ∀ x ∈ p, ∀ y ∈ p', x = y → x = (0 : M) :=
   disjoint_def.trans
     ⟨fun h x hx y hy hxy => h x hx <| hxy.symm ▸ hy, fun h x hx hx' => h _ hx x hx' rfl⟩
 #align submodule.disjoint_def' Submodule.disjoint_def'
 
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 theorem eq_zero_of_coe_mem_of_disjoint (hpq : Disjoint p q) {a : p} (ha : (a : M) ∈ q) : a = 0 := by
   exact_mod_cast disjoint_def.mp hpq a (coe_mem a) ha
 #align submodule.eq_zero_of_coe_mem_of_disjoint Submodule.eq_zero_of_coe_mem_of_disjoint
@@ -582,12 +348,6 @@ end Submodule
 
 section NatSubmodule
 
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-Case conversion may be inaccurate. Consider using '#align add_submonoid.to_nat_submodule AddSubmonoid.toNatSubmoduleₓ'. -/
 /-- An additive submonoid is equivalent to a ℕ-submodule. -/
 def AddSubmonoid.toNatSubmodule : AddSubmonoid M ≃o Submodule ℕ M
     where
@@ -598,35 +358,23 @@ def AddSubmonoid.toNatSubmodule : AddSubmonoid M ≃o Submodule ℕ M
   map_rel_iff' a b := Iff.rfl
 #align add_submonoid.to_nat_submodule AddSubmonoid.toNatSubmodule
 
-/- warning: add_submonoid.to_nat_submodule_symm -> AddSubmonoid.toNatSubmodule_symm is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align add_submonoid.to_nat_submodule_symm AddSubmonoid.toNatSubmodule_symmₓ'. -/
 @[simp]
 theorem AddSubmonoid.toNatSubmodule_symm :
     ⇑(AddSubmonoid.toNatSubmodule.symm : _ ≃o AddSubmonoid M) = Submodule.toAddSubmonoid :=
   rfl
 #align add_submonoid.to_nat_submodule_symm AddSubmonoid.toNatSubmodule_symm
 
-/- warning: add_submonoid.coe_to_nat_submodule -> AddSubmonoid.coe_toNatSubmodule is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align add_submonoid.coe_to_nat_submodule AddSubmonoid.coe_toNatSubmoduleₓ'. -/
 @[simp]
 theorem AddSubmonoid.coe_toNatSubmodule (S : AddSubmonoid M) : (S.toNatSubmodule : Set M) = S :=
   rfl
 #align add_submonoid.coe_to_nat_submodule AddSubmonoid.coe_toNatSubmodule
 
-/- warning: add_submonoid.to_nat_submodule_to_add_submonoid -> AddSubmonoid.toNatSubmodule_toAddSubmonoid is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align add_submonoid.to_nat_submodule_to_add_submonoid AddSubmonoid.toNatSubmodule_toAddSubmonoidₓ'. -/
 @[simp]
 theorem AddSubmonoid.toNatSubmodule_toAddSubmonoid (S : AddSubmonoid M) :
     S.toNatSubmodule.toAddSubmonoid = S :=
   AddSubmonoid.toNatSubmodule.symm_apply_apply S
 #align add_submonoid.to_nat_submodule_to_add_submonoid AddSubmonoid.toNatSubmodule_toAddSubmonoid
 
-/- warning: submodule.to_add_submonoid_to_nat_submodule -> Submodule.toAddSubmonoid_toNatSubmodule is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align submodule.to_add_submonoid_to_nat_submodule Submodule.toAddSubmonoid_toNatSubmoduleₓ'. -/
 @[simp]
 theorem Submodule.toAddSubmonoid_toNatSubmodule (S : Submodule ℕ M) :
     S.toAddSubmonoid.toNatSubmodule = S :=
@@ -641,12 +389,6 @@ section IntSubmodule
 
 variable [AddCommGroup M]
 
-/- warning: add_subgroup.to_int_submodule -> AddSubgroup.toIntSubmodule is a dubious translation:
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-Case conversion may be inaccurate. Consider using '#align add_subgroup.to_int_submodule AddSubgroup.toIntSubmoduleₓ'. -/
 /-- An additive subgroup is equivalent to a ℤ-submodule. -/
 def AddSubgroup.toIntSubmodule : AddSubgroup M ≃o Submodule ℤ M
     where
@@ -657,35 +399,23 @@ def AddSubgroup.toIntSubmodule : AddSubgroup M ≃o Submodule ℤ M
   map_rel_iff' a b := Iff.rfl
 #align add_subgroup.to_int_submodule AddSubgroup.toIntSubmodule
 
-/- warning: add_subgroup.to_int_submodule_symm -> AddSubgroup.toIntSubmodule_symm is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align add_subgroup.to_int_submodule_symm AddSubgroup.toIntSubmodule_symmₓ'. -/
 @[simp]
 theorem AddSubgroup.toIntSubmodule_symm :
     ⇑(AddSubgroup.toIntSubmodule.symm : _ ≃o AddSubgroup M) = Submodule.toAddSubgroup :=
   rfl
 #align add_subgroup.to_int_submodule_symm AddSubgroup.toIntSubmodule_symm
 
-/- warning: add_subgroup.coe_to_int_submodule -> AddSubgroup.coe_toIntSubmodule is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align add_subgroup.coe_to_int_submodule AddSubgroup.coe_toIntSubmoduleₓ'. -/
 @[simp]
 theorem AddSubgroup.coe_toIntSubmodule (S : AddSubgroup M) : (S.toIntSubmodule : Set M) = S :=
   rfl
 #align add_subgroup.coe_to_int_submodule AddSubgroup.coe_toIntSubmodule
 
-/- warning: add_subgroup.to_int_submodule_to_add_subgroup -> AddSubgroup.toIntSubmodule_toAddSubgroup is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align add_subgroup.to_int_submodule_to_add_subgroup AddSubgroup.toIntSubmodule_toAddSubgroupₓ'. -/
 @[simp]
 theorem AddSubgroup.toIntSubmodule_toAddSubgroup (S : AddSubgroup M) :
     S.toIntSubmodule.toAddSubgroup = S :=
   AddSubgroup.toIntSubmodule.symm_apply_apply S
 #align add_subgroup.to_int_submodule_to_add_subgroup AddSubgroup.toIntSubmodule_toAddSubgroup
 
-/- warning: submodule.to_add_subgroup_to_int_submodule -> Submodule.toAddSubgroup_toIntSubmodule is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align submodule.to_add_subgroup_to_int_submodule Submodule.toAddSubgroup_toIntSubmoduleₓ'. -/
 @[simp]
 theorem Submodule.toAddSubgroup_toIntSubmodule (S : Submodule ℤ M) :
     S.toAddSubgroup.toIntSubmodule = S :=

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

@@ -162,10 +162,8 @@ lean 3 declaration is
 but is expected to have type
   forall {R : Type.{u2}} {M : Type.{u1}} [_inst_1 : Semiring.{u2} R] [_inst_3 : AddCommMonoid.{u1} M] [_inst_4 : Module.{u2, u1} R M _inst_1 _inst_3] (p : Submodule.{u2, u1} R M _inst_1 _inst_3 _inst_4), Iff (Ne.{succ u1} (Submodule.{u2, u1} R M _inst_1 _inst_3 _inst_4) p (Bot.bot.{u1} (Submodule.{u2, u1} R M _inst_1 _inst_3 _inst_4) (Submodule.instBotSubmodule.{u2, u1} R M _inst_1 _inst_3 _inst_4))) (Exists.{succ u1} M (fun (x : M) => And (Membership.mem.{u1, u1} M (Submodule.{u2, u1} R M _inst_1 _inst_3 _inst_4) (SetLike.instMembership.{u1, u1} (Submodule.{u2, u1} R M _inst_1 _inst_3 _inst_4) M (Submodule.setLike.{u2, u1} R M _inst_1 _inst_3 _inst_4)) x p) (Ne.{succ u1} M x (OfNat.ofNat.{u1} M 0 (Zero.toOfNat0.{u1} M (AddMonoid.toZero.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3)))))))
 Case conversion may be inaccurate. Consider using '#align submodule.ne_bot_iff Submodule.ne_bot_iffₓ'. -/
-protected theorem ne_bot_iff (p : Submodule R M) : p ≠ ⊥ ↔ ∃ x ∈ p, x ≠ (0 : M) :=
-  by
-  haveI := Classical.propDecidable
-  simp_rw [Ne.def, p.eq_bot_iff, not_forall]
+protected theorem ne_bot_iff (p : Submodule R M) : p ≠ ⊥ ↔ ∃ x ∈ p, x ≠ (0 : M) := by
+  haveI := Classical.propDecidable; simp_rw [Ne.def, p.eq_bot_iff, not_forall]
 #align submodule.ne_bot_iff Submodule.ne_bot_iff
 
 /- warning: submodule.nonzero_mem_of_bot_lt -> Submodule.nonzero_mem_of_bot_lt is a dubious translation:
@@ -202,18 +200,10 @@ def botEquivPUnit : (⊥ : Submodule R M) ≃ₗ[R] PUnit
     where
   toFun x := PUnit.unit
   invFun x := 0
-  map_add' := by
-    intros
-    ext
-  map_smul' := by
-    intros
-    ext
-  left_inv := by
-    intro x
-    ext
-  right_inv := by
-    intro x
-    ext
+  map_add' := by intros ; ext
+  map_smul' := by intros ; ext
+  left_inv := by intro x; ext
+  right_inv := by intro x; ext
 #align submodule.bot_equiv_punit Submodule.botEquivPUnit
 
 /- warning: submodule.eq_bot_of_subsingleton -> Submodule.eq_bot_of_subsingleton is a dubious translation:
@@ -324,19 +314,10 @@ def topEquiv : (⊤ : Submodule R M) ≃ₗ[R] M
     where
   toFun x := x
   invFun x := ⟨x, by simp⟩
-  map_add' := by
-    intros
-    rfl
-  map_smul' := by
-    intros
-    rfl
-  left_inv := by
-    intro x
-    ext
-    rfl
-  right_inv := by
-    intro x
-    rfl
+  map_add' := by intros ; rfl
+  map_smul' := by intros ; rfl
+  left_inv := by intro x; ext; rfl
+  right_inv := by intro x; rfl
 #align submodule.top_equiv Submodule.topEquiv
 
 instance : InfSet (Submodule R M) :=

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

@@ -348,11 +348,9 @@ instance : InfSet (Submodule R M) :=
 
 private theorem Inf_le' {S : Set (Submodule R M)} {p} : p ∈ S → sInf S ≤ p :=
   Set.biInter_subset_of_mem
-#align submodule.Inf_le' submodule.Inf_le'
 
 private theorem le_Inf' {S : Set (Submodule R M)} {p} : (∀ q ∈ S, p ≤ q) → p ≤ sInf S :=
   Set.subset_iInter₂
-#align submodule.le_Inf' submodule.le_Inf'
 
 instance : Inf (Submodule R M) :=
   ⟨fun p q =>
@@ -620,10 +618,7 @@ def AddSubmonoid.toNatSubmodule : AddSubmonoid M ≃o Submodule ℕ M
 #align add_submonoid.to_nat_submodule AddSubmonoid.toNatSubmodule
 
 /- warning: add_submonoid.to_nat_submodule_symm -> AddSubmonoid.toNatSubmodule_symm is a dubious translation:
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+<too large>
 Case conversion may be inaccurate. Consider using '#align add_submonoid.to_nat_submodule_symm AddSubmonoid.toNatSubmodule_symmₓ'. -/
 @[simp]
 theorem AddSubmonoid.toNatSubmodule_symm :
@@ -632,10 +627,7 @@ theorem AddSubmonoid.toNatSubmodule_symm :
 #align add_submonoid.to_nat_submodule_symm AddSubmonoid.toNatSubmodule_symm
 
 /- warning: add_submonoid.coe_to_nat_submodule -> AddSubmonoid.coe_toNatSubmodule is a dubious translation:
-lean 3 declaration is
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+<too large>
 Case conversion may be inaccurate. Consider using '#align add_submonoid.coe_to_nat_submodule AddSubmonoid.coe_toNatSubmoduleₓ'. -/
 @[simp]
 theorem AddSubmonoid.coe_toNatSubmodule (S : AddSubmonoid M) : (S.toNatSubmodule : Set M) = S :=
@@ -643,10 +635,7 @@ theorem AddSubmonoid.coe_toNatSubmodule (S : AddSubmonoid M) : (S.toNatSubmodule
 #align add_submonoid.coe_to_nat_submodule AddSubmonoid.coe_toNatSubmodule
 
 /- warning: add_submonoid.to_nat_submodule_to_add_submonoid -> AddSubmonoid.toNatSubmodule_toAddSubmonoid is a dubious translation:
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+<too large>
 Case conversion may be inaccurate. Consider using '#align add_submonoid.to_nat_submodule_to_add_submonoid AddSubmonoid.toNatSubmodule_toAddSubmonoidₓ'. -/
 @[simp]
 theorem AddSubmonoid.toNatSubmodule_toAddSubmonoid (S : AddSubmonoid M) :
@@ -655,10 +644,7 @@ theorem AddSubmonoid.toNatSubmodule_toAddSubmonoid (S : AddSubmonoid M) :
 #align add_submonoid.to_nat_submodule_to_add_submonoid AddSubmonoid.toNatSubmodule_toAddSubmonoid
 
 /- warning: submodule.to_add_submonoid_to_nat_submodule -> Submodule.toAddSubmonoid_toNatSubmodule is a dubious translation:
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(AddCommMonoid.natModule.{u1} M _inst_3)) (RelHomClass.toFunLike.{u1, u1, u1} (RelIso.{u1, u1} (AddSubmonoid.{u1} M (AddMonoid.toAddZeroClass.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3))) (Submodule.{0, u1} Nat M Nat.semiring _inst_3 (AddCommMonoid.natModule.{u1} M _inst_3)) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1285 : AddSubmonoid.{u1} M (AddMonoid.toAddZeroClass.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3))) (x._@.Mathlib.Order.Hom.Basic._hyg.1287 : AddSubmonoid.{u1} M (AddMonoid.toAddZeroClass.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3))) => LE.le.{u1} (AddSubmonoid.{u1} M (AddMonoid.toAddZeroClass.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3))) (Preorder.toLE.{u1} (AddSubmonoid.{u1} M (AddMonoid.toAddZeroClass.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3))) (PartialOrder.toPreorder.{u1} (AddSubmonoid.{u1} M (AddMonoid.toAddZeroClass.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3))) (CompleteSemilatticeInf.toPartialOrder.{u1} (AddSubmonoid.{u1} M 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(AddCommMonoid.natModule.{u1} M _inst_3)) (CompleteSemilatticeInf.toPartialOrder.{u1} (Submodule.{0, u1} Nat M Nat.semiring _inst_3 (AddCommMonoid.natModule.{u1} M _inst_3)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (Submodule.{0, u1} Nat M Nat.semiring _inst_3 (AddCommMonoid.natModule.{u1} M _inst_3)) (Submodule.completeLattice.{0, u1} Nat M Nat.semiring _inst_3 (AddCommMonoid.natModule.{u1} M _inst_3)))))) x._@.Mathlib.Order.Hom.Basic._hyg.1300 x._@.Mathlib.Order.Hom.Basic._hyg.1302)) (AddSubmonoid.{u1} M (AddMonoid.toAddZeroClass.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3))) (Submodule.{0, u1} Nat M Nat.semiring _inst_3 (AddCommMonoid.natModule.{u1} M _inst_3)) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1285 : AddSubmonoid.{u1} M (AddMonoid.toAddZeroClass.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3))) (x._@.Mathlib.Order.Hom.Basic._hyg.1287 : AddSubmonoid.{u1} M (AddMonoid.toAddZeroClass.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3))) => LE.le.{u1} (AddSubmonoid.{u1} M (AddMonoid.toAddZeroClass.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3))) (Preorder.toLE.{u1} (AddSubmonoid.{u1} M (AddMonoid.toAddZeroClass.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3))) (PartialOrder.toPreorder.{u1} (AddSubmonoid.{u1} M (AddMonoid.toAddZeroClass.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3))) (CompleteSemilatticeInf.toPartialOrder.{u1} (AddSubmonoid.{u1} M (AddMonoid.toAddZeroClass.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3))) (CompleteLattice.toCompleteSemilatticeInf.{u1} (AddSubmonoid.{u1} M (AddMonoid.toAddZeroClass.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3))) (AddSubmonoid.instCompleteLatticeAddSubmonoid.{u1} M (AddMonoid.toAddZeroClass.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3))))))) x._@.Mathlib.Order.Hom.Basic._hyg.1285 x._@.Mathlib.Order.Hom.Basic._hyg.1287) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1300 : Submodule.{0, u1} Nat M Nat.semiring _inst_3 (AddCommMonoid.natModule.{u1} M _inst_3)) 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+<too large>
 Case conversion may be inaccurate. Consider using '#align submodule.to_add_submonoid_to_nat_submodule Submodule.toAddSubmonoid_toNatSubmoduleₓ'. -/
 @[simp]
 theorem Submodule.toAddSubmonoid_toNatSubmodule (S : Submodule ℕ M) :
@@ -691,10 +677,7 @@ def AddSubgroup.toIntSubmodule : AddSubgroup M ≃o Submodule ℤ M
 #align add_subgroup.to_int_submodule AddSubgroup.toIntSubmodule
 
 /- warning: add_subgroup.to_int_submodule_symm -> AddSubgroup.toIntSubmodule_symm is a dubious translation:
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(CompleteLattice.toCompleteSemilatticeInf.{u1} (Submodule.{0, u1} Int M Int.semiring (AddCommGroup.toAddCommMonoid.{u1} M _inst_1) (AddCommGroup.intModule.{u1} M _inst_1)) (Submodule.completeLattice.{0, u1} Int M Int.semiring (AddCommGroup.toAddCommMonoid.{u1} M _inst_1) (AddCommGroup.intModule.{u1} M _inst_1)))))) (Preorder.toHasLe.{u1} (AddSubgroup.{u1} M (AddCommGroup.toAddGroup.{u1} M _inst_1)) (PartialOrder.toPreorder.{u1} (AddSubgroup.{u1} M (AddCommGroup.toAddGroup.{u1} M _inst_1)) (CompleteSemilatticeInf.toPartialOrder.{u1} (AddSubgroup.{u1} M (AddCommGroup.toAddGroup.{u1} M _inst_1)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (AddSubgroup.{u1} M (AddCommGroup.toAddGroup.{u1} M _inst_1)) (AddSubgroup.completeLattice.{u1} M (AddCommGroup.toAddGroup.{u1} M _inst_1))))))) (fun (_x : RelIso.{u1, u1} (Submodule.{0, u1} Int M Int.semiring (AddCommGroup.toAddCommMonoid.{u1} M _inst_1) (AddCommGroup.intModule.{u1} M _inst_1)) (AddSubgroup.{u1} M (AddCommGroup.toAddGroup.{u1} M _inst_1)) (LE.le.{u1} (Submodule.{0, u1} Int M Int.semiring (AddCommGroup.toAddCommMonoid.{u1} M _inst_1) (AddCommGroup.intModule.{u1} M _inst_1)) (Preorder.toHasLe.{u1} (Submodule.{0, u1} Int M Int.semiring (AddCommGroup.toAddCommMonoid.{u1} M _inst_1) (AddCommGroup.intModule.{u1} M _inst_1)) (PartialOrder.toPreorder.{u1} (Submodule.{0, u1} Int M Int.semiring (AddCommGroup.toAddCommMonoid.{u1} M _inst_1) (AddCommGroup.intModule.{u1} M _inst_1)) (CompleteSemilatticeInf.toPartialOrder.{u1} (Submodule.{0, u1} Int M Int.semiring (AddCommGroup.toAddCommMonoid.{u1} M _inst_1) (AddCommGroup.intModule.{u1} M _inst_1)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (Submodule.{0, u1} Int M Int.semiring (AddCommGroup.toAddCommMonoid.{u1} M _inst_1) (AddCommGroup.intModule.{u1} M _inst_1)) (Submodule.completeLattice.{0, u1} Int M Int.semiring (AddCommGroup.toAddCommMonoid.{u1} M _inst_1) (AddCommGroup.intModule.{u1} M _inst_1))))))) (LE.le.{u1} (AddSubgroup.{u1} M (AddCommGroup.toAddGroup.{u1} M 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(PartialOrder.toPreorder.{u1} (AddSubgroup.{u1} M (AddCommGroup.toAddGroup.{u1} M _inst_1)) (CompleteSemilatticeInf.toPartialOrder.{u1} (AddSubgroup.{u1} M (AddCommGroup.toAddGroup.{u1} M _inst_1)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (AddSubgroup.{u1} M (AddCommGroup.toAddGroup.{u1} M _inst_1)) (AddSubgroup.completeLattice.{u1} M (AddCommGroup.toAddGroup.{u1} M _inst_1)))))))) (OrderIso.symm.{u1, u1} (AddSubgroup.{u1} M (AddCommGroup.toAddGroup.{u1} M _inst_1)) (Submodule.{0, u1} Int M Int.semiring (AddCommGroup.toAddCommMonoid.{u1} M _inst_1) (AddCommGroup.intModule.{u1} M _inst_1)) (Preorder.toHasLe.{u1} (AddSubgroup.{u1} M (AddCommGroup.toAddGroup.{u1} M _inst_1)) (PartialOrder.toPreorder.{u1} (AddSubgroup.{u1} M (AddCommGroup.toAddGroup.{u1} M _inst_1)) (CompleteSemilatticeInf.toPartialOrder.{u1} (AddSubgroup.{u1} M (AddCommGroup.toAddGroup.{u1} M _inst_1)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (AddSubgroup.{u1} M (AddCommGroup.toAddGroup.{u1} M _inst_1)) (AddSubgroup.completeLattice.{u1} M (AddCommGroup.toAddGroup.{u1} M _inst_1)))))) (Preorder.toHasLe.{u1} (Submodule.{0, u1} Int M Int.semiring (AddCommGroup.toAddCommMonoid.{u1} M _inst_1) (AddCommGroup.intModule.{u1} M _inst_1)) (PartialOrder.toPreorder.{u1} (Submodule.{0, u1} Int M Int.semiring (AddCommGroup.toAddCommMonoid.{u1} M _inst_1) (AddCommGroup.intModule.{u1} M _inst_1)) (CompleteSemilatticeInf.toPartialOrder.{u1} (Submodule.{0, u1} Int M Int.semiring (AddCommGroup.toAddCommMonoid.{u1} M _inst_1) (AddCommGroup.intModule.{u1} M _inst_1)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (Submodule.{0, u1} Int M Int.semiring (AddCommGroup.toAddCommMonoid.{u1} M _inst_1) (AddCommGroup.intModule.{u1} M _inst_1)) (Submodule.completeLattice.{0, u1} Int M Int.semiring (AddCommGroup.toAddCommMonoid.{u1} M _inst_1) (AddCommGroup.intModule.{u1} M _inst_1)))))) (AddSubgroup.toIntSubmodule.{u1} M _inst_1))) (Submodule.toAddSubgroup.{0, u1} Int M Int.ring _inst_1 (AddCommGroup.intModule.{u1} M _inst_1))
-but is expected to have type
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(AddCommGroup.intModule.{u1} M _inst_1)) (Preorder.toLE.{u1} (Submodule.{0, u1} Int M Int.instSemiringInt (AddCommGroup.toAddCommMonoid.{u1} M _inst_1) (AddCommGroup.intModule.{u1} M _inst_1)) (PartialOrder.toPreorder.{u1} (Submodule.{0, u1} Int M Int.instSemiringInt (AddCommGroup.toAddCommMonoid.{u1} M _inst_1) (AddCommGroup.intModule.{u1} M _inst_1)) (CompleteSemilatticeInf.toPartialOrder.{u1} (Submodule.{0, u1} Int M Int.instSemiringInt (AddCommGroup.toAddCommMonoid.{u1} M _inst_1) (AddCommGroup.intModule.{u1} M _inst_1)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (Submodule.{0, u1} Int M Int.instSemiringInt (AddCommGroup.toAddCommMonoid.{u1} M _inst_1) (AddCommGroup.intModule.{u1} M _inst_1)) (Submodule.completeLattice.{0, u1} Int M Int.instSemiringInt (AddCommGroup.toAddCommMonoid.{u1} M _inst_1) (AddCommGroup.intModule.{u1} M _inst_1)))))) x._@.Mathlib.Order.Hom.Basic._hyg.1285 x._@.Mathlib.Order.Hom.Basic._hyg.1287) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1300 : AddSubgroup.{u1} M (AddCommGroup.toAddGroup.{u1} M _inst_1)) (x._@.Mathlib.Order.Hom.Basic._hyg.1302 : AddSubgroup.{u1} M (AddCommGroup.toAddGroup.{u1} M _inst_1)) => LE.le.{u1} (AddSubgroup.{u1} M (AddCommGroup.toAddGroup.{u1} M _inst_1)) (Preorder.toLE.{u1} (AddSubgroup.{u1} M (AddCommGroup.toAddGroup.{u1} M _inst_1)) (PartialOrder.toPreorder.{u1} (AddSubgroup.{u1} M (AddCommGroup.toAddGroup.{u1} M _inst_1)) (CompleteSemilatticeInf.toPartialOrder.{u1} (AddSubgroup.{u1} M (AddCommGroup.toAddGroup.{u1} M _inst_1)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (AddSubgroup.{u1} M (AddCommGroup.toAddGroup.{u1} M _inst_1)) (AddSubgroup.instCompleteLatticeAddSubgroup.{u1} M (AddCommGroup.toAddGroup.{u1} M _inst_1)))))) x._@.Mathlib.Order.Hom.Basic._hyg.1300 x._@.Mathlib.Order.Hom.Basic._hyg.1302)) (Submodule.{0, u1} Int M Int.instSemiringInt (AddCommGroup.toAddCommMonoid.{u1} M _inst_1) (AddCommGroup.intModule.{u1} M _inst_1)) (fun (_x : Submodule.{0, u1} Int M Int.instSemiringInt (AddCommGroup.toAddCommMonoid.{u1} M _inst_1) (AddCommGroup.intModule.{u1} M _inst_1)) => AddSubgroup.{u1} M (AddCommGroup.toAddGroup.{u1} M _inst_1)) (RelHomClass.toFunLike.{u1, u1, u1} (RelIso.{u1, u1} (Submodule.{0, u1} Int M Int.instSemiringInt (AddCommGroup.toAddCommMonoid.{u1} M _inst_1) (AddCommGroup.intModule.{u1} M _inst_1)) (AddSubgroup.{u1} M (AddCommGroup.toAddGroup.{u1} M _inst_1)) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1285 : Submodule.{0, u1} Int M Int.instSemiringInt (AddCommGroup.toAddCommMonoid.{u1} M _inst_1) (AddCommGroup.intModule.{u1} M _inst_1)) (x._@.Mathlib.Order.Hom.Basic._hyg.1287 : Submodule.{0, u1} Int M Int.instSemiringInt (AddCommGroup.toAddCommMonoid.{u1} M _inst_1) (AddCommGroup.intModule.{u1} M _inst_1)) => LE.le.{u1} (Submodule.{0, u1} Int M Int.instSemiringInt (AddCommGroup.toAddCommMonoid.{u1} M _inst_1) (AddCommGroup.intModule.{u1} M _inst_1)) (Preorder.toLE.{u1} (Submodule.{0, u1} Int M Int.instSemiringInt (AddCommGroup.toAddCommMonoid.{u1} M _inst_1) (AddCommGroup.intModule.{u1} M _inst_1)) (PartialOrder.toPreorder.{u1} (Submodule.{0, u1} Int M Int.instSemiringInt (AddCommGroup.toAddCommMonoid.{u1} M _inst_1) (AddCommGroup.intModule.{u1} M _inst_1)) (CompleteSemilatticeInf.toPartialOrder.{u1} (Submodule.{0, u1} Int M Int.instSemiringInt (AddCommGroup.toAddCommMonoid.{u1} M _inst_1) (AddCommGroup.intModule.{u1} M _inst_1)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (Submodule.{0, u1} Int M Int.instSemiringInt (AddCommGroup.toAddCommMonoid.{u1} M _inst_1) (AddCommGroup.intModule.{u1} M _inst_1)) (Submodule.completeLattice.{0, u1} Int M Int.instSemiringInt (AddCommGroup.toAddCommMonoid.{u1} M _inst_1) (AddCommGroup.intModule.{u1} M _inst_1)))))) x._@.Mathlib.Order.Hom.Basic._hyg.1285 x._@.Mathlib.Order.Hom.Basic._hyg.1287) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1300 : AddSubgroup.{u1} M (AddCommGroup.toAddGroup.{u1} M _inst_1)) (x._@.Mathlib.Order.Hom.Basic._hyg.1302 : AddSubgroup.{u1} M (AddCommGroup.toAddGroup.{u1} M _inst_1)) => LE.le.{u1} (AddSubgroup.{u1} M (AddCommGroup.toAddGroup.{u1} M _inst_1)) (Preorder.toLE.{u1} (AddSubgroup.{u1} M (AddCommGroup.toAddGroup.{u1} M _inst_1)) (PartialOrder.toPreorder.{u1} (AddSubgroup.{u1} M (AddCommGroup.toAddGroup.{u1} M _inst_1)) (CompleteSemilatticeInf.toPartialOrder.{u1} (AddSubgroup.{u1} M (AddCommGroup.toAddGroup.{u1} M _inst_1)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (AddSubgroup.{u1} M (AddCommGroup.toAddGroup.{u1} M _inst_1)) (AddSubgroup.instCompleteLatticeAddSubgroup.{u1} M (AddCommGroup.toAddGroup.{u1} M _inst_1)))))) x._@.Mathlib.Order.Hom.Basic._hyg.1300 x._@.Mathlib.Order.Hom.Basic._hyg.1302)) (Submodule.{0, u1} Int M Int.instSemiringInt (AddCommGroup.toAddCommMonoid.{u1} M _inst_1) (AddCommGroup.intModule.{u1} M _inst_1)) (AddSubgroup.{u1} M (AddCommGroup.toAddGroup.{u1} M _inst_1)) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1285 : Submodule.{0, u1} Int M Int.instSemiringInt (AddCommGroup.toAddCommMonoid.{u1} M _inst_1) (AddCommGroup.intModule.{u1} M _inst_1)) (x._@.Mathlib.Order.Hom.Basic._hyg.1287 : Submodule.{0, u1} Int M Int.instSemiringInt (AddCommGroup.toAddCommMonoid.{u1} M _inst_1) (AddCommGroup.intModule.{u1} M _inst_1)) => LE.le.{u1} (Submodule.{0, u1} Int M Int.instSemiringInt (AddCommGroup.toAddCommMonoid.{u1} M _inst_1) (AddCommGroup.intModule.{u1} M _inst_1)) (Preorder.toLE.{u1} (Submodule.{0, u1} Int M Int.instSemiringInt (AddCommGroup.toAddCommMonoid.{u1} M _inst_1) (AddCommGroup.intModule.{u1} M _inst_1)) (PartialOrder.toPreorder.{u1} (Submodule.{0, u1} Int M Int.instSemiringInt (AddCommGroup.toAddCommMonoid.{u1} M _inst_1) (AddCommGroup.intModule.{u1} M _inst_1)) (CompleteSemilatticeInf.toPartialOrder.{u1} (Submodule.{0, u1} Int M Int.instSemiringInt (AddCommGroup.toAddCommMonoid.{u1} M _inst_1) (AddCommGroup.intModule.{u1} M _inst_1)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (Submodule.{0, u1} Int M Int.instSemiringInt (AddCommGroup.toAddCommMonoid.{u1} M _inst_1) (AddCommGroup.intModule.{u1} M _inst_1)) (Submodule.completeLattice.{0, u1} Int M Int.instSemiringInt (AddCommGroup.toAddCommMonoid.{u1} M _inst_1) (AddCommGroup.intModule.{u1} M _inst_1)))))) x._@.Mathlib.Order.Hom.Basic._hyg.1285 x._@.Mathlib.Order.Hom.Basic._hyg.1287) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1300 : AddSubgroup.{u1} M (AddCommGroup.toAddGroup.{u1} M _inst_1)) (x._@.Mathlib.Order.Hom.Basic._hyg.1302 : AddSubgroup.{u1} M (AddCommGroup.toAddGroup.{u1} M _inst_1)) => LE.le.{u1} (AddSubgroup.{u1} M (AddCommGroup.toAddGroup.{u1} M _inst_1)) (Preorder.toLE.{u1} (AddSubgroup.{u1} M (AddCommGroup.toAddGroup.{u1} M _inst_1)) (PartialOrder.toPreorder.{u1} (AddSubgroup.{u1} M (AddCommGroup.toAddGroup.{u1} M _inst_1)) (CompleteSemilatticeInf.toPartialOrder.{u1} (AddSubgroup.{u1} M (AddCommGroup.toAddGroup.{u1} M _inst_1)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (AddSubgroup.{u1} M (AddCommGroup.toAddGroup.{u1} M _inst_1)) (AddSubgroup.instCompleteLatticeAddSubgroup.{u1} M (AddCommGroup.toAddGroup.{u1} M _inst_1)))))) x._@.Mathlib.Order.Hom.Basic._hyg.1300 x._@.Mathlib.Order.Hom.Basic._hyg.1302) (RelIso.instRelHomClassRelIso.{u1, u1} (Submodule.{0, u1} Int M Int.instSemiringInt (AddCommGroup.toAddCommMonoid.{u1} M _inst_1) (AddCommGroup.intModule.{u1} M _inst_1)) (AddSubgroup.{u1} M (AddCommGroup.toAddGroup.{u1} M _inst_1)) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1285 : Submodule.{0, u1} Int M Int.instSemiringInt (AddCommGroup.toAddCommMonoid.{u1} M _inst_1) (AddCommGroup.intModule.{u1} M _inst_1)) (x._@.Mathlib.Order.Hom.Basic._hyg.1287 : Submodule.{0, u1} Int M Int.instSemiringInt (AddCommGroup.toAddCommMonoid.{u1} M _inst_1) (AddCommGroup.intModule.{u1} M _inst_1)) => LE.le.{u1} (Submodule.{0, u1} Int M Int.instSemiringInt (AddCommGroup.toAddCommMonoid.{u1} M _inst_1) (AddCommGroup.intModule.{u1} M _inst_1)) (Preorder.toLE.{u1} (Submodule.{0, u1} Int M Int.instSemiringInt (AddCommGroup.toAddCommMonoid.{u1} M _inst_1) (AddCommGroup.intModule.{u1} M 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+<too large>
 Case conversion may be inaccurate. Consider using '#align add_subgroup.to_int_submodule_symm AddSubgroup.toIntSubmodule_symmₓ'. -/
 @[simp]
 theorem AddSubgroup.toIntSubmodule_symm :
@@ -703,10 +686,7 @@ theorem AddSubgroup.toIntSubmodule_symm :
 #align add_subgroup.to_int_submodule_symm AddSubgroup.toIntSubmodule_symm
 
 /- warning: add_subgroup.coe_to_int_submodule -> AddSubgroup.coe_toIntSubmodule is a dubious translation:
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+<too large>
 Case conversion may be inaccurate. Consider using '#align add_subgroup.coe_to_int_submodule AddSubgroup.coe_toIntSubmoduleₓ'. -/
 @[simp]
 theorem AddSubgroup.coe_toIntSubmodule (S : AddSubgroup M) : (S.toIntSubmodule : Set M) = S :=
@@ -714,10 +694,7 @@ theorem AddSubgroup.coe_toIntSubmodule (S : AddSubgroup M) : (S.toIntSubmodule :
 #align add_subgroup.coe_to_int_submodule AddSubgroup.coe_toIntSubmodule
 
 /- warning: add_subgroup.to_int_submodule_to_add_subgroup -> AddSubgroup.toIntSubmodule_toAddSubgroup is a dubious translation:
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+<too large>
 Case conversion may be inaccurate. Consider using '#align add_subgroup.to_int_submodule_to_add_subgroup AddSubgroup.toIntSubmodule_toAddSubgroupₓ'. -/
 @[simp]
 theorem AddSubgroup.toIntSubmodule_toAddSubgroup (S : AddSubgroup M) :
@@ -726,10 +703,7 @@ theorem AddSubgroup.toIntSubmodule_toAddSubgroup (S : AddSubgroup M) :
 #align add_subgroup.to_int_submodule_to_add_subgroup AddSubgroup.toIntSubmodule_toAddSubgroup
 
 /- warning: submodule.to_add_subgroup_to_int_submodule -> Submodule.toAddSubgroup_toIntSubmodule is a dubious translation:
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(AddSubgroup.{u1} M (AddCommGroup.toAddGroup.{u1} M _inst_1)) (AddSubgroup.instCompleteLatticeAddSubgroup.{u1} M (AddCommGroup.toAddGroup.{u1} M _inst_1)))))) x._@.Mathlib.Order.Hom.Basic._hyg.1285 x._@.Mathlib.Order.Hom.Basic._hyg.1287) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1300 : Submodule.{0, u1} Int M Int.instSemiringInt (AddCommGroup.toAddCommMonoid.{u1} M _inst_1) (AddCommGroup.intModule.{u1} M _inst_1)) (x._@.Mathlib.Order.Hom.Basic._hyg.1302 : Submodule.{0, u1} Int M Int.instSemiringInt (AddCommGroup.toAddCommMonoid.{u1} M _inst_1) (AddCommGroup.intModule.{u1} M _inst_1)) => LE.le.{u1} (Submodule.{0, u1} Int M Int.instSemiringInt (AddCommGroup.toAddCommMonoid.{u1} M _inst_1) (AddCommGroup.intModule.{u1} M _inst_1)) (Preorder.toLE.{u1} (Submodule.{0, u1} Int M Int.instSemiringInt (AddCommGroup.toAddCommMonoid.{u1} M _inst_1) (AddCommGroup.intModule.{u1} M _inst_1)) (PartialOrder.toPreorder.{u1} (Submodule.{0, u1} Int M Int.instSemiringInt (AddCommGroup.toAddCommMonoid.{u1} M 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(AddCommGroup.toAddGroup.{u1} M _inst_1)) => LE.le.{u1} (AddSubgroup.{u1} M (AddCommGroup.toAddGroup.{u1} M _inst_1)) (Preorder.toLE.{u1} (AddSubgroup.{u1} M (AddCommGroup.toAddGroup.{u1} M _inst_1)) (PartialOrder.toPreorder.{u1} (AddSubgroup.{u1} M (AddCommGroup.toAddGroup.{u1} M _inst_1)) (CompleteSemilatticeInf.toPartialOrder.{u1} (AddSubgroup.{u1} M (AddCommGroup.toAddGroup.{u1} M _inst_1)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (AddSubgroup.{u1} M (AddCommGroup.toAddGroup.{u1} M _inst_1)) (AddSubgroup.instCompleteLatticeAddSubgroup.{u1} M (AddCommGroup.toAddGroup.{u1} M _inst_1)))))) x._@.Mathlib.Order.Hom.Basic._hyg.1285 x._@.Mathlib.Order.Hom.Basic._hyg.1287) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1300 : Submodule.{0, u1} Int M Int.instSemiringInt (AddCommGroup.toAddCommMonoid.{u1} M _inst_1) (AddCommGroup.intModule.{u1} M _inst_1)) (x._@.Mathlib.Order.Hom.Basic._hyg.1302 : Submodule.{0, u1} Int M Int.instSemiringInt (AddCommGroup.toAddCommMonoid.{u1} M _inst_1) (AddCommGroup.intModule.{u1} M _inst_1)) => LE.le.{u1} (Submodule.{0, u1} Int M Int.instSemiringInt (AddCommGroup.toAddCommMonoid.{u1} M _inst_1) (AddCommGroup.intModule.{u1} M _inst_1)) (Preorder.toLE.{u1} (Submodule.{0, u1} Int M Int.instSemiringInt (AddCommGroup.toAddCommMonoid.{u1} M _inst_1) (AddCommGroup.intModule.{u1} M _inst_1)) (PartialOrder.toPreorder.{u1} (Submodule.{0, u1} Int M Int.instSemiringInt (AddCommGroup.toAddCommMonoid.{u1} M _inst_1) (AddCommGroup.intModule.{u1} M _inst_1)) (CompleteSemilatticeInf.toPartialOrder.{u1} (Submodule.{0, u1} Int M Int.instSemiringInt (AddCommGroup.toAddCommMonoid.{u1} M _inst_1) (AddCommGroup.intModule.{u1} M _inst_1)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (Submodule.{0, u1} Int M Int.instSemiringInt (AddCommGroup.toAddCommMonoid.{u1} M _inst_1) (AddCommGroup.intModule.{u1} M _inst_1)) (Submodule.completeLattice.{0, u1} Int M Int.instSemiringInt (AddCommGroup.toAddCommMonoid.{u1} M _inst_1) (AddCommGroup.intModule.{u1} M _inst_1)))))) x._@.Mathlib.Order.Hom.Basic._hyg.1300 x._@.Mathlib.Order.Hom.Basic._hyg.1302) (RelIso.instRelHomClassRelIso.{u1, u1} (AddSubgroup.{u1} M (AddCommGroup.toAddGroup.{u1} M _inst_1)) (Submodule.{0, u1} Int M Int.instSemiringInt (AddCommGroup.toAddCommMonoid.{u1} M _inst_1) (AddCommGroup.intModule.{u1} M _inst_1)) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1285 : AddSubgroup.{u1} M (AddCommGroup.toAddGroup.{u1} M _inst_1)) (x._@.Mathlib.Order.Hom.Basic._hyg.1287 : AddSubgroup.{u1} M (AddCommGroup.toAddGroup.{u1} M _inst_1)) => LE.le.{u1} (AddSubgroup.{u1} M (AddCommGroup.toAddGroup.{u1} M _inst_1)) (Preorder.toLE.{u1} (AddSubgroup.{u1} M (AddCommGroup.toAddGroup.{u1} M _inst_1)) (PartialOrder.toPreorder.{u1} (AddSubgroup.{u1} M (AddCommGroup.toAddGroup.{u1} M _inst_1)) (CompleteSemilatticeInf.toPartialOrder.{u1} (AddSubgroup.{u1} M (AddCommGroup.toAddGroup.{u1} M _inst_1)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (AddSubgroup.{u1} M (AddCommGroup.toAddGroup.{u1} M _inst_1)) (AddSubgroup.instCompleteLatticeAddSubgroup.{u1} M (AddCommGroup.toAddGroup.{u1} M _inst_1)))))) x._@.Mathlib.Order.Hom.Basic._hyg.1285 x._@.Mathlib.Order.Hom.Basic._hyg.1287) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1300 : Submodule.{0, u1} Int M Int.instSemiringInt (AddCommGroup.toAddCommMonoid.{u1} M _inst_1) (AddCommGroup.intModule.{u1} M _inst_1)) (x._@.Mathlib.Order.Hom.Basic._hyg.1302 : Submodule.{0, u1} Int M Int.instSemiringInt (AddCommGroup.toAddCommMonoid.{u1} M _inst_1) (AddCommGroup.intModule.{u1} M _inst_1)) => LE.le.{u1} (Submodule.{0, u1} Int M Int.instSemiringInt (AddCommGroup.toAddCommMonoid.{u1} M _inst_1) (AddCommGroup.intModule.{u1} M _inst_1)) (Preorder.toLE.{u1} (Submodule.{0, u1} Int M Int.instSemiringInt (AddCommGroup.toAddCommMonoid.{u1} M _inst_1) (AddCommGroup.intModule.{u1} M _inst_1)) (PartialOrder.toPreorder.{u1} (Submodule.{0, u1} Int M Int.instSemiringInt (AddCommGroup.toAddCommMonoid.{u1} M _inst_1) (AddCommGroup.intModule.{u1} M _inst_1)) (CompleteSemilatticeInf.toPartialOrder.{u1} (Submodule.{0, u1} Int M Int.instSemiringInt (AddCommGroup.toAddCommMonoid.{u1} M _inst_1) (AddCommGroup.intModule.{u1} M _inst_1)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (Submodule.{0, u1} Int M Int.instSemiringInt (AddCommGroup.toAddCommMonoid.{u1} M _inst_1) (AddCommGroup.intModule.{u1} M _inst_1)) (Submodule.completeLattice.{0, u1} Int M Int.instSemiringInt (AddCommGroup.toAddCommMonoid.{u1} M _inst_1) (AddCommGroup.intModule.{u1} M _inst_1)))))) x._@.Mathlib.Order.Hom.Basic._hyg.1300 x._@.Mathlib.Order.Hom.Basic._hyg.1302))) (AddSubgroup.toIntSubmodule.{u1} M _inst_1) (Submodule.toAddSubgroup.{0, u1} Int M Int.instRingInt _inst_1 (AddCommGroup.intModule.{u1} M _inst_1) S)) S
+<too large>
 Case conversion may be inaccurate. Consider using '#align submodule.to_add_subgroup_to_int_submodule Submodule.toAddSubgroup_toIntSubmoduleₓ'. -/
 @[simp]
 theorem Submodule.toAddSubgroup_toIntSubmodule (S : Submodule ℤ M) :

mathlib commit https://github.com/leanprover-community/mathlib/commit/95a87616d63b3cb49d3fe678d416fbe9c4217bf4

@@ -623,7 +623,7 @@ def AddSubmonoid.toNatSubmodule : AddSubmonoid M ≃o Submodule ℕ M
 lean 3 declaration is
   forall {M : Type.{u1}} [_inst_3 : AddCommMonoid.{u1} M], Eq.{succ u1} ((Submodule.{0, u1} Nat M Nat.semiring _inst_3 (AddCommMonoid.natModule.{u1} M _inst_3)) -> (AddSubmonoid.{u1} M (AddMonoid.toAddZeroClass.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3)))) (coeFn.{succ u1, succ u1} (OrderIso.{u1, u1} (Submodule.{0, u1} Nat M Nat.semiring _inst_3 (AddCommMonoid.natModule.{u1} M _inst_3)) (AddSubmonoid.{u1} M (AddMonoid.toAddZeroClass.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3))) (Preorder.toHasLe.{u1} (Submodule.{0, u1} Nat M Nat.semiring _inst_3 (AddCommMonoid.natModule.{u1} M _inst_3)) (PartialOrder.toPreorder.{u1} (Submodule.{0, u1} Nat M Nat.semiring _inst_3 (AddCommMonoid.natModule.{u1} M _inst_3)) (CompleteSemilatticeInf.toPartialOrder.{u1} (Submodule.{0, u1} Nat M Nat.semiring _inst_3 (AddCommMonoid.natModule.{u1} M _inst_3)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (Submodule.{0, u1} Nat M Nat.semiring _inst_3 (AddCommMonoid.natModule.{u1} M _inst_3)) (Submodule.completeLattice.{0, u1} Nat M Nat.semiring _inst_3 (AddCommMonoid.natModule.{u1} M _inst_3)))))) (Preorder.toHasLe.{u1} (AddSubmonoid.{u1} M (AddMonoid.toAddZeroClass.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3))) (PartialOrder.toPreorder.{u1} (AddSubmonoid.{u1} M (AddMonoid.toAddZeroClass.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3))) (CompleteSemilatticeInf.toPartialOrder.{u1} (AddSubmonoid.{u1} M (AddMonoid.toAddZeroClass.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3))) (CompleteLattice.toCompleteSemilatticeInf.{u1} (AddSubmonoid.{u1} M (AddMonoid.toAddZeroClass.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3))) (AddSubmonoid.completeLattice.{u1} M (AddMonoid.toAddZeroClass.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3)))))))) (fun (_x : RelIso.{u1, u1} (Submodule.{0, u1} Nat M Nat.semiring _inst_3 (AddCommMonoid.natModule.{u1} M _inst_3)) (AddSubmonoid.{u1} M (AddMonoid.toAddZeroClass.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3))) (LE.le.{u1} (Submodule.{0, u1} Nat M Nat.semiring _inst_3 (AddCommMonoid.natModule.{u1} M _inst_3)) (Preorder.toHasLe.{u1} (Submodule.{0, u1} Nat M Nat.semiring _inst_3 (AddCommMonoid.natModule.{u1} M _inst_3)) (PartialOrder.toPreorder.{u1} (Submodule.{0, u1} Nat M Nat.semiring _inst_3 (AddCommMonoid.natModule.{u1} M _inst_3)) (CompleteSemilatticeInf.toPartialOrder.{u1} (Submodule.{0, u1} Nat M Nat.semiring _inst_3 (AddCommMonoid.natModule.{u1} M _inst_3)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (Submodule.{0, u1} Nat M Nat.semiring _inst_3 (AddCommMonoid.natModule.{u1} M _inst_3)) (Submodule.completeLattice.{0, u1} Nat M Nat.semiring _inst_3 (AddCommMonoid.natModule.{u1} M _inst_3))))))) (LE.le.{u1} (AddSubmonoid.{u1} M (AddMonoid.toAddZeroClass.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3))) (Preorder.toHasLe.{u1} (AddSubmonoid.{u1} M (AddMonoid.toAddZeroClass.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3))) (PartialOrder.toPreorder.{u1} (AddSubmonoid.{u1} M (AddMonoid.toAddZeroClass.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3))) (CompleteSemilatticeInf.toPartialOrder.{u1} (AddSubmonoid.{u1} M (AddMonoid.toAddZeroClass.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3))) (CompleteLattice.toCompleteSemilatticeInf.{u1} (AddSubmonoid.{u1} M (AddMonoid.toAddZeroClass.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3))) (AddSubmonoid.completeLattice.{u1} M (AddMonoid.toAddZeroClass.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3))))))))) => (Submodule.{0, u1} Nat M Nat.semiring _inst_3 (AddCommMonoid.natModule.{u1} M _inst_3)) -> (AddSubmonoid.{u1} M (AddMonoid.toAddZeroClass.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3)))) (RelIso.hasCoeToFun.{u1, u1} (Submodule.{0, u1} Nat M Nat.semiring _inst_3 (AddCommMonoid.natModule.{u1} M _inst_3)) (AddSubmonoid.{u1} M (AddMonoid.toAddZeroClass.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3))) (LE.le.{u1} (Submodule.{0, u1} Nat M Nat.semiring _inst_3 (AddCommMonoid.natModule.{u1} M _inst_3)) (Preorder.toHasLe.{u1} (Submodule.{0, u1} Nat M Nat.semiring _inst_3 (AddCommMonoid.natModule.{u1} M _inst_3)) (PartialOrder.toPreorder.{u1} (Submodule.{0, u1} Nat M Nat.semiring _inst_3 (AddCommMonoid.natModule.{u1} M _inst_3)) (CompleteSemilatticeInf.toPartialOrder.{u1} (Submodule.{0, u1} Nat M Nat.semiring _inst_3 (AddCommMonoid.natModule.{u1} M _inst_3)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (Submodule.{0, u1} Nat M Nat.semiring _inst_3 (AddCommMonoid.natModule.{u1} M _inst_3)) (Submodule.completeLattice.{0, u1} Nat M Nat.semiring _inst_3 (AddCommMonoid.natModule.{u1} M _inst_3))))))) (LE.le.{u1} (AddSubmonoid.{u1} M (AddMonoid.toAddZeroClass.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3))) (Preorder.toHasLe.{u1} (AddSubmonoid.{u1} M (AddMonoid.toAddZeroClass.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3))) (PartialOrder.toPreorder.{u1} (AddSubmonoid.{u1} M (AddMonoid.toAddZeroClass.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3))) (CompleteSemilatticeInf.toPartialOrder.{u1} (AddSubmonoid.{u1} M (AddMonoid.toAddZeroClass.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3))) (CompleteLattice.toCompleteSemilatticeInf.{u1} (AddSubmonoid.{u1} M (AddMonoid.toAddZeroClass.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3))) (AddSubmonoid.completeLattice.{u1} M (AddMonoid.toAddZeroClass.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3))))))))) (OrderIso.symm.{u1, u1} (AddSubmonoid.{u1} M (AddMonoid.toAddZeroClass.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3))) (Submodule.{0, u1} Nat M Nat.semiring _inst_3 (AddCommMonoid.natModule.{u1} M _inst_3)) (Preorder.toHasLe.{u1} (AddSubmonoid.{u1} M (AddMonoid.toAddZeroClass.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3))) (PartialOrder.toPreorder.{u1} (AddSubmonoid.{u1} M (AddMonoid.toAddZeroClass.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3))) (CompleteSemilatticeInf.toPartialOrder.{u1} (AddSubmonoid.{u1} M (AddMonoid.toAddZeroClass.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3))) (CompleteLattice.toCompleteSemilatticeInf.{u1} (AddSubmonoid.{u1} M (AddMonoid.toAddZeroClass.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3))) (AddSubmonoid.completeLattice.{u1} M (AddMonoid.toAddZeroClass.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3))))))) (Preorder.toHasLe.{u1} (Submodule.{0, u1} Nat M Nat.semiring _inst_3 (AddCommMonoid.natModule.{u1} M _inst_3)) (PartialOrder.toPreorder.{u1} (Submodule.{0, u1} Nat M Nat.semiring _inst_3 (AddCommMonoid.natModule.{u1} M _inst_3)) (CompleteSemilatticeInf.toPartialOrder.{u1} (Submodule.{0, u1} Nat M Nat.semiring _inst_3 (AddCommMonoid.natModule.{u1} M _inst_3)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (Submodule.{0, u1} Nat M Nat.semiring _inst_3 (AddCommMonoid.natModule.{u1} M _inst_3)) (Submodule.completeLattice.{0, u1} Nat M Nat.semiring _inst_3 (AddCommMonoid.natModule.{u1} M _inst_3)))))) (AddSubmonoid.toNatSubmodule.{u1} M _inst_3))) (Submodule.toAddSubmonoid.{0, u1} Nat M Nat.semiring _inst_3 (AddCommMonoid.natModule.{u1} M _inst_3))
 but is expected to have type
-  forall {M : Type.{u1}} [_inst_3 : AddCommMonoid.{u1} M], Eq.{succ u1} ((Submodule.{0, u1} Nat M Nat.semiring _inst_3 (AddCommMonoid.natModule.{u1} M _inst_3)) -> (AddSubmonoid.{u1} M (AddMonoid.toAddZeroClass.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3)))) (FunLike.coe.{succ u1, succ u1, succ u1} (RelIso.{u1, u1} (Submodule.{0, u1} Nat M Nat.semiring _inst_3 (AddCommMonoid.natModule.{u1} M _inst_3)) (AddSubmonoid.{u1} M (AddMonoid.toAddZeroClass.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3))) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1281 : Submodule.{0, u1} Nat M Nat.semiring _inst_3 (AddCommMonoid.natModule.{u1} M _inst_3)) (x._@.Mathlib.Order.Hom.Basic._hyg.1283 : Submodule.{0, u1} Nat M Nat.semiring _inst_3 (AddCommMonoid.natModule.{u1} M _inst_3)) => LE.le.{u1} (Submodule.{0, u1} Nat M Nat.semiring _inst_3 (AddCommMonoid.natModule.{u1} M _inst_3)) (Preorder.toLE.{u1} (Submodule.{0, u1} Nat M Nat.semiring _inst_3 (AddCommMonoid.natModule.{u1} M _inst_3)) (PartialOrder.toPreorder.{u1} (Submodule.{0, u1} Nat M Nat.semiring _inst_3 (AddCommMonoid.natModule.{u1} M _inst_3)) (CompleteSemilatticeInf.toPartialOrder.{u1} (Submodule.{0, u1} Nat M Nat.semiring _inst_3 (AddCommMonoid.natModule.{u1} M _inst_3)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (Submodule.{0, u1} Nat M Nat.semiring _inst_3 (AddCommMonoid.natModule.{u1} M _inst_3)) (Submodule.completeLattice.{0, u1} Nat M Nat.semiring _inst_3 (AddCommMonoid.natModule.{u1} M _inst_3)))))) x._@.Mathlib.Order.Hom.Basic._hyg.1281 x._@.Mathlib.Order.Hom.Basic._hyg.1283) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1296 : AddSubmonoid.{u1} M (AddMonoid.toAddZeroClass.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3))) (x._@.Mathlib.Order.Hom.Basic._hyg.1298 : AddSubmonoid.{u1} M (AddMonoid.toAddZeroClass.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3))) => LE.le.{u1} (AddSubmonoid.{u1} M (AddMonoid.toAddZeroClass.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3))) (Preorder.toLE.{u1} (AddSubmonoid.{u1} M (AddMonoid.toAddZeroClass.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3))) (PartialOrder.toPreorder.{u1} (AddSubmonoid.{u1} M (AddMonoid.toAddZeroClass.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3))) (CompleteSemilatticeInf.toPartialOrder.{u1} (AddSubmonoid.{u1} M (AddMonoid.toAddZeroClass.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3))) (CompleteLattice.toCompleteSemilatticeInf.{u1} (AddSubmonoid.{u1} M (AddMonoid.toAddZeroClass.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3))) (AddSubmonoid.instCompleteLatticeAddSubmonoid.{u1} M (AddMonoid.toAddZeroClass.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3))))))) x._@.Mathlib.Order.Hom.Basic._hyg.1296 x._@.Mathlib.Order.Hom.Basic._hyg.1298)) (Submodule.{0, u1} Nat M Nat.semiring _inst_3 (AddCommMonoid.natModule.{u1} M _inst_3)) (fun (_x : Submodule.{0, u1} Nat M Nat.semiring _inst_3 (AddCommMonoid.natModule.{u1} M _inst_3)) => AddSubmonoid.{u1} M (AddMonoid.toAddZeroClass.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3))) (RelHomClass.toFunLike.{u1, u1, u1} (RelIso.{u1, u1} (Submodule.{0, u1} Nat M Nat.semiring _inst_3 (AddCommMonoid.natModule.{u1} M _inst_3)) (AddSubmonoid.{u1} M (AddMonoid.toAddZeroClass.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3))) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1281 : Submodule.{0, u1} Nat M Nat.semiring _inst_3 (AddCommMonoid.natModule.{u1} M _inst_3)) (x._@.Mathlib.Order.Hom.Basic._hyg.1283 : Submodule.{0, u1} Nat M Nat.semiring _inst_3 (AddCommMonoid.natModule.{u1} M _inst_3)) => LE.le.{u1} (Submodule.{0, u1} Nat M Nat.semiring _inst_3 (AddCommMonoid.natModule.{u1} M _inst_3)) (Preorder.toLE.{u1} (Submodule.{0, u1} Nat M Nat.semiring _inst_3 (AddCommMonoid.natModule.{u1} M _inst_3)) (PartialOrder.toPreorder.{u1} (Submodule.{0, u1} Nat M Nat.semiring _inst_3 (AddCommMonoid.natModule.{u1} M _inst_3)) (CompleteSemilatticeInf.toPartialOrder.{u1} (Submodule.{0, u1} Nat M Nat.semiring _inst_3 (AddCommMonoid.natModule.{u1} M _inst_3)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (Submodule.{0, u1} Nat M Nat.semiring _inst_3 (AddCommMonoid.natModule.{u1} M _inst_3)) (Submodule.completeLattice.{0, u1} Nat M Nat.semiring _inst_3 (AddCommMonoid.natModule.{u1} M _inst_3)))))) x._@.Mathlib.Order.Hom.Basic._hyg.1281 x._@.Mathlib.Order.Hom.Basic._hyg.1283) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1296 : AddSubmonoid.{u1} M (AddMonoid.toAddZeroClass.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3))) (x._@.Mathlib.Order.Hom.Basic._hyg.1298 : AddSubmonoid.{u1} M (AddMonoid.toAddZeroClass.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3))) => LE.le.{u1} (AddSubmonoid.{u1} M (AddMonoid.toAddZeroClass.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3))) (Preorder.toLE.{u1} (AddSubmonoid.{u1} M (AddMonoid.toAddZeroClass.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3))) (PartialOrder.toPreorder.{u1} (AddSubmonoid.{u1} M (AddMonoid.toAddZeroClass.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3))) (CompleteSemilatticeInf.toPartialOrder.{u1} (AddSubmonoid.{u1} M (AddMonoid.toAddZeroClass.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3))) (CompleteLattice.toCompleteSemilatticeInf.{u1} (AddSubmonoid.{u1} M (AddMonoid.toAddZeroClass.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3))) (AddSubmonoid.instCompleteLatticeAddSubmonoid.{u1} M (AddMonoid.toAddZeroClass.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3))))))) x._@.Mathlib.Order.Hom.Basic._hyg.1296 x._@.Mathlib.Order.Hom.Basic._hyg.1298)) (Submodule.{0, u1} Nat M Nat.semiring _inst_3 (AddCommMonoid.natModule.{u1} M _inst_3)) (AddSubmonoid.{u1} M (AddMonoid.toAddZeroClass.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3))) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1281 : Submodule.{0, u1} Nat M Nat.semiring _inst_3 (AddCommMonoid.natModule.{u1} M _inst_3)) (x._@.Mathlib.Order.Hom.Basic._hyg.1283 : Submodule.{0, u1} Nat M Nat.semiring _inst_3 (AddCommMonoid.natModule.{u1} M _inst_3)) => LE.le.{u1} (Submodule.{0, u1} Nat M Nat.semiring _inst_3 (AddCommMonoid.natModule.{u1} M _inst_3)) (Preorder.toLE.{u1} (Submodule.{0, u1} Nat M Nat.semiring _inst_3 (AddCommMonoid.natModule.{u1} M _inst_3)) (PartialOrder.toPreorder.{u1} (Submodule.{0, u1} Nat M Nat.semiring _inst_3 (AddCommMonoid.natModule.{u1} M _inst_3)) (CompleteSemilatticeInf.toPartialOrder.{u1} (Submodule.{0, u1} Nat M Nat.semiring _inst_3 (AddCommMonoid.natModule.{u1} M _inst_3)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (Submodule.{0, u1} Nat M Nat.semiring _inst_3 (AddCommMonoid.natModule.{u1} M _inst_3)) (Submodule.completeLattice.{0, u1} Nat M Nat.semiring _inst_3 (AddCommMonoid.natModule.{u1} M _inst_3)))))) x._@.Mathlib.Order.Hom.Basic._hyg.1281 x._@.Mathlib.Order.Hom.Basic._hyg.1283) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1296 : AddSubmonoid.{u1} M (AddMonoid.toAddZeroClass.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3))) (x._@.Mathlib.Order.Hom.Basic._hyg.1298 : AddSubmonoid.{u1} M (AddMonoid.toAddZeroClass.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3))) => LE.le.{u1} (AddSubmonoid.{u1} M (AddMonoid.toAddZeroClass.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3))) (Preorder.toLE.{u1} (AddSubmonoid.{u1} M (AddMonoid.toAddZeroClass.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3))) (PartialOrder.toPreorder.{u1} (AddSubmonoid.{u1} M (AddMonoid.toAddZeroClass.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3))) (CompleteSemilatticeInf.toPartialOrder.{u1} (AddSubmonoid.{u1} M (AddMonoid.toAddZeroClass.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3))) (CompleteLattice.toCompleteSemilatticeInf.{u1} (AddSubmonoid.{u1} M (AddMonoid.toAddZeroClass.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3))) (AddSubmonoid.instCompleteLatticeAddSubmonoid.{u1} M (AddMonoid.toAddZeroClass.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3))))))) x._@.Mathlib.Order.Hom.Basic._hyg.1296 x._@.Mathlib.Order.Hom.Basic._hyg.1298) (RelIso.instRelHomClassRelIso.{u1, u1} (Submodule.{0, u1} Nat M Nat.semiring _inst_3 (AddCommMonoid.natModule.{u1} M _inst_3)) (AddSubmonoid.{u1} M (AddMonoid.toAddZeroClass.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3))) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1281 : Submodule.{0, u1} Nat M Nat.semiring _inst_3 (AddCommMonoid.natModule.{u1} M _inst_3)) (x._@.Mathlib.Order.Hom.Basic._hyg.1283 : Submodule.{0, u1} Nat M Nat.semiring _inst_3 (AddCommMonoid.natModule.{u1} M _inst_3)) => LE.le.{u1} (Submodule.{0, u1} Nat M Nat.semiring _inst_3 (AddCommMonoid.natModule.{u1} M _inst_3)) (Preorder.toLE.{u1} (Submodule.{0, u1} Nat M Nat.semiring _inst_3 (AddCommMonoid.natModule.{u1} M _inst_3)) (PartialOrder.toPreorder.{u1} (Submodule.{0, u1} Nat M Nat.semiring _inst_3 (AddCommMonoid.natModule.{u1} M _inst_3)) (CompleteSemilatticeInf.toPartialOrder.{u1} (Submodule.{0, u1} Nat M Nat.semiring _inst_3 (AddCommMonoid.natModule.{u1} M _inst_3)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (Submodule.{0, u1} Nat M Nat.semiring _inst_3 (AddCommMonoid.natModule.{u1} M _inst_3)) (Submodule.completeLattice.{0, u1} Nat M Nat.semiring _inst_3 (AddCommMonoid.natModule.{u1} M _inst_3)))))) x._@.Mathlib.Order.Hom.Basic._hyg.1281 x._@.Mathlib.Order.Hom.Basic._hyg.1283) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1296 : AddSubmonoid.{u1} M (AddMonoid.toAddZeroClass.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3))) (x._@.Mathlib.Order.Hom.Basic._hyg.1298 : AddSubmonoid.{u1} M (AddMonoid.toAddZeroClass.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3))) => LE.le.{u1} (AddSubmonoid.{u1} M (AddMonoid.toAddZeroClass.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3))) (Preorder.toLE.{u1} (AddSubmonoid.{u1} M (AddMonoid.toAddZeroClass.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3))) (PartialOrder.toPreorder.{u1} (AddSubmonoid.{u1} M (AddMonoid.toAddZeroClass.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3))) (CompleteSemilatticeInf.toPartialOrder.{u1} (AddSubmonoid.{u1} M (AddMonoid.toAddZeroClass.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3))) (CompleteLattice.toCompleteSemilatticeInf.{u1} (AddSubmonoid.{u1} M (AddMonoid.toAddZeroClass.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3))) (AddSubmonoid.instCompleteLatticeAddSubmonoid.{u1} M (AddMonoid.toAddZeroClass.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3))))))) x._@.Mathlib.Order.Hom.Basic._hyg.1296 x._@.Mathlib.Order.Hom.Basic._hyg.1298))) (OrderIso.symm.{u1, u1} (AddSubmonoid.{u1} M (AddMonoid.toAddZeroClass.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3))) (Submodule.{0, u1} Nat M Nat.semiring _inst_3 (AddCommMonoid.natModule.{u1} M _inst_3)) (Preorder.toLE.{u1} (AddSubmonoid.{u1} M (AddMonoid.toAddZeroClass.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3))) (PartialOrder.toPreorder.{u1} (AddSubmonoid.{u1} M (AddMonoid.toAddZeroClass.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3))) (CompleteSemilatticeInf.toPartialOrder.{u1} (AddSubmonoid.{u1} M (AddMonoid.toAddZeroClass.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3))) (CompleteLattice.toCompleteSemilatticeInf.{u1} (AddSubmonoid.{u1} M (AddMonoid.toAddZeroClass.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3))) (AddSubmonoid.instCompleteLatticeAddSubmonoid.{u1} M (AddMonoid.toAddZeroClass.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3))))))) (Preorder.toLE.{u1} (Submodule.{0, u1} Nat M Nat.semiring _inst_3 (AddCommMonoid.natModule.{u1} M _inst_3)) (PartialOrder.toPreorder.{u1} (Submodule.{0, u1} Nat M Nat.semiring _inst_3 (AddCommMonoid.natModule.{u1} M _inst_3)) (CompleteSemilatticeInf.toPartialOrder.{u1} (Submodule.{0, u1} Nat M Nat.semiring _inst_3 (AddCommMonoid.natModule.{u1} M _inst_3)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (Submodule.{0, u1} Nat M Nat.semiring _inst_3 (AddCommMonoid.natModule.{u1} M _inst_3)) (Submodule.completeLattice.{0, u1} Nat M Nat.semiring _inst_3 (AddCommMonoid.natModule.{u1} M _inst_3)))))) (AddSubmonoid.toNatSubmodule.{u1} M _inst_3))) (Submodule.toAddSubmonoid.{0, u1} Nat M Nat.semiring _inst_3 (AddCommMonoid.natModule.{u1} M _inst_3))
+  forall {M : Type.{u1}} [_inst_3 : AddCommMonoid.{u1} M], Eq.{succ u1} ((Submodule.{0, u1} Nat M Nat.semiring _inst_3 (AddCommMonoid.natModule.{u1} M _inst_3)) -> (AddSubmonoid.{u1} M (AddMonoid.toAddZeroClass.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3)))) (FunLike.coe.{succ u1, succ u1, succ u1} (RelIso.{u1, u1} (Submodule.{0, u1} Nat M Nat.semiring _inst_3 (AddCommMonoid.natModule.{u1} M _inst_3)) (AddSubmonoid.{u1} M (AddMonoid.toAddZeroClass.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3))) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1285 : Submodule.{0, u1} Nat M Nat.semiring _inst_3 (AddCommMonoid.natModule.{u1} M _inst_3)) (x._@.Mathlib.Order.Hom.Basic._hyg.1287 : Submodule.{0, u1} Nat M Nat.semiring _inst_3 (AddCommMonoid.natModule.{u1} M _inst_3)) => LE.le.{u1} (Submodule.{0, u1} Nat M Nat.semiring _inst_3 (AddCommMonoid.natModule.{u1} M _inst_3)) (Preorder.toLE.{u1} (Submodule.{0, u1} Nat M Nat.semiring _inst_3 (AddCommMonoid.natModule.{u1} M _inst_3)) (PartialOrder.toPreorder.{u1} (Submodule.{0, u1} Nat M Nat.semiring _inst_3 (AddCommMonoid.natModule.{u1} M _inst_3)) (CompleteSemilatticeInf.toPartialOrder.{u1} (Submodule.{0, u1} Nat M Nat.semiring _inst_3 (AddCommMonoid.natModule.{u1} M _inst_3)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (Submodule.{0, u1} Nat M Nat.semiring _inst_3 (AddCommMonoid.natModule.{u1} M _inst_3)) (Submodule.completeLattice.{0, u1} Nat M Nat.semiring _inst_3 (AddCommMonoid.natModule.{u1} M _inst_3)))))) x._@.Mathlib.Order.Hom.Basic._hyg.1285 x._@.Mathlib.Order.Hom.Basic._hyg.1287) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1300 : AddSubmonoid.{u1} M (AddMonoid.toAddZeroClass.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3))) (x._@.Mathlib.Order.Hom.Basic._hyg.1302 : AddSubmonoid.{u1} M (AddMonoid.toAddZeroClass.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3))) => LE.le.{u1} (AddSubmonoid.{u1} M (AddMonoid.toAddZeroClass.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3))) (Preorder.toLE.{u1} (AddSubmonoid.{u1} M (AddMonoid.toAddZeroClass.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3))) (PartialOrder.toPreorder.{u1} (AddSubmonoid.{u1} M (AddMonoid.toAddZeroClass.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3))) (CompleteSemilatticeInf.toPartialOrder.{u1} (AddSubmonoid.{u1} M (AddMonoid.toAddZeroClass.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3))) (CompleteLattice.toCompleteSemilatticeInf.{u1} (AddSubmonoid.{u1} M (AddMonoid.toAddZeroClass.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3))) (AddSubmonoid.instCompleteLatticeAddSubmonoid.{u1} M (AddMonoid.toAddZeroClass.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3))))))) x._@.Mathlib.Order.Hom.Basic._hyg.1300 x._@.Mathlib.Order.Hom.Basic._hyg.1302)) (Submodule.{0, u1} Nat M Nat.semiring _inst_3 (AddCommMonoid.natModule.{u1} M _inst_3)) (fun (_x : Submodule.{0, u1} Nat M Nat.semiring _inst_3 (AddCommMonoid.natModule.{u1} M _inst_3)) => AddSubmonoid.{u1} M (AddMonoid.toAddZeroClass.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3))) (RelHomClass.toFunLike.{u1, u1, u1} (RelIso.{u1, u1} (Submodule.{0, u1} Nat M Nat.semiring _inst_3 (AddCommMonoid.natModule.{u1} M _inst_3)) (AddSubmonoid.{u1} M (AddMonoid.toAddZeroClass.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3))) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1285 : Submodule.{0, u1} Nat M Nat.semiring _inst_3 (AddCommMonoid.natModule.{u1} M _inst_3)) (x._@.Mathlib.Order.Hom.Basic._hyg.1287 : Submodule.{0, u1} Nat M Nat.semiring _inst_3 (AddCommMonoid.natModule.{u1} M _inst_3)) => LE.le.{u1} (Submodule.{0, u1} Nat M Nat.semiring _inst_3 (AddCommMonoid.natModule.{u1} M _inst_3)) (Preorder.toLE.{u1} (Submodule.{0, u1} Nat M Nat.semiring _inst_3 (AddCommMonoid.natModule.{u1} M _inst_3)) (PartialOrder.toPreorder.{u1} (Submodule.{0, u1} Nat M Nat.semiring _inst_3 (AddCommMonoid.natModule.{u1} M _inst_3)) (CompleteSemilatticeInf.toPartialOrder.{u1} (Submodule.{0, u1} Nat M Nat.semiring _inst_3 (AddCommMonoid.natModule.{u1} M _inst_3)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (Submodule.{0, u1} Nat M Nat.semiring _inst_3 (AddCommMonoid.natModule.{u1} M _inst_3)) (Submodule.completeLattice.{0, u1} Nat M Nat.semiring _inst_3 (AddCommMonoid.natModule.{u1} M _inst_3)))))) x._@.Mathlib.Order.Hom.Basic._hyg.1285 x._@.Mathlib.Order.Hom.Basic._hyg.1287) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1300 : AddSubmonoid.{u1} M (AddMonoid.toAddZeroClass.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3))) (x._@.Mathlib.Order.Hom.Basic._hyg.1302 : AddSubmonoid.{u1} M (AddMonoid.toAddZeroClass.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3))) => LE.le.{u1} (AddSubmonoid.{u1} M (AddMonoid.toAddZeroClass.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3))) (Preorder.toLE.{u1} (AddSubmonoid.{u1} M (AddMonoid.toAddZeroClass.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3))) (PartialOrder.toPreorder.{u1} (AddSubmonoid.{u1} M (AddMonoid.toAddZeroClass.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3))) (CompleteSemilatticeInf.toPartialOrder.{u1} (AddSubmonoid.{u1} M (AddMonoid.toAddZeroClass.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3))) (CompleteLattice.toCompleteSemilatticeInf.{u1} (AddSubmonoid.{u1} M (AddMonoid.toAddZeroClass.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3))) (AddSubmonoid.instCompleteLatticeAddSubmonoid.{u1} M (AddMonoid.toAddZeroClass.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3))))))) x._@.Mathlib.Order.Hom.Basic._hyg.1300 x._@.Mathlib.Order.Hom.Basic._hyg.1302)) (Submodule.{0, u1} Nat M Nat.semiring _inst_3 (AddCommMonoid.natModule.{u1} M _inst_3)) (AddSubmonoid.{u1} M (AddMonoid.toAddZeroClass.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3))) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1285 : Submodule.{0, u1} Nat M Nat.semiring _inst_3 (AddCommMonoid.natModule.{u1} M _inst_3)) (x._@.Mathlib.Order.Hom.Basic._hyg.1287 : Submodule.{0, u1} Nat M Nat.semiring _inst_3 (AddCommMonoid.natModule.{u1} M _inst_3)) => LE.le.{u1} (Submodule.{0, u1} Nat M Nat.semiring _inst_3 (AddCommMonoid.natModule.{u1} M _inst_3)) (Preorder.toLE.{u1} (Submodule.{0, u1} Nat M Nat.semiring _inst_3 (AddCommMonoid.natModule.{u1} M _inst_3)) (PartialOrder.toPreorder.{u1} (Submodule.{0, u1} Nat M Nat.semiring _inst_3 (AddCommMonoid.natModule.{u1} M _inst_3)) (CompleteSemilatticeInf.toPartialOrder.{u1} (Submodule.{0, u1} Nat M Nat.semiring _inst_3 (AddCommMonoid.natModule.{u1} M _inst_3)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (Submodule.{0, u1} Nat M Nat.semiring _inst_3 (AddCommMonoid.natModule.{u1} M _inst_3)) (Submodule.completeLattice.{0, u1} Nat M Nat.semiring _inst_3 (AddCommMonoid.natModule.{u1} M _inst_3)))))) x._@.Mathlib.Order.Hom.Basic._hyg.1285 x._@.Mathlib.Order.Hom.Basic._hyg.1287) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1300 : AddSubmonoid.{u1} M (AddMonoid.toAddZeroClass.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3))) (x._@.Mathlib.Order.Hom.Basic._hyg.1302 : AddSubmonoid.{u1} M (AddMonoid.toAddZeroClass.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3))) => LE.le.{u1} (AddSubmonoid.{u1} M (AddMonoid.toAddZeroClass.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3))) (Preorder.toLE.{u1} (AddSubmonoid.{u1} M (AddMonoid.toAddZeroClass.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3))) (PartialOrder.toPreorder.{u1} (AddSubmonoid.{u1} M (AddMonoid.toAddZeroClass.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3))) (CompleteSemilatticeInf.toPartialOrder.{u1} (AddSubmonoid.{u1} M (AddMonoid.toAddZeroClass.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3))) (CompleteLattice.toCompleteSemilatticeInf.{u1} (AddSubmonoid.{u1} M (AddMonoid.toAddZeroClass.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3))) (AddSubmonoid.instCompleteLatticeAddSubmonoid.{u1} M (AddMonoid.toAddZeroClass.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3))))))) x._@.Mathlib.Order.Hom.Basic._hyg.1300 x._@.Mathlib.Order.Hom.Basic._hyg.1302) (RelIso.instRelHomClassRelIso.{u1, u1} (Submodule.{0, u1} Nat M Nat.semiring _inst_3 (AddCommMonoid.natModule.{u1} M _inst_3)) (AddSubmonoid.{u1} M (AddMonoid.toAddZeroClass.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3))) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1285 : Submodule.{0, u1} Nat M Nat.semiring _inst_3 (AddCommMonoid.natModule.{u1} M _inst_3)) (x._@.Mathlib.Order.Hom.Basic._hyg.1287 : Submodule.{0, u1} Nat M Nat.semiring _inst_3 (AddCommMonoid.natModule.{u1} M _inst_3)) => LE.le.{u1} (Submodule.{0, u1} Nat M Nat.semiring _inst_3 (AddCommMonoid.natModule.{u1} M _inst_3)) (Preorder.toLE.{u1} (Submodule.{0, u1} Nat M Nat.semiring _inst_3 (AddCommMonoid.natModule.{u1} M _inst_3)) (PartialOrder.toPreorder.{u1} (Submodule.{0, u1} Nat M Nat.semiring _inst_3 (AddCommMonoid.natModule.{u1} M _inst_3)) (CompleteSemilatticeInf.toPartialOrder.{u1} (Submodule.{0, u1} Nat M Nat.semiring _inst_3 (AddCommMonoid.natModule.{u1} M _inst_3)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (Submodule.{0, u1} Nat M Nat.semiring _inst_3 (AddCommMonoid.natModule.{u1} M _inst_3)) (Submodule.completeLattice.{0, u1} Nat M Nat.semiring _inst_3 (AddCommMonoid.natModule.{u1} M _inst_3)))))) x._@.Mathlib.Order.Hom.Basic._hyg.1285 x._@.Mathlib.Order.Hom.Basic._hyg.1287) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1300 : AddSubmonoid.{u1} M (AddMonoid.toAddZeroClass.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3))) (x._@.Mathlib.Order.Hom.Basic._hyg.1302 : AddSubmonoid.{u1} M (AddMonoid.toAddZeroClass.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3))) => LE.le.{u1} (AddSubmonoid.{u1} M (AddMonoid.toAddZeroClass.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3))) (Preorder.toLE.{u1} (AddSubmonoid.{u1} M (AddMonoid.toAddZeroClass.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3))) (PartialOrder.toPreorder.{u1} (AddSubmonoid.{u1} M (AddMonoid.toAddZeroClass.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3))) (CompleteSemilatticeInf.toPartialOrder.{u1} (AddSubmonoid.{u1} M (AddMonoid.toAddZeroClass.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3))) (CompleteLattice.toCompleteSemilatticeInf.{u1} (AddSubmonoid.{u1} M (AddMonoid.toAddZeroClass.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3))) (AddSubmonoid.instCompleteLatticeAddSubmonoid.{u1} M (AddMonoid.toAddZeroClass.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3))))))) x._@.Mathlib.Order.Hom.Basic._hyg.1300 x._@.Mathlib.Order.Hom.Basic._hyg.1302))) (OrderIso.symm.{u1, u1} (AddSubmonoid.{u1} M (AddMonoid.toAddZeroClass.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3))) (Submodule.{0, u1} Nat M Nat.semiring _inst_3 (AddCommMonoid.natModule.{u1} M _inst_3)) (Preorder.toLE.{u1} (AddSubmonoid.{u1} M (AddMonoid.toAddZeroClass.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3))) (PartialOrder.toPreorder.{u1} (AddSubmonoid.{u1} M (AddMonoid.toAddZeroClass.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3))) (CompleteSemilatticeInf.toPartialOrder.{u1} (AddSubmonoid.{u1} M (AddMonoid.toAddZeroClass.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3))) (CompleteLattice.toCompleteSemilatticeInf.{u1} (AddSubmonoid.{u1} M (AddMonoid.toAddZeroClass.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3))) (AddSubmonoid.instCompleteLatticeAddSubmonoid.{u1} M (AddMonoid.toAddZeroClass.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3))))))) (Preorder.toLE.{u1} (Submodule.{0, u1} Nat M Nat.semiring _inst_3 (AddCommMonoid.natModule.{u1} M _inst_3)) (PartialOrder.toPreorder.{u1} (Submodule.{0, u1} Nat M Nat.semiring _inst_3 (AddCommMonoid.natModule.{u1} M _inst_3)) (CompleteSemilatticeInf.toPartialOrder.{u1} (Submodule.{0, u1} Nat M Nat.semiring _inst_3 (AddCommMonoid.natModule.{u1} M _inst_3)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (Submodule.{0, u1} Nat M Nat.semiring _inst_3 (AddCommMonoid.natModule.{u1} M _inst_3)) (Submodule.completeLattice.{0, u1} Nat M Nat.semiring _inst_3 (AddCommMonoid.natModule.{u1} M _inst_3)))))) (AddSubmonoid.toNatSubmodule.{u1} M _inst_3))) (Submodule.toAddSubmonoid.{0, u1} Nat M Nat.semiring _inst_3 (AddCommMonoid.natModule.{u1} M _inst_3))
 Case conversion may be inaccurate. Consider using '#align add_submonoid.to_nat_submodule_symm AddSubmonoid.toNatSubmodule_symmₓ'. -/
 @[simp]
 theorem AddSubmonoid.toNatSubmodule_symm :
@@ -635,7 +635,7 @@ theorem AddSubmonoid.toNatSubmodule_symm :
 lean 3 declaration is
   forall {M : Type.{u1}} [_inst_3 : AddCommMonoid.{u1} M] (S : AddSubmonoid.{u1} M (AddMonoid.toAddZeroClass.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3))), Eq.{succ u1} (Set.{u1} M) ((fun (a : Type.{u1}) (b : Type.{u1}) [self : HasLiftT.{succ u1, succ u1} a b] => self.0) (Submodule.{0, u1} Nat M Nat.semiring _inst_3 (AddCommMonoid.natModule.{u1} M _inst_3)) (Set.{u1} M) (HasLiftT.mk.{succ u1, succ u1} (Submodule.{0, u1} Nat M Nat.semiring _inst_3 (AddCommMonoid.natModule.{u1} M _inst_3)) (Set.{u1} M) (CoeTCₓ.coe.{succ u1, succ u1} (Submodule.{0, u1} Nat M Nat.semiring _inst_3 (AddCommMonoid.natModule.{u1} M _inst_3)) (Set.{u1} M) (SetLike.Set.hasCoeT.{u1, u1} (Submodule.{0, u1} Nat M Nat.semiring _inst_3 (AddCommMonoid.natModule.{u1} M _inst_3)) M (Submodule.setLike.{0, u1} Nat M Nat.semiring _inst_3 (AddCommMonoid.natModule.{u1} M _inst_3))))) (coeFn.{succ u1, succ u1} (OrderIso.{u1, u1} (AddSubmonoid.{u1} M (AddMonoid.toAddZeroClass.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3))) (Submodule.{0, u1} Nat M Nat.semiring _inst_3 (AddCommMonoid.natModule.{u1} M _inst_3)) (Preorder.toHasLe.{u1} (AddSubmonoid.{u1} M (AddMonoid.toAddZeroClass.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3))) (PartialOrder.toPreorder.{u1} (AddSubmonoid.{u1} M (AddMonoid.toAddZeroClass.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3))) (CompleteSemilatticeInf.toPartialOrder.{u1} (AddSubmonoid.{u1} M (AddMonoid.toAddZeroClass.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3))) (CompleteLattice.toCompleteSemilatticeInf.{u1} (AddSubmonoid.{u1} M (AddMonoid.toAddZeroClass.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3))) (AddSubmonoid.completeLattice.{u1} M (AddMonoid.toAddZeroClass.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3))))))) (Preorder.toHasLe.{u1} (Submodule.{0, u1} Nat M Nat.semiring _inst_3 (AddCommMonoid.natModule.{u1} M _inst_3)) (PartialOrder.toPreorder.{u1} (Submodule.{0, u1} Nat M Nat.semiring _inst_3 (AddCommMonoid.natModule.{u1} M _inst_3)) (CompleteSemilatticeInf.toPartialOrder.{u1} (Submodule.{0, u1} Nat M Nat.semiring _inst_3 (AddCommMonoid.natModule.{u1} M _inst_3)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (Submodule.{0, u1} Nat M Nat.semiring _inst_3 (AddCommMonoid.natModule.{u1} M _inst_3)) (Submodule.completeLattice.{0, u1} Nat M Nat.semiring _inst_3 (AddCommMonoid.natModule.{u1} M _inst_3))))))) (fun (_x : RelIso.{u1, u1} (AddSubmonoid.{u1} M (AddMonoid.toAddZeroClass.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3))) (Submodule.{0, u1} Nat M Nat.semiring _inst_3 (AddCommMonoid.natModule.{u1} M _inst_3)) (LE.le.{u1} (AddSubmonoid.{u1} M (AddMonoid.toAddZeroClass.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3))) (Preorder.toHasLe.{u1} (AddSubmonoid.{u1} M (AddMonoid.toAddZeroClass.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3))) (PartialOrder.toPreorder.{u1} (AddSubmonoid.{u1} M (AddMonoid.toAddZeroClass.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3))) (CompleteSemilatticeInf.toPartialOrder.{u1} (AddSubmonoid.{u1} M (AddMonoid.toAddZeroClass.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3))) (CompleteLattice.toCompleteSemilatticeInf.{u1} (AddSubmonoid.{u1} M (AddMonoid.toAddZeroClass.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3))) (AddSubmonoid.completeLattice.{u1} M (AddMonoid.toAddZeroClass.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3)))))))) (LE.le.{u1} (Submodule.{0, u1} Nat M Nat.semiring _inst_3 (AddCommMonoid.natModule.{u1} M _inst_3)) (Preorder.toHasLe.{u1} (Submodule.{0, u1} Nat M Nat.semiring _inst_3 (AddCommMonoid.natModule.{u1} M _inst_3)) (PartialOrder.toPreorder.{u1} (Submodule.{0, u1} Nat M Nat.semiring _inst_3 (AddCommMonoid.natModule.{u1} M _inst_3)) (CompleteSemilatticeInf.toPartialOrder.{u1} (Submodule.{0, u1} Nat M Nat.semiring _inst_3 (AddCommMonoid.natModule.{u1} M _inst_3)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (Submodule.{0, u1} Nat M Nat.semiring _inst_3 (AddCommMonoid.natModule.{u1} M _inst_3)) (Submodule.completeLattice.{0, u1} Nat M Nat.semiring _inst_3 (AddCommMonoid.natModule.{u1} M _inst_3)))))))) => (AddSubmonoid.{u1} M (AddMonoid.toAddZeroClass.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3))) -> (Submodule.{0, u1} Nat M Nat.semiring _inst_3 (AddCommMonoid.natModule.{u1} M _inst_3))) (RelIso.hasCoeToFun.{u1, u1} (AddSubmonoid.{u1} M (AddMonoid.toAddZeroClass.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3))) (Submodule.{0, u1} Nat M Nat.semiring _inst_3 (AddCommMonoid.natModule.{u1} M _inst_3)) (LE.le.{u1} (AddSubmonoid.{u1} M (AddMonoid.toAddZeroClass.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3))) (Preorder.toHasLe.{u1} (AddSubmonoid.{u1} M (AddMonoid.toAddZeroClass.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3))) (PartialOrder.toPreorder.{u1} (AddSubmonoid.{u1} M (AddMonoid.toAddZeroClass.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3))) (CompleteSemilatticeInf.toPartialOrder.{u1} (AddSubmonoid.{u1} M (AddMonoid.toAddZeroClass.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3))) (CompleteLattice.toCompleteSemilatticeInf.{u1} (AddSubmonoid.{u1} M (AddMonoid.toAddZeroClass.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3))) (AddSubmonoid.completeLattice.{u1} M (AddMonoid.toAddZeroClass.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3)))))))) (LE.le.{u1} (Submodule.{0, u1} Nat M Nat.semiring _inst_3 (AddCommMonoid.natModule.{u1} M _inst_3)) (Preorder.toHasLe.{u1} (Submodule.{0, u1} Nat M Nat.semiring _inst_3 (AddCommMonoid.natModule.{u1} M _inst_3)) (PartialOrder.toPreorder.{u1} (Submodule.{0, u1} Nat M Nat.semiring _inst_3 (AddCommMonoid.natModule.{u1} M _inst_3)) (CompleteSemilatticeInf.toPartialOrder.{u1} (Submodule.{0, u1} Nat M Nat.semiring _inst_3 (AddCommMonoid.natModule.{u1} M _inst_3)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (Submodule.{0, u1} Nat M Nat.semiring _inst_3 (AddCommMonoid.natModule.{u1} M _inst_3)) (Submodule.completeLattice.{0, u1} Nat M Nat.semiring _inst_3 (AddCommMonoid.natModule.{u1} M _inst_3)))))))) (AddSubmonoid.toNatSubmodule.{u1} M _inst_3) S)) ((fun (a : Type.{u1}) (b : Type.{u1}) [self : HasLiftT.{succ u1, succ u1} a b] => self.0) (AddSubmonoid.{u1} M (AddMonoid.toAddZeroClass.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3))) (Set.{u1} M) (HasLiftT.mk.{succ u1, succ u1} (AddSubmonoid.{u1} M (AddMonoid.toAddZeroClass.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3))) (Set.{u1} M) (CoeTCₓ.coe.{succ u1, succ u1} (AddSubmonoid.{u1} M (AddMonoid.toAddZeroClass.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3))) (Set.{u1} M) (SetLike.Set.hasCoeT.{u1, u1} (AddSubmonoid.{u1} M (AddMonoid.toAddZeroClass.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3))) M (AddSubmonoid.setLike.{u1} M (AddMonoid.toAddZeroClass.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3)))))) S)
 but is expected to have type
-  forall {M : Type.{u1}} [_inst_3 : AddCommMonoid.{u1} M] (S : AddSubmonoid.{u1} M (AddMonoid.toAddZeroClass.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3))), Eq.{succ u1} (Set.{u1} M) (SetLike.coe.{u1, u1} (Submodule.{0, u1} Nat M Nat.semiring _inst_3 (AddCommMonoid.natModule.{u1} M _inst_3)) M (Submodule.setLike.{0, u1} Nat M Nat.semiring _inst_3 (AddCommMonoid.natModule.{u1} M _inst_3)) (FunLike.coe.{succ u1, succ u1, succ u1} (RelIso.{u1, u1} (AddSubmonoid.{u1} M (AddMonoid.toAddZeroClass.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3))) (Submodule.{0, u1} Nat M Nat.semiring _inst_3 (AddCommMonoid.natModule.{u1} M _inst_3)) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1281 : AddSubmonoid.{u1} M (AddMonoid.toAddZeroClass.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3))) (x._@.Mathlib.Order.Hom.Basic._hyg.1283 : AddSubmonoid.{u1} M (AddMonoid.toAddZeroClass.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3))) => LE.le.{u1} (AddSubmonoid.{u1} M (AddMonoid.toAddZeroClass.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3))) (Preorder.toLE.{u1} (AddSubmonoid.{u1} M (AddMonoid.toAddZeroClass.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3))) (PartialOrder.toPreorder.{u1} (AddSubmonoid.{u1} M (AddMonoid.toAddZeroClass.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3))) (CompleteSemilatticeInf.toPartialOrder.{u1} (AddSubmonoid.{u1} M (AddMonoid.toAddZeroClass.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3))) (CompleteLattice.toCompleteSemilatticeInf.{u1} (AddSubmonoid.{u1} M (AddMonoid.toAddZeroClass.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3))) (AddSubmonoid.instCompleteLatticeAddSubmonoid.{u1} M (AddMonoid.toAddZeroClass.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3))))))) x._@.Mathlib.Order.Hom.Basic._hyg.1281 x._@.Mathlib.Order.Hom.Basic._hyg.1283) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1296 : Submodule.{0, u1} Nat M Nat.semiring _inst_3 (AddCommMonoid.natModule.{u1} M _inst_3)) (x._@.Mathlib.Order.Hom.Basic._hyg.1298 : Submodule.{0, u1} Nat M Nat.semiring _inst_3 (AddCommMonoid.natModule.{u1} M _inst_3)) => LE.le.{u1} (Submodule.{0, u1} Nat M Nat.semiring _inst_3 (AddCommMonoid.natModule.{u1} M _inst_3)) (Preorder.toLE.{u1} (Submodule.{0, u1} Nat M Nat.semiring _inst_3 (AddCommMonoid.natModule.{u1} M _inst_3)) (PartialOrder.toPreorder.{u1} (Submodule.{0, u1} Nat M Nat.semiring _inst_3 (AddCommMonoid.natModule.{u1} M _inst_3)) (CompleteSemilatticeInf.toPartialOrder.{u1} (Submodule.{0, u1} Nat M Nat.semiring _inst_3 (AddCommMonoid.natModule.{u1} M _inst_3)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (Submodule.{0, u1} Nat M Nat.semiring _inst_3 (AddCommMonoid.natModule.{u1} M _inst_3)) (Submodule.completeLattice.{0, u1} Nat M Nat.semiring _inst_3 (AddCommMonoid.natModule.{u1} M _inst_3)))))) x._@.Mathlib.Order.Hom.Basic._hyg.1296 x._@.Mathlib.Order.Hom.Basic._hyg.1298)) (AddSubmonoid.{u1} M (AddMonoid.toAddZeroClass.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3))) (fun (_x : AddSubmonoid.{u1} M (AddMonoid.toAddZeroClass.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3))) => Submodule.{0, u1} Nat M Nat.semiring _inst_3 (AddCommMonoid.natModule.{u1} M _inst_3)) (RelHomClass.toFunLike.{u1, u1, u1} (RelIso.{u1, u1} (AddSubmonoid.{u1} M (AddMonoid.toAddZeroClass.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3))) (Submodule.{0, u1} Nat M Nat.semiring _inst_3 (AddCommMonoid.natModule.{u1} M _inst_3)) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1281 : AddSubmonoid.{u1} M (AddMonoid.toAddZeroClass.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3))) (x._@.Mathlib.Order.Hom.Basic._hyg.1283 : AddSubmonoid.{u1} M (AddMonoid.toAddZeroClass.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3))) => LE.le.{u1} (AddSubmonoid.{u1} M (AddMonoid.toAddZeroClass.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3))) (Preorder.toLE.{u1} (AddSubmonoid.{u1} M (AddMonoid.toAddZeroClass.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3))) (PartialOrder.toPreorder.{u1} (AddSubmonoid.{u1} M (AddMonoid.toAddZeroClass.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3))) (CompleteSemilatticeInf.toPartialOrder.{u1} (AddSubmonoid.{u1} M (AddMonoid.toAddZeroClass.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3))) (CompleteLattice.toCompleteSemilatticeInf.{u1} (AddSubmonoid.{u1} M (AddMonoid.toAddZeroClass.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3))) (AddSubmonoid.instCompleteLatticeAddSubmonoid.{u1} M (AddMonoid.toAddZeroClass.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3))))))) x._@.Mathlib.Order.Hom.Basic._hyg.1281 x._@.Mathlib.Order.Hom.Basic._hyg.1283) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1296 : Submodule.{0, u1} Nat M Nat.semiring _inst_3 (AddCommMonoid.natModule.{u1} M _inst_3)) (x._@.Mathlib.Order.Hom.Basic._hyg.1298 : Submodule.{0, u1} Nat M Nat.semiring _inst_3 (AddCommMonoid.natModule.{u1} M _inst_3)) => LE.le.{u1} (Submodule.{0, u1} Nat M Nat.semiring _inst_3 (AddCommMonoid.natModule.{u1} M _inst_3)) (Preorder.toLE.{u1} (Submodule.{0, u1} Nat M Nat.semiring _inst_3 (AddCommMonoid.natModule.{u1} M _inst_3)) (PartialOrder.toPreorder.{u1} (Submodule.{0, u1} Nat M Nat.semiring _inst_3 (AddCommMonoid.natModule.{u1} M _inst_3)) (CompleteSemilatticeInf.toPartialOrder.{u1} (Submodule.{0, u1} Nat M Nat.semiring _inst_3 (AddCommMonoid.natModule.{u1} M _inst_3)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (Submodule.{0, u1} Nat M Nat.semiring _inst_3 (AddCommMonoid.natModule.{u1} M _inst_3)) (Submodule.completeLattice.{0, u1} Nat M Nat.semiring _inst_3 (AddCommMonoid.natModule.{u1} M _inst_3)))))) x._@.Mathlib.Order.Hom.Basic._hyg.1296 x._@.Mathlib.Order.Hom.Basic._hyg.1298)) (AddSubmonoid.{u1} M (AddMonoid.toAddZeroClass.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3))) (Submodule.{0, u1} Nat M Nat.semiring _inst_3 (AddCommMonoid.natModule.{u1} M _inst_3)) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1281 : AddSubmonoid.{u1} M (AddMonoid.toAddZeroClass.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3))) (x._@.Mathlib.Order.Hom.Basic._hyg.1283 : AddSubmonoid.{u1} M (AddMonoid.toAddZeroClass.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3))) => LE.le.{u1} (AddSubmonoid.{u1} M (AddMonoid.toAddZeroClass.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3))) (Preorder.toLE.{u1} (AddSubmonoid.{u1} M (AddMonoid.toAddZeroClass.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3))) (PartialOrder.toPreorder.{u1} (AddSubmonoid.{u1} M (AddMonoid.toAddZeroClass.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3))) (CompleteSemilatticeInf.toPartialOrder.{u1} (AddSubmonoid.{u1} M (AddMonoid.toAddZeroClass.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3))) (CompleteLattice.toCompleteSemilatticeInf.{u1} (AddSubmonoid.{u1} M (AddMonoid.toAddZeroClass.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3))) (AddSubmonoid.instCompleteLatticeAddSubmonoid.{u1} M (AddMonoid.toAddZeroClass.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3))))))) x._@.Mathlib.Order.Hom.Basic._hyg.1281 x._@.Mathlib.Order.Hom.Basic._hyg.1283) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1296 : Submodule.{0, u1} Nat M Nat.semiring _inst_3 (AddCommMonoid.natModule.{u1} M _inst_3)) (x._@.Mathlib.Order.Hom.Basic._hyg.1298 : Submodule.{0, u1} Nat M Nat.semiring _inst_3 (AddCommMonoid.natModule.{u1} M _inst_3)) => LE.le.{u1} (Submodule.{0, u1} Nat M Nat.semiring _inst_3 (AddCommMonoid.natModule.{u1} M _inst_3)) (Preorder.toLE.{u1} (Submodule.{0, u1} Nat M Nat.semiring _inst_3 (AddCommMonoid.natModule.{u1} M _inst_3)) (PartialOrder.toPreorder.{u1} (Submodule.{0, u1} Nat M Nat.semiring _inst_3 (AddCommMonoid.natModule.{u1} M _inst_3)) (CompleteSemilatticeInf.toPartialOrder.{u1} (Submodule.{0, u1} Nat M Nat.semiring _inst_3 (AddCommMonoid.natModule.{u1} M _inst_3)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (Submodule.{0, u1} Nat M Nat.semiring _inst_3 (AddCommMonoid.natModule.{u1} M _inst_3)) (Submodule.completeLattice.{0, u1} Nat M Nat.semiring _inst_3 (AddCommMonoid.natModule.{u1} M _inst_3)))))) x._@.Mathlib.Order.Hom.Basic._hyg.1296 x._@.Mathlib.Order.Hom.Basic._hyg.1298) (RelIso.instRelHomClassRelIso.{u1, u1} (AddSubmonoid.{u1} M (AddMonoid.toAddZeroClass.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3))) (Submodule.{0, u1} Nat M Nat.semiring _inst_3 (AddCommMonoid.natModule.{u1} M _inst_3)) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1281 : AddSubmonoid.{u1} M (AddMonoid.toAddZeroClass.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3))) (x._@.Mathlib.Order.Hom.Basic._hyg.1283 : AddSubmonoid.{u1} M (AddMonoid.toAddZeroClass.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3))) => LE.le.{u1} (AddSubmonoid.{u1} M (AddMonoid.toAddZeroClass.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3))) (Preorder.toLE.{u1} (AddSubmonoid.{u1} M (AddMonoid.toAddZeroClass.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3))) (PartialOrder.toPreorder.{u1} (AddSubmonoid.{u1} M (AddMonoid.toAddZeroClass.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3))) (CompleteSemilatticeInf.toPartialOrder.{u1} (AddSubmonoid.{u1} M (AddMonoid.toAddZeroClass.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3))) (CompleteLattice.toCompleteSemilatticeInf.{u1} (AddSubmonoid.{u1} M (AddMonoid.toAddZeroClass.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3))) (AddSubmonoid.instCompleteLatticeAddSubmonoid.{u1} M (AddMonoid.toAddZeroClass.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3))))))) x._@.Mathlib.Order.Hom.Basic._hyg.1281 x._@.Mathlib.Order.Hom.Basic._hyg.1283) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1296 : Submodule.{0, u1} Nat M Nat.semiring _inst_3 (AddCommMonoid.natModule.{u1} M _inst_3)) (x._@.Mathlib.Order.Hom.Basic._hyg.1298 : Submodule.{0, u1} Nat M Nat.semiring _inst_3 (AddCommMonoid.natModule.{u1} M _inst_3)) => LE.le.{u1} (Submodule.{0, u1} Nat M Nat.semiring _inst_3 (AddCommMonoid.natModule.{u1} M _inst_3)) (Preorder.toLE.{u1} (Submodule.{0, u1} Nat M Nat.semiring _inst_3 (AddCommMonoid.natModule.{u1} M _inst_3)) (PartialOrder.toPreorder.{u1} (Submodule.{0, u1} Nat M Nat.semiring _inst_3 (AddCommMonoid.natModule.{u1} M _inst_3)) (CompleteSemilatticeInf.toPartialOrder.{u1} (Submodule.{0, u1} Nat M Nat.semiring _inst_3 (AddCommMonoid.natModule.{u1} M _inst_3)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (Submodule.{0, u1} Nat M Nat.semiring _inst_3 (AddCommMonoid.natModule.{u1} M _inst_3)) (Submodule.completeLattice.{0, u1} Nat M Nat.semiring _inst_3 (AddCommMonoid.natModule.{u1} M _inst_3)))))) x._@.Mathlib.Order.Hom.Basic._hyg.1296 x._@.Mathlib.Order.Hom.Basic._hyg.1298))) (AddSubmonoid.toNatSubmodule.{u1} M _inst_3) S)) (SetLike.coe.{u1, u1} (AddSubmonoid.{u1} M (AddMonoid.toAddZeroClass.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3))) M (AddSubmonoid.instSetLikeAddSubmonoid.{u1} M (AddMonoid.toAddZeroClass.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3))) S)
+  forall {M : Type.{u1}} [_inst_3 : AddCommMonoid.{u1} M] (S : AddSubmonoid.{u1} M (AddMonoid.toAddZeroClass.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3))), Eq.{succ u1} (Set.{u1} M) (SetLike.coe.{u1, u1} (Submodule.{0, u1} Nat M Nat.semiring _inst_3 (AddCommMonoid.natModule.{u1} M _inst_3)) M (Submodule.setLike.{0, u1} Nat M Nat.semiring _inst_3 (AddCommMonoid.natModule.{u1} M _inst_3)) (FunLike.coe.{succ u1, succ u1, succ u1} (RelIso.{u1, u1} (AddSubmonoid.{u1} M (AddMonoid.toAddZeroClass.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3))) (Submodule.{0, u1} Nat M Nat.semiring _inst_3 (AddCommMonoid.natModule.{u1} M _inst_3)) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1285 : AddSubmonoid.{u1} M (AddMonoid.toAddZeroClass.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3))) (x._@.Mathlib.Order.Hom.Basic._hyg.1287 : AddSubmonoid.{u1} M (AddMonoid.toAddZeroClass.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3))) => LE.le.{u1} (AddSubmonoid.{u1} M (AddMonoid.toAddZeroClass.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3))) (Preorder.toLE.{u1} (AddSubmonoid.{u1} M (AddMonoid.toAddZeroClass.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3))) (PartialOrder.toPreorder.{u1} (AddSubmonoid.{u1} M (AddMonoid.toAddZeroClass.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3))) (CompleteSemilatticeInf.toPartialOrder.{u1} (AddSubmonoid.{u1} M (AddMonoid.toAddZeroClass.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3))) (CompleteLattice.toCompleteSemilatticeInf.{u1} (AddSubmonoid.{u1} M (AddMonoid.toAddZeroClass.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3))) (AddSubmonoid.instCompleteLatticeAddSubmonoid.{u1} M (AddMonoid.toAddZeroClass.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3))))))) x._@.Mathlib.Order.Hom.Basic._hyg.1285 x._@.Mathlib.Order.Hom.Basic._hyg.1287) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1300 : Submodule.{0, u1} Nat M Nat.semiring _inst_3 (AddCommMonoid.natModule.{u1} M _inst_3)) (x._@.Mathlib.Order.Hom.Basic._hyg.1302 : Submodule.{0, u1} Nat M Nat.semiring _inst_3 (AddCommMonoid.natModule.{u1} M _inst_3)) => LE.le.{u1} (Submodule.{0, u1} Nat M Nat.semiring _inst_3 (AddCommMonoid.natModule.{u1} M _inst_3)) (Preorder.toLE.{u1} (Submodule.{0, u1} Nat M Nat.semiring _inst_3 (AddCommMonoid.natModule.{u1} M _inst_3)) (PartialOrder.toPreorder.{u1} (Submodule.{0, u1} Nat M Nat.semiring _inst_3 (AddCommMonoid.natModule.{u1} M _inst_3)) (CompleteSemilatticeInf.toPartialOrder.{u1} (Submodule.{0, u1} Nat M Nat.semiring _inst_3 (AddCommMonoid.natModule.{u1} M _inst_3)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (Submodule.{0, u1} Nat M Nat.semiring _inst_3 (AddCommMonoid.natModule.{u1} M _inst_3)) (Submodule.completeLattice.{0, u1} Nat M Nat.semiring _inst_3 (AddCommMonoid.natModule.{u1} M _inst_3)))))) x._@.Mathlib.Order.Hom.Basic._hyg.1300 x._@.Mathlib.Order.Hom.Basic._hyg.1302)) (AddSubmonoid.{u1} M (AddMonoid.toAddZeroClass.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3))) (fun (_x : AddSubmonoid.{u1} M (AddMonoid.toAddZeroClass.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3))) => Submodule.{0, u1} Nat M Nat.semiring _inst_3 (AddCommMonoid.natModule.{u1} M _inst_3)) (RelHomClass.toFunLike.{u1, u1, u1} (RelIso.{u1, u1} (AddSubmonoid.{u1} M (AddMonoid.toAddZeroClass.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3))) (Submodule.{0, u1} Nat M Nat.semiring _inst_3 (AddCommMonoid.natModule.{u1} M _inst_3)) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1285 : AddSubmonoid.{u1} M (AddMonoid.toAddZeroClass.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3))) (x._@.Mathlib.Order.Hom.Basic._hyg.1287 : AddSubmonoid.{u1} M (AddMonoid.toAddZeroClass.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3))) => LE.le.{u1} (AddSubmonoid.{u1} M (AddMonoid.toAddZeroClass.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3))) (Preorder.toLE.{u1} (AddSubmonoid.{u1} M (AddMonoid.toAddZeroClass.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3))) (PartialOrder.toPreorder.{u1} (AddSubmonoid.{u1} M (AddMonoid.toAddZeroClass.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3))) (CompleteSemilatticeInf.toPartialOrder.{u1} (AddSubmonoid.{u1} M (AddMonoid.toAddZeroClass.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3))) (CompleteLattice.toCompleteSemilatticeInf.{u1} (AddSubmonoid.{u1} M (AddMonoid.toAddZeroClass.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3))) (AddSubmonoid.instCompleteLatticeAddSubmonoid.{u1} M (AddMonoid.toAddZeroClass.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3))))))) x._@.Mathlib.Order.Hom.Basic._hyg.1285 x._@.Mathlib.Order.Hom.Basic._hyg.1287) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1300 : Submodule.{0, u1} Nat M Nat.semiring _inst_3 (AddCommMonoid.natModule.{u1} M _inst_3)) (x._@.Mathlib.Order.Hom.Basic._hyg.1302 : Submodule.{0, u1} Nat M Nat.semiring _inst_3 (AddCommMonoid.natModule.{u1} M _inst_3)) => LE.le.{u1} (Submodule.{0, u1} Nat M Nat.semiring _inst_3 (AddCommMonoid.natModule.{u1} M _inst_3)) (Preorder.toLE.{u1} (Submodule.{0, u1} Nat M Nat.semiring _inst_3 (AddCommMonoid.natModule.{u1} M _inst_3)) (PartialOrder.toPreorder.{u1} (Submodule.{0, u1} Nat M Nat.semiring _inst_3 (AddCommMonoid.natModule.{u1} M _inst_3)) (CompleteSemilatticeInf.toPartialOrder.{u1} (Submodule.{0, u1} Nat M Nat.semiring _inst_3 (AddCommMonoid.natModule.{u1} M _inst_3)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (Submodule.{0, u1} Nat M Nat.semiring _inst_3 (AddCommMonoid.natModule.{u1} M _inst_3)) (Submodule.completeLattice.{0, u1} Nat M Nat.semiring _inst_3 (AddCommMonoid.natModule.{u1} M _inst_3)))))) x._@.Mathlib.Order.Hom.Basic._hyg.1300 x._@.Mathlib.Order.Hom.Basic._hyg.1302)) (AddSubmonoid.{u1} M (AddMonoid.toAddZeroClass.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3))) (Submodule.{0, u1} Nat M Nat.semiring _inst_3 (AddCommMonoid.natModule.{u1} M _inst_3)) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1285 : AddSubmonoid.{u1} M (AddMonoid.toAddZeroClass.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3))) (x._@.Mathlib.Order.Hom.Basic._hyg.1287 : AddSubmonoid.{u1} M (AddMonoid.toAddZeroClass.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3))) => LE.le.{u1} (AddSubmonoid.{u1} M (AddMonoid.toAddZeroClass.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3))) (Preorder.toLE.{u1} (AddSubmonoid.{u1} M (AddMonoid.toAddZeroClass.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3))) (PartialOrder.toPreorder.{u1} (AddSubmonoid.{u1} M (AddMonoid.toAddZeroClass.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3))) (CompleteSemilatticeInf.toPartialOrder.{u1} (AddSubmonoid.{u1} M (AddMonoid.toAddZeroClass.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3))) (CompleteLattice.toCompleteSemilatticeInf.{u1} (AddSubmonoid.{u1} M (AddMonoid.toAddZeroClass.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3))) (AddSubmonoid.instCompleteLatticeAddSubmonoid.{u1} M (AddMonoid.toAddZeroClass.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3))))))) x._@.Mathlib.Order.Hom.Basic._hyg.1285 x._@.Mathlib.Order.Hom.Basic._hyg.1287) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1300 : Submodule.{0, u1} Nat M Nat.semiring _inst_3 (AddCommMonoid.natModule.{u1} M _inst_3)) (x._@.Mathlib.Order.Hom.Basic._hyg.1302 : Submodule.{0, u1} Nat M Nat.semiring _inst_3 (AddCommMonoid.natModule.{u1} M _inst_3)) => LE.le.{u1} (Submodule.{0, u1} Nat M Nat.semiring _inst_3 (AddCommMonoid.natModule.{u1} M _inst_3)) (Preorder.toLE.{u1} (Submodule.{0, u1} Nat M Nat.semiring _inst_3 (AddCommMonoid.natModule.{u1} M _inst_3)) (PartialOrder.toPreorder.{u1} (Submodule.{0, u1} Nat M Nat.semiring _inst_3 (AddCommMonoid.natModule.{u1} M _inst_3)) (CompleteSemilatticeInf.toPartialOrder.{u1} (Submodule.{0, u1} Nat M Nat.semiring _inst_3 (AddCommMonoid.natModule.{u1} M _inst_3)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (Submodule.{0, u1} Nat M Nat.semiring _inst_3 (AddCommMonoid.natModule.{u1} M _inst_3)) (Submodule.completeLattice.{0, u1} Nat M Nat.semiring _inst_3 (AddCommMonoid.natModule.{u1} M _inst_3)))))) x._@.Mathlib.Order.Hom.Basic._hyg.1300 x._@.Mathlib.Order.Hom.Basic._hyg.1302) (RelIso.instRelHomClassRelIso.{u1, u1} (AddSubmonoid.{u1} M (AddMonoid.toAddZeroClass.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3))) (Submodule.{0, u1} Nat M Nat.semiring _inst_3 (AddCommMonoid.natModule.{u1} M _inst_3)) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1285 : AddSubmonoid.{u1} M (AddMonoid.toAddZeroClass.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3))) (x._@.Mathlib.Order.Hom.Basic._hyg.1287 : AddSubmonoid.{u1} M (AddMonoid.toAddZeroClass.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3))) => LE.le.{u1} (AddSubmonoid.{u1} M (AddMonoid.toAddZeroClass.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3))) (Preorder.toLE.{u1} (AddSubmonoid.{u1} M (AddMonoid.toAddZeroClass.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3))) (PartialOrder.toPreorder.{u1} (AddSubmonoid.{u1} M (AddMonoid.toAddZeroClass.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3))) (CompleteSemilatticeInf.toPartialOrder.{u1} (AddSubmonoid.{u1} M (AddMonoid.toAddZeroClass.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3))) (CompleteLattice.toCompleteSemilatticeInf.{u1} (AddSubmonoid.{u1} M (AddMonoid.toAddZeroClass.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3))) (AddSubmonoid.instCompleteLatticeAddSubmonoid.{u1} M (AddMonoid.toAddZeroClass.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3))))))) x._@.Mathlib.Order.Hom.Basic._hyg.1285 x._@.Mathlib.Order.Hom.Basic._hyg.1287) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1300 : Submodule.{0, u1} Nat M Nat.semiring _inst_3 (AddCommMonoid.natModule.{u1} M _inst_3)) (x._@.Mathlib.Order.Hom.Basic._hyg.1302 : Submodule.{0, u1} Nat M Nat.semiring _inst_3 (AddCommMonoid.natModule.{u1} M _inst_3)) => LE.le.{u1} (Submodule.{0, u1} Nat M Nat.semiring _inst_3 (AddCommMonoid.natModule.{u1} M _inst_3)) (Preorder.toLE.{u1} (Submodule.{0, u1} Nat M Nat.semiring _inst_3 (AddCommMonoid.natModule.{u1} M _inst_3)) (PartialOrder.toPreorder.{u1} (Submodule.{0, u1} Nat M Nat.semiring _inst_3 (AddCommMonoid.natModule.{u1} M _inst_3)) (CompleteSemilatticeInf.toPartialOrder.{u1} (Submodule.{0, u1} Nat M Nat.semiring _inst_3 (AddCommMonoid.natModule.{u1} M _inst_3)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (Submodule.{0, u1} Nat M Nat.semiring _inst_3 (AddCommMonoid.natModule.{u1} M _inst_3)) (Submodule.completeLattice.{0, u1} Nat M Nat.semiring _inst_3 (AddCommMonoid.natModule.{u1} M _inst_3)))))) x._@.Mathlib.Order.Hom.Basic._hyg.1300 x._@.Mathlib.Order.Hom.Basic._hyg.1302))) (AddSubmonoid.toNatSubmodule.{u1} M _inst_3) S)) (SetLike.coe.{u1, u1} (AddSubmonoid.{u1} M (AddMonoid.toAddZeroClass.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3))) M (AddSubmonoid.instSetLikeAddSubmonoid.{u1} M (AddMonoid.toAddZeroClass.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3))) S)
 Case conversion may be inaccurate. Consider using '#align add_submonoid.coe_to_nat_submodule AddSubmonoid.coe_toNatSubmoduleₓ'. -/
 @[simp]
 theorem AddSubmonoid.coe_toNatSubmodule (S : AddSubmonoid M) : (S.toNatSubmodule : Set M) = S :=
@@ -646,7 +646,7 @@ theorem AddSubmonoid.coe_toNatSubmodule (S : AddSubmonoid M) : (S.toNatSubmodule
 lean 3 declaration is
   forall {M : Type.{u1}} [_inst_3 : AddCommMonoid.{u1} M] (S : AddSubmonoid.{u1} M (AddMonoid.toAddZeroClass.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3))), Eq.{succ u1} (AddSubmonoid.{u1} M (AddMonoid.toAddZeroClass.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3))) (Submodule.toAddSubmonoid.{0, u1} Nat M Nat.semiring _inst_3 (AddCommMonoid.natModule.{u1} M _inst_3) (coeFn.{succ u1, succ u1} (OrderIso.{u1, u1} (AddSubmonoid.{u1} M (AddMonoid.toAddZeroClass.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3))) (Submodule.{0, u1} Nat M Nat.semiring _inst_3 (AddCommMonoid.natModule.{u1} M _inst_3)) (Preorder.toHasLe.{u1} (AddSubmonoid.{u1} M (AddMonoid.toAddZeroClass.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3))) (PartialOrder.toPreorder.{u1} (AddSubmonoid.{u1} M (AddMonoid.toAddZeroClass.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3))) (CompleteSemilatticeInf.toPartialOrder.{u1} (AddSubmonoid.{u1} M (AddMonoid.toAddZeroClass.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3))) (CompleteLattice.toCompleteSemilatticeInf.{u1} (AddSubmonoid.{u1} M (AddMonoid.toAddZeroClass.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3))) (AddSubmonoid.completeLattice.{u1} M (AddMonoid.toAddZeroClass.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3))))))) (Preorder.toHasLe.{u1} (Submodule.{0, u1} Nat M Nat.semiring _inst_3 (AddCommMonoid.natModule.{u1} M _inst_3)) (PartialOrder.toPreorder.{u1} (Submodule.{0, u1} Nat M Nat.semiring _inst_3 (AddCommMonoid.natModule.{u1} M _inst_3)) (CompleteSemilatticeInf.toPartialOrder.{u1} (Submodule.{0, u1} Nat M Nat.semiring _inst_3 (AddCommMonoid.natModule.{u1} M _inst_3)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (Submodule.{0, u1} Nat M Nat.semiring _inst_3 (AddCommMonoid.natModule.{u1} M _inst_3)) (Submodule.completeLattice.{0, u1} Nat M Nat.semiring _inst_3 (AddCommMonoid.natModule.{u1} M _inst_3))))))) (fun (_x : RelIso.{u1, u1} (AddSubmonoid.{u1} M (AddMonoid.toAddZeroClass.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3))) (Submodule.{0, u1} Nat M Nat.semiring _inst_3 (AddCommMonoid.natModule.{u1} M _inst_3)) (LE.le.{u1} (AddSubmonoid.{u1} M (AddMonoid.toAddZeroClass.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3))) (Preorder.toHasLe.{u1} (AddSubmonoid.{u1} M (AddMonoid.toAddZeroClass.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3))) (PartialOrder.toPreorder.{u1} (AddSubmonoid.{u1} M (AddMonoid.toAddZeroClass.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3))) (CompleteSemilatticeInf.toPartialOrder.{u1} (AddSubmonoid.{u1} M (AddMonoid.toAddZeroClass.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3))) (CompleteLattice.toCompleteSemilatticeInf.{u1} (AddSubmonoid.{u1} M (AddMonoid.toAddZeroClass.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3))) (AddSubmonoid.completeLattice.{u1} M (AddMonoid.toAddZeroClass.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3)))))))) (LE.le.{u1} (Submodule.{0, u1} Nat M Nat.semiring _inst_3 (AddCommMonoid.natModule.{u1} M _inst_3)) (Preorder.toHasLe.{u1} (Submodule.{0, u1} Nat M Nat.semiring _inst_3 (AddCommMonoid.natModule.{u1} M _inst_3)) (PartialOrder.toPreorder.{u1} (Submodule.{0, u1} Nat M Nat.semiring _inst_3 (AddCommMonoid.natModule.{u1} M _inst_3)) (CompleteSemilatticeInf.toPartialOrder.{u1} (Submodule.{0, u1} Nat M Nat.semiring _inst_3 (AddCommMonoid.natModule.{u1} M _inst_3)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (Submodule.{0, u1} Nat M Nat.semiring _inst_3 (AddCommMonoid.natModule.{u1} M _inst_3)) (Submodule.completeLattice.{0, u1} Nat M Nat.semiring _inst_3 (AddCommMonoid.natModule.{u1} M _inst_3)))))))) => (AddSubmonoid.{u1} M (AddMonoid.toAddZeroClass.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3))) -> (Submodule.{0, u1} Nat M Nat.semiring _inst_3 (AddCommMonoid.natModule.{u1} M _inst_3))) (RelIso.hasCoeToFun.{u1, u1} (AddSubmonoid.{u1} M (AddMonoid.toAddZeroClass.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3))) (Submodule.{0, u1} Nat M Nat.semiring _inst_3 (AddCommMonoid.natModule.{u1} M _inst_3)) (LE.le.{u1} (AddSubmonoid.{u1} M (AddMonoid.toAddZeroClass.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3))) (Preorder.toHasLe.{u1} (AddSubmonoid.{u1} M (AddMonoid.toAddZeroClass.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3))) (PartialOrder.toPreorder.{u1} (AddSubmonoid.{u1} M (AddMonoid.toAddZeroClass.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3))) (CompleteSemilatticeInf.toPartialOrder.{u1} (AddSubmonoid.{u1} M (AddMonoid.toAddZeroClass.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3))) (CompleteLattice.toCompleteSemilatticeInf.{u1} (AddSubmonoid.{u1} M (AddMonoid.toAddZeroClass.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3))) (AddSubmonoid.completeLattice.{u1} M (AddMonoid.toAddZeroClass.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3)))))))) (LE.le.{u1} (Submodule.{0, u1} Nat M Nat.semiring _inst_3 (AddCommMonoid.natModule.{u1} M _inst_3)) (Preorder.toHasLe.{u1} (Submodule.{0, u1} Nat M Nat.semiring _inst_3 (AddCommMonoid.natModule.{u1} M _inst_3)) (PartialOrder.toPreorder.{u1} (Submodule.{0, u1} Nat M Nat.semiring _inst_3 (AddCommMonoid.natModule.{u1} M _inst_3)) (CompleteSemilatticeInf.toPartialOrder.{u1} (Submodule.{0, u1} Nat M Nat.semiring _inst_3 (AddCommMonoid.natModule.{u1} M _inst_3)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (Submodule.{0, u1} Nat M Nat.semiring _inst_3 (AddCommMonoid.natModule.{u1} M _inst_3)) (Submodule.completeLattice.{0, u1} Nat M Nat.semiring _inst_3 (AddCommMonoid.natModule.{u1} M _inst_3)))))))) (AddSubmonoid.toNatSubmodule.{u1} M _inst_3) S)) S
 but is expected to have type
-  forall {M : Type.{u1}} [_inst_3 : AddCommMonoid.{u1} M] (S : AddSubmonoid.{u1} M (AddMonoid.toAddZeroClass.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3))), Eq.{succ u1} (AddSubmonoid.{u1} M (AddMonoid.toAddZeroClass.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3))) (Submodule.toAddSubmonoid.{0, u1} Nat M Nat.semiring _inst_3 (AddCommMonoid.natModule.{u1} M _inst_3) (FunLike.coe.{succ u1, succ u1, succ u1} (RelIso.{u1, u1} (AddSubmonoid.{u1} M (AddMonoid.toAddZeroClass.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3))) (Submodule.{0, u1} Nat M Nat.semiring _inst_3 (AddCommMonoid.natModule.{u1} M _inst_3)) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1281 : AddSubmonoid.{u1} M (AddMonoid.toAddZeroClass.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3))) (x._@.Mathlib.Order.Hom.Basic._hyg.1283 : AddSubmonoid.{u1} M (AddMonoid.toAddZeroClass.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3))) => LE.le.{u1} (AddSubmonoid.{u1} M (AddMonoid.toAddZeroClass.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3))) (Preorder.toLE.{u1} (AddSubmonoid.{u1} M (AddMonoid.toAddZeroClass.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3))) (PartialOrder.toPreorder.{u1} (AddSubmonoid.{u1} M (AddMonoid.toAddZeroClass.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3))) (CompleteSemilatticeInf.toPartialOrder.{u1} (AddSubmonoid.{u1} M (AddMonoid.toAddZeroClass.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3))) (CompleteLattice.toCompleteSemilatticeInf.{u1} (AddSubmonoid.{u1} M (AddMonoid.toAddZeroClass.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3))) (AddSubmonoid.instCompleteLatticeAddSubmonoid.{u1} M (AddMonoid.toAddZeroClass.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3))))))) x._@.Mathlib.Order.Hom.Basic._hyg.1281 x._@.Mathlib.Order.Hom.Basic._hyg.1283) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1296 : Submodule.{0, u1} Nat M Nat.semiring _inst_3 (AddCommMonoid.natModule.{u1} M _inst_3)) (x._@.Mathlib.Order.Hom.Basic._hyg.1298 : Submodule.{0, u1} Nat M Nat.semiring _inst_3 (AddCommMonoid.natModule.{u1} M _inst_3)) => LE.le.{u1} (Submodule.{0, u1} Nat M Nat.semiring _inst_3 (AddCommMonoid.natModule.{u1} M _inst_3)) (Preorder.toLE.{u1} (Submodule.{0, u1} Nat M Nat.semiring _inst_3 (AddCommMonoid.natModule.{u1} M _inst_3)) (PartialOrder.toPreorder.{u1} (Submodule.{0, u1} Nat M Nat.semiring _inst_3 (AddCommMonoid.natModule.{u1} M _inst_3)) (CompleteSemilatticeInf.toPartialOrder.{u1} (Submodule.{0, u1} Nat M Nat.semiring _inst_3 (AddCommMonoid.natModule.{u1} M _inst_3)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (Submodule.{0, u1} Nat M Nat.semiring _inst_3 (AddCommMonoid.natModule.{u1} M _inst_3)) (Submodule.completeLattice.{0, u1} Nat M Nat.semiring _inst_3 (AddCommMonoid.natModule.{u1} M _inst_3)))))) x._@.Mathlib.Order.Hom.Basic._hyg.1296 x._@.Mathlib.Order.Hom.Basic._hyg.1298)) (AddSubmonoid.{u1} M (AddMonoid.toAddZeroClass.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3))) (fun (_x : AddSubmonoid.{u1} M (AddMonoid.toAddZeroClass.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3))) => Submodule.{0, u1} Nat M Nat.semiring _inst_3 (AddCommMonoid.natModule.{u1} M _inst_3)) (RelHomClass.toFunLike.{u1, u1, u1} (RelIso.{u1, u1} (AddSubmonoid.{u1} M (AddMonoid.toAddZeroClass.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3))) (Submodule.{0, u1} Nat M Nat.semiring _inst_3 (AddCommMonoid.natModule.{u1} M _inst_3)) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1281 : AddSubmonoid.{u1} M (AddMonoid.toAddZeroClass.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3))) (x._@.Mathlib.Order.Hom.Basic._hyg.1283 : AddSubmonoid.{u1} M (AddMonoid.toAddZeroClass.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3))) => LE.le.{u1} (AddSubmonoid.{u1} M (AddMonoid.toAddZeroClass.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3))) (Preorder.toLE.{u1} (AddSubmonoid.{u1} M (AddMonoid.toAddZeroClass.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3))) (PartialOrder.toPreorder.{u1} (AddSubmonoid.{u1} M (AddMonoid.toAddZeroClass.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3))) (CompleteSemilatticeInf.toPartialOrder.{u1} (AddSubmonoid.{u1} M (AddMonoid.toAddZeroClass.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3))) (CompleteLattice.toCompleteSemilatticeInf.{u1} (AddSubmonoid.{u1} M (AddMonoid.toAddZeroClass.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3))) (AddSubmonoid.instCompleteLatticeAddSubmonoid.{u1} M (AddMonoid.toAddZeroClass.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3))))))) x._@.Mathlib.Order.Hom.Basic._hyg.1281 x._@.Mathlib.Order.Hom.Basic._hyg.1283) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1296 : Submodule.{0, u1} Nat M Nat.semiring _inst_3 (AddCommMonoid.natModule.{u1} M _inst_3)) (x._@.Mathlib.Order.Hom.Basic._hyg.1298 : Submodule.{0, u1} Nat M Nat.semiring _inst_3 (AddCommMonoid.natModule.{u1} M _inst_3)) => LE.le.{u1} (Submodule.{0, u1} Nat M Nat.semiring _inst_3 (AddCommMonoid.natModule.{u1} M _inst_3)) (Preorder.toLE.{u1} (Submodule.{0, u1} Nat M Nat.semiring _inst_3 (AddCommMonoid.natModule.{u1} M _inst_3)) (PartialOrder.toPreorder.{u1} (Submodule.{0, u1} Nat M Nat.semiring _inst_3 (AddCommMonoid.natModule.{u1} M _inst_3)) (CompleteSemilatticeInf.toPartialOrder.{u1} (Submodule.{0, u1} Nat M Nat.semiring _inst_3 (AddCommMonoid.natModule.{u1} M _inst_3)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (Submodule.{0, u1} Nat M Nat.semiring _inst_3 (AddCommMonoid.natModule.{u1} M _inst_3)) (Submodule.completeLattice.{0, u1} Nat M Nat.semiring _inst_3 (AddCommMonoid.natModule.{u1} M _inst_3)))))) x._@.Mathlib.Order.Hom.Basic._hyg.1296 x._@.Mathlib.Order.Hom.Basic._hyg.1298)) (AddSubmonoid.{u1} M (AddMonoid.toAddZeroClass.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3))) (Submodule.{0, u1} Nat M Nat.semiring _inst_3 (AddCommMonoid.natModule.{u1} M _inst_3)) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1281 : AddSubmonoid.{u1} M (AddMonoid.toAddZeroClass.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3))) (x._@.Mathlib.Order.Hom.Basic._hyg.1283 : AddSubmonoid.{u1} M (AddMonoid.toAddZeroClass.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3))) => LE.le.{u1} (AddSubmonoid.{u1} M (AddMonoid.toAddZeroClass.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3))) (Preorder.toLE.{u1} (AddSubmonoid.{u1} M (AddMonoid.toAddZeroClass.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3))) (PartialOrder.toPreorder.{u1} (AddSubmonoid.{u1} M (AddMonoid.toAddZeroClass.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3))) (CompleteSemilatticeInf.toPartialOrder.{u1} (AddSubmonoid.{u1} M (AddMonoid.toAddZeroClass.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3))) (CompleteLattice.toCompleteSemilatticeInf.{u1} (AddSubmonoid.{u1} M (AddMonoid.toAddZeroClass.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3))) (AddSubmonoid.instCompleteLatticeAddSubmonoid.{u1} M (AddMonoid.toAddZeroClass.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3))))))) x._@.Mathlib.Order.Hom.Basic._hyg.1281 x._@.Mathlib.Order.Hom.Basic._hyg.1283) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1296 : Submodule.{0, u1} Nat M Nat.semiring _inst_3 (AddCommMonoid.natModule.{u1} M _inst_3)) (x._@.Mathlib.Order.Hom.Basic._hyg.1298 : Submodule.{0, u1} Nat M Nat.semiring _inst_3 (AddCommMonoid.natModule.{u1} M _inst_3)) => LE.le.{u1} (Submodule.{0, u1} Nat M Nat.semiring _inst_3 (AddCommMonoid.natModule.{u1} M _inst_3)) (Preorder.toLE.{u1} (Submodule.{0, u1} Nat M Nat.semiring _inst_3 (AddCommMonoid.natModule.{u1} M _inst_3)) (PartialOrder.toPreorder.{u1} (Submodule.{0, u1} Nat M Nat.semiring _inst_3 (AddCommMonoid.natModule.{u1} M _inst_3)) (CompleteSemilatticeInf.toPartialOrder.{u1} (Submodule.{0, u1} Nat M Nat.semiring _inst_3 (AddCommMonoid.natModule.{u1} M _inst_3)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (Submodule.{0, u1} Nat M Nat.semiring _inst_3 (AddCommMonoid.natModule.{u1} M _inst_3)) (Submodule.completeLattice.{0, u1} Nat M Nat.semiring _inst_3 (AddCommMonoid.natModule.{u1} M _inst_3)))))) x._@.Mathlib.Order.Hom.Basic._hyg.1296 x._@.Mathlib.Order.Hom.Basic._hyg.1298) (RelIso.instRelHomClassRelIso.{u1, u1} (AddSubmonoid.{u1} M (AddMonoid.toAddZeroClass.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3))) (Submodule.{0, u1} Nat M Nat.semiring _inst_3 (AddCommMonoid.natModule.{u1} M _inst_3)) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1281 : AddSubmonoid.{u1} M (AddMonoid.toAddZeroClass.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3))) (x._@.Mathlib.Order.Hom.Basic._hyg.1283 : AddSubmonoid.{u1} M (AddMonoid.toAddZeroClass.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3))) => LE.le.{u1} (AddSubmonoid.{u1} M (AddMonoid.toAddZeroClass.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3))) (Preorder.toLE.{u1} (AddSubmonoid.{u1} M (AddMonoid.toAddZeroClass.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3))) (PartialOrder.toPreorder.{u1} (AddSubmonoid.{u1} M (AddMonoid.toAddZeroClass.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3))) (CompleteSemilatticeInf.toPartialOrder.{u1} (AddSubmonoid.{u1} M (AddMonoid.toAddZeroClass.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3))) (CompleteLattice.toCompleteSemilatticeInf.{u1} (AddSubmonoid.{u1} M (AddMonoid.toAddZeroClass.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3))) (AddSubmonoid.instCompleteLatticeAddSubmonoid.{u1} M (AddMonoid.toAddZeroClass.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3))))))) x._@.Mathlib.Order.Hom.Basic._hyg.1281 x._@.Mathlib.Order.Hom.Basic._hyg.1283) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1296 : Submodule.{0, u1} Nat M Nat.semiring _inst_3 (AddCommMonoid.natModule.{u1} M _inst_3)) (x._@.Mathlib.Order.Hom.Basic._hyg.1298 : Submodule.{0, u1} Nat M Nat.semiring _inst_3 (AddCommMonoid.natModule.{u1} M _inst_3)) => LE.le.{u1} (Submodule.{0, u1} Nat M Nat.semiring _inst_3 (AddCommMonoid.natModule.{u1} M _inst_3)) (Preorder.toLE.{u1} (Submodule.{0, u1} Nat M Nat.semiring _inst_3 (AddCommMonoid.natModule.{u1} M _inst_3)) (PartialOrder.toPreorder.{u1} (Submodule.{0, u1} Nat M Nat.semiring _inst_3 (AddCommMonoid.natModule.{u1} M _inst_3)) (CompleteSemilatticeInf.toPartialOrder.{u1} (Submodule.{0, u1} Nat M Nat.semiring _inst_3 (AddCommMonoid.natModule.{u1} M _inst_3)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (Submodule.{0, u1} Nat M Nat.semiring _inst_3 (AddCommMonoid.natModule.{u1} M _inst_3)) (Submodule.completeLattice.{0, u1} Nat M Nat.semiring _inst_3 (AddCommMonoid.natModule.{u1} M _inst_3)))))) x._@.Mathlib.Order.Hom.Basic._hyg.1296 x._@.Mathlib.Order.Hom.Basic._hyg.1298))) (AddSubmonoid.toNatSubmodule.{u1} M _inst_3) S)) S
+  forall {M : Type.{u1}} [_inst_3 : AddCommMonoid.{u1} M] (S : AddSubmonoid.{u1} M (AddMonoid.toAddZeroClass.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3))), Eq.{succ u1} (AddSubmonoid.{u1} M (AddMonoid.toAddZeroClass.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3))) (Submodule.toAddSubmonoid.{0, u1} Nat M Nat.semiring _inst_3 (AddCommMonoid.natModule.{u1} M _inst_3) (FunLike.coe.{succ u1, succ u1, succ u1} (RelIso.{u1, u1} (AddSubmonoid.{u1} M (AddMonoid.toAddZeroClass.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3))) (Submodule.{0, u1} Nat M Nat.semiring _inst_3 (AddCommMonoid.natModule.{u1} M _inst_3)) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1285 : AddSubmonoid.{u1} M (AddMonoid.toAddZeroClass.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3))) (x._@.Mathlib.Order.Hom.Basic._hyg.1287 : AddSubmonoid.{u1} M (AddMonoid.toAddZeroClass.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3))) => LE.le.{u1} (AddSubmonoid.{u1} M (AddMonoid.toAddZeroClass.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3))) (Preorder.toLE.{u1} (AddSubmonoid.{u1} M (AddMonoid.toAddZeroClass.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3))) (PartialOrder.toPreorder.{u1} (AddSubmonoid.{u1} M (AddMonoid.toAddZeroClass.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3))) (CompleteSemilatticeInf.toPartialOrder.{u1} (AddSubmonoid.{u1} M (AddMonoid.toAddZeroClass.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3))) (CompleteLattice.toCompleteSemilatticeInf.{u1} (AddSubmonoid.{u1} M (AddMonoid.toAddZeroClass.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3))) (AddSubmonoid.instCompleteLatticeAddSubmonoid.{u1} M (AddMonoid.toAddZeroClass.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3))))))) x._@.Mathlib.Order.Hom.Basic._hyg.1285 x._@.Mathlib.Order.Hom.Basic._hyg.1287) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1300 : Submodule.{0, u1} Nat M Nat.semiring _inst_3 (AddCommMonoid.natModule.{u1} M _inst_3)) (x._@.Mathlib.Order.Hom.Basic._hyg.1302 : Submodule.{0, u1} Nat M Nat.semiring _inst_3 (AddCommMonoid.natModule.{u1} M _inst_3)) => LE.le.{u1} (Submodule.{0, u1} Nat M Nat.semiring _inst_3 (AddCommMonoid.natModule.{u1} M _inst_3)) (Preorder.toLE.{u1} (Submodule.{0, u1} Nat M Nat.semiring _inst_3 (AddCommMonoid.natModule.{u1} M _inst_3)) (PartialOrder.toPreorder.{u1} (Submodule.{0, u1} Nat M Nat.semiring _inst_3 (AddCommMonoid.natModule.{u1} M _inst_3)) (CompleteSemilatticeInf.toPartialOrder.{u1} (Submodule.{0, u1} Nat M Nat.semiring _inst_3 (AddCommMonoid.natModule.{u1} M _inst_3)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (Submodule.{0, u1} Nat M Nat.semiring _inst_3 (AddCommMonoid.natModule.{u1} M _inst_3)) (Submodule.completeLattice.{0, u1} Nat M Nat.semiring _inst_3 (AddCommMonoid.natModule.{u1} M _inst_3)))))) x._@.Mathlib.Order.Hom.Basic._hyg.1300 x._@.Mathlib.Order.Hom.Basic._hyg.1302)) (AddSubmonoid.{u1} M (AddMonoid.toAddZeroClass.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3))) (fun (_x : AddSubmonoid.{u1} M (AddMonoid.toAddZeroClass.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3))) => Submodule.{0, u1} Nat M Nat.semiring _inst_3 (AddCommMonoid.natModule.{u1} M _inst_3)) (RelHomClass.toFunLike.{u1, u1, u1} (RelIso.{u1, u1} (AddSubmonoid.{u1} M (AddMonoid.toAddZeroClass.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3))) (Submodule.{0, u1} Nat M Nat.semiring _inst_3 (AddCommMonoid.natModule.{u1} M _inst_3)) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1285 : AddSubmonoid.{u1} M (AddMonoid.toAddZeroClass.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3))) (x._@.Mathlib.Order.Hom.Basic._hyg.1287 : AddSubmonoid.{u1} M (AddMonoid.toAddZeroClass.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3))) => LE.le.{u1} (AddSubmonoid.{u1} M (AddMonoid.toAddZeroClass.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3))) (Preorder.toLE.{u1} (AddSubmonoid.{u1} M (AddMonoid.toAddZeroClass.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3))) (PartialOrder.toPreorder.{u1} (AddSubmonoid.{u1} M (AddMonoid.toAddZeroClass.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3))) (CompleteSemilatticeInf.toPartialOrder.{u1} (AddSubmonoid.{u1} M (AddMonoid.toAddZeroClass.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3))) (CompleteLattice.toCompleteSemilatticeInf.{u1} (AddSubmonoid.{u1} M (AddMonoid.toAddZeroClass.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3))) (AddSubmonoid.instCompleteLatticeAddSubmonoid.{u1} M (AddMonoid.toAddZeroClass.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3))))))) x._@.Mathlib.Order.Hom.Basic._hyg.1285 x._@.Mathlib.Order.Hom.Basic._hyg.1287) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1300 : Submodule.{0, u1} Nat M Nat.semiring _inst_3 (AddCommMonoid.natModule.{u1} M _inst_3)) (x._@.Mathlib.Order.Hom.Basic._hyg.1302 : Submodule.{0, u1} Nat M Nat.semiring _inst_3 (AddCommMonoid.natModule.{u1} M _inst_3)) => LE.le.{u1} (Submodule.{0, u1} Nat M Nat.semiring _inst_3 (AddCommMonoid.natModule.{u1} M _inst_3)) (Preorder.toLE.{u1} (Submodule.{0, u1} Nat M Nat.semiring _inst_3 (AddCommMonoid.natModule.{u1} M _inst_3)) (PartialOrder.toPreorder.{u1} (Submodule.{0, u1} Nat M Nat.semiring _inst_3 (AddCommMonoid.natModule.{u1} M _inst_3)) (CompleteSemilatticeInf.toPartialOrder.{u1} (Submodule.{0, u1} Nat M Nat.semiring _inst_3 (AddCommMonoid.natModule.{u1} M _inst_3)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (Submodule.{0, u1} Nat M Nat.semiring _inst_3 (AddCommMonoid.natModule.{u1} M _inst_3)) (Submodule.completeLattice.{0, u1} Nat M Nat.semiring _inst_3 (AddCommMonoid.natModule.{u1} M _inst_3)))))) x._@.Mathlib.Order.Hom.Basic._hyg.1300 x._@.Mathlib.Order.Hom.Basic._hyg.1302)) (AddSubmonoid.{u1} M (AddMonoid.toAddZeroClass.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3))) (Submodule.{0, u1} Nat M Nat.semiring _inst_3 (AddCommMonoid.natModule.{u1} M _inst_3)) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1285 : AddSubmonoid.{u1} M (AddMonoid.toAddZeroClass.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3))) (x._@.Mathlib.Order.Hom.Basic._hyg.1287 : AddSubmonoid.{u1} M (AddMonoid.toAddZeroClass.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3))) => LE.le.{u1} (AddSubmonoid.{u1} M (AddMonoid.toAddZeroClass.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3))) (Preorder.toLE.{u1} (AddSubmonoid.{u1} M (AddMonoid.toAddZeroClass.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3))) (PartialOrder.toPreorder.{u1} (AddSubmonoid.{u1} M (AddMonoid.toAddZeroClass.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3))) (CompleteSemilatticeInf.toPartialOrder.{u1} (AddSubmonoid.{u1} M (AddMonoid.toAddZeroClass.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3))) (CompleteLattice.toCompleteSemilatticeInf.{u1} (AddSubmonoid.{u1} M (AddMonoid.toAddZeroClass.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3))) (AddSubmonoid.instCompleteLatticeAddSubmonoid.{u1} M (AddMonoid.toAddZeroClass.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3))))))) x._@.Mathlib.Order.Hom.Basic._hyg.1285 x._@.Mathlib.Order.Hom.Basic._hyg.1287) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1300 : Submodule.{0, u1} Nat M Nat.semiring _inst_3 (AddCommMonoid.natModule.{u1} M _inst_3)) (x._@.Mathlib.Order.Hom.Basic._hyg.1302 : Submodule.{0, u1} Nat M Nat.semiring _inst_3 (AddCommMonoid.natModule.{u1} M _inst_3)) => LE.le.{u1} (Submodule.{0, u1} Nat M Nat.semiring _inst_3 (AddCommMonoid.natModule.{u1} M _inst_3)) (Preorder.toLE.{u1} (Submodule.{0, u1} Nat M Nat.semiring _inst_3 (AddCommMonoid.natModule.{u1} M _inst_3)) (PartialOrder.toPreorder.{u1} (Submodule.{0, u1} Nat M Nat.semiring _inst_3 (AddCommMonoid.natModule.{u1} M _inst_3)) (CompleteSemilatticeInf.toPartialOrder.{u1} (Submodule.{0, u1} Nat M Nat.semiring _inst_3 (AddCommMonoid.natModule.{u1} M _inst_3)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (Submodule.{0, u1} Nat M Nat.semiring _inst_3 (AddCommMonoid.natModule.{u1} M _inst_3)) (Submodule.completeLattice.{0, u1} Nat M Nat.semiring _inst_3 (AddCommMonoid.natModule.{u1} M _inst_3)))))) x._@.Mathlib.Order.Hom.Basic._hyg.1300 x._@.Mathlib.Order.Hom.Basic._hyg.1302) (RelIso.instRelHomClassRelIso.{u1, u1} (AddSubmonoid.{u1} M (AddMonoid.toAddZeroClass.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3))) (Submodule.{0, u1} Nat M Nat.semiring _inst_3 (AddCommMonoid.natModule.{u1} M _inst_3)) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1285 : AddSubmonoid.{u1} M (AddMonoid.toAddZeroClass.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3))) (x._@.Mathlib.Order.Hom.Basic._hyg.1287 : AddSubmonoid.{u1} M (AddMonoid.toAddZeroClass.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3))) => LE.le.{u1} (AddSubmonoid.{u1} M (AddMonoid.toAddZeroClass.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3))) (Preorder.toLE.{u1} (AddSubmonoid.{u1} M (AddMonoid.toAddZeroClass.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3))) (PartialOrder.toPreorder.{u1} (AddSubmonoid.{u1} M (AddMonoid.toAddZeroClass.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3))) (CompleteSemilatticeInf.toPartialOrder.{u1} (AddSubmonoid.{u1} M (AddMonoid.toAddZeroClass.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3))) (CompleteLattice.toCompleteSemilatticeInf.{u1} (AddSubmonoid.{u1} M (AddMonoid.toAddZeroClass.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3))) (AddSubmonoid.instCompleteLatticeAddSubmonoid.{u1} M (AddMonoid.toAddZeroClass.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3))))))) x._@.Mathlib.Order.Hom.Basic._hyg.1285 x._@.Mathlib.Order.Hom.Basic._hyg.1287) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1300 : Submodule.{0, u1} Nat M Nat.semiring _inst_3 (AddCommMonoid.natModule.{u1} M _inst_3)) (x._@.Mathlib.Order.Hom.Basic._hyg.1302 : Submodule.{0, u1} Nat M Nat.semiring _inst_3 (AddCommMonoid.natModule.{u1} M _inst_3)) => LE.le.{u1} (Submodule.{0, u1} Nat M Nat.semiring _inst_3 (AddCommMonoid.natModule.{u1} M _inst_3)) (Preorder.toLE.{u1} (Submodule.{0, u1} Nat M Nat.semiring _inst_3 (AddCommMonoid.natModule.{u1} M _inst_3)) (PartialOrder.toPreorder.{u1} (Submodule.{0, u1} Nat M Nat.semiring _inst_3 (AddCommMonoid.natModule.{u1} M _inst_3)) (CompleteSemilatticeInf.toPartialOrder.{u1} (Submodule.{0, u1} Nat M Nat.semiring _inst_3 (AddCommMonoid.natModule.{u1} M _inst_3)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (Submodule.{0, u1} Nat M Nat.semiring _inst_3 (AddCommMonoid.natModule.{u1} M _inst_3)) (Submodule.completeLattice.{0, u1} Nat M Nat.semiring _inst_3 (AddCommMonoid.natModule.{u1} M _inst_3)))))) x._@.Mathlib.Order.Hom.Basic._hyg.1300 x._@.Mathlib.Order.Hom.Basic._hyg.1302))) (AddSubmonoid.toNatSubmodule.{u1} M _inst_3) S)) S
 Case conversion may be inaccurate. Consider using '#align add_submonoid.to_nat_submodule_to_add_submonoid AddSubmonoid.toNatSubmodule_toAddSubmonoidₓ'. -/
 @[simp]
 theorem AddSubmonoid.toNatSubmodule_toAddSubmonoid (S : AddSubmonoid M) :
@@ -658,7 +658,7 @@ theorem AddSubmonoid.toNatSubmodule_toAddSubmonoid (S : AddSubmonoid M) :
 lean 3 declaration is
   forall {M : Type.{u1}} [_inst_3 : AddCommMonoid.{u1} M] (S : Submodule.{0, u1} Nat M Nat.semiring _inst_3 (AddCommMonoid.natModule.{u1} M _inst_3)), Eq.{succ u1} (Submodule.{0, u1} Nat M Nat.semiring _inst_3 (AddCommMonoid.natModule.{u1} M _inst_3)) (coeFn.{succ u1, succ u1} (OrderIso.{u1, u1} (AddSubmonoid.{u1} M (AddMonoid.toAddZeroClass.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3))) (Submodule.{0, u1} Nat M Nat.semiring _inst_3 (AddCommMonoid.natModule.{u1} M _inst_3)) (Preorder.toHasLe.{u1} (AddSubmonoid.{u1} M (AddMonoid.toAddZeroClass.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3))) (PartialOrder.toPreorder.{u1} (AddSubmonoid.{u1} M (AddMonoid.toAddZeroClass.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3))) (CompleteSemilatticeInf.toPartialOrder.{u1} (AddSubmonoid.{u1} M (AddMonoid.toAddZeroClass.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3))) (CompleteLattice.toCompleteSemilatticeInf.{u1} (AddSubmonoid.{u1} M (AddMonoid.toAddZeroClass.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3))) (AddSubmonoid.completeLattice.{u1} M (AddMonoid.toAddZeroClass.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3))))))) (Preorder.toHasLe.{u1} (Submodule.{0, u1} Nat M Nat.semiring _inst_3 (AddCommMonoid.natModule.{u1} M _inst_3)) (PartialOrder.toPreorder.{u1} (Submodule.{0, u1} Nat M Nat.semiring _inst_3 (AddCommMonoid.natModule.{u1} M _inst_3)) (CompleteSemilatticeInf.toPartialOrder.{u1} (Submodule.{0, u1} Nat M Nat.semiring _inst_3 (AddCommMonoid.natModule.{u1} M _inst_3)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (Submodule.{0, u1} Nat M Nat.semiring _inst_3 (AddCommMonoid.natModule.{u1} M _inst_3)) (Submodule.completeLattice.{0, u1} Nat M Nat.semiring _inst_3 (AddCommMonoid.natModule.{u1} M _inst_3))))))) (fun (_x : RelIso.{u1, u1} (AddSubmonoid.{u1} M (AddMonoid.toAddZeroClass.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3))) (Submodule.{0, u1} Nat M Nat.semiring _inst_3 (AddCommMonoid.natModule.{u1} M _inst_3)) (LE.le.{u1} (AddSubmonoid.{u1} M (AddMonoid.toAddZeroClass.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3))) (Preorder.toHasLe.{u1} (AddSubmonoid.{u1} M (AddMonoid.toAddZeroClass.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3))) (PartialOrder.toPreorder.{u1} (AddSubmonoid.{u1} M (AddMonoid.toAddZeroClass.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3))) (CompleteSemilatticeInf.toPartialOrder.{u1} (AddSubmonoid.{u1} M (AddMonoid.toAddZeroClass.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3))) (CompleteLattice.toCompleteSemilatticeInf.{u1} (AddSubmonoid.{u1} M (AddMonoid.toAddZeroClass.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3))) (AddSubmonoid.completeLattice.{u1} M (AddMonoid.toAddZeroClass.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3)))))))) (LE.le.{u1} (Submodule.{0, u1} Nat M Nat.semiring _inst_3 (AddCommMonoid.natModule.{u1} M _inst_3)) (Preorder.toHasLe.{u1} (Submodule.{0, u1} Nat M Nat.semiring _inst_3 (AddCommMonoid.natModule.{u1} M _inst_3)) (PartialOrder.toPreorder.{u1} (Submodule.{0, u1} Nat M Nat.semiring _inst_3 (AddCommMonoid.natModule.{u1} M _inst_3)) (CompleteSemilatticeInf.toPartialOrder.{u1} (Submodule.{0, u1} Nat M Nat.semiring _inst_3 (AddCommMonoid.natModule.{u1} M _inst_3)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (Submodule.{0, u1} Nat M Nat.semiring _inst_3 (AddCommMonoid.natModule.{u1} M _inst_3)) (Submodule.completeLattice.{0, u1} Nat M Nat.semiring _inst_3 (AddCommMonoid.natModule.{u1} M _inst_3)))))))) => (AddSubmonoid.{u1} M (AddMonoid.toAddZeroClass.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3))) -> (Submodule.{0, u1} Nat M Nat.semiring _inst_3 (AddCommMonoid.natModule.{u1} M _inst_3))) (RelIso.hasCoeToFun.{u1, u1} (AddSubmonoid.{u1} M (AddMonoid.toAddZeroClass.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3))) (Submodule.{0, u1} Nat M Nat.semiring _inst_3 (AddCommMonoid.natModule.{u1} M _inst_3)) (LE.le.{u1} (AddSubmonoid.{u1} M (AddMonoid.toAddZeroClass.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3))) (Preorder.toHasLe.{u1} (AddSubmonoid.{u1} M (AddMonoid.toAddZeroClass.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3))) (PartialOrder.toPreorder.{u1} (AddSubmonoid.{u1} M (AddMonoid.toAddZeroClass.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3))) (CompleteSemilatticeInf.toPartialOrder.{u1} (AddSubmonoid.{u1} M (AddMonoid.toAddZeroClass.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3))) (CompleteLattice.toCompleteSemilatticeInf.{u1} (AddSubmonoid.{u1} M (AddMonoid.toAddZeroClass.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3))) (AddSubmonoid.completeLattice.{u1} M (AddMonoid.toAddZeroClass.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3)))))))) (LE.le.{u1} (Submodule.{0, u1} Nat M Nat.semiring _inst_3 (AddCommMonoid.natModule.{u1} M _inst_3)) (Preorder.toHasLe.{u1} (Submodule.{0, u1} Nat M Nat.semiring _inst_3 (AddCommMonoid.natModule.{u1} M _inst_3)) (PartialOrder.toPreorder.{u1} (Submodule.{0, u1} Nat M Nat.semiring _inst_3 (AddCommMonoid.natModule.{u1} M _inst_3)) (CompleteSemilatticeInf.toPartialOrder.{u1} (Submodule.{0, u1} Nat M Nat.semiring _inst_3 (AddCommMonoid.natModule.{u1} M _inst_3)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (Submodule.{0, u1} Nat M Nat.semiring _inst_3 (AddCommMonoid.natModule.{u1} M _inst_3)) (Submodule.completeLattice.{0, u1} Nat M Nat.semiring _inst_3 (AddCommMonoid.natModule.{u1} M _inst_3)))))))) (AddSubmonoid.toNatSubmodule.{u1} M _inst_3) (Submodule.toAddSubmonoid.{0, u1} Nat M Nat.semiring _inst_3 (AddCommMonoid.natModule.{u1} M _inst_3) S)) S
 but is expected to have type
-  forall {M : Type.{u1}} [_inst_3 : AddCommMonoid.{u1} M] (S : Submodule.{0, u1} Nat M Nat.semiring _inst_3 (AddCommMonoid.natModule.{u1} M _inst_3)), Eq.{succ u1} (Submodule.{0, u1} Nat M Nat.semiring _inst_3 (AddCommMonoid.natModule.{u1} M _inst_3)) (FunLike.coe.{succ u1, succ u1, succ u1} (RelIso.{u1, u1} (AddSubmonoid.{u1} M (AddMonoid.toAddZeroClass.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3))) (Submodule.{0, u1} Nat M Nat.semiring _inst_3 (AddCommMonoid.natModule.{u1} M _inst_3)) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1281 : AddSubmonoid.{u1} M (AddMonoid.toAddZeroClass.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3))) (x._@.Mathlib.Order.Hom.Basic._hyg.1283 : AddSubmonoid.{u1} M (AddMonoid.toAddZeroClass.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3))) => LE.le.{u1} (AddSubmonoid.{u1} M (AddMonoid.toAddZeroClass.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3))) (Preorder.toLE.{u1} (AddSubmonoid.{u1} M (AddMonoid.toAddZeroClass.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3))) (PartialOrder.toPreorder.{u1} (AddSubmonoid.{u1} M (AddMonoid.toAddZeroClass.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3))) (CompleteSemilatticeInf.toPartialOrder.{u1} (AddSubmonoid.{u1} M (AddMonoid.toAddZeroClass.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3))) (CompleteLattice.toCompleteSemilatticeInf.{u1} (AddSubmonoid.{u1} M (AddMonoid.toAddZeroClass.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3))) (AddSubmonoid.instCompleteLatticeAddSubmonoid.{u1} M (AddMonoid.toAddZeroClass.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3))))))) x._@.Mathlib.Order.Hom.Basic._hyg.1281 x._@.Mathlib.Order.Hom.Basic._hyg.1283) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1296 : Submodule.{0, u1} Nat M Nat.semiring _inst_3 (AddCommMonoid.natModule.{u1} M _inst_3)) (x._@.Mathlib.Order.Hom.Basic._hyg.1298 : Submodule.{0, u1} Nat M Nat.semiring _inst_3 (AddCommMonoid.natModule.{u1} M _inst_3)) => LE.le.{u1} (Submodule.{0, u1} Nat M Nat.semiring _inst_3 (AddCommMonoid.natModule.{u1} M _inst_3)) (Preorder.toLE.{u1} (Submodule.{0, u1} Nat M Nat.semiring _inst_3 (AddCommMonoid.natModule.{u1} M _inst_3)) (PartialOrder.toPreorder.{u1} (Submodule.{0, u1} Nat M Nat.semiring _inst_3 (AddCommMonoid.natModule.{u1} M _inst_3)) (CompleteSemilatticeInf.toPartialOrder.{u1} (Submodule.{0, u1} Nat M Nat.semiring _inst_3 (AddCommMonoid.natModule.{u1} M _inst_3)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (Submodule.{0, u1} Nat M Nat.semiring _inst_3 (AddCommMonoid.natModule.{u1} M _inst_3)) (Submodule.completeLattice.{0, u1} Nat M Nat.semiring _inst_3 (AddCommMonoid.natModule.{u1} M _inst_3)))))) x._@.Mathlib.Order.Hom.Basic._hyg.1296 x._@.Mathlib.Order.Hom.Basic._hyg.1298)) (AddSubmonoid.{u1} M (AddMonoid.toAddZeroClass.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3))) (fun (_x : AddSubmonoid.{u1} M (AddMonoid.toAddZeroClass.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3))) => Submodule.{0, u1} Nat M Nat.semiring _inst_3 (AddCommMonoid.natModule.{u1} M _inst_3)) (RelHomClass.toFunLike.{u1, u1, u1} (RelIso.{u1, u1} (AddSubmonoid.{u1} M (AddMonoid.toAddZeroClass.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3))) (Submodule.{0, u1} Nat M Nat.semiring _inst_3 (AddCommMonoid.natModule.{u1} M _inst_3)) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1281 : AddSubmonoid.{u1} M (AddMonoid.toAddZeroClass.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3))) (x._@.Mathlib.Order.Hom.Basic._hyg.1283 : AddSubmonoid.{u1} M (AddMonoid.toAddZeroClass.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3))) => LE.le.{u1} (AddSubmonoid.{u1} M (AddMonoid.toAddZeroClass.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3))) (Preorder.toLE.{u1} (AddSubmonoid.{u1} M (AddMonoid.toAddZeroClass.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3))) (PartialOrder.toPreorder.{u1} (AddSubmonoid.{u1} M (AddMonoid.toAddZeroClass.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3))) (CompleteSemilatticeInf.toPartialOrder.{u1} (AddSubmonoid.{u1} M (AddMonoid.toAddZeroClass.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3))) (CompleteLattice.toCompleteSemilatticeInf.{u1} (AddSubmonoid.{u1} M (AddMonoid.toAddZeroClass.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3))) (AddSubmonoid.instCompleteLatticeAddSubmonoid.{u1} M (AddMonoid.toAddZeroClass.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3))))))) x._@.Mathlib.Order.Hom.Basic._hyg.1281 x._@.Mathlib.Order.Hom.Basic._hyg.1283) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1296 : Submodule.{0, u1} Nat M Nat.semiring _inst_3 (AddCommMonoid.natModule.{u1} M _inst_3)) (x._@.Mathlib.Order.Hom.Basic._hyg.1298 : Submodule.{0, u1} Nat M Nat.semiring _inst_3 (AddCommMonoid.natModule.{u1} M _inst_3)) => LE.le.{u1} (Submodule.{0, u1} Nat M Nat.semiring _inst_3 (AddCommMonoid.natModule.{u1} M _inst_3)) (Preorder.toLE.{u1} (Submodule.{0, u1} Nat M Nat.semiring _inst_3 (AddCommMonoid.natModule.{u1} M _inst_3)) (PartialOrder.toPreorder.{u1} (Submodule.{0, u1} Nat M Nat.semiring _inst_3 (AddCommMonoid.natModule.{u1} M _inst_3)) (CompleteSemilatticeInf.toPartialOrder.{u1} (Submodule.{0, u1} Nat M Nat.semiring _inst_3 (AddCommMonoid.natModule.{u1} M _inst_3)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (Submodule.{0, u1} Nat M Nat.semiring _inst_3 (AddCommMonoid.natModule.{u1} M _inst_3)) (Submodule.completeLattice.{0, u1} Nat M Nat.semiring _inst_3 (AddCommMonoid.natModule.{u1} M _inst_3)))))) x._@.Mathlib.Order.Hom.Basic._hyg.1296 x._@.Mathlib.Order.Hom.Basic._hyg.1298)) (AddSubmonoid.{u1} M (AddMonoid.toAddZeroClass.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3))) (Submodule.{0, u1} Nat M Nat.semiring _inst_3 (AddCommMonoid.natModule.{u1} M _inst_3)) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1281 : AddSubmonoid.{u1} M (AddMonoid.toAddZeroClass.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3))) (x._@.Mathlib.Order.Hom.Basic._hyg.1283 : AddSubmonoid.{u1} M (AddMonoid.toAddZeroClass.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3))) => LE.le.{u1} (AddSubmonoid.{u1} M (AddMonoid.toAddZeroClass.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3))) (Preorder.toLE.{u1} (AddSubmonoid.{u1} M (AddMonoid.toAddZeroClass.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3))) (PartialOrder.toPreorder.{u1} (AddSubmonoid.{u1} M (AddMonoid.toAddZeroClass.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3))) (CompleteSemilatticeInf.toPartialOrder.{u1} (AddSubmonoid.{u1} M (AddMonoid.toAddZeroClass.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3))) (CompleteLattice.toCompleteSemilatticeInf.{u1} (AddSubmonoid.{u1} M (AddMonoid.toAddZeroClass.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3))) (AddSubmonoid.instCompleteLatticeAddSubmonoid.{u1} M (AddMonoid.toAddZeroClass.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3))))))) x._@.Mathlib.Order.Hom.Basic._hyg.1281 x._@.Mathlib.Order.Hom.Basic._hyg.1283) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1296 : Submodule.{0, u1} Nat M Nat.semiring _inst_3 (AddCommMonoid.natModule.{u1} M _inst_3)) (x._@.Mathlib.Order.Hom.Basic._hyg.1298 : Submodule.{0, u1} Nat M Nat.semiring _inst_3 (AddCommMonoid.natModule.{u1} M _inst_3)) => LE.le.{u1} (Submodule.{0, u1} Nat M Nat.semiring _inst_3 (AddCommMonoid.natModule.{u1} M _inst_3)) (Preorder.toLE.{u1} (Submodule.{0, u1} Nat M Nat.semiring _inst_3 (AddCommMonoid.natModule.{u1} M _inst_3)) (PartialOrder.toPreorder.{u1} (Submodule.{0, u1} Nat M Nat.semiring _inst_3 (AddCommMonoid.natModule.{u1} M _inst_3)) (CompleteSemilatticeInf.toPartialOrder.{u1} (Submodule.{0, u1} Nat M Nat.semiring _inst_3 (AddCommMonoid.natModule.{u1} M _inst_3)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (Submodule.{0, u1} Nat M Nat.semiring _inst_3 (AddCommMonoid.natModule.{u1} M _inst_3)) (Submodule.completeLattice.{0, u1} Nat M Nat.semiring _inst_3 (AddCommMonoid.natModule.{u1} M _inst_3)))))) x._@.Mathlib.Order.Hom.Basic._hyg.1296 x._@.Mathlib.Order.Hom.Basic._hyg.1298) (RelIso.instRelHomClassRelIso.{u1, u1} (AddSubmonoid.{u1} M (AddMonoid.toAddZeroClass.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3))) (Submodule.{0, u1} Nat M Nat.semiring _inst_3 (AddCommMonoid.natModule.{u1} M _inst_3)) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1281 : AddSubmonoid.{u1} M (AddMonoid.toAddZeroClass.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3))) (x._@.Mathlib.Order.Hom.Basic._hyg.1283 : AddSubmonoid.{u1} M (AddMonoid.toAddZeroClass.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3))) => LE.le.{u1} (AddSubmonoid.{u1} M (AddMonoid.toAddZeroClass.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3))) (Preorder.toLE.{u1} (AddSubmonoid.{u1} M (AddMonoid.toAddZeroClass.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3))) (PartialOrder.toPreorder.{u1} (AddSubmonoid.{u1} M (AddMonoid.toAddZeroClass.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3))) (CompleteSemilatticeInf.toPartialOrder.{u1} (AddSubmonoid.{u1} M (AddMonoid.toAddZeroClass.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3))) (CompleteLattice.toCompleteSemilatticeInf.{u1} (AddSubmonoid.{u1} M (AddMonoid.toAddZeroClass.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3))) (AddSubmonoid.instCompleteLatticeAddSubmonoid.{u1} M (AddMonoid.toAddZeroClass.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3))))))) x._@.Mathlib.Order.Hom.Basic._hyg.1281 x._@.Mathlib.Order.Hom.Basic._hyg.1283) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1296 : Submodule.{0, u1} Nat M Nat.semiring _inst_3 (AddCommMonoid.natModule.{u1} M _inst_3)) (x._@.Mathlib.Order.Hom.Basic._hyg.1298 : Submodule.{0, u1} Nat M Nat.semiring _inst_3 (AddCommMonoid.natModule.{u1} M _inst_3)) => LE.le.{u1} (Submodule.{0, u1} Nat M Nat.semiring _inst_3 (AddCommMonoid.natModule.{u1} M _inst_3)) (Preorder.toLE.{u1} (Submodule.{0, u1} Nat M Nat.semiring _inst_3 (AddCommMonoid.natModule.{u1} M _inst_3)) (PartialOrder.toPreorder.{u1} (Submodule.{0, u1} Nat M Nat.semiring _inst_3 (AddCommMonoid.natModule.{u1} M _inst_3)) (CompleteSemilatticeInf.toPartialOrder.{u1} (Submodule.{0, u1} Nat M Nat.semiring _inst_3 (AddCommMonoid.natModule.{u1} M _inst_3)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (Submodule.{0, u1} Nat M Nat.semiring _inst_3 (AddCommMonoid.natModule.{u1} M _inst_3)) (Submodule.completeLattice.{0, u1} Nat M Nat.semiring _inst_3 (AddCommMonoid.natModule.{u1} M _inst_3)))))) x._@.Mathlib.Order.Hom.Basic._hyg.1296 x._@.Mathlib.Order.Hom.Basic._hyg.1298))) (AddSubmonoid.toNatSubmodule.{u1} M _inst_3) (Submodule.toAddSubmonoid.{0, u1} Nat M Nat.semiring _inst_3 (AddCommMonoid.natModule.{u1} M _inst_3) S)) S
+  forall {M : Type.{u1}} [_inst_3 : AddCommMonoid.{u1} M] (S : Submodule.{0, u1} Nat M Nat.semiring _inst_3 (AddCommMonoid.natModule.{u1} M _inst_3)), Eq.{succ u1} (Submodule.{0, u1} Nat M Nat.semiring _inst_3 (AddCommMonoid.natModule.{u1} M _inst_3)) (FunLike.coe.{succ u1, succ u1, succ u1} (RelIso.{u1, u1} (AddSubmonoid.{u1} M (AddMonoid.toAddZeroClass.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3))) (Submodule.{0, u1} Nat M Nat.semiring _inst_3 (AddCommMonoid.natModule.{u1} M _inst_3)) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1285 : AddSubmonoid.{u1} M (AddMonoid.toAddZeroClass.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3))) (x._@.Mathlib.Order.Hom.Basic._hyg.1287 : AddSubmonoid.{u1} M (AddMonoid.toAddZeroClass.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3))) => LE.le.{u1} (AddSubmonoid.{u1} M (AddMonoid.toAddZeroClass.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3))) (Preorder.toLE.{u1} (AddSubmonoid.{u1} M (AddMonoid.toAddZeroClass.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3))) (PartialOrder.toPreorder.{u1} (AddSubmonoid.{u1} M (AddMonoid.toAddZeroClass.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3))) (CompleteSemilatticeInf.toPartialOrder.{u1} (AddSubmonoid.{u1} M (AddMonoid.toAddZeroClass.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3))) (CompleteLattice.toCompleteSemilatticeInf.{u1} (AddSubmonoid.{u1} M (AddMonoid.toAddZeroClass.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3))) (AddSubmonoid.instCompleteLatticeAddSubmonoid.{u1} M (AddMonoid.toAddZeroClass.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3))))))) x._@.Mathlib.Order.Hom.Basic._hyg.1285 x._@.Mathlib.Order.Hom.Basic._hyg.1287) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1300 : Submodule.{0, u1} Nat M Nat.semiring _inst_3 (AddCommMonoid.natModule.{u1} M _inst_3)) (x._@.Mathlib.Order.Hom.Basic._hyg.1302 : Submodule.{0, u1} Nat M Nat.semiring _inst_3 (AddCommMonoid.natModule.{u1} M _inst_3)) => LE.le.{u1} (Submodule.{0, u1} Nat M Nat.semiring _inst_3 (AddCommMonoid.natModule.{u1} M _inst_3)) (Preorder.toLE.{u1} (Submodule.{0, u1} Nat M Nat.semiring _inst_3 (AddCommMonoid.natModule.{u1} M _inst_3)) (PartialOrder.toPreorder.{u1} (Submodule.{0, u1} Nat M Nat.semiring _inst_3 (AddCommMonoid.natModule.{u1} M _inst_3)) (CompleteSemilatticeInf.toPartialOrder.{u1} (Submodule.{0, u1} Nat M Nat.semiring _inst_3 (AddCommMonoid.natModule.{u1} M _inst_3)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (Submodule.{0, u1} Nat M Nat.semiring _inst_3 (AddCommMonoid.natModule.{u1} M _inst_3)) (Submodule.completeLattice.{0, u1} Nat M Nat.semiring _inst_3 (AddCommMonoid.natModule.{u1} M _inst_3)))))) x._@.Mathlib.Order.Hom.Basic._hyg.1300 x._@.Mathlib.Order.Hom.Basic._hyg.1302)) (AddSubmonoid.{u1} M (AddMonoid.toAddZeroClass.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3))) (fun (_x : AddSubmonoid.{u1} M (AddMonoid.toAddZeroClass.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3))) => Submodule.{0, u1} Nat M Nat.semiring _inst_3 (AddCommMonoid.natModule.{u1} M _inst_3)) (RelHomClass.toFunLike.{u1, u1, u1} (RelIso.{u1, u1} (AddSubmonoid.{u1} M (AddMonoid.toAddZeroClass.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3))) (Submodule.{0, u1} Nat M Nat.semiring _inst_3 (AddCommMonoid.natModule.{u1} M _inst_3)) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1285 : AddSubmonoid.{u1} M (AddMonoid.toAddZeroClass.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3))) (x._@.Mathlib.Order.Hom.Basic._hyg.1287 : AddSubmonoid.{u1} M (AddMonoid.toAddZeroClass.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3))) => LE.le.{u1} (AddSubmonoid.{u1} M (AddMonoid.toAddZeroClass.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3))) (Preorder.toLE.{u1} (AddSubmonoid.{u1} M (AddMonoid.toAddZeroClass.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3))) (PartialOrder.toPreorder.{u1} (AddSubmonoid.{u1} M (AddMonoid.toAddZeroClass.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3))) (CompleteSemilatticeInf.toPartialOrder.{u1} (AddSubmonoid.{u1} M (AddMonoid.toAddZeroClass.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3))) (CompleteLattice.toCompleteSemilatticeInf.{u1} (AddSubmonoid.{u1} M (AddMonoid.toAddZeroClass.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3))) (AddSubmonoid.instCompleteLatticeAddSubmonoid.{u1} M (AddMonoid.toAddZeroClass.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3))))))) x._@.Mathlib.Order.Hom.Basic._hyg.1285 x._@.Mathlib.Order.Hom.Basic._hyg.1287) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1300 : Submodule.{0, u1} Nat M Nat.semiring _inst_3 (AddCommMonoid.natModule.{u1} M _inst_3)) (x._@.Mathlib.Order.Hom.Basic._hyg.1302 : Submodule.{0, u1} Nat M Nat.semiring _inst_3 (AddCommMonoid.natModule.{u1} M _inst_3)) => LE.le.{u1} (Submodule.{0, u1} Nat M Nat.semiring _inst_3 (AddCommMonoid.natModule.{u1} M _inst_3)) (Preorder.toLE.{u1} (Submodule.{0, u1} Nat M Nat.semiring _inst_3 (AddCommMonoid.natModule.{u1} M _inst_3)) (PartialOrder.toPreorder.{u1} (Submodule.{0, u1} Nat M Nat.semiring _inst_3 (AddCommMonoid.natModule.{u1} M _inst_3)) (CompleteSemilatticeInf.toPartialOrder.{u1} (Submodule.{0, u1} Nat M Nat.semiring _inst_3 (AddCommMonoid.natModule.{u1} M _inst_3)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (Submodule.{0, u1} Nat M Nat.semiring _inst_3 (AddCommMonoid.natModule.{u1} M _inst_3)) (Submodule.completeLattice.{0, u1} Nat M Nat.semiring _inst_3 (AddCommMonoid.natModule.{u1} M _inst_3)))))) x._@.Mathlib.Order.Hom.Basic._hyg.1300 x._@.Mathlib.Order.Hom.Basic._hyg.1302)) (AddSubmonoid.{u1} M (AddMonoid.toAddZeroClass.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3))) (Submodule.{0, u1} Nat M Nat.semiring _inst_3 (AddCommMonoid.natModule.{u1} M _inst_3)) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1285 : AddSubmonoid.{u1} M (AddMonoid.toAddZeroClass.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3))) (x._@.Mathlib.Order.Hom.Basic._hyg.1287 : AddSubmonoid.{u1} M (AddMonoid.toAddZeroClass.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3))) => LE.le.{u1} (AddSubmonoid.{u1} M (AddMonoid.toAddZeroClass.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3))) (Preorder.toLE.{u1} (AddSubmonoid.{u1} M (AddMonoid.toAddZeroClass.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3))) (PartialOrder.toPreorder.{u1} (AddSubmonoid.{u1} M (AddMonoid.toAddZeroClass.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3))) (CompleteSemilatticeInf.toPartialOrder.{u1} (AddSubmonoid.{u1} M (AddMonoid.toAddZeroClass.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3))) (CompleteLattice.toCompleteSemilatticeInf.{u1} (AddSubmonoid.{u1} M (AddMonoid.toAddZeroClass.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3))) (AddSubmonoid.instCompleteLatticeAddSubmonoid.{u1} M (AddMonoid.toAddZeroClass.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3))))))) x._@.Mathlib.Order.Hom.Basic._hyg.1285 x._@.Mathlib.Order.Hom.Basic._hyg.1287) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1300 : Submodule.{0, u1} Nat M Nat.semiring _inst_3 (AddCommMonoid.natModule.{u1} M _inst_3)) (x._@.Mathlib.Order.Hom.Basic._hyg.1302 : Submodule.{0, u1} Nat M Nat.semiring _inst_3 (AddCommMonoid.natModule.{u1} M _inst_3)) => LE.le.{u1} (Submodule.{0, u1} Nat M Nat.semiring _inst_3 (AddCommMonoid.natModule.{u1} M _inst_3)) (Preorder.toLE.{u1} (Submodule.{0, u1} Nat M Nat.semiring _inst_3 (AddCommMonoid.natModule.{u1} M _inst_3)) (PartialOrder.toPreorder.{u1} (Submodule.{0, u1} Nat M Nat.semiring _inst_3 (AddCommMonoid.natModule.{u1} M _inst_3)) (CompleteSemilatticeInf.toPartialOrder.{u1} (Submodule.{0, u1} Nat M Nat.semiring _inst_3 (AddCommMonoid.natModule.{u1} M _inst_3)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (Submodule.{0, u1} Nat M Nat.semiring _inst_3 (AddCommMonoid.natModule.{u1} M _inst_3)) (Submodule.completeLattice.{0, u1} Nat M Nat.semiring _inst_3 (AddCommMonoid.natModule.{u1} M _inst_3)))))) x._@.Mathlib.Order.Hom.Basic._hyg.1300 x._@.Mathlib.Order.Hom.Basic._hyg.1302) (RelIso.instRelHomClassRelIso.{u1, u1} (AddSubmonoid.{u1} M (AddMonoid.toAddZeroClass.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3))) (Submodule.{0, u1} Nat M Nat.semiring _inst_3 (AddCommMonoid.natModule.{u1} M _inst_3)) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1285 : AddSubmonoid.{u1} M (AddMonoid.toAddZeroClass.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3))) (x._@.Mathlib.Order.Hom.Basic._hyg.1287 : AddSubmonoid.{u1} M (AddMonoid.toAddZeroClass.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3))) => LE.le.{u1} (AddSubmonoid.{u1} M (AddMonoid.toAddZeroClass.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3))) (Preorder.toLE.{u1} (AddSubmonoid.{u1} M (AddMonoid.toAddZeroClass.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3))) (PartialOrder.toPreorder.{u1} (AddSubmonoid.{u1} M (AddMonoid.toAddZeroClass.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3))) (CompleteSemilatticeInf.toPartialOrder.{u1} (AddSubmonoid.{u1} M (AddMonoid.toAddZeroClass.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3))) (CompleteLattice.toCompleteSemilatticeInf.{u1} (AddSubmonoid.{u1} M (AddMonoid.toAddZeroClass.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3))) (AddSubmonoid.instCompleteLatticeAddSubmonoid.{u1} M (AddMonoid.toAddZeroClass.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3))))))) x._@.Mathlib.Order.Hom.Basic._hyg.1285 x._@.Mathlib.Order.Hom.Basic._hyg.1287) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1300 : Submodule.{0, u1} Nat M Nat.semiring _inst_3 (AddCommMonoid.natModule.{u1} M _inst_3)) (x._@.Mathlib.Order.Hom.Basic._hyg.1302 : Submodule.{0, u1} Nat M Nat.semiring _inst_3 (AddCommMonoid.natModule.{u1} M _inst_3)) => LE.le.{u1} (Submodule.{0, u1} Nat M Nat.semiring _inst_3 (AddCommMonoid.natModule.{u1} M _inst_3)) (Preorder.toLE.{u1} (Submodule.{0, u1} Nat M Nat.semiring _inst_3 (AddCommMonoid.natModule.{u1} M _inst_3)) (PartialOrder.toPreorder.{u1} (Submodule.{0, u1} Nat M Nat.semiring _inst_3 (AddCommMonoid.natModule.{u1} M _inst_3)) (CompleteSemilatticeInf.toPartialOrder.{u1} (Submodule.{0, u1} Nat M Nat.semiring _inst_3 (AddCommMonoid.natModule.{u1} M _inst_3)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (Submodule.{0, u1} Nat M Nat.semiring _inst_3 (AddCommMonoid.natModule.{u1} M _inst_3)) (Submodule.completeLattice.{0, u1} Nat M Nat.semiring _inst_3 (AddCommMonoid.natModule.{u1} M _inst_3)))))) x._@.Mathlib.Order.Hom.Basic._hyg.1300 x._@.Mathlib.Order.Hom.Basic._hyg.1302))) (AddSubmonoid.toNatSubmodule.{u1} M _inst_3) (Submodule.toAddSubmonoid.{0, u1} Nat M Nat.semiring _inst_3 (AddCommMonoid.natModule.{u1} M _inst_3) S)) S
 Case conversion may be inaccurate. Consider using '#align submodule.to_add_submonoid_to_nat_submodule Submodule.toAddSubmonoid_toNatSubmoduleₓ'. -/
 @[simp]
 theorem Submodule.toAddSubmonoid_toNatSubmodule (S : Submodule ℕ M) :
@@ -694,7 +694,7 @@ def AddSubgroup.toIntSubmodule : AddSubgroup M ≃o Submodule ℤ M
 lean 3 declaration is
   forall {M : Type.{u1}} [_inst_1 : AddCommGroup.{u1} M], Eq.{succ u1} ((Submodule.{0, u1} Int M Int.semiring (AddCommGroup.toAddCommMonoid.{u1} M _inst_1) (AddCommGroup.intModule.{u1} M _inst_1)) -> (AddSubgroup.{u1} M (AddCommGroup.toAddGroup.{u1} M _inst_1))) (coeFn.{succ u1, succ u1} (OrderIso.{u1, u1} (Submodule.{0, u1} Int M Int.semiring (AddCommGroup.toAddCommMonoid.{u1} M _inst_1) (AddCommGroup.intModule.{u1} M _inst_1)) (AddSubgroup.{u1} M (AddCommGroup.toAddGroup.{u1} M _inst_1)) (Preorder.toHasLe.{u1} (Submodule.{0, u1} Int M Int.semiring (AddCommGroup.toAddCommMonoid.{u1} M _inst_1) (AddCommGroup.intModule.{u1} M _inst_1)) (PartialOrder.toPreorder.{u1} (Submodule.{0, u1} Int M Int.semiring (AddCommGroup.toAddCommMonoid.{u1} M _inst_1) (AddCommGroup.intModule.{u1} M _inst_1)) (CompleteSemilatticeInf.toPartialOrder.{u1} (Submodule.{0, u1} Int M Int.semiring (AddCommGroup.toAddCommMonoid.{u1} M _inst_1) (AddCommGroup.intModule.{u1} M _inst_1)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (Submodule.{0, u1} Int M Int.semiring (AddCommGroup.toAddCommMonoid.{u1} M _inst_1) (AddCommGroup.intModule.{u1} M _inst_1)) (Submodule.completeLattice.{0, u1} Int M Int.semiring (AddCommGroup.toAddCommMonoid.{u1} M _inst_1) (AddCommGroup.intModule.{u1} M _inst_1)))))) (Preorder.toHasLe.{u1} (AddSubgroup.{u1} M (AddCommGroup.toAddGroup.{u1} M _inst_1)) (PartialOrder.toPreorder.{u1} (AddSubgroup.{u1} M (AddCommGroup.toAddGroup.{u1} M _inst_1)) (CompleteSemilatticeInf.toPartialOrder.{u1} (AddSubgroup.{u1} M (AddCommGroup.toAddGroup.{u1} M _inst_1)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (AddSubgroup.{u1} M (AddCommGroup.toAddGroup.{u1} M _inst_1)) (AddSubgroup.completeLattice.{u1} M (AddCommGroup.toAddGroup.{u1} M _inst_1))))))) (fun (_x : RelIso.{u1, u1} (Submodule.{0, u1} Int M Int.semiring (AddCommGroup.toAddCommMonoid.{u1} M _inst_1) (AddCommGroup.intModule.{u1} M _inst_1)) (AddSubgroup.{u1} M (AddCommGroup.toAddGroup.{u1} M _inst_1)) (LE.le.{u1} (Submodule.{0, u1} Int M Int.semiring (AddCommGroup.toAddCommMonoid.{u1} M _inst_1) (AddCommGroup.intModule.{u1} M _inst_1)) (Preorder.toHasLe.{u1} (Submodule.{0, u1} Int M Int.semiring (AddCommGroup.toAddCommMonoid.{u1} M _inst_1) (AddCommGroup.intModule.{u1} M _inst_1)) (PartialOrder.toPreorder.{u1} (Submodule.{0, u1} Int M Int.semiring (AddCommGroup.toAddCommMonoid.{u1} M _inst_1) (AddCommGroup.intModule.{u1} M _inst_1)) (CompleteSemilatticeInf.toPartialOrder.{u1} (Submodule.{0, u1} Int M Int.semiring (AddCommGroup.toAddCommMonoid.{u1} M _inst_1) (AddCommGroup.intModule.{u1} M _inst_1)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (Submodule.{0, u1} Int M Int.semiring (AddCommGroup.toAddCommMonoid.{u1} M _inst_1) (AddCommGroup.intModule.{u1} M _inst_1)) (Submodule.completeLattice.{0, u1} Int M Int.semiring (AddCommGroup.toAddCommMonoid.{u1} M _inst_1) (AddCommGroup.intModule.{u1} M _inst_1))))))) (LE.le.{u1} (AddSubgroup.{u1} M (AddCommGroup.toAddGroup.{u1} M _inst_1)) (Preorder.toHasLe.{u1} (AddSubgroup.{u1} M (AddCommGroup.toAddGroup.{u1} M _inst_1)) (PartialOrder.toPreorder.{u1} (AddSubgroup.{u1} M (AddCommGroup.toAddGroup.{u1} M _inst_1)) (CompleteSemilatticeInf.toPartialOrder.{u1} (AddSubgroup.{u1} M (AddCommGroup.toAddGroup.{u1} M _inst_1)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (AddSubgroup.{u1} M (AddCommGroup.toAddGroup.{u1} M _inst_1)) (AddSubgroup.completeLattice.{u1} M (AddCommGroup.toAddGroup.{u1} M _inst_1)))))))) => (Submodule.{0, u1} Int M Int.semiring (AddCommGroup.toAddCommMonoid.{u1} M _inst_1) (AddCommGroup.intModule.{u1} M _inst_1)) -> (AddSubgroup.{u1} M (AddCommGroup.toAddGroup.{u1} M _inst_1))) (RelIso.hasCoeToFun.{u1, u1} (Submodule.{0, u1} Int M Int.semiring (AddCommGroup.toAddCommMonoid.{u1} M _inst_1) (AddCommGroup.intModule.{u1} M _inst_1)) (AddSubgroup.{u1} M (AddCommGroup.toAddGroup.{u1} M _inst_1)) (LE.le.{u1} (Submodule.{0, u1} Int M Int.semiring (AddCommGroup.toAddCommMonoid.{u1} M _inst_1) (AddCommGroup.intModule.{u1} M _inst_1)) (Preorder.toHasLe.{u1} (Submodule.{0, u1} Int M Int.semiring (AddCommGroup.toAddCommMonoid.{u1} M _inst_1) (AddCommGroup.intModule.{u1} M _inst_1)) (PartialOrder.toPreorder.{u1} (Submodule.{0, u1} Int M Int.semiring (AddCommGroup.toAddCommMonoid.{u1} M _inst_1) (AddCommGroup.intModule.{u1} M _inst_1)) (CompleteSemilatticeInf.toPartialOrder.{u1} (Submodule.{0, u1} Int M Int.semiring (AddCommGroup.toAddCommMonoid.{u1} M _inst_1) (AddCommGroup.intModule.{u1} M _inst_1)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (Submodule.{0, u1} Int M Int.semiring (AddCommGroup.toAddCommMonoid.{u1} M _inst_1) (AddCommGroup.intModule.{u1} M _inst_1)) (Submodule.completeLattice.{0, u1} Int M Int.semiring (AddCommGroup.toAddCommMonoid.{u1} M _inst_1) (AddCommGroup.intModule.{u1} M _inst_1))))))) (LE.le.{u1} (AddSubgroup.{u1} M (AddCommGroup.toAddGroup.{u1} M _inst_1)) (Preorder.toHasLe.{u1} (AddSubgroup.{u1} M (AddCommGroup.toAddGroup.{u1} M _inst_1)) (PartialOrder.toPreorder.{u1} (AddSubgroup.{u1} M (AddCommGroup.toAddGroup.{u1} M _inst_1)) (CompleteSemilatticeInf.toPartialOrder.{u1} (AddSubgroup.{u1} M (AddCommGroup.toAddGroup.{u1} M _inst_1)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (AddSubgroup.{u1} M (AddCommGroup.toAddGroup.{u1} M _inst_1)) (AddSubgroup.completeLattice.{u1} M (AddCommGroup.toAddGroup.{u1} M _inst_1)))))))) (OrderIso.symm.{u1, u1} (AddSubgroup.{u1} M (AddCommGroup.toAddGroup.{u1} M _inst_1)) (Submodule.{0, u1} Int M Int.semiring (AddCommGroup.toAddCommMonoid.{u1} M _inst_1) (AddCommGroup.intModule.{u1} M _inst_1)) (Preorder.toHasLe.{u1} (AddSubgroup.{u1} M (AddCommGroup.toAddGroup.{u1} M _inst_1)) (PartialOrder.toPreorder.{u1} (AddSubgroup.{u1} M (AddCommGroup.toAddGroup.{u1} M _inst_1)) (CompleteSemilatticeInf.toPartialOrder.{u1} (AddSubgroup.{u1} M (AddCommGroup.toAddGroup.{u1} M _inst_1)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (AddSubgroup.{u1} M (AddCommGroup.toAddGroup.{u1} M _inst_1)) (AddSubgroup.completeLattice.{u1} M (AddCommGroup.toAddGroup.{u1} M _inst_1)))))) (Preorder.toHasLe.{u1} (Submodule.{0, u1} Int M Int.semiring (AddCommGroup.toAddCommMonoid.{u1} M _inst_1) (AddCommGroup.intModule.{u1} M _inst_1)) (PartialOrder.toPreorder.{u1} (Submodule.{0, u1} Int M Int.semiring (AddCommGroup.toAddCommMonoid.{u1} M _inst_1) (AddCommGroup.intModule.{u1} M _inst_1)) (CompleteSemilatticeInf.toPartialOrder.{u1} (Submodule.{0, u1} Int M Int.semiring (AddCommGroup.toAddCommMonoid.{u1} M _inst_1) (AddCommGroup.intModule.{u1} M _inst_1)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (Submodule.{0, u1} Int M Int.semiring (AddCommGroup.toAddCommMonoid.{u1} M _inst_1) (AddCommGroup.intModule.{u1} M _inst_1)) (Submodule.completeLattice.{0, u1} Int M Int.semiring (AddCommGroup.toAddCommMonoid.{u1} M _inst_1) (AddCommGroup.intModule.{u1} M _inst_1)))))) (AddSubgroup.toIntSubmodule.{u1} M _inst_1))) (Submodule.toAddSubgroup.{0, u1} Int M Int.ring _inst_1 (AddCommGroup.intModule.{u1} M _inst_1))
 but is expected to have type
-  forall {M : Type.{u1}} [_inst_1 : AddCommGroup.{u1} M], Eq.{succ u1} ((Submodule.{0, u1} Int M Int.instSemiringInt (AddCommGroup.toAddCommMonoid.{u1} M _inst_1) (AddCommGroup.intModule.{u1} M _inst_1)) -> (AddSubgroup.{u1} M (AddCommGroup.toAddGroup.{u1} M _inst_1))) (FunLike.coe.{succ u1, succ u1, succ u1} (RelIso.{u1, u1} (Submodule.{0, u1} Int M Int.instSemiringInt (AddCommGroup.toAddCommMonoid.{u1} M _inst_1) (AddCommGroup.intModule.{u1} M _inst_1)) (AddSubgroup.{u1} M (AddCommGroup.toAddGroup.{u1} M _inst_1)) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1281 : Submodule.{0, u1} Int M Int.instSemiringInt (AddCommGroup.toAddCommMonoid.{u1} M _inst_1) (AddCommGroup.intModule.{u1} M _inst_1)) (x._@.Mathlib.Order.Hom.Basic._hyg.1283 : Submodule.{0, u1} Int M Int.instSemiringInt (AddCommGroup.toAddCommMonoid.{u1} M _inst_1) (AddCommGroup.intModule.{u1} M _inst_1)) => LE.le.{u1} (Submodule.{0, u1} Int M Int.instSemiringInt (AddCommGroup.toAddCommMonoid.{u1} M _inst_1) (AddCommGroup.intModule.{u1} M _inst_1)) (Preorder.toLE.{u1} (Submodule.{0, u1} Int M Int.instSemiringInt (AddCommGroup.toAddCommMonoid.{u1} M _inst_1) (AddCommGroup.intModule.{u1} M _inst_1)) (PartialOrder.toPreorder.{u1} (Submodule.{0, u1} Int M Int.instSemiringInt (AddCommGroup.toAddCommMonoid.{u1} M _inst_1) (AddCommGroup.intModule.{u1} M _inst_1)) (CompleteSemilatticeInf.toPartialOrder.{u1} (Submodule.{0, u1} Int M Int.instSemiringInt (AddCommGroup.toAddCommMonoid.{u1} M _inst_1) (AddCommGroup.intModule.{u1} M _inst_1)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (Submodule.{0, u1} Int M Int.instSemiringInt (AddCommGroup.toAddCommMonoid.{u1} M _inst_1) (AddCommGroup.intModule.{u1} M _inst_1)) (Submodule.completeLattice.{0, u1} Int M Int.instSemiringInt (AddCommGroup.toAddCommMonoid.{u1} M _inst_1) (AddCommGroup.intModule.{u1} M _inst_1)))))) x._@.Mathlib.Order.Hom.Basic._hyg.1281 x._@.Mathlib.Order.Hom.Basic._hyg.1283) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1296 : AddSubgroup.{u1} M (AddCommGroup.toAddGroup.{u1} M _inst_1)) (x._@.Mathlib.Order.Hom.Basic._hyg.1298 : AddSubgroup.{u1} M (AddCommGroup.toAddGroup.{u1} M _inst_1)) => LE.le.{u1} (AddSubgroup.{u1} M (AddCommGroup.toAddGroup.{u1} M _inst_1)) (Preorder.toLE.{u1} (AddSubgroup.{u1} M (AddCommGroup.toAddGroup.{u1} M _inst_1)) (PartialOrder.toPreorder.{u1} (AddSubgroup.{u1} M (AddCommGroup.toAddGroup.{u1} M _inst_1)) (CompleteSemilatticeInf.toPartialOrder.{u1} (AddSubgroup.{u1} M (AddCommGroup.toAddGroup.{u1} M _inst_1)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (AddSubgroup.{u1} M (AddCommGroup.toAddGroup.{u1} M _inst_1)) (AddSubgroup.instCompleteLatticeAddSubgroup.{u1} M (AddCommGroup.toAddGroup.{u1} M _inst_1)))))) x._@.Mathlib.Order.Hom.Basic._hyg.1296 x._@.Mathlib.Order.Hom.Basic._hyg.1298)) (Submodule.{0, u1} Int M Int.instSemiringInt (AddCommGroup.toAddCommMonoid.{u1} M _inst_1) (AddCommGroup.intModule.{u1} M _inst_1)) (fun (_x : Submodule.{0, u1} Int M Int.instSemiringInt (AddCommGroup.toAddCommMonoid.{u1} M _inst_1) (AddCommGroup.intModule.{u1} M _inst_1)) => AddSubgroup.{u1} M (AddCommGroup.toAddGroup.{u1} M _inst_1)) (RelHomClass.toFunLike.{u1, u1, u1} (RelIso.{u1, u1} (Submodule.{0, u1} Int M Int.instSemiringInt (AddCommGroup.toAddCommMonoid.{u1} M _inst_1) (AddCommGroup.intModule.{u1} M _inst_1)) (AddSubgroup.{u1} M (AddCommGroup.toAddGroup.{u1} M _inst_1)) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1281 : Submodule.{0, u1} Int M Int.instSemiringInt (AddCommGroup.toAddCommMonoid.{u1} M _inst_1) (AddCommGroup.intModule.{u1} M _inst_1)) (x._@.Mathlib.Order.Hom.Basic._hyg.1283 : Submodule.{0, u1} Int M Int.instSemiringInt (AddCommGroup.toAddCommMonoid.{u1} M _inst_1) (AddCommGroup.intModule.{u1} M _inst_1)) => LE.le.{u1} (Submodule.{0, u1} Int M Int.instSemiringInt (AddCommGroup.toAddCommMonoid.{u1} M _inst_1) (AddCommGroup.intModule.{u1} M _inst_1)) (Preorder.toLE.{u1} (Submodule.{0, u1} Int M Int.instSemiringInt (AddCommGroup.toAddCommMonoid.{u1} M _inst_1) (AddCommGroup.intModule.{u1} M _inst_1)) (PartialOrder.toPreorder.{u1} (Submodule.{0, u1} Int M Int.instSemiringInt (AddCommGroup.toAddCommMonoid.{u1} M _inst_1) (AddCommGroup.intModule.{u1} M _inst_1)) (CompleteSemilatticeInf.toPartialOrder.{u1} (Submodule.{0, u1} Int M Int.instSemiringInt (AddCommGroup.toAddCommMonoid.{u1} M _inst_1) (AddCommGroup.intModule.{u1} M _inst_1)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (Submodule.{0, u1} Int M Int.instSemiringInt (AddCommGroup.toAddCommMonoid.{u1} M _inst_1) (AddCommGroup.intModule.{u1} M _inst_1)) (Submodule.completeLattice.{0, u1} Int M Int.instSemiringInt (AddCommGroup.toAddCommMonoid.{u1} M _inst_1) (AddCommGroup.intModule.{u1} M _inst_1)))))) x._@.Mathlib.Order.Hom.Basic._hyg.1281 x._@.Mathlib.Order.Hom.Basic._hyg.1283) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1296 : AddSubgroup.{u1} M (AddCommGroup.toAddGroup.{u1} M _inst_1)) (x._@.Mathlib.Order.Hom.Basic._hyg.1298 : AddSubgroup.{u1} M (AddCommGroup.toAddGroup.{u1} M _inst_1)) => LE.le.{u1} (AddSubgroup.{u1} M (AddCommGroup.toAddGroup.{u1} M _inst_1)) (Preorder.toLE.{u1} (AddSubgroup.{u1} M (AddCommGroup.toAddGroup.{u1} M _inst_1)) (PartialOrder.toPreorder.{u1} (AddSubgroup.{u1} M (AddCommGroup.toAddGroup.{u1} M _inst_1)) (CompleteSemilatticeInf.toPartialOrder.{u1} (AddSubgroup.{u1} M (AddCommGroup.toAddGroup.{u1} M _inst_1)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (AddSubgroup.{u1} M (AddCommGroup.toAddGroup.{u1} M _inst_1)) (AddSubgroup.instCompleteLatticeAddSubgroup.{u1} M (AddCommGroup.toAddGroup.{u1} M _inst_1)))))) x._@.Mathlib.Order.Hom.Basic._hyg.1296 x._@.Mathlib.Order.Hom.Basic._hyg.1298)) (Submodule.{0, u1} Int M Int.instSemiringInt (AddCommGroup.toAddCommMonoid.{u1} M _inst_1) (AddCommGroup.intModule.{u1} M _inst_1)) (AddSubgroup.{u1} M (AddCommGroup.toAddGroup.{u1} M _inst_1)) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1281 : Submodule.{0, u1} Int M Int.instSemiringInt (AddCommGroup.toAddCommMonoid.{u1} M _inst_1) (AddCommGroup.intModule.{u1} M _inst_1)) (x._@.Mathlib.Order.Hom.Basic._hyg.1283 : Submodule.{0, u1} Int M Int.instSemiringInt (AddCommGroup.toAddCommMonoid.{u1} M _inst_1) (AddCommGroup.intModule.{u1} M _inst_1)) => LE.le.{u1} (Submodule.{0, u1} Int M Int.instSemiringInt (AddCommGroup.toAddCommMonoid.{u1} M _inst_1) (AddCommGroup.intModule.{u1} M _inst_1)) (Preorder.toLE.{u1} (Submodule.{0, u1} Int M Int.instSemiringInt (AddCommGroup.toAddCommMonoid.{u1} M _inst_1) (AddCommGroup.intModule.{u1} M _inst_1)) (PartialOrder.toPreorder.{u1} (Submodule.{0, u1} Int M Int.instSemiringInt (AddCommGroup.toAddCommMonoid.{u1} M _inst_1) (AddCommGroup.intModule.{u1} M _inst_1)) (CompleteSemilatticeInf.toPartialOrder.{u1} (Submodule.{0, u1} Int M Int.instSemiringInt (AddCommGroup.toAddCommMonoid.{u1} M _inst_1) (AddCommGroup.intModule.{u1} M _inst_1)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (Submodule.{0, u1} Int M Int.instSemiringInt (AddCommGroup.toAddCommMonoid.{u1} M _inst_1) (AddCommGroup.intModule.{u1} M _inst_1)) (Submodule.completeLattice.{0, u1} Int M Int.instSemiringInt (AddCommGroup.toAddCommMonoid.{u1} M _inst_1) (AddCommGroup.intModule.{u1} M _inst_1)))))) x._@.Mathlib.Order.Hom.Basic._hyg.1281 x._@.Mathlib.Order.Hom.Basic._hyg.1283) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1296 : AddSubgroup.{u1} M (AddCommGroup.toAddGroup.{u1} M _inst_1)) (x._@.Mathlib.Order.Hom.Basic._hyg.1298 : AddSubgroup.{u1} M (AddCommGroup.toAddGroup.{u1} M _inst_1)) => LE.le.{u1} (AddSubgroup.{u1} M (AddCommGroup.toAddGroup.{u1} M _inst_1)) (Preorder.toLE.{u1} (AddSubgroup.{u1} M (AddCommGroup.toAddGroup.{u1} M _inst_1)) (PartialOrder.toPreorder.{u1} (AddSubgroup.{u1} M (AddCommGroup.toAddGroup.{u1} M _inst_1)) (CompleteSemilatticeInf.toPartialOrder.{u1} (AddSubgroup.{u1} M (AddCommGroup.toAddGroup.{u1} M _inst_1)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (AddSubgroup.{u1} M (AddCommGroup.toAddGroup.{u1} M _inst_1)) (AddSubgroup.instCompleteLatticeAddSubgroup.{u1} M (AddCommGroup.toAddGroup.{u1} M _inst_1)))))) x._@.Mathlib.Order.Hom.Basic._hyg.1296 x._@.Mathlib.Order.Hom.Basic._hyg.1298) (RelIso.instRelHomClassRelIso.{u1, u1} (Submodule.{0, u1} Int M Int.instSemiringInt (AddCommGroup.toAddCommMonoid.{u1} M _inst_1) (AddCommGroup.intModule.{u1} M _inst_1)) (AddSubgroup.{u1} M (AddCommGroup.toAddGroup.{u1} M _inst_1)) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1281 : Submodule.{0, u1} Int M Int.instSemiringInt (AddCommGroup.toAddCommMonoid.{u1} M _inst_1) (AddCommGroup.intModule.{u1} M _inst_1)) (x._@.Mathlib.Order.Hom.Basic._hyg.1283 : Submodule.{0, u1} Int M Int.instSemiringInt (AddCommGroup.toAddCommMonoid.{u1} M _inst_1) (AddCommGroup.intModule.{u1} M _inst_1)) => LE.le.{u1} (Submodule.{0, u1} Int M Int.instSemiringInt (AddCommGroup.toAddCommMonoid.{u1} M _inst_1) (AddCommGroup.intModule.{u1} M _inst_1)) (Preorder.toLE.{u1} (Submodule.{0, u1} Int M Int.instSemiringInt (AddCommGroup.toAddCommMonoid.{u1} M _inst_1) (AddCommGroup.intModule.{u1} M _inst_1)) (PartialOrder.toPreorder.{u1} (Submodule.{0, u1} Int M Int.instSemiringInt (AddCommGroup.toAddCommMonoid.{u1} M _inst_1) (AddCommGroup.intModule.{u1} M _inst_1)) (CompleteSemilatticeInf.toPartialOrder.{u1} (Submodule.{0, u1} Int M Int.instSemiringInt (AddCommGroup.toAddCommMonoid.{u1} M _inst_1) (AddCommGroup.intModule.{u1} M _inst_1)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (Submodule.{0, u1} Int M Int.instSemiringInt (AddCommGroup.toAddCommMonoid.{u1} M _inst_1) (AddCommGroup.intModule.{u1} M _inst_1)) (Submodule.completeLattice.{0, u1} Int M Int.instSemiringInt (AddCommGroup.toAddCommMonoid.{u1} M _inst_1) (AddCommGroup.intModule.{u1} M _inst_1)))))) x._@.Mathlib.Order.Hom.Basic._hyg.1281 x._@.Mathlib.Order.Hom.Basic._hyg.1283) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1296 : AddSubgroup.{u1} M (AddCommGroup.toAddGroup.{u1} M _inst_1)) (x._@.Mathlib.Order.Hom.Basic._hyg.1298 : AddSubgroup.{u1} M (AddCommGroup.toAddGroup.{u1} M _inst_1)) => LE.le.{u1} (AddSubgroup.{u1} M (AddCommGroup.toAddGroup.{u1} M _inst_1)) (Preorder.toLE.{u1} (AddSubgroup.{u1} M (AddCommGroup.toAddGroup.{u1} M _inst_1)) (PartialOrder.toPreorder.{u1} (AddSubgroup.{u1} M (AddCommGroup.toAddGroup.{u1} M _inst_1)) (CompleteSemilatticeInf.toPartialOrder.{u1} (AddSubgroup.{u1} M (AddCommGroup.toAddGroup.{u1} M _inst_1)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (AddSubgroup.{u1} M (AddCommGroup.toAddGroup.{u1} M _inst_1)) (AddSubgroup.instCompleteLatticeAddSubgroup.{u1} M (AddCommGroup.toAddGroup.{u1} M _inst_1)))))) x._@.Mathlib.Order.Hom.Basic._hyg.1296 x._@.Mathlib.Order.Hom.Basic._hyg.1298))) (OrderIso.symm.{u1, u1} (AddSubgroup.{u1} M (AddCommGroup.toAddGroup.{u1} M _inst_1)) (Submodule.{0, u1} Int M Int.instSemiringInt (AddCommGroup.toAddCommMonoid.{u1} M _inst_1) (AddCommGroup.intModule.{u1} M _inst_1)) (Preorder.toLE.{u1} (AddSubgroup.{u1} M (AddCommGroup.toAddGroup.{u1} M _inst_1)) (PartialOrder.toPreorder.{u1} (AddSubgroup.{u1} M (AddCommGroup.toAddGroup.{u1} M _inst_1)) (CompleteSemilatticeInf.toPartialOrder.{u1} (AddSubgroup.{u1} M (AddCommGroup.toAddGroup.{u1} M _inst_1)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (AddSubgroup.{u1} M (AddCommGroup.toAddGroup.{u1} M _inst_1)) (AddSubgroup.instCompleteLatticeAddSubgroup.{u1} M (AddCommGroup.toAddGroup.{u1} M _inst_1)))))) (Preorder.toLE.{u1} (Submodule.{0, u1} Int M Int.instSemiringInt (AddCommGroup.toAddCommMonoid.{u1} M _inst_1) (AddCommGroup.intModule.{u1} M _inst_1)) (PartialOrder.toPreorder.{u1} (Submodule.{0, u1} Int M Int.instSemiringInt (AddCommGroup.toAddCommMonoid.{u1} M _inst_1) (AddCommGroup.intModule.{u1} M _inst_1)) (CompleteSemilatticeInf.toPartialOrder.{u1} (Submodule.{0, u1} Int M Int.instSemiringInt (AddCommGroup.toAddCommMonoid.{u1} M _inst_1) (AddCommGroup.intModule.{u1} M _inst_1)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (Submodule.{0, u1} Int M Int.instSemiringInt (AddCommGroup.toAddCommMonoid.{u1} M _inst_1) (AddCommGroup.intModule.{u1} M _inst_1)) (Submodule.completeLattice.{0, u1} Int M Int.instSemiringInt (AddCommGroup.toAddCommMonoid.{u1} M _inst_1) (AddCommGroup.intModule.{u1} M _inst_1)))))) (AddSubgroup.toIntSubmodule.{u1} M _inst_1))) (Submodule.toAddSubgroup.{0, u1} Int M Int.instRingInt _inst_1 (AddCommGroup.intModule.{u1} M _inst_1))
+  forall {M : Type.{u1}} [_inst_1 : AddCommGroup.{u1} M], Eq.{succ u1} ((Submodule.{0, u1} Int M Int.instSemiringInt (AddCommGroup.toAddCommMonoid.{u1} M _inst_1) (AddCommGroup.intModule.{u1} M _inst_1)) -> (AddSubgroup.{u1} M (AddCommGroup.toAddGroup.{u1} M _inst_1))) (FunLike.coe.{succ u1, succ u1, succ u1} (RelIso.{u1, u1} (Submodule.{0, u1} Int M Int.instSemiringInt (AddCommGroup.toAddCommMonoid.{u1} M _inst_1) (AddCommGroup.intModule.{u1} M _inst_1)) (AddSubgroup.{u1} M (AddCommGroup.toAddGroup.{u1} M _inst_1)) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1285 : Submodule.{0, u1} Int M Int.instSemiringInt (AddCommGroup.toAddCommMonoid.{u1} M _inst_1) (AddCommGroup.intModule.{u1} M _inst_1)) (x._@.Mathlib.Order.Hom.Basic._hyg.1287 : Submodule.{0, u1} Int M Int.instSemiringInt (AddCommGroup.toAddCommMonoid.{u1} M _inst_1) (AddCommGroup.intModule.{u1} M _inst_1)) => LE.le.{u1} (Submodule.{0, u1} Int M Int.instSemiringInt (AddCommGroup.toAddCommMonoid.{u1} M _inst_1) (AddCommGroup.intModule.{u1} M _inst_1)) (Preorder.toLE.{u1} (Submodule.{0, u1} Int M Int.instSemiringInt (AddCommGroup.toAddCommMonoid.{u1} M _inst_1) (AddCommGroup.intModule.{u1} M _inst_1)) (PartialOrder.toPreorder.{u1} (Submodule.{0, u1} Int M Int.instSemiringInt (AddCommGroup.toAddCommMonoid.{u1} M _inst_1) (AddCommGroup.intModule.{u1} M _inst_1)) (CompleteSemilatticeInf.toPartialOrder.{u1} (Submodule.{0, u1} Int M Int.instSemiringInt (AddCommGroup.toAddCommMonoid.{u1} M _inst_1) (AddCommGroup.intModule.{u1} M _inst_1)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (Submodule.{0, u1} Int M Int.instSemiringInt (AddCommGroup.toAddCommMonoid.{u1} M _inst_1) (AddCommGroup.intModule.{u1} M _inst_1)) (Submodule.completeLattice.{0, u1} Int M Int.instSemiringInt (AddCommGroup.toAddCommMonoid.{u1} M _inst_1) (AddCommGroup.intModule.{u1} M _inst_1)))))) x._@.Mathlib.Order.Hom.Basic._hyg.1285 x._@.Mathlib.Order.Hom.Basic._hyg.1287) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1300 : AddSubgroup.{u1} M (AddCommGroup.toAddGroup.{u1} M _inst_1)) (x._@.Mathlib.Order.Hom.Basic._hyg.1302 : AddSubgroup.{u1} M (AddCommGroup.toAddGroup.{u1} M _inst_1)) => LE.le.{u1} (AddSubgroup.{u1} M (AddCommGroup.toAddGroup.{u1} M _inst_1)) (Preorder.toLE.{u1} (AddSubgroup.{u1} M (AddCommGroup.toAddGroup.{u1} M _inst_1)) (PartialOrder.toPreorder.{u1} (AddSubgroup.{u1} M (AddCommGroup.toAddGroup.{u1} M _inst_1)) (CompleteSemilatticeInf.toPartialOrder.{u1} (AddSubgroup.{u1} M (AddCommGroup.toAddGroup.{u1} M _inst_1)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (AddSubgroup.{u1} M (AddCommGroup.toAddGroup.{u1} M _inst_1)) (AddSubgroup.instCompleteLatticeAddSubgroup.{u1} M (AddCommGroup.toAddGroup.{u1} M _inst_1)))))) x._@.Mathlib.Order.Hom.Basic._hyg.1300 x._@.Mathlib.Order.Hom.Basic._hyg.1302)) (Submodule.{0, u1} Int M Int.instSemiringInt (AddCommGroup.toAddCommMonoid.{u1} M _inst_1) (AddCommGroup.intModule.{u1} M _inst_1)) (fun (_x : Submodule.{0, u1} Int M Int.instSemiringInt (AddCommGroup.toAddCommMonoid.{u1} M _inst_1) (AddCommGroup.intModule.{u1} M _inst_1)) => AddSubgroup.{u1} M (AddCommGroup.toAddGroup.{u1} M _inst_1)) (RelHomClass.toFunLike.{u1, u1, u1} (RelIso.{u1, u1} (Submodule.{0, u1} Int M Int.instSemiringInt (AddCommGroup.toAddCommMonoid.{u1} M _inst_1) (AddCommGroup.intModule.{u1} M _inst_1)) (AddSubgroup.{u1} M (AddCommGroup.toAddGroup.{u1} M _inst_1)) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1285 : Submodule.{0, u1} Int M Int.instSemiringInt (AddCommGroup.toAddCommMonoid.{u1} M _inst_1) (AddCommGroup.intModule.{u1} M _inst_1)) (x._@.Mathlib.Order.Hom.Basic._hyg.1287 : Submodule.{0, u1} Int M Int.instSemiringInt (AddCommGroup.toAddCommMonoid.{u1} M _inst_1) (AddCommGroup.intModule.{u1} M _inst_1)) => LE.le.{u1} (Submodule.{0, u1} Int M Int.instSemiringInt (AddCommGroup.toAddCommMonoid.{u1} M _inst_1) (AddCommGroup.intModule.{u1} M _inst_1)) (Preorder.toLE.{u1} (Submodule.{0, u1} Int M Int.instSemiringInt (AddCommGroup.toAddCommMonoid.{u1} M _inst_1) (AddCommGroup.intModule.{u1} M _inst_1)) (PartialOrder.toPreorder.{u1} (Submodule.{0, u1} Int M Int.instSemiringInt (AddCommGroup.toAddCommMonoid.{u1} M _inst_1) (AddCommGroup.intModule.{u1} M _inst_1)) (CompleteSemilatticeInf.toPartialOrder.{u1} (Submodule.{0, u1} Int M Int.instSemiringInt (AddCommGroup.toAddCommMonoid.{u1} M _inst_1) (AddCommGroup.intModule.{u1} M _inst_1)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (Submodule.{0, u1} Int M Int.instSemiringInt (AddCommGroup.toAddCommMonoid.{u1} M _inst_1) (AddCommGroup.intModule.{u1} M _inst_1)) (Submodule.completeLattice.{0, u1} Int M Int.instSemiringInt (AddCommGroup.toAddCommMonoid.{u1} M _inst_1) (AddCommGroup.intModule.{u1} M _inst_1)))))) x._@.Mathlib.Order.Hom.Basic._hyg.1285 x._@.Mathlib.Order.Hom.Basic._hyg.1287) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1300 : AddSubgroup.{u1} M (AddCommGroup.toAddGroup.{u1} M _inst_1)) (x._@.Mathlib.Order.Hom.Basic._hyg.1302 : AddSubgroup.{u1} M (AddCommGroup.toAddGroup.{u1} M _inst_1)) => LE.le.{u1} (AddSubgroup.{u1} M (AddCommGroup.toAddGroup.{u1} M _inst_1)) (Preorder.toLE.{u1} (AddSubgroup.{u1} M (AddCommGroup.toAddGroup.{u1} M _inst_1)) (PartialOrder.toPreorder.{u1} (AddSubgroup.{u1} M (AddCommGroup.toAddGroup.{u1} M _inst_1)) (CompleteSemilatticeInf.toPartialOrder.{u1} (AddSubgroup.{u1} M (AddCommGroup.toAddGroup.{u1} M _inst_1)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (AddSubgroup.{u1} M (AddCommGroup.toAddGroup.{u1} M _inst_1)) (AddSubgroup.instCompleteLatticeAddSubgroup.{u1} M (AddCommGroup.toAddGroup.{u1} M _inst_1)))))) x._@.Mathlib.Order.Hom.Basic._hyg.1300 x._@.Mathlib.Order.Hom.Basic._hyg.1302)) (Submodule.{0, u1} Int M Int.instSemiringInt (AddCommGroup.toAddCommMonoid.{u1} M _inst_1) (AddCommGroup.intModule.{u1} M _inst_1)) (AddSubgroup.{u1} M (AddCommGroup.toAddGroup.{u1} M _inst_1)) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1285 : Submodule.{0, u1} Int M Int.instSemiringInt (AddCommGroup.toAddCommMonoid.{u1} M _inst_1) (AddCommGroup.intModule.{u1} M _inst_1)) (x._@.Mathlib.Order.Hom.Basic._hyg.1287 : Submodule.{0, u1} Int M Int.instSemiringInt (AddCommGroup.toAddCommMonoid.{u1} M _inst_1) (AddCommGroup.intModule.{u1} M _inst_1)) => LE.le.{u1} (Submodule.{0, u1} Int M Int.instSemiringInt (AddCommGroup.toAddCommMonoid.{u1} M _inst_1) (AddCommGroup.intModule.{u1} M _inst_1)) (Preorder.toLE.{u1} (Submodule.{0, u1} Int M Int.instSemiringInt (AddCommGroup.toAddCommMonoid.{u1} M _inst_1) (AddCommGroup.intModule.{u1} M _inst_1)) (PartialOrder.toPreorder.{u1} (Submodule.{0, u1} Int M Int.instSemiringInt (AddCommGroup.toAddCommMonoid.{u1} M _inst_1) (AddCommGroup.intModule.{u1} M _inst_1)) (CompleteSemilatticeInf.toPartialOrder.{u1} (Submodule.{0, u1} Int M Int.instSemiringInt (AddCommGroup.toAddCommMonoid.{u1} M _inst_1) (AddCommGroup.intModule.{u1} M _inst_1)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (Submodule.{0, u1} Int M Int.instSemiringInt (AddCommGroup.toAddCommMonoid.{u1} M _inst_1) (AddCommGroup.intModule.{u1} M _inst_1)) (Submodule.completeLattice.{0, u1} Int M Int.instSemiringInt (AddCommGroup.toAddCommMonoid.{u1} M _inst_1) (AddCommGroup.intModule.{u1} M _inst_1)))))) x._@.Mathlib.Order.Hom.Basic._hyg.1285 x._@.Mathlib.Order.Hom.Basic._hyg.1287) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1300 : AddSubgroup.{u1} M (AddCommGroup.toAddGroup.{u1} M _inst_1)) (x._@.Mathlib.Order.Hom.Basic._hyg.1302 : AddSubgroup.{u1} M (AddCommGroup.toAddGroup.{u1} M _inst_1)) => LE.le.{u1} (AddSubgroup.{u1} M (AddCommGroup.toAddGroup.{u1} M _inst_1)) (Preorder.toLE.{u1} (AddSubgroup.{u1} M (AddCommGroup.toAddGroup.{u1} M _inst_1)) (PartialOrder.toPreorder.{u1} (AddSubgroup.{u1} M (AddCommGroup.toAddGroup.{u1} M _inst_1)) (CompleteSemilatticeInf.toPartialOrder.{u1} (AddSubgroup.{u1} M (AddCommGroup.toAddGroup.{u1} M _inst_1)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (AddSubgroup.{u1} M (AddCommGroup.toAddGroup.{u1} M _inst_1)) (AddSubgroup.instCompleteLatticeAddSubgroup.{u1} M (AddCommGroup.toAddGroup.{u1} M _inst_1)))))) x._@.Mathlib.Order.Hom.Basic._hyg.1300 x._@.Mathlib.Order.Hom.Basic._hyg.1302) (RelIso.instRelHomClassRelIso.{u1, u1} (Submodule.{0, u1} Int M Int.instSemiringInt (AddCommGroup.toAddCommMonoid.{u1} M _inst_1) (AddCommGroup.intModule.{u1} M _inst_1)) (AddSubgroup.{u1} M (AddCommGroup.toAddGroup.{u1} M _inst_1)) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1285 : Submodule.{0, u1} Int M Int.instSemiringInt (AddCommGroup.toAddCommMonoid.{u1} M _inst_1) (AddCommGroup.intModule.{u1} M _inst_1)) (x._@.Mathlib.Order.Hom.Basic._hyg.1287 : Submodule.{0, u1} Int M Int.instSemiringInt (AddCommGroup.toAddCommMonoid.{u1} M _inst_1) (AddCommGroup.intModule.{u1} M _inst_1)) => LE.le.{u1} (Submodule.{0, u1} Int M Int.instSemiringInt (AddCommGroup.toAddCommMonoid.{u1} M _inst_1) (AddCommGroup.intModule.{u1} M _inst_1)) (Preorder.toLE.{u1} (Submodule.{0, u1} Int M Int.instSemiringInt (AddCommGroup.toAddCommMonoid.{u1} M _inst_1) (AddCommGroup.intModule.{u1} M _inst_1)) (PartialOrder.toPreorder.{u1} (Submodule.{0, u1} Int M Int.instSemiringInt (AddCommGroup.toAddCommMonoid.{u1} M _inst_1) (AddCommGroup.intModule.{u1} M _inst_1)) (CompleteSemilatticeInf.toPartialOrder.{u1} (Submodule.{0, u1} Int M Int.instSemiringInt (AddCommGroup.toAddCommMonoid.{u1} M _inst_1) (AddCommGroup.intModule.{u1} M _inst_1)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (Submodule.{0, u1} Int M Int.instSemiringInt (AddCommGroup.toAddCommMonoid.{u1} M _inst_1) (AddCommGroup.intModule.{u1} M _inst_1)) (Submodule.completeLattice.{0, u1} Int M Int.instSemiringInt (AddCommGroup.toAddCommMonoid.{u1} M _inst_1) (AddCommGroup.intModule.{u1} M _inst_1)))))) x._@.Mathlib.Order.Hom.Basic._hyg.1285 x._@.Mathlib.Order.Hom.Basic._hyg.1287) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1300 : AddSubgroup.{u1} M (AddCommGroup.toAddGroup.{u1} M _inst_1)) (x._@.Mathlib.Order.Hom.Basic._hyg.1302 : AddSubgroup.{u1} M (AddCommGroup.toAddGroup.{u1} M _inst_1)) => LE.le.{u1} (AddSubgroup.{u1} M (AddCommGroup.toAddGroup.{u1} M _inst_1)) (Preorder.toLE.{u1} (AddSubgroup.{u1} M (AddCommGroup.toAddGroup.{u1} M _inst_1)) (PartialOrder.toPreorder.{u1} (AddSubgroup.{u1} M (AddCommGroup.toAddGroup.{u1} M _inst_1)) (CompleteSemilatticeInf.toPartialOrder.{u1} (AddSubgroup.{u1} M (AddCommGroup.toAddGroup.{u1} M _inst_1)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (AddSubgroup.{u1} M (AddCommGroup.toAddGroup.{u1} M _inst_1)) (AddSubgroup.instCompleteLatticeAddSubgroup.{u1} M (AddCommGroup.toAddGroup.{u1} M _inst_1)))))) x._@.Mathlib.Order.Hom.Basic._hyg.1300 x._@.Mathlib.Order.Hom.Basic._hyg.1302))) (OrderIso.symm.{u1, u1} (AddSubgroup.{u1} M (AddCommGroup.toAddGroup.{u1} M _inst_1)) (Submodule.{0, u1} Int M Int.instSemiringInt (AddCommGroup.toAddCommMonoid.{u1} M _inst_1) (AddCommGroup.intModule.{u1} M _inst_1)) (Preorder.toLE.{u1} (AddSubgroup.{u1} M (AddCommGroup.toAddGroup.{u1} M _inst_1)) (PartialOrder.toPreorder.{u1} (AddSubgroup.{u1} M (AddCommGroup.toAddGroup.{u1} M _inst_1)) (CompleteSemilatticeInf.toPartialOrder.{u1} (AddSubgroup.{u1} M (AddCommGroup.toAddGroup.{u1} M _inst_1)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (AddSubgroup.{u1} M (AddCommGroup.toAddGroup.{u1} M _inst_1)) (AddSubgroup.instCompleteLatticeAddSubgroup.{u1} M (AddCommGroup.toAddGroup.{u1} M _inst_1)))))) (Preorder.toLE.{u1} (Submodule.{0, u1} Int M Int.instSemiringInt (AddCommGroup.toAddCommMonoid.{u1} M _inst_1) (AddCommGroup.intModule.{u1} M _inst_1)) (PartialOrder.toPreorder.{u1} (Submodule.{0, u1} Int M Int.instSemiringInt (AddCommGroup.toAddCommMonoid.{u1} M _inst_1) (AddCommGroup.intModule.{u1} M _inst_1)) (CompleteSemilatticeInf.toPartialOrder.{u1} (Submodule.{0, u1} Int M Int.instSemiringInt (AddCommGroup.toAddCommMonoid.{u1} M _inst_1) (AddCommGroup.intModule.{u1} M _inst_1)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (Submodule.{0, u1} Int M Int.instSemiringInt (AddCommGroup.toAddCommMonoid.{u1} M _inst_1) (AddCommGroup.intModule.{u1} M _inst_1)) (Submodule.completeLattice.{0, u1} Int M Int.instSemiringInt (AddCommGroup.toAddCommMonoid.{u1} M _inst_1) (AddCommGroup.intModule.{u1} M _inst_1)))))) (AddSubgroup.toIntSubmodule.{u1} M _inst_1))) (Submodule.toAddSubgroup.{0, u1} Int M Int.instRingInt _inst_1 (AddCommGroup.intModule.{u1} M _inst_1))
 Case conversion may be inaccurate. Consider using '#align add_subgroup.to_int_submodule_symm AddSubgroup.toIntSubmodule_symmₓ'. -/
 @[simp]
 theorem AddSubgroup.toIntSubmodule_symm :
@@ -706,7 +706,7 @@ theorem AddSubgroup.toIntSubmodule_symm :
 lean 3 declaration is
   forall {M : Type.{u1}} [_inst_1 : AddCommGroup.{u1} M] (S : AddSubgroup.{u1} M (AddCommGroup.toAddGroup.{u1} M _inst_1)), Eq.{succ u1} (Set.{u1} M) ((fun (a : Type.{u1}) (b : Type.{u1}) [self : HasLiftT.{succ u1, succ u1} a b] => self.0) (Submodule.{0, u1} Int M Int.semiring (AddCommGroup.toAddCommMonoid.{u1} M _inst_1) (AddCommGroup.intModule.{u1} M _inst_1)) (Set.{u1} M) (HasLiftT.mk.{succ u1, succ u1} (Submodule.{0, u1} Int M Int.semiring (AddCommGroup.toAddCommMonoid.{u1} M _inst_1) (AddCommGroup.intModule.{u1} M _inst_1)) (Set.{u1} M) (CoeTCₓ.coe.{succ u1, succ u1} (Submodule.{0, u1} Int M Int.semiring (AddCommGroup.toAddCommMonoid.{u1} M _inst_1) (AddCommGroup.intModule.{u1} M _inst_1)) (Set.{u1} M) (SetLike.Set.hasCoeT.{u1, u1} (Submodule.{0, u1} Int M Int.semiring (AddCommGroup.toAddCommMonoid.{u1} M _inst_1) (AddCommGroup.intModule.{u1} M _inst_1)) M (Submodule.setLike.{0, u1} Int M Int.semiring (AddCommGroup.toAddCommMonoid.{u1} M _inst_1) (AddCommGroup.intModule.{u1} M _inst_1))))) (coeFn.{succ u1, succ u1} (OrderIso.{u1, u1} (AddSubgroup.{u1} M (AddCommGroup.toAddGroup.{u1} M _inst_1)) (Submodule.{0, u1} Int M Int.semiring (AddCommGroup.toAddCommMonoid.{u1} M _inst_1) (AddCommGroup.intModule.{u1} M _inst_1)) (Preorder.toHasLe.{u1} (AddSubgroup.{u1} M (AddCommGroup.toAddGroup.{u1} M _inst_1)) (PartialOrder.toPreorder.{u1} (AddSubgroup.{u1} M (AddCommGroup.toAddGroup.{u1} M _inst_1)) (CompleteSemilatticeInf.toPartialOrder.{u1} (AddSubgroup.{u1} M (AddCommGroup.toAddGroup.{u1} M _inst_1)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (AddSubgroup.{u1} M (AddCommGroup.toAddGroup.{u1} M _inst_1)) (AddSubgroup.completeLattice.{u1} M (AddCommGroup.toAddGroup.{u1} M _inst_1)))))) (Preorder.toHasLe.{u1} (Submodule.{0, u1} Int M Int.semiring (AddCommGroup.toAddCommMonoid.{u1} M _inst_1) (AddCommGroup.intModule.{u1} M _inst_1)) (PartialOrder.toPreorder.{u1} (Submodule.{0, u1} Int M Int.semiring (AddCommGroup.toAddCommMonoid.{u1} M _inst_1) (AddCommGroup.intModule.{u1} M _inst_1)) (CompleteSemilatticeInf.toPartialOrder.{u1} (Submodule.{0, u1} Int M Int.semiring (AddCommGroup.toAddCommMonoid.{u1} M _inst_1) (AddCommGroup.intModule.{u1} M _inst_1)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (Submodule.{0, u1} Int M Int.semiring (AddCommGroup.toAddCommMonoid.{u1} M _inst_1) (AddCommGroup.intModule.{u1} M _inst_1)) (Submodule.completeLattice.{0, u1} Int M Int.semiring (AddCommGroup.toAddCommMonoid.{u1} M _inst_1) (AddCommGroup.intModule.{u1} M _inst_1))))))) (fun (_x : RelIso.{u1, u1} (AddSubgroup.{u1} M (AddCommGroup.toAddGroup.{u1} M _inst_1)) (Submodule.{0, u1} Int M Int.semiring (AddCommGroup.toAddCommMonoid.{u1} M _inst_1) (AddCommGroup.intModule.{u1} M _inst_1)) (LE.le.{u1} (AddSubgroup.{u1} M (AddCommGroup.toAddGroup.{u1} M _inst_1)) (Preorder.toHasLe.{u1} (AddSubgroup.{u1} M (AddCommGroup.toAddGroup.{u1} M _inst_1)) (PartialOrder.toPreorder.{u1} (AddSubgroup.{u1} M (AddCommGroup.toAddGroup.{u1} M _inst_1)) (CompleteSemilatticeInf.toPartialOrder.{u1} (AddSubgroup.{u1} M (AddCommGroup.toAddGroup.{u1} M _inst_1)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (AddSubgroup.{u1} M (AddCommGroup.toAddGroup.{u1} M _inst_1)) (AddSubgroup.completeLattice.{u1} M (AddCommGroup.toAddGroup.{u1} M _inst_1))))))) (LE.le.{u1} (Submodule.{0, u1} Int M Int.semiring (AddCommGroup.toAddCommMonoid.{u1} M _inst_1) (AddCommGroup.intModule.{u1} M _inst_1)) (Preorder.toHasLe.{u1} (Submodule.{0, u1} Int M Int.semiring (AddCommGroup.toAddCommMonoid.{u1} M _inst_1) (AddCommGroup.intModule.{u1} M _inst_1)) (PartialOrder.toPreorder.{u1} (Submodule.{0, u1} Int M Int.semiring (AddCommGroup.toAddCommMonoid.{u1} M _inst_1) (AddCommGroup.intModule.{u1} M _inst_1)) (CompleteSemilatticeInf.toPartialOrder.{u1} (Submodule.{0, u1} Int M Int.semiring (AddCommGroup.toAddCommMonoid.{u1} M _inst_1) (AddCommGroup.intModule.{u1} M _inst_1)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (Submodule.{0, u1} Int M Int.semiring (AddCommGroup.toAddCommMonoid.{u1} M _inst_1) (AddCommGroup.intModule.{u1} M _inst_1)) (Submodule.completeLattice.{0, u1} Int M Int.semiring (AddCommGroup.toAddCommMonoid.{u1} M _inst_1) (AddCommGroup.intModule.{u1} M _inst_1)))))))) => (AddSubgroup.{u1} M (AddCommGroup.toAddGroup.{u1} M _inst_1)) -> (Submodule.{0, u1} Int M Int.semiring (AddCommGroup.toAddCommMonoid.{u1} M _inst_1) (AddCommGroup.intModule.{u1} M _inst_1))) (RelIso.hasCoeToFun.{u1, u1} (AddSubgroup.{u1} M (AddCommGroup.toAddGroup.{u1} M _inst_1)) (Submodule.{0, u1} Int M Int.semiring (AddCommGroup.toAddCommMonoid.{u1} M _inst_1) (AddCommGroup.intModule.{u1} M _inst_1)) (LE.le.{u1} (AddSubgroup.{u1} M (AddCommGroup.toAddGroup.{u1} M _inst_1)) (Preorder.toHasLe.{u1} (AddSubgroup.{u1} M (AddCommGroup.toAddGroup.{u1} M _inst_1)) (PartialOrder.toPreorder.{u1} (AddSubgroup.{u1} M (AddCommGroup.toAddGroup.{u1} M _inst_1)) (CompleteSemilatticeInf.toPartialOrder.{u1} (AddSubgroup.{u1} M (AddCommGroup.toAddGroup.{u1} M _inst_1)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (AddSubgroup.{u1} M (AddCommGroup.toAddGroup.{u1} M _inst_1)) (AddSubgroup.completeLattice.{u1} M (AddCommGroup.toAddGroup.{u1} M _inst_1))))))) (LE.le.{u1} (Submodule.{0, u1} Int M Int.semiring (AddCommGroup.toAddCommMonoid.{u1} M _inst_1) (AddCommGroup.intModule.{u1} M _inst_1)) (Preorder.toHasLe.{u1} (Submodule.{0, u1} Int M Int.semiring (AddCommGroup.toAddCommMonoid.{u1} M _inst_1) (AddCommGroup.intModule.{u1} M _inst_1)) (PartialOrder.toPreorder.{u1} (Submodule.{0, u1} Int M Int.semiring (AddCommGroup.toAddCommMonoid.{u1} M _inst_1) (AddCommGroup.intModule.{u1} M _inst_1)) (CompleteSemilatticeInf.toPartialOrder.{u1} (Submodule.{0, u1} Int M Int.semiring (AddCommGroup.toAddCommMonoid.{u1} M _inst_1) (AddCommGroup.intModule.{u1} M _inst_1)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (Submodule.{0, u1} Int M Int.semiring (AddCommGroup.toAddCommMonoid.{u1} M _inst_1) (AddCommGroup.intModule.{u1} M _inst_1)) (Submodule.completeLattice.{0, u1} Int M Int.semiring (AddCommGroup.toAddCommMonoid.{u1} M _inst_1) (AddCommGroup.intModule.{u1} M _inst_1)))))))) (AddSubgroup.toIntSubmodule.{u1} M _inst_1) S)) ((fun (a : Type.{u1}) (b : Type.{u1}) [self : HasLiftT.{succ u1, succ u1} a b] => self.0) (AddSubgroup.{u1} M (AddCommGroup.toAddGroup.{u1} M _inst_1)) (Set.{u1} M) (HasLiftT.mk.{succ u1, succ u1} (AddSubgroup.{u1} M (AddCommGroup.toAddGroup.{u1} M _inst_1)) (Set.{u1} M) (CoeTCₓ.coe.{succ u1, succ u1} (AddSubgroup.{u1} M (AddCommGroup.toAddGroup.{u1} M _inst_1)) (Set.{u1} M) (SetLike.Set.hasCoeT.{u1, u1} (AddSubgroup.{u1} M (AddCommGroup.toAddGroup.{u1} M _inst_1)) M (AddSubgroup.setLike.{u1} M (AddCommGroup.toAddGroup.{u1} M _inst_1))))) S)
 but is expected to have type
-  forall {M : Type.{u1}} [_inst_1 : AddCommGroup.{u1} M] (S : AddSubgroup.{u1} M (AddCommGroup.toAddGroup.{u1} M _inst_1)), Eq.{succ u1} (Set.{u1} M) (SetLike.coe.{u1, u1} (Submodule.{0, u1} Int M Int.instSemiringInt (AddCommGroup.toAddCommMonoid.{u1} M _inst_1) (AddCommGroup.intModule.{u1} M _inst_1)) M (Submodule.setLike.{0, u1} Int M Int.instSemiringInt (AddCommGroup.toAddCommMonoid.{u1} M _inst_1) (AddCommGroup.intModule.{u1} M _inst_1)) (FunLike.coe.{succ u1, succ u1, succ u1} (RelIso.{u1, u1} (AddSubgroup.{u1} M (AddCommGroup.toAddGroup.{u1} M _inst_1)) (Submodule.{0, u1} Int M Int.instSemiringInt (AddCommGroup.toAddCommMonoid.{u1} M _inst_1) (AddCommGroup.intModule.{u1} M _inst_1)) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1281 : AddSubgroup.{u1} M (AddCommGroup.toAddGroup.{u1} M _inst_1)) (x._@.Mathlib.Order.Hom.Basic._hyg.1283 : AddSubgroup.{u1} M (AddCommGroup.toAddGroup.{u1} M _inst_1)) => LE.le.{u1} (AddSubgroup.{u1} M (AddCommGroup.toAddGroup.{u1} M _inst_1)) (Preorder.toLE.{u1} (AddSubgroup.{u1} M (AddCommGroup.toAddGroup.{u1} M _inst_1)) (PartialOrder.toPreorder.{u1} (AddSubgroup.{u1} M (AddCommGroup.toAddGroup.{u1} M _inst_1)) (CompleteSemilatticeInf.toPartialOrder.{u1} (AddSubgroup.{u1} M (AddCommGroup.toAddGroup.{u1} M _inst_1)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (AddSubgroup.{u1} M (AddCommGroup.toAddGroup.{u1} M _inst_1)) (AddSubgroup.instCompleteLatticeAddSubgroup.{u1} M (AddCommGroup.toAddGroup.{u1} M _inst_1)))))) x._@.Mathlib.Order.Hom.Basic._hyg.1281 x._@.Mathlib.Order.Hom.Basic._hyg.1283) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1296 : Submodule.{0, u1} Int M Int.instSemiringInt (AddCommGroup.toAddCommMonoid.{u1} M _inst_1) (AddCommGroup.intModule.{u1} M _inst_1)) (x._@.Mathlib.Order.Hom.Basic._hyg.1298 : Submodule.{0, u1} Int M Int.instSemiringInt (AddCommGroup.toAddCommMonoid.{u1} M _inst_1) (AddCommGroup.intModule.{u1} M _inst_1)) => LE.le.{u1} (Submodule.{0, u1} Int M Int.instSemiringInt (AddCommGroup.toAddCommMonoid.{u1} M _inst_1) (AddCommGroup.intModule.{u1} M _inst_1)) (Preorder.toLE.{u1} (Submodule.{0, u1} Int M Int.instSemiringInt (AddCommGroup.toAddCommMonoid.{u1} M _inst_1) (AddCommGroup.intModule.{u1} M _inst_1)) (PartialOrder.toPreorder.{u1} (Submodule.{0, u1} Int M Int.instSemiringInt (AddCommGroup.toAddCommMonoid.{u1} M _inst_1) (AddCommGroup.intModule.{u1} M _inst_1)) (CompleteSemilatticeInf.toPartialOrder.{u1} (Submodule.{0, u1} Int M Int.instSemiringInt (AddCommGroup.toAddCommMonoid.{u1} M _inst_1) (AddCommGroup.intModule.{u1} M _inst_1)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (Submodule.{0, u1} Int M Int.instSemiringInt (AddCommGroup.toAddCommMonoid.{u1} M _inst_1) (AddCommGroup.intModule.{u1} M _inst_1)) (Submodule.completeLattice.{0, u1} Int M Int.instSemiringInt (AddCommGroup.toAddCommMonoid.{u1} M _inst_1) (AddCommGroup.intModule.{u1} M _inst_1)))))) x._@.Mathlib.Order.Hom.Basic._hyg.1296 x._@.Mathlib.Order.Hom.Basic._hyg.1298)) (AddSubgroup.{u1} M (AddCommGroup.toAddGroup.{u1} M _inst_1)) (fun (_x : AddSubgroup.{u1} M (AddCommGroup.toAddGroup.{u1} M _inst_1)) => Submodule.{0, u1} Int M Int.instSemiringInt (AddCommGroup.toAddCommMonoid.{u1} M _inst_1) (AddCommGroup.intModule.{u1} M _inst_1)) (RelHomClass.toFunLike.{u1, u1, u1} (RelIso.{u1, u1} (AddSubgroup.{u1} M (AddCommGroup.toAddGroup.{u1} M _inst_1)) (Submodule.{0, u1} Int M Int.instSemiringInt (AddCommGroup.toAddCommMonoid.{u1} M _inst_1) (AddCommGroup.intModule.{u1} M _inst_1)) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1281 : AddSubgroup.{u1} M (AddCommGroup.toAddGroup.{u1} M _inst_1)) (x._@.Mathlib.Order.Hom.Basic._hyg.1283 : AddSubgroup.{u1} M (AddCommGroup.toAddGroup.{u1} M _inst_1)) => LE.le.{u1} (AddSubgroup.{u1} M (AddCommGroup.toAddGroup.{u1} M _inst_1)) (Preorder.toLE.{u1} (AddSubgroup.{u1} M (AddCommGroup.toAddGroup.{u1} M _inst_1)) (PartialOrder.toPreorder.{u1} (AddSubgroup.{u1} M (AddCommGroup.toAddGroup.{u1} M _inst_1)) (CompleteSemilatticeInf.toPartialOrder.{u1} (AddSubgroup.{u1} M (AddCommGroup.toAddGroup.{u1} M _inst_1)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (AddSubgroup.{u1} M (AddCommGroup.toAddGroup.{u1} M _inst_1)) (AddSubgroup.instCompleteLatticeAddSubgroup.{u1} M (AddCommGroup.toAddGroup.{u1} M _inst_1)))))) x._@.Mathlib.Order.Hom.Basic._hyg.1281 x._@.Mathlib.Order.Hom.Basic._hyg.1283) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1296 : Submodule.{0, u1} Int M Int.instSemiringInt (AddCommGroup.toAddCommMonoid.{u1} M _inst_1) (AddCommGroup.intModule.{u1} M _inst_1)) (x._@.Mathlib.Order.Hom.Basic._hyg.1298 : Submodule.{0, u1} Int M Int.instSemiringInt (AddCommGroup.toAddCommMonoid.{u1} M _inst_1) (AddCommGroup.intModule.{u1} M _inst_1)) => LE.le.{u1} (Submodule.{0, u1} Int M Int.instSemiringInt (AddCommGroup.toAddCommMonoid.{u1} M _inst_1) (AddCommGroup.intModule.{u1} M _inst_1)) (Preorder.toLE.{u1} (Submodule.{0, u1} Int M Int.instSemiringInt (AddCommGroup.toAddCommMonoid.{u1} M _inst_1) (AddCommGroup.intModule.{u1} M _inst_1)) (PartialOrder.toPreorder.{u1} (Submodule.{0, u1} Int M Int.instSemiringInt (AddCommGroup.toAddCommMonoid.{u1} M _inst_1) (AddCommGroup.intModule.{u1} M _inst_1)) (CompleteSemilatticeInf.toPartialOrder.{u1} (Submodule.{0, u1} Int M Int.instSemiringInt (AddCommGroup.toAddCommMonoid.{u1} M _inst_1) (AddCommGroup.intModule.{u1} M _inst_1)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (Submodule.{0, u1} Int M Int.instSemiringInt (AddCommGroup.toAddCommMonoid.{u1} M _inst_1) (AddCommGroup.intModule.{u1} M _inst_1)) (Submodule.completeLattice.{0, u1} Int M Int.instSemiringInt (AddCommGroup.toAddCommMonoid.{u1} M _inst_1) (AddCommGroup.intModule.{u1} M _inst_1)))))) x._@.Mathlib.Order.Hom.Basic._hyg.1296 x._@.Mathlib.Order.Hom.Basic._hyg.1298)) (AddSubgroup.{u1} M (AddCommGroup.toAddGroup.{u1} M _inst_1)) (Submodule.{0, u1} Int M Int.instSemiringInt (AddCommGroup.toAddCommMonoid.{u1} M _inst_1) (AddCommGroup.intModule.{u1} M _inst_1)) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1281 : AddSubgroup.{u1} M (AddCommGroup.toAddGroup.{u1} M _inst_1)) (x._@.Mathlib.Order.Hom.Basic._hyg.1283 : AddSubgroup.{u1} M (AddCommGroup.toAddGroup.{u1} M _inst_1)) => LE.le.{u1} (AddSubgroup.{u1} M (AddCommGroup.toAddGroup.{u1} M _inst_1)) (Preorder.toLE.{u1} (AddSubgroup.{u1} M (AddCommGroup.toAddGroup.{u1} M _inst_1)) (PartialOrder.toPreorder.{u1} (AddSubgroup.{u1} M (AddCommGroup.toAddGroup.{u1} M _inst_1)) (CompleteSemilatticeInf.toPartialOrder.{u1} (AddSubgroup.{u1} M (AddCommGroup.toAddGroup.{u1} M _inst_1)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (AddSubgroup.{u1} M (AddCommGroup.toAddGroup.{u1} M _inst_1)) (AddSubgroup.instCompleteLatticeAddSubgroup.{u1} M (AddCommGroup.toAddGroup.{u1} M _inst_1)))))) x._@.Mathlib.Order.Hom.Basic._hyg.1281 x._@.Mathlib.Order.Hom.Basic._hyg.1283) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1296 : Submodule.{0, u1} Int M Int.instSemiringInt (AddCommGroup.toAddCommMonoid.{u1} M _inst_1) (AddCommGroup.intModule.{u1} M _inst_1)) (x._@.Mathlib.Order.Hom.Basic._hyg.1298 : Submodule.{0, u1} Int M Int.instSemiringInt (AddCommGroup.toAddCommMonoid.{u1} M _inst_1) (AddCommGroup.intModule.{u1} M _inst_1)) => LE.le.{u1} (Submodule.{0, u1} Int M Int.instSemiringInt (AddCommGroup.toAddCommMonoid.{u1} M _inst_1) (AddCommGroup.intModule.{u1} M _inst_1)) (Preorder.toLE.{u1} (Submodule.{0, u1} Int M Int.instSemiringInt (AddCommGroup.toAddCommMonoid.{u1} M _inst_1) (AddCommGroup.intModule.{u1} M _inst_1)) (PartialOrder.toPreorder.{u1} (Submodule.{0, u1} Int M Int.instSemiringInt (AddCommGroup.toAddCommMonoid.{u1} M _inst_1) (AddCommGroup.intModule.{u1} M _inst_1)) (CompleteSemilatticeInf.toPartialOrder.{u1} (Submodule.{0, u1} Int M Int.instSemiringInt (AddCommGroup.toAddCommMonoid.{u1} M _inst_1) (AddCommGroup.intModule.{u1} M _inst_1)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (Submodule.{0, u1} Int M Int.instSemiringInt (AddCommGroup.toAddCommMonoid.{u1} M _inst_1) (AddCommGroup.intModule.{u1} M _inst_1)) (Submodule.completeLattice.{0, u1} Int M Int.instSemiringInt (AddCommGroup.toAddCommMonoid.{u1} M _inst_1) (AddCommGroup.intModule.{u1} M _inst_1)))))) x._@.Mathlib.Order.Hom.Basic._hyg.1296 x._@.Mathlib.Order.Hom.Basic._hyg.1298) (RelIso.instRelHomClassRelIso.{u1, u1} (AddSubgroup.{u1} M (AddCommGroup.toAddGroup.{u1} M _inst_1)) (Submodule.{0, u1} Int M Int.instSemiringInt (AddCommGroup.toAddCommMonoid.{u1} M _inst_1) (AddCommGroup.intModule.{u1} M _inst_1)) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1281 : AddSubgroup.{u1} M (AddCommGroup.toAddGroup.{u1} M _inst_1)) (x._@.Mathlib.Order.Hom.Basic._hyg.1283 : AddSubgroup.{u1} M (AddCommGroup.toAddGroup.{u1} M _inst_1)) => LE.le.{u1} (AddSubgroup.{u1} M (AddCommGroup.toAddGroup.{u1} M _inst_1)) (Preorder.toLE.{u1} (AddSubgroup.{u1} M (AddCommGroup.toAddGroup.{u1} M _inst_1)) (PartialOrder.toPreorder.{u1} (AddSubgroup.{u1} M (AddCommGroup.toAddGroup.{u1} M _inst_1)) (CompleteSemilatticeInf.toPartialOrder.{u1} (AddSubgroup.{u1} M (AddCommGroup.toAddGroup.{u1} M _inst_1)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (AddSubgroup.{u1} M (AddCommGroup.toAddGroup.{u1} M _inst_1)) (AddSubgroup.instCompleteLatticeAddSubgroup.{u1} M (AddCommGroup.toAddGroup.{u1} M _inst_1)))))) x._@.Mathlib.Order.Hom.Basic._hyg.1281 x._@.Mathlib.Order.Hom.Basic._hyg.1283) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1296 : Submodule.{0, u1} Int M Int.instSemiringInt (AddCommGroup.toAddCommMonoid.{u1} M _inst_1) (AddCommGroup.intModule.{u1} M _inst_1)) (x._@.Mathlib.Order.Hom.Basic._hyg.1298 : Submodule.{0, u1} Int M Int.instSemiringInt (AddCommGroup.toAddCommMonoid.{u1} M _inst_1) (AddCommGroup.intModule.{u1} M _inst_1)) => LE.le.{u1} (Submodule.{0, u1} Int M Int.instSemiringInt (AddCommGroup.toAddCommMonoid.{u1} M _inst_1) (AddCommGroup.intModule.{u1} M _inst_1)) (Preorder.toLE.{u1} (Submodule.{0, u1} Int M Int.instSemiringInt (AddCommGroup.toAddCommMonoid.{u1} M _inst_1) (AddCommGroup.intModule.{u1} M _inst_1)) (PartialOrder.toPreorder.{u1} (Submodule.{0, u1} Int M Int.instSemiringInt (AddCommGroup.toAddCommMonoid.{u1} M _inst_1) (AddCommGroup.intModule.{u1} M _inst_1)) (CompleteSemilatticeInf.toPartialOrder.{u1} (Submodule.{0, u1} Int M Int.instSemiringInt (AddCommGroup.toAddCommMonoid.{u1} M _inst_1) (AddCommGroup.intModule.{u1} M _inst_1)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (Submodule.{0, u1} Int M Int.instSemiringInt (AddCommGroup.toAddCommMonoid.{u1} M _inst_1) (AddCommGroup.intModule.{u1} M _inst_1)) (Submodule.completeLattice.{0, u1} Int M Int.instSemiringInt (AddCommGroup.toAddCommMonoid.{u1} M _inst_1) (AddCommGroup.intModule.{u1} M _inst_1)))))) x._@.Mathlib.Order.Hom.Basic._hyg.1296 x._@.Mathlib.Order.Hom.Basic._hyg.1298))) (AddSubgroup.toIntSubmodule.{u1} M _inst_1) S)) (SetLike.coe.{u1, u1} (AddSubgroup.{u1} M (AddCommGroup.toAddGroup.{u1} M _inst_1)) M (AddSubgroup.instSetLikeAddSubgroup.{u1} M (AddCommGroup.toAddGroup.{u1} M _inst_1)) S)
+  forall {M : Type.{u1}} [_inst_1 : AddCommGroup.{u1} M] (S : AddSubgroup.{u1} M (AddCommGroup.toAddGroup.{u1} M _inst_1)), Eq.{succ u1} (Set.{u1} M) (SetLike.coe.{u1, u1} (Submodule.{0, u1} Int M Int.instSemiringInt (AddCommGroup.toAddCommMonoid.{u1} M _inst_1) (AddCommGroup.intModule.{u1} M _inst_1)) M (Submodule.setLike.{0, u1} Int M Int.instSemiringInt (AddCommGroup.toAddCommMonoid.{u1} M _inst_1) (AddCommGroup.intModule.{u1} M _inst_1)) (FunLike.coe.{succ u1, succ u1, succ u1} (RelIso.{u1, u1} (AddSubgroup.{u1} M (AddCommGroup.toAddGroup.{u1} M _inst_1)) (Submodule.{0, u1} Int M Int.instSemiringInt (AddCommGroup.toAddCommMonoid.{u1} M _inst_1) (AddCommGroup.intModule.{u1} M _inst_1)) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1285 : AddSubgroup.{u1} M (AddCommGroup.toAddGroup.{u1} M _inst_1)) (x._@.Mathlib.Order.Hom.Basic._hyg.1287 : AddSubgroup.{u1} M (AddCommGroup.toAddGroup.{u1} M _inst_1)) => LE.le.{u1} (AddSubgroup.{u1} M (AddCommGroup.toAddGroup.{u1} M _inst_1)) (Preorder.toLE.{u1} (AddSubgroup.{u1} M (AddCommGroup.toAddGroup.{u1} M _inst_1)) (PartialOrder.toPreorder.{u1} (AddSubgroup.{u1} M (AddCommGroup.toAddGroup.{u1} M _inst_1)) (CompleteSemilatticeInf.toPartialOrder.{u1} (AddSubgroup.{u1} M (AddCommGroup.toAddGroup.{u1} M _inst_1)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (AddSubgroup.{u1} M (AddCommGroup.toAddGroup.{u1} M _inst_1)) (AddSubgroup.instCompleteLatticeAddSubgroup.{u1} M (AddCommGroup.toAddGroup.{u1} M _inst_1)))))) x._@.Mathlib.Order.Hom.Basic._hyg.1285 x._@.Mathlib.Order.Hom.Basic._hyg.1287) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1300 : Submodule.{0, u1} Int M Int.instSemiringInt (AddCommGroup.toAddCommMonoid.{u1} M _inst_1) (AddCommGroup.intModule.{u1} M _inst_1)) (x._@.Mathlib.Order.Hom.Basic._hyg.1302 : Submodule.{0, u1} Int M Int.instSemiringInt (AddCommGroup.toAddCommMonoid.{u1} M _inst_1) (AddCommGroup.intModule.{u1} M _inst_1)) => LE.le.{u1} (Submodule.{0, u1} Int M Int.instSemiringInt (AddCommGroup.toAddCommMonoid.{u1} M _inst_1) (AddCommGroup.intModule.{u1} M _inst_1)) (Preorder.toLE.{u1} (Submodule.{0, u1} Int M Int.instSemiringInt (AddCommGroup.toAddCommMonoid.{u1} M _inst_1) (AddCommGroup.intModule.{u1} M _inst_1)) (PartialOrder.toPreorder.{u1} (Submodule.{0, u1} Int M Int.instSemiringInt (AddCommGroup.toAddCommMonoid.{u1} M _inst_1) (AddCommGroup.intModule.{u1} M _inst_1)) (CompleteSemilatticeInf.toPartialOrder.{u1} (Submodule.{0, u1} Int M Int.instSemiringInt (AddCommGroup.toAddCommMonoid.{u1} M _inst_1) (AddCommGroup.intModule.{u1} M _inst_1)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (Submodule.{0, u1} Int M Int.instSemiringInt (AddCommGroup.toAddCommMonoid.{u1} M _inst_1) (AddCommGroup.intModule.{u1} M _inst_1)) (Submodule.completeLattice.{0, u1} Int M Int.instSemiringInt (AddCommGroup.toAddCommMonoid.{u1} M _inst_1) (AddCommGroup.intModule.{u1} M _inst_1)))))) x._@.Mathlib.Order.Hom.Basic._hyg.1300 x._@.Mathlib.Order.Hom.Basic._hyg.1302)) (AddSubgroup.{u1} M (AddCommGroup.toAddGroup.{u1} M _inst_1)) (fun (_x : AddSubgroup.{u1} M (AddCommGroup.toAddGroup.{u1} M _inst_1)) => Submodule.{0, u1} Int M Int.instSemiringInt (AddCommGroup.toAddCommMonoid.{u1} M _inst_1) (AddCommGroup.intModule.{u1} M _inst_1)) (RelHomClass.toFunLike.{u1, u1, u1} (RelIso.{u1, u1} (AddSubgroup.{u1} M (AddCommGroup.toAddGroup.{u1} M _inst_1)) (Submodule.{0, u1} Int M Int.instSemiringInt (AddCommGroup.toAddCommMonoid.{u1} M _inst_1) (AddCommGroup.intModule.{u1} M _inst_1)) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1285 : AddSubgroup.{u1} M (AddCommGroup.toAddGroup.{u1} M _inst_1)) (x._@.Mathlib.Order.Hom.Basic._hyg.1287 : AddSubgroup.{u1} M (AddCommGroup.toAddGroup.{u1} M _inst_1)) => LE.le.{u1} (AddSubgroup.{u1} M (AddCommGroup.toAddGroup.{u1} M _inst_1)) (Preorder.toLE.{u1} (AddSubgroup.{u1} M (AddCommGroup.toAddGroup.{u1} M _inst_1)) (PartialOrder.toPreorder.{u1} (AddSubgroup.{u1} M (AddCommGroup.toAddGroup.{u1} M _inst_1)) (CompleteSemilatticeInf.toPartialOrder.{u1} (AddSubgroup.{u1} M (AddCommGroup.toAddGroup.{u1} M _inst_1)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (AddSubgroup.{u1} M (AddCommGroup.toAddGroup.{u1} M _inst_1)) (AddSubgroup.instCompleteLatticeAddSubgroup.{u1} M (AddCommGroup.toAddGroup.{u1} M _inst_1)))))) x._@.Mathlib.Order.Hom.Basic._hyg.1285 x._@.Mathlib.Order.Hom.Basic._hyg.1287) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1300 : Submodule.{0, u1} Int M Int.instSemiringInt (AddCommGroup.toAddCommMonoid.{u1} M _inst_1) (AddCommGroup.intModule.{u1} M _inst_1)) (x._@.Mathlib.Order.Hom.Basic._hyg.1302 : Submodule.{0, u1} Int M Int.instSemiringInt (AddCommGroup.toAddCommMonoid.{u1} M _inst_1) (AddCommGroup.intModule.{u1} M _inst_1)) => LE.le.{u1} (Submodule.{0, u1} Int M Int.instSemiringInt (AddCommGroup.toAddCommMonoid.{u1} M _inst_1) (AddCommGroup.intModule.{u1} M _inst_1)) (Preorder.toLE.{u1} (Submodule.{0, u1} Int M Int.instSemiringInt (AddCommGroup.toAddCommMonoid.{u1} M _inst_1) (AddCommGroup.intModule.{u1} M _inst_1)) (PartialOrder.toPreorder.{u1} (Submodule.{0, u1} Int M Int.instSemiringInt (AddCommGroup.toAddCommMonoid.{u1} M _inst_1) (AddCommGroup.intModule.{u1} M _inst_1)) (CompleteSemilatticeInf.toPartialOrder.{u1} (Submodule.{0, u1} Int M Int.instSemiringInt (AddCommGroup.toAddCommMonoid.{u1} M _inst_1) (AddCommGroup.intModule.{u1} M _inst_1)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (Submodule.{0, u1} Int M Int.instSemiringInt (AddCommGroup.toAddCommMonoid.{u1} M _inst_1) (AddCommGroup.intModule.{u1} M _inst_1)) (Submodule.completeLattice.{0, u1} Int M Int.instSemiringInt (AddCommGroup.toAddCommMonoid.{u1} M _inst_1) (AddCommGroup.intModule.{u1} M _inst_1)))))) x._@.Mathlib.Order.Hom.Basic._hyg.1300 x._@.Mathlib.Order.Hom.Basic._hyg.1302)) (AddSubgroup.{u1} M (AddCommGroup.toAddGroup.{u1} M _inst_1)) (Submodule.{0, u1} Int M Int.instSemiringInt (AddCommGroup.toAddCommMonoid.{u1} M _inst_1) (AddCommGroup.intModule.{u1} M _inst_1)) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1285 : AddSubgroup.{u1} M (AddCommGroup.toAddGroup.{u1} M _inst_1)) (x._@.Mathlib.Order.Hom.Basic._hyg.1287 : AddSubgroup.{u1} M (AddCommGroup.toAddGroup.{u1} M _inst_1)) => LE.le.{u1} (AddSubgroup.{u1} M (AddCommGroup.toAddGroup.{u1} M _inst_1)) (Preorder.toLE.{u1} (AddSubgroup.{u1} M (AddCommGroup.toAddGroup.{u1} M _inst_1)) (PartialOrder.toPreorder.{u1} (AddSubgroup.{u1} M (AddCommGroup.toAddGroup.{u1} M _inst_1)) (CompleteSemilatticeInf.toPartialOrder.{u1} (AddSubgroup.{u1} M (AddCommGroup.toAddGroup.{u1} M _inst_1)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (AddSubgroup.{u1} M (AddCommGroup.toAddGroup.{u1} M _inst_1)) (AddSubgroup.instCompleteLatticeAddSubgroup.{u1} M (AddCommGroup.toAddGroup.{u1} M _inst_1)))))) x._@.Mathlib.Order.Hom.Basic._hyg.1285 x._@.Mathlib.Order.Hom.Basic._hyg.1287) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1300 : Submodule.{0, u1} Int M Int.instSemiringInt (AddCommGroup.toAddCommMonoid.{u1} M _inst_1) (AddCommGroup.intModule.{u1} M _inst_1)) (x._@.Mathlib.Order.Hom.Basic._hyg.1302 : Submodule.{0, u1} Int M Int.instSemiringInt (AddCommGroup.toAddCommMonoid.{u1} M _inst_1) (AddCommGroup.intModule.{u1} M _inst_1)) => LE.le.{u1} (Submodule.{0, u1} Int M Int.instSemiringInt (AddCommGroup.toAddCommMonoid.{u1} M _inst_1) (AddCommGroup.intModule.{u1} M _inst_1)) (Preorder.toLE.{u1} (Submodule.{0, u1} Int M Int.instSemiringInt (AddCommGroup.toAddCommMonoid.{u1} M _inst_1) (AddCommGroup.intModule.{u1} M _inst_1)) (PartialOrder.toPreorder.{u1} (Submodule.{0, u1} Int M Int.instSemiringInt (AddCommGroup.toAddCommMonoid.{u1} M _inst_1) (AddCommGroup.intModule.{u1} M _inst_1)) (CompleteSemilatticeInf.toPartialOrder.{u1} (Submodule.{0, u1} Int M Int.instSemiringInt (AddCommGroup.toAddCommMonoid.{u1} M _inst_1) (AddCommGroup.intModule.{u1} M _inst_1)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (Submodule.{0, u1} Int M Int.instSemiringInt (AddCommGroup.toAddCommMonoid.{u1} M _inst_1) (AddCommGroup.intModule.{u1} M _inst_1)) (Submodule.completeLattice.{0, u1} Int M Int.instSemiringInt (AddCommGroup.toAddCommMonoid.{u1} M _inst_1) (AddCommGroup.intModule.{u1} M _inst_1)))))) x._@.Mathlib.Order.Hom.Basic._hyg.1300 x._@.Mathlib.Order.Hom.Basic._hyg.1302) (RelIso.instRelHomClassRelIso.{u1, u1} (AddSubgroup.{u1} M (AddCommGroup.toAddGroup.{u1} M _inst_1)) (Submodule.{0, u1} Int M Int.instSemiringInt (AddCommGroup.toAddCommMonoid.{u1} M _inst_1) (AddCommGroup.intModule.{u1} M _inst_1)) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1285 : AddSubgroup.{u1} M (AddCommGroup.toAddGroup.{u1} M _inst_1)) (x._@.Mathlib.Order.Hom.Basic._hyg.1287 : AddSubgroup.{u1} M (AddCommGroup.toAddGroup.{u1} M _inst_1)) => LE.le.{u1} (AddSubgroup.{u1} M (AddCommGroup.toAddGroup.{u1} M _inst_1)) (Preorder.toLE.{u1} (AddSubgroup.{u1} M (AddCommGroup.toAddGroup.{u1} M _inst_1)) (PartialOrder.toPreorder.{u1} (AddSubgroup.{u1} M (AddCommGroup.toAddGroup.{u1} M _inst_1)) (CompleteSemilatticeInf.toPartialOrder.{u1} (AddSubgroup.{u1} M (AddCommGroup.toAddGroup.{u1} M _inst_1)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (AddSubgroup.{u1} M (AddCommGroup.toAddGroup.{u1} M _inst_1)) (AddSubgroup.instCompleteLatticeAddSubgroup.{u1} M (AddCommGroup.toAddGroup.{u1} M _inst_1)))))) x._@.Mathlib.Order.Hom.Basic._hyg.1285 x._@.Mathlib.Order.Hom.Basic._hyg.1287) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1300 : Submodule.{0, u1} Int M Int.instSemiringInt (AddCommGroup.toAddCommMonoid.{u1} M _inst_1) (AddCommGroup.intModule.{u1} M _inst_1)) (x._@.Mathlib.Order.Hom.Basic._hyg.1302 : Submodule.{0, u1} Int M Int.instSemiringInt (AddCommGroup.toAddCommMonoid.{u1} M _inst_1) (AddCommGroup.intModule.{u1} M _inst_1)) => LE.le.{u1} (Submodule.{0, u1} Int M Int.instSemiringInt (AddCommGroup.toAddCommMonoid.{u1} M _inst_1) (AddCommGroup.intModule.{u1} M _inst_1)) (Preorder.toLE.{u1} (Submodule.{0, u1} Int M Int.instSemiringInt (AddCommGroup.toAddCommMonoid.{u1} M _inst_1) (AddCommGroup.intModule.{u1} M _inst_1)) (PartialOrder.toPreorder.{u1} (Submodule.{0, u1} Int M Int.instSemiringInt (AddCommGroup.toAddCommMonoid.{u1} M _inst_1) (AddCommGroup.intModule.{u1} M _inst_1)) (CompleteSemilatticeInf.toPartialOrder.{u1} (Submodule.{0, u1} Int M Int.instSemiringInt (AddCommGroup.toAddCommMonoid.{u1} M _inst_1) (AddCommGroup.intModule.{u1} M _inst_1)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (Submodule.{0, u1} Int M Int.instSemiringInt (AddCommGroup.toAddCommMonoid.{u1} M _inst_1) (AddCommGroup.intModule.{u1} M _inst_1)) (Submodule.completeLattice.{0, u1} Int M Int.instSemiringInt (AddCommGroup.toAddCommMonoid.{u1} M _inst_1) (AddCommGroup.intModule.{u1} M _inst_1)))))) x._@.Mathlib.Order.Hom.Basic._hyg.1300 x._@.Mathlib.Order.Hom.Basic._hyg.1302))) (AddSubgroup.toIntSubmodule.{u1} M _inst_1) S)) (SetLike.coe.{u1, u1} (AddSubgroup.{u1} M (AddCommGroup.toAddGroup.{u1} M _inst_1)) M (AddSubgroup.instSetLikeAddSubgroup.{u1} M (AddCommGroup.toAddGroup.{u1} M _inst_1)) S)
 Case conversion may be inaccurate. Consider using '#align add_subgroup.coe_to_int_submodule AddSubgroup.coe_toIntSubmoduleₓ'. -/
 @[simp]
 theorem AddSubgroup.coe_toIntSubmodule (S : AddSubgroup M) : (S.toIntSubmodule : Set M) = S :=
@@ -717,7 +717,7 @@ theorem AddSubgroup.coe_toIntSubmodule (S : AddSubgroup M) : (S.toIntSubmodule :
 lean 3 declaration is
   forall {M : Type.{u1}} [_inst_1 : AddCommGroup.{u1} M] (S : AddSubgroup.{u1} M (AddCommGroup.toAddGroup.{u1} M _inst_1)), Eq.{succ u1} (AddSubgroup.{u1} M (AddCommGroup.toAddGroup.{u1} M _inst_1)) (Submodule.toAddSubgroup.{0, u1} Int M Int.ring _inst_1 (AddCommGroup.intModule.{u1} M _inst_1) (coeFn.{succ u1, succ u1} (OrderIso.{u1, u1} (AddSubgroup.{u1} M (AddCommGroup.toAddGroup.{u1} M _inst_1)) (Submodule.{0, u1} Int M Int.semiring (AddCommGroup.toAddCommMonoid.{u1} M _inst_1) (AddCommGroup.intModule.{u1} M _inst_1)) (Preorder.toHasLe.{u1} (AddSubgroup.{u1} M (AddCommGroup.toAddGroup.{u1} M _inst_1)) (PartialOrder.toPreorder.{u1} (AddSubgroup.{u1} M (AddCommGroup.toAddGroup.{u1} M _inst_1)) (CompleteSemilatticeInf.toPartialOrder.{u1} (AddSubgroup.{u1} M (AddCommGroup.toAddGroup.{u1} M _inst_1)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (AddSubgroup.{u1} M (AddCommGroup.toAddGroup.{u1} M _inst_1)) (AddSubgroup.completeLattice.{u1} M (AddCommGroup.toAddGroup.{u1} M _inst_1)))))) (Preorder.toHasLe.{u1} (Submodule.{0, u1} Int M Int.semiring (AddCommGroup.toAddCommMonoid.{u1} M _inst_1) (AddCommGroup.intModule.{u1} M _inst_1)) (PartialOrder.toPreorder.{u1} (Submodule.{0, u1} Int M Int.semiring (AddCommGroup.toAddCommMonoid.{u1} M _inst_1) (AddCommGroup.intModule.{u1} M _inst_1)) (CompleteSemilatticeInf.toPartialOrder.{u1} (Submodule.{0, u1} Int M Int.semiring (AddCommGroup.toAddCommMonoid.{u1} M _inst_1) (AddCommGroup.intModule.{u1} M _inst_1)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (Submodule.{0, u1} Int M Int.semiring (AddCommGroup.toAddCommMonoid.{u1} M _inst_1) (AddCommGroup.intModule.{u1} M _inst_1)) (Submodule.completeLattice.{0, u1} Int M Int.semiring (AddCommGroup.toAddCommMonoid.{u1} M _inst_1) (AddCommGroup.intModule.{u1} M _inst_1))))))) (fun (_x : RelIso.{u1, u1} (AddSubgroup.{u1} M (AddCommGroup.toAddGroup.{u1} M _inst_1)) (Submodule.{0, u1} Int M Int.semiring (AddCommGroup.toAddCommMonoid.{u1} M _inst_1) (AddCommGroup.intModule.{u1} M _inst_1)) (LE.le.{u1} (AddSubgroup.{u1} M (AddCommGroup.toAddGroup.{u1} M _inst_1)) (Preorder.toHasLe.{u1} (AddSubgroup.{u1} M (AddCommGroup.toAddGroup.{u1} M _inst_1)) (PartialOrder.toPreorder.{u1} (AddSubgroup.{u1} M (AddCommGroup.toAddGroup.{u1} M _inst_1)) (CompleteSemilatticeInf.toPartialOrder.{u1} (AddSubgroup.{u1} M (AddCommGroup.toAddGroup.{u1} M _inst_1)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (AddSubgroup.{u1} M (AddCommGroup.toAddGroup.{u1} M _inst_1)) (AddSubgroup.completeLattice.{u1} M (AddCommGroup.toAddGroup.{u1} M _inst_1))))))) (LE.le.{u1} (Submodule.{0, u1} Int M Int.semiring (AddCommGroup.toAddCommMonoid.{u1} M _inst_1) (AddCommGroup.intModule.{u1} M _inst_1)) (Preorder.toHasLe.{u1} (Submodule.{0, u1} Int M Int.semiring (AddCommGroup.toAddCommMonoid.{u1} M _inst_1) (AddCommGroup.intModule.{u1} M _inst_1)) (PartialOrder.toPreorder.{u1} (Submodule.{0, u1} Int M Int.semiring (AddCommGroup.toAddCommMonoid.{u1} M _inst_1) (AddCommGroup.intModule.{u1} M _inst_1)) (CompleteSemilatticeInf.toPartialOrder.{u1} (Submodule.{0, u1} Int M Int.semiring (AddCommGroup.toAddCommMonoid.{u1} M _inst_1) (AddCommGroup.intModule.{u1} M _inst_1)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (Submodule.{0, u1} Int M Int.semiring (AddCommGroup.toAddCommMonoid.{u1} M _inst_1) (AddCommGroup.intModule.{u1} M _inst_1)) (Submodule.completeLattice.{0, u1} Int M Int.semiring (AddCommGroup.toAddCommMonoid.{u1} M _inst_1) (AddCommGroup.intModule.{u1} M _inst_1)))))))) => (AddSubgroup.{u1} M (AddCommGroup.toAddGroup.{u1} M _inst_1)) -> (Submodule.{0, u1} Int M Int.semiring (AddCommGroup.toAddCommMonoid.{u1} M _inst_1) (AddCommGroup.intModule.{u1} M _inst_1))) (RelIso.hasCoeToFun.{u1, u1} (AddSubgroup.{u1} M (AddCommGroup.toAddGroup.{u1} M _inst_1)) (Submodule.{0, u1} Int M Int.semiring (AddCommGroup.toAddCommMonoid.{u1} M _inst_1) (AddCommGroup.intModule.{u1} M _inst_1)) (LE.le.{u1} (AddSubgroup.{u1} M (AddCommGroup.toAddGroup.{u1} M _inst_1)) (Preorder.toHasLe.{u1} (AddSubgroup.{u1} M (AddCommGroup.toAddGroup.{u1} M _inst_1)) (PartialOrder.toPreorder.{u1} (AddSubgroup.{u1} M (AddCommGroup.toAddGroup.{u1} M _inst_1)) (CompleteSemilatticeInf.toPartialOrder.{u1} (AddSubgroup.{u1} M (AddCommGroup.toAddGroup.{u1} M _inst_1)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (AddSubgroup.{u1} M (AddCommGroup.toAddGroup.{u1} M _inst_1)) (AddSubgroup.completeLattice.{u1} M (AddCommGroup.toAddGroup.{u1} M _inst_1))))))) (LE.le.{u1} (Submodule.{0, u1} Int M Int.semiring (AddCommGroup.toAddCommMonoid.{u1} M _inst_1) (AddCommGroup.intModule.{u1} M _inst_1)) (Preorder.toHasLe.{u1} (Submodule.{0, u1} Int M Int.semiring (AddCommGroup.toAddCommMonoid.{u1} M _inst_1) (AddCommGroup.intModule.{u1} M _inst_1)) (PartialOrder.toPreorder.{u1} (Submodule.{0, u1} Int M Int.semiring (AddCommGroup.toAddCommMonoid.{u1} M _inst_1) (AddCommGroup.intModule.{u1} M _inst_1)) (CompleteSemilatticeInf.toPartialOrder.{u1} (Submodule.{0, u1} Int M Int.semiring (AddCommGroup.toAddCommMonoid.{u1} M _inst_1) (AddCommGroup.intModule.{u1} M _inst_1)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (Submodule.{0, u1} Int M Int.semiring (AddCommGroup.toAddCommMonoid.{u1} M _inst_1) (AddCommGroup.intModule.{u1} M _inst_1)) (Submodule.completeLattice.{0, u1} Int M Int.semiring (AddCommGroup.toAddCommMonoid.{u1} M _inst_1) (AddCommGroup.intModule.{u1} M _inst_1)))))))) (AddSubgroup.toIntSubmodule.{u1} M _inst_1) S)) S
 but is expected to have type
-  forall {M : Type.{u1}} [_inst_1 : AddCommGroup.{u1} M] (S : AddSubgroup.{u1} M (AddCommGroup.toAddGroup.{u1} M _inst_1)), Eq.{succ u1} (AddSubgroup.{u1} M (AddCommGroup.toAddGroup.{u1} M _inst_1)) (Submodule.toAddSubgroup.{0, u1} Int M Int.instRingInt _inst_1 (AddCommGroup.intModule.{u1} M _inst_1) (FunLike.coe.{succ u1, succ u1, succ u1} (RelIso.{u1, u1} (AddSubgroup.{u1} M (AddCommGroup.toAddGroup.{u1} M _inst_1)) (Submodule.{0, u1} Int M Int.instSemiringInt (AddCommGroup.toAddCommMonoid.{u1} M _inst_1) (AddCommGroup.intModule.{u1} M _inst_1)) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1281 : AddSubgroup.{u1} M (AddCommGroup.toAddGroup.{u1} M _inst_1)) (x._@.Mathlib.Order.Hom.Basic._hyg.1283 : AddSubgroup.{u1} M (AddCommGroup.toAddGroup.{u1} M _inst_1)) => LE.le.{u1} (AddSubgroup.{u1} M (AddCommGroup.toAddGroup.{u1} M _inst_1)) (Preorder.toLE.{u1} (AddSubgroup.{u1} M (AddCommGroup.toAddGroup.{u1} M _inst_1)) (PartialOrder.toPreorder.{u1} (AddSubgroup.{u1} M (AddCommGroup.toAddGroup.{u1} M _inst_1)) (CompleteSemilatticeInf.toPartialOrder.{u1} (AddSubgroup.{u1} M (AddCommGroup.toAddGroup.{u1} M _inst_1)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (AddSubgroup.{u1} M (AddCommGroup.toAddGroup.{u1} M _inst_1)) (AddSubgroup.instCompleteLatticeAddSubgroup.{u1} M (AddCommGroup.toAddGroup.{u1} M _inst_1)))))) x._@.Mathlib.Order.Hom.Basic._hyg.1281 x._@.Mathlib.Order.Hom.Basic._hyg.1283) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1296 : Submodule.{0, u1} Int M Int.instSemiringInt (AddCommGroup.toAddCommMonoid.{u1} M _inst_1) (AddCommGroup.intModule.{u1} M _inst_1)) (x._@.Mathlib.Order.Hom.Basic._hyg.1298 : Submodule.{0, u1} Int M Int.instSemiringInt (AddCommGroup.toAddCommMonoid.{u1} M _inst_1) (AddCommGroup.intModule.{u1} M _inst_1)) => LE.le.{u1} (Submodule.{0, u1} Int M Int.instSemiringInt (AddCommGroup.toAddCommMonoid.{u1} M _inst_1) (AddCommGroup.intModule.{u1} M _inst_1)) (Preorder.toLE.{u1} (Submodule.{0, u1} Int M Int.instSemiringInt (AddCommGroup.toAddCommMonoid.{u1} M _inst_1) (AddCommGroup.intModule.{u1} M _inst_1)) (PartialOrder.toPreorder.{u1} (Submodule.{0, u1} Int M Int.instSemiringInt (AddCommGroup.toAddCommMonoid.{u1} M _inst_1) (AddCommGroup.intModule.{u1} M _inst_1)) (CompleteSemilatticeInf.toPartialOrder.{u1} (Submodule.{0, u1} Int M Int.instSemiringInt (AddCommGroup.toAddCommMonoid.{u1} M _inst_1) (AddCommGroup.intModule.{u1} M _inst_1)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (Submodule.{0, u1} Int M Int.instSemiringInt (AddCommGroup.toAddCommMonoid.{u1} M _inst_1) (AddCommGroup.intModule.{u1} M _inst_1)) (Submodule.completeLattice.{0, u1} Int M Int.instSemiringInt (AddCommGroup.toAddCommMonoid.{u1} M _inst_1) (AddCommGroup.intModule.{u1} M _inst_1)))))) x._@.Mathlib.Order.Hom.Basic._hyg.1296 x._@.Mathlib.Order.Hom.Basic._hyg.1298)) (AddSubgroup.{u1} M (AddCommGroup.toAddGroup.{u1} M _inst_1)) (fun (_x : AddSubgroup.{u1} M (AddCommGroup.toAddGroup.{u1} M _inst_1)) => Submodule.{0, u1} Int M Int.instSemiringInt (AddCommGroup.toAddCommMonoid.{u1} M _inst_1) (AddCommGroup.intModule.{u1} M _inst_1)) (RelHomClass.toFunLike.{u1, u1, u1} (RelIso.{u1, u1} (AddSubgroup.{u1} M (AddCommGroup.toAddGroup.{u1} M _inst_1)) (Submodule.{0, u1} Int M Int.instSemiringInt (AddCommGroup.toAddCommMonoid.{u1} M _inst_1) (AddCommGroup.intModule.{u1} M _inst_1)) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1281 : AddSubgroup.{u1} M (AddCommGroup.toAddGroup.{u1} M _inst_1)) (x._@.Mathlib.Order.Hom.Basic._hyg.1283 : AddSubgroup.{u1} M (AddCommGroup.toAddGroup.{u1} M _inst_1)) => LE.le.{u1} (AddSubgroup.{u1} M (AddCommGroup.toAddGroup.{u1} M _inst_1)) (Preorder.toLE.{u1} (AddSubgroup.{u1} M (AddCommGroup.toAddGroup.{u1} M _inst_1)) (PartialOrder.toPreorder.{u1} (AddSubgroup.{u1} M (AddCommGroup.toAddGroup.{u1} M _inst_1)) (CompleteSemilatticeInf.toPartialOrder.{u1} (AddSubgroup.{u1} M (AddCommGroup.toAddGroup.{u1} M _inst_1)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (AddSubgroup.{u1} M (AddCommGroup.toAddGroup.{u1} M _inst_1)) (AddSubgroup.instCompleteLatticeAddSubgroup.{u1} M (AddCommGroup.toAddGroup.{u1} M _inst_1)))))) x._@.Mathlib.Order.Hom.Basic._hyg.1281 x._@.Mathlib.Order.Hom.Basic._hyg.1283) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1296 : Submodule.{0, u1} Int M Int.instSemiringInt (AddCommGroup.toAddCommMonoid.{u1} M _inst_1) (AddCommGroup.intModule.{u1} M _inst_1)) (x._@.Mathlib.Order.Hom.Basic._hyg.1298 : Submodule.{0, u1} Int M Int.instSemiringInt (AddCommGroup.toAddCommMonoid.{u1} M _inst_1) (AddCommGroup.intModule.{u1} M _inst_1)) => LE.le.{u1} (Submodule.{0, u1} Int M Int.instSemiringInt (AddCommGroup.toAddCommMonoid.{u1} M _inst_1) (AddCommGroup.intModule.{u1} M _inst_1)) (Preorder.toLE.{u1} (Submodule.{0, u1} Int M Int.instSemiringInt (AddCommGroup.toAddCommMonoid.{u1} M _inst_1) (AddCommGroup.intModule.{u1} M _inst_1)) (PartialOrder.toPreorder.{u1} (Submodule.{0, u1} Int M Int.instSemiringInt (AddCommGroup.toAddCommMonoid.{u1} M _inst_1) (AddCommGroup.intModule.{u1} M _inst_1)) (CompleteSemilatticeInf.toPartialOrder.{u1} (Submodule.{0, u1} Int M Int.instSemiringInt (AddCommGroup.toAddCommMonoid.{u1} M _inst_1) (AddCommGroup.intModule.{u1} M _inst_1)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (Submodule.{0, u1} Int M Int.instSemiringInt (AddCommGroup.toAddCommMonoid.{u1} M _inst_1) (AddCommGroup.intModule.{u1} M _inst_1)) (Submodule.completeLattice.{0, u1} Int M Int.instSemiringInt (AddCommGroup.toAddCommMonoid.{u1} M _inst_1) (AddCommGroup.intModule.{u1} M _inst_1)))))) x._@.Mathlib.Order.Hom.Basic._hyg.1296 x._@.Mathlib.Order.Hom.Basic._hyg.1298)) (AddSubgroup.{u1} M (AddCommGroup.toAddGroup.{u1} M _inst_1)) (Submodule.{0, u1} Int M Int.instSemiringInt (AddCommGroup.toAddCommMonoid.{u1} M _inst_1) (AddCommGroup.intModule.{u1} M _inst_1)) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1281 : AddSubgroup.{u1} M (AddCommGroup.toAddGroup.{u1} M _inst_1)) (x._@.Mathlib.Order.Hom.Basic._hyg.1283 : AddSubgroup.{u1} M (AddCommGroup.toAddGroup.{u1} M _inst_1)) => LE.le.{u1} (AddSubgroup.{u1} M (AddCommGroup.toAddGroup.{u1} M _inst_1)) (Preorder.toLE.{u1} (AddSubgroup.{u1} M (AddCommGroup.toAddGroup.{u1} M _inst_1)) (PartialOrder.toPreorder.{u1} (AddSubgroup.{u1} M (AddCommGroup.toAddGroup.{u1} M _inst_1)) (CompleteSemilatticeInf.toPartialOrder.{u1} (AddSubgroup.{u1} M (AddCommGroup.toAddGroup.{u1} M _inst_1)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (AddSubgroup.{u1} M (AddCommGroup.toAddGroup.{u1} M _inst_1)) (AddSubgroup.instCompleteLatticeAddSubgroup.{u1} M (AddCommGroup.toAddGroup.{u1} M _inst_1)))))) x._@.Mathlib.Order.Hom.Basic._hyg.1281 x._@.Mathlib.Order.Hom.Basic._hyg.1283) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1296 : Submodule.{0, u1} Int M Int.instSemiringInt (AddCommGroup.toAddCommMonoid.{u1} M _inst_1) (AddCommGroup.intModule.{u1} M _inst_1)) (x._@.Mathlib.Order.Hom.Basic._hyg.1298 : Submodule.{0, u1} Int M Int.instSemiringInt (AddCommGroup.toAddCommMonoid.{u1} M _inst_1) (AddCommGroup.intModule.{u1} M _inst_1)) => LE.le.{u1} (Submodule.{0, u1} Int M Int.instSemiringInt (AddCommGroup.toAddCommMonoid.{u1} M _inst_1) (AddCommGroup.intModule.{u1} M _inst_1)) (Preorder.toLE.{u1} (Submodule.{0, u1} Int M Int.instSemiringInt (AddCommGroup.toAddCommMonoid.{u1} M _inst_1) (AddCommGroup.intModule.{u1} M _inst_1)) (PartialOrder.toPreorder.{u1} (Submodule.{0, u1} Int M Int.instSemiringInt (AddCommGroup.toAddCommMonoid.{u1} M _inst_1) (AddCommGroup.intModule.{u1} M _inst_1)) (CompleteSemilatticeInf.toPartialOrder.{u1} (Submodule.{0, u1} Int M Int.instSemiringInt (AddCommGroup.toAddCommMonoid.{u1} M _inst_1) (AddCommGroup.intModule.{u1} M _inst_1)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (Submodule.{0, u1} Int M Int.instSemiringInt (AddCommGroup.toAddCommMonoid.{u1} M _inst_1) (AddCommGroup.intModule.{u1} M _inst_1)) (Submodule.completeLattice.{0, u1} Int M Int.instSemiringInt (AddCommGroup.toAddCommMonoid.{u1} M _inst_1) (AddCommGroup.intModule.{u1} M _inst_1)))))) x._@.Mathlib.Order.Hom.Basic._hyg.1296 x._@.Mathlib.Order.Hom.Basic._hyg.1298) (RelIso.instRelHomClassRelIso.{u1, u1} (AddSubgroup.{u1} M (AddCommGroup.toAddGroup.{u1} M _inst_1)) (Submodule.{0, u1} Int M Int.instSemiringInt (AddCommGroup.toAddCommMonoid.{u1} M _inst_1) (AddCommGroup.intModule.{u1} M _inst_1)) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1281 : AddSubgroup.{u1} M (AddCommGroup.toAddGroup.{u1} M _inst_1)) (x._@.Mathlib.Order.Hom.Basic._hyg.1283 : AddSubgroup.{u1} M (AddCommGroup.toAddGroup.{u1} M _inst_1)) => LE.le.{u1} (AddSubgroup.{u1} M (AddCommGroup.toAddGroup.{u1} M _inst_1)) (Preorder.toLE.{u1} (AddSubgroup.{u1} M (AddCommGroup.toAddGroup.{u1} M _inst_1)) (PartialOrder.toPreorder.{u1} (AddSubgroup.{u1} M (AddCommGroup.toAddGroup.{u1} M _inst_1)) (CompleteSemilatticeInf.toPartialOrder.{u1} (AddSubgroup.{u1} M (AddCommGroup.toAddGroup.{u1} M _inst_1)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (AddSubgroup.{u1} M (AddCommGroup.toAddGroup.{u1} M _inst_1)) (AddSubgroup.instCompleteLatticeAddSubgroup.{u1} M (AddCommGroup.toAddGroup.{u1} M _inst_1)))))) x._@.Mathlib.Order.Hom.Basic._hyg.1281 x._@.Mathlib.Order.Hom.Basic._hyg.1283) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1296 : Submodule.{0, u1} Int M Int.instSemiringInt (AddCommGroup.toAddCommMonoid.{u1} M _inst_1) (AddCommGroup.intModule.{u1} M _inst_1)) (x._@.Mathlib.Order.Hom.Basic._hyg.1298 : Submodule.{0, u1} Int M Int.instSemiringInt (AddCommGroup.toAddCommMonoid.{u1} M _inst_1) (AddCommGroup.intModule.{u1} M _inst_1)) => LE.le.{u1} (Submodule.{0, u1} Int M Int.instSemiringInt (AddCommGroup.toAddCommMonoid.{u1} M _inst_1) (AddCommGroup.intModule.{u1} M _inst_1)) (Preorder.toLE.{u1} (Submodule.{0, u1} Int M Int.instSemiringInt (AddCommGroup.toAddCommMonoid.{u1} M _inst_1) (AddCommGroup.intModule.{u1} M _inst_1)) (PartialOrder.toPreorder.{u1} (Submodule.{0, u1} Int M Int.instSemiringInt (AddCommGroup.toAddCommMonoid.{u1} M _inst_1) (AddCommGroup.intModule.{u1} M _inst_1)) (CompleteSemilatticeInf.toPartialOrder.{u1} (Submodule.{0, u1} Int M Int.instSemiringInt (AddCommGroup.toAddCommMonoid.{u1} M _inst_1) (AddCommGroup.intModule.{u1} M _inst_1)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (Submodule.{0, u1} Int M Int.instSemiringInt (AddCommGroup.toAddCommMonoid.{u1} M _inst_1) (AddCommGroup.intModule.{u1} M _inst_1)) (Submodule.completeLattice.{0, u1} Int M Int.instSemiringInt (AddCommGroup.toAddCommMonoid.{u1} M _inst_1) (AddCommGroup.intModule.{u1} M _inst_1)))))) x._@.Mathlib.Order.Hom.Basic._hyg.1296 x._@.Mathlib.Order.Hom.Basic._hyg.1298))) (AddSubgroup.toIntSubmodule.{u1} M _inst_1) S)) S
+  forall {M : Type.{u1}} [_inst_1 : AddCommGroup.{u1} M] (S : AddSubgroup.{u1} M (AddCommGroup.toAddGroup.{u1} M _inst_1)), Eq.{succ u1} (AddSubgroup.{u1} M (AddCommGroup.toAddGroup.{u1} M _inst_1)) (Submodule.toAddSubgroup.{0, u1} Int M Int.instRingInt _inst_1 (AddCommGroup.intModule.{u1} M _inst_1) (FunLike.coe.{succ u1, succ u1, succ u1} (RelIso.{u1, u1} (AddSubgroup.{u1} M (AddCommGroup.toAddGroup.{u1} M _inst_1)) (Submodule.{0, u1} Int M Int.instSemiringInt (AddCommGroup.toAddCommMonoid.{u1} M _inst_1) (AddCommGroup.intModule.{u1} M _inst_1)) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1285 : AddSubgroup.{u1} M (AddCommGroup.toAddGroup.{u1} M _inst_1)) (x._@.Mathlib.Order.Hom.Basic._hyg.1287 : AddSubgroup.{u1} M (AddCommGroup.toAddGroup.{u1} M _inst_1)) => LE.le.{u1} (AddSubgroup.{u1} M (AddCommGroup.toAddGroup.{u1} M _inst_1)) (Preorder.toLE.{u1} (AddSubgroup.{u1} M (AddCommGroup.toAddGroup.{u1} M _inst_1)) (PartialOrder.toPreorder.{u1} (AddSubgroup.{u1} M (AddCommGroup.toAddGroup.{u1} M _inst_1)) (CompleteSemilatticeInf.toPartialOrder.{u1} (AddSubgroup.{u1} M (AddCommGroup.toAddGroup.{u1} M _inst_1)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (AddSubgroup.{u1} M (AddCommGroup.toAddGroup.{u1} M _inst_1)) (AddSubgroup.instCompleteLatticeAddSubgroup.{u1} M (AddCommGroup.toAddGroup.{u1} M _inst_1)))))) x._@.Mathlib.Order.Hom.Basic._hyg.1285 x._@.Mathlib.Order.Hom.Basic._hyg.1287) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1300 : Submodule.{0, u1} Int M Int.instSemiringInt (AddCommGroup.toAddCommMonoid.{u1} M _inst_1) (AddCommGroup.intModule.{u1} M _inst_1)) (x._@.Mathlib.Order.Hom.Basic._hyg.1302 : Submodule.{0, u1} Int M Int.instSemiringInt (AddCommGroup.toAddCommMonoid.{u1} M _inst_1) (AddCommGroup.intModule.{u1} M _inst_1)) => LE.le.{u1} (Submodule.{0, u1} Int M Int.instSemiringInt (AddCommGroup.toAddCommMonoid.{u1} M _inst_1) (AddCommGroup.intModule.{u1} M _inst_1)) (Preorder.toLE.{u1} (Submodule.{0, u1} Int M Int.instSemiringInt (AddCommGroup.toAddCommMonoid.{u1} M _inst_1) (AddCommGroup.intModule.{u1} M _inst_1)) (PartialOrder.toPreorder.{u1} (Submodule.{0, u1} Int M Int.instSemiringInt (AddCommGroup.toAddCommMonoid.{u1} M _inst_1) (AddCommGroup.intModule.{u1} M _inst_1)) (CompleteSemilatticeInf.toPartialOrder.{u1} (Submodule.{0, u1} Int M Int.instSemiringInt (AddCommGroup.toAddCommMonoid.{u1} M _inst_1) (AddCommGroup.intModule.{u1} M _inst_1)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (Submodule.{0, u1} Int M Int.instSemiringInt (AddCommGroup.toAddCommMonoid.{u1} M _inst_1) (AddCommGroup.intModule.{u1} M _inst_1)) (Submodule.completeLattice.{0, u1} Int M Int.instSemiringInt (AddCommGroup.toAddCommMonoid.{u1} M _inst_1) (AddCommGroup.intModule.{u1} M _inst_1)))))) x._@.Mathlib.Order.Hom.Basic._hyg.1300 x._@.Mathlib.Order.Hom.Basic._hyg.1302)) (AddSubgroup.{u1} M (AddCommGroup.toAddGroup.{u1} M _inst_1)) (fun (_x : AddSubgroup.{u1} M (AddCommGroup.toAddGroup.{u1} M _inst_1)) => Submodule.{0, u1} Int M Int.instSemiringInt (AddCommGroup.toAddCommMonoid.{u1} M _inst_1) (AddCommGroup.intModule.{u1} M _inst_1)) (RelHomClass.toFunLike.{u1, u1, u1} (RelIso.{u1, u1} (AddSubgroup.{u1} M (AddCommGroup.toAddGroup.{u1} M _inst_1)) (Submodule.{0, u1} Int M Int.instSemiringInt (AddCommGroup.toAddCommMonoid.{u1} M _inst_1) (AddCommGroup.intModule.{u1} M _inst_1)) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1285 : AddSubgroup.{u1} M (AddCommGroup.toAddGroup.{u1} M _inst_1)) (x._@.Mathlib.Order.Hom.Basic._hyg.1287 : AddSubgroup.{u1} M (AddCommGroup.toAddGroup.{u1} M _inst_1)) => LE.le.{u1} (AddSubgroup.{u1} M (AddCommGroup.toAddGroup.{u1} M _inst_1)) (Preorder.toLE.{u1} (AddSubgroup.{u1} M (AddCommGroup.toAddGroup.{u1} M _inst_1)) (PartialOrder.toPreorder.{u1} (AddSubgroup.{u1} M (AddCommGroup.toAddGroup.{u1} M _inst_1)) (CompleteSemilatticeInf.toPartialOrder.{u1} (AddSubgroup.{u1} M (AddCommGroup.toAddGroup.{u1} M _inst_1)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (AddSubgroup.{u1} M (AddCommGroup.toAddGroup.{u1} M _inst_1)) (AddSubgroup.instCompleteLatticeAddSubgroup.{u1} M (AddCommGroup.toAddGroup.{u1} M _inst_1)))))) x._@.Mathlib.Order.Hom.Basic._hyg.1285 x._@.Mathlib.Order.Hom.Basic._hyg.1287) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1300 : Submodule.{0, u1} Int M Int.instSemiringInt (AddCommGroup.toAddCommMonoid.{u1} M _inst_1) (AddCommGroup.intModule.{u1} M _inst_1)) (x._@.Mathlib.Order.Hom.Basic._hyg.1302 : Submodule.{0, u1} Int M Int.instSemiringInt (AddCommGroup.toAddCommMonoid.{u1} M _inst_1) (AddCommGroup.intModule.{u1} M _inst_1)) => LE.le.{u1} (Submodule.{0, u1} Int M Int.instSemiringInt (AddCommGroup.toAddCommMonoid.{u1} M _inst_1) (AddCommGroup.intModule.{u1} M _inst_1)) (Preorder.toLE.{u1} (Submodule.{0, u1} Int M Int.instSemiringInt (AddCommGroup.toAddCommMonoid.{u1} M _inst_1) (AddCommGroup.intModule.{u1} M _inst_1)) (PartialOrder.toPreorder.{u1} (Submodule.{0, u1} Int M Int.instSemiringInt (AddCommGroup.toAddCommMonoid.{u1} M _inst_1) (AddCommGroup.intModule.{u1} M _inst_1)) (CompleteSemilatticeInf.toPartialOrder.{u1} (Submodule.{0, u1} Int M Int.instSemiringInt (AddCommGroup.toAddCommMonoid.{u1} M _inst_1) (AddCommGroup.intModule.{u1} M _inst_1)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (Submodule.{0, u1} Int M Int.instSemiringInt (AddCommGroup.toAddCommMonoid.{u1} M _inst_1) (AddCommGroup.intModule.{u1} M _inst_1)) (Submodule.completeLattice.{0, u1} Int M Int.instSemiringInt (AddCommGroup.toAddCommMonoid.{u1} M _inst_1) (AddCommGroup.intModule.{u1} M _inst_1)))))) x._@.Mathlib.Order.Hom.Basic._hyg.1300 x._@.Mathlib.Order.Hom.Basic._hyg.1302)) (AddSubgroup.{u1} M (AddCommGroup.toAddGroup.{u1} M _inst_1)) (Submodule.{0, u1} Int M Int.instSemiringInt (AddCommGroup.toAddCommMonoid.{u1} M _inst_1) (AddCommGroup.intModule.{u1} M _inst_1)) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1285 : AddSubgroup.{u1} M (AddCommGroup.toAddGroup.{u1} M _inst_1)) (x._@.Mathlib.Order.Hom.Basic._hyg.1287 : AddSubgroup.{u1} M (AddCommGroup.toAddGroup.{u1} M _inst_1)) => LE.le.{u1} (AddSubgroup.{u1} M (AddCommGroup.toAddGroup.{u1} M _inst_1)) (Preorder.toLE.{u1} (AddSubgroup.{u1} M (AddCommGroup.toAddGroup.{u1} M _inst_1)) (PartialOrder.toPreorder.{u1} (AddSubgroup.{u1} M (AddCommGroup.toAddGroup.{u1} M _inst_1)) (CompleteSemilatticeInf.toPartialOrder.{u1} (AddSubgroup.{u1} M (AddCommGroup.toAddGroup.{u1} M _inst_1)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (AddSubgroup.{u1} M (AddCommGroup.toAddGroup.{u1} M _inst_1)) (AddSubgroup.instCompleteLatticeAddSubgroup.{u1} M (AddCommGroup.toAddGroup.{u1} M _inst_1)))))) x._@.Mathlib.Order.Hom.Basic._hyg.1285 x._@.Mathlib.Order.Hom.Basic._hyg.1287) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1300 : Submodule.{0, u1} Int M Int.instSemiringInt (AddCommGroup.toAddCommMonoid.{u1} M _inst_1) (AddCommGroup.intModule.{u1} M _inst_1)) (x._@.Mathlib.Order.Hom.Basic._hyg.1302 : Submodule.{0, u1} Int M Int.instSemiringInt (AddCommGroup.toAddCommMonoid.{u1} M _inst_1) (AddCommGroup.intModule.{u1} M _inst_1)) => LE.le.{u1} (Submodule.{0, u1} Int M Int.instSemiringInt (AddCommGroup.toAddCommMonoid.{u1} M _inst_1) (AddCommGroup.intModule.{u1} M _inst_1)) (Preorder.toLE.{u1} (Submodule.{0, u1} Int M Int.instSemiringInt (AddCommGroup.toAddCommMonoid.{u1} M _inst_1) (AddCommGroup.intModule.{u1} M _inst_1)) (PartialOrder.toPreorder.{u1} (Submodule.{0, u1} Int M Int.instSemiringInt (AddCommGroup.toAddCommMonoid.{u1} M _inst_1) (AddCommGroup.intModule.{u1} M _inst_1)) (CompleteSemilatticeInf.toPartialOrder.{u1} (Submodule.{0, u1} Int M Int.instSemiringInt (AddCommGroup.toAddCommMonoid.{u1} M _inst_1) (AddCommGroup.intModule.{u1} M _inst_1)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (Submodule.{0, u1} Int M Int.instSemiringInt (AddCommGroup.toAddCommMonoid.{u1} M _inst_1) (AddCommGroup.intModule.{u1} M _inst_1)) (Submodule.completeLattice.{0, u1} Int M Int.instSemiringInt (AddCommGroup.toAddCommMonoid.{u1} M _inst_1) (AddCommGroup.intModule.{u1} M _inst_1)))))) x._@.Mathlib.Order.Hom.Basic._hyg.1300 x._@.Mathlib.Order.Hom.Basic._hyg.1302) (RelIso.instRelHomClassRelIso.{u1, u1} (AddSubgroup.{u1} M (AddCommGroup.toAddGroup.{u1} M _inst_1)) (Submodule.{0, u1} Int M Int.instSemiringInt (AddCommGroup.toAddCommMonoid.{u1} M _inst_1) (AddCommGroup.intModule.{u1} M _inst_1)) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1285 : AddSubgroup.{u1} M (AddCommGroup.toAddGroup.{u1} M _inst_1)) (x._@.Mathlib.Order.Hom.Basic._hyg.1287 : AddSubgroup.{u1} M (AddCommGroup.toAddGroup.{u1} M _inst_1)) => LE.le.{u1} (AddSubgroup.{u1} M (AddCommGroup.toAddGroup.{u1} M _inst_1)) (Preorder.toLE.{u1} (AddSubgroup.{u1} M (AddCommGroup.toAddGroup.{u1} M _inst_1)) (PartialOrder.toPreorder.{u1} (AddSubgroup.{u1} M (AddCommGroup.toAddGroup.{u1} M _inst_1)) (CompleteSemilatticeInf.toPartialOrder.{u1} (AddSubgroup.{u1} M (AddCommGroup.toAddGroup.{u1} M _inst_1)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (AddSubgroup.{u1} M (AddCommGroup.toAddGroup.{u1} M _inst_1)) (AddSubgroup.instCompleteLatticeAddSubgroup.{u1} M (AddCommGroup.toAddGroup.{u1} M _inst_1)))))) x._@.Mathlib.Order.Hom.Basic._hyg.1285 x._@.Mathlib.Order.Hom.Basic._hyg.1287) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1300 : Submodule.{0, u1} Int M Int.instSemiringInt (AddCommGroup.toAddCommMonoid.{u1} M _inst_1) (AddCommGroup.intModule.{u1} M _inst_1)) (x._@.Mathlib.Order.Hom.Basic._hyg.1302 : Submodule.{0, u1} Int M Int.instSemiringInt (AddCommGroup.toAddCommMonoid.{u1} M _inst_1) (AddCommGroup.intModule.{u1} M _inst_1)) => LE.le.{u1} (Submodule.{0, u1} Int M Int.instSemiringInt (AddCommGroup.toAddCommMonoid.{u1} M _inst_1) (AddCommGroup.intModule.{u1} M _inst_1)) (Preorder.toLE.{u1} (Submodule.{0, u1} Int M Int.instSemiringInt (AddCommGroup.toAddCommMonoid.{u1} M _inst_1) (AddCommGroup.intModule.{u1} M _inst_1)) (PartialOrder.toPreorder.{u1} (Submodule.{0, u1} Int M Int.instSemiringInt (AddCommGroup.toAddCommMonoid.{u1} M _inst_1) (AddCommGroup.intModule.{u1} M _inst_1)) (CompleteSemilatticeInf.toPartialOrder.{u1} (Submodule.{0, u1} Int M Int.instSemiringInt (AddCommGroup.toAddCommMonoid.{u1} M _inst_1) (AddCommGroup.intModule.{u1} M _inst_1)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (Submodule.{0, u1} Int M Int.instSemiringInt (AddCommGroup.toAddCommMonoid.{u1} M _inst_1) (AddCommGroup.intModule.{u1} M _inst_1)) (Submodule.completeLattice.{0, u1} Int M Int.instSemiringInt (AddCommGroup.toAddCommMonoid.{u1} M _inst_1) (AddCommGroup.intModule.{u1} M _inst_1)))))) x._@.Mathlib.Order.Hom.Basic._hyg.1300 x._@.Mathlib.Order.Hom.Basic._hyg.1302))) (AddSubgroup.toIntSubmodule.{u1} M _inst_1) S)) S
 Case conversion may be inaccurate. Consider using '#align add_subgroup.to_int_submodule_to_add_subgroup AddSubgroup.toIntSubmodule_toAddSubgroupₓ'. -/
 @[simp]
 theorem AddSubgroup.toIntSubmodule_toAddSubgroup (S : AddSubgroup M) :
@@ -729,7 +729,7 @@ theorem AddSubgroup.toIntSubmodule_toAddSubgroup (S : AddSubgroup M) :
 lean 3 declaration is
   forall {M : Type.{u1}} [_inst_1 : AddCommGroup.{u1} M] (S : Submodule.{0, u1} Int M Int.semiring (AddCommGroup.toAddCommMonoid.{u1} M _inst_1) (AddCommGroup.intModule.{u1} M _inst_1)), Eq.{succ u1} (Submodule.{0, u1} Int M Int.semiring (AddCommGroup.toAddCommMonoid.{u1} M _inst_1) (AddCommGroup.intModule.{u1} M _inst_1)) (coeFn.{succ u1, succ u1} (OrderIso.{u1, u1} (AddSubgroup.{u1} M (AddCommGroup.toAddGroup.{u1} M _inst_1)) (Submodule.{0, u1} Int M Int.semiring (AddCommGroup.toAddCommMonoid.{u1} M _inst_1) (AddCommGroup.intModule.{u1} M _inst_1)) (Preorder.toHasLe.{u1} (AddSubgroup.{u1} M (AddCommGroup.toAddGroup.{u1} M _inst_1)) (PartialOrder.toPreorder.{u1} (AddSubgroup.{u1} M (AddCommGroup.toAddGroup.{u1} M _inst_1)) (CompleteSemilatticeInf.toPartialOrder.{u1} (AddSubgroup.{u1} M (AddCommGroup.toAddGroup.{u1} M _inst_1)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (AddSubgroup.{u1} M (AddCommGroup.toAddGroup.{u1} M _inst_1)) (AddSubgroup.completeLattice.{u1} M (AddCommGroup.toAddGroup.{u1} M _inst_1)))))) (Preorder.toHasLe.{u1} (Submodule.{0, u1} Int M Int.semiring (AddCommGroup.toAddCommMonoid.{u1} M _inst_1) (AddCommGroup.intModule.{u1} M _inst_1)) (PartialOrder.toPreorder.{u1} (Submodule.{0, u1} Int M Int.semiring (AddCommGroup.toAddCommMonoid.{u1} M _inst_1) (AddCommGroup.intModule.{u1} M _inst_1)) (CompleteSemilatticeInf.toPartialOrder.{u1} (Submodule.{0, u1} Int M Int.semiring (AddCommGroup.toAddCommMonoid.{u1} M _inst_1) (AddCommGroup.intModule.{u1} M _inst_1)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (Submodule.{0, u1} Int M Int.semiring (AddCommGroup.toAddCommMonoid.{u1} M _inst_1) (AddCommGroup.intModule.{u1} M _inst_1)) (Submodule.completeLattice.{0, u1} Int M Int.semiring (AddCommGroup.toAddCommMonoid.{u1} M _inst_1) (AddCommGroup.intModule.{u1} M _inst_1))))))) (fun (_x : RelIso.{u1, u1} (AddSubgroup.{u1} M (AddCommGroup.toAddGroup.{u1} M _inst_1)) (Submodule.{0, u1} Int M Int.semiring (AddCommGroup.toAddCommMonoid.{u1} M _inst_1) (AddCommGroup.intModule.{u1} M _inst_1)) (LE.le.{u1} (AddSubgroup.{u1} M (AddCommGroup.toAddGroup.{u1} M _inst_1)) (Preorder.toHasLe.{u1} (AddSubgroup.{u1} M (AddCommGroup.toAddGroup.{u1} M _inst_1)) (PartialOrder.toPreorder.{u1} (AddSubgroup.{u1} M (AddCommGroup.toAddGroup.{u1} M _inst_1)) (CompleteSemilatticeInf.toPartialOrder.{u1} (AddSubgroup.{u1} M (AddCommGroup.toAddGroup.{u1} M _inst_1)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (AddSubgroup.{u1} M (AddCommGroup.toAddGroup.{u1} M _inst_1)) (AddSubgroup.completeLattice.{u1} M (AddCommGroup.toAddGroup.{u1} M _inst_1))))))) (LE.le.{u1} (Submodule.{0, u1} Int M Int.semiring (AddCommGroup.toAddCommMonoid.{u1} M _inst_1) (AddCommGroup.intModule.{u1} M _inst_1)) (Preorder.toHasLe.{u1} (Submodule.{0, u1} Int M Int.semiring (AddCommGroup.toAddCommMonoid.{u1} M _inst_1) (AddCommGroup.intModule.{u1} M _inst_1)) (PartialOrder.toPreorder.{u1} (Submodule.{0, u1} Int M Int.semiring (AddCommGroup.toAddCommMonoid.{u1} M _inst_1) (AddCommGroup.intModule.{u1} M _inst_1)) (CompleteSemilatticeInf.toPartialOrder.{u1} (Submodule.{0, u1} Int M Int.semiring (AddCommGroup.toAddCommMonoid.{u1} M _inst_1) (AddCommGroup.intModule.{u1} M _inst_1)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (Submodule.{0, u1} Int M Int.semiring (AddCommGroup.toAddCommMonoid.{u1} M _inst_1) (AddCommGroup.intModule.{u1} M _inst_1)) (Submodule.completeLattice.{0, u1} Int M Int.semiring (AddCommGroup.toAddCommMonoid.{u1} M _inst_1) (AddCommGroup.intModule.{u1} M _inst_1)))))))) => (AddSubgroup.{u1} M (AddCommGroup.toAddGroup.{u1} M _inst_1)) -> (Submodule.{0, u1} Int M Int.semiring (AddCommGroup.toAddCommMonoid.{u1} M _inst_1) (AddCommGroup.intModule.{u1} M _inst_1))) (RelIso.hasCoeToFun.{u1, u1} (AddSubgroup.{u1} M (AddCommGroup.toAddGroup.{u1} M _inst_1)) (Submodule.{0, u1} Int M Int.semiring (AddCommGroup.toAddCommMonoid.{u1} M _inst_1) (AddCommGroup.intModule.{u1} M _inst_1)) (LE.le.{u1} (AddSubgroup.{u1} M (AddCommGroup.toAddGroup.{u1} M _inst_1)) (Preorder.toHasLe.{u1} (AddSubgroup.{u1} M (AddCommGroup.toAddGroup.{u1} M _inst_1)) (PartialOrder.toPreorder.{u1} (AddSubgroup.{u1} M (AddCommGroup.toAddGroup.{u1} M _inst_1)) (CompleteSemilatticeInf.toPartialOrder.{u1} (AddSubgroup.{u1} M (AddCommGroup.toAddGroup.{u1} M _inst_1)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (AddSubgroup.{u1} M (AddCommGroup.toAddGroup.{u1} M _inst_1)) (AddSubgroup.completeLattice.{u1} M (AddCommGroup.toAddGroup.{u1} M _inst_1))))))) (LE.le.{u1} (Submodule.{0, u1} Int M Int.semiring (AddCommGroup.toAddCommMonoid.{u1} M _inst_1) (AddCommGroup.intModule.{u1} M _inst_1)) (Preorder.toHasLe.{u1} (Submodule.{0, u1} Int M Int.semiring (AddCommGroup.toAddCommMonoid.{u1} M _inst_1) (AddCommGroup.intModule.{u1} M _inst_1)) (PartialOrder.toPreorder.{u1} (Submodule.{0, u1} Int M Int.semiring (AddCommGroup.toAddCommMonoid.{u1} M _inst_1) (AddCommGroup.intModule.{u1} M _inst_1)) (CompleteSemilatticeInf.toPartialOrder.{u1} (Submodule.{0, u1} Int M Int.semiring (AddCommGroup.toAddCommMonoid.{u1} M _inst_1) (AddCommGroup.intModule.{u1} M _inst_1)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (Submodule.{0, u1} Int M Int.semiring (AddCommGroup.toAddCommMonoid.{u1} M _inst_1) (AddCommGroup.intModule.{u1} M _inst_1)) (Submodule.completeLattice.{0, u1} Int M Int.semiring (AddCommGroup.toAddCommMonoid.{u1} M _inst_1) (AddCommGroup.intModule.{u1} M _inst_1)))))))) (AddSubgroup.toIntSubmodule.{u1} M _inst_1) (Submodule.toAddSubgroup.{0, u1} Int M Int.ring _inst_1 (AddCommGroup.intModule.{u1} M _inst_1) S)) S
 but is expected to have type
-  forall {M : Type.{u1}} [_inst_1 : AddCommGroup.{u1} M] (S : Submodule.{0, u1} Int M Int.instSemiringInt (AddCommGroup.toAddCommMonoid.{u1} M _inst_1) (AddCommGroup.intModule.{u1} M _inst_1)), Eq.{succ u1} (Submodule.{0, u1} Int M Int.instSemiringInt (AddCommGroup.toAddCommMonoid.{u1} M _inst_1) (AddCommGroup.intModule.{u1} M _inst_1)) (FunLike.coe.{succ u1, succ u1, succ u1} (RelIso.{u1, u1} (AddSubgroup.{u1} M (AddCommGroup.toAddGroup.{u1} M _inst_1)) (Submodule.{0, u1} Int M Int.instSemiringInt (AddCommGroup.toAddCommMonoid.{u1} M _inst_1) (AddCommGroup.intModule.{u1} M _inst_1)) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1281 : AddSubgroup.{u1} M (AddCommGroup.toAddGroup.{u1} M _inst_1)) (x._@.Mathlib.Order.Hom.Basic._hyg.1283 : AddSubgroup.{u1} M (AddCommGroup.toAddGroup.{u1} M _inst_1)) => LE.le.{u1} (AddSubgroup.{u1} M (AddCommGroup.toAddGroup.{u1} M _inst_1)) (Preorder.toLE.{u1} (AddSubgroup.{u1} M (AddCommGroup.toAddGroup.{u1} M _inst_1)) (PartialOrder.toPreorder.{u1} (AddSubgroup.{u1} M (AddCommGroup.toAddGroup.{u1} M _inst_1)) (CompleteSemilatticeInf.toPartialOrder.{u1} (AddSubgroup.{u1} M (AddCommGroup.toAddGroup.{u1} M _inst_1)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (AddSubgroup.{u1} M (AddCommGroup.toAddGroup.{u1} M _inst_1)) (AddSubgroup.instCompleteLatticeAddSubgroup.{u1} M (AddCommGroup.toAddGroup.{u1} M _inst_1)))))) x._@.Mathlib.Order.Hom.Basic._hyg.1281 x._@.Mathlib.Order.Hom.Basic._hyg.1283) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1296 : Submodule.{0, u1} Int M Int.instSemiringInt (AddCommGroup.toAddCommMonoid.{u1} M _inst_1) (AddCommGroup.intModule.{u1} M _inst_1)) (x._@.Mathlib.Order.Hom.Basic._hyg.1298 : Submodule.{0, u1} Int M Int.instSemiringInt (AddCommGroup.toAddCommMonoid.{u1} M _inst_1) (AddCommGroup.intModule.{u1} M _inst_1)) => LE.le.{u1} (Submodule.{0, u1} Int M Int.instSemiringInt (AddCommGroup.toAddCommMonoid.{u1} M _inst_1) (AddCommGroup.intModule.{u1} M _inst_1)) (Preorder.toLE.{u1} (Submodule.{0, u1} Int M Int.instSemiringInt (AddCommGroup.toAddCommMonoid.{u1} M _inst_1) (AddCommGroup.intModule.{u1} M _inst_1)) (PartialOrder.toPreorder.{u1} (Submodule.{0, u1} Int M Int.instSemiringInt (AddCommGroup.toAddCommMonoid.{u1} M _inst_1) (AddCommGroup.intModule.{u1} M _inst_1)) (CompleteSemilatticeInf.toPartialOrder.{u1} (Submodule.{0, u1} Int M Int.instSemiringInt (AddCommGroup.toAddCommMonoid.{u1} M _inst_1) (AddCommGroup.intModule.{u1} M _inst_1)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (Submodule.{0, u1} Int M Int.instSemiringInt (AddCommGroup.toAddCommMonoid.{u1} M _inst_1) (AddCommGroup.intModule.{u1} M _inst_1)) (Submodule.completeLattice.{0, u1} Int M Int.instSemiringInt (AddCommGroup.toAddCommMonoid.{u1} M _inst_1) (AddCommGroup.intModule.{u1} M _inst_1)))))) x._@.Mathlib.Order.Hom.Basic._hyg.1296 x._@.Mathlib.Order.Hom.Basic._hyg.1298)) (AddSubgroup.{u1} M (AddCommGroup.toAddGroup.{u1} M _inst_1)) (fun (_x : AddSubgroup.{u1} M (AddCommGroup.toAddGroup.{u1} M _inst_1)) => Submodule.{0, u1} Int M Int.instSemiringInt (AddCommGroup.toAddCommMonoid.{u1} M _inst_1) (AddCommGroup.intModule.{u1} M _inst_1)) (RelHomClass.toFunLike.{u1, u1, u1} (RelIso.{u1, u1} (AddSubgroup.{u1} M (AddCommGroup.toAddGroup.{u1} M _inst_1)) (Submodule.{0, u1} Int M Int.instSemiringInt (AddCommGroup.toAddCommMonoid.{u1} M _inst_1) (AddCommGroup.intModule.{u1} M _inst_1)) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1281 : AddSubgroup.{u1} M (AddCommGroup.toAddGroup.{u1} M _inst_1)) (x._@.Mathlib.Order.Hom.Basic._hyg.1283 : AddSubgroup.{u1} M (AddCommGroup.toAddGroup.{u1} M _inst_1)) => LE.le.{u1} (AddSubgroup.{u1} M (AddCommGroup.toAddGroup.{u1} M _inst_1)) (Preorder.toLE.{u1} (AddSubgroup.{u1} M (AddCommGroup.toAddGroup.{u1} M _inst_1)) (PartialOrder.toPreorder.{u1} (AddSubgroup.{u1} M (AddCommGroup.toAddGroup.{u1} M _inst_1)) (CompleteSemilatticeInf.toPartialOrder.{u1} (AddSubgroup.{u1} M (AddCommGroup.toAddGroup.{u1} M _inst_1)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (AddSubgroup.{u1} M (AddCommGroup.toAddGroup.{u1} M _inst_1)) (AddSubgroup.instCompleteLatticeAddSubgroup.{u1} M (AddCommGroup.toAddGroup.{u1} M _inst_1)))))) x._@.Mathlib.Order.Hom.Basic._hyg.1281 x._@.Mathlib.Order.Hom.Basic._hyg.1283) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1296 : Submodule.{0, u1} Int M Int.instSemiringInt (AddCommGroup.toAddCommMonoid.{u1} M _inst_1) (AddCommGroup.intModule.{u1} M _inst_1)) (x._@.Mathlib.Order.Hom.Basic._hyg.1298 : Submodule.{0, u1} Int M Int.instSemiringInt (AddCommGroup.toAddCommMonoid.{u1} M _inst_1) (AddCommGroup.intModule.{u1} M _inst_1)) => LE.le.{u1} (Submodule.{0, u1} Int M Int.instSemiringInt (AddCommGroup.toAddCommMonoid.{u1} M _inst_1) (AddCommGroup.intModule.{u1} M _inst_1)) (Preorder.toLE.{u1} (Submodule.{0, u1} Int M Int.instSemiringInt (AddCommGroup.toAddCommMonoid.{u1} M _inst_1) (AddCommGroup.intModule.{u1} M _inst_1)) (PartialOrder.toPreorder.{u1} (Submodule.{0, u1} Int M Int.instSemiringInt (AddCommGroup.toAddCommMonoid.{u1} M _inst_1) (AddCommGroup.intModule.{u1} M _inst_1)) (CompleteSemilatticeInf.toPartialOrder.{u1} (Submodule.{0, u1} Int M Int.instSemiringInt (AddCommGroup.toAddCommMonoid.{u1} M _inst_1) (AddCommGroup.intModule.{u1} M _inst_1)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (Submodule.{0, u1} Int M Int.instSemiringInt (AddCommGroup.toAddCommMonoid.{u1} M _inst_1) (AddCommGroup.intModule.{u1} M _inst_1)) (Submodule.completeLattice.{0, u1} Int M Int.instSemiringInt (AddCommGroup.toAddCommMonoid.{u1} M _inst_1) (AddCommGroup.intModule.{u1} M _inst_1)))))) x._@.Mathlib.Order.Hom.Basic._hyg.1296 x._@.Mathlib.Order.Hom.Basic._hyg.1298)) (AddSubgroup.{u1} M (AddCommGroup.toAddGroup.{u1} M _inst_1)) (Submodule.{0, u1} Int M Int.instSemiringInt (AddCommGroup.toAddCommMonoid.{u1} M _inst_1) (AddCommGroup.intModule.{u1} M _inst_1)) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1281 : AddSubgroup.{u1} M (AddCommGroup.toAddGroup.{u1} M _inst_1)) (x._@.Mathlib.Order.Hom.Basic._hyg.1283 : AddSubgroup.{u1} M (AddCommGroup.toAddGroup.{u1} M _inst_1)) => LE.le.{u1} (AddSubgroup.{u1} M (AddCommGroup.toAddGroup.{u1} M _inst_1)) (Preorder.toLE.{u1} (AddSubgroup.{u1} M (AddCommGroup.toAddGroup.{u1} M _inst_1)) (PartialOrder.toPreorder.{u1} (AddSubgroup.{u1} M (AddCommGroup.toAddGroup.{u1} M _inst_1)) (CompleteSemilatticeInf.toPartialOrder.{u1} (AddSubgroup.{u1} M (AddCommGroup.toAddGroup.{u1} M _inst_1)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (AddSubgroup.{u1} M (AddCommGroup.toAddGroup.{u1} M _inst_1)) (AddSubgroup.instCompleteLatticeAddSubgroup.{u1} M (AddCommGroup.toAddGroup.{u1} M _inst_1)))))) x._@.Mathlib.Order.Hom.Basic._hyg.1281 x._@.Mathlib.Order.Hom.Basic._hyg.1283) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1296 : Submodule.{0, u1} Int M Int.instSemiringInt (AddCommGroup.toAddCommMonoid.{u1} M _inst_1) (AddCommGroup.intModule.{u1} M _inst_1)) (x._@.Mathlib.Order.Hom.Basic._hyg.1298 : Submodule.{0, u1} Int M Int.instSemiringInt (AddCommGroup.toAddCommMonoid.{u1} M _inst_1) (AddCommGroup.intModule.{u1} M _inst_1)) => LE.le.{u1} (Submodule.{0, u1} Int M Int.instSemiringInt (AddCommGroup.toAddCommMonoid.{u1} M _inst_1) (AddCommGroup.intModule.{u1} M _inst_1)) (Preorder.toLE.{u1} (Submodule.{0, u1} Int M Int.instSemiringInt (AddCommGroup.toAddCommMonoid.{u1} M _inst_1) (AddCommGroup.intModule.{u1} M _inst_1)) (PartialOrder.toPreorder.{u1} (Submodule.{0, u1} Int M Int.instSemiringInt (AddCommGroup.toAddCommMonoid.{u1} M _inst_1) (AddCommGroup.intModule.{u1} M _inst_1)) (CompleteSemilatticeInf.toPartialOrder.{u1} (Submodule.{0, u1} Int M Int.instSemiringInt (AddCommGroup.toAddCommMonoid.{u1} M _inst_1) (AddCommGroup.intModule.{u1} M _inst_1)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (Submodule.{0, u1} Int M Int.instSemiringInt (AddCommGroup.toAddCommMonoid.{u1} M _inst_1) (AddCommGroup.intModule.{u1} M _inst_1)) (Submodule.completeLattice.{0, u1} Int M Int.instSemiringInt (AddCommGroup.toAddCommMonoid.{u1} M _inst_1) (AddCommGroup.intModule.{u1} M _inst_1)))))) x._@.Mathlib.Order.Hom.Basic._hyg.1296 x._@.Mathlib.Order.Hom.Basic._hyg.1298) (RelIso.instRelHomClassRelIso.{u1, u1} (AddSubgroup.{u1} M (AddCommGroup.toAddGroup.{u1} M _inst_1)) (Submodule.{0, u1} Int M Int.instSemiringInt (AddCommGroup.toAddCommMonoid.{u1} M _inst_1) (AddCommGroup.intModule.{u1} M _inst_1)) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1281 : AddSubgroup.{u1} M (AddCommGroup.toAddGroup.{u1} M _inst_1)) (x._@.Mathlib.Order.Hom.Basic._hyg.1283 : AddSubgroup.{u1} M (AddCommGroup.toAddGroup.{u1} M _inst_1)) => LE.le.{u1} (AddSubgroup.{u1} M (AddCommGroup.toAddGroup.{u1} M _inst_1)) (Preorder.toLE.{u1} (AddSubgroup.{u1} M (AddCommGroup.toAddGroup.{u1} M _inst_1)) (PartialOrder.toPreorder.{u1} (AddSubgroup.{u1} M (AddCommGroup.toAddGroup.{u1} M _inst_1)) (CompleteSemilatticeInf.toPartialOrder.{u1} (AddSubgroup.{u1} M (AddCommGroup.toAddGroup.{u1} M _inst_1)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (AddSubgroup.{u1} M (AddCommGroup.toAddGroup.{u1} M _inst_1)) (AddSubgroup.instCompleteLatticeAddSubgroup.{u1} M (AddCommGroup.toAddGroup.{u1} M _inst_1)))))) x._@.Mathlib.Order.Hom.Basic._hyg.1281 x._@.Mathlib.Order.Hom.Basic._hyg.1283) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1296 : Submodule.{0, u1} Int M Int.instSemiringInt (AddCommGroup.toAddCommMonoid.{u1} M _inst_1) (AddCommGroup.intModule.{u1} M _inst_1)) (x._@.Mathlib.Order.Hom.Basic._hyg.1298 : Submodule.{0, u1} Int M Int.instSemiringInt (AddCommGroup.toAddCommMonoid.{u1} M _inst_1) (AddCommGroup.intModule.{u1} M _inst_1)) => LE.le.{u1} (Submodule.{0, u1} Int M Int.instSemiringInt (AddCommGroup.toAddCommMonoid.{u1} M _inst_1) (AddCommGroup.intModule.{u1} M _inst_1)) (Preorder.toLE.{u1} (Submodule.{0, u1} Int M Int.instSemiringInt (AddCommGroup.toAddCommMonoid.{u1} M _inst_1) (AddCommGroup.intModule.{u1} M _inst_1)) (PartialOrder.toPreorder.{u1} (Submodule.{0, u1} Int M Int.instSemiringInt (AddCommGroup.toAddCommMonoid.{u1} M _inst_1) (AddCommGroup.intModule.{u1} M _inst_1)) (CompleteSemilatticeInf.toPartialOrder.{u1} (Submodule.{0, u1} Int M Int.instSemiringInt (AddCommGroup.toAddCommMonoid.{u1} M _inst_1) (AddCommGroup.intModule.{u1} M _inst_1)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (Submodule.{0, u1} Int M Int.instSemiringInt (AddCommGroup.toAddCommMonoid.{u1} M _inst_1) (AddCommGroup.intModule.{u1} M _inst_1)) (Submodule.completeLattice.{0, u1} Int M Int.instSemiringInt (AddCommGroup.toAddCommMonoid.{u1} M _inst_1) (AddCommGroup.intModule.{u1} M _inst_1)))))) x._@.Mathlib.Order.Hom.Basic._hyg.1296 x._@.Mathlib.Order.Hom.Basic._hyg.1298))) (AddSubgroup.toIntSubmodule.{u1} M _inst_1) (Submodule.toAddSubgroup.{0, u1} Int M Int.instRingInt _inst_1 (AddCommGroup.intModule.{u1} M _inst_1) S)) S
+  forall {M : Type.{u1}} [_inst_1 : AddCommGroup.{u1} M] (S : Submodule.{0, u1} Int M Int.instSemiringInt (AddCommGroup.toAddCommMonoid.{u1} M _inst_1) (AddCommGroup.intModule.{u1} M _inst_1)), Eq.{succ u1} (Submodule.{0, u1} Int M Int.instSemiringInt (AddCommGroup.toAddCommMonoid.{u1} M _inst_1) (AddCommGroup.intModule.{u1} M _inst_1)) (FunLike.coe.{succ u1, succ u1, succ u1} (RelIso.{u1, u1} (AddSubgroup.{u1} M (AddCommGroup.toAddGroup.{u1} M _inst_1)) (Submodule.{0, u1} Int M Int.instSemiringInt (AddCommGroup.toAddCommMonoid.{u1} M _inst_1) (AddCommGroup.intModule.{u1} M _inst_1)) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1285 : AddSubgroup.{u1} M (AddCommGroup.toAddGroup.{u1} M _inst_1)) (x._@.Mathlib.Order.Hom.Basic._hyg.1287 : AddSubgroup.{u1} M (AddCommGroup.toAddGroup.{u1} M _inst_1)) => LE.le.{u1} (AddSubgroup.{u1} M (AddCommGroup.toAddGroup.{u1} M _inst_1)) (Preorder.toLE.{u1} (AddSubgroup.{u1} M (AddCommGroup.toAddGroup.{u1} M _inst_1)) (PartialOrder.toPreorder.{u1} (AddSubgroup.{u1} M (AddCommGroup.toAddGroup.{u1} M _inst_1)) (CompleteSemilatticeInf.toPartialOrder.{u1} (AddSubgroup.{u1} M (AddCommGroup.toAddGroup.{u1} M _inst_1)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (AddSubgroup.{u1} M (AddCommGroup.toAddGroup.{u1} M _inst_1)) (AddSubgroup.instCompleteLatticeAddSubgroup.{u1} M (AddCommGroup.toAddGroup.{u1} M _inst_1)))))) x._@.Mathlib.Order.Hom.Basic._hyg.1285 x._@.Mathlib.Order.Hom.Basic._hyg.1287) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1300 : Submodule.{0, u1} Int M Int.instSemiringInt (AddCommGroup.toAddCommMonoid.{u1} M _inst_1) (AddCommGroup.intModule.{u1} M _inst_1)) (x._@.Mathlib.Order.Hom.Basic._hyg.1302 : Submodule.{0, u1} Int M Int.instSemiringInt (AddCommGroup.toAddCommMonoid.{u1} M _inst_1) (AddCommGroup.intModule.{u1} M _inst_1)) => LE.le.{u1} (Submodule.{0, u1} Int M Int.instSemiringInt (AddCommGroup.toAddCommMonoid.{u1} M _inst_1) (AddCommGroup.intModule.{u1} M _inst_1)) (Preorder.toLE.{u1} (Submodule.{0, u1} Int M Int.instSemiringInt (AddCommGroup.toAddCommMonoid.{u1} M _inst_1) (AddCommGroup.intModule.{u1} M _inst_1)) (PartialOrder.toPreorder.{u1} (Submodule.{0, u1} Int M Int.instSemiringInt (AddCommGroup.toAddCommMonoid.{u1} M _inst_1) (AddCommGroup.intModule.{u1} M _inst_1)) (CompleteSemilatticeInf.toPartialOrder.{u1} (Submodule.{0, u1} Int M Int.instSemiringInt (AddCommGroup.toAddCommMonoid.{u1} M _inst_1) (AddCommGroup.intModule.{u1} M _inst_1)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (Submodule.{0, u1} Int M Int.instSemiringInt (AddCommGroup.toAddCommMonoid.{u1} M _inst_1) (AddCommGroup.intModule.{u1} M _inst_1)) (Submodule.completeLattice.{0, u1} Int M Int.instSemiringInt (AddCommGroup.toAddCommMonoid.{u1} M _inst_1) (AddCommGroup.intModule.{u1} M _inst_1)))))) x._@.Mathlib.Order.Hom.Basic._hyg.1300 x._@.Mathlib.Order.Hom.Basic._hyg.1302)) (AddSubgroup.{u1} M (AddCommGroup.toAddGroup.{u1} M _inst_1)) (fun (_x : AddSubgroup.{u1} M (AddCommGroup.toAddGroup.{u1} M _inst_1)) => Submodule.{0, u1} Int M Int.instSemiringInt (AddCommGroup.toAddCommMonoid.{u1} M _inst_1) (AddCommGroup.intModule.{u1} M _inst_1)) (RelHomClass.toFunLike.{u1, u1, u1} (RelIso.{u1, u1} (AddSubgroup.{u1} M (AddCommGroup.toAddGroup.{u1} M _inst_1)) (Submodule.{0, u1} Int M Int.instSemiringInt (AddCommGroup.toAddCommMonoid.{u1} M _inst_1) (AddCommGroup.intModule.{u1} M _inst_1)) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1285 : AddSubgroup.{u1} M (AddCommGroup.toAddGroup.{u1} M _inst_1)) (x._@.Mathlib.Order.Hom.Basic._hyg.1287 : AddSubgroup.{u1} M (AddCommGroup.toAddGroup.{u1} M _inst_1)) => LE.le.{u1} (AddSubgroup.{u1} M (AddCommGroup.toAddGroup.{u1} M _inst_1)) (Preorder.toLE.{u1} (AddSubgroup.{u1} M (AddCommGroup.toAddGroup.{u1} M _inst_1)) (PartialOrder.toPreorder.{u1} (AddSubgroup.{u1} M (AddCommGroup.toAddGroup.{u1} M _inst_1)) (CompleteSemilatticeInf.toPartialOrder.{u1} (AddSubgroup.{u1} M (AddCommGroup.toAddGroup.{u1} M _inst_1)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (AddSubgroup.{u1} M (AddCommGroup.toAddGroup.{u1} M _inst_1)) (AddSubgroup.instCompleteLatticeAddSubgroup.{u1} M (AddCommGroup.toAddGroup.{u1} M _inst_1)))))) x._@.Mathlib.Order.Hom.Basic._hyg.1285 x._@.Mathlib.Order.Hom.Basic._hyg.1287) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1300 : Submodule.{0, u1} Int M Int.instSemiringInt (AddCommGroup.toAddCommMonoid.{u1} M _inst_1) (AddCommGroup.intModule.{u1} M _inst_1)) (x._@.Mathlib.Order.Hom.Basic._hyg.1302 : Submodule.{0, u1} Int M Int.instSemiringInt (AddCommGroup.toAddCommMonoid.{u1} M _inst_1) (AddCommGroup.intModule.{u1} M _inst_1)) => LE.le.{u1} (Submodule.{0, u1} Int M Int.instSemiringInt (AddCommGroup.toAddCommMonoid.{u1} M _inst_1) (AddCommGroup.intModule.{u1} M _inst_1)) (Preorder.toLE.{u1} (Submodule.{0, u1} Int M Int.instSemiringInt (AddCommGroup.toAddCommMonoid.{u1} M _inst_1) (AddCommGroup.intModule.{u1} M _inst_1)) (PartialOrder.toPreorder.{u1} (Submodule.{0, u1} Int M Int.instSemiringInt (AddCommGroup.toAddCommMonoid.{u1} M _inst_1) (AddCommGroup.intModule.{u1} M _inst_1)) (CompleteSemilatticeInf.toPartialOrder.{u1} (Submodule.{0, u1} Int M Int.instSemiringInt (AddCommGroup.toAddCommMonoid.{u1} M _inst_1) (AddCommGroup.intModule.{u1} M _inst_1)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (Submodule.{0, u1} Int M Int.instSemiringInt (AddCommGroup.toAddCommMonoid.{u1} M _inst_1) (AddCommGroup.intModule.{u1} M _inst_1)) (Submodule.completeLattice.{0, u1} Int M Int.instSemiringInt (AddCommGroup.toAddCommMonoid.{u1} M _inst_1) (AddCommGroup.intModule.{u1} M _inst_1)))))) x._@.Mathlib.Order.Hom.Basic._hyg.1300 x._@.Mathlib.Order.Hom.Basic._hyg.1302)) (AddSubgroup.{u1} M (AddCommGroup.toAddGroup.{u1} M _inst_1)) (Submodule.{0, u1} Int M Int.instSemiringInt (AddCommGroup.toAddCommMonoid.{u1} M _inst_1) (AddCommGroup.intModule.{u1} M _inst_1)) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1285 : AddSubgroup.{u1} M (AddCommGroup.toAddGroup.{u1} M _inst_1)) (x._@.Mathlib.Order.Hom.Basic._hyg.1287 : AddSubgroup.{u1} M (AddCommGroup.toAddGroup.{u1} M _inst_1)) => LE.le.{u1} (AddSubgroup.{u1} M (AddCommGroup.toAddGroup.{u1} M _inst_1)) (Preorder.toLE.{u1} (AddSubgroup.{u1} M (AddCommGroup.toAddGroup.{u1} M _inst_1)) (PartialOrder.toPreorder.{u1} (AddSubgroup.{u1} M (AddCommGroup.toAddGroup.{u1} M _inst_1)) (CompleteSemilatticeInf.toPartialOrder.{u1} (AddSubgroup.{u1} M (AddCommGroup.toAddGroup.{u1} M _inst_1)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (AddSubgroup.{u1} M (AddCommGroup.toAddGroup.{u1} M _inst_1)) (AddSubgroup.instCompleteLatticeAddSubgroup.{u1} M (AddCommGroup.toAddGroup.{u1} M _inst_1)))))) x._@.Mathlib.Order.Hom.Basic._hyg.1285 x._@.Mathlib.Order.Hom.Basic._hyg.1287) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1300 : Submodule.{0, u1} Int M Int.instSemiringInt (AddCommGroup.toAddCommMonoid.{u1} M _inst_1) (AddCommGroup.intModule.{u1} M _inst_1)) (x._@.Mathlib.Order.Hom.Basic._hyg.1302 : Submodule.{0, u1} Int M Int.instSemiringInt (AddCommGroup.toAddCommMonoid.{u1} M _inst_1) (AddCommGroup.intModule.{u1} M _inst_1)) => LE.le.{u1} (Submodule.{0, u1} Int M Int.instSemiringInt (AddCommGroup.toAddCommMonoid.{u1} M _inst_1) (AddCommGroup.intModule.{u1} M _inst_1)) (Preorder.toLE.{u1} (Submodule.{0, u1} Int M Int.instSemiringInt (AddCommGroup.toAddCommMonoid.{u1} M _inst_1) (AddCommGroup.intModule.{u1} M _inst_1)) (PartialOrder.toPreorder.{u1} (Submodule.{0, u1} Int M Int.instSemiringInt (AddCommGroup.toAddCommMonoid.{u1} M _inst_1) (AddCommGroup.intModule.{u1} M _inst_1)) (CompleteSemilatticeInf.toPartialOrder.{u1} (Submodule.{0, u1} Int M Int.instSemiringInt (AddCommGroup.toAddCommMonoid.{u1} M _inst_1) (AddCommGroup.intModule.{u1} M _inst_1)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (Submodule.{0, u1} Int M Int.instSemiringInt (AddCommGroup.toAddCommMonoid.{u1} M _inst_1) (AddCommGroup.intModule.{u1} M _inst_1)) (Submodule.completeLattice.{0, u1} Int M Int.instSemiringInt (AddCommGroup.toAddCommMonoid.{u1} M _inst_1) (AddCommGroup.intModule.{u1} M _inst_1)))))) x._@.Mathlib.Order.Hom.Basic._hyg.1300 x._@.Mathlib.Order.Hom.Basic._hyg.1302) (RelIso.instRelHomClassRelIso.{u1, u1} (AddSubgroup.{u1} M (AddCommGroup.toAddGroup.{u1} M _inst_1)) (Submodule.{0, u1} Int M Int.instSemiringInt (AddCommGroup.toAddCommMonoid.{u1} M _inst_1) (AddCommGroup.intModule.{u1} M _inst_1)) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1285 : AddSubgroup.{u1} M (AddCommGroup.toAddGroup.{u1} M _inst_1)) (x._@.Mathlib.Order.Hom.Basic._hyg.1287 : AddSubgroup.{u1} M (AddCommGroup.toAddGroup.{u1} M _inst_1)) => LE.le.{u1} (AddSubgroup.{u1} M (AddCommGroup.toAddGroup.{u1} M _inst_1)) (Preorder.toLE.{u1} (AddSubgroup.{u1} M (AddCommGroup.toAddGroup.{u1} M _inst_1)) (PartialOrder.toPreorder.{u1} (AddSubgroup.{u1} M (AddCommGroup.toAddGroup.{u1} M _inst_1)) (CompleteSemilatticeInf.toPartialOrder.{u1} (AddSubgroup.{u1} M (AddCommGroup.toAddGroup.{u1} M _inst_1)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (AddSubgroup.{u1} M (AddCommGroup.toAddGroup.{u1} M _inst_1)) (AddSubgroup.instCompleteLatticeAddSubgroup.{u1} M (AddCommGroup.toAddGroup.{u1} M _inst_1)))))) x._@.Mathlib.Order.Hom.Basic._hyg.1285 x._@.Mathlib.Order.Hom.Basic._hyg.1287) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1300 : Submodule.{0, u1} Int M Int.instSemiringInt (AddCommGroup.toAddCommMonoid.{u1} M _inst_1) (AddCommGroup.intModule.{u1} M _inst_1)) (x._@.Mathlib.Order.Hom.Basic._hyg.1302 : Submodule.{0, u1} Int M Int.instSemiringInt (AddCommGroup.toAddCommMonoid.{u1} M _inst_1) (AddCommGroup.intModule.{u1} M _inst_1)) => LE.le.{u1} (Submodule.{0, u1} Int M Int.instSemiringInt (AddCommGroup.toAddCommMonoid.{u1} M _inst_1) (AddCommGroup.intModule.{u1} M _inst_1)) (Preorder.toLE.{u1} (Submodule.{0, u1} Int M Int.instSemiringInt (AddCommGroup.toAddCommMonoid.{u1} M _inst_1) (AddCommGroup.intModule.{u1} M _inst_1)) (PartialOrder.toPreorder.{u1} (Submodule.{0, u1} Int M Int.instSemiringInt (AddCommGroup.toAddCommMonoid.{u1} M _inst_1) (AddCommGroup.intModule.{u1} M _inst_1)) (CompleteSemilatticeInf.toPartialOrder.{u1} (Submodule.{0, u1} Int M Int.instSemiringInt (AddCommGroup.toAddCommMonoid.{u1} M _inst_1) (AddCommGroup.intModule.{u1} M _inst_1)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (Submodule.{0, u1} Int M Int.instSemiringInt (AddCommGroup.toAddCommMonoid.{u1} M _inst_1) (AddCommGroup.intModule.{u1} M _inst_1)) (Submodule.completeLattice.{0, u1} Int M Int.instSemiringInt (AddCommGroup.toAddCommMonoid.{u1} M _inst_1) (AddCommGroup.intModule.{u1} M _inst_1)))))) x._@.Mathlib.Order.Hom.Basic._hyg.1300 x._@.Mathlib.Order.Hom.Basic._hyg.1302))) (AddSubgroup.toIntSubmodule.{u1} M _inst_1) (Submodule.toAddSubgroup.{0, u1} Int M Int.instRingInt _inst_1 (AddCommGroup.intModule.{u1} M _inst_1) S)) S
 Case conversion may be inaccurate. Consider using '#align submodule.to_add_subgroup_to_int_submodule Submodule.toAddSubgroup_toIntSubmoduleₓ'. -/
 @[simp]
 theorem Submodule.toAddSubgroup_toIntSubmodule (S : Submodule ℤ M) :

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

@@ -170,7 +170,7 @@ protected theorem ne_bot_iff (p : Submodule R M) : p ≠ ⊥ ↔ ∃ x ∈ p, x
 
 /- warning: submodule.nonzero_mem_of_bot_lt -> Submodule.nonzero_mem_of_bot_lt is a dubious translation:
 lean 3 declaration is
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+  forall {R : Type.{u1}} {M : Type.{u2}} [_inst_1 : Semiring.{u1} R] [_inst_3 : AddCommMonoid.{u2} M] [_inst_4 : Module.{u1, u2} R M _inst_1 _inst_3] {p : Submodule.{u1, u2} R M _inst_1 _inst_3 _inst_4}, (LT.lt.{u2} (Submodule.{u1, u2} R M _inst_1 _inst_3 _inst_4) (Preorder.toHasLt.{u2} (Submodule.{u1, u2} R M _inst_1 _inst_3 _inst_4) (PartialOrder.toPreorder.{u2} (Submodule.{u1, u2} R M _inst_1 _inst_3 _inst_4) (SetLike.partialOrder.{u2, u2} (Submodule.{u1, u2} R M _inst_1 _inst_3 _inst_4) M (Submodule.setLike.{u1, u2} R M _inst_1 _inst_3 _inst_4)))) (Bot.bot.{u2} (Submodule.{u1, u2} R M _inst_1 _inst_3 _inst_4) (Submodule.hasBot.{u1, u2} R M _inst_1 _inst_3 _inst_4)) p) -> (Exists.{succ u2} (coeSort.{succ u2, succ (succ u2)} (Submodule.{u1, u2} R M _inst_1 _inst_3 _inst_4) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Submodule.{u1, u2} R M _inst_1 _inst_3 _inst_4) M (Submodule.setLike.{u1, u2} R M _inst_1 _inst_3 _inst_4)) p) (fun (a : coeSort.{succ u2, succ (succ u2)} (Submodule.{u1, u2} R M _inst_1 _inst_3 _inst_4) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Submodule.{u1, u2} R M _inst_1 _inst_3 _inst_4) M (Submodule.setLike.{u1, u2} R M _inst_1 _inst_3 _inst_4)) p) => Ne.{succ u2} (coeSort.{succ u2, succ (succ u2)} (Submodule.{u1, u2} R M _inst_1 _inst_3 _inst_4) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Submodule.{u1, u2} R M _inst_1 _inst_3 _inst_4) M (Submodule.setLike.{u1, u2} R M _inst_1 _inst_3 _inst_4)) p) a (OfNat.ofNat.{u2} (coeSort.{succ u2, succ (succ u2)} (Submodule.{u1, u2} R M _inst_1 _inst_3 _inst_4) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Submodule.{u1, u2} R M _inst_1 _inst_3 _inst_4) M (Submodule.setLike.{u1, u2} R M _inst_1 _inst_3 _inst_4)) p) 0 (OfNat.mk.{u2} (coeSort.{succ u2, succ (succ u2)} (Submodule.{u1, u2} R M _inst_1 _inst_3 _inst_4) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Submodule.{u1, u2} R M _inst_1 _inst_3 _inst_4) M (Submodule.setLike.{u1, u2} R M _inst_1 _inst_3 _inst_4)) p) 0 (Zero.zero.{u2} (coeSort.{succ u2, succ (succ u2)} (Submodule.{u1, u2} R M _inst_1 _inst_3 _inst_4) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Submodule.{u1, u2} R M _inst_1 _inst_3 _inst_4) M (Submodule.setLike.{u1, u2} R M _inst_1 _inst_3 _inst_4)) p) (Submodule.zero.{u1, u2} R M _inst_1 _inst_3 _inst_4 p))))))
 but is expected to have type
   forall {R : Type.{u2}} {M : Type.{u1}} [_inst_1 : Semiring.{u2} R] [_inst_3 : AddCommMonoid.{u1} M] [_inst_4 : Module.{u2, u1} R M _inst_1 _inst_3] {p : Submodule.{u2, u1} R M _inst_1 _inst_3 _inst_4}, (LT.lt.{u1} (Submodule.{u2, u1} R M _inst_1 _inst_3 _inst_4) (Preorder.toLT.{u1} (Submodule.{u2, u1} R M _inst_1 _inst_3 _inst_4) (PartialOrder.toPreorder.{u1} (Submodule.{u2, u1} R M _inst_1 _inst_3 _inst_4) (SetLike.instPartialOrder.{u1, u1} (Submodule.{u2, u1} R M _inst_1 _inst_3 _inst_4) M (Submodule.setLike.{u2, u1} R M _inst_1 _inst_3 _inst_4)))) (Bot.bot.{u1} (Submodule.{u2, u1} R M _inst_1 _inst_3 _inst_4) (Submodule.instBotSubmodule.{u2, u1} R M _inst_1 _inst_3 _inst_4)) p) -> (Exists.{succ u1} (Subtype.{succ u1} M (fun (x : M) => Membership.mem.{u1, u1} M (Submodule.{u2, u1} R M _inst_1 _inst_3 _inst_4) (SetLike.instMembership.{u1, u1} (Submodule.{u2, u1} R M _inst_1 _inst_3 _inst_4) M (Submodule.setLike.{u2, u1} R M _inst_1 _inst_3 _inst_4)) x p)) (fun (a : Subtype.{succ u1} M (fun (x : M) => Membership.mem.{u1, u1} M (Submodule.{u2, u1} R M _inst_1 _inst_3 _inst_4) (SetLike.instMembership.{u1, u1} (Submodule.{u2, u1} R M _inst_1 _inst_3 _inst_4) M (Submodule.setLike.{u2, u1} R M _inst_1 _inst_3 _inst_4)) x p)) => Ne.{succ u1} (Subtype.{succ u1} M (fun (x : M) => Membership.mem.{u1, u1} M (Submodule.{u2, u1} R M _inst_1 _inst_3 _inst_4) (SetLike.instMembership.{u1, u1} (Submodule.{u2, u1} R M _inst_1 _inst_3 _inst_4) M (Submodule.setLike.{u2, u1} R M _inst_1 _inst_3 _inst_4)) x p)) a (OfNat.ofNat.{u1} (Subtype.{succ u1} M (fun (x : M) => Membership.mem.{u1, u1} M (Submodule.{u2, u1} R M _inst_1 _inst_3 _inst_4) (SetLike.instMembership.{u1, u1} (Submodule.{u2, u1} R M _inst_1 _inst_3 _inst_4) M (Submodule.setLike.{u2, u1} R M _inst_1 _inst_3 _inst_4)) x p)) 0 (Zero.toOfNat0.{u1} (Subtype.{succ u1} M (fun (x : M) => Membership.mem.{u1, u1} M (Submodule.{u2, u1} R M _inst_1 _inst_3 _inst_4) (SetLike.instMembership.{u1, u1} (Submodule.{u2, u1} R M _inst_1 _inst_3 _inst_4) M (Submodule.setLike.{u2, u1} R M _inst_1 _inst_3 _inst_4)) x p)) (Submodule.zero.{u2, u1} R M _inst_1 _inst_3 _inst_4 p)))))
 Case conversion may be inaccurate. Consider using '#align submodule.nonzero_mem_of_bot_lt Submodule.nonzero_mem_of_bot_ltₓ'. -/
@@ -605,7 +605,7 @@ section NatSubmodule
 
 /- warning: add_submonoid.to_nat_submodule -> AddSubmonoid.toNatSubmodule is a dubious translation:
 lean 3 declaration is
-  forall {M : Type.{u1}} [_inst_3 : AddCommMonoid.{u1} M], OrderIso.{u1, u1} (AddSubmonoid.{u1} M (AddMonoid.toAddZeroClass.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3))) (Submodule.{0, u1} Nat M Nat.semiring _inst_3 (AddCommMonoid.natModule.{u1} M _inst_3)) (Preorder.toLE.{u1} (AddSubmonoid.{u1} M (AddMonoid.toAddZeroClass.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3))) (PartialOrder.toPreorder.{u1} (AddSubmonoid.{u1} M (AddMonoid.toAddZeroClass.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3))) (CompleteSemilatticeInf.toPartialOrder.{u1} (AddSubmonoid.{u1} M (AddMonoid.toAddZeroClass.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3))) (CompleteLattice.toCompleteSemilatticeInf.{u1} (AddSubmonoid.{u1} M (AddMonoid.toAddZeroClass.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3))) (AddSubmonoid.completeLattice.{u1} M (AddMonoid.toAddZeroClass.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3))))))) (Preorder.toLE.{u1} (Submodule.{0, u1} Nat M Nat.semiring _inst_3 (AddCommMonoid.natModule.{u1} M _inst_3)) (PartialOrder.toPreorder.{u1} (Submodule.{0, u1} Nat M Nat.semiring _inst_3 (AddCommMonoid.natModule.{u1} M _inst_3)) (CompleteSemilatticeInf.toPartialOrder.{u1} (Submodule.{0, u1} Nat M Nat.semiring _inst_3 (AddCommMonoid.natModule.{u1} M _inst_3)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (Submodule.{0, u1} Nat M Nat.semiring _inst_3 (AddCommMonoid.natModule.{u1} M _inst_3)) (Submodule.completeLattice.{0, u1} Nat M Nat.semiring _inst_3 (AddCommMonoid.natModule.{u1} M _inst_3))))))
+  forall {M : Type.{u1}} [_inst_3 : AddCommMonoid.{u1} M], OrderIso.{u1, u1} (AddSubmonoid.{u1} M (AddMonoid.toAddZeroClass.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3))) (Submodule.{0, u1} Nat M Nat.semiring _inst_3 (AddCommMonoid.natModule.{u1} M _inst_3)) (Preorder.toHasLe.{u1} (AddSubmonoid.{u1} M (AddMonoid.toAddZeroClass.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3))) (PartialOrder.toPreorder.{u1} (AddSubmonoid.{u1} M (AddMonoid.toAddZeroClass.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3))) (CompleteSemilatticeInf.toPartialOrder.{u1} (AddSubmonoid.{u1} M (AddMonoid.toAddZeroClass.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3))) (CompleteLattice.toCompleteSemilatticeInf.{u1} (AddSubmonoid.{u1} M (AddMonoid.toAddZeroClass.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3))) (AddSubmonoid.completeLattice.{u1} M (AddMonoid.toAddZeroClass.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3))))))) (Preorder.toHasLe.{u1} (Submodule.{0, u1} Nat M Nat.semiring _inst_3 (AddCommMonoid.natModule.{u1} M _inst_3)) (PartialOrder.toPreorder.{u1} (Submodule.{0, u1} Nat M Nat.semiring _inst_3 (AddCommMonoid.natModule.{u1} M _inst_3)) (CompleteSemilatticeInf.toPartialOrder.{u1} (Submodule.{0, u1} Nat M Nat.semiring _inst_3 (AddCommMonoid.natModule.{u1} M _inst_3)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (Submodule.{0, u1} Nat M Nat.semiring _inst_3 (AddCommMonoid.natModule.{u1} M _inst_3)) (Submodule.completeLattice.{0, u1} Nat M Nat.semiring _inst_3 (AddCommMonoid.natModule.{u1} M _inst_3))))))
 but is expected to have type
   forall {M : Type.{u1}} [_inst_3 : AddCommMonoid.{u1} M], OrderIso.{u1, u1} (AddSubmonoid.{u1} M (AddMonoid.toAddZeroClass.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3))) (Submodule.{0, u1} Nat M Nat.semiring _inst_3 (AddCommMonoid.natModule.{u1} M _inst_3)) (Preorder.toLE.{u1} (AddSubmonoid.{u1} M (AddMonoid.toAddZeroClass.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3))) (PartialOrder.toPreorder.{u1} (AddSubmonoid.{u1} M (AddMonoid.toAddZeroClass.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3))) (CompleteSemilatticeInf.toPartialOrder.{u1} (AddSubmonoid.{u1} M (AddMonoid.toAddZeroClass.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3))) (CompleteLattice.toCompleteSemilatticeInf.{u1} (AddSubmonoid.{u1} M (AddMonoid.toAddZeroClass.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3))) (AddSubmonoid.instCompleteLatticeAddSubmonoid.{u1} M (AddMonoid.toAddZeroClass.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3))))))) (Preorder.toLE.{u1} (Submodule.{0, u1} Nat M Nat.semiring _inst_3 (AddCommMonoid.natModule.{u1} M _inst_3)) (PartialOrder.toPreorder.{u1} (Submodule.{0, u1} Nat M Nat.semiring _inst_3 (AddCommMonoid.natModule.{u1} M _inst_3)) (CompleteSemilatticeInf.toPartialOrder.{u1} (Submodule.{0, u1} Nat M Nat.semiring _inst_3 (AddCommMonoid.natModule.{u1} M _inst_3)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (Submodule.{0, u1} Nat M Nat.semiring _inst_3 (AddCommMonoid.natModule.{u1} M _inst_3)) (Submodule.completeLattice.{0, u1} Nat M Nat.semiring _inst_3 (AddCommMonoid.natModule.{u1} M _inst_3))))))
 Case conversion may be inaccurate. Consider using '#align add_submonoid.to_nat_submodule AddSubmonoid.toNatSubmoduleₓ'. -/
@@ -621,7 +621,7 @@ def AddSubmonoid.toNatSubmodule : AddSubmonoid M ≃o Submodule ℕ M
 
 /- warning: add_submonoid.to_nat_submodule_symm -> AddSubmonoid.toNatSubmodule_symm is a dubious translation:
 lean 3 declaration is
-  forall {M : Type.{u1}} [_inst_3 : AddCommMonoid.{u1} M], Eq.{succ u1} ((Submodule.{0, u1} Nat M Nat.semiring _inst_3 (AddCommMonoid.natModule.{u1} M _inst_3)) -> (AddSubmonoid.{u1} M (AddMonoid.toAddZeroClass.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3)))) (coeFn.{succ u1, succ u1} (OrderIso.{u1, u1} (Submodule.{0, u1} Nat M Nat.semiring _inst_3 (AddCommMonoid.natModule.{u1} M _inst_3)) (AddSubmonoid.{u1} M (AddMonoid.toAddZeroClass.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3))) (Preorder.toLE.{u1} (Submodule.{0, u1} Nat M Nat.semiring _inst_3 (AddCommMonoid.natModule.{u1} M _inst_3)) (PartialOrder.toPreorder.{u1} (Submodule.{0, u1} Nat M Nat.semiring _inst_3 (AddCommMonoid.natModule.{u1} M _inst_3)) (CompleteSemilatticeInf.toPartialOrder.{u1} (Submodule.{0, u1} Nat M Nat.semiring _inst_3 (AddCommMonoid.natModule.{u1} M _inst_3)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (Submodule.{0, u1} Nat M Nat.semiring _inst_3 (AddCommMonoid.natModule.{u1} M _inst_3)) (Submodule.completeLattice.{0, u1} Nat M Nat.semiring _inst_3 (AddCommMonoid.natModule.{u1} M _inst_3)))))) (Preorder.toLE.{u1} (AddSubmonoid.{u1} M (AddMonoid.toAddZeroClass.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3))) (PartialOrder.toPreorder.{u1} (AddSubmonoid.{u1} M (AddMonoid.toAddZeroClass.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3))) (CompleteSemilatticeInf.toPartialOrder.{u1} (AddSubmonoid.{u1} M (AddMonoid.toAddZeroClass.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3))) (CompleteLattice.toCompleteSemilatticeInf.{u1} (AddSubmonoid.{u1} M (AddMonoid.toAddZeroClass.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3))) (AddSubmonoid.completeLattice.{u1} M (AddMonoid.toAddZeroClass.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3)))))))) (fun (_x : RelIso.{u1, u1} (Submodule.{0, u1} Nat M Nat.semiring _inst_3 (AddCommMonoid.natModule.{u1} M _inst_3)) (AddSubmonoid.{u1} M (AddMonoid.toAddZeroClass.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3))) (LE.le.{u1} (Submodule.{0, u1} Nat M Nat.semiring _inst_3 (AddCommMonoid.natModule.{u1} M _inst_3)) (Preorder.toLE.{u1} (Submodule.{0, u1} Nat M Nat.semiring _inst_3 (AddCommMonoid.natModule.{u1} M _inst_3)) (PartialOrder.toPreorder.{u1} (Submodule.{0, u1} Nat M Nat.semiring _inst_3 (AddCommMonoid.natModule.{u1} M _inst_3)) (CompleteSemilatticeInf.toPartialOrder.{u1} (Submodule.{0, u1} Nat M Nat.semiring _inst_3 (AddCommMonoid.natModule.{u1} M _inst_3)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (Submodule.{0, u1} Nat M Nat.semiring _inst_3 (AddCommMonoid.natModule.{u1} M _inst_3)) (Submodule.completeLattice.{0, u1} Nat M Nat.semiring _inst_3 (AddCommMonoid.natModule.{u1} M _inst_3))))))) (LE.le.{u1} (AddSubmonoid.{u1} M (AddMonoid.toAddZeroClass.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3))) (Preorder.toLE.{u1} (AddSubmonoid.{u1} M (AddMonoid.toAddZeroClass.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3))) (PartialOrder.toPreorder.{u1} (AddSubmonoid.{u1} M (AddMonoid.toAddZeroClass.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3))) (CompleteSemilatticeInf.toPartialOrder.{u1} (AddSubmonoid.{u1} M (AddMonoid.toAddZeroClass.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3))) (CompleteLattice.toCompleteSemilatticeInf.{u1} (AddSubmonoid.{u1} M (AddMonoid.toAddZeroClass.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3))) (AddSubmonoid.completeLattice.{u1} M (AddMonoid.toAddZeroClass.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3))))))))) => (Submodule.{0, u1} Nat M Nat.semiring _inst_3 (AddCommMonoid.natModule.{u1} M _inst_3)) -> (AddSubmonoid.{u1} M (AddMonoid.toAddZeroClass.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3)))) (RelIso.hasCoeToFun.{u1, u1} (Submodule.{0, u1} Nat M Nat.semiring _inst_3 (AddCommMonoid.natModule.{u1} M _inst_3)) (AddSubmonoid.{u1} M (AddMonoid.toAddZeroClass.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3))) (LE.le.{u1} (Submodule.{0, u1} Nat M Nat.semiring _inst_3 (AddCommMonoid.natModule.{u1} M _inst_3)) (Preorder.toLE.{u1} (Submodule.{0, u1} Nat M Nat.semiring _inst_3 (AddCommMonoid.natModule.{u1} M _inst_3)) (PartialOrder.toPreorder.{u1} (Submodule.{0, u1} Nat M Nat.semiring _inst_3 (AddCommMonoid.natModule.{u1} M _inst_3)) (CompleteSemilatticeInf.toPartialOrder.{u1} (Submodule.{0, u1} Nat M Nat.semiring _inst_3 (AddCommMonoid.natModule.{u1} M _inst_3)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (Submodule.{0, u1} Nat M Nat.semiring _inst_3 (AddCommMonoid.natModule.{u1} M _inst_3)) (Submodule.completeLattice.{0, u1} Nat M Nat.semiring _inst_3 (AddCommMonoid.natModule.{u1} M _inst_3))))))) (LE.le.{u1} (AddSubmonoid.{u1} M (AddMonoid.toAddZeroClass.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3))) (Preorder.toLE.{u1} (AddSubmonoid.{u1} M (AddMonoid.toAddZeroClass.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3))) (PartialOrder.toPreorder.{u1} (AddSubmonoid.{u1} M (AddMonoid.toAddZeroClass.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3))) (CompleteSemilatticeInf.toPartialOrder.{u1} (AddSubmonoid.{u1} M (AddMonoid.toAddZeroClass.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3))) (CompleteLattice.toCompleteSemilatticeInf.{u1} (AddSubmonoid.{u1} M (AddMonoid.toAddZeroClass.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3))) (AddSubmonoid.completeLattice.{u1} M (AddMonoid.toAddZeroClass.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3))))))))) (OrderIso.symm.{u1, u1} (AddSubmonoid.{u1} M (AddMonoid.toAddZeroClass.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3))) (Submodule.{0, u1} Nat M Nat.semiring _inst_3 (AddCommMonoid.natModule.{u1} M _inst_3)) (Preorder.toLE.{u1} (AddSubmonoid.{u1} M (AddMonoid.toAddZeroClass.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3))) (PartialOrder.toPreorder.{u1} (AddSubmonoid.{u1} M (AddMonoid.toAddZeroClass.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3))) (CompleteSemilatticeInf.toPartialOrder.{u1} (AddSubmonoid.{u1} M (AddMonoid.toAddZeroClass.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3))) (CompleteLattice.toCompleteSemilatticeInf.{u1} (AddSubmonoid.{u1} M (AddMonoid.toAddZeroClass.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3))) (AddSubmonoid.completeLattice.{u1} M (AddMonoid.toAddZeroClass.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3))))))) (Preorder.toLE.{u1} (Submodule.{0, u1} Nat M Nat.semiring _inst_3 (AddCommMonoid.natModule.{u1} M _inst_3)) (PartialOrder.toPreorder.{u1} (Submodule.{0, u1} Nat M Nat.semiring _inst_3 (AddCommMonoid.natModule.{u1} M _inst_3)) (CompleteSemilatticeInf.toPartialOrder.{u1} (Submodule.{0, u1} Nat M Nat.semiring _inst_3 (AddCommMonoid.natModule.{u1} M _inst_3)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (Submodule.{0, u1} Nat M Nat.semiring _inst_3 (AddCommMonoid.natModule.{u1} M _inst_3)) (Submodule.completeLattice.{0, u1} Nat M Nat.semiring _inst_3 (AddCommMonoid.natModule.{u1} M _inst_3)))))) (AddSubmonoid.toNatSubmodule.{u1} M _inst_3))) (Submodule.toAddSubmonoid.{0, u1} Nat M Nat.semiring _inst_3 (AddCommMonoid.natModule.{u1} M _inst_3))
+  forall {M : Type.{u1}} [_inst_3 : AddCommMonoid.{u1} M], Eq.{succ u1} ((Submodule.{0, u1} Nat M Nat.semiring _inst_3 (AddCommMonoid.natModule.{u1} M _inst_3)) -> (AddSubmonoid.{u1} M (AddMonoid.toAddZeroClass.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3)))) (coeFn.{succ u1, succ u1} (OrderIso.{u1, u1} (Submodule.{0, u1} Nat M Nat.semiring _inst_3 (AddCommMonoid.natModule.{u1} M _inst_3)) (AddSubmonoid.{u1} M (AddMonoid.toAddZeroClass.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3))) (Preorder.toHasLe.{u1} (Submodule.{0, u1} Nat M Nat.semiring _inst_3 (AddCommMonoid.natModule.{u1} M _inst_3)) (PartialOrder.toPreorder.{u1} (Submodule.{0, u1} Nat M Nat.semiring _inst_3 (AddCommMonoid.natModule.{u1} M _inst_3)) (CompleteSemilatticeInf.toPartialOrder.{u1} (Submodule.{0, u1} Nat M Nat.semiring _inst_3 (AddCommMonoid.natModule.{u1} M _inst_3)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (Submodule.{0, u1} Nat M Nat.semiring _inst_3 (AddCommMonoid.natModule.{u1} M _inst_3)) (Submodule.completeLattice.{0, u1} Nat M Nat.semiring _inst_3 (AddCommMonoid.natModule.{u1} M _inst_3)))))) (Preorder.toHasLe.{u1} (AddSubmonoid.{u1} M (AddMonoid.toAddZeroClass.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3))) (PartialOrder.toPreorder.{u1} (AddSubmonoid.{u1} M (AddMonoid.toAddZeroClass.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3))) (CompleteSemilatticeInf.toPartialOrder.{u1} (AddSubmonoid.{u1} M (AddMonoid.toAddZeroClass.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3))) (CompleteLattice.toCompleteSemilatticeInf.{u1} (AddSubmonoid.{u1} M (AddMonoid.toAddZeroClass.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3))) (AddSubmonoid.completeLattice.{u1} M (AddMonoid.toAddZeroClass.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3)))))))) (fun (_x : RelIso.{u1, u1} (Submodule.{0, u1} Nat M Nat.semiring _inst_3 (AddCommMonoid.natModule.{u1} M _inst_3)) (AddSubmonoid.{u1} M (AddMonoid.toAddZeroClass.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3))) (LE.le.{u1} (Submodule.{0, u1} Nat M Nat.semiring _inst_3 (AddCommMonoid.natModule.{u1} M _inst_3)) (Preorder.toHasLe.{u1} (Submodule.{0, u1} Nat M Nat.semiring _inst_3 (AddCommMonoid.natModule.{u1} M _inst_3)) (PartialOrder.toPreorder.{u1} (Submodule.{0, u1} Nat M Nat.semiring _inst_3 (AddCommMonoid.natModule.{u1} M _inst_3)) (CompleteSemilatticeInf.toPartialOrder.{u1} (Submodule.{0, u1} Nat M Nat.semiring _inst_3 (AddCommMonoid.natModule.{u1} M _inst_3)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (Submodule.{0, u1} Nat M Nat.semiring _inst_3 (AddCommMonoid.natModule.{u1} M _inst_3)) (Submodule.completeLattice.{0, u1} Nat M Nat.semiring _inst_3 (AddCommMonoid.natModule.{u1} M _inst_3))))))) (LE.le.{u1} (AddSubmonoid.{u1} M (AddMonoid.toAddZeroClass.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3))) (Preorder.toHasLe.{u1} (AddSubmonoid.{u1} M (AddMonoid.toAddZeroClass.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3))) (PartialOrder.toPreorder.{u1} (AddSubmonoid.{u1} M (AddMonoid.toAddZeroClass.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3))) (CompleteSemilatticeInf.toPartialOrder.{u1} (AddSubmonoid.{u1} M (AddMonoid.toAddZeroClass.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3))) (CompleteLattice.toCompleteSemilatticeInf.{u1} (AddSubmonoid.{u1} M (AddMonoid.toAddZeroClass.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3))) (AddSubmonoid.completeLattice.{u1} M (AddMonoid.toAddZeroClass.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3))))))))) => (Submodule.{0, u1} Nat M Nat.semiring _inst_3 (AddCommMonoid.natModule.{u1} M _inst_3)) -> (AddSubmonoid.{u1} M (AddMonoid.toAddZeroClass.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3)))) (RelIso.hasCoeToFun.{u1, u1} (Submodule.{0, u1} Nat M Nat.semiring _inst_3 (AddCommMonoid.natModule.{u1} M _inst_3)) (AddSubmonoid.{u1} M (AddMonoid.toAddZeroClass.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3))) (LE.le.{u1} (Submodule.{0, u1} Nat M Nat.semiring _inst_3 (AddCommMonoid.natModule.{u1} M _inst_3)) (Preorder.toHasLe.{u1} (Submodule.{0, u1} Nat M Nat.semiring _inst_3 (AddCommMonoid.natModule.{u1} M _inst_3)) (PartialOrder.toPreorder.{u1} (Submodule.{0, u1} Nat M Nat.semiring _inst_3 (AddCommMonoid.natModule.{u1} M _inst_3)) (CompleteSemilatticeInf.toPartialOrder.{u1} (Submodule.{0, u1} Nat M Nat.semiring _inst_3 (AddCommMonoid.natModule.{u1} M _inst_3)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (Submodule.{0, u1} Nat M Nat.semiring _inst_3 (AddCommMonoid.natModule.{u1} M _inst_3)) (Submodule.completeLattice.{0, u1} Nat M Nat.semiring _inst_3 (AddCommMonoid.natModule.{u1} M _inst_3))))))) (LE.le.{u1} (AddSubmonoid.{u1} M (AddMonoid.toAddZeroClass.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3))) (Preorder.toHasLe.{u1} (AddSubmonoid.{u1} M (AddMonoid.toAddZeroClass.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3))) (PartialOrder.toPreorder.{u1} (AddSubmonoid.{u1} M (AddMonoid.toAddZeroClass.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3))) (CompleteSemilatticeInf.toPartialOrder.{u1} (AddSubmonoid.{u1} M (AddMonoid.toAddZeroClass.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3))) (CompleteLattice.toCompleteSemilatticeInf.{u1} (AddSubmonoid.{u1} M (AddMonoid.toAddZeroClass.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3))) (AddSubmonoid.completeLattice.{u1} M (AddMonoid.toAddZeroClass.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3))))))))) (OrderIso.symm.{u1, u1} (AddSubmonoid.{u1} M (AddMonoid.toAddZeroClass.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3))) (Submodule.{0, u1} Nat M Nat.semiring _inst_3 (AddCommMonoid.natModule.{u1} M _inst_3)) (Preorder.toHasLe.{u1} (AddSubmonoid.{u1} M (AddMonoid.toAddZeroClass.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3))) (PartialOrder.toPreorder.{u1} (AddSubmonoid.{u1} M (AddMonoid.toAddZeroClass.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3))) (CompleteSemilatticeInf.toPartialOrder.{u1} (AddSubmonoid.{u1} M (AddMonoid.toAddZeroClass.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3))) (CompleteLattice.toCompleteSemilatticeInf.{u1} (AddSubmonoid.{u1} M (AddMonoid.toAddZeroClass.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3))) (AddSubmonoid.completeLattice.{u1} M (AddMonoid.toAddZeroClass.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3))))))) (Preorder.toHasLe.{u1} (Submodule.{0, u1} Nat M Nat.semiring _inst_3 (AddCommMonoid.natModule.{u1} M _inst_3)) (PartialOrder.toPreorder.{u1} (Submodule.{0, u1} Nat M Nat.semiring _inst_3 (AddCommMonoid.natModule.{u1} M _inst_3)) (CompleteSemilatticeInf.toPartialOrder.{u1} (Submodule.{0, u1} Nat M Nat.semiring _inst_3 (AddCommMonoid.natModule.{u1} M _inst_3)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (Submodule.{0, u1} Nat M Nat.semiring _inst_3 (AddCommMonoid.natModule.{u1} M _inst_3)) (Submodule.completeLattice.{0, u1} Nat M Nat.semiring _inst_3 (AddCommMonoid.natModule.{u1} M _inst_3)))))) (AddSubmonoid.toNatSubmodule.{u1} M _inst_3))) (Submodule.toAddSubmonoid.{0, u1} Nat M Nat.semiring _inst_3 (AddCommMonoid.natModule.{u1} M _inst_3))
 but is expected to have type
   forall {M : Type.{u1}} [_inst_3 : AddCommMonoid.{u1} M], Eq.{succ u1} ((Submodule.{0, u1} Nat M Nat.semiring _inst_3 (AddCommMonoid.natModule.{u1} M _inst_3)) -> (AddSubmonoid.{u1} M (AddMonoid.toAddZeroClass.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3)))) (FunLike.coe.{succ u1, succ u1, succ u1} (RelIso.{u1, u1} (Submodule.{0, u1} Nat M Nat.semiring _inst_3 (AddCommMonoid.natModule.{u1} M _inst_3)) (AddSubmonoid.{u1} M (AddMonoid.toAddZeroClass.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3))) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1281 : Submodule.{0, u1} Nat M Nat.semiring _inst_3 (AddCommMonoid.natModule.{u1} M _inst_3)) (x._@.Mathlib.Order.Hom.Basic._hyg.1283 : Submodule.{0, u1} Nat M Nat.semiring _inst_3 (AddCommMonoid.natModule.{u1} M _inst_3)) => LE.le.{u1} (Submodule.{0, u1} Nat M Nat.semiring _inst_3 (AddCommMonoid.natModule.{u1} M _inst_3)) (Preorder.toLE.{u1} (Submodule.{0, u1} Nat M Nat.semiring _inst_3 (AddCommMonoid.natModule.{u1} M _inst_3)) (PartialOrder.toPreorder.{u1} (Submodule.{0, u1} Nat M Nat.semiring _inst_3 (AddCommMonoid.natModule.{u1} M _inst_3)) (CompleteSemilatticeInf.toPartialOrder.{u1} (Submodule.{0, u1} Nat M Nat.semiring _inst_3 (AddCommMonoid.natModule.{u1} M _inst_3)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (Submodule.{0, u1} Nat M Nat.semiring _inst_3 (AddCommMonoid.natModule.{u1} M _inst_3)) (Submodule.completeLattice.{0, u1} Nat M Nat.semiring _inst_3 (AddCommMonoid.natModule.{u1} M _inst_3)))))) x._@.Mathlib.Order.Hom.Basic._hyg.1281 x._@.Mathlib.Order.Hom.Basic._hyg.1283) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1296 : AddSubmonoid.{u1} M (AddMonoid.toAddZeroClass.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3))) (x._@.Mathlib.Order.Hom.Basic._hyg.1298 : AddSubmonoid.{u1} M (AddMonoid.toAddZeroClass.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3))) => LE.le.{u1} (AddSubmonoid.{u1} M (AddMonoid.toAddZeroClass.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3))) (Preorder.toLE.{u1} (AddSubmonoid.{u1} M (AddMonoid.toAddZeroClass.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3))) (PartialOrder.toPreorder.{u1} (AddSubmonoid.{u1} M (AddMonoid.toAddZeroClass.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3))) (CompleteSemilatticeInf.toPartialOrder.{u1} (AddSubmonoid.{u1} M (AddMonoid.toAddZeroClass.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3))) (CompleteLattice.toCompleteSemilatticeInf.{u1} (AddSubmonoid.{u1} M (AddMonoid.toAddZeroClass.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3))) (AddSubmonoid.instCompleteLatticeAddSubmonoid.{u1} M (AddMonoid.toAddZeroClass.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3))))))) x._@.Mathlib.Order.Hom.Basic._hyg.1296 x._@.Mathlib.Order.Hom.Basic._hyg.1298)) (Submodule.{0, u1} Nat M Nat.semiring _inst_3 (AddCommMonoid.natModule.{u1} M _inst_3)) (fun (_x : Submodule.{0, u1} Nat M Nat.semiring _inst_3 (AddCommMonoid.natModule.{u1} M _inst_3)) => AddSubmonoid.{u1} M (AddMonoid.toAddZeroClass.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3))) (RelHomClass.toFunLike.{u1, u1, u1} (RelIso.{u1, u1} (Submodule.{0, u1} Nat M Nat.semiring _inst_3 (AddCommMonoid.natModule.{u1} M _inst_3)) (AddSubmonoid.{u1} M (AddMonoid.toAddZeroClass.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3))) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1281 : Submodule.{0, u1} Nat M Nat.semiring _inst_3 (AddCommMonoid.natModule.{u1} M _inst_3)) (x._@.Mathlib.Order.Hom.Basic._hyg.1283 : Submodule.{0, u1} Nat M Nat.semiring _inst_3 (AddCommMonoid.natModule.{u1} M _inst_3)) => LE.le.{u1} (Submodule.{0, u1} Nat M Nat.semiring _inst_3 (AddCommMonoid.natModule.{u1} M _inst_3)) (Preorder.toLE.{u1} (Submodule.{0, u1} Nat M Nat.semiring _inst_3 (AddCommMonoid.natModule.{u1} M _inst_3)) (PartialOrder.toPreorder.{u1} (Submodule.{0, u1} Nat M Nat.semiring _inst_3 (AddCommMonoid.natModule.{u1} M _inst_3)) (CompleteSemilatticeInf.toPartialOrder.{u1} (Submodule.{0, u1} Nat M Nat.semiring _inst_3 (AddCommMonoid.natModule.{u1} M _inst_3)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (Submodule.{0, u1} Nat M Nat.semiring _inst_3 (AddCommMonoid.natModule.{u1} M _inst_3)) (Submodule.completeLattice.{0, u1} Nat M Nat.semiring _inst_3 (AddCommMonoid.natModule.{u1} M _inst_3)))))) x._@.Mathlib.Order.Hom.Basic._hyg.1281 x._@.Mathlib.Order.Hom.Basic._hyg.1283) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1296 : AddSubmonoid.{u1} M (AddMonoid.toAddZeroClass.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3))) (x._@.Mathlib.Order.Hom.Basic._hyg.1298 : AddSubmonoid.{u1} M (AddMonoid.toAddZeroClass.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3))) => LE.le.{u1} (AddSubmonoid.{u1} M (AddMonoid.toAddZeroClass.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3))) (Preorder.toLE.{u1} (AddSubmonoid.{u1} M (AddMonoid.toAddZeroClass.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3))) (PartialOrder.toPreorder.{u1} (AddSubmonoid.{u1} M (AddMonoid.toAddZeroClass.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3))) (CompleteSemilatticeInf.toPartialOrder.{u1} (AddSubmonoid.{u1} M (AddMonoid.toAddZeroClass.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3))) (CompleteLattice.toCompleteSemilatticeInf.{u1} (AddSubmonoid.{u1} M (AddMonoid.toAddZeroClass.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3))) (AddSubmonoid.instCompleteLatticeAddSubmonoid.{u1} M (AddMonoid.toAddZeroClass.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3))))))) x._@.Mathlib.Order.Hom.Basic._hyg.1296 x._@.Mathlib.Order.Hom.Basic._hyg.1298)) (Submodule.{0, u1} Nat M Nat.semiring _inst_3 (AddCommMonoid.natModule.{u1} M _inst_3)) (AddSubmonoid.{u1} M (AddMonoid.toAddZeroClass.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3))) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1281 : Submodule.{0, u1} Nat M Nat.semiring _inst_3 (AddCommMonoid.natModule.{u1} M _inst_3)) (x._@.Mathlib.Order.Hom.Basic._hyg.1283 : Submodule.{0, u1} Nat M Nat.semiring _inst_3 (AddCommMonoid.natModule.{u1} M _inst_3)) => LE.le.{u1} (Submodule.{0, u1} Nat M Nat.semiring _inst_3 (AddCommMonoid.natModule.{u1} M _inst_3)) (Preorder.toLE.{u1} (Submodule.{0, u1} Nat M Nat.semiring _inst_3 (AddCommMonoid.natModule.{u1} M _inst_3)) (PartialOrder.toPreorder.{u1} (Submodule.{0, u1} Nat M Nat.semiring _inst_3 (AddCommMonoid.natModule.{u1} M _inst_3)) (CompleteSemilatticeInf.toPartialOrder.{u1} (Submodule.{0, u1} Nat M Nat.semiring _inst_3 (AddCommMonoid.natModule.{u1} M _inst_3)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (Submodule.{0, u1} Nat M Nat.semiring _inst_3 (AddCommMonoid.natModule.{u1} M _inst_3)) (Submodule.completeLattice.{0, u1} Nat M Nat.semiring _inst_3 (AddCommMonoid.natModule.{u1} M _inst_3)))))) x._@.Mathlib.Order.Hom.Basic._hyg.1281 x._@.Mathlib.Order.Hom.Basic._hyg.1283) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1296 : AddSubmonoid.{u1} M (AddMonoid.toAddZeroClass.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3))) (x._@.Mathlib.Order.Hom.Basic._hyg.1298 : AddSubmonoid.{u1} M (AddMonoid.toAddZeroClass.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3))) => LE.le.{u1} (AddSubmonoid.{u1} M (AddMonoid.toAddZeroClass.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3))) (Preorder.toLE.{u1} (AddSubmonoid.{u1} M (AddMonoid.toAddZeroClass.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3))) (PartialOrder.toPreorder.{u1} (AddSubmonoid.{u1} M (AddMonoid.toAddZeroClass.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3))) (CompleteSemilatticeInf.toPartialOrder.{u1} (AddSubmonoid.{u1} M (AddMonoid.toAddZeroClass.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3))) (CompleteLattice.toCompleteSemilatticeInf.{u1} (AddSubmonoid.{u1} M (AddMonoid.toAddZeroClass.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3))) (AddSubmonoid.instCompleteLatticeAddSubmonoid.{u1} M (AddMonoid.toAddZeroClass.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3))))))) x._@.Mathlib.Order.Hom.Basic._hyg.1296 x._@.Mathlib.Order.Hom.Basic._hyg.1298) (RelIso.instRelHomClassRelIso.{u1, u1} (Submodule.{0, u1} Nat M Nat.semiring _inst_3 (AddCommMonoid.natModule.{u1} M _inst_3)) (AddSubmonoid.{u1} M (AddMonoid.toAddZeroClass.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3))) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1281 : Submodule.{0, u1} Nat M Nat.semiring _inst_3 (AddCommMonoid.natModule.{u1} M _inst_3)) (x._@.Mathlib.Order.Hom.Basic._hyg.1283 : Submodule.{0, u1} Nat M Nat.semiring _inst_3 (AddCommMonoid.natModule.{u1} M _inst_3)) => LE.le.{u1} (Submodule.{0, u1} Nat M Nat.semiring _inst_3 (AddCommMonoid.natModule.{u1} M _inst_3)) (Preorder.toLE.{u1} (Submodule.{0, u1} Nat M Nat.semiring _inst_3 (AddCommMonoid.natModule.{u1} M _inst_3)) (PartialOrder.toPreorder.{u1} (Submodule.{0, u1} Nat M Nat.semiring _inst_3 (AddCommMonoid.natModule.{u1} M _inst_3)) (CompleteSemilatticeInf.toPartialOrder.{u1} (Submodule.{0, u1} Nat M Nat.semiring _inst_3 (AddCommMonoid.natModule.{u1} M _inst_3)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (Submodule.{0, u1} Nat M Nat.semiring _inst_3 (AddCommMonoid.natModule.{u1} M _inst_3)) (Submodule.completeLattice.{0, u1} Nat M Nat.semiring _inst_3 (AddCommMonoid.natModule.{u1} M _inst_3)))))) x._@.Mathlib.Order.Hom.Basic._hyg.1281 x._@.Mathlib.Order.Hom.Basic._hyg.1283) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1296 : AddSubmonoid.{u1} M (AddMonoid.toAddZeroClass.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3))) (x._@.Mathlib.Order.Hom.Basic._hyg.1298 : AddSubmonoid.{u1} M (AddMonoid.toAddZeroClass.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3))) => LE.le.{u1} (AddSubmonoid.{u1} M (AddMonoid.toAddZeroClass.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3))) (Preorder.toLE.{u1} (AddSubmonoid.{u1} M (AddMonoid.toAddZeroClass.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3))) (PartialOrder.toPreorder.{u1} (AddSubmonoid.{u1} M (AddMonoid.toAddZeroClass.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3))) (CompleteSemilatticeInf.toPartialOrder.{u1} (AddSubmonoid.{u1} M (AddMonoid.toAddZeroClass.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3))) (CompleteLattice.toCompleteSemilatticeInf.{u1} (AddSubmonoid.{u1} M (AddMonoid.toAddZeroClass.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3))) (AddSubmonoid.instCompleteLatticeAddSubmonoid.{u1} M (AddMonoid.toAddZeroClass.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3))))))) x._@.Mathlib.Order.Hom.Basic._hyg.1296 x._@.Mathlib.Order.Hom.Basic._hyg.1298))) (OrderIso.symm.{u1, u1} (AddSubmonoid.{u1} M (AddMonoid.toAddZeroClass.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3))) (Submodule.{0, u1} Nat M Nat.semiring _inst_3 (AddCommMonoid.natModule.{u1} M _inst_3)) (Preorder.toLE.{u1} (AddSubmonoid.{u1} M (AddMonoid.toAddZeroClass.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3))) (PartialOrder.toPreorder.{u1} (AddSubmonoid.{u1} M (AddMonoid.toAddZeroClass.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3))) (CompleteSemilatticeInf.toPartialOrder.{u1} (AddSubmonoid.{u1} M (AddMonoid.toAddZeroClass.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3))) (CompleteLattice.toCompleteSemilatticeInf.{u1} (AddSubmonoid.{u1} M (AddMonoid.toAddZeroClass.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3))) (AddSubmonoid.instCompleteLatticeAddSubmonoid.{u1} M (AddMonoid.toAddZeroClass.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3))))))) (Preorder.toLE.{u1} (Submodule.{0, u1} Nat M Nat.semiring _inst_3 (AddCommMonoid.natModule.{u1} M _inst_3)) (PartialOrder.toPreorder.{u1} (Submodule.{0, u1} Nat M Nat.semiring _inst_3 (AddCommMonoid.natModule.{u1} M _inst_3)) (CompleteSemilatticeInf.toPartialOrder.{u1} (Submodule.{0, u1} Nat M Nat.semiring _inst_3 (AddCommMonoid.natModule.{u1} M _inst_3)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (Submodule.{0, u1} Nat M Nat.semiring _inst_3 (AddCommMonoid.natModule.{u1} M _inst_3)) (Submodule.completeLattice.{0, u1} Nat M Nat.semiring _inst_3 (AddCommMonoid.natModule.{u1} M _inst_3)))))) (AddSubmonoid.toNatSubmodule.{u1} M _inst_3))) (Submodule.toAddSubmonoid.{0, u1} Nat M Nat.semiring _inst_3 (AddCommMonoid.natModule.{u1} M _inst_3))
 Case conversion may be inaccurate. Consider using '#align add_submonoid.to_nat_submodule_symm AddSubmonoid.toNatSubmodule_symmₓ'. -/
@@ -633,7 +633,7 @@ theorem AddSubmonoid.toNatSubmodule_symm :
 
 /- warning: add_submonoid.coe_to_nat_submodule -> AddSubmonoid.coe_toNatSubmodule is a dubious translation:
 lean 3 declaration is
-  forall {M : Type.{u1}} [_inst_3 : AddCommMonoid.{u1} M] (S : AddSubmonoid.{u1} M (AddMonoid.toAddZeroClass.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3))), Eq.{succ u1} (Set.{u1} M) ((fun (a : Type.{u1}) (b : Type.{u1}) [self : HasLiftT.{succ u1, succ u1} a b] => self.0) (Submodule.{0, u1} Nat M Nat.semiring _inst_3 (AddCommMonoid.natModule.{u1} M _inst_3)) (Set.{u1} M) (HasLiftT.mk.{succ u1, succ u1} (Submodule.{0, u1} Nat M Nat.semiring _inst_3 (AddCommMonoid.natModule.{u1} M _inst_3)) (Set.{u1} M) (CoeTCₓ.coe.{succ u1, succ u1} (Submodule.{0, u1} Nat M Nat.semiring _inst_3 (AddCommMonoid.natModule.{u1} M _inst_3)) (Set.{u1} M) (SetLike.Set.hasCoeT.{u1, u1} (Submodule.{0, u1} Nat M Nat.semiring _inst_3 (AddCommMonoid.natModule.{u1} M _inst_3)) M (Submodule.setLike.{0, u1} Nat M Nat.semiring _inst_3 (AddCommMonoid.natModule.{u1} M _inst_3))))) (coeFn.{succ u1, succ u1} (OrderIso.{u1, u1} (AddSubmonoid.{u1} M (AddMonoid.toAddZeroClass.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3))) (Submodule.{0, u1} Nat M Nat.semiring _inst_3 (AddCommMonoid.natModule.{u1} M _inst_3)) (Preorder.toLE.{u1} (AddSubmonoid.{u1} M (AddMonoid.toAddZeroClass.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3))) (PartialOrder.toPreorder.{u1} (AddSubmonoid.{u1} M (AddMonoid.toAddZeroClass.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3))) (CompleteSemilatticeInf.toPartialOrder.{u1} (AddSubmonoid.{u1} M (AddMonoid.toAddZeroClass.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3))) (CompleteLattice.toCompleteSemilatticeInf.{u1} (AddSubmonoid.{u1} M (AddMonoid.toAddZeroClass.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3))) (AddSubmonoid.completeLattice.{u1} M (AddMonoid.toAddZeroClass.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3))))))) (Preorder.toLE.{u1} (Submodule.{0, u1} Nat M Nat.semiring _inst_3 (AddCommMonoid.natModule.{u1} M _inst_3)) (PartialOrder.toPreorder.{u1} (Submodule.{0, u1} Nat M Nat.semiring _inst_3 (AddCommMonoid.natModule.{u1} M _inst_3)) (CompleteSemilatticeInf.toPartialOrder.{u1} (Submodule.{0, u1} Nat M Nat.semiring _inst_3 (AddCommMonoid.natModule.{u1} M _inst_3)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (Submodule.{0, u1} Nat M Nat.semiring _inst_3 (AddCommMonoid.natModule.{u1} M _inst_3)) (Submodule.completeLattice.{0, u1} Nat M Nat.semiring _inst_3 (AddCommMonoid.natModule.{u1} M _inst_3))))))) (fun (_x : RelIso.{u1, u1} (AddSubmonoid.{u1} M (AddMonoid.toAddZeroClass.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3))) (Submodule.{0, u1} Nat M Nat.semiring _inst_3 (AddCommMonoid.natModule.{u1} M _inst_3)) (LE.le.{u1} (AddSubmonoid.{u1} M (AddMonoid.toAddZeroClass.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3))) (Preorder.toLE.{u1} (AddSubmonoid.{u1} M (AddMonoid.toAddZeroClass.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3))) (PartialOrder.toPreorder.{u1} (AddSubmonoid.{u1} M (AddMonoid.toAddZeroClass.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3))) (CompleteSemilatticeInf.toPartialOrder.{u1} (AddSubmonoid.{u1} M (AddMonoid.toAddZeroClass.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3))) (CompleteLattice.toCompleteSemilatticeInf.{u1} (AddSubmonoid.{u1} M (AddMonoid.toAddZeroClass.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3))) (AddSubmonoid.completeLattice.{u1} M (AddMonoid.toAddZeroClass.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3)))))))) (LE.le.{u1} (Submodule.{0, u1} Nat M Nat.semiring _inst_3 (AddCommMonoid.natModule.{u1} M _inst_3)) (Preorder.toLE.{u1} (Submodule.{0, u1} Nat M Nat.semiring _inst_3 (AddCommMonoid.natModule.{u1} M _inst_3)) (PartialOrder.toPreorder.{u1} (Submodule.{0, u1} Nat M Nat.semiring _inst_3 (AddCommMonoid.natModule.{u1} M _inst_3)) (CompleteSemilatticeInf.toPartialOrder.{u1} (Submodule.{0, u1} Nat M Nat.semiring _inst_3 (AddCommMonoid.natModule.{u1} M _inst_3)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (Submodule.{0, u1} Nat M Nat.semiring _inst_3 (AddCommMonoid.natModule.{u1} M _inst_3)) (Submodule.completeLattice.{0, u1} Nat M Nat.semiring _inst_3 (AddCommMonoid.natModule.{u1} M _inst_3)))))))) => (AddSubmonoid.{u1} M (AddMonoid.toAddZeroClass.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3))) -> (Submodule.{0, u1} Nat M Nat.semiring _inst_3 (AddCommMonoid.natModule.{u1} M _inst_3))) (RelIso.hasCoeToFun.{u1, u1} (AddSubmonoid.{u1} M (AddMonoid.toAddZeroClass.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3))) (Submodule.{0, u1} Nat M Nat.semiring _inst_3 (AddCommMonoid.natModule.{u1} M _inst_3)) (LE.le.{u1} (AddSubmonoid.{u1} M (AddMonoid.toAddZeroClass.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3))) (Preorder.toLE.{u1} (AddSubmonoid.{u1} M (AddMonoid.toAddZeroClass.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3))) (PartialOrder.toPreorder.{u1} (AddSubmonoid.{u1} M (AddMonoid.toAddZeroClass.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3))) (CompleteSemilatticeInf.toPartialOrder.{u1} (AddSubmonoid.{u1} M (AddMonoid.toAddZeroClass.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3))) (CompleteLattice.toCompleteSemilatticeInf.{u1} (AddSubmonoid.{u1} M (AddMonoid.toAddZeroClass.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3))) (AddSubmonoid.completeLattice.{u1} M (AddMonoid.toAddZeroClass.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3)))))))) (LE.le.{u1} (Submodule.{0, u1} Nat M Nat.semiring _inst_3 (AddCommMonoid.natModule.{u1} M _inst_3)) (Preorder.toLE.{u1} (Submodule.{0, u1} Nat M Nat.semiring _inst_3 (AddCommMonoid.natModule.{u1} M _inst_3)) (PartialOrder.toPreorder.{u1} (Submodule.{0, u1} Nat M Nat.semiring _inst_3 (AddCommMonoid.natModule.{u1} M _inst_3)) (CompleteSemilatticeInf.toPartialOrder.{u1} (Submodule.{0, u1} Nat M Nat.semiring _inst_3 (AddCommMonoid.natModule.{u1} M _inst_3)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (Submodule.{0, u1} Nat M Nat.semiring _inst_3 (AddCommMonoid.natModule.{u1} M _inst_3)) (Submodule.completeLattice.{0, u1} Nat M Nat.semiring _inst_3 (AddCommMonoid.natModule.{u1} M _inst_3)))))))) (AddSubmonoid.toNatSubmodule.{u1} M _inst_3) S)) ((fun (a : Type.{u1}) (b : Type.{u1}) [self : HasLiftT.{succ u1, succ u1} a b] => self.0) (AddSubmonoid.{u1} M (AddMonoid.toAddZeroClass.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3))) (Set.{u1} M) (HasLiftT.mk.{succ u1, succ u1} (AddSubmonoid.{u1} M (AddMonoid.toAddZeroClass.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3))) (Set.{u1} M) (CoeTCₓ.coe.{succ u1, succ u1} (AddSubmonoid.{u1} M (AddMonoid.toAddZeroClass.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3))) (Set.{u1} M) (SetLike.Set.hasCoeT.{u1, u1} (AddSubmonoid.{u1} M (AddMonoid.toAddZeroClass.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3))) M (AddSubmonoid.setLike.{u1} M (AddMonoid.toAddZeroClass.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3)))))) S)
+  forall {M : Type.{u1}} [_inst_3 : AddCommMonoid.{u1} M] (S : AddSubmonoid.{u1} M (AddMonoid.toAddZeroClass.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3))), Eq.{succ u1} (Set.{u1} M) ((fun (a : Type.{u1}) (b : Type.{u1}) [self : HasLiftT.{succ u1, succ u1} a b] => self.0) (Submodule.{0, u1} Nat M Nat.semiring _inst_3 (AddCommMonoid.natModule.{u1} M _inst_3)) (Set.{u1} M) (HasLiftT.mk.{succ u1, succ u1} (Submodule.{0, u1} Nat M Nat.semiring _inst_3 (AddCommMonoid.natModule.{u1} M _inst_3)) (Set.{u1} M) (CoeTCₓ.coe.{succ u1, succ u1} (Submodule.{0, u1} Nat M Nat.semiring _inst_3 (AddCommMonoid.natModule.{u1} M _inst_3)) (Set.{u1} M) (SetLike.Set.hasCoeT.{u1, u1} (Submodule.{0, u1} Nat M Nat.semiring _inst_3 (AddCommMonoid.natModule.{u1} M _inst_3)) M (Submodule.setLike.{0, u1} Nat M Nat.semiring _inst_3 (AddCommMonoid.natModule.{u1} M _inst_3))))) (coeFn.{succ u1, succ u1} (OrderIso.{u1, u1} (AddSubmonoid.{u1} M (AddMonoid.toAddZeroClass.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3))) (Submodule.{0, u1} Nat M Nat.semiring _inst_3 (AddCommMonoid.natModule.{u1} M _inst_3)) (Preorder.toHasLe.{u1} (AddSubmonoid.{u1} M (AddMonoid.toAddZeroClass.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3))) (PartialOrder.toPreorder.{u1} (AddSubmonoid.{u1} M (AddMonoid.toAddZeroClass.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3))) (CompleteSemilatticeInf.toPartialOrder.{u1} (AddSubmonoid.{u1} M (AddMonoid.toAddZeroClass.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3))) (CompleteLattice.toCompleteSemilatticeInf.{u1} (AddSubmonoid.{u1} M (AddMonoid.toAddZeroClass.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3))) (AddSubmonoid.completeLattice.{u1} M (AddMonoid.toAddZeroClass.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3))))))) (Preorder.toHasLe.{u1} (Submodule.{0, u1} Nat M Nat.semiring _inst_3 (AddCommMonoid.natModule.{u1} M _inst_3)) (PartialOrder.toPreorder.{u1} (Submodule.{0, u1} Nat M Nat.semiring _inst_3 (AddCommMonoid.natModule.{u1} M _inst_3)) (CompleteSemilatticeInf.toPartialOrder.{u1} (Submodule.{0, u1} Nat M Nat.semiring _inst_3 (AddCommMonoid.natModule.{u1} M _inst_3)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (Submodule.{0, u1} Nat M Nat.semiring _inst_3 (AddCommMonoid.natModule.{u1} M _inst_3)) (Submodule.completeLattice.{0, u1} Nat M Nat.semiring _inst_3 (AddCommMonoid.natModule.{u1} M _inst_3))))))) (fun (_x : RelIso.{u1, u1} (AddSubmonoid.{u1} M (AddMonoid.toAddZeroClass.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3))) (Submodule.{0, u1} Nat M Nat.semiring _inst_3 (AddCommMonoid.natModule.{u1} M _inst_3)) (LE.le.{u1} (AddSubmonoid.{u1} M (AddMonoid.toAddZeroClass.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3))) (Preorder.toHasLe.{u1} (AddSubmonoid.{u1} M (AddMonoid.toAddZeroClass.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3))) (PartialOrder.toPreorder.{u1} (AddSubmonoid.{u1} M (AddMonoid.toAddZeroClass.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3))) (CompleteSemilatticeInf.toPartialOrder.{u1} (AddSubmonoid.{u1} M (AddMonoid.toAddZeroClass.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3))) (CompleteLattice.toCompleteSemilatticeInf.{u1} (AddSubmonoid.{u1} M (AddMonoid.toAddZeroClass.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3))) (AddSubmonoid.completeLattice.{u1} M (AddMonoid.toAddZeroClass.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3)))))))) (LE.le.{u1} (Submodule.{0, u1} Nat M Nat.semiring _inst_3 (AddCommMonoid.natModule.{u1} M _inst_3)) (Preorder.toHasLe.{u1} (Submodule.{0, u1} Nat M Nat.semiring _inst_3 (AddCommMonoid.natModule.{u1} M _inst_3)) (PartialOrder.toPreorder.{u1} (Submodule.{0, u1} Nat M Nat.semiring _inst_3 (AddCommMonoid.natModule.{u1} M _inst_3)) (CompleteSemilatticeInf.toPartialOrder.{u1} (Submodule.{0, u1} Nat M Nat.semiring _inst_3 (AddCommMonoid.natModule.{u1} M _inst_3)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (Submodule.{0, u1} Nat M Nat.semiring _inst_3 (AddCommMonoid.natModule.{u1} M _inst_3)) (Submodule.completeLattice.{0, u1} Nat M Nat.semiring _inst_3 (AddCommMonoid.natModule.{u1} M _inst_3)))))))) => (AddSubmonoid.{u1} M (AddMonoid.toAddZeroClass.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3))) -> (Submodule.{0, u1} Nat M Nat.semiring _inst_3 (AddCommMonoid.natModule.{u1} M _inst_3))) (RelIso.hasCoeToFun.{u1, u1} (AddSubmonoid.{u1} M (AddMonoid.toAddZeroClass.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3))) (Submodule.{0, u1} Nat M Nat.semiring _inst_3 (AddCommMonoid.natModule.{u1} M _inst_3)) (LE.le.{u1} (AddSubmonoid.{u1} M (AddMonoid.toAddZeroClass.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3))) (Preorder.toHasLe.{u1} (AddSubmonoid.{u1} M (AddMonoid.toAddZeroClass.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3))) (PartialOrder.toPreorder.{u1} (AddSubmonoid.{u1} M (AddMonoid.toAddZeroClass.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3))) (CompleteSemilatticeInf.toPartialOrder.{u1} (AddSubmonoid.{u1} M (AddMonoid.toAddZeroClass.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3))) (CompleteLattice.toCompleteSemilatticeInf.{u1} (AddSubmonoid.{u1} M (AddMonoid.toAddZeroClass.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3))) (AddSubmonoid.completeLattice.{u1} M (AddMonoid.toAddZeroClass.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3)))))))) (LE.le.{u1} (Submodule.{0, u1} Nat M Nat.semiring _inst_3 (AddCommMonoid.natModule.{u1} M _inst_3)) (Preorder.toHasLe.{u1} (Submodule.{0, u1} Nat M Nat.semiring _inst_3 (AddCommMonoid.natModule.{u1} M _inst_3)) (PartialOrder.toPreorder.{u1} (Submodule.{0, u1} Nat M Nat.semiring _inst_3 (AddCommMonoid.natModule.{u1} M _inst_3)) (CompleteSemilatticeInf.toPartialOrder.{u1} (Submodule.{0, u1} Nat M Nat.semiring _inst_3 (AddCommMonoid.natModule.{u1} M _inst_3)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (Submodule.{0, u1} Nat M Nat.semiring _inst_3 (AddCommMonoid.natModule.{u1} M _inst_3)) (Submodule.completeLattice.{0, u1} Nat M Nat.semiring _inst_3 (AddCommMonoid.natModule.{u1} M _inst_3)))))))) (AddSubmonoid.toNatSubmodule.{u1} M _inst_3) S)) ((fun (a : Type.{u1}) (b : Type.{u1}) [self : HasLiftT.{succ u1, succ u1} a b] => self.0) (AddSubmonoid.{u1} M (AddMonoid.toAddZeroClass.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3))) (Set.{u1} M) (HasLiftT.mk.{succ u1, succ u1} (AddSubmonoid.{u1} M (AddMonoid.toAddZeroClass.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3))) (Set.{u1} M) (CoeTCₓ.coe.{succ u1, succ u1} (AddSubmonoid.{u1} M (AddMonoid.toAddZeroClass.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3))) (Set.{u1} M) (SetLike.Set.hasCoeT.{u1, u1} (AddSubmonoid.{u1} M (AddMonoid.toAddZeroClass.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3))) M (AddSubmonoid.setLike.{u1} M (AddMonoid.toAddZeroClass.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3)))))) S)
 but is expected to have type
   forall {M : Type.{u1}} [_inst_3 : AddCommMonoid.{u1} M] (S : AddSubmonoid.{u1} M (AddMonoid.toAddZeroClass.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3))), Eq.{succ u1} (Set.{u1} M) (SetLike.coe.{u1, u1} (Submodule.{0, u1} Nat M Nat.semiring _inst_3 (AddCommMonoid.natModule.{u1} M _inst_3)) M (Submodule.setLike.{0, u1} Nat M Nat.semiring _inst_3 (AddCommMonoid.natModule.{u1} M _inst_3)) (FunLike.coe.{succ u1, succ u1, succ u1} (RelIso.{u1, u1} (AddSubmonoid.{u1} M (AddMonoid.toAddZeroClass.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3))) (Submodule.{0, u1} Nat M Nat.semiring _inst_3 (AddCommMonoid.natModule.{u1} M _inst_3)) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1281 : AddSubmonoid.{u1} M (AddMonoid.toAddZeroClass.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3))) (x._@.Mathlib.Order.Hom.Basic._hyg.1283 : AddSubmonoid.{u1} M (AddMonoid.toAddZeroClass.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3))) => LE.le.{u1} (AddSubmonoid.{u1} M (AddMonoid.toAddZeroClass.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3))) (Preorder.toLE.{u1} (AddSubmonoid.{u1} M (AddMonoid.toAddZeroClass.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3))) (PartialOrder.toPreorder.{u1} (AddSubmonoid.{u1} M (AddMonoid.toAddZeroClass.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3))) (CompleteSemilatticeInf.toPartialOrder.{u1} (AddSubmonoid.{u1} M (AddMonoid.toAddZeroClass.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3))) (CompleteLattice.toCompleteSemilatticeInf.{u1} (AddSubmonoid.{u1} M (AddMonoid.toAddZeroClass.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3))) (AddSubmonoid.instCompleteLatticeAddSubmonoid.{u1} M (AddMonoid.toAddZeroClass.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3))))))) x._@.Mathlib.Order.Hom.Basic._hyg.1281 x._@.Mathlib.Order.Hom.Basic._hyg.1283) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1296 : Submodule.{0, u1} Nat M Nat.semiring _inst_3 (AddCommMonoid.natModule.{u1} M _inst_3)) (x._@.Mathlib.Order.Hom.Basic._hyg.1298 : Submodule.{0, u1} Nat M Nat.semiring _inst_3 (AddCommMonoid.natModule.{u1} M _inst_3)) => LE.le.{u1} (Submodule.{0, u1} Nat M Nat.semiring _inst_3 (AddCommMonoid.natModule.{u1} M _inst_3)) (Preorder.toLE.{u1} (Submodule.{0, u1} Nat M Nat.semiring _inst_3 (AddCommMonoid.natModule.{u1} M _inst_3)) (PartialOrder.toPreorder.{u1} (Submodule.{0, u1} Nat M Nat.semiring _inst_3 (AddCommMonoid.natModule.{u1} M _inst_3)) (CompleteSemilatticeInf.toPartialOrder.{u1} (Submodule.{0, u1} Nat M Nat.semiring _inst_3 (AddCommMonoid.natModule.{u1} M _inst_3)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (Submodule.{0, u1} Nat M Nat.semiring _inst_3 (AddCommMonoid.natModule.{u1} M _inst_3)) (Submodule.completeLattice.{0, u1} Nat M Nat.semiring _inst_3 (AddCommMonoid.natModule.{u1} M _inst_3)))))) x._@.Mathlib.Order.Hom.Basic._hyg.1296 x._@.Mathlib.Order.Hom.Basic._hyg.1298)) (AddSubmonoid.{u1} M (AddMonoid.toAddZeroClass.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3))) (fun (_x : AddSubmonoid.{u1} M (AddMonoid.toAddZeroClass.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3))) => Submodule.{0, u1} Nat M Nat.semiring _inst_3 (AddCommMonoid.natModule.{u1} M _inst_3)) (RelHomClass.toFunLike.{u1, u1, u1} (RelIso.{u1, u1} (AddSubmonoid.{u1} M (AddMonoid.toAddZeroClass.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3))) (Submodule.{0, u1} Nat M Nat.semiring _inst_3 (AddCommMonoid.natModule.{u1} M _inst_3)) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1281 : AddSubmonoid.{u1} M (AddMonoid.toAddZeroClass.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3))) (x._@.Mathlib.Order.Hom.Basic._hyg.1283 : AddSubmonoid.{u1} M (AddMonoid.toAddZeroClass.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3))) => LE.le.{u1} (AddSubmonoid.{u1} M (AddMonoid.toAddZeroClass.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3))) (Preorder.toLE.{u1} (AddSubmonoid.{u1} M (AddMonoid.toAddZeroClass.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3))) (PartialOrder.toPreorder.{u1} (AddSubmonoid.{u1} M (AddMonoid.toAddZeroClass.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3))) (CompleteSemilatticeInf.toPartialOrder.{u1} (AddSubmonoid.{u1} M (AddMonoid.toAddZeroClass.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3))) (CompleteLattice.toCompleteSemilatticeInf.{u1} (AddSubmonoid.{u1} M (AddMonoid.toAddZeroClass.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3))) (AddSubmonoid.instCompleteLatticeAddSubmonoid.{u1} M (AddMonoid.toAddZeroClass.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3))))))) x._@.Mathlib.Order.Hom.Basic._hyg.1281 x._@.Mathlib.Order.Hom.Basic._hyg.1283) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1296 : Submodule.{0, u1} Nat M Nat.semiring _inst_3 (AddCommMonoid.natModule.{u1} M _inst_3)) (x._@.Mathlib.Order.Hom.Basic._hyg.1298 : Submodule.{0, u1} Nat M Nat.semiring _inst_3 (AddCommMonoid.natModule.{u1} M _inst_3)) => LE.le.{u1} (Submodule.{0, u1} Nat M Nat.semiring _inst_3 (AddCommMonoid.natModule.{u1} M _inst_3)) (Preorder.toLE.{u1} (Submodule.{0, u1} Nat M Nat.semiring _inst_3 (AddCommMonoid.natModule.{u1} M _inst_3)) (PartialOrder.toPreorder.{u1} (Submodule.{0, u1} Nat M Nat.semiring _inst_3 (AddCommMonoid.natModule.{u1} M _inst_3)) (CompleteSemilatticeInf.toPartialOrder.{u1} (Submodule.{0, u1} Nat M Nat.semiring _inst_3 (AddCommMonoid.natModule.{u1} M _inst_3)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (Submodule.{0, u1} Nat M Nat.semiring _inst_3 (AddCommMonoid.natModule.{u1} M _inst_3)) (Submodule.completeLattice.{0, u1} Nat M Nat.semiring _inst_3 (AddCommMonoid.natModule.{u1} M _inst_3)))))) x._@.Mathlib.Order.Hom.Basic._hyg.1296 x._@.Mathlib.Order.Hom.Basic._hyg.1298)) (AddSubmonoid.{u1} M (AddMonoid.toAddZeroClass.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3))) (Submodule.{0, u1} Nat M Nat.semiring _inst_3 (AddCommMonoid.natModule.{u1} M _inst_3)) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1281 : AddSubmonoid.{u1} M (AddMonoid.toAddZeroClass.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3))) (x._@.Mathlib.Order.Hom.Basic._hyg.1283 : AddSubmonoid.{u1} M (AddMonoid.toAddZeroClass.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3))) => LE.le.{u1} (AddSubmonoid.{u1} M (AddMonoid.toAddZeroClass.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3))) (Preorder.toLE.{u1} (AddSubmonoid.{u1} M (AddMonoid.toAddZeroClass.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3))) (PartialOrder.toPreorder.{u1} (AddSubmonoid.{u1} M (AddMonoid.toAddZeroClass.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3))) (CompleteSemilatticeInf.toPartialOrder.{u1} (AddSubmonoid.{u1} M (AddMonoid.toAddZeroClass.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3))) (CompleteLattice.toCompleteSemilatticeInf.{u1} (AddSubmonoid.{u1} M (AddMonoid.toAddZeroClass.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3))) (AddSubmonoid.instCompleteLatticeAddSubmonoid.{u1} M (AddMonoid.toAddZeroClass.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3))))))) x._@.Mathlib.Order.Hom.Basic._hyg.1281 x._@.Mathlib.Order.Hom.Basic._hyg.1283) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1296 : Submodule.{0, u1} Nat M Nat.semiring _inst_3 (AddCommMonoid.natModule.{u1} M _inst_3)) (x._@.Mathlib.Order.Hom.Basic._hyg.1298 : Submodule.{0, u1} Nat M Nat.semiring _inst_3 (AddCommMonoid.natModule.{u1} M _inst_3)) => LE.le.{u1} (Submodule.{0, u1} Nat M Nat.semiring _inst_3 (AddCommMonoid.natModule.{u1} M _inst_3)) (Preorder.toLE.{u1} (Submodule.{0, u1} Nat M Nat.semiring _inst_3 (AddCommMonoid.natModule.{u1} M _inst_3)) (PartialOrder.toPreorder.{u1} (Submodule.{0, u1} Nat M Nat.semiring _inst_3 (AddCommMonoid.natModule.{u1} M _inst_3)) (CompleteSemilatticeInf.toPartialOrder.{u1} (Submodule.{0, u1} Nat M Nat.semiring _inst_3 (AddCommMonoid.natModule.{u1} M _inst_3)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (Submodule.{0, u1} Nat M Nat.semiring _inst_3 (AddCommMonoid.natModule.{u1} M _inst_3)) (Submodule.completeLattice.{0, u1} Nat M Nat.semiring _inst_3 (AddCommMonoid.natModule.{u1} M _inst_3)))))) x._@.Mathlib.Order.Hom.Basic._hyg.1296 x._@.Mathlib.Order.Hom.Basic._hyg.1298) (RelIso.instRelHomClassRelIso.{u1, u1} (AddSubmonoid.{u1} M (AddMonoid.toAddZeroClass.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3))) (Submodule.{0, u1} Nat M Nat.semiring _inst_3 (AddCommMonoid.natModule.{u1} M _inst_3)) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1281 : AddSubmonoid.{u1} M (AddMonoid.toAddZeroClass.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3))) (x._@.Mathlib.Order.Hom.Basic._hyg.1283 : AddSubmonoid.{u1} M (AddMonoid.toAddZeroClass.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3))) => LE.le.{u1} (AddSubmonoid.{u1} M (AddMonoid.toAddZeroClass.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3))) (Preorder.toLE.{u1} (AddSubmonoid.{u1} M (AddMonoid.toAddZeroClass.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3))) (PartialOrder.toPreorder.{u1} (AddSubmonoid.{u1} M (AddMonoid.toAddZeroClass.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3))) (CompleteSemilatticeInf.toPartialOrder.{u1} (AddSubmonoid.{u1} M (AddMonoid.toAddZeroClass.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3))) (CompleteLattice.toCompleteSemilatticeInf.{u1} (AddSubmonoid.{u1} M (AddMonoid.toAddZeroClass.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3))) (AddSubmonoid.instCompleteLatticeAddSubmonoid.{u1} M (AddMonoid.toAddZeroClass.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3))))))) x._@.Mathlib.Order.Hom.Basic._hyg.1281 x._@.Mathlib.Order.Hom.Basic._hyg.1283) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1296 : Submodule.{0, u1} Nat M Nat.semiring _inst_3 (AddCommMonoid.natModule.{u1} M _inst_3)) (x._@.Mathlib.Order.Hom.Basic._hyg.1298 : Submodule.{0, u1} Nat M Nat.semiring _inst_3 (AddCommMonoid.natModule.{u1} M _inst_3)) => LE.le.{u1} (Submodule.{0, u1} Nat M Nat.semiring _inst_3 (AddCommMonoid.natModule.{u1} M _inst_3)) (Preorder.toLE.{u1} (Submodule.{0, u1} Nat M Nat.semiring _inst_3 (AddCommMonoid.natModule.{u1} M _inst_3)) (PartialOrder.toPreorder.{u1} (Submodule.{0, u1} Nat M Nat.semiring _inst_3 (AddCommMonoid.natModule.{u1} M _inst_3)) (CompleteSemilatticeInf.toPartialOrder.{u1} (Submodule.{0, u1} Nat M Nat.semiring _inst_3 (AddCommMonoid.natModule.{u1} M _inst_3)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (Submodule.{0, u1} Nat M Nat.semiring _inst_3 (AddCommMonoid.natModule.{u1} M _inst_3)) (Submodule.completeLattice.{0, u1} Nat M Nat.semiring _inst_3 (AddCommMonoid.natModule.{u1} M _inst_3)))))) x._@.Mathlib.Order.Hom.Basic._hyg.1296 x._@.Mathlib.Order.Hom.Basic._hyg.1298))) (AddSubmonoid.toNatSubmodule.{u1} M _inst_3) S)) (SetLike.coe.{u1, u1} (AddSubmonoid.{u1} M (AddMonoid.toAddZeroClass.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3))) M (AddSubmonoid.instSetLikeAddSubmonoid.{u1} M (AddMonoid.toAddZeroClass.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3))) S)
 Case conversion may be inaccurate. Consider using '#align add_submonoid.coe_to_nat_submodule AddSubmonoid.coe_toNatSubmoduleₓ'. -/
@@ -644,7 +644,7 @@ theorem AddSubmonoid.coe_toNatSubmodule (S : AddSubmonoid M) : (S.toNatSubmodule
 
 /- warning: add_submonoid.to_nat_submodule_to_add_submonoid -> AddSubmonoid.toNatSubmodule_toAddSubmonoid is a dubious translation:
 lean 3 declaration is
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(CompleteLattice.toCompleteSemilatticeInf.{u1} (AddSubmonoid.{u1} M (AddMonoid.toAddZeroClass.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3))) (AddSubmonoid.completeLattice.{u1} M (AddMonoid.toAddZeroClass.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3))))))) (Preorder.toLE.{u1} (Submodule.{0, u1} Nat M Nat.semiring _inst_3 (AddCommMonoid.natModule.{u1} M _inst_3)) (PartialOrder.toPreorder.{u1} (Submodule.{0, u1} Nat M Nat.semiring _inst_3 (AddCommMonoid.natModule.{u1} M _inst_3)) (CompleteSemilatticeInf.toPartialOrder.{u1} (Submodule.{0, u1} Nat M Nat.semiring _inst_3 (AddCommMonoid.natModule.{u1} M _inst_3)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (Submodule.{0, u1} Nat M Nat.semiring _inst_3 (AddCommMonoid.natModule.{u1} M _inst_3)) (Submodule.completeLattice.{0, u1} Nat M Nat.semiring _inst_3 (AddCommMonoid.natModule.{u1} M _inst_3))))))) (fun (_x : RelIso.{u1, u1} (AddSubmonoid.{u1} M (AddMonoid.toAddZeroClass.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3))) (Submodule.{0, u1} Nat M Nat.semiring _inst_3 (AddCommMonoid.natModule.{u1} M _inst_3)) (LE.le.{u1} (AddSubmonoid.{u1} M (AddMonoid.toAddZeroClass.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3))) (Preorder.toLE.{u1} (AddSubmonoid.{u1} M (AddMonoid.toAddZeroClass.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3))) (PartialOrder.toPreorder.{u1} (AddSubmonoid.{u1} M (AddMonoid.toAddZeroClass.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3))) (CompleteSemilatticeInf.toPartialOrder.{u1} (AddSubmonoid.{u1} M (AddMonoid.toAddZeroClass.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3))) (CompleteLattice.toCompleteSemilatticeInf.{u1} (AddSubmonoid.{u1} M (AddMonoid.toAddZeroClass.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3))) (AddSubmonoid.completeLattice.{u1} M (AddMonoid.toAddZeroClass.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3)))))))) (LE.le.{u1} (Submodule.{0, u1} Nat M Nat.semiring _inst_3 (AddCommMonoid.natModule.{u1} M _inst_3)) (Preorder.toLE.{u1} (Submodule.{0, u1} Nat M Nat.semiring _inst_3 (AddCommMonoid.natModule.{u1} M _inst_3)) (PartialOrder.toPreorder.{u1} (Submodule.{0, u1} Nat M Nat.semiring _inst_3 (AddCommMonoid.natModule.{u1} M _inst_3)) (CompleteSemilatticeInf.toPartialOrder.{u1} (Submodule.{0, u1} Nat M Nat.semiring _inst_3 (AddCommMonoid.natModule.{u1} M _inst_3)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (Submodule.{0, u1} Nat M Nat.semiring _inst_3 (AddCommMonoid.natModule.{u1} M _inst_3)) (Submodule.completeLattice.{0, u1} Nat M Nat.semiring _inst_3 (AddCommMonoid.natModule.{u1} M _inst_3)))))))) => (AddSubmonoid.{u1} M (AddMonoid.toAddZeroClass.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3))) -> (Submodule.{0, u1} Nat M Nat.semiring _inst_3 (AddCommMonoid.natModule.{u1} M _inst_3))) (RelIso.hasCoeToFun.{u1, u1} (AddSubmonoid.{u1} M (AddMonoid.toAddZeroClass.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3))) (Submodule.{0, u1} Nat M Nat.semiring _inst_3 (AddCommMonoid.natModule.{u1} M _inst_3)) (LE.le.{u1} (AddSubmonoid.{u1} M (AddMonoid.toAddZeroClass.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3))) (Preorder.toLE.{u1} (AddSubmonoid.{u1} M (AddMonoid.toAddZeroClass.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3))) (PartialOrder.toPreorder.{u1} (AddSubmonoid.{u1} M (AddMonoid.toAddZeroClass.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3))) (CompleteSemilatticeInf.toPartialOrder.{u1} (AddSubmonoid.{u1} M (AddMonoid.toAddZeroClass.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3))) (CompleteLattice.toCompleteSemilatticeInf.{u1} (AddSubmonoid.{u1} M (AddMonoid.toAddZeroClass.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3))) (AddSubmonoid.completeLattice.{u1} M (AddMonoid.toAddZeroClass.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3)))))))) (LE.le.{u1} (Submodule.{0, u1} Nat M Nat.semiring _inst_3 (AddCommMonoid.natModule.{u1} M _inst_3)) (Preorder.toLE.{u1} (Submodule.{0, u1} Nat M Nat.semiring _inst_3 (AddCommMonoid.natModule.{u1} M _inst_3)) (PartialOrder.toPreorder.{u1} (Submodule.{0, u1} Nat M Nat.semiring _inst_3 (AddCommMonoid.natModule.{u1} M _inst_3)) (CompleteSemilatticeInf.toPartialOrder.{u1} (Submodule.{0, u1} Nat M Nat.semiring _inst_3 (AddCommMonoid.natModule.{u1} M _inst_3)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (Submodule.{0, u1} Nat M Nat.semiring _inst_3 (AddCommMonoid.natModule.{u1} M _inst_3)) (Submodule.completeLattice.{0, u1} Nat M Nat.semiring _inst_3 (AddCommMonoid.natModule.{u1} M _inst_3)))))))) (AddSubmonoid.toNatSubmodule.{u1} M _inst_3) S)) S
+  forall {M : Type.{u1}} [_inst_3 : AddCommMonoid.{u1} M] (S : AddSubmonoid.{u1} M (AddMonoid.toAddZeroClass.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3))), Eq.{succ u1} (AddSubmonoid.{u1} M (AddMonoid.toAddZeroClass.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3))) (Submodule.toAddSubmonoid.{0, u1} Nat M Nat.semiring _inst_3 (AddCommMonoid.natModule.{u1} M _inst_3) (coeFn.{succ u1, succ u1} (OrderIso.{u1, u1} (AddSubmonoid.{u1} M (AddMonoid.toAddZeroClass.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3))) (Submodule.{0, u1} Nat M Nat.semiring _inst_3 (AddCommMonoid.natModule.{u1} M _inst_3)) (Preorder.toHasLe.{u1} (AddSubmonoid.{u1} M (AddMonoid.toAddZeroClass.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3))) (PartialOrder.toPreorder.{u1} (AddSubmonoid.{u1} M (AddMonoid.toAddZeroClass.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3))) (CompleteSemilatticeInf.toPartialOrder.{u1} (AddSubmonoid.{u1} M (AddMonoid.toAddZeroClass.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3))) (CompleteLattice.toCompleteSemilatticeInf.{u1} (AddSubmonoid.{u1} M (AddMonoid.toAddZeroClass.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3))) (AddSubmonoid.completeLattice.{u1} M (AddMonoid.toAddZeroClass.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3))))))) (Preorder.toHasLe.{u1} (Submodule.{0, u1} Nat M Nat.semiring _inst_3 (AddCommMonoid.natModule.{u1} M _inst_3)) (PartialOrder.toPreorder.{u1} (Submodule.{0, u1} Nat M Nat.semiring _inst_3 (AddCommMonoid.natModule.{u1} M _inst_3)) (CompleteSemilatticeInf.toPartialOrder.{u1} (Submodule.{0, u1} Nat M Nat.semiring _inst_3 (AddCommMonoid.natModule.{u1} M _inst_3)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (Submodule.{0, u1} Nat M Nat.semiring _inst_3 (AddCommMonoid.natModule.{u1} M _inst_3)) (Submodule.completeLattice.{0, u1} Nat M Nat.semiring _inst_3 (AddCommMonoid.natModule.{u1} M _inst_3))))))) (fun (_x : RelIso.{u1, u1} (AddSubmonoid.{u1} M (AddMonoid.toAddZeroClass.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3))) (Submodule.{0, u1} Nat M Nat.semiring _inst_3 (AddCommMonoid.natModule.{u1} M _inst_3)) (LE.le.{u1} (AddSubmonoid.{u1} M (AddMonoid.toAddZeroClass.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3))) (Preorder.toHasLe.{u1} (AddSubmonoid.{u1} M (AddMonoid.toAddZeroClass.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3))) (PartialOrder.toPreorder.{u1} (AddSubmonoid.{u1} M (AddMonoid.toAddZeroClass.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3))) (CompleteSemilatticeInf.toPartialOrder.{u1} (AddSubmonoid.{u1} M (AddMonoid.toAddZeroClass.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3))) (CompleteLattice.toCompleteSemilatticeInf.{u1} (AddSubmonoid.{u1} M (AddMonoid.toAddZeroClass.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3))) (AddSubmonoid.completeLattice.{u1} M (AddMonoid.toAddZeroClass.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3)))))))) (LE.le.{u1} (Submodule.{0, u1} Nat M Nat.semiring _inst_3 (AddCommMonoid.natModule.{u1} M _inst_3)) (Preorder.toHasLe.{u1} (Submodule.{0, u1} Nat M Nat.semiring _inst_3 (AddCommMonoid.natModule.{u1} M _inst_3)) (PartialOrder.toPreorder.{u1} (Submodule.{0, u1} Nat M Nat.semiring _inst_3 (AddCommMonoid.natModule.{u1} M _inst_3)) (CompleteSemilatticeInf.toPartialOrder.{u1} (Submodule.{0, u1} Nat M Nat.semiring _inst_3 (AddCommMonoid.natModule.{u1} M _inst_3)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (Submodule.{0, u1} Nat M Nat.semiring _inst_3 (AddCommMonoid.natModule.{u1} M _inst_3)) (Submodule.completeLattice.{0, u1} Nat M Nat.semiring _inst_3 (AddCommMonoid.natModule.{u1} M _inst_3)))))))) => (AddSubmonoid.{u1} M (AddMonoid.toAddZeroClass.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3))) -> (Submodule.{0, u1} Nat M Nat.semiring _inst_3 (AddCommMonoid.natModule.{u1} M _inst_3))) (RelIso.hasCoeToFun.{u1, u1} (AddSubmonoid.{u1} M (AddMonoid.toAddZeroClass.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3))) (Submodule.{0, u1} Nat M Nat.semiring _inst_3 (AddCommMonoid.natModule.{u1} M _inst_3)) (LE.le.{u1} (AddSubmonoid.{u1} M (AddMonoid.toAddZeroClass.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3))) (Preorder.toHasLe.{u1} (AddSubmonoid.{u1} M (AddMonoid.toAddZeroClass.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3))) (PartialOrder.toPreorder.{u1} (AddSubmonoid.{u1} M (AddMonoid.toAddZeroClass.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3))) (CompleteSemilatticeInf.toPartialOrder.{u1} (AddSubmonoid.{u1} M (AddMonoid.toAddZeroClass.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3))) (CompleteLattice.toCompleteSemilatticeInf.{u1} (AddSubmonoid.{u1} M (AddMonoid.toAddZeroClass.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3))) (AddSubmonoid.completeLattice.{u1} M (AddMonoid.toAddZeroClass.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3)))))))) (LE.le.{u1} (Submodule.{0, u1} Nat M Nat.semiring _inst_3 (AddCommMonoid.natModule.{u1} M _inst_3)) (Preorder.toHasLe.{u1} (Submodule.{0, u1} Nat M Nat.semiring _inst_3 (AddCommMonoid.natModule.{u1} M _inst_3)) (PartialOrder.toPreorder.{u1} (Submodule.{0, u1} Nat M Nat.semiring _inst_3 (AddCommMonoid.natModule.{u1} M _inst_3)) (CompleteSemilatticeInf.toPartialOrder.{u1} (Submodule.{0, u1} Nat M Nat.semiring _inst_3 (AddCommMonoid.natModule.{u1} M _inst_3)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (Submodule.{0, u1} Nat M Nat.semiring _inst_3 (AddCommMonoid.natModule.{u1} M _inst_3)) (Submodule.completeLattice.{0, u1} Nat M Nat.semiring _inst_3 (AddCommMonoid.natModule.{u1} M _inst_3)))))))) (AddSubmonoid.toNatSubmodule.{u1} M _inst_3) S)) S
 but is expected to have type
   forall {M : Type.{u1}} [_inst_3 : AddCommMonoid.{u1} M] (S : AddSubmonoid.{u1} M (AddMonoid.toAddZeroClass.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3))), Eq.{succ u1} (AddSubmonoid.{u1} M (AddMonoid.toAddZeroClass.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3))) (Submodule.toAddSubmonoid.{0, u1} Nat M Nat.semiring _inst_3 (AddCommMonoid.natModule.{u1} M _inst_3) (FunLike.coe.{succ u1, succ u1, succ u1} (RelIso.{u1, u1} (AddSubmonoid.{u1} M (AddMonoid.toAddZeroClass.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3))) (Submodule.{0, u1} Nat M Nat.semiring _inst_3 (AddCommMonoid.natModule.{u1} M _inst_3)) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1281 : AddSubmonoid.{u1} M (AddMonoid.toAddZeroClass.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3))) (x._@.Mathlib.Order.Hom.Basic._hyg.1283 : AddSubmonoid.{u1} M (AddMonoid.toAddZeroClass.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3))) => LE.le.{u1} (AddSubmonoid.{u1} M (AddMonoid.toAddZeroClass.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3))) (Preorder.toLE.{u1} (AddSubmonoid.{u1} M (AddMonoid.toAddZeroClass.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3))) (PartialOrder.toPreorder.{u1} (AddSubmonoid.{u1} M (AddMonoid.toAddZeroClass.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3))) (CompleteSemilatticeInf.toPartialOrder.{u1} (AddSubmonoid.{u1} M (AddMonoid.toAddZeroClass.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3))) (CompleteLattice.toCompleteSemilatticeInf.{u1} (AddSubmonoid.{u1} M (AddMonoid.toAddZeroClass.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3))) (AddSubmonoid.instCompleteLatticeAddSubmonoid.{u1} M (AddMonoid.toAddZeroClass.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3))))))) x._@.Mathlib.Order.Hom.Basic._hyg.1281 x._@.Mathlib.Order.Hom.Basic._hyg.1283) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1296 : Submodule.{0, u1} Nat M Nat.semiring _inst_3 (AddCommMonoid.natModule.{u1} M _inst_3)) (x._@.Mathlib.Order.Hom.Basic._hyg.1298 : Submodule.{0, u1} Nat M Nat.semiring _inst_3 (AddCommMonoid.natModule.{u1} M _inst_3)) => LE.le.{u1} (Submodule.{0, u1} Nat M Nat.semiring _inst_3 (AddCommMonoid.natModule.{u1} M _inst_3)) (Preorder.toLE.{u1} (Submodule.{0, u1} Nat M Nat.semiring _inst_3 (AddCommMonoid.natModule.{u1} M _inst_3)) (PartialOrder.toPreorder.{u1} (Submodule.{0, u1} Nat M Nat.semiring _inst_3 (AddCommMonoid.natModule.{u1} M _inst_3)) (CompleteSemilatticeInf.toPartialOrder.{u1} (Submodule.{0, u1} Nat M Nat.semiring _inst_3 (AddCommMonoid.natModule.{u1} M _inst_3)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (Submodule.{0, u1} Nat M Nat.semiring _inst_3 (AddCommMonoid.natModule.{u1} M _inst_3)) (Submodule.completeLattice.{0, u1} Nat M Nat.semiring _inst_3 (AddCommMonoid.natModule.{u1} M _inst_3)))))) x._@.Mathlib.Order.Hom.Basic._hyg.1296 x._@.Mathlib.Order.Hom.Basic._hyg.1298)) (AddSubmonoid.{u1} M (AddMonoid.toAddZeroClass.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3))) (fun (_x : AddSubmonoid.{u1} M (AddMonoid.toAddZeroClass.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3))) => Submodule.{0, u1} Nat M Nat.semiring _inst_3 (AddCommMonoid.natModule.{u1} M _inst_3)) (RelHomClass.toFunLike.{u1, u1, u1} (RelIso.{u1, u1} (AddSubmonoid.{u1} M (AddMonoid.toAddZeroClass.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3))) (Submodule.{0, u1} Nat M Nat.semiring _inst_3 (AddCommMonoid.natModule.{u1} M _inst_3)) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1281 : AddSubmonoid.{u1} M (AddMonoid.toAddZeroClass.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3))) (x._@.Mathlib.Order.Hom.Basic._hyg.1283 : AddSubmonoid.{u1} M (AddMonoid.toAddZeroClass.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3))) => LE.le.{u1} (AddSubmonoid.{u1} M (AddMonoid.toAddZeroClass.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3))) (Preorder.toLE.{u1} (AddSubmonoid.{u1} M (AddMonoid.toAddZeroClass.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3))) (PartialOrder.toPreorder.{u1} (AddSubmonoid.{u1} M (AddMonoid.toAddZeroClass.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3))) (CompleteSemilatticeInf.toPartialOrder.{u1} (AddSubmonoid.{u1} M (AddMonoid.toAddZeroClass.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3))) (CompleteLattice.toCompleteSemilatticeInf.{u1} (AddSubmonoid.{u1} M (AddMonoid.toAddZeroClass.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3))) (AddSubmonoid.instCompleteLatticeAddSubmonoid.{u1} M (AddMonoid.toAddZeroClass.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3))))))) x._@.Mathlib.Order.Hom.Basic._hyg.1281 x._@.Mathlib.Order.Hom.Basic._hyg.1283) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1296 : Submodule.{0, u1} Nat M Nat.semiring _inst_3 (AddCommMonoid.natModule.{u1} M _inst_3)) (x._@.Mathlib.Order.Hom.Basic._hyg.1298 : Submodule.{0, u1} Nat M Nat.semiring _inst_3 (AddCommMonoid.natModule.{u1} M _inst_3)) => LE.le.{u1} (Submodule.{0, u1} Nat M Nat.semiring _inst_3 (AddCommMonoid.natModule.{u1} M _inst_3)) (Preorder.toLE.{u1} (Submodule.{0, u1} Nat M Nat.semiring _inst_3 (AddCommMonoid.natModule.{u1} M _inst_3)) (PartialOrder.toPreorder.{u1} (Submodule.{0, u1} Nat M Nat.semiring _inst_3 (AddCommMonoid.natModule.{u1} M _inst_3)) (CompleteSemilatticeInf.toPartialOrder.{u1} (Submodule.{0, u1} Nat M Nat.semiring _inst_3 (AddCommMonoid.natModule.{u1} M _inst_3)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (Submodule.{0, u1} Nat M Nat.semiring _inst_3 (AddCommMonoid.natModule.{u1} M _inst_3)) (Submodule.completeLattice.{0, u1} Nat M Nat.semiring _inst_3 (AddCommMonoid.natModule.{u1} M _inst_3)))))) x._@.Mathlib.Order.Hom.Basic._hyg.1296 x._@.Mathlib.Order.Hom.Basic._hyg.1298)) (AddSubmonoid.{u1} M (AddMonoid.toAddZeroClass.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3))) (Submodule.{0, u1} Nat M Nat.semiring _inst_3 (AddCommMonoid.natModule.{u1} M _inst_3)) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1281 : AddSubmonoid.{u1} M (AddMonoid.toAddZeroClass.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3))) (x._@.Mathlib.Order.Hom.Basic._hyg.1283 : AddSubmonoid.{u1} M (AddMonoid.toAddZeroClass.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3))) => LE.le.{u1} (AddSubmonoid.{u1} M (AddMonoid.toAddZeroClass.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3))) (Preorder.toLE.{u1} (AddSubmonoid.{u1} M (AddMonoid.toAddZeroClass.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3))) (PartialOrder.toPreorder.{u1} (AddSubmonoid.{u1} M (AddMonoid.toAddZeroClass.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3))) (CompleteSemilatticeInf.toPartialOrder.{u1} (AddSubmonoid.{u1} M (AddMonoid.toAddZeroClass.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3))) (CompleteLattice.toCompleteSemilatticeInf.{u1} (AddSubmonoid.{u1} M (AddMonoid.toAddZeroClass.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3))) (AddSubmonoid.instCompleteLatticeAddSubmonoid.{u1} M (AddMonoid.toAddZeroClass.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3))))))) x._@.Mathlib.Order.Hom.Basic._hyg.1281 x._@.Mathlib.Order.Hom.Basic._hyg.1283) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1296 : Submodule.{0, u1} Nat M Nat.semiring _inst_3 (AddCommMonoid.natModule.{u1} M _inst_3)) (x._@.Mathlib.Order.Hom.Basic._hyg.1298 : Submodule.{0, u1} Nat M Nat.semiring _inst_3 (AddCommMonoid.natModule.{u1} M _inst_3)) => LE.le.{u1} (Submodule.{0, u1} Nat M Nat.semiring _inst_3 (AddCommMonoid.natModule.{u1} M _inst_3)) (Preorder.toLE.{u1} (Submodule.{0, u1} Nat M Nat.semiring _inst_3 (AddCommMonoid.natModule.{u1} M _inst_3)) (PartialOrder.toPreorder.{u1} (Submodule.{0, u1} Nat M Nat.semiring _inst_3 (AddCommMonoid.natModule.{u1} M _inst_3)) (CompleteSemilatticeInf.toPartialOrder.{u1} (Submodule.{0, u1} Nat M Nat.semiring _inst_3 (AddCommMonoid.natModule.{u1} M _inst_3)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (Submodule.{0, u1} Nat M Nat.semiring _inst_3 (AddCommMonoid.natModule.{u1} M _inst_3)) (Submodule.completeLattice.{0, u1} Nat M Nat.semiring _inst_3 (AddCommMonoid.natModule.{u1} M _inst_3)))))) x._@.Mathlib.Order.Hom.Basic._hyg.1296 x._@.Mathlib.Order.Hom.Basic._hyg.1298) (RelIso.instRelHomClassRelIso.{u1, u1} (AddSubmonoid.{u1} M (AddMonoid.toAddZeroClass.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3))) (Submodule.{0, u1} Nat M Nat.semiring _inst_3 (AddCommMonoid.natModule.{u1} M _inst_3)) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1281 : AddSubmonoid.{u1} M (AddMonoid.toAddZeroClass.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3))) (x._@.Mathlib.Order.Hom.Basic._hyg.1283 : AddSubmonoid.{u1} M (AddMonoid.toAddZeroClass.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3))) => LE.le.{u1} (AddSubmonoid.{u1} M (AddMonoid.toAddZeroClass.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3))) (Preorder.toLE.{u1} (AddSubmonoid.{u1} M (AddMonoid.toAddZeroClass.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3))) (PartialOrder.toPreorder.{u1} (AddSubmonoid.{u1} M (AddMonoid.toAddZeroClass.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3))) (CompleteSemilatticeInf.toPartialOrder.{u1} (AddSubmonoid.{u1} M (AddMonoid.toAddZeroClass.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3))) (CompleteLattice.toCompleteSemilatticeInf.{u1} (AddSubmonoid.{u1} M (AddMonoid.toAddZeroClass.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3))) (AddSubmonoid.instCompleteLatticeAddSubmonoid.{u1} M (AddMonoid.toAddZeroClass.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3))))))) x._@.Mathlib.Order.Hom.Basic._hyg.1281 x._@.Mathlib.Order.Hom.Basic._hyg.1283) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1296 : Submodule.{0, u1} Nat M Nat.semiring _inst_3 (AddCommMonoid.natModule.{u1} M _inst_3)) (x._@.Mathlib.Order.Hom.Basic._hyg.1298 : Submodule.{0, u1} Nat M Nat.semiring _inst_3 (AddCommMonoid.natModule.{u1} M _inst_3)) => LE.le.{u1} (Submodule.{0, u1} Nat M Nat.semiring _inst_3 (AddCommMonoid.natModule.{u1} M _inst_3)) (Preorder.toLE.{u1} (Submodule.{0, u1} Nat M Nat.semiring _inst_3 (AddCommMonoid.natModule.{u1} M _inst_3)) (PartialOrder.toPreorder.{u1} (Submodule.{0, u1} Nat M Nat.semiring _inst_3 (AddCommMonoid.natModule.{u1} M _inst_3)) (CompleteSemilatticeInf.toPartialOrder.{u1} (Submodule.{0, u1} Nat M Nat.semiring _inst_3 (AddCommMonoid.natModule.{u1} M _inst_3)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (Submodule.{0, u1} Nat M Nat.semiring _inst_3 (AddCommMonoid.natModule.{u1} M _inst_3)) (Submodule.completeLattice.{0, u1} Nat M Nat.semiring _inst_3 (AddCommMonoid.natModule.{u1} M _inst_3)))))) x._@.Mathlib.Order.Hom.Basic._hyg.1296 x._@.Mathlib.Order.Hom.Basic._hyg.1298))) (AddSubmonoid.toNatSubmodule.{u1} M _inst_3) S)) S
 Case conversion may be inaccurate. Consider using '#align add_submonoid.to_nat_submodule_to_add_submonoid AddSubmonoid.toNatSubmodule_toAddSubmonoidₓ'. -/
@@ -656,7 +656,7 @@ theorem AddSubmonoid.toNatSubmodule_toAddSubmonoid (S : AddSubmonoid M) :
 
 /- warning: submodule.to_add_submonoid_to_nat_submodule -> Submodule.toAddSubmonoid_toNatSubmodule is a dubious translation:
 lean 3 declaration is
-  forall {M : Type.{u1}} [_inst_3 : AddCommMonoid.{u1} M] (S : Submodule.{0, u1} Nat M Nat.semiring _inst_3 (AddCommMonoid.natModule.{u1} M _inst_3)), Eq.{succ u1} (Submodule.{0, u1} Nat M Nat.semiring _inst_3 (AddCommMonoid.natModule.{u1} M _inst_3)) (coeFn.{succ u1, succ u1} (OrderIso.{u1, u1} (AddSubmonoid.{u1} M (AddMonoid.toAddZeroClass.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3))) (Submodule.{0, u1} Nat M Nat.semiring _inst_3 (AddCommMonoid.natModule.{u1} M _inst_3)) (Preorder.toLE.{u1} (AddSubmonoid.{u1} M (AddMonoid.toAddZeroClass.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3))) (PartialOrder.toPreorder.{u1} (AddSubmonoid.{u1} M (AddMonoid.toAddZeroClass.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3))) (CompleteSemilatticeInf.toPartialOrder.{u1} (AddSubmonoid.{u1} M (AddMonoid.toAddZeroClass.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3))) (CompleteLattice.toCompleteSemilatticeInf.{u1} (AddSubmonoid.{u1} M (AddMonoid.toAddZeroClass.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3))) (AddSubmonoid.completeLattice.{u1} M (AddMonoid.toAddZeroClass.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3))))))) (Preorder.toLE.{u1} (Submodule.{0, u1} Nat M Nat.semiring _inst_3 (AddCommMonoid.natModule.{u1} M _inst_3)) (PartialOrder.toPreorder.{u1} (Submodule.{0, u1} Nat M Nat.semiring _inst_3 (AddCommMonoid.natModule.{u1} M _inst_3)) (CompleteSemilatticeInf.toPartialOrder.{u1} (Submodule.{0, u1} Nat M Nat.semiring _inst_3 (AddCommMonoid.natModule.{u1} M _inst_3)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (Submodule.{0, u1} Nat M Nat.semiring _inst_3 (AddCommMonoid.natModule.{u1} M _inst_3)) (Submodule.completeLattice.{0, u1} Nat M Nat.semiring _inst_3 (AddCommMonoid.natModule.{u1} M _inst_3))))))) (fun (_x : RelIso.{u1, u1} (AddSubmonoid.{u1} M (AddMonoid.toAddZeroClass.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3))) (Submodule.{0, u1} Nat M Nat.semiring _inst_3 (AddCommMonoid.natModule.{u1} M _inst_3)) (LE.le.{u1} (AddSubmonoid.{u1} M (AddMonoid.toAddZeroClass.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3))) (Preorder.toLE.{u1} (AddSubmonoid.{u1} M (AddMonoid.toAddZeroClass.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3))) (PartialOrder.toPreorder.{u1} (AddSubmonoid.{u1} M (AddMonoid.toAddZeroClass.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3))) (CompleteSemilatticeInf.toPartialOrder.{u1} (AddSubmonoid.{u1} M (AddMonoid.toAddZeroClass.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3))) (CompleteLattice.toCompleteSemilatticeInf.{u1} (AddSubmonoid.{u1} M (AddMonoid.toAddZeroClass.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3))) (AddSubmonoid.completeLattice.{u1} M (AddMonoid.toAddZeroClass.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3)))))))) (LE.le.{u1} (Submodule.{0, u1} Nat M Nat.semiring _inst_3 (AddCommMonoid.natModule.{u1} M _inst_3)) (Preorder.toLE.{u1} (Submodule.{0, u1} Nat M Nat.semiring _inst_3 (AddCommMonoid.natModule.{u1} M _inst_3)) (PartialOrder.toPreorder.{u1} (Submodule.{0, u1} Nat M Nat.semiring _inst_3 (AddCommMonoid.natModule.{u1} M _inst_3)) (CompleteSemilatticeInf.toPartialOrder.{u1} (Submodule.{0, u1} Nat M Nat.semiring _inst_3 (AddCommMonoid.natModule.{u1} M _inst_3)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (Submodule.{0, u1} Nat M Nat.semiring _inst_3 (AddCommMonoid.natModule.{u1} M _inst_3)) (Submodule.completeLattice.{0, u1} Nat M Nat.semiring _inst_3 (AddCommMonoid.natModule.{u1} M _inst_3)))))))) => (AddSubmonoid.{u1} M (AddMonoid.toAddZeroClass.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3))) -> (Submodule.{0, u1} Nat M Nat.semiring _inst_3 (AddCommMonoid.natModule.{u1} M _inst_3))) (RelIso.hasCoeToFun.{u1, u1} (AddSubmonoid.{u1} M (AddMonoid.toAddZeroClass.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3))) (Submodule.{0, u1} Nat M Nat.semiring _inst_3 (AddCommMonoid.natModule.{u1} M _inst_3)) (LE.le.{u1} (AddSubmonoid.{u1} M (AddMonoid.toAddZeroClass.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3))) (Preorder.toLE.{u1} (AddSubmonoid.{u1} M (AddMonoid.toAddZeroClass.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3))) (PartialOrder.toPreorder.{u1} (AddSubmonoid.{u1} M (AddMonoid.toAddZeroClass.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3))) (CompleteSemilatticeInf.toPartialOrder.{u1} (AddSubmonoid.{u1} M (AddMonoid.toAddZeroClass.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3))) (CompleteLattice.toCompleteSemilatticeInf.{u1} (AddSubmonoid.{u1} M (AddMonoid.toAddZeroClass.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3))) (AddSubmonoid.completeLattice.{u1} M (AddMonoid.toAddZeroClass.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3)))))))) (LE.le.{u1} (Submodule.{0, u1} Nat M Nat.semiring _inst_3 (AddCommMonoid.natModule.{u1} M _inst_3)) (Preorder.toLE.{u1} (Submodule.{0, u1} Nat M Nat.semiring _inst_3 (AddCommMonoid.natModule.{u1} M _inst_3)) (PartialOrder.toPreorder.{u1} (Submodule.{0, u1} Nat M Nat.semiring _inst_3 (AddCommMonoid.natModule.{u1} M _inst_3)) (CompleteSemilatticeInf.toPartialOrder.{u1} (Submodule.{0, u1} Nat M Nat.semiring _inst_3 (AddCommMonoid.natModule.{u1} M _inst_3)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (Submodule.{0, u1} Nat M Nat.semiring _inst_3 (AddCommMonoid.natModule.{u1} M _inst_3)) (Submodule.completeLattice.{0, u1} Nat M Nat.semiring _inst_3 (AddCommMonoid.natModule.{u1} M _inst_3)))))))) (AddSubmonoid.toNatSubmodule.{u1} M _inst_3) (Submodule.toAddSubmonoid.{0, u1} Nat M Nat.semiring _inst_3 (AddCommMonoid.natModule.{u1} M _inst_3) S)) S
+  forall {M : Type.{u1}} [_inst_3 : AddCommMonoid.{u1} M] (S : Submodule.{0, u1} Nat M Nat.semiring _inst_3 (AddCommMonoid.natModule.{u1} M _inst_3)), Eq.{succ u1} (Submodule.{0, u1} Nat M Nat.semiring _inst_3 (AddCommMonoid.natModule.{u1} M _inst_3)) (coeFn.{succ u1, succ u1} (OrderIso.{u1, u1} (AddSubmonoid.{u1} M (AddMonoid.toAddZeroClass.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3))) (Submodule.{0, u1} Nat M Nat.semiring _inst_3 (AddCommMonoid.natModule.{u1} M _inst_3)) (Preorder.toHasLe.{u1} (AddSubmonoid.{u1} M (AddMonoid.toAddZeroClass.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3))) (PartialOrder.toPreorder.{u1} (AddSubmonoid.{u1} M (AddMonoid.toAddZeroClass.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3))) (CompleteSemilatticeInf.toPartialOrder.{u1} (AddSubmonoid.{u1} M (AddMonoid.toAddZeroClass.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3))) (CompleteLattice.toCompleteSemilatticeInf.{u1} (AddSubmonoid.{u1} M (AddMonoid.toAddZeroClass.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3))) (AddSubmonoid.completeLattice.{u1} M (AddMonoid.toAddZeroClass.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3))))))) (Preorder.toHasLe.{u1} (Submodule.{0, u1} Nat M Nat.semiring _inst_3 (AddCommMonoid.natModule.{u1} M _inst_3)) (PartialOrder.toPreorder.{u1} (Submodule.{0, u1} Nat M Nat.semiring _inst_3 (AddCommMonoid.natModule.{u1} M _inst_3)) (CompleteSemilatticeInf.toPartialOrder.{u1} (Submodule.{0, u1} Nat M Nat.semiring _inst_3 (AddCommMonoid.natModule.{u1} M _inst_3)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (Submodule.{0, u1} Nat M Nat.semiring _inst_3 (AddCommMonoid.natModule.{u1} M _inst_3)) (Submodule.completeLattice.{0, u1} Nat M Nat.semiring _inst_3 (AddCommMonoid.natModule.{u1} M _inst_3))))))) (fun (_x : RelIso.{u1, u1} (AddSubmonoid.{u1} M (AddMonoid.toAddZeroClass.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3))) (Submodule.{0, u1} Nat M Nat.semiring _inst_3 (AddCommMonoid.natModule.{u1} M _inst_3)) (LE.le.{u1} (AddSubmonoid.{u1} M (AddMonoid.toAddZeroClass.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3))) (Preorder.toHasLe.{u1} (AddSubmonoid.{u1} M (AddMonoid.toAddZeroClass.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3))) (PartialOrder.toPreorder.{u1} (AddSubmonoid.{u1} M (AddMonoid.toAddZeroClass.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3))) (CompleteSemilatticeInf.toPartialOrder.{u1} (AddSubmonoid.{u1} M (AddMonoid.toAddZeroClass.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3))) (CompleteLattice.toCompleteSemilatticeInf.{u1} (AddSubmonoid.{u1} M (AddMonoid.toAddZeroClass.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3))) (AddSubmonoid.completeLattice.{u1} M (AddMonoid.toAddZeroClass.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3)))))))) (LE.le.{u1} (Submodule.{0, u1} Nat M Nat.semiring _inst_3 (AddCommMonoid.natModule.{u1} M _inst_3)) (Preorder.toHasLe.{u1} (Submodule.{0, u1} Nat M Nat.semiring _inst_3 (AddCommMonoid.natModule.{u1} M _inst_3)) (PartialOrder.toPreorder.{u1} (Submodule.{0, u1} Nat M Nat.semiring _inst_3 (AddCommMonoid.natModule.{u1} M _inst_3)) (CompleteSemilatticeInf.toPartialOrder.{u1} (Submodule.{0, u1} Nat M Nat.semiring _inst_3 (AddCommMonoid.natModule.{u1} M _inst_3)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (Submodule.{0, u1} Nat M Nat.semiring _inst_3 (AddCommMonoid.natModule.{u1} M _inst_3)) (Submodule.completeLattice.{0, u1} Nat M Nat.semiring _inst_3 (AddCommMonoid.natModule.{u1} M _inst_3)))))))) => (AddSubmonoid.{u1} M (AddMonoid.toAddZeroClass.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3))) -> (Submodule.{0, u1} Nat M Nat.semiring _inst_3 (AddCommMonoid.natModule.{u1} M _inst_3))) (RelIso.hasCoeToFun.{u1, u1} (AddSubmonoid.{u1} M (AddMonoid.toAddZeroClass.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3))) (Submodule.{0, u1} Nat M Nat.semiring _inst_3 (AddCommMonoid.natModule.{u1} M _inst_3)) (LE.le.{u1} (AddSubmonoid.{u1} M (AddMonoid.toAddZeroClass.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3))) (Preorder.toHasLe.{u1} (AddSubmonoid.{u1} M (AddMonoid.toAddZeroClass.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3))) (PartialOrder.toPreorder.{u1} (AddSubmonoid.{u1} M (AddMonoid.toAddZeroClass.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3))) (CompleteSemilatticeInf.toPartialOrder.{u1} (AddSubmonoid.{u1} M (AddMonoid.toAddZeroClass.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3))) (CompleteLattice.toCompleteSemilatticeInf.{u1} (AddSubmonoid.{u1} M (AddMonoid.toAddZeroClass.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3))) (AddSubmonoid.completeLattice.{u1} M (AddMonoid.toAddZeroClass.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3)))))))) (LE.le.{u1} (Submodule.{0, u1} Nat M Nat.semiring _inst_3 (AddCommMonoid.natModule.{u1} M _inst_3)) (Preorder.toHasLe.{u1} (Submodule.{0, u1} Nat M Nat.semiring _inst_3 (AddCommMonoid.natModule.{u1} M _inst_3)) (PartialOrder.toPreorder.{u1} (Submodule.{0, u1} Nat M Nat.semiring _inst_3 (AddCommMonoid.natModule.{u1} M _inst_3)) (CompleteSemilatticeInf.toPartialOrder.{u1} (Submodule.{0, u1} Nat M Nat.semiring _inst_3 (AddCommMonoid.natModule.{u1} M _inst_3)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (Submodule.{0, u1} Nat M Nat.semiring _inst_3 (AddCommMonoid.natModule.{u1} M _inst_3)) (Submodule.completeLattice.{0, u1} Nat M Nat.semiring _inst_3 (AddCommMonoid.natModule.{u1} M _inst_3)))))))) (AddSubmonoid.toNatSubmodule.{u1} M _inst_3) (Submodule.toAddSubmonoid.{0, u1} Nat M Nat.semiring _inst_3 (AddCommMonoid.natModule.{u1} M _inst_3) S)) S
 but is expected to have type
   forall {M : Type.{u1}} [_inst_3 : AddCommMonoid.{u1} M] (S : Submodule.{0, u1} Nat M Nat.semiring _inst_3 (AddCommMonoid.natModule.{u1} M _inst_3)), Eq.{succ u1} (Submodule.{0, u1} Nat M Nat.semiring _inst_3 (AddCommMonoid.natModule.{u1} M _inst_3)) (FunLike.coe.{succ u1, succ u1, succ u1} (RelIso.{u1, u1} (AddSubmonoid.{u1} M (AddMonoid.toAddZeroClass.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3))) (Submodule.{0, u1} Nat M Nat.semiring _inst_3 (AddCommMonoid.natModule.{u1} M _inst_3)) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1281 : AddSubmonoid.{u1} M (AddMonoid.toAddZeroClass.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3))) (x._@.Mathlib.Order.Hom.Basic._hyg.1283 : AddSubmonoid.{u1} M (AddMonoid.toAddZeroClass.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3))) => LE.le.{u1} (AddSubmonoid.{u1} M (AddMonoid.toAddZeroClass.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3))) (Preorder.toLE.{u1} (AddSubmonoid.{u1} M (AddMonoid.toAddZeroClass.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3))) (PartialOrder.toPreorder.{u1} (AddSubmonoid.{u1} M (AddMonoid.toAddZeroClass.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3))) (CompleteSemilatticeInf.toPartialOrder.{u1} (AddSubmonoid.{u1} M (AddMonoid.toAddZeroClass.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3))) (CompleteLattice.toCompleteSemilatticeInf.{u1} (AddSubmonoid.{u1} M (AddMonoid.toAddZeroClass.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3))) (AddSubmonoid.instCompleteLatticeAddSubmonoid.{u1} M (AddMonoid.toAddZeroClass.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3))))))) x._@.Mathlib.Order.Hom.Basic._hyg.1281 x._@.Mathlib.Order.Hom.Basic._hyg.1283) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1296 : Submodule.{0, u1} Nat M Nat.semiring _inst_3 (AddCommMonoid.natModule.{u1} M _inst_3)) (x._@.Mathlib.Order.Hom.Basic._hyg.1298 : Submodule.{0, u1} Nat M Nat.semiring _inst_3 (AddCommMonoid.natModule.{u1} M _inst_3)) => LE.le.{u1} (Submodule.{0, u1} Nat M Nat.semiring _inst_3 (AddCommMonoid.natModule.{u1} M _inst_3)) (Preorder.toLE.{u1} (Submodule.{0, u1} Nat M Nat.semiring _inst_3 (AddCommMonoid.natModule.{u1} M _inst_3)) (PartialOrder.toPreorder.{u1} (Submodule.{0, u1} Nat M Nat.semiring _inst_3 (AddCommMonoid.natModule.{u1} M _inst_3)) (CompleteSemilatticeInf.toPartialOrder.{u1} (Submodule.{0, u1} Nat M Nat.semiring _inst_3 (AddCommMonoid.natModule.{u1} M _inst_3)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (Submodule.{0, u1} Nat M Nat.semiring _inst_3 (AddCommMonoid.natModule.{u1} M _inst_3)) (Submodule.completeLattice.{0, u1} Nat M Nat.semiring _inst_3 (AddCommMonoid.natModule.{u1} M _inst_3)))))) x._@.Mathlib.Order.Hom.Basic._hyg.1296 x._@.Mathlib.Order.Hom.Basic._hyg.1298)) (AddSubmonoid.{u1} M (AddMonoid.toAddZeroClass.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3))) (fun (_x : AddSubmonoid.{u1} M (AddMonoid.toAddZeroClass.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3))) => Submodule.{0, u1} Nat M Nat.semiring _inst_3 (AddCommMonoid.natModule.{u1} M _inst_3)) (RelHomClass.toFunLike.{u1, u1, u1} (RelIso.{u1, u1} (AddSubmonoid.{u1} M (AddMonoid.toAddZeroClass.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3))) (Submodule.{0, u1} Nat M Nat.semiring _inst_3 (AddCommMonoid.natModule.{u1} M _inst_3)) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1281 : AddSubmonoid.{u1} M (AddMonoid.toAddZeroClass.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3))) (x._@.Mathlib.Order.Hom.Basic._hyg.1283 : AddSubmonoid.{u1} M (AddMonoid.toAddZeroClass.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3))) => LE.le.{u1} (AddSubmonoid.{u1} M (AddMonoid.toAddZeroClass.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3))) (Preorder.toLE.{u1} (AddSubmonoid.{u1} M (AddMonoid.toAddZeroClass.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3))) (PartialOrder.toPreorder.{u1} (AddSubmonoid.{u1} M (AddMonoid.toAddZeroClass.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3))) (CompleteSemilatticeInf.toPartialOrder.{u1} (AddSubmonoid.{u1} M (AddMonoid.toAddZeroClass.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3))) (CompleteLattice.toCompleteSemilatticeInf.{u1} (AddSubmonoid.{u1} M (AddMonoid.toAddZeroClass.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3))) (AddSubmonoid.instCompleteLatticeAddSubmonoid.{u1} M (AddMonoid.toAddZeroClass.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3))))))) x._@.Mathlib.Order.Hom.Basic._hyg.1281 x._@.Mathlib.Order.Hom.Basic._hyg.1283) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1296 : Submodule.{0, u1} Nat M Nat.semiring _inst_3 (AddCommMonoid.natModule.{u1} M _inst_3)) (x._@.Mathlib.Order.Hom.Basic._hyg.1298 : Submodule.{0, u1} Nat M Nat.semiring _inst_3 (AddCommMonoid.natModule.{u1} M _inst_3)) => LE.le.{u1} (Submodule.{0, u1} Nat M Nat.semiring _inst_3 (AddCommMonoid.natModule.{u1} M _inst_3)) (Preorder.toLE.{u1} (Submodule.{0, u1} Nat M Nat.semiring _inst_3 (AddCommMonoid.natModule.{u1} M _inst_3)) (PartialOrder.toPreorder.{u1} (Submodule.{0, u1} Nat M Nat.semiring _inst_3 (AddCommMonoid.natModule.{u1} M _inst_3)) (CompleteSemilatticeInf.toPartialOrder.{u1} (Submodule.{0, u1} Nat M Nat.semiring _inst_3 (AddCommMonoid.natModule.{u1} M _inst_3)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (Submodule.{0, u1} Nat M Nat.semiring _inst_3 (AddCommMonoid.natModule.{u1} M _inst_3)) (Submodule.completeLattice.{0, u1} Nat M Nat.semiring _inst_3 (AddCommMonoid.natModule.{u1} M _inst_3)))))) x._@.Mathlib.Order.Hom.Basic._hyg.1296 x._@.Mathlib.Order.Hom.Basic._hyg.1298)) (AddSubmonoid.{u1} M (AddMonoid.toAddZeroClass.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3))) (Submodule.{0, u1} Nat M Nat.semiring _inst_3 (AddCommMonoid.natModule.{u1} M _inst_3)) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1281 : AddSubmonoid.{u1} M (AddMonoid.toAddZeroClass.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3))) (x._@.Mathlib.Order.Hom.Basic._hyg.1283 : AddSubmonoid.{u1} M (AddMonoid.toAddZeroClass.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3))) => LE.le.{u1} (AddSubmonoid.{u1} M (AddMonoid.toAddZeroClass.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3))) (Preorder.toLE.{u1} (AddSubmonoid.{u1} M (AddMonoid.toAddZeroClass.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3))) (PartialOrder.toPreorder.{u1} (AddSubmonoid.{u1} M (AddMonoid.toAddZeroClass.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3))) (CompleteSemilatticeInf.toPartialOrder.{u1} (AddSubmonoid.{u1} M (AddMonoid.toAddZeroClass.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3))) (CompleteLattice.toCompleteSemilatticeInf.{u1} (AddSubmonoid.{u1} M (AddMonoid.toAddZeroClass.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3))) (AddSubmonoid.instCompleteLatticeAddSubmonoid.{u1} M (AddMonoid.toAddZeroClass.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3))))))) x._@.Mathlib.Order.Hom.Basic._hyg.1281 x._@.Mathlib.Order.Hom.Basic._hyg.1283) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1296 : Submodule.{0, u1} Nat M Nat.semiring _inst_3 (AddCommMonoid.natModule.{u1} M _inst_3)) (x._@.Mathlib.Order.Hom.Basic._hyg.1298 : Submodule.{0, u1} Nat M Nat.semiring _inst_3 (AddCommMonoid.natModule.{u1} M _inst_3)) => LE.le.{u1} (Submodule.{0, u1} Nat M Nat.semiring _inst_3 (AddCommMonoid.natModule.{u1} M _inst_3)) (Preorder.toLE.{u1} (Submodule.{0, u1} Nat M Nat.semiring _inst_3 (AddCommMonoid.natModule.{u1} M _inst_3)) (PartialOrder.toPreorder.{u1} (Submodule.{0, u1} Nat M Nat.semiring _inst_3 (AddCommMonoid.natModule.{u1} M _inst_3)) (CompleteSemilatticeInf.toPartialOrder.{u1} (Submodule.{0, u1} Nat M Nat.semiring _inst_3 (AddCommMonoid.natModule.{u1} M _inst_3)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (Submodule.{0, u1} Nat M Nat.semiring _inst_3 (AddCommMonoid.natModule.{u1} M _inst_3)) (Submodule.completeLattice.{0, u1} Nat M Nat.semiring _inst_3 (AddCommMonoid.natModule.{u1} M _inst_3)))))) x._@.Mathlib.Order.Hom.Basic._hyg.1296 x._@.Mathlib.Order.Hom.Basic._hyg.1298) (RelIso.instRelHomClassRelIso.{u1, u1} (AddSubmonoid.{u1} M (AddMonoid.toAddZeroClass.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3))) (Submodule.{0, u1} Nat M Nat.semiring _inst_3 (AddCommMonoid.natModule.{u1} M _inst_3)) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1281 : AddSubmonoid.{u1} M (AddMonoid.toAddZeroClass.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3))) (x._@.Mathlib.Order.Hom.Basic._hyg.1283 : AddSubmonoid.{u1} M (AddMonoid.toAddZeroClass.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3))) => LE.le.{u1} (AddSubmonoid.{u1} M (AddMonoid.toAddZeroClass.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3))) (Preorder.toLE.{u1} (AddSubmonoid.{u1} M (AddMonoid.toAddZeroClass.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3))) (PartialOrder.toPreorder.{u1} (AddSubmonoid.{u1} M (AddMonoid.toAddZeroClass.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3))) (CompleteSemilatticeInf.toPartialOrder.{u1} (AddSubmonoid.{u1} M (AddMonoid.toAddZeroClass.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3))) (CompleteLattice.toCompleteSemilatticeInf.{u1} (AddSubmonoid.{u1} M (AddMonoid.toAddZeroClass.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3))) (AddSubmonoid.instCompleteLatticeAddSubmonoid.{u1} M (AddMonoid.toAddZeroClass.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3))))))) x._@.Mathlib.Order.Hom.Basic._hyg.1281 x._@.Mathlib.Order.Hom.Basic._hyg.1283) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1296 : Submodule.{0, u1} Nat M Nat.semiring _inst_3 (AddCommMonoid.natModule.{u1} M _inst_3)) (x._@.Mathlib.Order.Hom.Basic._hyg.1298 : Submodule.{0, u1} Nat M Nat.semiring _inst_3 (AddCommMonoid.natModule.{u1} M _inst_3)) => LE.le.{u1} (Submodule.{0, u1} Nat M Nat.semiring _inst_3 (AddCommMonoid.natModule.{u1} M _inst_3)) (Preorder.toLE.{u1} (Submodule.{0, u1} Nat M Nat.semiring _inst_3 (AddCommMonoid.natModule.{u1} M _inst_3)) (PartialOrder.toPreorder.{u1} (Submodule.{0, u1} Nat M Nat.semiring _inst_3 (AddCommMonoid.natModule.{u1} M _inst_3)) (CompleteSemilatticeInf.toPartialOrder.{u1} (Submodule.{0, u1} Nat M Nat.semiring _inst_3 (AddCommMonoid.natModule.{u1} M _inst_3)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (Submodule.{0, u1} Nat M Nat.semiring _inst_3 (AddCommMonoid.natModule.{u1} M _inst_3)) (Submodule.completeLattice.{0, u1} Nat M Nat.semiring _inst_3 (AddCommMonoid.natModule.{u1} M _inst_3)))))) x._@.Mathlib.Order.Hom.Basic._hyg.1296 x._@.Mathlib.Order.Hom.Basic._hyg.1298))) (AddSubmonoid.toNatSubmodule.{u1} M _inst_3) (Submodule.toAddSubmonoid.{0, u1} Nat M Nat.semiring _inst_3 (AddCommMonoid.natModule.{u1} M _inst_3) S)) S
 Case conversion may be inaccurate. Consider using '#align submodule.to_add_submonoid_to_nat_submodule Submodule.toAddSubmonoid_toNatSubmoduleₓ'. -/
@@ -676,7 +676,7 @@ variable [AddCommGroup M]
 
 /- warning: add_subgroup.to_int_submodule -> AddSubgroup.toIntSubmodule is a dubious translation:
 lean 3 declaration is
-  forall {M : Type.{u1}} [_inst_1 : AddCommGroup.{u1} M], OrderIso.{u1, u1} (AddSubgroup.{u1} M (AddCommGroup.toAddGroup.{u1} M _inst_1)) (Submodule.{0, u1} Int M Int.semiring (AddCommGroup.toAddCommMonoid.{u1} M _inst_1) (AddCommGroup.intModule.{u1} M _inst_1)) (Preorder.toLE.{u1} (AddSubgroup.{u1} M (AddCommGroup.toAddGroup.{u1} M _inst_1)) (PartialOrder.toPreorder.{u1} (AddSubgroup.{u1} M (AddCommGroup.toAddGroup.{u1} M _inst_1)) (CompleteSemilatticeInf.toPartialOrder.{u1} (AddSubgroup.{u1} M (AddCommGroup.toAddGroup.{u1} M _inst_1)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (AddSubgroup.{u1} M (AddCommGroup.toAddGroup.{u1} M _inst_1)) (AddSubgroup.completeLattice.{u1} M (AddCommGroup.toAddGroup.{u1} M _inst_1)))))) (Preorder.toLE.{u1} (Submodule.{0, u1} Int M Int.semiring (AddCommGroup.toAddCommMonoid.{u1} M _inst_1) (AddCommGroup.intModule.{u1} M _inst_1)) (PartialOrder.toPreorder.{u1} (Submodule.{0, u1} Int M Int.semiring (AddCommGroup.toAddCommMonoid.{u1} M _inst_1) (AddCommGroup.intModule.{u1} M _inst_1)) (CompleteSemilatticeInf.toPartialOrder.{u1} (Submodule.{0, u1} Int M Int.semiring (AddCommGroup.toAddCommMonoid.{u1} M _inst_1) (AddCommGroup.intModule.{u1} M _inst_1)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (Submodule.{0, u1} Int M Int.semiring (AddCommGroup.toAddCommMonoid.{u1} M _inst_1) (AddCommGroup.intModule.{u1} M _inst_1)) (Submodule.completeLattice.{0, u1} Int M Int.semiring (AddCommGroup.toAddCommMonoid.{u1} M _inst_1) (AddCommGroup.intModule.{u1} M _inst_1))))))
+  forall {M : Type.{u1}} [_inst_1 : AddCommGroup.{u1} M], OrderIso.{u1, u1} (AddSubgroup.{u1} M (AddCommGroup.toAddGroup.{u1} M _inst_1)) (Submodule.{0, u1} Int M Int.semiring (AddCommGroup.toAddCommMonoid.{u1} M _inst_1) (AddCommGroup.intModule.{u1} M _inst_1)) (Preorder.toHasLe.{u1} (AddSubgroup.{u1} M (AddCommGroup.toAddGroup.{u1} M _inst_1)) (PartialOrder.toPreorder.{u1} (AddSubgroup.{u1} M (AddCommGroup.toAddGroup.{u1} M _inst_1)) (CompleteSemilatticeInf.toPartialOrder.{u1} (AddSubgroup.{u1} M (AddCommGroup.toAddGroup.{u1} M _inst_1)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (AddSubgroup.{u1} M (AddCommGroup.toAddGroup.{u1} M _inst_1)) (AddSubgroup.completeLattice.{u1} M (AddCommGroup.toAddGroup.{u1} M _inst_1)))))) (Preorder.toHasLe.{u1} (Submodule.{0, u1} Int M Int.semiring (AddCommGroup.toAddCommMonoid.{u1} M _inst_1) (AddCommGroup.intModule.{u1} M _inst_1)) (PartialOrder.toPreorder.{u1} (Submodule.{0, u1} Int M Int.semiring (AddCommGroup.toAddCommMonoid.{u1} M _inst_1) (AddCommGroup.intModule.{u1} M _inst_1)) (CompleteSemilatticeInf.toPartialOrder.{u1} (Submodule.{0, u1} Int M Int.semiring (AddCommGroup.toAddCommMonoid.{u1} M _inst_1) (AddCommGroup.intModule.{u1} M _inst_1)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (Submodule.{0, u1} Int M Int.semiring (AddCommGroup.toAddCommMonoid.{u1} M _inst_1) (AddCommGroup.intModule.{u1} M _inst_1)) (Submodule.completeLattice.{0, u1} Int M Int.semiring (AddCommGroup.toAddCommMonoid.{u1} M _inst_1) (AddCommGroup.intModule.{u1} M _inst_1))))))
 but is expected to have type
   forall {M : Type.{u1}} [_inst_1 : AddCommGroup.{u1} M], OrderIso.{u1, u1} (AddSubgroup.{u1} M (AddCommGroup.toAddGroup.{u1} M _inst_1)) (Submodule.{0, u1} Int M Int.instSemiringInt (AddCommGroup.toAddCommMonoid.{u1} M _inst_1) (AddCommGroup.intModule.{u1} M _inst_1)) (Preorder.toLE.{u1} (AddSubgroup.{u1} M (AddCommGroup.toAddGroup.{u1} M _inst_1)) (PartialOrder.toPreorder.{u1} (AddSubgroup.{u1} M (AddCommGroup.toAddGroup.{u1} M _inst_1)) (CompleteSemilatticeInf.toPartialOrder.{u1} (AddSubgroup.{u1} M (AddCommGroup.toAddGroup.{u1} M _inst_1)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (AddSubgroup.{u1} M (AddCommGroup.toAddGroup.{u1} M _inst_1)) (AddSubgroup.instCompleteLatticeAddSubgroup.{u1} M (AddCommGroup.toAddGroup.{u1} M _inst_1)))))) (Preorder.toLE.{u1} (Submodule.{0, u1} Int M Int.instSemiringInt (AddCommGroup.toAddCommMonoid.{u1} M _inst_1) (AddCommGroup.intModule.{u1} M _inst_1)) (PartialOrder.toPreorder.{u1} (Submodule.{0, u1} Int M Int.instSemiringInt (AddCommGroup.toAddCommMonoid.{u1} M _inst_1) (AddCommGroup.intModule.{u1} M _inst_1)) (CompleteSemilatticeInf.toPartialOrder.{u1} (Submodule.{0, u1} Int M Int.instSemiringInt (AddCommGroup.toAddCommMonoid.{u1} M _inst_1) (AddCommGroup.intModule.{u1} M _inst_1)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (Submodule.{0, u1} Int M Int.instSemiringInt (AddCommGroup.toAddCommMonoid.{u1} M _inst_1) (AddCommGroup.intModule.{u1} M _inst_1)) (Submodule.completeLattice.{0, u1} Int M Int.instSemiringInt (AddCommGroup.toAddCommMonoid.{u1} M _inst_1) (AddCommGroup.intModule.{u1} M _inst_1))))))
 Case conversion may be inaccurate. Consider using '#align add_subgroup.to_int_submodule AddSubgroup.toIntSubmoduleₓ'. -/
@@ -692,7 +692,7 @@ def AddSubgroup.toIntSubmodule : AddSubgroup M ≃o Submodule ℤ M
 
 /- warning: add_subgroup.to_int_submodule_symm -> AddSubgroup.toIntSubmodule_symm is a dubious translation:
 lean 3 declaration is
-  forall {M : Type.{u1}} [_inst_1 : AddCommGroup.{u1} M], Eq.{succ u1} ((Submodule.{0, u1} Int M Int.semiring (AddCommGroup.toAddCommMonoid.{u1} M _inst_1) (AddCommGroup.intModule.{u1} M _inst_1)) -> (AddSubgroup.{u1} M (AddCommGroup.toAddGroup.{u1} M _inst_1))) (coeFn.{succ u1, succ u1} (OrderIso.{u1, u1} (Submodule.{0, u1} Int M Int.semiring (AddCommGroup.toAddCommMonoid.{u1} M _inst_1) (AddCommGroup.intModule.{u1} M _inst_1)) (AddSubgroup.{u1} M (AddCommGroup.toAddGroup.{u1} M _inst_1)) (Preorder.toLE.{u1} (Submodule.{0, u1} Int M Int.semiring (AddCommGroup.toAddCommMonoid.{u1} M _inst_1) (AddCommGroup.intModule.{u1} M _inst_1)) (PartialOrder.toPreorder.{u1} (Submodule.{0, u1} Int M Int.semiring (AddCommGroup.toAddCommMonoid.{u1} M _inst_1) (AddCommGroup.intModule.{u1} M _inst_1)) (CompleteSemilatticeInf.toPartialOrder.{u1} (Submodule.{0, u1} Int M Int.semiring (AddCommGroup.toAddCommMonoid.{u1} M _inst_1) (AddCommGroup.intModule.{u1} M _inst_1)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (Submodule.{0, u1} Int M Int.semiring (AddCommGroup.toAddCommMonoid.{u1} M _inst_1) (AddCommGroup.intModule.{u1} M _inst_1)) (Submodule.completeLattice.{0, u1} Int M Int.semiring (AddCommGroup.toAddCommMonoid.{u1} M _inst_1) (AddCommGroup.intModule.{u1} M _inst_1)))))) (Preorder.toLE.{u1} (AddSubgroup.{u1} M (AddCommGroup.toAddGroup.{u1} M _inst_1)) (PartialOrder.toPreorder.{u1} (AddSubgroup.{u1} M (AddCommGroup.toAddGroup.{u1} M _inst_1)) (CompleteSemilatticeInf.toPartialOrder.{u1} (AddSubgroup.{u1} M (AddCommGroup.toAddGroup.{u1} M _inst_1)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (AddSubgroup.{u1} M (AddCommGroup.toAddGroup.{u1} M _inst_1)) (AddSubgroup.completeLattice.{u1} M (AddCommGroup.toAddGroup.{u1} M _inst_1))))))) (fun (_x : RelIso.{u1, u1} (Submodule.{0, u1} Int M Int.semiring (AddCommGroup.toAddCommMonoid.{u1} M _inst_1) (AddCommGroup.intModule.{u1} M _inst_1)) (AddSubgroup.{u1} M (AddCommGroup.toAddGroup.{u1} M _inst_1)) (LE.le.{u1} (Submodule.{0, u1} Int M Int.semiring (AddCommGroup.toAddCommMonoid.{u1} M _inst_1) (AddCommGroup.intModule.{u1} M _inst_1)) (Preorder.toLE.{u1} (Submodule.{0, u1} Int M Int.semiring (AddCommGroup.toAddCommMonoid.{u1} M _inst_1) (AddCommGroup.intModule.{u1} M _inst_1)) (PartialOrder.toPreorder.{u1} (Submodule.{0, u1} Int M Int.semiring (AddCommGroup.toAddCommMonoid.{u1} M _inst_1) (AddCommGroup.intModule.{u1} M _inst_1)) (CompleteSemilatticeInf.toPartialOrder.{u1} (Submodule.{0, u1} Int M Int.semiring (AddCommGroup.toAddCommMonoid.{u1} M _inst_1) (AddCommGroup.intModule.{u1} M _inst_1)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (Submodule.{0, u1} Int M Int.semiring (AddCommGroup.toAddCommMonoid.{u1} M _inst_1) (AddCommGroup.intModule.{u1} M _inst_1)) (Submodule.completeLattice.{0, u1} Int M Int.semiring (AddCommGroup.toAddCommMonoid.{u1} M _inst_1) (AddCommGroup.intModule.{u1} M _inst_1))))))) (LE.le.{u1} (AddSubgroup.{u1} M (AddCommGroup.toAddGroup.{u1} M _inst_1)) (Preorder.toLE.{u1} (AddSubgroup.{u1} M (AddCommGroup.toAddGroup.{u1} M _inst_1)) (PartialOrder.toPreorder.{u1} (AddSubgroup.{u1} M (AddCommGroup.toAddGroup.{u1} M _inst_1)) (CompleteSemilatticeInf.toPartialOrder.{u1} (AddSubgroup.{u1} M (AddCommGroup.toAddGroup.{u1} M _inst_1)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (AddSubgroup.{u1} M (AddCommGroup.toAddGroup.{u1} M _inst_1)) (AddSubgroup.completeLattice.{u1} M (AddCommGroup.toAddGroup.{u1} M _inst_1)))))))) => (Submodule.{0, u1} Int M Int.semiring (AddCommGroup.toAddCommMonoid.{u1} M _inst_1) (AddCommGroup.intModule.{u1} M _inst_1)) -> (AddSubgroup.{u1} M (AddCommGroup.toAddGroup.{u1} M _inst_1))) (RelIso.hasCoeToFun.{u1, u1} (Submodule.{0, u1} Int M Int.semiring (AddCommGroup.toAddCommMonoid.{u1} M _inst_1) (AddCommGroup.intModule.{u1} M _inst_1)) (AddSubgroup.{u1} M (AddCommGroup.toAddGroup.{u1} M _inst_1)) (LE.le.{u1} (Submodule.{0, u1} Int M Int.semiring (AddCommGroup.toAddCommMonoid.{u1} M _inst_1) (AddCommGroup.intModule.{u1} M _inst_1)) (Preorder.toLE.{u1} (Submodule.{0, u1} Int M Int.semiring (AddCommGroup.toAddCommMonoid.{u1} M _inst_1) (AddCommGroup.intModule.{u1} M _inst_1)) (PartialOrder.toPreorder.{u1} (Submodule.{0, u1} Int M Int.semiring (AddCommGroup.toAddCommMonoid.{u1} M _inst_1) (AddCommGroup.intModule.{u1} M _inst_1)) (CompleteSemilatticeInf.toPartialOrder.{u1} (Submodule.{0, u1} Int M Int.semiring (AddCommGroup.toAddCommMonoid.{u1} M _inst_1) (AddCommGroup.intModule.{u1} M _inst_1)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (Submodule.{0, u1} Int M Int.semiring (AddCommGroup.toAddCommMonoid.{u1} M _inst_1) (AddCommGroup.intModule.{u1} M _inst_1)) (Submodule.completeLattice.{0, u1} Int M Int.semiring (AddCommGroup.toAddCommMonoid.{u1} M _inst_1) (AddCommGroup.intModule.{u1} M _inst_1))))))) (LE.le.{u1} (AddSubgroup.{u1} M (AddCommGroup.toAddGroup.{u1} M _inst_1)) (Preorder.toLE.{u1} (AddSubgroup.{u1} M (AddCommGroup.toAddGroup.{u1} M _inst_1)) (PartialOrder.toPreorder.{u1} (AddSubgroup.{u1} M (AddCommGroup.toAddGroup.{u1} M _inst_1)) (CompleteSemilatticeInf.toPartialOrder.{u1} (AddSubgroup.{u1} M (AddCommGroup.toAddGroup.{u1} M _inst_1)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (AddSubgroup.{u1} M (AddCommGroup.toAddGroup.{u1} M _inst_1)) (AddSubgroup.completeLattice.{u1} M (AddCommGroup.toAddGroup.{u1} M _inst_1)))))))) (OrderIso.symm.{u1, u1} (AddSubgroup.{u1} M (AddCommGroup.toAddGroup.{u1} M _inst_1)) (Submodule.{0, u1} Int M Int.semiring (AddCommGroup.toAddCommMonoid.{u1} M _inst_1) (AddCommGroup.intModule.{u1} M _inst_1)) (Preorder.toLE.{u1} (AddSubgroup.{u1} M (AddCommGroup.toAddGroup.{u1} M _inst_1)) (PartialOrder.toPreorder.{u1} (AddSubgroup.{u1} M (AddCommGroup.toAddGroup.{u1} M _inst_1)) (CompleteSemilatticeInf.toPartialOrder.{u1} (AddSubgroup.{u1} M (AddCommGroup.toAddGroup.{u1} M _inst_1)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (AddSubgroup.{u1} M (AddCommGroup.toAddGroup.{u1} M _inst_1)) (AddSubgroup.completeLattice.{u1} M (AddCommGroup.toAddGroup.{u1} M _inst_1)))))) (Preorder.toLE.{u1} (Submodule.{0, u1} Int M Int.semiring (AddCommGroup.toAddCommMonoid.{u1} M _inst_1) (AddCommGroup.intModule.{u1} M _inst_1)) (PartialOrder.toPreorder.{u1} (Submodule.{0, u1} Int M Int.semiring (AddCommGroup.toAddCommMonoid.{u1} M _inst_1) (AddCommGroup.intModule.{u1} M _inst_1)) (CompleteSemilatticeInf.toPartialOrder.{u1} (Submodule.{0, u1} Int M Int.semiring (AddCommGroup.toAddCommMonoid.{u1} M _inst_1) (AddCommGroup.intModule.{u1} M _inst_1)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (Submodule.{0, u1} Int M Int.semiring (AddCommGroup.toAddCommMonoid.{u1} M _inst_1) (AddCommGroup.intModule.{u1} M _inst_1)) (Submodule.completeLattice.{0, u1} Int M Int.semiring (AddCommGroup.toAddCommMonoid.{u1} M _inst_1) (AddCommGroup.intModule.{u1} M _inst_1)))))) (AddSubgroup.toIntSubmodule.{u1} M _inst_1))) (Submodule.toAddSubgroup.{0, u1} Int M Int.ring _inst_1 (AddCommGroup.intModule.{u1} M _inst_1))
+  forall {M : Type.{u1}} [_inst_1 : AddCommGroup.{u1} M], Eq.{succ u1} ((Submodule.{0, u1} Int M Int.semiring (AddCommGroup.toAddCommMonoid.{u1} M _inst_1) (AddCommGroup.intModule.{u1} M _inst_1)) -> (AddSubgroup.{u1} M (AddCommGroup.toAddGroup.{u1} M _inst_1))) (coeFn.{succ u1, succ u1} (OrderIso.{u1, u1} (Submodule.{0, u1} Int M Int.semiring (AddCommGroup.toAddCommMonoid.{u1} M _inst_1) (AddCommGroup.intModule.{u1} M _inst_1)) (AddSubgroup.{u1} M (AddCommGroup.toAddGroup.{u1} M _inst_1)) (Preorder.toHasLe.{u1} (Submodule.{0, u1} Int M Int.semiring (AddCommGroup.toAddCommMonoid.{u1} M _inst_1) (AddCommGroup.intModule.{u1} M _inst_1)) (PartialOrder.toPreorder.{u1} (Submodule.{0, u1} Int M Int.semiring (AddCommGroup.toAddCommMonoid.{u1} M _inst_1) (AddCommGroup.intModule.{u1} M _inst_1)) (CompleteSemilatticeInf.toPartialOrder.{u1} (Submodule.{0, u1} Int M Int.semiring (AddCommGroup.toAddCommMonoid.{u1} M _inst_1) (AddCommGroup.intModule.{u1} M _inst_1)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (Submodule.{0, u1} Int M Int.semiring (AddCommGroup.toAddCommMonoid.{u1} M _inst_1) (AddCommGroup.intModule.{u1} M _inst_1)) (Submodule.completeLattice.{0, u1} Int M Int.semiring (AddCommGroup.toAddCommMonoid.{u1} M _inst_1) (AddCommGroup.intModule.{u1} M _inst_1)))))) (Preorder.toHasLe.{u1} (AddSubgroup.{u1} M (AddCommGroup.toAddGroup.{u1} M _inst_1)) (PartialOrder.toPreorder.{u1} (AddSubgroup.{u1} M (AddCommGroup.toAddGroup.{u1} M _inst_1)) (CompleteSemilatticeInf.toPartialOrder.{u1} (AddSubgroup.{u1} M (AddCommGroup.toAddGroup.{u1} M _inst_1)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (AddSubgroup.{u1} M (AddCommGroup.toAddGroup.{u1} M _inst_1)) (AddSubgroup.completeLattice.{u1} M (AddCommGroup.toAddGroup.{u1} M _inst_1))))))) (fun (_x : RelIso.{u1, u1} (Submodule.{0, u1} Int M Int.semiring (AddCommGroup.toAddCommMonoid.{u1} M _inst_1) (AddCommGroup.intModule.{u1} M _inst_1)) (AddSubgroup.{u1} M (AddCommGroup.toAddGroup.{u1} M _inst_1)) (LE.le.{u1} (Submodule.{0, u1} Int M Int.semiring (AddCommGroup.toAddCommMonoid.{u1} M _inst_1) (AddCommGroup.intModule.{u1} M _inst_1)) (Preorder.toHasLe.{u1} (Submodule.{0, u1} Int M Int.semiring (AddCommGroup.toAddCommMonoid.{u1} M _inst_1) (AddCommGroup.intModule.{u1} M _inst_1)) (PartialOrder.toPreorder.{u1} (Submodule.{0, u1} Int M Int.semiring (AddCommGroup.toAddCommMonoid.{u1} M _inst_1) (AddCommGroup.intModule.{u1} M _inst_1)) (CompleteSemilatticeInf.toPartialOrder.{u1} (Submodule.{0, u1} Int M Int.semiring (AddCommGroup.toAddCommMonoid.{u1} M _inst_1) (AddCommGroup.intModule.{u1} M _inst_1)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (Submodule.{0, u1} Int M Int.semiring (AddCommGroup.toAddCommMonoid.{u1} M _inst_1) (AddCommGroup.intModule.{u1} M _inst_1)) (Submodule.completeLattice.{0, u1} Int M Int.semiring (AddCommGroup.toAddCommMonoid.{u1} M _inst_1) (AddCommGroup.intModule.{u1} M _inst_1))))))) (LE.le.{u1} (AddSubgroup.{u1} M (AddCommGroup.toAddGroup.{u1} M _inst_1)) (Preorder.toHasLe.{u1} (AddSubgroup.{u1} M (AddCommGroup.toAddGroup.{u1} M _inst_1)) (PartialOrder.toPreorder.{u1} (AddSubgroup.{u1} M (AddCommGroup.toAddGroup.{u1} M _inst_1)) (CompleteSemilatticeInf.toPartialOrder.{u1} (AddSubgroup.{u1} M (AddCommGroup.toAddGroup.{u1} M _inst_1)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (AddSubgroup.{u1} M (AddCommGroup.toAddGroup.{u1} M _inst_1)) (AddSubgroup.completeLattice.{u1} M (AddCommGroup.toAddGroup.{u1} M _inst_1)))))))) => (Submodule.{0, u1} Int M Int.semiring (AddCommGroup.toAddCommMonoid.{u1} M _inst_1) (AddCommGroup.intModule.{u1} M _inst_1)) -> (AddSubgroup.{u1} M (AddCommGroup.toAddGroup.{u1} M _inst_1))) (RelIso.hasCoeToFun.{u1, u1} (Submodule.{0, u1} Int M Int.semiring (AddCommGroup.toAddCommMonoid.{u1} M _inst_1) (AddCommGroup.intModule.{u1} M _inst_1)) (AddSubgroup.{u1} M (AddCommGroup.toAddGroup.{u1} M _inst_1)) (LE.le.{u1} (Submodule.{0, u1} Int M Int.semiring (AddCommGroup.toAddCommMonoid.{u1} M _inst_1) (AddCommGroup.intModule.{u1} M _inst_1)) (Preorder.toHasLe.{u1} (Submodule.{0, u1} Int M Int.semiring (AddCommGroup.toAddCommMonoid.{u1} M _inst_1) (AddCommGroup.intModule.{u1} M _inst_1)) (PartialOrder.toPreorder.{u1} (Submodule.{0, u1} Int M Int.semiring (AddCommGroup.toAddCommMonoid.{u1} M _inst_1) (AddCommGroup.intModule.{u1} M _inst_1)) (CompleteSemilatticeInf.toPartialOrder.{u1} (Submodule.{0, u1} Int M Int.semiring (AddCommGroup.toAddCommMonoid.{u1} M _inst_1) (AddCommGroup.intModule.{u1} M _inst_1)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (Submodule.{0, u1} Int M Int.semiring (AddCommGroup.toAddCommMonoid.{u1} M _inst_1) (AddCommGroup.intModule.{u1} M _inst_1)) (Submodule.completeLattice.{0, u1} Int M Int.semiring (AddCommGroup.toAddCommMonoid.{u1} M _inst_1) (AddCommGroup.intModule.{u1} M _inst_1))))))) (LE.le.{u1} (AddSubgroup.{u1} M (AddCommGroup.toAddGroup.{u1} M _inst_1)) (Preorder.toHasLe.{u1} (AddSubgroup.{u1} M (AddCommGroup.toAddGroup.{u1} M _inst_1)) (PartialOrder.toPreorder.{u1} (AddSubgroup.{u1} M (AddCommGroup.toAddGroup.{u1} M _inst_1)) (CompleteSemilatticeInf.toPartialOrder.{u1} (AddSubgroup.{u1} M (AddCommGroup.toAddGroup.{u1} M _inst_1)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (AddSubgroup.{u1} M (AddCommGroup.toAddGroup.{u1} M _inst_1)) (AddSubgroup.completeLattice.{u1} M (AddCommGroup.toAddGroup.{u1} M _inst_1)))))))) (OrderIso.symm.{u1, u1} (AddSubgroup.{u1} M (AddCommGroup.toAddGroup.{u1} M _inst_1)) (Submodule.{0, u1} Int M Int.semiring (AddCommGroup.toAddCommMonoid.{u1} M _inst_1) (AddCommGroup.intModule.{u1} M _inst_1)) (Preorder.toHasLe.{u1} (AddSubgroup.{u1} M (AddCommGroup.toAddGroup.{u1} M _inst_1)) (PartialOrder.toPreorder.{u1} (AddSubgroup.{u1} M (AddCommGroup.toAddGroup.{u1} M _inst_1)) (CompleteSemilatticeInf.toPartialOrder.{u1} (AddSubgroup.{u1} M (AddCommGroup.toAddGroup.{u1} M _inst_1)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (AddSubgroup.{u1} M (AddCommGroup.toAddGroup.{u1} M _inst_1)) (AddSubgroup.completeLattice.{u1} M (AddCommGroup.toAddGroup.{u1} M _inst_1)))))) (Preorder.toHasLe.{u1} (Submodule.{0, u1} Int M Int.semiring (AddCommGroup.toAddCommMonoid.{u1} M _inst_1) (AddCommGroup.intModule.{u1} M _inst_1)) (PartialOrder.toPreorder.{u1} (Submodule.{0, u1} Int M Int.semiring (AddCommGroup.toAddCommMonoid.{u1} M _inst_1) (AddCommGroup.intModule.{u1} M _inst_1)) (CompleteSemilatticeInf.toPartialOrder.{u1} (Submodule.{0, u1} Int M Int.semiring (AddCommGroup.toAddCommMonoid.{u1} M _inst_1) (AddCommGroup.intModule.{u1} M _inst_1)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (Submodule.{0, u1} Int M Int.semiring (AddCommGroup.toAddCommMonoid.{u1} M _inst_1) (AddCommGroup.intModule.{u1} M _inst_1)) (Submodule.completeLattice.{0, u1} Int M Int.semiring (AddCommGroup.toAddCommMonoid.{u1} M _inst_1) (AddCommGroup.intModule.{u1} M _inst_1)))))) (AddSubgroup.toIntSubmodule.{u1} M _inst_1))) (Submodule.toAddSubgroup.{0, u1} Int M Int.ring _inst_1 (AddCommGroup.intModule.{u1} M _inst_1))
 but is expected to have type
   forall {M : Type.{u1}} [_inst_1 : AddCommGroup.{u1} M], Eq.{succ u1} ((Submodule.{0, u1} Int M Int.instSemiringInt (AddCommGroup.toAddCommMonoid.{u1} M _inst_1) (AddCommGroup.intModule.{u1} M _inst_1)) -> (AddSubgroup.{u1} M (AddCommGroup.toAddGroup.{u1} M _inst_1))) (FunLike.coe.{succ u1, succ u1, succ u1} (RelIso.{u1, u1} (Submodule.{0, u1} Int M Int.instSemiringInt (AddCommGroup.toAddCommMonoid.{u1} M _inst_1) (AddCommGroup.intModule.{u1} M _inst_1)) (AddSubgroup.{u1} M (AddCommGroup.toAddGroup.{u1} M _inst_1)) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1281 : Submodule.{0, u1} Int M Int.instSemiringInt (AddCommGroup.toAddCommMonoid.{u1} M _inst_1) (AddCommGroup.intModule.{u1} M _inst_1)) (x._@.Mathlib.Order.Hom.Basic._hyg.1283 : Submodule.{0, u1} Int M Int.instSemiringInt (AddCommGroup.toAddCommMonoid.{u1} M _inst_1) (AddCommGroup.intModule.{u1} M _inst_1)) => LE.le.{u1} (Submodule.{0, u1} Int M Int.instSemiringInt (AddCommGroup.toAddCommMonoid.{u1} M _inst_1) (AddCommGroup.intModule.{u1} M _inst_1)) (Preorder.toLE.{u1} (Submodule.{0, u1} Int M Int.instSemiringInt (AddCommGroup.toAddCommMonoid.{u1} M _inst_1) (AddCommGroup.intModule.{u1} M _inst_1)) (PartialOrder.toPreorder.{u1} (Submodule.{0, u1} Int M Int.instSemiringInt (AddCommGroup.toAddCommMonoid.{u1} M _inst_1) (AddCommGroup.intModule.{u1} M _inst_1)) (CompleteSemilatticeInf.toPartialOrder.{u1} (Submodule.{0, u1} Int M Int.instSemiringInt (AddCommGroup.toAddCommMonoid.{u1} M _inst_1) (AddCommGroup.intModule.{u1} M _inst_1)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (Submodule.{0, u1} Int M Int.instSemiringInt (AddCommGroup.toAddCommMonoid.{u1} M _inst_1) (AddCommGroup.intModule.{u1} M _inst_1)) (Submodule.completeLattice.{0, u1} Int M Int.instSemiringInt (AddCommGroup.toAddCommMonoid.{u1} M _inst_1) (AddCommGroup.intModule.{u1} M _inst_1)))))) x._@.Mathlib.Order.Hom.Basic._hyg.1281 x._@.Mathlib.Order.Hom.Basic._hyg.1283) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1296 : AddSubgroup.{u1} M (AddCommGroup.toAddGroup.{u1} M _inst_1)) (x._@.Mathlib.Order.Hom.Basic._hyg.1298 : AddSubgroup.{u1} M (AddCommGroup.toAddGroup.{u1} M _inst_1)) => LE.le.{u1} (AddSubgroup.{u1} M (AddCommGroup.toAddGroup.{u1} M _inst_1)) (Preorder.toLE.{u1} (AddSubgroup.{u1} M (AddCommGroup.toAddGroup.{u1} M _inst_1)) (PartialOrder.toPreorder.{u1} (AddSubgroup.{u1} M (AddCommGroup.toAddGroup.{u1} M _inst_1)) (CompleteSemilatticeInf.toPartialOrder.{u1} (AddSubgroup.{u1} M (AddCommGroup.toAddGroup.{u1} M _inst_1)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (AddSubgroup.{u1} M (AddCommGroup.toAddGroup.{u1} M _inst_1)) (AddSubgroup.instCompleteLatticeAddSubgroup.{u1} M (AddCommGroup.toAddGroup.{u1} M _inst_1)))))) x._@.Mathlib.Order.Hom.Basic._hyg.1296 x._@.Mathlib.Order.Hom.Basic._hyg.1298)) (Submodule.{0, u1} Int M Int.instSemiringInt (AddCommGroup.toAddCommMonoid.{u1} M _inst_1) (AddCommGroup.intModule.{u1} M _inst_1)) (fun (_x : Submodule.{0, u1} Int M Int.instSemiringInt (AddCommGroup.toAddCommMonoid.{u1} M _inst_1) (AddCommGroup.intModule.{u1} M _inst_1)) => AddSubgroup.{u1} M (AddCommGroup.toAddGroup.{u1} M _inst_1)) (RelHomClass.toFunLike.{u1, u1, u1} (RelIso.{u1, u1} (Submodule.{0, u1} Int M Int.instSemiringInt (AddCommGroup.toAddCommMonoid.{u1} M _inst_1) (AddCommGroup.intModule.{u1} M _inst_1)) (AddSubgroup.{u1} M (AddCommGroup.toAddGroup.{u1} M _inst_1)) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1281 : Submodule.{0, u1} Int M Int.instSemiringInt (AddCommGroup.toAddCommMonoid.{u1} M _inst_1) (AddCommGroup.intModule.{u1} M _inst_1)) (x._@.Mathlib.Order.Hom.Basic._hyg.1283 : Submodule.{0, u1} Int M Int.instSemiringInt (AddCommGroup.toAddCommMonoid.{u1} M _inst_1) (AddCommGroup.intModule.{u1} M _inst_1)) => LE.le.{u1} (Submodule.{0, u1} Int M Int.instSemiringInt (AddCommGroup.toAddCommMonoid.{u1} M _inst_1) (AddCommGroup.intModule.{u1} M _inst_1)) (Preorder.toLE.{u1} (Submodule.{0, u1} Int M Int.instSemiringInt (AddCommGroup.toAddCommMonoid.{u1} M _inst_1) (AddCommGroup.intModule.{u1} M _inst_1)) (PartialOrder.toPreorder.{u1} (Submodule.{0, u1} Int M Int.instSemiringInt (AddCommGroup.toAddCommMonoid.{u1} M _inst_1) (AddCommGroup.intModule.{u1} M _inst_1)) (CompleteSemilatticeInf.toPartialOrder.{u1} (Submodule.{0, u1} Int M Int.instSemiringInt (AddCommGroup.toAddCommMonoid.{u1} M _inst_1) (AddCommGroup.intModule.{u1} M _inst_1)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (Submodule.{0, u1} Int M Int.instSemiringInt (AddCommGroup.toAddCommMonoid.{u1} M _inst_1) (AddCommGroup.intModule.{u1} M _inst_1)) (Submodule.completeLattice.{0, u1} Int M Int.instSemiringInt (AddCommGroup.toAddCommMonoid.{u1} M _inst_1) (AddCommGroup.intModule.{u1} M _inst_1)))))) x._@.Mathlib.Order.Hom.Basic._hyg.1281 x._@.Mathlib.Order.Hom.Basic._hyg.1283) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1296 : AddSubgroup.{u1} M (AddCommGroup.toAddGroup.{u1} M _inst_1)) (x._@.Mathlib.Order.Hom.Basic._hyg.1298 : AddSubgroup.{u1} M (AddCommGroup.toAddGroup.{u1} M _inst_1)) => LE.le.{u1} (AddSubgroup.{u1} M (AddCommGroup.toAddGroup.{u1} M _inst_1)) (Preorder.toLE.{u1} (AddSubgroup.{u1} M (AddCommGroup.toAddGroup.{u1} M _inst_1)) (PartialOrder.toPreorder.{u1} (AddSubgroup.{u1} M (AddCommGroup.toAddGroup.{u1} M _inst_1)) (CompleteSemilatticeInf.toPartialOrder.{u1} (AddSubgroup.{u1} M (AddCommGroup.toAddGroup.{u1} M _inst_1)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (AddSubgroup.{u1} M (AddCommGroup.toAddGroup.{u1} M _inst_1)) (AddSubgroup.instCompleteLatticeAddSubgroup.{u1} M (AddCommGroup.toAddGroup.{u1} M _inst_1)))))) x._@.Mathlib.Order.Hom.Basic._hyg.1296 x._@.Mathlib.Order.Hom.Basic._hyg.1298)) (Submodule.{0, u1} Int M Int.instSemiringInt (AddCommGroup.toAddCommMonoid.{u1} M _inst_1) (AddCommGroup.intModule.{u1} M _inst_1)) (AddSubgroup.{u1} M (AddCommGroup.toAddGroup.{u1} M _inst_1)) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1281 : Submodule.{0, u1} Int M Int.instSemiringInt (AddCommGroup.toAddCommMonoid.{u1} M _inst_1) (AddCommGroup.intModule.{u1} M _inst_1)) (x._@.Mathlib.Order.Hom.Basic._hyg.1283 : Submodule.{0, u1} Int M Int.instSemiringInt (AddCommGroup.toAddCommMonoid.{u1} M _inst_1) (AddCommGroup.intModule.{u1} M _inst_1)) => LE.le.{u1} (Submodule.{0, u1} Int M Int.instSemiringInt (AddCommGroup.toAddCommMonoid.{u1} M _inst_1) (AddCommGroup.intModule.{u1} M _inst_1)) (Preorder.toLE.{u1} (Submodule.{0, u1} Int M Int.instSemiringInt (AddCommGroup.toAddCommMonoid.{u1} M _inst_1) (AddCommGroup.intModule.{u1} M _inst_1)) (PartialOrder.toPreorder.{u1} (Submodule.{0, u1} Int M Int.instSemiringInt (AddCommGroup.toAddCommMonoid.{u1} M _inst_1) (AddCommGroup.intModule.{u1} M _inst_1)) (CompleteSemilatticeInf.toPartialOrder.{u1} (Submodule.{0, u1} Int M Int.instSemiringInt (AddCommGroup.toAddCommMonoid.{u1} M _inst_1) (AddCommGroup.intModule.{u1} M _inst_1)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (Submodule.{0, u1} Int M Int.instSemiringInt (AddCommGroup.toAddCommMonoid.{u1} M _inst_1) (AddCommGroup.intModule.{u1} M _inst_1)) (Submodule.completeLattice.{0, u1} Int M Int.instSemiringInt (AddCommGroup.toAddCommMonoid.{u1} M _inst_1) (AddCommGroup.intModule.{u1} M _inst_1)))))) x._@.Mathlib.Order.Hom.Basic._hyg.1281 x._@.Mathlib.Order.Hom.Basic._hyg.1283) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1296 : AddSubgroup.{u1} M (AddCommGroup.toAddGroup.{u1} M _inst_1)) (x._@.Mathlib.Order.Hom.Basic._hyg.1298 : AddSubgroup.{u1} M (AddCommGroup.toAddGroup.{u1} M _inst_1)) => LE.le.{u1} (AddSubgroup.{u1} M (AddCommGroup.toAddGroup.{u1} M _inst_1)) (Preorder.toLE.{u1} (AddSubgroup.{u1} M (AddCommGroup.toAddGroup.{u1} M _inst_1)) (PartialOrder.toPreorder.{u1} (AddSubgroup.{u1} M (AddCommGroup.toAddGroup.{u1} M _inst_1)) (CompleteSemilatticeInf.toPartialOrder.{u1} (AddSubgroup.{u1} M (AddCommGroup.toAddGroup.{u1} M _inst_1)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (AddSubgroup.{u1} M (AddCommGroup.toAddGroup.{u1} M _inst_1)) (AddSubgroup.instCompleteLatticeAddSubgroup.{u1} M (AddCommGroup.toAddGroup.{u1} M _inst_1)))))) x._@.Mathlib.Order.Hom.Basic._hyg.1296 x._@.Mathlib.Order.Hom.Basic._hyg.1298) (RelIso.instRelHomClassRelIso.{u1, u1} (Submodule.{0, u1} Int M Int.instSemiringInt (AddCommGroup.toAddCommMonoid.{u1} M _inst_1) (AddCommGroup.intModule.{u1} M _inst_1)) (AddSubgroup.{u1} M (AddCommGroup.toAddGroup.{u1} M _inst_1)) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1281 : Submodule.{0, u1} Int M Int.instSemiringInt (AddCommGroup.toAddCommMonoid.{u1} M _inst_1) (AddCommGroup.intModule.{u1} M _inst_1)) (x._@.Mathlib.Order.Hom.Basic._hyg.1283 : Submodule.{0, u1} Int M Int.instSemiringInt (AddCommGroup.toAddCommMonoid.{u1} M _inst_1) (AddCommGroup.intModule.{u1} M _inst_1)) => LE.le.{u1} (Submodule.{0, u1} Int M Int.instSemiringInt (AddCommGroup.toAddCommMonoid.{u1} M _inst_1) (AddCommGroup.intModule.{u1} M _inst_1)) (Preorder.toLE.{u1} (Submodule.{0, u1} Int M Int.instSemiringInt (AddCommGroup.toAddCommMonoid.{u1} M _inst_1) (AddCommGroup.intModule.{u1} M _inst_1)) (PartialOrder.toPreorder.{u1} (Submodule.{0, u1} Int M Int.instSemiringInt (AddCommGroup.toAddCommMonoid.{u1} M _inst_1) (AddCommGroup.intModule.{u1} M _inst_1)) (CompleteSemilatticeInf.toPartialOrder.{u1} (Submodule.{0, u1} Int M Int.instSemiringInt (AddCommGroup.toAddCommMonoid.{u1} M _inst_1) (AddCommGroup.intModule.{u1} M _inst_1)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (Submodule.{0, u1} Int M Int.instSemiringInt (AddCommGroup.toAddCommMonoid.{u1} M _inst_1) (AddCommGroup.intModule.{u1} M _inst_1)) (Submodule.completeLattice.{0, u1} Int M Int.instSemiringInt (AddCommGroup.toAddCommMonoid.{u1} M _inst_1) (AddCommGroup.intModule.{u1} M _inst_1)))))) x._@.Mathlib.Order.Hom.Basic._hyg.1281 x._@.Mathlib.Order.Hom.Basic._hyg.1283) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1296 : AddSubgroup.{u1} M (AddCommGroup.toAddGroup.{u1} M _inst_1)) (x._@.Mathlib.Order.Hom.Basic._hyg.1298 : AddSubgroup.{u1} M (AddCommGroup.toAddGroup.{u1} M _inst_1)) => LE.le.{u1} (AddSubgroup.{u1} M (AddCommGroup.toAddGroup.{u1} M _inst_1)) (Preorder.toLE.{u1} (AddSubgroup.{u1} M (AddCommGroup.toAddGroup.{u1} M _inst_1)) (PartialOrder.toPreorder.{u1} (AddSubgroup.{u1} M (AddCommGroup.toAddGroup.{u1} M _inst_1)) (CompleteSemilatticeInf.toPartialOrder.{u1} (AddSubgroup.{u1} M (AddCommGroup.toAddGroup.{u1} M _inst_1)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (AddSubgroup.{u1} M (AddCommGroup.toAddGroup.{u1} M _inst_1)) (AddSubgroup.instCompleteLatticeAddSubgroup.{u1} M (AddCommGroup.toAddGroup.{u1} M _inst_1)))))) x._@.Mathlib.Order.Hom.Basic._hyg.1296 x._@.Mathlib.Order.Hom.Basic._hyg.1298))) (OrderIso.symm.{u1, u1} (AddSubgroup.{u1} M (AddCommGroup.toAddGroup.{u1} M _inst_1)) (Submodule.{0, u1} Int M Int.instSemiringInt (AddCommGroup.toAddCommMonoid.{u1} M _inst_1) (AddCommGroup.intModule.{u1} M _inst_1)) (Preorder.toLE.{u1} (AddSubgroup.{u1} M (AddCommGroup.toAddGroup.{u1} M _inst_1)) (PartialOrder.toPreorder.{u1} (AddSubgroup.{u1} M (AddCommGroup.toAddGroup.{u1} M _inst_1)) (CompleteSemilatticeInf.toPartialOrder.{u1} (AddSubgroup.{u1} M (AddCommGroup.toAddGroup.{u1} M _inst_1)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (AddSubgroup.{u1} M (AddCommGroup.toAddGroup.{u1} M _inst_1)) (AddSubgroup.instCompleteLatticeAddSubgroup.{u1} M (AddCommGroup.toAddGroup.{u1} M _inst_1)))))) (Preorder.toLE.{u1} (Submodule.{0, u1} Int M Int.instSemiringInt (AddCommGroup.toAddCommMonoid.{u1} M _inst_1) (AddCommGroup.intModule.{u1} M _inst_1)) (PartialOrder.toPreorder.{u1} (Submodule.{0, u1} Int M Int.instSemiringInt (AddCommGroup.toAddCommMonoid.{u1} M _inst_1) (AddCommGroup.intModule.{u1} M _inst_1)) (CompleteSemilatticeInf.toPartialOrder.{u1} (Submodule.{0, u1} Int M Int.instSemiringInt (AddCommGroup.toAddCommMonoid.{u1} M _inst_1) (AddCommGroup.intModule.{u1} M _inst_1)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (Submodule.{0, u1} Int M Int.instSemiringInt (AddCommGroup.toAddCommMonoid.{u1} M _inst_1) (AddCommGroup.intModule.{u1} M _inst_1)) (Submodule.completeLattice.{0, u1} Int M Int.instSemiringInt (AddCommGroup.toAddCommMonoid.{u1} M _inst_1) (AddCommGroup.intModule.{u1} M _inst_1)))))) (AddSubgroup.toIntSubmodule.{u1} M _inst_1))) (Submodule.toAddSubgroup.{0, u1} Int M Int.instRingInt _inst_1 (AddCommGroup.intModule.{u1} M _inst_1))
 Case conversion may be inaccurate. Consider using '#align add_subgroup.to_int_submodule_symm AddSubgroup.toIntSubmodule_symmₓ'. -/
@@ -704,7 +704,7 @@ theorem AddSubgroup.toIntSubmodule_symm :
 
 /- warning: add_subgroup.coe_to_int_submodule -> AddSubgroup.coe_toIntSubmodule is a dubious translation:
 lean 3 declaration is
-  forall {M : Type.{u1}} [_inst_1 : AddCommGroup.{u1} M] (S : AddSubgroup.{u1} M (AddCommGroup.toAddGroup.{u1} M _inst_1)), Eq.{succ u1} (Set.{u1} M) ((fun (a : Type.{u1}) (b : Type.{u1}) [self : HasLiftT.{succ u1, succ u1} a b] => self.0) (Submodule.{0, u1} Int M Int.semiring (AddCommGroup.toAddCommMonoid.{u1} M _inst_1) (AddCommGroup.intModule.{u1} M _inst_1)) (Set.{u1} M) (HasLiftT.mk.{succ u1, succ u1} (Submodule.{0, u1} Int M Int.semiring (AddCommGroup.toAddCommMonoid.{u1} M _inst_1) (AddCommGroup.intModule.{u1} M _inst_1)) (Set.{u1} M) (CoeTCₓ.coe.{succ u1, succ u1} (Submodule.{0, u1} Int M Int.semiring (AddCommGroup.toAddCommMonoid.{u1} M _inst_1) (AddCommGroup.intModule.{u1} M _inst_1)) (Set.{u1} M) (SetLike.Set.hasCoeT.{u1, u1} (Submodule.{0, u1} Int M Int.semiring (AddCommGroup.toAddCommMonoid.{u1} M _inst_1) (AddCommGroup.intModule.{u1} M _inst_1)) M (Submodule.setLike.{0, u1} Int M Int.semiring (AddCommGroup.toAddCommMonoid.{u1} M _inst_1) (AddCommGroup.intModule.{u1} M _inst_1))))) (coeFn.{succ u1, succ u1} (OrderIso.{u1, u1} (AddSubgroup.{u1} M (AddCommGroup.toAddGroup.{u1} M _inst_1)) (Submodule.{0, u1} Int M Int.semiring (AddCommGroup.toAddCommMonoid.{u1} M _inst_1) (AddCommGroup.intModule.{u1} M _inst_1)) (Preorder.toLE.{u1} (AddSubgroup.{u1} M (AddCommGroup.toAddGroup.{u1} M _inst_1)) (PartialOrder.toPreorder.{u1} (AddSubgroup.{u1} M (AddCommGroup.toAddGroup.{u1} M _inst_1)) (CompleteSemilatticeInf.toPartialOrder.{u1} (AddSubgroup.{u1} M (AddCommGroup.toAddGroup.{u1} M _inst_1)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (AddSubgroup.{u1} M (AddCommGroup.toAddGroup.{u1} M _inst_1)) (AddSubgroup.completeLattice.{u1} M (AddCommGroup.toAddGroup.{u1} M _inst_1)))))) (Preorder.toLE.{u1} (Submodule.{0, u1} Int M Int.semiring (AddCommGroup.toAddCommMonoid.{u1} M _inst_1) (AddCommGroup.intModule.{u1} M _inst_1)) (PartialOrder.toPreorder.{u1} (Submodule.{0, u1} Int M Int.semiring (AddCommGroup.toAddCommMonoid.{u1} M _inst_1) (AddCommGroup.intModule.{u1} M _inst_1)) (CompleteSemilatticeInf.toPartialOrder.{u1} (Submodule.{0, u1} Int M Int.semiring (AddCommGroup.toAddCommMonoid.{u1} M _inst_1) (AddCommGroup.intModule.{u1} M _inst_1)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (Submodule.{0, u1} Int M Int.semiring (AddCommGroup.toAddCommMonoid.{u1} M _inst_1) (AddCommGroup.intModule.{u1} M _inst_1)) (Submodule.completeLattice.{0, u1} Int M Int.semiring (AddCommGroup.toAddCommMonoid.{u1} M _inst_1) (AddCommGroup.intModule.{u1} M _inst_1))))))) (fun (_x : RelIso.{u1, u1} (AddSubgroup.{u1} M (AddCommGroup.toAddGroup.{u1} M _inst_1)) (Submodule.{0, u1} Int M Int.semiring (AddCommGroup.toAddCommMonoid.{u1} M _inst_1) (AddCommGroup.intModule.{u1} M _inst_1)) (LE.le.{u1} (AddSubgroup.{u1} M (AddCommGroup.toAddGroup.{u1} M _inst_1)) (Preorder.toLE.{u1} (AddSubgroup.{u1} M (AddCommGroup.toAddGroup.{u1} M _inst_1)) (PartialOrder.toPreorder.{u1} (AddSubgroup.{u1} M (AddCommGroup.toAddGroup.{u1} M _inst_1)) (CompleteSemilatticeInf.toPartialOrder.{u1} (AddSubgroup.{u1} M (AddCommGroup.toAddGroup.{u1} M _inst_1)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (AddSubgroup.{u1} M (AddCommGroup.toAddGroup.{u1} M _inst_1)) (AddSubgroup.completeLattice.{u1} M (AddCommGroup.toAddGroup.{u1} M _inst_1))))))) (LE.le.{u1} (Submodule.{0, u1} Int M Int.semiring (AddCommGroup.toAddCommMonoid.{u1} M _inst_1) (AddCommGroup.intModule.{u1} M _inst_1)) (Preorder.toLE.{u1} (Submodule.{0, u1} Int M Int.semiring (AddCommGroup.toAddCommMonoid.{u1} M _inst_1) (AddCommGroup.intModule.{u1} M _inst_1)) (PartialOrder.toPreorder.{u1} (Submodule.{0, u1} Int M Int.semiring (AddCommGroup.toAddCommMonoid.{u1} M _inst_1) (AddCommGroup.intModule.{u1} M _inst_1)) (CompleteSemilatticeInf.toPartialOrder.{u1} (Submodule.{0, u1} Int M Int.semiring (AddCommGroup.toAddCommMonoid.{u1} M _inst_1) (AddCommGroup.intModule.{u1} M _inst_1)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (Submodule.{0, u1} Int M Int.semiring (AddCommGroup.toAddCommMonoid.{u1} M _inst_1) (AddCommGroup.intModule.{u1} M _inst_1)) (Submodule.completeLattice.{0, u1} Int M Int.semiring (AddCommGroup.toAddCommMonoid.{u1} M _inst_1) (AddCommGroup.intModule.{u1} M _inst_1)))))))) => (AddSubgroup.{u1} M (AddCommGroup.toAddGroup.{u1} M _inst_1)) -> (Submodule.{0, u1} Int M Int.semiring (AddCommGroup.toAddCommMonoid.{u1} M _inst_1) (AddCommGroup.intModule.{u1} M _inst_1))) (RelIso.hasCoeToFun.{u1, u1} (AddSubgroup.{u1} M (AddCommGroup.toAddGroup.{u1} M _inst_1)) (Submodule.{0, u1} Int M Int.semiring (AddCommGroup.toAddCommMonoid.{u1} M _inst_1) (AddCommGroup.intModule.{u1} M _inst_1)) (LE.le.{u1} (AddSubgroup.{u1} M (AddCommGroup.toAddGroup.{u1} M _inst_1)) (Preorder.toLE.{u1} (AddSubgroup.{u1} M (AddCommGroup.toAddGroup.{u1} M _inst_1)) (PartialOrder.toPreorder.{u1} (AddSubgroup.{u1} M (AddCommGroup.toAddGroup.{u1} M _inst_1)) (CompleteSemilatticeInf.toPartialOrder.{u1} (AddSubgroup.{u1} M (AddCommGroup.toAddGroup.{u1} M _inst_1)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (AddSubgroup.{u1} M (AddCommGroup.toAddGroup.{u1} M _inst_1)) (AddSubgroup.completeLattice.{u1} M (AddCommGroup.toAddGroup.{u1} M _inst_1))))))) (LE.le.{u1} (Submodule.{0, u1} Int M Int.semiring (AddCommGroup.toAddCommMonoid.{u1} M _inst_1) (AddCommGroup.intModule.{u1} M _inst_1)) (Preorder.toLE.{u1} (Submodule.{0, u1} Int M Int.semiring (AddCommGroup.toAddCommMonoid.{u1} M _inst_1) (AddCommGroup.intModule.{u1} M _inst_1)) (PartialOrder.toPreorder.{u1} (Submodule.{0, u1} Int M Int.semiring (AddCommGroup.toAddCommMonoid.{u1} M _inst_1) (AddCommGroup.intModule.{u1} M _inst_1)) (CompleteSemilatticeInf.toPartialOrder.{u1} (Submodule.{0, u1} Int M Int.semiring (AddCommGroup.toAddCommMonoid.{u1} M _inst_1) (AddCommGroup.intModule.{u1} M _inst_1)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (Submodule.{0, u1} Int M Int.semiring (AddCommGroup.toAddCommMonoid.{u1} M _inst_1) (AddCommGroup.intModule.{u1} M _inst_1)) (Submodule.completeLattice.{0, u1} Int M Int.semiring (AddCommGroup.toAddCommMonoid.{u1} M _inst_1) (AddCommGroup.intModule.{u1} M _inst_1)))))))) (AddSubgroup.toIntSubmodule.{u1} M _inst_1) S)) ((fun (a : Type.{u1}) (b : Type.{u1}) [self : HasLiftT.{succ u1, succ u1} a b] => self.0) (AddSubgroup.{u1} M (AddCommGroup.toAddGroup.{u1} M _inst_1)) (Set.{u1} M) (HasLiftT.mk.{succ u1, succ u1} (AddSubgroup.{u1} M (AddCommGroup.toAddGroup.{u1} M _inst_1)) (Set.{u1} M) (CoeTCₓ.coe.{succ u1, succ u1} (AddSubgroup.{u1} M (AddCommGroup.toAddGroup.{u1} M _inst_1)) (Set.{u1} M) (SetLike.Set.hasCoeT.{u1, u1} (AddSubgroup.{u1} M (AddCommGroup.toAddGroup.{u1} M _inst_1)) M (AddSubgroup.setLike.{u1} M (AddCommGroup.toAddGroup.{u1} M _inst_1))))) S)
+  forall {M : Type.{u1}} [_inst_1 : AddCommGroup.{u1} M] (S : AddSubgroup.{u1} M (AddCommGroup.toAddGroup.{u1} M _inst_1)), Eq.{succ u1} (Set.{u1} M) ((fun (a : Type.{u1}) (b : Type.{u1}) [self : HasLiftT.{succ u1, succ u1} a b] => self.0) (Submodule.{0, u1} Int M Int.semiring (AddCommGroup.toAddCommMonoid.{u1} M _inst_1) (AddCommGroup.intModule.{u1} M _inst_1)) (Set.{u1} M) (HasLiftT.mk.{succ u1, succ u1} (Submodule.{0, u1} Int M Int.semiring (AddCommGroup.toAddCommMonoid.{u1} M _inst_1) (AddCommGroup.intModule.{u1} M _inst_1)) (Set.{u1} M) (CoeTCₓ.coe.{succ u1, succ u1} (Submodule.{0, u1} Int M Int.semiring (AddCommGroup.toAddCommMonoid.{u1} M _inst_1) (AddCommGroup.intModule.{u1} M _inst_1)) (Set.{u1} M) (SetLike.Set.hasCoeT.{u1, u1} (Submodule.{0, u1} Int M Int.semiring (AddCommGroup.toAddCommMonoid.{u1} M _inst_1) (AddCommGroup.intModule.{u1} M _inst_1)) M (Submodule.setLike.{0, u1} Int M Int.semiring (AddCommGroup.toAddCommMonoid.{u1} M _inst_1) (AddCommGroup.intModule.{u1} M _inst_1))))) (coeFn.{succ u1, succ u1} (OrderIso.{u1, u1} (AddSubgroup.{u1} M (AddCommGroup.toAddGroup.{u1} M _inst_1)) (Submodule.{0, u1} Int M Int.semiring (AddCommGroup.toAddCommMonoid.{u1} M _inst_1) (AddCommGroup.intModule.{u1} M _inst_1)) (Preorder.toHasLe.{u1} (AddSubgroup.{u1} M (AddCommGroup.toAddGroup.{u1} M _inst_1)) (PartialOrder.toPreorder.{u1} (AddSubgroup.{u1} M (AddCommGroup.toAddGroup.{u1} M _inst_1)) (CompleteSemilatticeInf.toPartialOrder.{u1} (AddSubgroup.{u1} M (AddCommGroup.toAddGroup.{u1} M _inst_1)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (AddSubgroup.{u1} M (AddCommGroup.toAddGroup.{u1} M _inst_1)) (AddSubgroup.completeLattice.{u1} M (AddCommGroup.toAddGroup.{u1} M _inst_1)))))) (Preorder.toHasLe.{u1} (Submodule.{0, u1} Int M Int.semiring (AddCommGroup.toAddCommMonoid.{u1} M _inst_1) (AddCommGroup.intModule.{u1} M _inst_1)) (PartialOrder.toPreorder.{u1} (Submodule.{0, u1} Int M Int.semiring (AddCommGroup.toAddCommMonoid.{u1} M _inst_1) (AddCommGroup.intModule.{u1} M _inst_1)) (CompleteSemilatticeInf.toPartialOrder.{u1} (Submodule.{0, u1} Int M Int.semiring (AddCommGroup.toAddCommMonoid.{u1} M _inst_1) (AddCommGroup.intModule.{u1} M _inst_1)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (Submodule.{0, u1} Int M Int.semiring (AddCommGroup.toAddCommMonoid.{u1} M _inst_1) (AddCommGroup.intModule.{u1} M _inst_1)) (Submodule.completeLattice.{0, u1} Int M Int.semiring (AddCommGroup.toAddCommMonoid.{u1} M _inst_1) (AddCommGroup.intModule.{u1} M _inst_1))))))) (fun (_x : RelIso.{u1, u1} (AddSubgroup.{u1} M (AddCommGroup.toAddGroup.{u1} M _inst_1)) (Submodule.{0, u1} Int M Int.semiring (AddCommGroup.toAddCommMonoid.{u1} M _inst_1) (AddCommGroup.intModule.{u1} M _inst_1)) (LE.le.{u1} (AddSubgroup.{u1} M (AddCommGroup.toAddGroup.{u1} M _inst_1)) (Preorder.toHasLe.{u1} (AddSubgroup.{u1} M (AddCommGroup.toAddGroup.{u1} M _inst_1)) (PartialOrder.toPreorder.{u1} (AddSubgroup.{u1} M (AddCommGroup.toAddGroup.{u1} M _inst_1)) (CompleteSemilatticeInf.toPartialOrder.{u1} (AddSubgroup.{u1} M (AddCommGroup.toAddGroup.{u1} M _inst_1)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (AddSubgroup.{u1} M (AddCommGroup.toAddGroup.{u1} M _inst_1)) (AddSubgroup.completeLattice.{u1} M (AddCommGroup.toAddGroup.{u1} M _inst_1))))))) (LE.le.{u1} (Submodule.{0, u1} Int M Int.semiring (AddCommGroup.toAddCommMonoid.{u1} M _inst_1) (AddCommGroup.intModule.{u1} M _inst_1)) (Preorder.toHasLe.{u1} (Submodule.{0, u1} Int M Int.semiring (AddCommGroup.toAddCommMonoid.{u1} M _inst_1) (AddCommGroup.intModule.{u1} M _inst_1)) (PartialOrder.toPreorder.{u1} (Submodule.{0, u1} Int M Int.semiring (AddCommGroup.toAddCommMonoid.{u1} M _inst_1) (AddCommGroup.intModule.{u1} M _inst_1)) (CompleteSemilatticeInf.toPartialOrder.{u1} (Submodule.{0, u1} Int M Int.semiring (AddCommGroup.toAddCommMonoid.{u1} M _inst_1) (AddCommGroup.intModule.{u1} M _inst_1)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (Submodule.{0, u1} Int M Int.semiring (AddCommGroup.toAddCommMonoid.{u1} M _inst_1) (AddCommGroup.intModule.{u1} M _inst_1)) (Submodule.completeLattice.{0, u1} Int M Int.semiring (AddCommGroup.toAddCommMonoid.{u1} M _inst_1) (AddCommGroup.intModule.{u1} M _inst_1)))))))) => (AddSubgroup.{u1} M (AddCommGroup.toAddGroup.{u1} M _inst_1)) -> (Submodule.{0, u1} Int M Int.semiring (AddCommGroup.toAddCommMonoid.{u1} M _inst_1) (AddCommGroup.intModule.{u1} M _inst_1))) (RelIso.hasCoeToFun.{u1, u1} (AddSubgroup.{u1} M (AddCommGroup.toAddGroup.{u1} M _inst_1)) (Submodule.{0, u1} Int M Int.semiring (AddCommGroup.toAddCommMonoid.{u1} M _inst_1) (AddCommGroup.intModule.{u1} M _inst_1)) (LE.le.{u1} (AddSubgroup.{u1} M (AddCommGroup.toAddGroup.{u1} M _inst_1)) (Preorder.toHasLe.{u1} (AddSubgroup.{u1} M (AddCommGroup.toAddGroup.{u1} M _inst_1)) (PartialOrder.toPreorder.{u1} (AddSubgroup.{u1} M (AddCommGroup.toAddGroup.{u1} M _inst_1)) (CompleteSemilatticeInf.toPartialOrder.{u1} (AddSubgroup.{u1} M (AddCommGroup.toAddGroup.{u1} M _inst_1)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (AddSubgroup.{u1} M (AddCommGroup.toAddGroup.{u1} M _inst_1)) (AddSubgroup.completeLattice.{u1} M (AddCommGroup.toAddGroup.{u1} M _inst_1))))))) (LE.le.{u1} (Submodule.{0, u1} Int M Int.semiring (AddCommGroup.toAddCommMonoid.{u1} M _inst_1) (AddCommGroup.intModule.{u1} M _inst_1)) (Preorder.toHasLe.{u1} (Submodule.{0, u1} Int M Int.semiring (AddCommGroup.toAddCommMonoid.{u1} M _inst_1) (AddCommGroup.intModule.{u1} M _inst_1)) (PartialOrder.toPreorder.{u1} (Submodule.{0, u1} Int M Int.semiring (AddCommGroup.toAddCommMonoid.{u1} M _inst_1) (AddCommGroup.intModule.{u1} M _inst_1)) (CompleteSemilatticeInf.toPartialOrder.{u1} (Submodule.{0, u1} Int M Int.semiring (AddCommGroup.toAddCommMonoid.{u1} M _inst_1) (AddCommGroup.intModule.{u1} M _inst_1)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (Submodule.{0, u1} Int M Int.semiring (AddCommGroup.toAddCommMonoid.{u1} M _inst_1) (AddCommGroup.intModule.{u1} M _inst_1)) (Submodule.completeLattice.{0, u1} Int M Int.semiring (AddCommGroup.toAddCommMonoid.{u1} M _inst_1) (AddCommGroup.intModule.{u1} M _inst_1)))))))) (AddSubgroup.toIntSubmodule.{u1} M _inst_1) S)) ((fun (a : Type.{u1}) (b : Type.{u1}) [self : HasLiftT.{succ u1, succ u1} a b] => self.0) (AddSubgroup.{u1} M (AddCommGroup.toAddGroup.{u1} M _inst_1)) (Set.{u1} M) (HasLiftT.mk.{succ u1, succ u1} (AddSubgroup.{u1} M (AddCommGroup.toAddGroup.{u1} M _inst_1)) (Set.{u1} M) (CoeTCₓ.coe.{succ u1, succ u1} (AddSubgroup.{u1} M (AddCommGroup.toAddGroup.{u1} M _inst_1)) (Set.{u1} M) (SetLike.Set.hasCoeT.{u1, u1} (AddSubgroup.{u1} M (AddCommGroup.toAddGroup.{u1} M _inst_1)) M (AddSubgroup.setLike.{u1} M (AddCommGroup.toAddGroup.{u1} M _inst_1))))) S)
 but is expected to have type
   forall {M : Type.{u1}} [_inst_1 : AddCommGroup.{u1} M] (S : AddSubgroup.{u1} M (AddCommGroup.toAddGroup.{u1} M _inst_1)), Eq.{succ u1} (Set.{u1} M) (SetLike.coe.{u1, u1} (Submodule.{0, u1} Int M Int.instSemiringInt (AddCommGroup.toAddCommMonoid.{u1} M _inst_1) (AddCommGroup.intModule.{u1} M _inst_1)) M (Submodule.setLike.{0, u1} Int M Int.instSemiringInt (AddCommGroup.toAddCommMonoid.{u1} M _inst_1) (AddCommGroup.intModule.{u1} M _inst_1)) (FunLike.coe.{succ u1, succ u1, succ u1} (RelIso.{u1, u1} (AddSubgroup.{u1} M (AddCommGroup.toAddGroup.{u1} M _inst_1)) (Submodule.{0, u1} Int M Int.instSemiringInt (AddCommGroup.toAddCommMonoid.{u1} M _inst_1) (AddCommGroup.intModule.{u1} M _inst_1)) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1281 : AddSubgroup.{u1} M (AddCommGroup.toAddGroup.{u1} M _inst_1)) (x._@.Mathlib.Order.Hom.Basic._hyg.1283 : AddSubgroup.{u1} M (AddCommGroup.toAddGroup.{u1} M _inst_1)) => LE.le.{u1} (AddSubgroup.{u1} M (AddCommGroup.toAddGroup.{u1} M _inst_1)) (Preorder.toLE.{u1} (AddSubgroup.{u1} M (AddCommGroup.toAddGroup.{u1} M _inst_1)) (PartialOrder.toPreorder.{u1} (AddSubgroup.{u1} M (AddCommGroup.toAddGroup.{u1} M _inst_1)) (CompleteSemilatticeInf.toPartialOrder.{u1} (AddSubgroup.{u1} M (AddCommGroup.toAddGroup.{u1} M _inst_1)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (AddSubgroup.{u1} M (AddCommGroup.toAddGroup.{u1} M _inst_1)) (AddSubgroup.instCompleteLatticeAddSubgroup.{u1} M (AddCommGroup.toAddGroup.{u1} M _inst_1)))))) x._@.Mathlib.Order.Hom.Basic._hyg.1281 x._@.Mathlib.Order.Hom.Basic._hyg.1283) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1296 : Submodule.{0, u1} Int M Int.instSemiringInt (AddCommGroup.toAddCommMonoid.{u1} M _inst_1) (AddCommGroup.intModule.{u1} M _inst_1)) (x._@.Mathlib.Order.Hom.Basic._hyg.1298 : Submodule.{0, u1} Int M Int.instSemiringInt (AddCommGroup.toAddCommMonoid.{u1} M _inst_1) (AddCommGroup.intModule.{u1} M _inst_1)) => LE.le.{u1} (Submodule.{0, u1} Int M Int.instSemiringInt (AddCommGroup.toAddCommMonoid.{u1} M _inst_1) (AddCommGroup.intModule.{u1} M _inst_1)) (Preorder.toLE.{u1} (Submodule.{0, u1} Int M Int.instSemiringInt (AddCommGroup.toAddCommMonoid.{u1} M _inst_1) (AddCommGroup.intModule.{u1} M _inst_1)) (PartialOrder.toPreorder.{u1} (Submodule.{0, u1} Int M Int.instSemiringInt (AddCommGroup.toAddCommMonoid.{u1} M _inst_1) (AddCommGroup.intModule.{u1} M _inst_1)) (CompleteSemilatticeInf.toPartialOrder.{u1} (Submodule.{0, u1} Int M Int.instSemiringInt (AddCommGroup.toAddCommMonoid.{u1} M _inst_1) (AddCommGroup.intModule.{u1} M _inst_1)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (Submodule.{0, u1} Int M Int.instSemiringInt (AddCommGroup.toAddCommMonoid.{u1} M _inst_1) (AddCommGroup.intModule.{u1} M _inst_1)) (Submodule.completeLattice.{0, u1} Int M Int.instSemiringInt (AddCommGroup.toAddCommMonoid.{u1} M _inst_1) (AddCommGroup.intModule.{u1} M _inst_1)))))) x._@.Mathlib.Order.Hom.Basic._hyg.1296 x._@.Mathlib.Order.Hom.Basic._hyg.1298)) (AddSubgroup.{u1} M (AddCommGroup.toAddGroup.{u1} M _inst_1)) (fun (_x : AddSubgroup.{u1} M (AddCommGroup.toAddGroup.{u1} M _inst_1)) => Submodule.{0, u1} Int M Int.instSemiringInt (AddCommGroup.toAddCommMonoid.{u1} M _inst_1) (AddCommGroup.intModule.{u1} M _inst_1)) (RelHomClass.toFunLike.{u1, u1, u1} (RelIso.{u1, u1} (AddSubgroup.{u1} M (AddCommGroup.toAddGroup.{u1} M _inst_1)) (Submodule.{0, u1} Int M Int.instSemiringInt (AddCommGroup.toAddCommMonoid.{u1} M _inst_1) (AddCommGroup.intModule.{u1} M _inst_1)) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1281 : AddSubgroup.{u1} M (AddCommGroup.toAddGroup.{u1} M _inst_1)) (x._@.Mathlib.Order.Hom.Basic._hyg.1283 : AddSubgroup.{u1} M (AddCommGroup.toAddGroup.{u1} M _inst_1)) => LE.le.{u1} (AddSubgroup.{u1} M (AddCommGroup.toAddGroup.{u1} M _inst_1)) (Preorder.toLE.{u1} (AddSubgroup.{u1} M (AddCommGroup.toAddGroup.{u1} M _inst_1)) (PartialOrder.toPreorder.{u1} (AddSubgroup.{u1} M (AddCommGroup.toAddGroup.{u1} M _inst_1)) (CompleteSemilatticeInf.toPartialOrder.{u1} (AddSubgroup.{u1} M (AddCommGroup.toAddGroup.{u1} M _inst_1)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (AddSubgroup.{u1} M (AddCommGroup.toAddGroup.{u1} M _inst_1)) (AddSubgroup.instCompleteLatticeAddSubgroup.{u1} M (AddCommGroup.toAddGroup.{u1} M _inst_1)))))) x._@.Mathlib.Order.Hom.Basic._hyg.1281 x._@.Mathlib.Order.Hom.Basic._hyg.1283) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1296 : Submodule.{0, u1} Int M Int.instSemiringInt (AddCommGroup.toAddCommMonoid.{u1} M _inst_1) (AddCommGroup.intModule.{u1} M _inst_1)) (x._@.Mathlib.Order.Hom.Basic._hyg.1298 : Submodule.{0, u1} Int M Int.instSemiringInt (AddCommGroup.toAddCommMonoid.{u1} M _inst_1) (AddCommGroup.intModule.{u1} M _inst_1)) => LE.le.{u1} (Submodule.{0, u1} Int M Int.instSemiringInt (AddCommGroup.toAddCommMonoid.{u1} M _inst_1) (AddCommGroup.intModule.{u1} M _inst_1)) (Preorder.toLE.{u1} (Submodule.{0, u1} Int M Int.instSemiringInt (AddCommGroup.toAddCommMonoid.{u1} M _inst_1) (AddCommGroup.intModule.{u1} M _inst_1)) (PartialOrder.toPreorder.{u1} (Submodule.{0, u1} Int M Int.instSemiringInt (AddCommGroup.toAddCommMonoid.{u1} M _inst_1) (AddCommGroup.intModule.{u1} M _inst_1)) (CompleteSemilatticeInf.toPartialOrder.{u1} (Submodule.{0, u1} Int M Int.instSemiringInt (AddCommGroup.toAddCommMonoid.{u1} M _inst_1) (AddCommGroup.intModule.{u1} M _inst_1)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (Submodule.{0, u1} Int M Int.instSemiringInt (AddCommGroup.toAddCommMonoid.{u1} M _inst_1) (AddCommGroup.intModule.{u1} M _inst_1)) (Submodule.completeLattice.{0, u1} Int M Int.instSemiringInt (AddCommGroup.toAddCommMonoid.{u1} M _inst_1) (AddCommGroup.intModule.{u1} M _inst_1)))))) x._@.Mathlib.Order.Hom.Basic._hyg.1296 x._@.Mathlib.Order.Hom.Basic._hyg.1298)) (AddSubgroup.{u1} M (AddCommGroup.toAddGroup.{u1} M _inst_1)) (Submodule.{0, u1} Int M Int.instSemiringInt (AddCommGroup.toAddCommMonoid.{u1} M _inst_1) (AddCommGroup.intModule.{u1} M _inst_1)) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1281 : AddSubgroup.{u1} M (AddCommGroup.toAddGroup.{u1} M _inst_1)) (x._@.Mathlib.Order.Hom.Basic._hyg.1283 : AddSubgroup.{u1} M (AddCommGroup.toAddGroup.{u1} M _inst_1)) => LE.le.{u1} (AddSubgroup.{u1} M (AddCommGroup.toAddGroup.{u1} M _inst_1)) (Preorder.toLE.{u1} (AddSubgroup.{u1} M (AddCommGroup.toAddGroup.{u1} M _inst_1)) (PartialOrder.toPreorder.{u1} (AddSubgroup.{u1} M (AddCommGroup.toAddGroup.{u1} M _inst_1)) (CompleteSemilatticeInf.toPartialOrder.{u1} (AddSubgroup.{u1} M (AddCommGroup.toAddGroup.{u1} M _inst_1)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (AddSubgroup.{u1} M (AddCommGroup.toAddGroup.{u1} M _inst_1)) (AddSubgroup.instCompleteLatticeAddSubgroup.{u1} M (AddCommGroup.toAddGroup.{u1} M _inst_1)))))) x._@.Mathlib.Order.Hom.Basic._hyg.1281 x._@.Mathlib.Order.Hom.Basic._hyg.1283) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1296 : Submodule.{0, u1} Int M Int.instSemiringInt (AddCommGroup.toAddCommMonoid.{u1} M _inst_1) (AddCommGroup.intModule.{u1} M _inst_1)) (x._@.Mathlib.Order.Hom.Basic._hyg.1298 : Submodule.{0, u1} Int M Int.instSemiringInt (AddCommGroup.toAddCommMonoid.{u1} M _inst_1) (AddCommGroup.intModule.{u1} M _inst_1)) => LE.le.{u1} (Submodule.{0, u1} Int M Int.instSemiringInt (AddCommGroup.toAddCommMonoid.{u1} M _inst_1) (AddCommGroup.intModule.{u1} M _inst_1)) (Preorder.toLE.{u1} (Submodule.{0, u1} Int M Int.instSemiringInt (AddCommGroup.toAddCommMonoid.{u1} M _inst_1) (AddCommGroup.intModule.{u1} M _inst_1)) (PartialOrder.toPreorder.{u1} (Submodule.{0, u1} Int M Int.instSemiringInt (AddCommGroup.toAddCommMonoid.{u1} M _inst_1) (AddCommGroup.intModule.{u1} M _inst_1)) (CompleteSemilatticeInf.toPartialOrder.{u1} (Submodule.{0, u1} Int M Int.instSemiringInt (AddCommGroup.toAddCommMonoid.{u1} M _inst_1) (AddCommGroup.intModule.{u1} M _inst_1)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (Submodule.{0, u1} Int M Int.instSemiringInt (AddCommGroup.toAddCommMonoid.{u1} M _inst_1) (AddCommGroup.intModule.{u1} M _inst_1)) (Submodule.completeLattice.{0, u1} Int M Int.instSemiringInt (AddCommGroup.toAddCommMonoid.{u1} M _inst_1) (AddCommGroup.intModule.{u1} M _inst_1)))))) x._@.Mathlib.Order.Hom.Basic._hyg.1296 x._@.Mathlib.Order.Hom.Basic._hyg.1298) (RelIso.instRelHomClassRelIso.{u1, u1} (AddSubgroup.{u1} M (AddCommGroup.toAddGroup.{u1} M _inst_1)) (Submodule.{0, u1} Int M Int.instSemiringInt (AddCommGroup.toAddCommMonoid.{u1} M _inst_1) (AddCommGroup.intModule.{u1} M _inst_1)) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1281 : AddSubgroup.{u1} M (AddCommGroup.toAddGroup.{u1} M _inst_1)) (x._@.Mathlib.Order.Hom.Basic._hyg.1283 : AddSubgroup.{u1} M (AddCommGroup.toAddGroup.{u1} M _inst_1)) => LE.le.{u1} (AddSubgroup.{u1} M (AddCommGroup.toAddGroup.{u1} M _inst_1)) (Preorder.toLE.{u1} (AddSubgroup.{u1} M (AddCommGroup.toAddGroup.{u1} M _inst_1)) (PartialOrder.toPreorder.{u1} (AddSubgroup.{u1} M (AddCommGroup.toAddGroup.{u1} M _inst_1)) (CompleteSemilatticeInf.toPartialOrder.{u1} (AddSubgroup.{u1} M (AddCommGroup.toAddGroup.{u1} M _inst_1)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (AddSubgroup.{u1} M (AddCommGroup.toAddGroup.{u1} M _inst_1)) (AddSubgroup.instCompleteLatticeAddSubgroup.{u1} M (AddCommGroup.toAddGroup.{u1} M _inst_1)))))) x._@.Mathlib.Order.Hom.Basic._hyg.1281 x._@.Mathlib.Order.Hom.Basic._hyg.1283) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1296 : Submodule.{0, u1} Int M Int.instSemiringInt (AddCommGroup.toAddCommMonoid.{u1} M _inst_1) (AddCommGroup.intModule.{u1} M _inst_1)) (x._@.Mathlib.Order.Hom.Basic._hyg.1298 : Submodule.{0, u1} Int M Int.instSemiringInt (AddCommGroup.toAddCommMonoid.{u1} M _inst_1) (AddCommGroup.intModule.{u1} M _inst_1)) => LE.le.{u1} (Submodule.{0, u1} Int M Int.instSemiringInt (AddCommGroup.toAddCommMonoid.{u1} M _inst_1) (AddCommGroup.intModule.{u1} M _inst_1)) (Preorder.toLE.{u1} (Submodule.{0, u1} Int M Int.instSemiringInt (AddCommGroup.toAddCommMonoid.{u1} M _inst_1) (AddCommGroup.intModule.{u1} M _inst_1)) (PartialOrder.toPreorder.{u1} (Submodule.{0, u1} Int M Int.instSemiringInt (AddCommGroup.toAddCommMonoid.{u1} M _inst_1) (AddCommGroup.intModule.{u1} M _inst_1)) (CompleteSemilatticeInf.toPartialOrder.{u1} (Submodule.{0, u1} Int M Int.instSemiringInt (AddCommGroup.toAddCommMonoid.{u1} M _inst_1) (AddCommGroup.intModule.{u1} M _inst_1)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (Submodule.{0, u1} Int M Int.instSemiringInt (AddCommGroup.toAddCommMonoid.{u1} M _inst_1) (AddCommGroup.intModule.{u1} M _inst_1)) (Submodule.completeLattice.{0, u1} Int M Int.instSemiringInt (AddCommGroup.toAddCommMonoid.{u1} M _inst_1) (AddCommGroup.intModule.{u1} M _inst_1)))))) x._@.Mathlib.Order.Hom.Basic._hyg.1296 x._@.Mathlib.Order.Hom.Basic._hyg.1298))) (AddSubgroup.toIntSubmodule.{u1} M _inst_1) S)) (SetLike.coe.{u1, u1} (AddSubgroup.{u1} M (AddCommGroup.toAddGroup.{u1} M _inst_1)) M (AddSubgroup.instSetLikeAddSubgroup.{u1} M (AddCommGroup.toAddGroup.{u1} M _inst_1)) S)
 Case conversion may be inaccurate. Consider using '#align add_subgroup.coe_to_int_submodule AddSubgroup.coe_toIntSubmoduleₓ'. -/
@@ -715,7 +715,7 @@ theorem AddSubgroup.coe_toIntSubmodule (S : AddSubgroup M) : (S.toIntSubmodule :
 
 /- warning: add_subgroup.to_int_submodule_to_add_subgroup -> AddSubgroup.toIntSubmodule_toAddSubgroup is a dubious translation:
 lean 3 declaration is
-  forall {M : Type.{u1}} [_inst_1 : AddCommGroup.{u1} M] (S : AddSubgroup.{u1} M (AddCommGroup.toAddGroup.{u1} M _inst_1)), Eq.{succ u1} (AddSubgroup.{u1} M (AddCommGroup.toAddGroup.{u1} M _inst_1)) (Submodule.toAddSubgroup.{0, u1} Int M Int.ring _inst_1 (AddCommGroup.intModule.{u1} M _inst_1) (coeFn.{succ u1, succ u1} (OrderIso.{u1, u1} (AddSubgroup.{u1} M (AddCommGroup.toAddGroup.{u1} M _inst_1)) (Submodule.{0, u1} Int M Int.semiring (AddCommGroup.toAddCommMonoid.{u1} M _inst_1) (AddCommGroup.intModule.{u1} M _inst_1)) (Preorder.toLE.{u1} (AddSubgroup.{u1} M (AddCommGroup.toAddGroup.{u1} M _inst_1)) (PartialOrder.toPreorder.{u1} (AddSubgroup.{u1} M (AddCommGroup.toAddGroup.{u1} M _inst_1)) (CompleteSemilatticeInf.toPartialOrder.{u1} (AddSubgroup.{u1} M (AddCommGroup.toAddGroup.{u1} M _inst_1)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (AddSubgroup.{u1} M (AddCommGroup.toAddGroup.{u1} M _inst_1)) (AddSubgroup.completeLattice.{u1} M (AddCommGroup.toAddGroup.{u1} M _inst_1)))))) (Preorder.toLE.{u1} (Submodule.{0, u1} Int M Int.semiring (AddCommGroup.toAddCommMonoid.{u1} M _inst_1) (AddCommGroup.intModule.{u1} M _inst_1)) (PartialOrder.toPreorder.{u1} (Submodule.{0, u1} Int M Int.semiring (AddCommGroup.toAddCommMonoid.{u1} M _inst_1) (AddCommGroup.intModule.{u1} M _inst_1)) (CompleteSemilatticeInf.toPartialOrder.{u1} (Submodule.{0, u1} Int M Int.semiring (AddCommGroup.toAddCommMonoid.{u1} M _inst_1) (AddCommGroup.intModule.{u1} M _inst_1)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (Submodule.{0, u1} Int M Int.semiring (AddCommGroup.toAddCommMonoid.{u1} M _inst_1) (AddCommGroup.intModule.{u1} M _inst_1)) (Submodule.completeLattice.{0, u1} Int M Int.semiring (AddCommGroup.toAddCommMonoid.{u1} M _inst_1) (AddCommGroup.intModule.{u1} M _inst_1))))))) (fun (_x : RelIso.{u1, u1} (AddSubgroup.{u1} M (AddCommGroup.toAddGroup.{u1} M _inst_1)) (Submodule.{0, u1} Int M Int.semiring (AddCommGroup.toAddCommMonoid.{u1} M _inst_1) (AddCommGroup.intModule.{u1} M _inst_1)) (LE.le.{u1} (AddSubgroup.{u1} M (AddCommGroup.toAddGroup.{u1} M _inst_1)) (Preorder.toLE.{u1} (AddSubgroup.{u1} M (AddCommGroup.toAddGroup.{u1} M _inst_1)) (PartialOrder.toPreorder.{u1} (AddSubgroup.{u1} M (AddCommGroup.toAddGroup.{u1} M _inst_1)) (CompleteSemilatticeInf.toPartialOrder.{u1} (AddSubgroup.{u1} M (AddCommGroup.toAddGroup.{u1} M _inst_1)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (AddSubgroup.{u1} M (AddCommGroup.toAddGroup.{u1} M _inst_1)) (AddSubgroup.completeLattice.{u1} M (AddCommGroup.toAddGroup.{u1} M _inst_1))))))) (LE.le.{u1} (Submodule.{0, u1} Int M Int.semiring (AddCommGroup.toAddCommMonoid.{u1} M _inst_1) (AddCommGroup.intModule.{u1} M _inst_1)) (Preorder.toLE.{u1} (Submodule.{0, u1} Int M Int.semiring (AddCommGroup.toAddCommMonoid.{u1} M _inst_1) (AddCommGroup.intModule.{u1} M _inst_1)) (PartialOrder.toPreorder.{u1} (Submodule.{0, u1} Int M Int.semiring (AddCommGroup.toAddCommMonoid.{u1} M _inst_1) (AddCommGroup.intModule.{u1} M _inst_1)) (CompleteSemilatticeInf.toPartialOrder.{u1} (Submodule.{0, u1} Int M Int.semiring (AddCommGroup.toAddCommMonoid.{u1} M _inst_1) (AddCommGroup.intModule.{u1} M _inst_1)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (Submodule.{0, u1} Int M Int.semiring (AddCommGroup.toAddCommMonoid.{u1} M _inst_1) (AddCommGroup.intModule.{u1} M _inst_1)) (Submodule.completeLattice.{0, u1} Int M Int.semiring (AddCommGroup.toAddCommMonoid.{u1} M _inst_1) (AddCommGroup.intModule.{u1} M _inst_1)))))))) => (AddSubgroup.{u1} M (AddCommGroup.toAddGroup.{u1} M _inst_1)) -> (Submodule.{0, u1} Int M Int.semiring (AddCommGroup.toAddCommMonoid.{u1} M _inst_1) (AddCommGroup.intModule.{u1} M _inst_1))) (RelIso.hasCoeToFun.{u1, u1} (AddSubgroup.{u1} M (AddCommGroup.toAddGroup.{u1} M _inst_1)) (Submodule.{0, u1} Int M Int.semiring (AddCommGroup.toAddCommMonoid.{u1} M _inst_1) (AddCommGroup.intModule.{u1} M _inst_1)) (LE.le.{u1} (AddSubgroup.{u1} M (AddCommGroup.toAddGroup.{u1} M _inst_1)) (Preorder.toLE.{u1} (AddSubgroup.{u1} M (AddCommGroup.toAddGroup.{u1} M _inst_1)) (PartialOrder.toPreorder.{u1} (AddSubgroup.{u1} M (AddCommGroup.toAddGroup.{u1} M _inst_1)) (CompleteSemilatticeInf.toPartialOrder.{u1} (AddSubgroup.{u1} M (AddCommGroup.toAddGroup.{u1} M _inst_1)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (AddSubgroup.{u1} M (AddCommGroup.toAddGroup.{u1} M _inst_1)) (AddSubgroup.completeLattice.{u1} M (AddCommGroup.toAddGroup.{u1} M _inst_1))))))) (LE.le.{u1} (Submodule.{0, u1} Int M Int.semiring (AddCommGroup.toAddCommMonoid.{u1} M _inst_1) (AddCommGroup.intModule.{u1} M _inst_1)) (Preorder.toLE.{u1} (Submodule.{0, u1} Int M Int.semiring (AddCommGroup.toAddCommMonoid.{u1} M _inst_1) (AddCommGroup.intModule.{u1} M _inst_1)) (PartialOrder.toPreorder.{u1} (Submodule.{0, u1} Int M Int.semiring (AddCommGroup.toAddCommMonoid.{u1} M _inst_1) (AddCommGroup.intModule.{u1} M _inst_1)) (CompleteSemilatticeInf.toPartialOrder.{u1} (Submodule.{0, u1} Int M Int.semiring (AddCommGroup.toAddCommMonoid.{u1} M _inst_1) (AddCommGroup.intModule.{u1} M _inst_1)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (Submodule.{0, u1} Int M Int.semiring (AddCommGroup.toAddCommMonoid.{u1} M _inst_1) (AddCommGroup.intModule.{u1} M _inst_1)) (Submodule.completeLattice.{0, u1} Int M Int.semiring (AddCommGroup.toAddCommMonoid.{u1} M _inst_1) (AddCommGroup.intModule.{u1} M _inst_1)))))))) (AddSubgroup.toIntSubmodule.{u1} M _inst_1) S)) S
+  forall {M : Type.{u1}} [_inst_1 : AddCommGroup.{u1} M] (S : AddSubgroup.{u1} M (AddCommGroup.toAddGroup.{u1} M _inst_1)), Eq.{succ u1} (AddSubgroup.{u1} M (AddCommGroup.toAddGroup.{u1} M _inst_1)) (Submodule.toAddSubgroup.{0, u1} Int M Int.ring _inst_1 (AddCommGroup.intModule.{u1} M _inst_1) (coeFn.{succ u1, succ u1} (OrderIso.{u1, u1} (AddSubgroup.{u1} M (AddCommGroup.toAddGroup.{u1} M _inst_1)) (Submodule.{0, u1} Int M Int.semiring (AddCommGroup.toAddCommMonoid.{u1} M _inst_1) (AddCommGroup.intModule.{u1} M _inst_1)) (Preorder.toHasLe.{u1} (AddSubgroup.{u1} M (AddCommGroup.toAddGroup.{u1} M _inst_1)) (PartialOrder.toPreorder.{u1} (AddSubgroup.{u1} M (AddCommGroup.toAddGroup.{u1} M _inst_1)) (CompleteSemilatticeInf.toPartialOrder.{u1} (AddSubgroup.{u1} M (AddCommGroup.toAddGroup.{u1} M _inst_1)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (AddSubgroup.{u1} M (AddCommGroup.toAddGroup.{u1} M _inst_1)) (AddSubgroup.completeLattice.{u1} M (AddCommGroup.toAddGroup.{u1} M _inst_1)))))) (Preorder.toHasLe.{u1} (Submodule.{0, u1} Int M Int.semiring (AddCommGroup.toAddCommMonoid.{u1} M _inst_1) (AddCommGroup.intModule.{u1} M _inst_1)) (PartialOrder.toPreorder.{u1} (Submodule.{0, u1} Int M Int.semiring (AddCommGroup.toAddCommMonoid.{u1} M _inst_1) (AddCommGroup.intModule.{u1} M _inst_1)) (CompleteSemilatticeInf.toPartialOrder.{u1} (Submodule.{0, u1} Int M Int.semiring (AddCommGroup.toAddCommMonoid.{u1} M _inst_1) (AddCommGroup.intModule.{u1} M _inst_1)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (Submodule.{0, u1} Int M Int.semiring (AddCommGroup.toAddCommMonoid.{u1} M _inst_1) (AddCommGroup.intModule.{u1} M _inst_1)) (Submodule.completeLattice.{0, u1} Int M Int.semiring (AddCommGroup.toAddCommMonoid.{u1} M _inst_1) (AddCommGroup.intModule.{u1} M _inst_1))))))) (fun (_x : RelIso.{u1, u1} (AddSubgroup.{u1} M (AddCommGroup.toAddGroup.{u1} M _inst_1)) (Submodule.{0, u1} Int M Int.semiring (AddCommGroup.toAddCommMonoid.{u1} M _inst_1) (AddCommGroup.intModule.{u1} M _inst_1)) (LE.le.{u1} (AddSubgroup.{u1} M (AddCommGroup.toAddGroup.{u1} M _inst_1)) (Preorder.toHasLe.{u1} (AddSubgroup.{u1} M (AddCommGroup.toAddGroup.{u1} M _inst_1)) (PartialOrder.toPreorder.{u1} (AddSubgroup.{u1} M (AddCommGroup.toAddGroup.{u1} M _inst_1)) (CompleteSemilatticeInf.toPartialOrder.{u1} (AddSubgroup.{u1} M (AddCommGroup.toAddGroup.{u1} M _inst_1)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (AddSubgroup.{u1} M (AddCommGroup.toAddGroup.{u1} M _inst_1)) (AddSubgroup.completeLattice.{u1} M (AddCommGroup.toAddGroup.{u1} M _inst_1))))))) (LE.le.{u1} (Submodule.{0, u1} Int M Int.semiring (AddCommGroup.toAddCommMonoid.{u1} M _inst_1) (AddCommGroup.intModule.{u1} M _inst_1)) (Preorder.toHasLe.{u1} (Submodule.{0, u1} Int M Int.semiring (AddCommGroup.toAddCommMonoid.{u1} M _inst_1) (AddCommGroup.intModule.{u1} M _inst_1)) (PartialOrder.toPreorder.{u1} (Submodule.{0, u1} Int M Int.semiring (AddCommGroup.toAddCommMonoid.{u1} M _inst_1) (AddCommGroup.intModule.{u1} M _inst_1)) (CompleteSemilatticeInf.toPartialOrder.{u1} (Submodule.{0, u1} Int M Int.semiring (AddCommGroup.toAddCommMonoid.{u1} M _inst_1) (AddCommGroup.intModule.{u1} M _inst_1)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (Submodule.{0, u1} Int M Int.semiring (AddCommGroup.toAddCommMonoid.{u1} M _inst_1) (AddCommGroup.intModule.{u1} M _inst_1)) (Submodule.completeLattice.{0, u1} Int M Int.semiring (AddCommGroup.toAddCommMonoid.{u1} M _inst_1) (AddCommGroup.intModule.{u1} M _inst_1)))))))) => (AddSubgroup.{u1} M (AddCommGroup.toAddGroup.{u1} M _inst_1)) -> (Submodule.{0, u1} Int M Int.semiring (AddCommGroup.toAddCommMonoid.{u1} M _inst_1) (AddCommGroup.intModule.{u1} M _inst_1))) (RelIso.hasCoeToFun.{u1, u1} (AddSubgroup.{u1} M (AddCommGroup.toAddGroup.{u1} M _inst_1)) (Submodule.{0, u1} Int M Int.semiring (AddCommGroup.toAddCommMonoid.{u1} M _inst_1) (AddCommGroup.intModule.{u1} M _inst_1)) (LE.le.{u1} (AddSubgroup.{u1} M (AddCommGroup.toAddGroup.{u1} M _inst_1)) (Preorder.toHasLe.{u1} (AddSubgroup.{u1} M (AddCommGroup.toAddGroup.{u1} M _inst_1)) (PartialOrder.toPreorder.{u1} (AddSubgroup.{u1} M (AddCommGroup.toAddGroup.{u1} M _inst_1)) (CompleteSemilatticeInf.toPartialOrder.{u1} (AddSubgroup.{u1} M (AddCommGroup.toAddGroup.{u1} M _inst_1)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (AddSubgroup.{u1} M (AddCommGroup.toAddGroup.{u1} M _inst_1)) (AddSubgroup.completeLattice.{u1} M (AddCommGroup.toAddGroup.{u1} M _inst_1))))))) (LE.le.{u1} (Submodule.{0, u1} Int M Int.semiring (AddCommGroup.toAddCommMonoid.{u1} M _inst_1) (AddCommGroup.intModule.{u1} M _inst_1)) (Preorder.toHasLe.{u1} (Submodule.{0, u1} Int M Int.semiring (AddCommGroup.toAddCommMonoid.{u1} M _inst_1) (AddCommGroup.intModule.{u1} M _inst_1)) (PartialOrder.toPreorder.{u1} (Submodule.{0, u1} Int M Int.semiring (AddCommGroup.toAddCommMonoid.{u1} M _inst_1) (AddCommGroup.intModule.{u1} M _inst_1)) (CompleteSemilatticeInf.toPartialOrder.{u1} (Submodule.{0, u1} Int M Int.semiring (AddCommGroup.toAddCommMonoid.{u1} M _inst_1) (AddCommGroup.intModule.{u1} M _inst_1)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (Submodule.{0, u1} Int M Int.semiring (AddCommGroup.toAddCommMonoid.{u1} M _inst_1) (AddCommGroup.intModule.{u1} M _inst_1)) (Submodule.completeLattice.{0, u1} Int M Int.semiring (AddCommGroup.toAddCommMonoid.{u1} M _inst_1) (AddCommGroup.intModule.{u1} M _inst_1)))))))) (AddSubgroup.toIntSubmodule.{u1} M _inst_1) S)) S
 but is expected to have type
   forall {M : Type.{u1}} [_inst_1 : AddCommGroup.{u1} M] (S : AddSubgroup.{u1} M (AddCommGroup.toAddGroup.{u1} M _inst_1)), Eq.{succ u1} (AddSubgroup.{u1} M (AddCommGroup.toAddGroup.{u1} M _inst_1)) (Submodule.toAddSubgroup.{0, u1} Int M Int.instRingInt _inst_1 (AddCommGroup.intModule.{u1} M _inst_1) (FunLike.coe.{succ u1, succ u1, succ u1} (RelIso.{u1, u1} (AddSubgroup.{u1} M (AddCommGroup.toAddGroup.{u1} M _inst_1)) (Submodule.{0, u1} Int M Int.instSemiringInt (AddCommGroup.toAddCommMonoid.{u1} M _inst_1) (AddCommGroup.intModule.{u1} M _inst_1)) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1281 : AddSubgroup.{u1} M (AddCommGroup.toAddGroup.{u1} M _inst_1)) (x._@.Mathlib.Order.Hom.Basic._hyg.1283 : AddSubgroup.{u1} M (AddCommGroup.toAddGroup.{u1} M _inst_1)) => LE.le.{u1} (AddSubgroup.{u1} M (AddCommGroup.toAddGroup.{u1} M _inst_1)) (Preorder.toLE.{u1} (AddSubgroup.{u1} M (AddCommGroup.toAddGroup.{u1} M _inst_1)) (PartialOrder.toPreorder.{u1} (AddSubgroup.{u1} M (AddCommGroup.toAddGroup.{u1} M _inst_1)) (CompleteSemilatticeInf.toPartialOrder.{u1} (AddSubgroup.{u1} M (AddCommGroup.toAddGroup.{u1} M _inst_1)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (AddSubgroup.{u1} M (AddCommGroup.toAddGroup.{u1} M _inst_1)) (AddSubgroup.instCompleteLatticeAddSubgroup.{u1} M (AddCommGroup.toAddGroup.{u1} M _inst_1)))))) x._@.Mathlib.Order.Hom.Basic._hyg.1281 x._@.Mathlib.Order.Hom.Basic._hyg.1283) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1296 : Submodule.{0, u1} Int M Int.instSemiringInt (AddCommGroup.toAddCommMonoid.{u1} M _inst_1) (AddCommGroup.intModule.{u1} M _inst_1)) (x._@.Mathlib.Order.Hom.Basic._hyg.1298 : Submodule.{0, u1} Int M Int.instSemiringInt (AddCommGroup.toAddCommMonoid.{u1} M _inst_1) (AddCommGroup.intModule.{u1} M _inst_1)) => LE.le.{u1} (Submodule.{0, u1} Int M Int.instSemiringInt (AddCommGroup.toAddCommMonoid.{u1} M _inst_1) (AddCommGroup.intModule.{u1} M _inst_1)) (Preorder.toLE.{u1} (Submodule.{0, u1} Int M Int.instSemiringInt (AddCommGroup.toAddCommMonoid.{u1} M _inst_1) (AddCommGroup.intModule.{u1} M _inst_1)) (PartialOrder.toPreorder.{u1} (Submodule.{0, u1} Int M Int.instSemiringInt (AddCommGroup.toAddCommMonoid.{u1} M _inst_1) (AddCommGroup.intModule.{u1} M _inst_1)) (CompleteSemilatticeInf.toPartialOrder.{u1} (Submodule.{0, u1} Int M Int.instSemiringInt (AddCommGroup.toAddCommMonoid.{u1} M _inst_1) (AddCommGroup.intModule.{u1} M _inst_1)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (Submodule.{0, u1} Int M Int.instSemiringInt (AddCommGroup.toAddCommMonoid.{u1} M _inst_1) (AddCommGroup.intModule.{u1} M _inst_1)) (Submodule.completeLattice.{0, u1} Int M Int.instSemiringInt (AddCommGroup.toAddCommMonoid.{u1} M _inst_1) (AddCommGroup.intModule.{u1} M _inst_1)))))) x._@.Mathlib.Order.Hom.Basic._hyg.1296 x._@.Mathlib.Order.Hom.Basic._hyg.1298)) (AddSubgroup.{u1} M (AddCommGroup.toAddGroup.{u1} M _inst_1)) (fun (_x : AddSubgroup.{u1} M (AddCommGroup.toAddGroup.{u1} M _inst_1)) => Submodule.{0, u1} Int M Int.instSemiringInt (AddCommGroup.toAddCommMonoid.{u1} M _inst_1) (AddCommGroup.intModule.{u1} M _inst_1)) (RelHomClass.toFunLike.{u1, u1, u1} (RelIso.{u1, u1} (AddSubgroup.{u1} M (AddCommGroup.toAddGroup.{u1} M _inst_1)) (Submodule.{0, u1} Int M Int.instSemiringInt (AddCommGroup.toAddCommMonoid.{u1} M _inst_1) (AddCommGroup.intModule.{u1} M _inst_1)) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1281 : AddSubgroup.{u1} M (AddCommGroup.toAddGroup.{u1} M _inst_1)) (x._@.Mathlib.Order.Hom.Basic._hyg.1283 : AddSubgroup.{u1} M (AddCommGroup.toAddGroup.{u1} M _inst_1)) => LE.le.{u1} (AddSubgroup.{u1} M (AddCommGroup.toAddGroup.{u1} M _inst_1)) (Preorder.toLE.{u1} (AddSubgroup.{u1} M (AddCommGroup.toAddGroup.{u1} M _inst_1)) (PartialOrder.toPreorder.{u1} (AddSubgroup.{u1} M (AddCommGroup.toAddGroup.{u1} M _inst_1)) (CompleteSemilatticeInf.toPartialOrder.{u1} (AddSubgroup.{u1} M (AddCommGroup.toAddGroup.{u1} M _inst_1)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (AddSubgroup.{u1} M (AddCommGroup.toAddGroup.{u1} M _inst_1)) (AddSubgroup.instCompleteLatticeAddSubgroup.{u1} M (AddCommGroup.toAddGroup.{u1} M _inst_1)))))) x._@.Mathlib.Order.Hom.Basic._hyg.1281 x._@.Mathlib.Order.Hom.Basic._hyg.1283) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1296 : Submodule.{0, u1} Int M Int.instSemiringInt (AddCommGroup.toAddCommMonoid.{u1} M _inst_1) (AddCommGroup.intModule.{u1} M _inst_1)) (x._@.Mathlib.Order.Hom.Basic._hyg.1298 : Submodule.{0, u1} Int M Int.instSemiringInt (AddCommGroup.toAddCommMonoid.{u1} M _inst_1) (AddCommGroup.intModule.{u1} M _inst_1)) => LE.le.{u1} (Submodule.{0, u1} Int M Int.instSemiringInt (AddCommGroup.toAddCommMonoid.{u1} M _inst_1) (AddCommGroup.intModule.{u1} M _inst_1)) (Preorder.toLE.{u1} (Submodule.{0, u1} Int M Int.instSemiringInt (AddCommGroup.toAddCommMonoid.{u1} M _inst_1) (AddCommGroup.intModule.{u1} M _inst_1)) (PartialOrder.toPreorder.{u1} (Submodule.{0, u1} Int M Int.instSemiringInt (AddCommGroup.toAddCommMonoid.{u1} M _inst_1) (AddCommGroup.intModule.{u1} M _inst_1)) (CompleteSemilatticeInf.toPartialOrder.{u1} (Submodule.{0, u1} Int M Int.instSemiringInt (AddCommGroup.toAddCommMonoid.{u1} M _inst_1) (AddCommGroup.intModule.{u1} M _inst_1)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (Submodule.{0, u1} Int M Int.instSemiringInt (AddCommGroup.toAddCommMonoid.{u1} M _inst_1) (AddCommGroup.intModule.{u1} M _inst_1)) (Submodule.completeLattice.{0, u1} Int M Int.instSemiringInt (AddCommGroup.toAddCommMonoid.{u1} M _inst_1) (AddCommGroup.intModule.{u1} M _inst_1)))))) x._@.Mathlib.Order.Hom.Basic._hyg.1296 x._@.Mathlib.Order.Hom.Basic._hyg.1298)) (AddSubgroup.{u1} M (AddCommGroup.toAddGroup.{u1} M _inst_1)) (Submodule.{0, u1} Int M Int.instSemiringInt (AddCommGroup.toAddCommMonoid.{u1} M _inst_1) (AddCommGroup.intModule.{u1} M _inst_1)) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1281 : AddSubgroup.{u1} M (AddCommGroup.toAddGroup.{u1} M _inst_1)) (x._@.Mathlib.Order.Hom.Basic._hyg.1283 : AddSubgroup.{u1} M (AddCommGroup.toAddGroup.{u1} M _inst_1)) => LE.le.{u1} (AddSubgroup.{u1} M (AddCommGroup.toAddGroup.{u1} M _inst_1)) (Preorder.toLE.{u1} (AddSubgroup.{u1} M (AddCommGroup.toAddGroup.{u1} M _inst_1)) (PartialOrder.toPreorder.{u1} (AddSubgroup.{u1} M (AddCommGroup.toAddGroup.{u1} M _inst_1)) (CompleteSemilatticeInf.toPartialOrder.{u1} (AddSubgroup.{u1} M (AddCommGroup.toAddGroup.{u1} M _inst_1)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (AddSubgroup.{u1} M (AddCommGroup.toAddGroup.{u1} M _inst_1)) (AddSubgroup.instCompleteLatticeAddSubgroup.{u1} M (AddCommGroup.toAddGroup.{u1} M _inst_1)))))) x._@.Mathlib.Order.Hom.Basic._hyg.1281 x._@.Mathlib.Order.Hom.Basic._hyg.1283) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1296 : Submodule.{0, u1} Int M Int.instSemiringInt (AddCommGroup.toAddCommMonoid.{u1} M _inst_1) (AddCommGroup.intModule.{u1} M _inst_1)) (x._@.Mathlib.Order.Hom.Basic._hyg.1298 : Submodule.{0, u1} Int M Int.instSemiringInt (AddCommGroup.toAddCommMonoid.{u1} M _inst_1) (AddCommGroup.intModule.{u1} M _inst_1)) => LE.le.{u1} (Submodule.{0, u1} Int M Int.instSemiringInt (AddCommGroup.toAddCommMonoid.{u1} M _inst_1) (AddCommGroup.intModule.{u1} M _inst_1)) (Preorder.toLE.{u1} (Submodule.{0, u1} Int M Int.instSemiringInt (AddCommGroup.toAddCommMonoid.{u1} M _inst_1) (AddCommGroup.intModule.{u1} M _inst_1)) (PartialOrder.toPreorder.{u1} (Submodule.{0, u1} Int M Int.instSemiringInt (AddCommGroup.toAddCommMonoid.{u1} M _inst_1) (AddCommGroup.intModule.{u1} M _inst_1)) (CompleteSemilatticeInf.toPartialOrder.{u1} (Submodule.{0, u1} Int M Int.instSemiringInt (AddCommGroup.toAddCommMonoid.{u1} M _inst_1) (AddCommGroup.intModule.{u1} M _inst_1)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (Submodule.{0, u1} Int M Int.instSemiringInt (AddCommGroup.toAddCommMonoid.{u1} M _inst_1) (AddCommGroup.intModule.{u1} M _inst_1)) (Submodule.completeLattice.{0, u1} Int M Int.instSemiringInt (AddCommGroup.toAddCommMonoid.{u1} M _inst_1) (AddCommGroup.intModule.{u1} M _inst_1)))))) x._@.Mathlib.Order.Hom.Basic._hyg.1296 x._@.Mathlib.Order.Hom.Basic._hyg.1298) (RelIso.instRelHomClassRelIso.{u1, u1} (AddSubgroup.{u1} M (AddCommGroup.toAddGroup.{u1} M _inst_1)) (Submodule.{0, u1} Int M Int.instSemiringInt (AddCommGroup.toAddCommMonoid.{u1} M _inst_1) (AddCommGroup.intModule.{u1} M _inst_1)) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1281 : AddSubgroup.{u1} M (AddCommGroup.toAddGroup.{u1} M _inst_1)) (x._@.Mathlib.Order.Hom.Basic._hyg.1283 : AddSubgroup.{u1} M (AddCommGroup.toAddGroup.{u1} M _inst_1)) => LE.le.{u1} (AddSubgroup.{u1} M (AddCommGroup.toAddGroup.{u1} M _inst_1)) (Preorder.toLE.{u1} (AddSubgroup.{u1} M (AddCommGroup.toAddGroup.{u1} M _inst_1)) (PartialOrder.toPreorder.{u1} (AddSubgroup.{u1} M (AddCommGroup.toAddGroup.{u1} M _inst_1)) (CompleteSemilatticeInf.toPartialOrder.{u1} (AddSubgroup.{u1} M (AddCommGroup.toAddGroup.{u1} M _inst_1)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (AddSubgroup.{u1} M (AddCommGroup.toAddGroup.{u1} M _inst_1)) (AddSubgroup.instCompleteLatticeAddSubgroup.{u1} M (AddCommGroup.toAddGroup.{u1} M _inst_1)))))) x._@.Mathlib.Order.Hom.Basic._hyg.1281 x._@.Mathlib.Order.Hom.Basic._hyg.1283) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1296 : Submodule.{0, u1} Int M Int.instSemiringInt (AddCommGroup.toAddCommMonoid.{u1} M _inst_1) (AddCommGroup.intModule.{u1} M _inst_1)) (x._@.Mathlib.Order.Hom.Basic._hyg.1298 : Submodule.{0, u1} Int M Int.instSemiringInt (AddCommGroup.toAddCommMonoid.{u1} M _inst_1) (AddCommGroup.intModule.{u1} M _inst_1)) => LE.le.{u1} (Submodule.{0, u1} Int M Int.instSemiringInt (AddCommGroup.toAddCommMonoid.{u1} M _inst_1) (AddCommGroup.intModule.{u1} M _inst_1)) (Preorder.toLE.{u1} (Submodule.{0, u1} Int M Int.instSemiringInt (AddCommGroup.toAddCommMonoid.{u1} M _inst_1) (AddCommGroup.intModule.{u1} M _inst_1)) (PartialOrder.toPreorder.{u1} (Submodule.{0, u1} Int M Int.instSemiringInt (AddCommGroup.toAddCommMonoid.{u1} M _inst_1) (AddCommGroup.intModule.{u1} M _inst_1)) (CompleteSemilatticeInf.toPartialOrder.{u1} (Submodule.{0, u1} Int M Int.instSemiringInt (AddCommGroup.toAddCommMonoid.{u1} M _inst_1) (AddCommGroup.intModule.{u1} M _inst_1)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (Submodule.{0, u1} Int M Int.instSemiringInt (AddCommGroup.toAddCommMonoid.{u1} M _inst_1) (AddCommGroup.intModule.{u1} M _inst_1)) (Submodule.completeLattice.{0, u1} Int M Int.instSemiringInt (AddCommGroup.toAddCommMonoid.{u1} M _inst_1) (AddCommGroup.intModule.{u1} M _inst_1)))))) x._@.Mathlib.Order.Hom.Basic._hyg.1296 x._@.Mathlib.Order.Hom.Basic._hyg.1298))) (AddSubgroup.toIntSubmodule.{u1} M _inst_1) S)) S
 Case conversion may be inaccurate. Consider using '#align add_subgroup.to_int_submodule_to_add_subgroup AddSubgroup.toIntSubmodule_toAddSubgroupₓ'. -/
@@ -727,7 +727,7 @@ theorem AddSubgroup.toIntSubmodule_toAddSubgroup (S : AddSubgroup M) :
 
 /- warning: submodule.to_add_subgroup_to_int_submodule -> Submodule.toAddSubgroup_toIntSubmodule is a dubious translation:
 lean 3 declaration is
-  forall {M : Type.{u1}} [_inst_1 : AddCommGroup.{u1} M] (S : Submodule.{0, u1} Int M Int.semiring (AddCommGroup.toAddCommMonoid.{u1} M _inst_1) (AddCommGroup.intModule.{u1} M _inst_1)), Eq.{succ u1} (Submodule.{0, u1} Int M Int.semiring (AddCommGroup.toAddCommMonoid.{u1} M _inst_1) (AddCommGroup.intModule.{u1} M _inst_1)) (coeFn.{succ u1, succ u1} (OrderIso.{u1, u1} (AddSubgroup.{u1} M (AddCommGroup.toAddGroup.{u1} M _inst_1)) (Submodule.{0, u1} Int M Int.semiring (AddCommGroup.toAddCommMonoid.{u1} M _inst_1) (AddCommGroup.intModule.{u1} M _inst_1)) (Preorder.toLE.{u1} (AddSubgroup.{u1} M (AddCommGroup.toAddGroup.{u1} M _inst_1)) (PartialOrder.toPreorder.{u1} (AddSubgroup.{u1} M (AddCommGroup.toAddGroup.{u1} M _inst_1)) (CompleteSemilatticeInf.toPartialOrder.{u1} (AddSubgroup.{u1} M (AddCommGroup.toAddGroup.{u1} M _inst_1)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (AddSubgroup.{u1} M (AddCommGroup.toAddGroup.{u1} M _inst_1)) (AddSubgroup.completeLattice.{u1} M (AddCommGroup.toAddGroup.{u1} M _inst_1)))))) (Preorder.toLE.{u1} (Submodule.{0, u1} Int M Int.semiring (AddCommGroup.toAddCommMonoid.{u1} M _inst_1) (AddCommGroup.intModule.{u1} M _inst_1)) (PartialOrder.toPreorder.{u1} (Submodule.{0, u1} Int M Int.semiring (AddCommGroup.toAddCommMonoid.{u1} M _inst_1) (AddCommGroup.intModule.{u1} M _inst_1)) (CompleteSemilatticeInf.toPartialOrder.{u1} (Submodule.{0, u1} Int M Int.semiring (AddCommGroup.toAddCommMonoid.{u1} M _inst_1) (AddCommGroup.intModule.{u1} M _inst_1)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (Submodule.{0, u1} Int M Int.semiring (AddCommGroup.toAddCommMonoid.{u1} M _inst_1) (AddCommGroup.intModule.{u1} M _inst_1)) (Submodule.completeLattice.{0, u1} Int M Int.semiring (AddCommGroup.toAddCommMonoid.{u1} M _inst_1) (AddCommGroup.intModule.{u1} M _inst_1))))))) (fun (_x : RelIso.{u1, u1} (AddSubgroup.{u1} M (AddCommGroup.toAddGroup.{u1} M _inst_1)) (Submodule.{0, u1} Int M Int.semiring (AddCommGroup.toAddCommMonoid.{u1} M _inst_1) (AddCommGroup.intModule.{u1} M _inst_1)) (LE.le.{u1} (AddSubgroup.{u1} M (AddCommGroup.toAddGroup.{u1} M _inst_1)) (Preorder.toLE.{u1} (AddSubgroup.{u1} M (AddCommGroup.toAddGroup.{u1} M _inst_1)) (PartialOrder.toPreorder.{u1} (AddSubgroup.{u1} M (AddCommGroup.toAddGroup.{u1} M _inst_1)) (CompleteSemilatticeInf.toPartialOrder.{u1} (AddSubgroup.{u1} M (AddCommGroup.toAddGroup.{u1} M _inst_1)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (AddSubgroup.{u1} M (AddCommGroup.toAddGroup.{u1} M _inst_1)) (AddSubgroup.completeLattice.{u1} M (AddCommGroup.toAddGroup.{u1} M _inst_1))))))) (LE.le.{u1} (Submodule.{0, u1} Int M Int.semiring (AddCommGroup.toAddCommMonoid.{u1} M _inst_1) (AddCommGroup.intModule.{u1} M _inst_1)) (Preorder.toLE.{u1} (Submodule.{0, u1} Int M Int.semiring (AddCommGroup.toAddCommMonoid.{u1} M _inst_1) (AddCommGroup.intModule.{u1} M _inst_1)) (PartialOrder.toPreorder.{u1} (Submodule.{0, u1} Int M Int.semiring (AddCommGroup.toAddCommMonoid.{u1} M _inst_1) (AddCommGroup.intModule.{u1} M _inst_1)) (CompleteSemilatticeInf.toPartialOrder.{u1} (Submodule.{0, u1} Int M Int.semiring (AddCommGroup.toAddCommMonoid.{u1} M _inst_1) (AddCommGroup.intModule.{u1} M _inst_1)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (Submodule.{0, u1} Int M Int.semiring (AddCommGroup.toAddCommMonoid.{u1} M _inst_1) (AddCommGroup.intModule.{u1} M _inst_1)) (Submodule.completeLattice.{0, u1} Int M Int.semiring (AddCommGroup.toAddCommMonoid.{u1} M _inst_1) (AddCommGroup.intModule.{u1} M _inst_1)))))))) => (AddSubgroup.{u1} M (AddCommGroup.toAddGroup.{u1} M _inst_1)) -> (Submodule.{0, u1} Int M Int.semiring (AddCommGroup.toAddCommMonoid.{u1} M _inst_1) (AddCommGroup.intModule.{u1} M _inst_1))) (RelIso.hasCoeToFun.{u1, u1} (AddSubgroup.{u1} M (AddCommGroup.toAddGroup.{u1} M _inst_1)) (Submodule.{0, u1} Int M Int.semiring (AddCommGroup.toAddCommMonoid.{u1} M _inst_1) (AddCommGroup.intModule.{u1} M _inst_1)) (LE.le.{u1} (AddSubgroup.{u1} M (AddCommGroup.toAddGroup.{u1} M _inst_1)) (Preorder.toLE.{u1} (AddSubgroup.{u1} M (AddCommGroup.toAddGroup.{u1} M _inst_1)) (PartialOrder.toPreorder.{u1} (AddSubgroup.{u1} M (AddCommGroup.toAddGroup.{u1} M _inst_1)) (CompleteSemilatticeInf.toPartialOrder.{u1} (AddSubgroup.{u1} M (AddCommGroup.toAddGroup.{u1} M _inst_1)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (AddSubgroup.{u1} M (AddCommGroup.toAddGroup.{u1} M _inst_1)) (AddSubgroup.completeLattice.{u1} M (AddCommGroup.toAddGroup.{u1} M _inst_1))))))) (LE.le.{u1} (Submodule.{0, u1} Int M Int.semiring (AddCommGroup.toAddCommMonoid.{u1} M _inst_1) (AddCommGroup.intModule.{u1} M _inst_1)) (Preorder.toLE.{u1} (Submodule.{0, u1} Int M Int.semiring (AddCommGroup.toAddCommMonoid.{u1} M _inst_1) (AddCommGroup.intModule.{u1} M _inst_1)) (PartialOrder.toPreorder.{u1} (Submodule.{0, u1} Int M Int.semiring (AddCommGroup.toAddCommMonoid.{u1} M _inst_1) (AddCommGroup.intModule.{u1} M _inst_1)) (CompleteSemilatticeInf.toPartialOrder.{u1} (Submodule.{0, u1} Int M Int.semiring (AddCommGroup.toAddCommMonoid.{u1} M _inst_1) (AddCommGroup.intModule.{u1} M _inst_1)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (Submodule.{0, u1} Int M Int.semiring (AddCommGroup.toAddCommMonoid.{u1} M _inst_1) (AddCommGroup.intModule.{u1} M _inst_1)) (Submodule.completeLattice.{0, u1} Int M Int.semiring (AddCommGroup.toAddCommMonoid.{u1} M _inst_1) (AddCommGroup.intModule.{u1} M _inst_1)))))))) (AddSubgroup.toIntSubmodule.{u1} M _inst_1) (Submodule.toAddSubgroup.{0, u1} Int M Int.ring _inst_1 (AddCommGroup.intModule.{u1} M _inst_1) S)) S
+  forall {M : Type.{u1}} [_inst_1 : AddCommGroup.{u1} M] (S : Submodule.{0, u1} Int M Int.semiring (AddCommGroup.toAddCommMonoid.{u1} M _inst_1) (AddCommGroup.intModule.{u1} M _inst_1)), Eq.{succ u1} (Submodule.{0, u1} Int M Int.semiring (AddCommGroup.toAddCommMonoid.{u1} M _inst_1) (AddCommGroup.intModule.{u1} M _inst_1)) (coeFn.{succ u1, succ u1} (OrderIso.{u1, u1} (AddSubgroup.{u1} M (AddCommGroup.toAddGroup.{u1} M _inst_1)) (Submodule.{0, u1} Int M Int.semiring (AddCommGroup.toAddCommMonoid.{u1} M _inst_1) (AddCommGroup.intModule.{u1} M _inst_1)) (Preorder.toHasLe.{u1} (AddSubgroup.{u1} M (AddCommGroup.toAddGroup.{u1} M _inst_1)) (PartialOrder.toPreorder.{u1} (AddSubgroup.{u1} M (AddCommGroup.toAddGroup.{u1} M _inst_1)) (CompleteSemilatticeInf.toPartialOrder.{u1} (AddSubgroup.{u1} M (AddCommGroup.toAddGroup.{u1} M _inst_1)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (AddSubgroup.{u1} M (AddCommGroup.toAddGroup.{u1} M _inst_1)) (AddSubgroup.completeLattice.{u1} M (AddCommGroup.toAddGroup.{u1} M _inst_1)))))) (Preorder.toHasLe.{u1} (Submodule.{0, u1} Int M Int.semiring (AddCommGroup.toAddCommMonoid.{u1} M _inst_1) (AddCommGroup.intModule.{u1} M _inst_1)) (PartialOrder.toPreorder.{u1} (Submodule.{0, u1} Int M Int.semiring (AddCommGroup.toAddCommMonoid.{u1} M _inst_1) (AddCommGroup.intModule.{u1} M _inst_1)) (CompleteSemilatticeInf.toPartialOrder.{u1} (Submodule.{0, u1} Int M Int.semiring (AddCommGroup.toAddCommMonoid.{u1} M _inst_1) (AddCommGroup.intModule.{u1} M _inst_1)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (Submodule.{0, u1} Int M Int.semiring (AddCommGroup.toAddCommMonoid.{u1} M _inst_1) (AddCommGroup.intModule.{u1} M _inst_1)) (Submodule.completeLattice.{0, u1} Int M Int.semiring (AddCommGroup.toAddCommMonoid.{u1} M _inst_1) (AddCommGroup.intModule.{u1} M _inst_1))))))) (fun (_x : RelIso.{u1, u1} (AddSubgroup.{u1} M (AddCommGroup.toAddGroup.{u1} M _inst_1)) (Submodule.{0, u1} Int M Int.semiring (AddCommGroup.toAddCommMonoid.{u1} M _inst_1) (AddCommGroup.intModule.{u1} M _inst_1)) (LE.le.{u1} (AddSubgroup.{u1} M (AddCommGroup.toAddGroup.{u1} M _inst_1)) (Preorder.toHasLe.{u1} (AddSubgroup.{u1} M (AddCommGroup.toAddGroup.{u1} M _inst_1)) (PartialOrder.toPreorder.{u1} (AddSubgroup.{u1} M (AddCommGroup.toAddGroup.{u1} M _inst_1)) (CompleteSemilatticeInf.toPartialOrder.{u1} (AddSubgroup.{u1} M (AddCommGroup.toAddGroup.{u1} M _inst_1)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (AddSubgroup.{u1} M (AddCommGroup.toAddGroup.{u1} M _inst_1)) (AddSubgroup.completeLattice.{u1} M (AddCommGroup.toAddGroup.{u1} M _inst_1))))))) (LE.le.{u1} (Submodule.{0, u1} Int M Int.semiring (AddCommGroup.toAddCommMonoid.{u1} M _inst_1) (AddCommGroup.intModule.{u1} M _inst_1)) (Preorder.toHasLe.{u1} (Submodule.{0, u1} Int M Int.semiring (AddCommGroup.toAddCommMonoid.{u1} M _inst_1) (AddCommGroup.intModule.{u1} M _inst_1)) (PartialOrder.toPreorder.{u1} (Submodule.{0, u1} Int M Int.semiring (AddCommGroup.toAddCommMonoid.{u1} M _inst_1) (AddCommGroup.intModule.{u1} M _inst_1)) (CompleteSemilatticeInf.toPartialOrder.{u1} (Submodule.{0, u1} Int M Int.semiring (AddCommGroup.toAddCommMonoid.{u1} M _inst_1) (AddCommGroup.intModule.{u1} M _inst_1)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (Submodule.{0, u1} Int M Int.semiring (AddCommGroup.toAddCommMonoid.{u1} M _inst_1) (AddCommGroup.intModule.{u1} M _inst_1)) (Submodule.completeLattice.{0, u1} Int M Int.semiring (AddCommGroup.toAddCommMonoid.{u1} M _inst_1) (AddCommGroup.intModule.{u1} M _inst_1)))))))) => (AddSubgroup.{u1} M (AddCommGroup.toAddGroup.{u1} M _inst_1)) -> (Submodule.{0, u1} Int M Int.semiring (AddCommGroup.toAddCommMonoid.{u1} M _inst_1) (AddCommGroup.intModule.{u1} M _inst_1))) (RelIso.hasCoeToFun.{u1, u1} (AddSubgroup.{u1} M (AddCommGroup.toAddGroup.{u1} M _inst_1)) (Submodule.{0, u1} Int M Int.semiring (AddCommGroup.toAddCommMonoid.{u1} M _inst_1) (AddCommGroup.intModule.{u1} M _inst_1)) (LE.le.{u1} (AddSubgroup.{u1} M (AddCommGroup.toAddGroup.{u1} M _inst_1)) (Preorder.toHasLe.{u1} (AddSubgroup.{u1} M (AddCommGroup.toAddGroup.{u1} M _inst_1)) (PartialOrder.toPreorder.{u1} (AddSubgroup.{u1} M (AddCommGroup.toAddGroup.{u1} M _inst_1)) (CompleteSemilatticeInf.toPartialOrder.{u1} (AddSubgroup.{u1} M (AddCommGroup.toAddGroup.{u1} M _inst_1)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (AddSubgroup.{u1} M (AddCommGroup.toAddGroup.{u1} M _inst_1)) (AddSubgroup.completeLattice.{u1} M (AddCommGroup.toAddGroup.{u1} M _inst_1))))))) (LE.le.{u1} (Submodule.{0, u1} Int M Int.semiring (AddCommGroup.toAddCommMonoid.{u1} M _inst_1) (AddCommGroup.intModule.{u1} M _inst_1)) (Preorder.toHasLe.{u1} (Submodule.{0, u1} Int M Int.semiring (AddCommGroup.toAddCommMonoid.{u1} M _inst_1) (AddCommGroup.intModule.{u1} M _inst_1)) (PartialOrder.toPreorder.{u1} (Submodule.{0, u1} Int M Int.semiring (AddCommGroup.toAddCommMonoid.{u1} M _inst_1) (AddCommGroup.intModule.{u1} M _inst_1)) (CompleteSemilatticeInf.toPartialOrder.{u1} (Submodule.{0, u1} Int M Int.semiring (AddCommGroup.toAddCommMonoid.{u1} M _inst_1) (AddCommGroup.intModule.{u1} M _inst_1)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (Submodule.{0, u1} Int M Int.semiring (AddCommGroup.toAddCommMonoid.{u1} M _inst_1) (AddCommGroup.intModule.{u1} M _inst_1)) (Submodule.completeLattice.{0, u1} Int M Int.semiring (AddCommGroup.toAddCommMonoid.{u1} M _inst_1) (AddCommGroup.intModule.{u1} M _inst_1)))))))) (AddSubgroup.toIntSubmodule.{u1} M _inst_1) (Submodule.toAddSubgroup.{0, u1} Int M Int.ring _inst_1 (AddCommGroup.intModule.{u1} M _inst_1) S)) S
 but is expected to have type
   forall {M : Type.{u1}} [_inst_1 : AddCommGroup.{u1} M] (S : Submodule.{0, u1} Int M Int.instSemiringInt (AddCommGroup.toAddCommMonoid.{u1} M _inst_1) (AddCommGroup.intModule.{u1} M _inst_1)), Eq.{succ u1} (Submodule.{0, u1} Int M Int.instSemiringInt (AddCommGroup.toAddCommMonoid.{u1} M _inst_1) (AddCommGroup.intModule.{u1} M _inst_1)) (FunLike.coe.{succ u1, succ u1, succ u1} (RelIso.{u1, u1} (AddSubgroup.{u1} M (AddCommGroup.toAddGroup.{u1} M _inst_1)) (Submodule.{0, u1} Int M Int.instSemiringInt (AddCommGroup.toAddCommMonoid.{u1} M _inst_1) (AddCommGroup.intModule.{u1} M _inst_1)) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1281 : AddSubgroup.{u1} M (AddCommGroup.toAddGroup.{u1} M _inst_1)) (x._@.Mathlib.Order.Hom.Basic._hyg.1283 : AddSubgroup.{u1} M (AddCommGroup.toAddGroup.{u1} M _inst_1)) => LE.le.{u1} (AddSubgroup.{u1} M (AddCommGroup.toAddGroup.{u1} M _inst_1)) (Preorder.toLE.{u1} (AddSubgroup.{u1} M (AddCommGroup.toAddGroup.{u1} M _inst_1)) (PartialOrder.toPreorder.{u1} (AddSubgroup.{u1} M (AddCommGroup.toAddGroup.{u1} M _inst_1)) (CompleteSemilatticeInf.toPartialOrder.{u1} (AddSubgroup.{u1} M (AddCommGroup.toAddGroup.{u1} M _inst_1)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (AddSubgroup.{u1} M (AddCommGroup.toAddGroup.{u1} M _inst_1)) (AddSubgroup.instCompleteLatticeAddSubgroup.{u1} M (AddCommGroup.toAddGroup.{u1} M _inst_1)))))) x._@.Mathlib.Order.Hom.Basic._hyg.1281 x._@.Mathlib.Order.Hom.Basic._hyg.1283) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1296 : Submodule.{0, u1} Int M Int.instSemiringInt (AddCommGroup.toAddCommMonoid.{u1} M _inst_1) (AddCommGroup.intModule.{u1} M _inst_1)) (x._@.Mathlib.Order.Hom.Basic._hyg.1298 : Submodule.{0, u1} Int M Int.instSemiringInt (AddCommGroup.toAddCommMonoid.{u1} M _inst_1) (AddCommGroup.intModule.{u1} M _inst_1)) => LE.le.{u1} (Submodule.{0, u1} Int M Int.instSemiringInt (AddCommGroup.toAddCommMonoid.{u1} M _inst_1) (AddCommGroup.intModule.{u1} M _inst_1)) (Preorder.toLE.{u1} (Submodule.{0, u1} Int M Int.instSemiringInt (AddCommGroup.toAddCommMonoid.{u1} M _inst_1) (AddCommGroup.intModule.{u1} M _inst_1)) (PartialOrder.toPreorder.{u1} (Submodule.{0, u1} Int M Int.instSemiringInt (AddCommGroup.toAddCommMonoid.{u1} M _inst_1) (AddCommGroup.intModule.{u1} M _inst_1)) (CompleteSemilatticeInf.toPartialOrder.{u1} (Submodule.{0, u1} Int M Int.instSemiringInt (AddCommGroup.toAddCommMonoid.{u1} M _inst_1) (AddCommGroup.intModule.{u1} M _inst_1)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (Submodule.{0, u1} Int M Int.instSemiringInt (AddCommGroup.toAddCommMonoid.{u1} M _inst_1) (AddCommGroup.intModule.{u1} M _inst_1)) (Submodule.completeLattice.{0, u1} Int M Int.instSemiringInt (AddCommGroup.toAddCommMonoid.{u1} M _inst_1) (AddCommGroup.intModule.{u1} M _inst_1)))))) x._@.Mathlib.Order.Hom.Basic._hyg.1296 x._@.Mathlib.Order.Hom.Basic._hyg.1298)) (AddSubgroup.{u1} M (AddCommGroup.toAddGroup.{u1} M _inst_1)) (fun (_x : AddSubgroup.{u1} M (AddCommGroup.toAddGroup.{u1} M _inst_1)) => Submodule.{0, u1} Int M Int.instSemiringInt (AddCommGroup.toAddCommMonoid.{u1} M _inst_1) (AddCommGroup.intModule.{u1} M _inst_1)) (RelHomClass.toFunLike.{u1, u1, u1} (RelIso.{u1, u1} (AddSubgroup.{u1} M (AddCommGroup.toAddGroup.{u1} M _inst_1)) (Submodule.{0, u1} Int M Int.instSemiringInt (AddCommGroup.toAddCommMonoid.{u1} M _inst_1) (AddCommGroup.intModule.{u1} M _inst_1)) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1281 : AddSubgroup.{u1} M (AddCommGroup.toAddGroup.{u1} M _inst_1)) (x._@.Mathlib.Order.Hom.Basic._hyg.1283 : AddSubgroup.{u1} M (AddCommGroup.toAddGroup.{u1} M _inst_1)) => LE.le.{u1} (AddSubgroup.{u1} M (AddCommGroup.toAddGroup.{u1} M _inst_1)) (Preorder.toLE.{u1} (AddSubgroup.{u1} M (AddCommGroup.toAddGroup.{u1} M _inst_1)) (PartialOrder.toPreorder.{u1} (AddSubgroup.{u1} M (AddCommGroup.toAddGroup.{u1} M _inst_1)) (CompleteSemilatticeInf.toPartialOrder.{u1} (AddSubgroup.{u1} M (AddCommGroup.toAddGroup.{u1} M _inst_1)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (AddSubgroup.{u1} M (AddCommGroup.toAddGroup.{u1} M _inst_1)) (AddSubgroup.instCompleteLatticeAddSubgroup.{u1} M (AddCommGroup.toAddGroup.{u1} M _inst_1)))))) x._@.Mathlib.Order.Hom.Basic._hyg.1281 x._@.Mathlib.Order.Hom.Basic._hyg.1283) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1296 : Submodule.{0, u1} Int M Int.instSemiringInt (AddCommGroup.toAddCommMonoid.{u1} M _inst_1) (AddCommGroup.intModule.{u1} M _inst_1)) (x._@.Mathlib.Order.Hom.Basic._hyg.1298 : Submodule.{0, u1} Int M Int.instSemiringInt (AddCommGroup.toAddCommMonoid.{u1} M _inst_1) (AddCommGroup.intModule.{u1} M _inst_1)) => LE.le.{u1} (Submodule.{0, u1} Int M Int.instSemiringInt (AddCommGroup.toAddCommMonoid.{u1} M _inst_1) (AddCommGroup.intModule.{u1} M _inst_1)) (Preorder.toLE.{u1} (Submodule.{0, u1} Int M Int.instSemiringInt (AddCommGroup.toAddCommMonoid.{u1} M _inst_1) (AddCommGroup.intModule.{u1} M _inst_1)) (PartialOrder.toPreorder.{u1} (Submodule.{0, u1} Int M Int.instSemiringInt (AddCommGroup.toAddCommMonoid.{u1} M _inst_1) (AddCommGroup.intModule.{u1} M _inst_1)) (CompleteSemilatticeInf.toPartialOrder.{u1} (Submodule.{0, u1} Int M Int.instSemiringInt (AddCommGroup.toAddCommMonoid.{u1} M _inst_1) (AddCommGroup.intModule.{u1} M _inst_1)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (Submodule.{0, u1} Int M Int.instSemiringInt (AddCommGroup.toAddCommMonoid.{u1} M _inst_1) (AddCommGroup.intModule.{u1} M _inst_1)) (Submodule.completeLattice.{0, u1} Int M Int.instSemiringInt (AddCommGroup.toAddCommMonoid.{u1} M _inst_1) (AddCommGroup.intModule.{u1} M _inst_1)))))) x._@.Mathlib.Order.Hom.Basic._hyg.1296 x._@.Mathlib.Order.Hom.Basic._hyg.1298)) (AddSubgroup.{u1} M (AddCommGroup.toAddGroup.{u1} M _inst_1)) (Submodule.{0, u1} Int M Int.instSemiringInt (AddCommGroup.toAddCommMonoid.{u1} M _inst_1) (AddCommGroup.intModule.{u1} M _inst_1)) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1281 : AddSubgroup.{u1} M (AddCommGroup.toAddGroup.{u1} M _inst_1)) (x._@.Mathlib.Order.Hom.Basic._hyg.1283 : AddSubgroup.{u1} M (AddCommGroup.toAddGroup.{u1} M _inst_1)) => LE.le.{u1} (AddSubgroup.{u1} M (AddCommGroup.toAddGroup.{u1} M _inst_1)) (Preorder.toLE.{u1} (AddSubgroup.{u1} M (AddCommGroup.toAddGroup.{u1} M _inst_1)) (PartialOrder.toPreorder.{u1} (AddSubgroup.{u1} M (AddCommGroup.toAddGroup.{u1} M _inst_1)) (CompleteSemilatticeInf.toPartialOrder.{u1} (AddSubgroup.{u1} M (AddCommGroup.toAddGroup.{u1} M _inst_1)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (AddSubgroup.{u1} M (AddCommGroup.toAddGroup.{u1} M _inst_1)) (AddSubgroup.instCompleteLatticeAddSubgroup.{u1} M (AddCommGroup.toAddGroup.{u1} M _inst_1)))))) x._@.Mathlib.Order.Hom.Basic._hyg.1281 x._@.Mathlib.Order.Hom.Basic._hyg.1283) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1296 : Submodule.{0, u1} Int M Int.instSemiringInt (AddCommGroup.toAddCommMonoid.{u1} M _inst_1) (AddCommGroup.intModule.{u1} M _inst_1)) (x._@.Mathlib.Order.Hom.Basic._hyg.1298 : Submodule.{0, u1} Int M Int.instSemiringInt (AddCommGroup.toAddCommMonoid.{u1} M _inst_1) (AddCommGroup.intModule.{u1} M _inst_1)) => LE.le.{u1} (Submodule.{0, u1} Int M Int.instSemiringInt (AddCommGroup.toAddCommMonoid.{u1} M _inst_1) (AddCommGroup.intModule.{u1} M _inst_1)) (Preorder.toLE.{u1} (Submodule.{0, u1} Int M Int.instSemiringInt (AddCommGroup.toAddCommMonoid.{u1} M _inst_1) (AddCommGroup.intModule.{u1} M _inst_1)) (PartialOrder.toPreorder.{u1} (Submodule.{0, u1} Int M Int.instSemiringInt (AddCommGroup.toAddCommMonoid.{u1} M _inst_1) (AddCommGroup.intModule.{u1} M _inst_1)) (CompleteSemilatticeInf.toPartialOrder.{u1} (Submodule.{0, u1} Int M Int.instSemiringInt (AddCommGroup.toAddCommMonoid.{u1} M _inst_1) (AddCommGroup.intModule.{u1} M _inst_1)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (Submodule.{0, u1} Int M Int.instSemiringInt (AddCommGroup.toAddCommMonoid.{u1} M _inst_1) (AddCommGroup.intModule.{u1} M _inst_1)) (Submodule.completeLattice.{0, u1} Int M Int.instSemiringInt (AddCommGroup.toAddCommMonoid.{u1} M _inst_1) (AddCommGroup.intModule.{u1} M _inst_1)))))) x._@.Mathlib.Order.Hom.Basic._hyg.1296 x._@.Mathlib.Order.Hom.Basic._hyg.1298) (RelIso.instRelHomClassRelIso.{u1, u1} (AddSubgroup.{u1} M (AddCommGroup.toAddGroup.{u1} M _inst_1)) (Submodule.{0, u1} Int M Int.instSemiringInt (AddCommGroup.toAddCommMonoid.{u1} M _inst_1) (AddCommGroup.intModule.{u1} M _inst_1)) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1281 : AddSubgroup.{u1} M (AddCommGroup.toAddGroup.{u1} M _inst_1)) (x._@.Mathlib.Order.Hom.Basic._hyg.1283 : AddSubgroup.{u1} M (AddCommGroup.toAddGroup.{u1} M _inst_1)) => LE.le.{u1} (AddSubgroup.{u1} M (AddCommGroup.toAddGroup.{u1} M _inst_1)) (Preorder.toLE.{u1} (AddSubgroup.{u1} M (AddCommGroup.toAddGroup.{u1} M _inst_1)) (PartialOrder.toPreorder.{u1} (AddSubgroup.{u1} M (AddCommGroup.toAddGroup.{u1} M _inst_1)) (CompleteSemilatticeInf.toPartialOrder.{u1} (AddSubgroup.{u1} M (AddCommGroup.toAddGroup.{u1} M _inst_1)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (AddSubgroup.{u1} M (AddCommGroup.toAddGroup.{u1} M _inst_1)) (AddSubgroup.instCompleteLatticeAddSubgroup.{u1} M (AddCommGroup.toAddGroup.{u1} M _inst_1)))))) x._@.Mathlib.Order.Hom.Basic._hyg.1281 x._@.Mathlib.Order.Hom.Basic._hyg.1283) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1296 : Submodule.{0, u1} Int M Int.instSemiringInt (AddCommGroup.toAddCommMonoid.{u1} M _inst_1) (AddCommGroup.intModule.{u1} M _inst_1)) (x._@.Mathlib.Order.Hom.Basic._hyg.1298 : Submodule.{0, u1} Int M Int.instSemiringInt (AddCommGroup.toAddCommMonoid.{u1} M _inst_1) (AddCommGroup.intModule.{u1} M _inst_1)) => LE.le.{u1} (Submodule.{0, u1} Int M Int.instSemiringInt (AddCommGroup.toAddCommMonoid.{u1} M _inst_1) (AddCommGroup.intModule.{u1} M _inst_1)) (Preorder.toLE.{u1} (Submodule.{0, u1} Int M Int.instSemiringInt (AddCommGroup.toAddCommMonoid.{u1} M _inst_1) (AddCommGroup.intModule.{u1} M _inst_1)) (PartialOrder.toPreorder.{u1} (Submodule.{0, u1} Int M Int.instSemiringInt (AddCommGroup.toAddCommMonoid.{u1} M _inst_1) (AddCommGroup.intModule.{u1} M _inst_1)) (CompleteSemilatticeInf.toPartialOrder.{u1} (Submodule.{0, u1} Int M Int.instSemiringInt (AddCommGroup.toAddCommMonoid.{u1} M _inst_1) (AddCommGroup.intModule.{u1} M _inst_1)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (Submodule.{0, u1} Int M Int.instSemiringInt (AddCommGroup.toAddCommMonoid.{u1} M _inst_1) (AddCommGroup.intModule.{u1} M _inst_1)) (Submodule.completeLattice.{0, u1} Int M Int.instSemiringInt (AddCommGroup.toAddCommMonoid.{u1} M _inst_1) (AddCommGroup.intModule.{u1} M _inst_1)))))) x._@.Mathlib.Order.Hom.Basic._hyg.1296 x._@.Mathlib.Order.Hom.Basic._hyg.1298))) (AddSubgroup.toIntSubmodule.{u1} M _inst_1) (Submodule.toAddSubgroup.{0, u1} Int M Int.instRingInt _inst_1 (AddCommGroup.intModule.{u1} M _inst_1) S)) S
 Case conversion may be inaccurate. Consider using '#align submodule.to_add_subgroup_to_int_submodule Submodule.toAddSubgroup_toIntSubmoduleₓ'. -/

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

@@ -194,7 +194,7 @@ theorem exists_mem_ne_zero_of_ne_bot {p : Submodule R M} (h : p ≠ ⊥) : ∃ b
 lean 3 declaration is
   forall {R : Type.{u1}} {M : Type.{u2}} [_inst_1 : Semiring.{u1} R] [_inst_3 : AddCommMonoid.{u2} M] [_inst_4 : Module.{u1, u2} R M _inst_1 _inst_3], LinearEquiv.{u1, u1, u2, u3} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R _inst_1) (RingHomInvPair.ids.{u1} R _inst_1) (coeSort.{succ u2, succ (succ u2)} (Submodule.{u1, u2} R M _inst_1 _inst_3 _inst_4) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Submodule.{u1, u2} R M _inst_1 _inst_3 _inst_4) M (Submodule.setLike.{u1, u2} R M _inst_1 _inst_3 _inst_4)) (Bot.bot.{u2} (Submodule.{u1, u2} R M _inst_1 _inst_3 _inst_4) (Submodule.hasBot.{u1, u2} R M _inst_1 _inst_3 _inst_4))) PUnit.{succ u3} (Submodule.addCommMonoid.{u1, u2} R M _inst_1 _inst_3 _inst_4 (Bot.bot.{u2} (Submodule.{u1, u2} R M _inst_1 _inst_3 _inst_4) (Submodule.hasBot.{u1, u2} R M _inst_1 _inst_3 _inst_4))) (AddCommGroup.toAddCommMonoid.{u3} PUnit.{succ u3} PUnit.addCommGroup.{u3}) (Submodule.module.{u1, u2} R M _inst_1 _inst_3 _inst_4 (Bot.bot.{u2} (Submodule.{u1, u2} R M _inst_1 _inst_3 _inst_4) (Submodule.hasBot.{u1, u2} R M _inst_1 _inst_3 _inst_4))) (PUnit.module.{u1, u3} R _inst_1)
 but is expected to have type
-  forall {R : Type.{u1}} {M : Type.{u2}} [_inst_1 : Semiring.{u1} R] [_inst_3 : AddCommMonoid.{u2} M] [_inst_4 : Module.{u1, u2} R M _inst_1 _inst_3], LinearEquiv.{u1, u1, u2, u3} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R _inst_1) (RingHomInvPair.ids.{u1} R _inst_1) (Subtype.{succ u2} M (fun (x : M) => Membership.mem.{u2, u2} M (Submodule.{u1, u2} R M _inst_1 _inst_3 _inst_4) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} R M _inst_1 _inst_3 _inst_4) M (Submodule.setLike.{u1, u2} R M _inst_1 _inst_3 _inst_4)) x (Bot.bot.{u2} (Submodule.{u1, u2} R M _inst_1 _inst_3 _inst_4) (Submodule.instBotSubmodule.{u1, u2} R M _inst_1 _inst_3 _inst_4)))) PUnit.{succ u3} (Submodule.addCommMonoid.{u1, u2} R M _inst_1 _inst_3 _inst_4 (Bot.bot.{u2} (Submodule.{u1, u2} R M _inst_1 _inst_3 _inst_4) (Submodule.instBotSubmodule.{u1, u2} R M _inst_1 _inst_3 _inst_4))) (OrderedCancelAddCommMonoid.toAddCommMonoid.{u3} PUnit.{succ u3} (LinearOrderedCancelAddCommMonoid.toOrderedCancelAddCommMonoid.{u3} PUnit.{succ u3} PUnit.linearOrderedCancelAddCommMonoid.{u3})) (Submodule.module.{u1, u2} R M _inst_1 _inst_3 _inst_4 (Bot.bot.{u2} (Submodule.{u1, u2} R M _inst_1 _inst_3 _inst_4) (Submodule.instBotSubmodule.{u1, u2} R M _inst_1 _inst_3 _inst_4))) (PUnit.module.{u1, u3} R _inst_1)
+  forall {R : Type.{u2}} {M : Type.{u3}} [_inst_1 : Semiring.{u2} R] [_inst_3 : AddCommMonoid.{u3} M] [_inst_4 : Module.{u2, u3} R M _inst_1 _inst_3], LinearEquiv.{u2, u2, u3, u1} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) (RingHomInvPair.ids.{u2} R _inst_1) (RingHomInvPair.ids.{u2} R _inst_1) (Subtype.{succ u3} M (fun (x : M) => Membership.mem.{u3, u3} M (Submodule.{u2, u3} R M _inst_1 _inst_3 _inst_4) (SetLike.instMembership.{u3, u3} (Submodule.{u2, u3} R M _inst_1 _inst_3 _inst_4) M (Submodule.setLike.{u2, u3} R M _inst_1 _inst_3 _inst_4)) x (Bot.bot.{u3} (Submodule.{u2, u3} R M _inst_1 _inst_3 _inst_4) (Submodule.instBotSubmodule.{u2, u3} R M _inst_1 _inst_3 _inst_4)))) PUnit.{succ u1} (Submodule.addCommMonoid.{u2, u3} R M _inst_1 _inst_3 _inst_4 (Bot.bot.{u3} (Submodule.{u2, u3} R M _inst_1 _inst_3 _inst_4) (Submodule.instBotSubmodule.{u2, u3} R M _inst_1 _inst_3 _inst_4))) (OrderedCancelAddCommMonoid.toAddCommMonoid.{u1} PUnit.{succ u1} (LinearOrderedCancelAddCommMonoid.toOrderedCancelAddCommMonoid.{u1} PUnit.{succ u1} PUnit.linearOrderedCancelAddCommMonoid.{u1})) (Submodule.module.{u2, u3} R M _inst_1 _inst_3 _inst_4 (Bot.bot.{u3} (Submodule.{u2, u3} R M _inst_1 _inst_3 _inst_4) (Submodule.instBotSubmodule.{u2, u3} R M _inst_1 _inst_3 _inst_4))) (PUnit.module.{u2, u1} R _inst_1)
 Case conversion may be inaccurate. Consider using '#align submodule.bot_equiv_punit Submodule.botEquivPUnitₓ'. -/
 /-- The bottom submodule is linearly equivalent to punit as an `R`-module. -/
 @[simps]

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

@@ -346,12 +346,12 @@ instance : InfSet (Submodule R M) :=
       add_mem' := by simp (config := { contextual := true }) [add_mem]
       smul_mem' := by simp (config := { contextual := true }) [smul_mem] }⟩
 
-private theorem Inf_le' {S : Set (Submodule R M)} {p} : p ∈ S → infₛ S ≤ p :=
-  Set.binterᵢ_subset_of_mem
+private theorem Inf_le' {S : Set (Submodule R M)} {p} : p ∈ S → sInf S ≤ p :=
+  Set.biInter_subset_of_mem
 #align submodule.Inf_le' submodule.Inf_le'
 
-private theorem le_Inf' {S : Set (Submodule R M)} {p} : (∀ q ∈ S, p ≤ q) → p ≤ infₛ S :=
-  Set.subset_interᵢ₂
+private theorem le_Inf' {S : Set (Submodule R M)} {p} : (∀ q ∈ S, p ≤ q) → p ≤ sInf S :=
+  Set.subset_iInter₂
 #align submodule.le_Inf' submodule.le_Inf'
 
 instance : Inf (Submodule R M) :=
@@ -364,20 +364,20 @@ instance : Inf (Submodule R M) :=
 instance : CompleteLattice (Submodule R M) :=
   { Submodule.orderTop, Submodule.orderBot,
     SetLike.partialOrder with
-    sup := fun a b => infₛ { x | a ≤ x ∧ b ≤ x }
+    sup := fun a b => sInf { x | a ≤ x ∧ b ≤ x }
     le_sup_left := fun a b => le_Inf' fun x ⟨ha, hb⟩ => ha
     le_sup_right := fun a b => le_Inf' fun x ⟨ha, hb⟩ => hb
-    sup_le := fun a b c h₁ h₂ => infₛ_le' ⟨h₁, h₂⟩
+    sup_le := fun a b c h₁ h₂ => sInf_le' ⟨h₁, h₂⟩
     inf := (· ⊓ ·)
     le_inf := fun a b c => Set.subset_inter
     inf_le_left := fun a b => Set.inter_subset_left _ _
     inf_le_right := fun a b => Set.inter_subset_right _ _
-    supₛ := fun tt => infₛ { t | ∀ t' ∈ tt, t' ≤ t }
+    sSup := fun tt => sInf { t | ∀ t' ∈ tt, t' ≤ t }
     le_sup := fun s p hs => le_Inf' fun q hq => hq _ hs
-    sup_le := fun s p hs => infₛ_le' hs
-    infₛ := infₛ
+    sup_le := fun s p hs => sInf_le' hs
+    sInf := sInf
     le_inf := fun s a => le_Inf'
-    inf_le := fun s a => infₛ_le' }
+    inf_le := fun s a => sInf_le' }
 
 /- warning: submodule.inf_coe -> Submodule.inf_coe is a dubious translation:
 lean 3 declaration is
@@ -401,22 +401,22 @@ theorem mem_inf {p q : Submodule R M} {x : M} : x ∈ p ⊓ q ↔ x ∈ p ∧ x
   Iff.rfl
 #align submodule.mem_inf Submodule.mem_inf
 
-/- warning: submodule.Inf_coe -> Submodule.infₛ_coe is a dubious translation:
+/- warning: submodule.Inf_coe -> Submodule.sInf_coe is a dubious translation:
 lean 3 declaration is
-  forall {R : Type.{u1}} {M : Type.{u2}} [_inst_1 : Semiring.{u1} R] [_inst_3 : AddCommMonoid.{u2} M] [_inst_4 : Module.{u1, u2} R M _inst_1 _inst_3] (P : Set.{u2} (Submodule.{u1, u2} R M _inst_1 _inst_3 _inst_4)), Eq.{succ u2} (Set.{u2} M) ((fun (a : Type.{u2}) (b : Type.{u2}) [self : HasLiftT.{succ u2, succ u2} a b] => self.0) (Submodule.{u1, u2} R M _inst_1 _inst_3 _inst_4) (Set.{u2} M) (HasLiftT.mk.{succ u2, succ u2} (Submodule.{u1, u2} R M _inst_1 _inst_3 _inst_4) (Set.{u2} M) (CoeTCₓ.coe.{succ u2, succ u2} (Submodule.{u1, u2} R M _inst_1 _inst_3 _inst_4) (Set.{u2} M) (SetLike.Set.hasCoeT.{u2, u2} (Submodule.{u1, u2} R M _inst_1 _inst_3 _inst_4) M (Submodule.setLike.{u1, u2} R M _inst_1 _inst_3 _inst_4)))) (InfSet.infₛ.{u2} (Submodule.{u1, u2} R M _inst_1 _inst_3 _inst_4) (Submodule.hasInf.{u1, u2} R M _inst_1 _inst_3 _inst_4) P)) (Set.interᵢ.{u2, succ u2} M (Submodule.{u1, u2} R M _inst_1 _inst_3 _inst_4) (fun (p : Submodule.{u1, u2} R M _inst_1 _inst_3 _inst_4) => Set.interᵢ.{u2, 0} M (Membership.Mem.{u2, u2} (Submodule.{u1, u2} R M _inst_1 _inst_3 _inst_4) (Set.{u2} (Submodule.{u1, u2} R M _inst_1 _inst_3 _inst_4)) (Set.hasMem.{u2} (Submodule.{u1, u2} R M _inst_1 _inst_3 _inst_4)) p P) (fun (H : Membership.Mem.{u2, u2} (Submodule.{u1, u2} R M _inst_1 _inst_3 _inst_4) (Set.{u2} (Submodule.{u1, u2} R M _inst_1 _inst_3 _inst_4)) (Set.hasMem.{u2} (Submodule.{u1, u2} R M _inst_1 _inst_3 _inst_4)) p P) => (fun (a : Type.{u2}) (b : Type.{u2}) [self : HasLiftT.{succ u2, succ u2} a b] => self.0) (Submodule.{u1, u2} R M _inst_1 _inst_3 _inst_4) (Set.{u2} M) (HasLiftT.mk.{succ u2, succ u2} (Submodule.{u1, u2} R M _inst_1 _inst_3 _inst_4) (Set.{u2} M) (CoeTCₓ.coe.{succ u2, succ u2} (Submodule.{u1, u2} R M _inst_1 _inst_3 _inst_4) (Set.{u2} M) (SetLike.Set.hasCoeT.{u2, u2} (Submodule.{u1, u2} R M _inst_1 _inst_3 _inst_4) M (Submodule.setLike.{u1, u2} R M _inst_1 _inst_3 _inst_4)))) p)))
+  forall {R : Type.{u1}} {M : Type.{u2}} [_inst_1 : Semiring.{u1} R] [_inst_3 : AddCommMonoid.{u2} M] [_inst_4 : Module.{u1, u2} R M _inst_1 _inst_3] (P : Set.{u2} (Submodule.{u1, u2} R M _inst_1 _inst_3 _inst_4)), Eq.{succ u2} (Set.{u2} M) ((fun (a : Type.{u2}) (b : Type.{u2}) [self : HasLiftT.{succ u2, succ u2} a b] => self.0) (Submodule.{u1, u2} R M _inst_1 _inst_3 _inst_4) (Set.{u2} M) (HasLiftT.mk.{succ u2, succ u2} (Submodule.{u1, u2} R M _inst_1 _inst_3 _inst_4) (Set.{u2} M) (CoeTCₓ.coe.{succ u2, succ u2} (Submodule.{u1, u2} R M _inst_1 _inst_3 _inst_4) (Set.{u2} M) (SetLike.Set.hasCoeT.{u2, u2} (Submodule.{u1, u2} R M _inst_1 _inst_3 _inst_4) M (Submodule.setLike.{u1, u2} R M _inst_1 _inst_3 _inst_4)))) (InfSet.sInf.{u2} (Submodule.{u1, u2} R M _inst_1 _inst_3 _inst_4) (Submodule.hasInf.{u1, u2} R M _inst_1 _inst_3 _inst_4) P)) (Set.iInter.{u2, succ u2} M (Submodule.{u1, u2} R M _inst_1 _inst_3 _inst_4) (fun (p : Submodule.{u1, u2} R M _inst_1 _inst_3 _inst_4) => Set.iInter.{u2, 0} M (Membership.Mem.{u2, u2} (Submodule.{u1, u2} R M _inst_1 _inst_3 _inst_4) (Set.{u2} (Submodule.{u1, u2} R M _inst_1 _inst_3 _inst_4)) (Set.hasMem.{u2} (Submodule.{u1, u2} R M _inst_1 _inst_3 _inst_4)) p P) (fun (H : Membership.Mem.{u2, u2} (Submodule.{u1, u2} R M _inst_1 _inst_3 _inst_4) (Set.{u2} (Submodule.{u1, u2} R M _inst_1 _inst_3 _inst_4)) (Set.hasMem.{u2} (Submodule.{u1, u2} R M _inst_1 _inst_3 _inst_4)) p P) => (fun (a : Type.{u2}) (b : Type.{u2}) [self : HasLiftT.{succ u2, succ u2} a b] => self.0) (Submodule.{u1, u2} R M _inst_1 _inst_3 _inst_4) (Set.{u2} M) (HasLiftT.mk.{succ u2, succ u2} (Submodule.{u1, u2} R M _inst_1 _inst_3 _inst_4) (Set.{u2} M) (CoeTCₓ.coe.{succ u2, succ u2} (Submodule.{u1, u2} R M _inst_1 _inst_3 _inst_4) (Set.{u2} M) (SetLike.Set.hasCoeT.{u2, u2} (Submodule.{u1, u2} R M _inst_1 _inst_3 _inst_4) M (Submodule.setLike.{u1, u2} R M _inst_1 _inst_3 _inst_4)))) p)))
 but is expected to have type
-  forall {R : Type.{u1}} {M : Type.{u2}} [_inst_1 : Semiring.{u1} R] [_inst_3 : AddCommMonoid.{u2} M] [_inst_4 : Module.{u1, u2} R M _inst_1 _inst_3] (P : Set.{u2} (Submodule.{u1, u2} R M _inst_1 _inst_3 _inst_4)), Eq.{succ u2} (Set.{u2} M) (SetLike.coe.{u2, u2} (Submodule.{u1, u2} R M _inst_1 _inst_3 _inst_4) M (Submodule.setLike.{u1, u2} R M _inst_1 _inst_3 _inst_4) (InfSet.infₛ.{u2} (Submodule.{u1, u2} R M _inst_1 _inst_3 _inst_4) (Submodule.instInfSetSubmodule.{u1, u2} R M _inst_1 _inst_3 _inst_4) P)) (Set.interᵢ.{u2, succ u2} M (Submodule.{u1, u2} R M _inst_1 _inst_3 _inst_4) (fun (p : Submodule.{u1, u2} R M _inst_1 _inst_3 _inst_4) => Set.interᵢ.{u2, 0} M (Membership.mem.{u2, u2} (Submodule.{u1, u2} R M _inst_1 _inst_3 _inst_4) (Set.{u2} (Submodule.{u1, u2} R M _inst_1 _inst_3 _inst_4)) (Set.instMembershipSet.{u2} (Submodule.{u1, u2} R M _inst_1 _inst_3 _inst_4)) p P) (fun (H : Membership.mem.{u2, u2} (Submodule.{u1, u2} R M _inst_1 _inst_3 _inst_4) (Set.{u2} (Submodule.{u1, u2} R M _inst_1 _inst_3 _inst_4)) (Set.instMembershipSet.{u2} (Submodule.{u1, u2} R M _inst_1 _inst_3 _inst_4)) p P) => SetLike.coe.{u2, u2} (Submodule.{u1, u2} R M _inst_1 _inst_3 _inst_4) M (Submodule.setLike.{u1, u2} R M _inst_1 _inst_3 _inst_4) p)))
-Case conversion may be inaccurate. Consider using '#align submodule.Inf_coe Submodule.infₛ_coeₓ'. -/
+  forall {R : Type.{u1}} {M : Type.{u2}} [_inst_1 : Semiring.{u1} R] [_inst_3 : AddCommMonoid.{u2} M] [_inst_4 : Module.{u1, u2} R M _inst_1 _inst_3] (P : Set.{u2} (Submodule.{u1, u2} R M _inst_1 _inst_3 _inst_4)), Eq.{succ u2} (Set.{u2} M) (SetLike.coe.{u2, u2} (Submodule.{u1, u2} R M _inst_1 _inst_3 _inst_4) M (Submodule.setLike.{u1, u2} R M _inst_1 _inst_3 _inst_4) (InfSet.sInf.{u2} (Submodule.{u1, u2} R M _inst_1 _inst_3 _inst_4) (Submodule.instInfSetSubmodule.{u1, u2} R M _inst_1 _inst_3 _inst_4) P)) (Set.iInter.{u2, succ u2} M (Submodule.{u1, u2} R M _inst_1 _inst_3 _inst_4) (fun (p : Submodule.{u1, u2} R M _inst_1 _inst_3 _inst_4) => Set.iInter.{u2, 0} M (Membership.mem.{u2, u2} (Submodule.{u1, u2} R M _inst_1 _inst_3 _inst_4) (Set.{u2} (Submodule.{u1, u2} R M _inst_1 _inst_3 _inst_4)) (Set.instMembershipSet.{u2} (Submodule.{u1, u2} R M _inst_1 _inst_3 _inst_4)) p P) (fun (H : Membership.mem.{u2, u2} (Submodule.{u1, u2} R M _inst_1 _inst_3 _inst_4) (Set.{u2} (Submodule.{u1, u2} R M _inst_1 _inst_3 _inst_4)) (Set.instMembershipSet.{u2} (Submodule.{u1, u2} R M _inst_1 _inst_3 _inst_4)) p P) => SetLike.coe.{u2, u2} (Submodule.{u1, u2} R M _inst_1 _inst_3 _inst_4) M (Submodule.setLike.{u1, u2} R M _inst_1 _inst_3 _inst_4) p)))
+Case conversion may be inaccurate. Consider using '#align submodule.Inf_coe Submodule.sInf_coeₓ'. -/
 @[simp]
-theorem infₛ_coe (P : Set (Submodule R M)) : (↑(infₛ P) : Set M) = ⋂ p ∈ P, ↑p :=
+theorem sInf_coe (P : Set (Submodule R M)) : (↑(sInf P) : Set M) = ⋂ p ∈ P, ↑p :=
   rfl
-#align submodule.Inf_coe Submodule.infₛ_coe
+#align submodule.Inf_coe Submodule.sInf_coe
 
 /- warning: submodule.finset_inf_coe -> Submodule.finset_inf_coe is a dubious translation:
 lean 3 declaration is
-  forall {R : Type.{u1}} {M : Type.{u2}} [_inst_1 : Semiring.{u1} R] [_inst_3 : AddCommMonoid.{u2} M] [_inst_4 : Module.{u1, u2} R M _inst_1 _inst_3] {ι : Type.{u3}} (s : Finset.{u3} ι) (p : ι -> (Submodule.{u1, u2} R M _inst_1 _inst_3 _inst_4)), Eq.{succ u2} (Set.{u2} M) ((fun (a : Type.{u2}) (b : Type.{u2}) [self : HasLiftT.{succ u2, succ u2} a b] => self.0) (Submodule.{u1, u2} R M _inst_1 _inst_3 _inst_4) (Set.{u2} M) (HasLiftT.mk.{succ u2, succ u2} (Submodule.{u1, u2} R M _inst_1 _inst_3 _inst_4) (Set.{u2} M) (CoeTCₓ.coe.{succ u2, succ u2} (Submodule.{u1, u2} R M _inst_1 _inst_3 _inst_4) (Set.{u2} M) (SetLike.Set.hasCoeT.{u2, u2} (Submodule.{u1, u2} R M _inst_1 _inst_3 _inst_4) M (Submodule.setLike.{u1, u2} R M _inst_1 _inst_3 _inst_4)))) (Finset.inf.{u2, u3} (Submodule.{u1, u2} R M _inst_1 _inst_3 _inst_4) ι (Lattice.toSemilatticeInf.{u2} (Submodule.{u1, u2} R M _inst_1 _inst_3 _inst_4) (CompleteLattice.toLattice.{u2} (Submodule.{u1, u2} R M _inst_1 _inst_3 _inst_4) (Submodule.completeLattice.{u1, u2} R M _inst_1 _inst_3 _inst_4))) (Submodule.orderTop.{u1, u2} R M _inst_1 _inst_3 _inst_4) s p)) (Set.interᵢ.{u2, succ u3} M ι (fun (i : ι) => Set.interᵢ.{u2, 0} M (Membership.Mem.{u3, u3} ι (Finset.{u3} ι) (Finset.hasMem.{u3} ι) i s) (fun (H : Membership.Mem.{u3, u3} ι (Finset.{u3} ι) (Finset.hasMem.{u3} ι) i s) => (fun (a : Type.{u2}) (b : Type.{u2}) [self : HasLiftT.{succ u2, succ u2} a b] => self.0) (Submodule.{u1, u2} R M _inst_1 _inst_3 _inst_4) (Set.{u2} M) (HasLiftT.mk.{succ u2, succ u2} (Submodule.{u1, u2} R M _inst_1 _inst_3 _inst_4) (Set.{u2} M) (CoeTCₓ.coe.{succ u2, succ u2} (Submodule.{u1, u2} R M _inst_1 _inst_3 _inst_4) (Set.{u2} M) (SetLike.Set.hasCoeT.{u2, u2} (Submodule.{u1, u2} R M _inst_1 _inst_3 _inst_4) M (Submodule.setLike.{u1, u2} R M _inst_1 _inst_3 _inst_4)))) (p i))))
+  forall {R : Type.{u1}} {M : Type.{u2}} [_inst_1 : Semiring.{u1} R] [_inst_3 : AddCommMonoid.{u2} M] [_inst_4 : Module.{u1, u2} R M _inst_1 _inst_3] {ι : Type.{u3}} (s : Finset.{u3} ι) (p : ι -> (Submodule.{u1, u2} R M _inst_1 _inst_3 _inst_4)), Eq.{succ u2} (Set.{u2} M) ((fun (a : Type.{u2}) (b : Type.{u2}) [self : HasLiftT.{succ u2, succ u2} a b] => self.0) (Submodule.{u1, u2} R M _inst_1 _inst_3 _inst_4) (Set.{u2} M) (HasLiftT.mk.{succ u2, succ u2} (Submodule.{u1, u2} R M _inst_1 _inst_3 _inst_4) (Set.{u2} M) (CoeTCₓ.coe.{succ u2, succ u2} (Submodule.{u1, u2} R M _inst_1 _inst_3 _inst_4) (Set.{u2} M) (SetLike.Set.hasCoeT.{u2, u2} (Submodule.{u1, u2} R M _inst_1 _inst_3 _inst_4) M (Submodule.setLike.{u1, u2} R M _inst_1 _inst_3 _inst_4)))) (Finset.inf.{u2, u3} (Submodule.{u1, u2} R M _inst_1 _inst_3 _inst_4) ι (Lattice.toSemilatticeInf.{u2} (Submodule.{u1, u2} R M _inst_1 _inst_3 _inst_4) (CompleteLattice.toLattice.{u2} (Submodule.{u1, u2} R M _inst_1 _inst_3 _inst_4) (Submodule.completeLattice.{u1, u2} R M _inst_1 _inst_3 _inst_4))) (Submodule.orderTop.{u1, u2} R M _inst_1 _inst_3 _inst_4) s p)) (Set.iInter.{u2, succ u3} M ι (fun (i : ι) => Set.iInter.{u2, 0} M (Membership.Mem.{u3, u3} ι (Finset.{u3} ι) (Finset.hasMem.{u3} ι) i s) (fun (H : Membership.Mem.{u3, u3} ι (Finset.{u3} ι) (Finset.hasMem.{u3} ι) i s) => (fun (a : Type.{u2}) (b : Type.{u2}) [self : HasLiftT.{succ u2, succ u2} a b] => self.0) (Submodule.{u1, u2} R M _inst_1 _inst_3 _inst_4) (Set.{u2} M) (HasLiftT.mk.{succ u2, succ u2} (Submodule.{u1, u2} R M _inst_1 _inst_3 _inst_4) (Set.{u2} M) (CoeTCₓ.coe.{succ u2, succ u2} (Submodule.{u1, u2} R M _inst_1 _inst_3 _inst_4) (Set.{u2} M) (SetLike.Set.hasCoeT.{u2, u2} (Submodule.{u1, u2} R M _inst_1 _inst_3 _inst_4) M (Submodule.setLike.{u1, u2} R M _inst_1 _inst_3 _inst_4)))) (p i))))
 but is expected to have type
-  forall {R : Type.{u2}} {M : Type.{u1}} [_inst_1 : Semiring.{u2} R] [_inst_3 : AddCommMonoid.{u1} M] [_inst_4 : Module.{u2, u1} R M _inst_1 _inst_3] {ι : Type.{u3}} (s : Finset.{u3} ι) (p : ι -> (Submodule.{u2, u1} R M _inst_1 _inst_3 _inst_4)), Eq.{succ u1} (Set.{u1} M) (SetLike.coe.{u1, u1} (Submodule.{u2, u1} R M _inst_1 _inst_3 _inst_4) M (Submodule.setLike.{u2, u1} R M _inst_1 _inst_3 _inst_4) (Finset.inf.{u1, u3} (Submodule.{u2, u1} R M _inst_1 _inst_3 _inst_4) ι (Lattice.toSemilatticeInf.{u1} (Submodule.{u2, u1} R M _inst_1 _inst_3 _inst_4) (CompleteLattice.toLattice.{u1} (Submodule.{u2, u1} R M _inst_1 _inst_3 _inst_4) (Submodule.completeLattice.{u2, u1} R M _inst_1 _inst_3 _inst_4))) (Submodule.instOrderTopSubmoduleToLEToPreorderInstPartialOrderSetLike.{u2, u1} R M _inst_1 _inst_3 _inst_4) s p)) (Set.interᵢ.{u1, succ u3} M ι (fun (i : ι) => Set.interᵢ.{u1, 0} M (Membership.mem.{u3, u3} ι (Finset.{u3} ι) (Finset.instMembershipFinset.{u3} ι) i s) (fun (H : Membership.mem.{u3, u3} ι (Finset.{u3} ι) (Finset.instMembershipFinset.{u3} ι) i s) => SetLike.coe.{u1, u1} (Submodule.{u2, u1} R M _inst_1 _inst_3 _inst_4) M (Submodule.setLike.{u2, u1} R M _inst_1 _inst_3 _inst_4) (p i))))
+  forall {R : Type.{u2}} {M : Type.{u1}} [_inst_1 : Semiring.{u2} R] [_inst_3 : AddCommMonoid.{u1} M] [_inst_4 : Module.{u2, u1} R M _inst_1 _inst_3] {ι : Type.{u3}} (s : Finset.{u3} ι) (p : ι -> (Submodule.{u2, u1} R M _inst_1 _inst_3 _inst_4)), Eq.{succ u1} (Set.{u1} M) (SetLike.coe.{u1, u1} (Submodule.{u2, u1} R M _inst_1 _inst_3 _inst_4) M (Submodule.setLike.{u2, u1} R M _inst_1 _inst_3 _inst_4) (Finset.inf.{u1, u3} (Submodule.{u2, u1} R M _inst_1 _inst_3 _inst_4) ι (Lattice.toSemilatticeInf.{u1} (Submodule.{u2, u1} R M _inst_1 _inst_3 _inst_4) (CompleteLattice.toLattice.{u1} (Submodule.{u2, u1} R M _inst_1 _inst_3 _inst_4) (Submodule.completeLattice.{u2, u1} R M _inst_1 _inst_3 _inst_4))) (Submodule.instOrderTopSubmoduleToLEToPreorderInstPartialOrderSetLike.{u2, u1} R M _inst_1 _inst_3 _inst_4) s p)) (Set.iInter.{u1, succ u3} M ι (fun (i : ι) => Set.iInter.{u1, 0} M (Membership.mem.{u3, u3} ι (Finset.{u3} ι) (Finset.instMembershipFinset.{u3} ι) i s) (fun (H : Membership.mem.{u3, u3} ι (Finset.{u3} ι) (Finset.instMembershipFinset.{u3} ι) i s) => SetLike.coe.{u1, u1} (Submodule.{u2, u1} R M _inst_1 _inst_3 _inst_4) M (Submodule.setLike.{u2, u1} R M _inst_1 _inst_3 _inst_4) (p i))))
 Case conversion may be inaccurate. Consider using '#align submodule.finset_inf_coe Submodule.finset_inf_coeₓ'. -/
 @[simp]
 theorem finset_inf_coe {ι} (s : Finset ι) (p : ι → Submodule R M) :
@@ -429,38 +429,38 @@ theorem finset_inf_coe {ι} (s : Finset ι) (p : ι → Submodule R M) :
     simp
 #align submodule.finset_inf_coe Submodule.finset_inf_coe
 
-/- warning: submodule.infi_coe -> Submodule.infᵢ_coe is a dubious translation:
+/- warning: submodule.infi_coe -> Submodule.iInf_coe is a dubious translation:
 lean 3 declaration is
-  forall {R : Type.{u1}} {M : Type.{u2}} [_inst_1 : Semiring.{u1} R] [_inst_3 : AddCommMonoid.{u2} M] [_inst_4 : Module.{u1, u2} R M _inst_1 _inst_3] {ι : Sort.{u3}} (p : ι -> (Submodule.{u1, u2} R M _inst_1 _inst_3 _inst_4)), Eq.{succ u2} (Set.{u2} M) ((fun (a : Type.{u2}) (b : Type.{u2}) [self : HasLiftT.{succ u2, succ u2} a b] => self.0) (Submodule.{u1, u2} R M _inst_1 _inst_3 _inst_4) (Set.{u2} M) (HasLiftT.mk.{succ u2, succ u2} (Submodule.{u1, u2} R M _inst_1 _inst_3 _inst_4) (Set.{u2} M) (CoeTCₓ.coe.{succ u2, succ u2} (Submodule.{u1, u2} R M _inst_1 _inst_3 _inst_4) (Set.{u2} M) (SetLike.Set.hasCoeT.{u2, u2} (Submodule.{u1, u2} R M _inst_1 _inst_3 _inst_4) M (Submodule.setLike.{u1, u2} R M _inst_1 _inst_3 _inst_4)))) (infᵢ.{u2, u3} (Submodule.{u1, u2} R M _inst_1 _inst_3 _inst_4) (Submodule.hasInf.{u1, u2} R M _inst_1 _inst_3 _inst_4) ι (fun (i : ι) => p i))) (Set.interᵢ.{u2, u3} M ι (fun (i : ι) => (fun (a : Type.{u2}) (b : Type.{u2}) [self : HasLiftT.{succ u2, succ u2} a b] => self.0) (Submodule.{u1, u2} R M _inst_1 _inst_3 _inst_4) (Set.{u2} M) (HasLiftT.mk.{succ u2, succ u2} (Submodule.{u1, u2} R M _inst_1 _inst_3 _inst_4) (Set.{u2} M) (CoeTCₓ.coe.{succ u2, succ u2} (Submodule.{u1, u2} R M _inst_1 _inst_3 _inst_4) (Set.{u2} M) (SetLike.Set.hasCoeT.{u2, u2} (Submodule.{u1, u2} R M _inst_1 _inst_3 _inst_4) M (Submodule.setLike.{u1, u2} R M _inst_1 _inst_3 _inst_4)))) (p i)))
+  forall {R : Type.{u1}} {M : Type.{u2}} [_inst_1 : Semiring.{u1} R] [_inst_3 : AddCommMonoid.{u2} M] [_inst_4 : Module.{u1, u2} R M _inst_1 _inst_3] {ι : Sort.{u3}} (p : ι -> (Submodule.{u1, u2} R M _inst_1 _inst_3 _inst_4)), Eq.{succ u2} (Set.{u2} M) ((fun (a : Type.{u2}) (b : Type.{u2}) [self : HasLiftT.{succ u2, succ u2} a b] => self.0) (Submodule.{u1, u2} R M _inst_1 _inst_3 _inst_4) (Set.{u2} M) (HasLiftT.mk.{succ u2, succ u2} (Submodule.{u1, u2} R M _inst_1 _inst_3 _inst_4) (Set.{u2} M) (CoeTCₓ.coe.{succ u2, succ u2} (Submodule.{u1, u2} R M _inst_1 _inst_3 _inst_4) (Set.{u2} M) (SetLike.Set.hasCoeT.{u2, u2} (Submodule.{u1, u2} R M _inst_1 _inst_3 _inst_4) M (Submodule.setLike.{u1, u2} R M _inst_1 _inst_3 _inst_4)))) (iInf.{u2, u3} (Submodule.{u1, u2} R M _inst_1 _inst_3 _inst_4) (Submodule.hasInf.{u1, u2} R M _inst_1 _inst_3 _inst_4) ι (fun (i : ι) => p i))) (Set.iInter.{u2, u3} M ι (fun (i : ι) => (fun (a : Type.{u2}) (b : Type.{u2}) [self : HasLiftT.{succ u2, succ u2} a b] => self.0) (Submodule.{u1, u2} R M _inst_1 _inst_3 _inst_4) (Set.{u2} M) (HasLiftT.mk.{succ u2, succ u2} (Submodule.{u1, u2} R M _inst_1 _inst_3 _inst_4) (Set.{u2} M) (CoeTCₓ.coe.{succ u2, succ u2} (Submodule.{u1, u2} R M _inst_1 _inst_3 _inst_4) (Set.{u2} M) (SetLike.Set.hasCoeT.{u2, u2} (Submodule.{u1, u2} R M _inst_1 _inst_3 _inst_4) M (Submodule.setLike.{u1, u2} R M _inst_1 _inst_3 _inst_4)))) (p i)))
 but is expected to have type
-  forall {R : Type.{u2}} {M : Type.{u1}} [_inst_1 : Semiring.{u2} R] [_inst_3 : AddCommMonoid.{u1} M] [_inst_4 : Module.{u2, u1} R M _inst_1 _inst_3] {ι : Sort.{u3}} (p : ι -> (Submodule.{u2, u1} R M _inst_1 _inst_3 _inst_4)), Eq.{succ u1} (Set.{u1} M) (SetLike.coe.{u1, u1} (Submodule.{u2, u1} R M _inst_1 _inst_3 _inst_4) M (Submodule.setLike.{u2, u1} R M _inst_1 _inst_3 _inst_4) (infᵢ.{u1, u3} (Submodule.{u2, u1} R M _inst_1 _inst_3 _inst_4) (Submodule.instInfSetSubmodule.{u2, u1} R M _inst_1 _inst_3 _inst_4) ι (fun (i : ι) => p i))) (Set.interᵢ.{u1, u3} M ι (fun (i : ι) => SetLike.coe.{u1, u1} (Submodule.{u2, u1} R M _inst_1 _inst_3 _inst_4) M (Submodule.setLike.{u2, u1} R M _inst_1 _inst_3 _inst_4) (p i)))
-Case conversion may be inaccurate. Consider using '#align submodule.infi_coe Submodule.infᵢ_coeₓ'. -/
+  forall {R : Type.{u2}} {M : Type.{u1}} [_inst_1 : Semiring.{u2} R] [_inst_3 : AddCommMonoid.{u1} M] [_inst_4 : Module.{u2, u1} R M _inst_1 _inst_3] {ι : Sort.{u3}} (p : ι -> (Submodule.{u2, u1} R M _inst_1 _inst_3 _inst_4)), Eq.{succ u1} (Set.{u1} M) (SetLike.coe.{u1, u1} (Submodule.{u2, u1} R M _inst_1 _inst_3 _inst_4) M (Submodule.setLike.{u2, u1} R M _inst_1 _inst_3 _inst_4) (iInf.{u1, u3} (Submodule.{u2, u1} R M _inst_1 _inst_3 _inst_4) (Submodule.instInfSetSubmodule.{u2, u1} R M _inst_1 _inst_3 _inst_4) ι (fun (i : ι) => p i))) (Set.iInter.{u1, u3} M ι (fun (i : ι) => SetLike.coe.{u1, u1} (Submodule.{u2, u1} R M _inst_1 _inst_3 _inst_4) M (Submodule.setLike.{u2, u1} R M _inst_1 _inst_3 _inst_4) (p i)))
+Case conversion may be inaccurate. Consider using '#align submodule.infi_coe Submodule.iInf_coeₓ'. -/
 @[simp]
-theorem infᵢ_coe {ι} (p : ι → Submodule R M) : (↑(⨅ i, p i) : Set M) = ⋂ i, ↑(p i) := by
-  rw [infᵢ, Inf_coe] <;> ext a <;> simp <;> exact ⟨fun h i => h _ i rfl, fun h i x e => e ▸ h _⟩
-#align submodule.infi_coe Submodule.infᵢ_coe
+theorem iInf_coe {ι} (p : ι → Submodule R M) : (↑(⨅ i, p i) : Set M) = ⋂ i, ↑(p i) := by
+  rw [iInf, Inf_coe] <;> ext a <;> simp <;> exact ⟨fun h i => h _ i rfl, fun h i x e => e ▸ h _⟩
+#align submodule.infi_coe Submodule.iInf_coe
 
-/- warning: submodule.mem_Inf -> Submodule.mem_infₛ is a dubious translation:
+/- warning: submodule.mem_Inf -> Submodule.mem_sInf is a dubious translation:
 lean 3 declaration is
-  forall {R : Type.{u1}} {M : Type.{u2}} [_inst_1 : Semiring.{u1} R] [_inst_3 : AddCommMonoid.{u2} M] [_inst_4 : Module.{u1, u2} R M _inst_1 _inst_3] {S : Set.{u2} (Submodule.{u1, u2} R M _inst_1 _inst_3 _inst_4)} {x : M}, Iff (Membership.Mem.{u2, u2} M (Submodule.{u1, u2} R M _inst_1 _inst_3 _inst_4) (SetLike.hasMem.{u2, u2} (Submodule.{u1, u2} R M _inst_1 _inst_3 _inst_4) M (Submodule.setLike.{u1, u2} R M _inst_1 _inst_3 _inst_4)) x (InfSet.infₛ.{u2} (Submodule.{u1, u2} R M _inst_1 _inst_3 _inst_4) (Submodule.hasInf.{u1, u2} R M _inst_1 _inst_3 _inst_4) S)) (forall (p : Submodule.{u1, u2} R M _inst_1 _inst_3 _inst_4), (Membership.Mem.{u2, u2} (Submodule.{u1, u2} R M _inst_1 _inst_3 _inst_4) (Set.{u2} (Submodule.{u1, u2} R M _inst_1 _inst_3 _inst_4)) (Set.hasMem.{u2} (Submodule.{u1, u2} R M _inst_1 _inst_3 _inst_4)) p S) -> (Membership.Mem.{u2, u2} M (Submodule.{u1, u2} R M _inst_1 _inst_3 _inst_4) (SetLike.hasMem.{u2, u2} (Submodule.{u1, u2} R M _inst_1 _inst_3 _inst_4) M (Submodule.setLike.{u1, u2} R M _inst_1 _inst_3 _inst_4)) x p))
+  forall {R : Type.{u1}} {M : Type.{u2}} [_inst_1 : Semiring.{u1} R] [_inst_3 : AddCommMonoid.{u2} M] [_inst_4 : Module.{u1, u2} R M _inst_1 _inst_3] {S : Set.{u2} (Submodule.{u1, u2} R M _inst_1 _inst_3 _inst_4)} {x : M}, Iff (Membership.Mem.{u2, u2} M (Submodule.{u1, u2} R M _inst_1 _inst_3 _inst_4) (SetLike.hasMem.{u2, u2} (Submodule.{u1, u2} R M _inst_1 _inst_3 _inst_4) M (Submodule.setLike.{u1, u2} R M _inst_1 _inst_3 _inst_4)) x (InfSet.sInf.{u2} (Submodule.{u1, u2} R M _inst_1 _inst_3 _inst_4) (Submodule.hasInf.{u1, u2} R M _inst_1 _inst_3 _inst_4) S)) (forall (p : Submodule.{u1, u2} R M _inst_1 _inst_3 _inst_4), (Membership.Mem.{u2, u2} (Submodule.{u1, u2} R M _inst_1 _inst_3 _inst_4) (Set.{u2} (Submodule.{u1, u2} R M _inst_1 _inst_3 _inst_4)) (Set.hasMem.{u2} (Submodule.{u1, u2} R M _inst_1 _inst_3 _inst_4)) p S) -> (Membership.Mem.{u2, u2} M (Submodule.{u1, u2} R M _inst_1 _inst_3 _inst_4) (SetLike.hasMem.{u2, u2} (Submodule.{u1, u2} R M _inst_1 _inst_3 _inst_4) M (Submodule.setLike.{u1, u2} R M _inst_1 _inst_3 _inst_4)) x p))
 but is expected to have type
-  forall {R : Type.{u1}} {M : Type.{u2}} [_inst_1 : Semiring.{u1} R] [_inst_3 : AddCommMonoid.{u2} M] [_inst_4 : Module.{u1, u2} R M _inst_1 _inst_3] {S : Set.{u2} (Submodule.{u1, u2} R M _inst_1 _inst_3 _inst_4)} {x : M}, Iff (Membership.mem.{u2, u2} M (Submodule.{u1, u2} R M _inst_1 _inst_3 _inst_4) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} R M _inst_1 _inst_3 _inst_4) M (Submodule.setLike.{u1, u2} R M _inst_1 _inst_3 _inst_4)) x (InfSet.infₛ.{u2} (Submodule.{u1, u2} R M _inst_1 _inst_3 _inst_4) (Submodule.instInfSetSubmodule.{u1, u2} R M _inst_1 _inst_3 _inst_4) S)) (forall (p : Submodule.{u1, u2} R M _inst_1 _inst_3 _inst_4), (Membership.mem.{u2, u2} (Submodule.{u1, u2} R M _inst_1 _inst_3 _inst_4) (Set.{u2} (Submodule.{u1, u2} R M _inst_1 _inst_3 _inst_4)) (Set.instMembershipSet.{u2} (Submodule.{u1, u2} R M _inst_1 _inst_3 _inst_4)) p S) -> (Membership.mem.{u2, u2} M (Submodule.{u1, u2} R M _inst_1 _inst_3 _inst_4) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} R M _inst_1 _inst_3 _inst_4) M (Submodule.setLike.{u1, u2} R M _inst_1 _inst_3 _inst_4)) x p))
-Case conversion may be inaccurate. Consider using '#align submodule.mem_Inf Submodule.mem_infₛₓ'. -/
+  forall {R : Type.{u1}} {M : Type.{u2}} [_inst_1 : Semiring.{u1} R] [_inst_3 : AddCommMonoid.{u2} M] [_inst_4 : Module.{u1, u2} R M _inst_1 _inst_3] {S : Set.{u2} (Submodule.{u1, u2} R M _inst_1 _inst_3 _inst_4)} {x : M}, Iff (Membership.mem.{u2, u2} M (Submodule.{u1, u2} R M _inst_1 _inst_3 _inst_4) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} R M _inst_1 _inst_3 _inst_4) M (Submodule.setLike.{u1, u2} R M _inst_1 _inst_3 _inst_4)) x (InfSet.sInf.{u2} (Submodule.{u1, u2} R M _inst_1 _inst_3 _inst_4) (Submodule.instInfSetSubmodule.{u1, u2} R M _inst_1 _inst_3 _inst_4) S)) (forall (p : Submodule.{u1, u2} R M _inst_1 _inst_3 _inst_4), (Membership.mem.{u2, u2} (Submodule.{u1, u2} R M _inst_1 _inst_3 _inst_4) (Set.{u2} (Submodule.{u1, u2} R M _inst_1 _inst_3 _inst_4)) (Set.instMembershipSet.{u2} (Submodule.{u1, u2} R M _inst_1 _inst_3 _inst_4)) p S) -> (Membership.mem.{u2, u2} M (Submodule.{u1, u2} R M _inst_1 _inst_3 _inst_4) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} R M _inst_1 _inst_3 _inst_4) M (Submodule.setLike.{u1, u2} R M _inst_1 _inst_3 _inst_4)) x p))
+Case conversion may be inaccurate. Consider using '#align submodule.mem_Inf Submodule.mem_sInfₓ'. -/
 @[simp]
-theorem mem_infₛ {S : Set (Submodule R M)} {x : M} : x ∈ infₛ S ↔ ∀ p ∈ S, x ∈ p :=
-  Set.mem_interᵢ₂
-#align submodule.mem_Inf Submodule.mem_infₛ
+theorem mem_sInf {S : Set (Submodule R M)} {x : M} : x ∈ sInf S ↔ ∀ p ∈ S, x ∈ p :=
+  Set.mem_iInter₂
+#align submodule.mem_Inf Submodule.mem_sInf
 
-/- warning: submodule.mem_infi -> Submodule.mem_infᵢ is a dubious translation:
+/- warning: submodule.mem_infi -> Submodule.mem_iInf is a dubious translation:
 lean 3 declaration is
-  forall {R : Type.{u1}} {M : Type.{u2}} [_inst_1 : Semiring.{u1} R] [_inst_3 : AddCommMonoid.{u2} M] [_inst_4 : Module.{u1, u2} R M _inst_1 _inst_3] {ι : Sort.{u3}} (p : ι -> (Submodule.{u1, u2} R M _inst_1 _inst_3 _inst_4)) {x : M}, Iff (Membership.Mem.{u2, u2} M (Submodule.{u1, u2} R M _inst_1 _inst_3 _inst_4) (SetLike.hasMem.{u2, u2} (Submodule.{u1, u2} R M _inst_1 _inst_3 _inst_4) M (Submodule.setLike.{u1, u2} R M _inst_1 _inst_3 _inst_4)) x (infᵢ.{u2, u3} (Submodule.{u1, u2} R M _inst_1 _inst_3 _inst_4) (Submodule.hasInf.{u1, u2} R M _inst_1 _inst_3 _inst_4) ι (fun (i : ι) => p i))) (forall (i : ι), Membership.Mem.{u2, u2} M (Submodule.{u1, u2} R M _inst_1 _inst_3 _inst_4) (SetLike.hasMem.{u2, u2} (Submodule.{u1, u2} R M _inst_1 _inst_3 _inst_4) M (Submodule.setLike.{u1, u2} R M _inst_1 _inst_3 _inst_4)) x (p i))
+  forall {R : Type.{u1}} {M : Type.{u2}} [_inst_1 : Semiring.{u1} R] [_inst_3 : AddCommMonoid.{u2} M] [_inst_4 : Module.{u1, u2} R M _inst_1 _inst_3] {ι : Sort.{u3}} (p : ι -> (Submodule.{u1, u2} R M _inst_1 _inst_3 _inst_4)) {x : M}, Iff (Membership.Mem.{u2, u2} M (Submodule.{u1, u2} R M _inst_1 _inst_3 _inst_4) (SetLike.hasMem.{u2, u2} (Submodule.{u1, u2} R M _inst_1 _inst_3 _inst_4) M (Submodule.setLike.{u1, u2} R M _inst_1 _inst_3 _inst_4)) x (iInf.{u2, u3} (Submodule.{u1, u2} R M _inst_1 _inst_3 _inst_4) (Submodule.hasInf.{u1, u2} R M _inst_1 _inst_3 _inst_4) ι (fun (i : ι) => p i))) (forall (i : ι), Membership.Mem.{u2, u2} M (Submodule.{u1, u2} R M _inst_1 _inst_3 _inst_4) (SetLike.hasMem.{u2, u2} (Submodule.{u1, u2} R M _inst_1 _inst_3 _inst_4) M (Submodule.setLike.{u1, u2} R M _inst_1 _inst_3 _inst_4)) x (p i))
 but is expected to have type
-  forall {R : Type.{u2}} {M : Type.{u1}} [_inst_1 : Semiring.{u2} R] [_inst_3 : AddCommMonoid.{u1} M] [_inst_4 : Module.{u2, u1} R M _inst_1 _inst_3] {ι : Sort.{u3}} (p : ι -> (Submodule.{u2, u1} R M _inst_1 _inst_3 _inst_4)) {x : M}, Iff (Membership.mem.{u1, u1} M (Submodule.{u2, u1} R M _inst_1 _inst_3 _inst_4) (SetLike.instMembership.{u1, u1} (Submodule.{u2, u1} R M _inst_1 _inst_3 _inst_4) M (Submodule.setLike.{u2, u1} R M _inst_1 _inst_3 _inst_4)) x (infᵢ.{u1, u3} (Submodule.{u2, u1} R M _inst_1 _inst_3 _inst_4) (Submodule.instInfSetSubmodule.{u2, u1} R M _inst_1 _inst_3 _inst_4) ι (fun (i : ι) => p i))) (forall (i : ι), Membership.mem.{u1, u1} M (Submodule.{u2, u1} R M _inst_1 _inst_3 _inst_4) (SetLike.instMembership.{u1, u1} (Submodule.{u2, u1} R M _inst_1 _inst_3 _inst_4) M (Submodule.setLike.{u2, u1} R M _inst_1 _inst_3 _inst_4)) x (p i))
-Case conversion may be inaccurate. Consider using '#align submodule.mem_infi Submodule.mem_infᵢₓ'. -/
+  forall {R : Type.{u2}} {M : Type.{u1}} [_inst_1 : Semiring.{u2} R] [_inst_3 : AddCommMonoid.{u1} M] [_inst_4 : Module.{u2, u1} R M _inst_1 _inst_3] {ι : Sort.{u3}} (p : ι -> (Submodule.{u2, u1} R M _inst_1 _inst_3 _inst_4)) {x : M}, Iff (Membership.mem.{u1, u1} M (Submodule.{u2, u1} R M _inst_1 _inst_3 _inst_4) (SetLike.instMembership.{u1, u1} (Submodule.{u2, u1} R M _inst_1 _inst_3 _inst_4) M (Submodule.setLike.{u2, u1} R M _inst_1 _inst_3 _inst_4)) x (iInf.{u1, u3} (Submodule.{u2, u1} R M _inst_1 _inst_3 _inst_4) (Submodule.instInfSetSubmodule.{u2, u1} R M _inst_1 _inst_3 _inst_4) ι (fun (i : ι) => p i))) (forall (i : ι), Membership.mem.{u1, u1} M (Submodule.{u2, u1} R M _inst_1 _inst_3 _inst_4) (SetLike.instMembership.{u1, u1} (Submodule.{u2, u1} R M _inst_1 _inst_3 _inst_4) M (Submodule.setLike.{u2, u1} R M _inst_1 _inst_3 _inst_4)) x (p i))
+Case conversion may be inaccurate. Consider using '#align submodule.mem_infi Submodule.mem_iInfₓ'. -/
 @[simp]
-theorem mem_infᵢ {ι} (p : ι → Submodule R M) {x} : (x ∈ ⨅ i, p i) ↔ ∀ i, x ∈ p i := by
-  rw [← SetLike.mem_coe, infi_coe, Set.mem_interᵢ] <;> rfl
-#align submodule.mem_infi Submodule.mem_infᵢ
+theorem mem_iInf {ι} (p : ι → Submodule R M) {x} : (x ∈ ⨅ i, p i) ↔ ∀ i, x ∈ p i := by
+  rw [← SetLike.mem_coe, infi_coe, Set.mem_iInter] <;> rfl
+#align submodule.mem_infi Submodule.mem_iInf
 
 /- warning: submodule.mem_finset_inf -> Submodule.mem_finset_inf is a dubious translation:
 lean 3 declaration is
@@ -471,7 +471,7 @@ Case conversion may be inaccurate. Consider using '#align submodule.mem_finset_i
 @[simp]
 theorem mem_finset_inf {ι} {s : Finset ι} {p : ι → Submodule R M} {x : M} :
     x ∈ s.inf p ↔ ∀ i ∈ s, x ∈ p i := by
-  simp only [← SetLike.mem_coe, finset_inf_coe, Set.mem_interᵢ]
+  simp only [← SetLike.mem_coe, finset_inf_coe, Set.mem_iInter]
 #align submodule.mem_finset_inf Submodule.mem_finset_inf
 
 /- warning: submodule.mem_sup_left -> Submodule.mem_sup_left is a dubious translation:
@@ -517,55 +517,55 @@ theorem sub_mem_sup {R' M' : Type _} [Ring R'] [AddCommGroup M'] [Module R' M']
   exact add_mem_sup hs (neg_mem ht)
 #align submodule.sub_mem_sup Submodule.sub_mem_sup
 
-/- warning: submodule.mem_supr_of_mem -> Submodule.mem_supᵢ_of_mem is a dubious translation:
+/- warning: submodule.mem_supr_of_mem -> Submodule.mem_iSup_of_mem is a dubious translation:
 lean 3 declaration is
-  forall {R : Type.{u1}} {M : Type.{u2}} [_inst_1 : Semiring.{u1} R] [_inst_3 : AddCommMonoid.{u2} M] [_inst_4 : Module.{u1, u2} R M _inst_1 _inst_3] {ι : Sort.{u3}} {b : M} {p : ι -> (Submodule.{u1, u2} R M _inst_1 _inst_3 _inst_4)} (i : ι), (Membership.Mem.{u2, u2} M (Submodule.{u1, u2} R M _inst_1 _inst_3 _inst_4) (SetLike.hasMem.{u2, u2} (Submodule.{u1, u2} R M _inst_1 _inst_3 _inst_4) M (Submodule.setLike.{u1, u2} R M _inst_1 _inst_3 _inst_4)) b (p i)) -> (Membership.Mem.{u2, u2} M (Submodule.{u1, u2} R M _inst_1 _inst_3 _inst_4) (SetLike.hasMem.{u2, u2} (Submodule.{u1, u2} R M _inst_1 _inst_3 _inst_4) M (Submodule.setLike.{u1, u2} R M _inst_1 _inst_3 _inst_4)) b (supᵢ.{u2, u3} (Submodule.{u1, u2} R M _inst_1 _inst_3 _inst_4) (CompleteSemilatticeSup.toHasSup.{u2} (Submodule.{u1, u2} R M _inst_1 _inst_3 _inst_4) (CompleteLattice.toCompleteSemilatticeSup.{u2} (Submodule.{u1, u2} R M _inst_1 _inst_3 _inst_4) (Submodule.completeLattice.{u1, u2} R M _inst_1 _inst_3 _inst_4))) ι (fun (i : ι) => p i)))
+  forall {R : Type.{u1}} {M : Type.{u2}} [_inst_1 : Semiring.{u1} R] [_inst_3 : AddCommMonoid.{u2} M] [_inst_4 : Module.{u1, u2} R M _inst_1 _inst_3] {ι : Sort.{u3}} {b : M} {p : ι -> (Submodule.{u1, u2} R M _inst_1 _inst_3 _inst_4)} (i : ι), (Membership.Mem.{u2, u2} M (Submodule.{u1, u2} R M _inst_1 _inst_3 _inst_4) (SetLike.hasMem.{u2, u2} (Submodule.{u1, u2} R M _inst_1 _inst_3 _inst_4) M (Submodule.setLike.{u1, u2} R M _inst_1 _inst_3 _inst_4)) b (p i)) -> (Membership.Mem.{u2, u2} M (Submodule.{u1, u2} R M _inst_1 _inst_3 _inst_4) (SetLike.hasMem.{u2, u2} (Submodule.{u1, u2} R M _inst_1 _inst_3 _inst_4) M (Submodule.setLike.{u1, u2} R M _inst_1 _inst_3 _inst_4)) b (iSup.{u2, u3} (Submodule.{u1, u2} R M _inst_1 _inst_3 _inst_4) (CompleteSemilatticeSup.toHasSup.{u2} (Submodule.{u1, u2} R M _inst_1 _inst_3 _inst_4) (CompleteLattice.toCompleteSemilatticeSup.{u2} (Submodule.{u1, u2} R M _inst_1 _inst_3 _inst_4) (Submodule.completeLattice.{u1, u2} R M _inst_1 _inst_3 _inst_4))) ι (fun (i : ι) => p i)))
 but is expected to have type
-  forall {R : Type.{u2}} {M : Type.{u1}} [_inst_1 : Semiring.{u2} R] [_inst_3 : AddCommMonoid.{u1} M] [_inst_4 : Module.{u2, u1} R M _inst_1 _inst_3] {ι : Sort.{u3}} {b : M} {p : ι -> (Submodule.{u2, u1} R M _inst_1 _inst_3 _inst_4)} (i : ι), (Membership.mem.{u1, u1} M (Submodule.{u2, u1} R M _inst_1 _inst_3 _inst_4) (SetLike.instMembership.{u1, u1} (Submodule.{u2, u1} R M _inst_1 _inst_3 _inst_4) M (Submodule.setLike.{u2, u1} R M _inst_1 _inst_3 _inst_4)) b (p i)) -> (Membership.mem.{u1, u1} M (Submodule.{u2, u1} R M _inst_1 _inst_3 _inst_4) (SetLike.instMembership.{u1, u1} (Submodule.{u2, u1} R M _inst_1 _inst_3 _inst_4) M (Submodule.setLike.{u2, u1} R M _inst_1 _inst_3 _inst_4)) b (supᵢ.{u1, u3} (Submodule.{u2, u1} R M _inst_1 _inst_3 _inst_4) (CompleteLattice.toSupSet.{u1} (Submodule.{u2, u1} R M _inst_1 _inst_3 _inst_4) (Submodule.completeLattice.{u2, u1} R M _inst_1 _inst_3 _inst_4)) ι (fun (i : ι) => p i)))
-Case conversion may be inaccurate. Consider using '#align submodule.mem_supr_of_mem Submodule.mem_supᵢ_of_memₓ'. -/
-theorem mem_supᵢ_of_mem {ι : Sort _} {b : M} {p : ι → Submodule R M} (i : ι) (h : b ∈ p i) :
+  forall {R : Type.{u2}} {M : Type.{u1}} [_inst_1 : Semiring.{u2} R] [_inst_3 : AddCommMonoid.{u1} M] [_inst_4 : Module.{u2, u1} R M _inst_1 _inst_3] {ι : Sort.{u3}} {b : M} {p : ι -> (Submodule.{u2, u1} R M _inst_1 _inst_3 _inst_4)} (i : ι), (Membership.mem.{u1, u1} M (Submodule.{u2, u1} R M _inst_1 _inst_3 _inst_4) (SetLike.instMembership.{u1, u1} (Submodule.{u2, u1} R M _inst_1 _inst_3 _inst_4) M (Submodule.setLike.{u2, u1} R M _inst_1 _inst_3 _inst_4)) b (p i)) -> (Membership.mem.{u1, u1} M (Submodule.{u2, u1} R M _inst_1 _inst_3 _inst_4) (SetLike.instMembership.{u1, u1} (Submodule.{u2, u1} R M _inst_1 _inst_3 _inst_4) M (Submodule.setLike.{u2, u1} R M _inst_1 _inst_3 _inst_4)) b (iSup.{u1, u3} (Submodule.{u2, u1} R M _inst_1 _inst_3 _inst_4) (CompleteLattice.toSupSet.{u1} (Submodule.{u2, u1} R M _inst_1 _inst_3 _inst_4) (Submodule.completeLattice.{u2, u1} R M _inst_1 _inst_3 _inst_4)) ι (fun (i : ι) => p i)))
+Case conversion may be inaccurate. Consider using '#align submodule.mem_supr_of_mem Submodule.mem_iSup_of_memₓ'. -/
+theorem mem_iSup_of_mem {ι : Sort _} {b : M} {p : ι → Submodule R M} (i : ι) (h : b ∈ p i) :
     b ∈ ⨆ i, p i :=
-  have : p i ≤ ⨆ i, p i := le_supᵢ p i
+  have : p i ≤ ⨆ i, p i := le_iSup p i
   @this b h
-#align submodule.mem_supr_of_mem Submodule.mem_supᵢ_of_mem
+#align submodule.mem_supr_of_mem Submodule.mem_iSup_of_mem
 
 open BigOperators
 
-/- warning: submodule.sum_mem_supr -> Submodule.sum_mem_supᵢ is a dubious translation:
+/- warning: submodule.sum_mem_supr -> Submodule.sum_mem_iSup is a dubious translation:
 lean 3 declaration is
-  forall {R : Type.{u1}} {M : Type.{u2}} [_inst_1 : Semiring.{u1} R] [_inst_3 : AddCommMonoid.{u2} M] [_inst_4 : Module.{u1, u2} R M _inst_1 _inst_3] {ι : Type.{u3}} [_inst_8 : Fintype.{u3} ι] {f : ι -> M} {p : ι -> (Submodule.{u1, u2} R M _inst_1 _inst_3 _inst_4)}, (forall (i : ι), Membership.Mem.{u2, u2} M (Submodule.{u1, u2} R M _inst_1 _inst_3 _inst_4) (SetLike.hasMem.{u2, u2} (Submodule.{u1, u2} R M _inst_1 _inst_3 _inst_4) M (Submodule.setLike.{u1, u2} R M _inst_1 _inst_3 _inst_4)) (f i) (p i)) -> (Membership.Mem.{u2, u2} M (Submodule.{u1, u2} R M _inst_1 _inst_3 _inst_4) (SetLike.hasMem.{u2, u2} (Submodule.{u1, u2} R M _inst_1 _inst_3 _inst_4) M (Submodule.setLike.{u1, u2} R M _inst_1 _inst_3 _inst_4)) (Finset.sum.{u2, u3} M ι _inst_3 (Finset.univ.{u3} ι _inst_8) (fun (i : ι) => f i)) (supᵢ.{u2, succ u3} (Submodule.{u1, u2} R M _inst_1 _inst_3 _inst_4) (CompleteSemilatticeSup.toHasSup.{u2} (Submodule.{u1, u2} R M _inst_1 _inst_3 _inst_4) (CompleteLattice.toCompleteSemilatticeSup.{u2} (Submodule.{u1, u2} R M _inst_1 _inst_3 _inst_4) (Submodule.completeLattice.{u1, u2} R M _inst_1 _inst_3 _inst_4))) ι (fun (i : ι) => p i)))
+  forall {R : Type.{u1}} {M : Type.{u2}} [_inst_1 : Semiring.{u1} R] [_inst_3 : AddCommMonoid.{u2} M] [_inst_4 : Module.{u1, u2} R M _inst_1 _inst_3] {ι : Type.{u3}} [_inst_8 : Fintype.{u3} ι] {f : ι -> M} {p : ι -> (Submodule.{u1, u2} R M _inst_1 _inst_3 _inst_4)}, (forall (i : ι), Membership.Mem.{u2, u2} M (Submodule.{u1, u2} R M _inst_1 _inst_3 _inst_4) (SetLike.hasMem.{u2, u2} (Submodule.{u1, u2} R M _inst_1 _inst_3 _inst_4) M (Submodule.setLike.{u1, u2} R M _inst_1 _inst_3 _inst_4)) (f i) (p i)) -> (Membership.Mem.{u2, u2} M (Submodule.{u1, u2} R M _inst_1 _inst_3 _inst_4) (SetLike.hasMem.{u2, u2} (Submodule.{u1, u2} R M _inst_1 _inst_3 _inst_4) M (Submodule.setLike.{u1, u2} R M _inst_1 _inst_3 _inst_4)) (Finset.sum.{u2, u3} M ι _inst_3 (Finset.univ.{u3} ι _inst_8) (fun (i : ι) => f i)) (iSup.{u2, succ u3} (Submodule.{u1, u2} R M _inst_1 _inst_3 _inst_4) (CompleteSemilatticeSup.toHasSup.{u2} (Submodule.{u1, u2} R M _inst_1 _inst_3 _inst_4) (CompleteLattice.toCompleteSemilatticeSup.{u2} (Submodule.{u1, u2} R M _inst_1 _inst_3 _inst_4) (Submodule.completeLattice.{u1, u2} R M _inst_1 _inst_3 _inst_4))) ι (fun (i : ι) => p i)))
 but is expected to have type
-  forall {R : Type.{u2}} {M : Type.{u1}} [_inst_1 : Semiring.{u2} R] [_inst_3 : AddCommMonoid.{u1} M] [_inst_4 : Module.{u2, u1} R M _inst_1 _inst_3] {ι : Type.{u3}} [_inst_8 : Fintype.{u3} ι] {f : ι -> M} {p : ι -> (Submodule.{u2, u1} R M _inst_1 _inst_3 _inst_4)}, (forall (i : ι), Membership.mem.{u1, u1} M (Submodule.{u2, u1} R M _inst_1 _inst_3 _inst_4) (SetLike.instMembership.{u1, u1} (Submodule.{u2, u1} R M _inst_1 _inst_3 _inst_4) M (Submodule.setLike.{u2, u1} R M _inst_1 _inst_3 _inst_4)) (f i) (p i)) -> (Membership.mem.{u1, u1} M (Submodule.{u2, u1} R M _inst_1 _inst_3 _inst_4) (SetLike.instMembership.{u1, u1} (Submodule.{u2, u1} R M _inst_1 _inst_3 _inst_4) M (Submodule.setLike.{u2, u1} R M _inst_1 _inst_3 _inst_4)) (Finset.sum.{u1, u3} M ι _inst_3 (Finset.univ.{u3} ι _inst_8) (fun (i : ι) => f i)) (supᵢ.{u1, succ u3} (Submodule.{u2, u1} R M _inst_1 _inst_3 _inst_4) (CompleteLattice.toSupSet.{u1} (Submodule.{u2, u1} R M _inst_1 _inst_3 _inst_4) (Submodule.completeLattice.{u2, u1} R M _inst_1 _inst_3 _inst_4)) ι (fun (i : ι) => p i)))
-Case conversion may be inaccurate. Consider using '#align submodule.sum_mem_supr Submodule.sum_mem_supᵢₓ'. -/
-theorem sum_mem_supᵢ {ι : Type _} [Fintype ι] {f : ι → M} {p : ι → Submodule R M}
+  forall {R : Type.{u2}} {M : Type.{u1}} [_inst_1 : Semiring.{u2} R] [_inst_3 : AddCommMonoid.{u1} M] [_inst_4 : Module.{u2, u1} R M _inst_1 _inst_3] {ι : Type.{u3}} [_inst_8 : Fintype.{u3} ι] {f : ι -> M} {p : ι -> (Submodule.{u2, u1} R M _inst_1 _inst_3 _inst_4)}, (forall (i : ι), Membership.mem.{u1, u1} M (Submodule.{u2, u1} R M _inst_1 _inst_3 _inst_4) (SetLike.instMembership.{u1, u1} (Submodule.{u2, u1} R M _inst_1 _inst_3 _inst_4) M (Submodule.setLike.{u2, u1} R M _inst_1 _inst_3 _inst_4)) (f i) (p i)) -> (Membership.mem.{u1, u1} M (Submodule.{u2, u1} R M _inst_1 _inst_3 _inst_4) (SetLike.instMembership.{u1, u1} (Submodule.{u2, u1} R M _inst_1 _inst_3 _inst_4) M (Submodule.setLike.{u2, u1} R M _inst_1 _inst_3 _inst_4)) (Finset.sum.{u1, u3} M ι _inst_3 (Finset.univ.{u3} ι _inst_8) (fun (i : ι) => f i)) (iSup.{u1, succ u3} (Submodule.{u2, u1} R M _inst_1 _inst_3 _inst_4) (CompleteLattice.toSupSet.{u1} (Submodule.{u2, u1} R M _inst_1 _inst_3 _inst_4) (Submodule.completeLattice.{u2, u1} R M _inst_1 _inst_3 _inst_4)) ι (fun (i : ι) => p i)))
+Case conversion may be inaccurate. Consider using '#align submodule.sum_mem_supr Submodule.sum_mem_iSupₓ'. -/
+theorem sum_mem_iSup {ι : Type _} [Fintype ι] {f : ι → M} {p : ι → Submodule R M}
     (h : ∀ i, f i ∈ p i) : (∑ i, f i) ∈ ⨆ i, p i :=
-  sum_mem fun i hi => mem_supᵢ_of_mem i (h i)
-#align submodule.sum_mem_supr Submodule.sum_mem_supᵢ
+  sum_mem fun i hi => mem_iSup_of_mem i (h i)
+#align submodule.sum_mem_supr Submodule.sum_mem_iSup
 
-/- warning: submodule.sum_mem_bsupr -> Submodule.sum_mem_bsupᵢ is a dubious translation:
+/- warning: submodule.sum_mem_bsupr -> Submodule.sum_mem_biSup is a dubious translation:
 lean 3 declaration is
-  forall {R : Type.{u1}} {M : Type.{u2}} [_inst_1 : Semiring.{u1} R] [_inst_3 : AddCommMonoid.{u2} M] [_inst_4 : Module.{u1, u2} R M _inst_1 _inst_3] {ι : Type.{u3}} {s : Finset.{u3} ι} {f : ι -> M} {p : ι -> (Submodule.{u1, u2} R M _inst_1 _inst_3 _inst_4)}, (forall (i : ι), (Membership.Mem.{u3, u3} ι (Finset.{u3} ι) (Finset.hasMem.{u3} ι) i s) -> (Membership.Mem.{u2, u2} M (Submodule.{u1, u2} R M _inst_1 _inst_3 _inst_4) (SetLike.hasMem.{u2, u2} (Submodule.{u1, u2} R M _inst_1 _inst_3 _inst_4) M (Submodule.setLike.{u1, u2} R M _inst_1 _inst_3 _inst_4)) (f i) (p i))) -> (Membership.Mem.{u2, u2} M (Submodule.{u1, u2} R M _inst_1 _inst_3 _inst_4) (SetLike.hasMem.{u2, u2} (Submodule.{u1, u2} R M _inst_1 _inst_3 _inst_4) M (Submodule.setLike.{u1, u2} R M _inst_1 _inst_3 _inst_4)) (Finset.sum.{u2, u3} M ι _inst_3 s (fun (i : ι) => f i)) (supᵢ.{u2, succ u3} (Submodule.{u1, u2} R M _inst_1 _inst_3 _inst_4) (CompleteSemilatticeSup.toHasSup.{u2} (Submodule.{u1, u2} R M _inst_1 _inst_3 _inst_4) (CompleteLattice.toCompleteSemilatticeSup.{u2} (Submodule.{u1, u2} R M _inst_1 _inst_3 _inst_4) (Submodule.completeLattice.{u1, u2} R M _inst_1 _inst_3 _inst_4))) ι (fun (i : ι) => supᵢ.{u2, 0} (Submodule.{u1, u2} R M _inst_1 _inst_3 _inst_4) (CompleteSemilatticeSup.toHasSup.{u2} (Submodule.{u1, u2} R M _inst_1 _inst_3 _inst_4) (CompleteLattice.toCompleteSemilatticeSup.{u2} (Submodule.{u1, u2} R M _inst_1 _inst_3 _inst_4) (Submodule.completeLattice.{u1, u2} R M _inst_1 _inst_3 _inst_4))) (Membership.Mem.{u3, u3} ι (Finset.{u3} ι) (Finset.hasMem.{u3} ι) i s) (fun (H : Membership.Mem.{u3, u3} ι (Finset.{u3} ι) (Finset.hasMem.{u3} ι) i s) => p i))))
+  forall {R : Type.{u1}} {M : Type.{u2}} [_inst_1 : Semiring.{u1} R] [_inst_3 : AddCommMonoid.{u2} M] [_inst_4 : Module.{u1, u2} R M _inst_1 _inst_3] {ι : Type.{u3}} {s : Finset.{u3} ι} {f : ι -> M} {p : ι -> (Submodule.{u1, u2} R M _inst_1 _inst_3 _inst_4)}, (forall (i : ι), (Membership.Mem.{u3, u3} ι (Finset.{u3} ι) (Finset.hasMem.{u3} ι) i s) -> (Membership.Mem.{u2, u2} M (Submodule.{u1, u2} R M _inst_1 _inst_3 _inst_4) (SetLike.hasMem.{u2, u2} (Submodule.{u1, u2} R M _inst_1 _inst_3 _inst_4) M (Submodule.setLike.{u1, u2} R M _inst_1 _inst_3 _inst_4)) (f i) (p i))) -> (Membership.Mem.{u2, u2} M (Submodule.{u1, u2} R M _inst_1 _inst_3 _inst_4) (SetLike.hasMem.{u2, u2} (Submodule.{u1, u2} R M _inst_1 _inst_3 _inst_4) M (Submodule.setLike.{u1, u2} R M _inst_1 _inst_3 _inst_4)) (Finset.sum.{u2, u3} M ι _inst_3 s (fun (i : ι) => f i)) (iSup.{u2, succ u3} (Submodule.{u1, u2} R M _inst_1 _inst_3 _inst_4) (CompleteSemilatticeSup.toHasSup.{u2} (Submodule.{u1, u2} R M _inst_1 _inst_3 _inst_4) (CompleteLattice.toCompleteSemilatticeSup.{u2} (Submodule.{u1, u2} R M _inst_1 _inst_3 _inst_4) (Submodule.completeLattice.{u1, u2} R M _inst_1 _inst_3 _inst_4))) ι (fun (i : ι) => iSup.{u2, 0} (Submodule.{u1, u2} R M _inst_1 _inst_3 _inst_4) (CompleteSemilatticeSup.toHasSup.{u2} (Submodule.{u1, u2} R M _inst_1 _inst_3 _inst_4) (CompleteLattice.toCompleteSemilatticeSup.{u2} (Submodule.{u1, u2} R M _inst_1 _inst_3 _inst_4) (Submodule.completeLattice.{u1, u2} R M _inst_1 _inst_3 _inst_4))) (Membership.Mem.{u3, u3} ι (Finset.{u3} ι) (Finset.hasMem.{u3} ι) i s) (fun (H : Membership.Mem.{u3, u3} ι (Finset.{u3} ι) (Finset.hasMem.{u3} ι) i s) => p i))))
 but is expected to have type
-  forall {R : Type.{u2}} {M : Type.{u1}} [_inst_1 : Semiring.{u2} R] [_inst_3 : AddCommMonoid.{u1} M] [_inst_4 : Module.{u2, u1} R M _inst_1 _inst_3] {ι : Type.{u3}} {s : Finset.{u3} ι} {f : ι -> M} {p : ι -> (Submodule.{u2, u1} R M _inst_1 _inst_3 _inst_4)}, (forall (i : ι), (Membership.mem.{u3, u3} ι (Finset.{u3} ι) (Finset.instMembershipFinset.{u3} ι) i s) -> (Membership.mem.{u1, u1} M (Submodule.{u2, u1} R M _inst_1 _inst_3 _inst_4) (SetLike.instMembership.{u1, u1} (Submodule.{u2, u1} R M _inst_1 _inst_3 _inst_4) M (Submodule.setLike.{u2, u1} R M _inst_1 _inst_3 _inst_4)) (f i) (p i))) -> (Membership.mem.{u1, u1} M (Submodule.{u2, u1} R M _inst_1 _inst_3 _inst_4) (SetLike.instMembership.{u1, u1} (Submodule.{u2, u1} R M _inst_1 _inst_3 _inst_4) M (Submodule.setLike.{u2, u1} R M _inst_1 _inst_3 _inst_4)) (Finset.sum.{u1, u3} M ι _inst_3 s (fun (i : ι) => f i)) (supᵢ.{u1, succ u3} (Submodule.{u2, u1} R M _inst_1 _inst_3 _inst_4) (CompleteLattice.toSupSet.{u1} (Submodule.{u2, u1} R M _inst_1 _inst_3 _inst_4) (Submodule.completeLattice.{u2, u1} R M _inst_1 _inst_3 _inst_4)) ι (fun (i : ι) => supᵢ.{u1, 0} (Submodule.{u2, u1} R M _inst_1 _inst_3 _inst_4) (CompleteLattice.toSupSet.{u1} (Submodule.{u2, u1} R M _inst_1 _inst_3 _inst_4) (Submodule.completeLattice.{u2, u1} R M _inst_1 _inst_3 _inst_4)) (Membership.mem.{u3, u3} ι (Finset.{u3} ι) (Finset.instMembershipFinset.{u3} ι) i s) (fun (H : Membership.mem.{u3, u3} ι (Finset.{u3} ι) (Finset.instMembershipFinset.{u3} ι) i s) => p i))))
-Case conversion may be inaccurate. Consider using '#align submodule.sum_mem_bsupr Submodule.sum_mem_bsupᵢₓ'. -/
-theorem sum_mem_bsupᵢ {ι : Type _} {s : Finset ι} {f : ι → M} {p : ι → Submodule R M}
+  forall {R : Type.{u2}} {M : Type.{u1}} [_inst_1 : Semiring.{u2} R] [_inst_3 : AddCommMonoid.{u1} M] [_inst_4 : Module.{u2, u1} R M _inst_1 _inst_3] {ι : Type.{u3}} {s : Finset.{u3} ι} {f : ι -> M} {p : ι -> (Submodule.{u2, u1} R M _inst_1 _inst_3 _inst_4)}, (forall (i : ι), (Membership.mem.{u3, u3} ι (Finset.{u3} ι) (Finset.instMembershipFinset.{u3} ι) i s) -> (Membership.mem.{u1, u1} M (Submodule.{u2, u1} R M _inst_1 _inst_3 _inst_4) (SetLike.instMembership.{u1, u1} (Submodule.{u2, u1} R M _inst_1 _inst_3 _inst_4) M (Submodule.setLike.{u2, u1} R M _inst_1 _inst_3 _inst_4)) (f i) (p i))) -> (Membership.mem.{u1, u1} M (Submodule.{u2, u1} R M _inst_1 _inst_3 _inst_4) (SetLike.instMembership.{u1, u1} (Submodule.{u2, u1} R M _inst_1 _inst_3 _inst_4) M (Submodule.setLike.{u2, u1} R M _inst_1 _inst_3 _inst_4)) (Finset.sum.{u1, u3} M ι _inst_3 s (fun (i : ι) => f i)) (iSup.{u1, succ u3} (Submodule.{u2, u1} R M _inst_1 _inst_3 _inst_4) (CompleteLattice.toSupSet.{u1} (Submodule.{u2, u1} R M _inst_1 _inst_3 _inst_4) (Submodule.completeLattice.{u2, u1} R M _inst_1 _inst_3 _inst_4)) ι (fun (i : ι) => iSup.{u1, 0} (Submodule.{u2, u1} R M _inst_1 _inst_3 _inst_4) (CompleteLattice.toSupSet.{u1} (Submodule.{u2, u1} R M _inst_1 _inst_3 _inst_4) (Submodule.completeLattice.{u2, u1} R M _inst_1 _inst_3 _inst_4)) (Membership.mem.{u3, u3} ι (Finset.{u3} ι) (Finset.instMembershipFinset.{u3} ι) i s) (fun (H : Membership.mem.{u3, u3} ι (Finset.{u3} ι) (Finset.instMembershipFinset.{u3} ι) i s) => p i))))
+Case conversion may be inaccurate. Consider using '#align submodule.sum_mem_bsupr Submodule.sum_mem_biSupₓ'. -/
+theorem sum_mem_biSup {ι : Type _} {s : Finset ι} {f : ι → M} {p : ι → Submodule R M}
     (h : ∀ i ∈ s, f i ∈ p i) : (∑ i in s, f i) ∈ ⨆ i ∈ s, p i :=
-  sum_mem fun i hi => mem_supᵢ_of_mem i <| mem_supᵢ_of_mem hi (h i hi)
-#align submodule.sum_mem_bsupr Submodule.sum_mem_bsupᵢ
+  sum_mem fun i hi => mem_iSup_of_mem i <| mem_iSup_of_mem hi (h i hi)
+#align submodule.sum_mem_bsupr Submodule.sum_mem_biSup
 
 /-! Note that `submodule.mem_supr` is provided in `linear_algebra/basic.lean`. -/
 
 
-/- warning: submodule.mem_Sup_of_mem -> Submodule.mem_supₛ_of_mem is a dubious translation:
+/- warning: submodule.mem_Sup_of_mem -> Submodule.mem_sSup_of_mem is a dubious translation:
 lean 3 declaration is
-  forall {R : Type.{u1}} {M : Type.{u2}} [_inst_1 : Semiring.{u1} R] [_inst_3 : AddCommMonoid.{u2} M] [_inst_4 : Module.{u1, u2} R M _inst_1 _inst_3] {S : Set.{u2} (Submodule.{u1, u2} R M _inst_1 _inst_3 _inst_4)} {s : Submodule.{u1, u2} R M _inst_1 _inst_3 _inst_4}, (Membership.Mem.{u2, u2} (Submodule.{u1, u2} R M _inst_1 _inst_3 _inst_4) (Set.{u2} (Submodule.{u1, u2} R M _inst_1 _inst_3 _inst_4)) (Set.hasMem.{u2} (Submodule.{u1, u2} R M _inst_1 _inst_3 _inst_4)) s S) -> (forall {x : M}, (Membership.Mem.{u2, u2} M (Submodule.{u1, u2} R M _inst_1 _inst_3 _inst_4) (SetLike.hasMem.{u2, u2} (Submodule.{u1, u2} R M _inst_1 _inst_3 _inst_4) M (Submodule.setLike.{u1, u2} R M _inst_1 _inst_3 _inst_4)) x s) -> (Membership.Mem.{u2, u2} M (Submodule.{u1, u2} R M _inst_1 _inst_3 _inst_4) (SetLike.hasMem.{u2, u2} (Submodule.{u1, u2} R M _inst_1 _inst_3 _inst_4) M (Submodule.setLike.{u1, u2} R M _inst_1 _inst_3 _inst_4)) x (SupSet.supₛ.{u2} (Submodule.{u1, u2} R M _inst_1 _inst_3 _inst_4) (CompleteSemilatticeSup.toHasSup.{u2} (Submodule.{u1, u2} R M _inst_1 _inst_3 _inst_4) (CompleteLattice.toCompleteSemilatticeSup.{u2} (Submodule.{u1, u2} R M _inst_1 _inst_3 _inst_4) (Submodule.completeLattice.{u1, u2} R M _inst_1 _inst_3 _inst_4))) S)))
+  forall {R : Type.{u1}} {M : Type.{u2}} [_inst_1 : Semiring.{u1} R] [_inst_3 : AddCommMonoid.{u2} M] [_inst_4 : Module.{u1, u2} R M _inst_1 _inst_3] {S : Set.{u2} (Submodule.{u1, u2} R M _inst_1 _inst_3 _inst_4)} {s : Submodule.{u1, u2} R M _inst_1 _inst_3 _inst_4}, (Membership.Mem.{u2, u2} (Submodule.{u1, u2} R M _inst_1 _inst_3 _inst_4) (Set.{u2} (Submodule.{u1, u2} R M _inst_1 _inst_3 _inst_4)) (Set.hasMem.{u2} (Submodule.{u1, u2} R M _inst_1 _inst_3 _inst_4)) s S) -> (forall {x : M}, (Membership.Mem.{u2, u2} M (Submodule.{u1, u2} R M _inst_1 _inst_3 _inst_4) (SetLike.hasMem.{u2, u2} (Submodule.{u1, u2} R M _inst_1 _inst_3 _inst_4) M (Submodule.setLike.{u1, u2} R M _inst_1 _inst_3 _inst_4)) x s) -> (Membership.Mem.{u2, u2} M (Submodule.{u1, u2} R M _inst_1 _inst_3 _inst_4) (SetLike.hasMem.{u2, u2} (Submodule.{u1, u2} R M _inst_1 _inst_3 _inst_4) M (Submodule.setLike.{u1, u2} R M _inst_1 _inst_3 _inst_4)) x (SupSet.sSup.{u2} (Submodule.{u1, u2} R M _inst_1 _inst_3 _inst_4) (CompleteSemilatticeSup.toHasSup.{u2} (Submodule.{u1, u2} R M _inst_1 _inst_3 _inst_4) (CompleteLattice.toCompleteSemilatticeSup.{u2} (Submodule.{u1, u2} R M _inst_1 _inst_3 _inst_4) (Submodule.completeLattice.{u1, u2} R M _inst_1 _inst_3 _inst_4))) S)))
 but is expected to have type
-  forall {R : Type.{u1}} {M : Type.{u2}} [_inst_1 : Semiring.{u1} R] [_inst_3 : AddCommMonoid.{u2} M] [_inst_4 : Module.{u1, u2} R M _inst_1 _inst_3] {S : Set.{u2} (Submodule.{u1, u2} R M _inst_1 _inst_3 _inst_4)} {s : Submodule.{u1, u2} R M _inst_1 _inst_3 _inst_4}, (Membership.mem.{u2, u2} (Submodule.{u1, u2} R M _inst_1 _inst_3 _inst_4) (Set.{u2} (Submodule.{u1, u2} R M _inst_1 _inst_3 _inst_4)) (Set.instMembershipSet.{u2} (Submodule.{u1, u2} R M _inst_1 _inst_3 _inst_4)) s S) -> (forall {x : M}, (Membership.mem.{u2, u2} M (Submodule.{u1, u2} R M _inst_1 _inst_3 _inst_4) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} R M _inst_1 _inst_3 _inst_4) M (Submodule.setLike.{u1, u2} R M _inst_1 _inst_3 _inst_4)) x s) -> (Membership.mem.{u2, u2} M (Submodule.{u1, u2} R M _inst_1 _inst_3 _inst_4) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} R M _inst_1 _inst_3 _inst_4) M (Submodule.setLike.{u1, u2} R M _inst_1 _inst_3 _inst_4)) x (SupSet.supₛ.{u2} (Submodule.{u1, u2} R M _inst_1 _inst_3 _inst_4) (CompleteLattice.toSupSet.{u2} (Submodule.{u1, u2} R M _inst_1 _inst_3 _inst_4) (Submodule.completeLattice.{u1, u2} R M _inst_1 _inst_3 _inst_4)) S)))
-Case conversion may be inaccurate. Consider using '#align submodule.mem_Sup_of_mem Submodule.mem_supₛ_of_memₓ'. -/
-theorem mem_supₛ_of_mem {S : Set (Submodule R M)} {s : Submodule R M} (hs : s ∈ S) :
-    ∀ {x : M}, x ∈ s → x ∈ supₛ S :=
-  show s ≤ supₛ S from le_supₛ hs
-#align submodule.mem_Sup_of_mem Submodule.mem_supₛ_of_mem
+  forall {R : Type.{u1}} {M : Type.{u2}} [_inst_1 : Semiring.{u1} R] [_inst_3 : AddCommMonoid.{u2} M] [_inst_4 : Module.{u1, u2} R M _inst_1 _inst_3] {S : Set.{u2} (Submodule.{u1, u2} R M _inst_1 _inst_3 _inst_4)} {s : Submodule.{u1, u2} R M _inst_1 _inst_3 _inst_4}, (Membership.mem.{u2, u2} (Submodule.{u1, u2} R M _inst_1 _inst_3 _inst_4) (Set.{u2} (Submodule.{u1, u2} R M _inst_1 _inst_3 _inst_4)) (Set.instMembershipSet.{u2} (Submodule.{u1, u2} R M _inst_1 _inst_3 _inst_4)) s S) -> (forall {x : M}, (Membership.mem.{u2, u2} M (Submodule.{u1, u2} R M _inst_1 _inst_3 _inst_4) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} R M _inst_1 _inst_3 _inst_4) M (Submodule.setLike.{u1, u2} R M _inst_1 _inst_3 _inst_4)) x s) -> (Membership.mem.{u2, u2} M (Submodule.{u1, u2} R M _inst_1 _inst_3 _inst_4) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} R M _inst_1 _inst_3 _inst_4) M (Submodule.setLike.{u1, u2} R M _inst_1 _inst_3 _inst_4)) x (SupSet.sSup.{u2} (Submodule.{u1, u2} R M _inst_1 _inst_3 _inst_4) (CompleteLattice.toSupSet.{u2} (Submodule.{u1, u2} R M _inst_1 _inst_3 _inst_4) (Submodule.completeLattice.{u1, u2} R M _inst_1 _inst_3 _inst_4)) S)))
+Case conversion may be inaccurate. Consider using '#align submodule.mem_Sup_of_mem Submodule.mem_sSup_of_memₓ'. -/
+theorem mem_sSup_of_mem {S : Set (Submodule R M)} {s : Submodule R M} (hs : s ∈ S) :
+    ∀ {x : M}, x ∈ s → x ∈ sSup S :=
+  show s ≤ sSup S from le_sSup hs
+#align submodule.mem_Sup_of_mem Submodule.mem_sSup_of_mem
 
 /- warning: submodule.disjoint_def -> Submodule.disjoint_def is a dubious translation:
 lean 3 declaration is

mathlib commit https://github.com/leanprover-community/mathlib/commit/730c6d4cab72b9d84fcfb9e95e8796e9cd8f40ba

@@ -623,7 +623,7 @@ def AddSubmonoid.toNatSubmodule : AddSubmonoid M ≃o Submodule ℕ M
 lean 3 declaration is
   forall {M : Type.{u1}} [_inst_3 : AddCommMonoid.{u1} M], Eq.{succ u1} ((Submodule.{0, u1} Nat M Nat.semiring _inst_3 (AddCommMonoid.natModule.{u1} M _inst_3)) -> (AddSubmonoid.{u1} M (AddMonoid.toAddZeroClass.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3)))) (coeFn.{succ u1, succ u1} (OrderIso.{u1, u1} (Submodule.{0, u1} Nat M Nat.semiring _inst_3 (AddCommMonoid.natModule.{u1} M _inst_3)) (AddSubmonoid.{u1} M (AddMonoid.toAddZeroClass.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3))) (Preorder.toLE.{u1} (Submodule.{0, u1} Nat M Nat.semiring _inst_3 (AddCommMonoid.natModule.{u1} M _inst_3)) (PartialOrder.toPreorder.{u1} (Submodule.{0, u1} Nat M Nat.semiring _inst_3 (AddCommMonoid.natModule.{u1} M _inst_3)) (CompleteSemilatticeInf.toPartialOrder.{u1} (Submodule.{0, u1} Nat M Nat.semiring _inst_3 (AddCommMonoid.natModule.{u1} M _inst_3)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (Submodule.{0, u1} Nat M Nat.semiring _inst_3 (AddCommMonoid.natModule.{u1} M _inst_3)) (Submodule.completeLattice.{0, u1} Nat M Nat.semiring _inst_3 (AddCommMonoid.natModule.{u1} M _inst_3)))))) (Preorder.toLE.{u1} (AddSubmonoid.{u1} M (AddMonoid.toAddZeroClass.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3))) (PartialOrder.toPreorder.{u1} (AddSubmonoid.{u1} M (AddMonoid.toAddZeroClass.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3))) (CompleteSemilatticeInf.toPartialOrder.{u1} (AddSubmonoid.{u1} M (AddMonoid.toAddZeroClass.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3))) (CompleteLattice.toCompleteSemilatticeInf.{u1} (AddSubmonoid.{u1} M (AddMonoid.toAddZeroClass.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3))) (AddSubmonoid.completeLattice.{u1} M (AddMonoid.toAddZeroClass.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3)))))))) (fun (_x : RelIso.{u1, u1} (Submodule.{0, u1} Nat M Nat.semiring _inst_3 (AddCommMonoid.natModule.{u1} M _inst_3)) (AddSubmonoid.{u1} M (AddMonoid.toAddZeroClass.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3))) (LE.le.{u1} (Submodule.{0, u1} Nat M Nat.semiring _inst_3 (AddCommMonoid.natModule.{u1} M _inst_3)) (Preorder.toLE.{u1} (Submodule.{0, u1} Nat M Nat.semiring _inst_3 (AddCommMonoid.natModule.{u1} M _inst_3)) (PartialOrder.toPreorder.{u1} (Submodule.{0, u1} Nat M Nat.semiring _inst_3 (AddCommMonoid.natModule.{u1} M _inst_3)) (CompleteSemilatticeInf.toPartialOrder.{u1} (Submodule.{0, u1} Nat M Nat.semiring _inst_3 (AddCommMonoid.natModule.{u1} M _inst_3)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (Submodule.{0, u1} Nat M Nat.semiring _inst_3 (AddCommMonoid.natModule.{u1} M _inst_3)) (Submodule.completeLattice.{0, u1} Nat M Nat.semiring _inst_3 (AddCommMonoid.natModule.{u1} M _inst_3))))))) (LE.le.{u1} (AddSubmonoid.{u1} M (AddMonoid.toAddZeroClass.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3))) (Preorder.toLE.{u1} (AddSubmonoid.{u1} M (AddMonoid.toAddZeroClass.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3))) (PartialOrder.toPreorder.{u1} (AddSubmonoid.{u1} M (AddMonoid.toAddZeroClass.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3))) (CompleteSemilatticeInf.toPartialOrder.{u1} (AddSubmonoid.{u1} M (AddMonoid.toAddZeroClass.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3))) (CompleteLattice.toCompleteSemilatticeInf.{u1} (AddSubmonoid.{u1} M (AddMonoid.toAddZeroClass.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3))) (AddSubmonoid.completeLattice.{u1} M (AddMonoid.toAddZeroClass.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3))))))))) => (Submodule.{0, u1} Nat M Nat.semiring _inst_3 (AddCommMonoid.natModule.{u1} M _inst_3)) -> (AddSubmonoid.{u1} M (AddMonoid.toAddZeroClass.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3)))) (RelIso.hasCoeToFun.{u1, u1} (Submodule.{0, u1} Nat M Nat.semiring _inst_3 (AddCommMonoid.natModule.{u1} M _inst_3)) (AddSubmonoid.{u1} M (AddMonoid.toAddZeroClass.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3))) (LE.le.{u1} (Submodule.{0, u1} Nat M Nat.semiring _inst_3 (AddCommMonoid.natModule.{u1} M _inst_3)) (Preorder.toLE.{u1} (Submodule.{0, u1} Nat M Nat.semiring _inst_3 (AddCommMonoid.natModule.{u1} M _inst_3)) (PartialOrder.toPreorder.{u1} (Submodule.{0, u1} Nat M Nat.semiring _inst_3 (AddCommMonoid.natModule.{u1} M _inst_3)) (CompleteSemilatticeInf.toPartialOrder.{u1} (Submodule.{0, u1} Nat M Nat.semiring _inst_3 (AddCommMonoid.natModule.{u1} M _inst_3)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (Submodule.{0, u1} Nat M Nat.semiring _inst_3 (AddCommMonoid.natModule.{u1} M _inst_3)) (Submodule.completeLattice.{0, u1} Nat M Nat.semiring _inst_3 (AddCommMonoid.natModule.{u1} M _inst_3))))))) (LE.le.{u1} (AddSubmonoid.{u1} M (AddMonoid.toAddZeroClass.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3))) (Preorder.toLE.{u1} (AddSubmonoid.{u1} M (AddMonoid.toAddZeroClass.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3))) (PartialOrder.toPreorder.{u1} (AddSubmonoid.{u1} M (AddMonoid.toAddZeroClass.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3))) (CompleteSemilatticeInf.toPartialOrder.{u1} (AddSubmonoid.{u1} M (AddMonoid.toAddZeroClass.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3))) (CompleteLattice.toCompleteSemilatticeInf.{u1} (AddSubmonoid.{u1} M (AddMonoid.toAddZeroClass.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3))) (AddSubmonoid.completeLattice.{u1} M (AddMonoid.toAddZeroClass.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3))))))))) (OrderIso.symm.{u1, u1} (AddSubmonoid.{u1} M (AddMonoid.toAddZeroClass.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3))) (Submodule.{0, u1} Nat M Nat.semiring _inst_3 (AddCommMonoid.natModule.{u1} M _inst_3)) (Preorder.toLE.{u1} (AddSubmonoid.{u1} M (AddMonoid.toAddZeroClass.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3))) (PartialOrder.toPreorder.{u1} (AddSubmonoid.{u1} M (AddMonoid.toAddZeroClass.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3))) (CompleteSemilatticeInf.toPartialOrder.{u1} (AddSubmonoid.{u1} M (AddMonoid.toAddZeroClass.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3))) (CompleteLattice.toCompleteSemilatticeInf.{u1} (AddSubmonoid.{u1} M (AddMonoid.toAddZeroClass.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3))) (AddSubmonoid.completeLattice.{u1} M (AddMonoid.toAddZeroClass.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3))))))) (Preorder.toLE.{u1} (Submodule.{0, u1} Nat M Nat.semiring _inst_3 (AddCommMonoid.natModule.{u1} M _inst_3)) (PartialOrder.toPreorder.{u1} (Submodule.{0, u1} Nat M Nat.semiring _inst_3 (AddCommMonoid.natModule.{u1} M _inst_3)) (CompleteSemilatticeInf.toPartialOrder.{u1} (Submodule.{0, u1} Nat M Nat.semiring _inst_3 (AddCommMonoid.natModule.{u1} M _inst_3)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (Submodule.{0, u1} Nat M Nat.semiring _inst_3 (AddCommMonoid.natModule.{u1} M _inst_3)) (Submodule.completeLattice.{0, u1} Nat M Nat.semiring _inst_3 (AddCommMonoid.natModule.{u1} M _inst_3)))))) (AddSubmonoid.toNatSubmodule.{u1} M _inst_3))) (Submodule.toAddSubmonoid.{0, u1} Nat M Nat.semiring _inst_3 (AddCommMonoid.natModule.{u1} M _inst_3))
 but is expected to have type
-  forall {M : Type.{u1}} [_inst_3 : AddCommMonoid.{u1} M], Eq.{succ u1} (forall (ᾰ : Submodule.{0, u1} Nat M Nat.semiring _inst_3 (AddCommMonoid.natModule.{u1} M _inst_3)), (fun (x._@.Mathlib.Data.FunLike.Embedding._hyg.19 : Submodule.{0, u1} Nat M Nat.semiring _inst_3 (AddCommMonoid.natModule.{u1} M _inst_3)) => AddSubmonoid.{u1} M (AddMonoid.toAddZeroClass.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3))) ᾰ) (FunLike.coe.{succ u1, succ u1, succ u1} (Function.Embedding.{succ u1, succ u1} (Submodule.{0, u1} Nat M Nat.semiring _inst_3 (AddCommMonoid.natModule.{u1} M _inst_3)) (AddSubmonoid.{u1} M (AddMonoid.toAddZeroClass.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3)))) (Submodule.{0, u1} Nat M Nat.semiring _inst_3 (AddCommMonoid.natModule.{u1} M _inst_3)) (fun (_x : Submodule.{0, u1} Nat M Nat.semiring _inst_3 (AddCommMonoid.natModule.{u1} M _inst_3)) => (fun (x._@.Mathlib.Data.FunLike.Embedding._hyg.19 : Submodule.{0, u1} Nat M Nat.semiring _inst_3 (AddCommMonoid.natModule.{u1} M _inst_3)) => AddSubmonoid.{u1} M (AddMonoid.toAddZeroClass.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3))) _x) (EmbeddingLike.toFunLike.{succ u1, succ u1, succ u1} (Function.Embedding.{succ u1, succ u1} (Submodule.{0, u1} Nat M Nat.semiring _inst_3 (AddCommMonoid.natModule.{u1} M _inst_3)) (AddSubmonoid.{u1} M (AddMonoid.toAddZeroClass.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3)))) (Submodule.{0, u1} Nat M Nat.semiring _inst_3 (AddCommMonoid.natModule.{u1} M _inst_3)) (AddSubmonoid.{u1} M (AddMonoid.toAddZeroClass.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3))) (Function.instEmbeddingLikeEmbedding.{succ u1, succ u1} (Submodule.{0, u1} Nat M Nat.semiring _inst_3 (AddCommMonoid.natModule.{u1} M _inst_3)) (AddSubmonoid.{u1} M (AddMonoid.toAddZeroClass.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3))))) (RelEmbedding.toEmbedding.{u1, u1} (Submodule.{0, u1} Nat M Nat.semiring _inst_3 (AddCommMonoid.natModule.{u1} M _inst_3)) (AddSubmonoid.{u1} M (AddMonoid.toAddZeroClass.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3))) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1281 : Submodule.{0, u1} Nat M Nat.semiring _inst_3 (AddCommMonoid.natModule.{u1} M _inst_3)) (x._@.Mathlib.Order.Hom.Basic._hyg.1283 : Submodule.{0, u1} Nat M Nat.semiring _inst_3 (AddCommMonoid.natModule.{u1} M _inst_3)) => LE.le.{u1} (Submodule.{0, u1} Nat M Nat.semiring _inst_3 (AddCommMonoid.natModule.{u1} M _inst_3)) (Preorder.toLE.{u1} (Submodule.{0, u1} Nat M Nat.semiring _inst_3 (AddCommMonoid.natModule.{u1} M _inst_3)) (PartialOrder.toPreorder.{u1} (Submodule.{0, u1} Nat M Nat.semiring _inst_3 (AddCommMonoid.natModule.{u1} M _inst_3)) (CompleteSemilatticeInf.toPartialOrder.{u1} (Submodule.{0, u1} Nat M Nat.semiring _inst_3 (AddCommMonoid.natModule.{u1} M _inst_3)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (Submodule.{0, u1} Nat M Nat.semiring _inst_3 (AddCommMonoid.natModule.{u1} M _inst_3)) (Submodule.completeLattice.{0, u1} Nat M Nat.semiring _inst_3 (AddCommMonoid.natModule.{u1} M _inst_3)))))) x._@.Mathlib.Order.Hom.Basic._hyg.1281 x._@.Mathlib.Order.Hom.Basic._hyg.1283) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1296 : AddSubmonoid.{u1} M (AddMonoid.toAddZeroClass.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3))) (x._@.Mathlib.Order.Hom.Basic._hyg.1298 : AddSubmonoid.{u1} M (AddMonoid.toAddZeroClass.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3))) => LE.le.{u1} (AddSubmonoid.{u1} M (AddMonoid.toAddZeroClass.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3))) (Preorder.toLE.{u1} (AddSubmonoid.{u1} M (AddMonoid.toAddZeroClass.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3))) (PartialOrder.toPreorder.{u1} (AddSubmonoid.{u1} M (AddMonoid.toAddZeroClass.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3))) (CompleteSemilatticeInf.toPartialOrder.{u1} (AddSubmonoid.{u1} M (AddMonoid.toAddZeroClass.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3))) (CompleteLattice.toCompleteSemilatticeInf.{u1} (AddSubmonoid.{u1} M (AddMonoid.toAddZeroClass.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3))) (AddSubmonoid.instCompleteLatticeAddSubmonoid.{u1} M (AddMonoid.toAddZeroClass.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3))))))) x._@.Mathlib.Order.Hom.Basic._hyg.1296 x._@.Mathlib.Order.Hom.Basic._hyg.1298) (RelIso.toRelEmbedding.{u1, u1} (Submodule.{0, u1} Nat M Nat.semiring _inst_3 (AddCommMonoid.natModule.{u1} M _inst_3)) (AddSubmonoid.{u1} M (AddMonoid.toAddZeroClass.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3))) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1281 : Submodule.{0, u1} Nat M Nat.semiring _inst_3 (AddCommMonoid.natModule.{u1} M _inst_3)) (x._@.Mathlib.Order.Hom.Basic._hyg.1283 : Submodule.{0, u1} Nat M Nat.semiring _inst_3 (AddCommMonoid.natModule.{u1} M _inst_3)) => LE.le.{u1} (Submodule.{0, u1} Nat M Nat.semiring _inst_3 (AddCommMonoid.natModule.{u1} M _inst_3)) (Preorder.toLE.{u1} (Submodule.{0, u1} Nat M Nat.semiring _inst_3 (AddCommMonoid.natModule.{u1} M _inst_3)) (PartialOrder.toPreorder.{u1} (Submodule.{0, u1} Nat M Nat.semiring _inst_3 (AddCommMonoid.natModule.{u1} M _inst_3)) (CompleteSemilatticeInf.toPartialOrder.{u1} (Submodule.{0, u1} Nat M Nat.semiring _inst_3 (AddCommMonoid.natModule.{u1} M _inst_3)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (Submodule.{0, u1} Nat M Nat.semiring _inst_3 (AddCommMonoid.natModule.{u1} M _inst_3)) (Submodule.completeLattice.{0, u1} Nat M Nat.semiring _inst_3 (AddCommMonoid.natModule.{u1} M _inst_3)))))) x._@.Mathlib.Order.Hom.Basic._hyg.1281 x._@.Mathlib.Order.Hom.Basic._hyg.1283) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1296 : AddSubmonoid.{u1} M (AddMonoid.toAddZeroClass.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3))) (x._@.Mathlib.Order.Hom.Basic._hyg.1298 : AddSubmonoid.{u1} M (AddMonoid.toAddZeroClass.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3))) => LE.le.{u1} (AddSubmonoid.{u1} M (AddMonoid.toAddZeroClass.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3))) (Preorder.toLE.{u1} (AddSubmonoid.{u1} M (AddMonoid.toAddZeroClass.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3))) (PartialOrder.toPreorder.{u1} (AddSubmonoid.{u1} M (AddMonoid.toAddZeroClass.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3))) (CompleteSemilatticeInf.toPartialOrder.{u1} (AddSubmonoid.{u1} M (AddMonoid.toAddZeroClass.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3))) (CompleteLattice.toCompleteSemilatticeInf.{u1} (AddSubmonoid.{u1} M (AddMonoid.toAddZeroClass.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3))) (AddSubmonoid.instCompleteLatticeAddSubmonoid.{u1} M (AddMonoid.toAddZeroClass.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3))))))) x._@.Mathlib.Order.Hom.Basic._hyg.1296 x._@.Mathlib.Order.Hom.Basic._hyg.1298) (OrderIso.symm.{u1, u1} (AddSubmonoid.{u1} M (AddMonoid.toAddZeroClass.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3))) (Submodule.{0, u1} Nat M Nat.semiring _inst_3 (AddCommMonoid.natModule.{u1} M _inst_3)) (Preorder.toLE.{u1} (AddSubmonoid.{u1} M (AddMonoid.toAddZeroClass.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3))) (PartialOrder.toPreorder.{u1} (AddSubmonoid.{u1} M (AddMonoid.toAddZeroClass.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3))) (CompleteSemilatticeInf.toPartialOrder.{u1} (AddSubmonoid.{u1} M (AddMonoid.toAddZeroClass.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3))) (CompleteLattice.toCompleteSemilatticeInf.{u1} (AddSubmonoid.{u1} M (AddMonoid.toAddZeroClass.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3))) (AddSubmonoid.instCompleteLatticeAddSubmonoid.{u1} M (AddMonoid.toAddZeroClass.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3))))))) (Preorder.toLE.{u1} (Submodule.{0, u1} Nat M Nat.semiring _inst_3 (AddCommMonoid.natModule.{u1} M _inst_3)) (PartialOrder.toPreorder.{u1} (Submodule.{0, u1} Nat M Nat.semiring _inst_3 (AddCommMonoid.natModule.{u1} M _inst_3)) (CompleteSemilatticeInf.toPartialOrder.{u1} (Submodule.{0, u1} Nat M Nat.semiring _inst_3 (AddCommMonoid.natModule.{u1} M _inst_3)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (Submodule.{0, u1} Nat M Nat.semiring _inst_3 (AddCommMonoid.natModule.{u1} M _inst_3)) (Submodule.completeLattice.{0, u1} Nat M Nat.semiring _inst_3 (AddCommMonoid.natModule.{u1} M _inst_3)))))) (AddSubmonoid.toNatSubmodule.{u1} M _inst_3))))) (Submodule.toAddSubmonoid.{0, u1} Nat M Nat.semiring _inst_3 (AddCommMonoid.natModule.{u1} M _inst_3))
+  forall {M : Type.{u1}} [_inst_3 : AddCommMonoid.{u1} M], Eq.{succ u1} ((Submodule.{0, u1} Nat M Nat.semiring _inst_3 (AddCommMonoid.natModule.{u1} M _inst_3)) -> (AddSubmonoid.{u1} M (AddMonoid.toAddZeroClass.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3)))) (FunLike.coe.{succ u1, succ u1, succ u1} (RelIso.{u1, u1} (Submodule.{0, u1} Nat M Nat.semiring _inst_3 (AddCommMonoid.natModule.{u1} M _inst_3)) (AddSubmonoid.{u1} M (AddMonoid.toAddZeroClass.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3))) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1281 : Submodule.{0, u1} Nat M Nat.semiring _inst_3 (AddCommMonoid.natModule.{u1} M _inst_3)) (x._@.Mathlib.Order.Hom.Basic._hyg.1283 : Submodule.{0, u1} Nat M Nat.semiring _inst_3 (AddCommMonoid.natModule.{u1} M _inst_3)) => LE.le.{u1} (Submodule.{0, u1} Nat M Nat.semiring _inst_3 (AddCommMonoid.natModule.{u1} M _inst_3)) (Preorder.toLE.{u1} (Submodule.{0, u1} Nat M Nat.semiring _inst_3 (AddCommMonoid.natModule.{u1} M _inst_3)) (PartialOrder.toPreorder.{u1} (Submodule.{0, u1} Nat M Nat.semiring _inst_3 (AddCommMonoid.natModule.{u1} M _inst_3)) (CompleteSemilatticeInf.toPartialOrder.{u1} (Submodule.{0, u1} Nat M Nat.semiring _inst_3 (AddCommMonoid.natModule.{u1} M _inst_3)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (Submodule.{0, u1} Nat M Nat.semiring _inst_3 (AddCommMonoid.natModule.{u1} M _inst_3)) (Submodule.completeLattice.{0, u1} Nat M Nat.semiring _inst_3 (AddCommMonoid.natModule.{u1} M _inst_3)))))) x._@.Mathlib.Order.Hom.Basic._hyg.1281 x._@.Mathlib.Order.Hom.Basic._hyg.1283) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1296 : AddSubmonoid.{u1} M (AddMonoid.toAddZeroClass.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3))) (x._@.Mathlib.Order.Hom.Basic._hyg.1298 : AddSubmonoid.{u1} M (AddMonoid.toAddZeroClass.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3))) => LE.le.{u1} (AddSubmonoid.{u1} M (AddMonoid.toAddZeroClass.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3))) (Preorder.toLE.{u1} (AddSubmonoid.{u1} M (AddMonoid.toAddZeroClass.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3))) (PartialOrder.toPreorder.{u1} (AddSubmonoid.{u1} M (AddMonoid.toAddZeroClass.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3))) (CompleteSemilatticeInf.toPartialOrder.{u1} (AddSubmonoid.{u1} M (AddMonoid.toAddZeroClass.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3))) (CompleteLattice.toCompleteSemilatticeInf.{u1} (AddSubmonoid.{u1} M (AddMonoid.toAddZeroClass.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3))) (AddSubmonoid.instCompleteLatticeAddSubmonoid.{u1} M (AddMonoid.toAddZeroClass.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3))))))) x._@.Mathlib.Order.Hom.Basic._hyg.1296 x._@.Mathlib.Order.Hom.Basic._hyg.1298)) (Submodule.{0, u1} Nat M Nat.semiring _inst_3 (AddCommMonoid.natModule.{u1} M _inst_3)) (fun (_x : Submodule.{0, u1} Nat M Nat.semiring _inst_3 (AddCommMonoid.natModule.{u1} M _inst_3)) => AddSubmonoid.{u1} M (AddMonoid.toAddZeroClass.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3))) (RelHomClass.toFunLike.{u1, u1, u1} (RelIso.{u1, u1} (Submodule.{0, u1} Nat M Nat.semiring _inst_3 (AddCommMonoid.natModule.{u1} M _inst_3)) (AddSubmonoid.{u1} M (AddMonoid.toAddZeroClass.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3))) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1281 : Submodule.{0, u1} Nat M Nat.semiring _inst_3 (AddCommMonoid.natModule.{u1} M _inst_3)) (x._@.Mathlib.Order.Hom.Basic._hyg.1283 : Submodule.{0, u1} Nat M Nat.semiring _inst_3 (AddCommMonoid.natModule.{u1} M _inst_3)) => LE.le.{u1} (Submodule.{0, u1} Nat M Nat.semiring _inst_3 (AddCommMonoid.natModule.{u1} M _inst_3)) (Preorder.toLE.{u1} (Submodule.{0, u1} Nat M Nat.semiring _inst_3 (AddCommMonoid.natModule.{u1} M _inst_3)) (PartialOrder.toPreorder.{u1} (Submodule.{0, u1} Nat M Nat.semiring _inst_3 (AddCommMonoid.natModule.{u1} M _inst_3)) (CompleteSemilatticeInf.toPartialOrder.{u1} (Submodule.{0, u1} Nat M Nat.semiring _inst_3 (AddCommMonoid.natModule.{u1} M _inst_3)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (Submodule.{0, u1} Nat M Nat.semiring _inst_3 (AddCommMonoid.natModule.{u1} M _inst_3)) (Submodule.completeLattice.{0, u1} Nat M Nat.semiring _inst_3 (AddCommMonoid.natModule.{u1} M _inst_3)))))) x._@.Mathlib.Order.Hom.Basic._hyg.1281 x._@.Mathlib.Order.Hom.Basic._hyg.1283) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1296 : AddSubmonoid.{u1} M (AddMonoid.toAddZeroClass.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3))) (x._@.Mathlib.Order.Hom.Basic._hyg.1298 : AddSubmonoid.{u1} M (AddMonoid.toAddZeroClass.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3))) => LE.le.{u1} (AddSubmonoid.{u1} M (AddMonoid.toAddZeroClass.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3))) (Preorder.toLE.{u1} (AddSubmonoid.{u1} M (AddMonoid.toAddZeroClass.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3))) (PartialOrder.toPreorder.{u1} (AddSubmonoid.{u1} M (AddMonoid.toAddZeroClass.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3))) (CompleteSemilatticeInf.toPartialOrder.{u1} (AddSubmonoid.{u1} M (AddMonoid.toAddZeroClass.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3))) (CompleteLattice.toCompleteSemilatticeInf.{u1} (AddSubmonoid.{u1} M (AddMonoid.toAddZeroClass.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3))) (AddSubmonoid.instCompleteLatticeAddSubmonoid.{u1} M (AddMonoid.toAddZeroClass.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3))))))) x._@.Mathlib.Order.Hom.Basic._hyg.1296 x._@.Mathlib.Order.Hom.Basic._hyg.1298)) (Submodule.{0, u1} Nat M Nat.semiring _inst_3 (AddCommMonoid.natModule.{u1} M _inst_3)) (AddSubmonoid.{u1} M (AddMonoid.toAddZeroClass.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3))) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1281 : Submodule.{0, u1} Nat M Nat.semiring _inst_3 (AddCommMonoid.natModule.{u1} M _inst_3)) (x._@.Mathlib.Order.Hom.Basic._hyg.1283 : Submodule.{0, u1} Nat M Nat.semiring _inst_3 (AddCommMonoid.natModule.{u1} M _inst_3)) => LE.le.{u1} (Submodule.{0, u1} Nat M Nat.semiring _inst_3 (AddCommMonoid.natModule.{u1} M _inst_3)) (Preorder.toLE.{u1} (Submodule.{0, u1} Nat M Nat.semiring _inst_3 (AddCommMonoid.natModule.{u1} M _inst_3)) (PartialOrder.toPreorder.{u1} (Submodule.{0, u1} Nat M Nat.semiring _inst_3 (AddCommMonoid.natModule.{u1} M _inst_3)) (CompleteSemilatticeInf.toPartialOrder.{u1} (Submodule.{0, u1} Nat M Nat.semiring _inst_3 (AddCommMonoid.natModule.{u1} M _inst_3)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (Submodule.{0, u1} Nat M Nat.semiring _inst_3 (AddCommMonoid.natModule.{u1} M _inst_3)) (Submodule.completeLattice.{0, u1} Nat M Nat.semiring _inst_3 (AddCommMonoid.natModule.{u1} M _inst_3)))))) x._@.Mathlib.Order.Hom.Basic._hyg.1281 x._@.Mathlib.Order.Hom.Basic._hyg.1283) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1296 : AddSubmonoid.{u1} M (AddMonoid.toAddZeroClass.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3))) (x._@.Mathlib.Order.Hom.Basic._hyg.1298 : AddSubmonoid.{u1} M (AddMonoid.toAddZeroClass.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3))) => LE.le.{u1} (AddSubmonoid.{u1} M (AddMonoid.toAddZeroClass.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3))) (Preorder.toLE.{u1} (AddSubmonoid.{u1} M (AddMonoid.toAddZeroClass.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3))) (PartialOrder.toPreorder.{u1} (AddSubmonoid.{u1} M (AddMonoid.toAddZeroClass.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3))) (CompleteSemilatticeInf.toPartialOrder.{u1} (AddSubmonoid.{u1} M (AddMonoid.toAddZeroClass.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3))) (CompleteLattice.toCompleteSemilatticeInf.{u1} (AddSubmonoid.{u1} M (AddMonoid.toAddZeroClass.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3))) (AddSubmonoid.instCompleteLatticeAddSubmonoid.{u1} M (AddMonoid.toAddZeroClass.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3))))))) x._@.Mathlib.Order.Hom.Basic._hyg.1296 x._@.Mathlib.Order.Hom.Basic._hyg.1298) (RelIso.instRelHomClassRelIso.{u1, u1} (Submodule.{0, u1} Nat M Nat.semiring _inst_3 (AddCommMonoid.natModule.{u1} M _inst_3)) (AddSubmonoid.{u1} M (AddMonoid.toAddZeroClass.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3))) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1281 : Submodule.{0, u1} Nat M Nat.semiring _inst_3 (AddCommMonoid.natModule.{u1} M _inst_3)) (x._@.Mathlib.Order.Hom.Basic._hyg.1283 : Submodule.{0, u1} Nat M Nat.semiring _inst_3 (AddCommMonoid.natModule.{u1} M _inst_3)) => LE.le.{u1} (Submodule.{0, u1} Nat M Nat.semiring _inst_3 (AddCommMonoid.natModule.{u1} M _inst_3)) (Preorder.toLE.{u1} (Submodule.{0, u1} Nat M Nat.semiring _inst_3 (AddCommMonoid.natModule.{u1} M _inst_3)) (PartialOrder.toPreorder.{u1} (Submodule.{0, u1} Nat M Nat.semiring _inst_3 (AddCommMonoid.natModule.{u1} M _inst_3)) (CompleteSemilatticeInf.toPartialOrder.{u1} (Submodule.{0, u1} Nat M Nat.semiring _inst_3 (AddCommMonoid.natModule.{u1} M _inst_3)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (Submodule.{0, u1} Nat M Nat.semiring _inst_3 (AddCommMonoid.natModule.{u1} M _inst_3)) (Submodule.completeLattice.{0, u1} Nat M Nat.semiring _inst_3 (AddCommMonoid.natModule.{u1} M _inst_3)))))) x._@.Mathlib.Order.Hom.Basic._hyg.1281 x._@.Mathlib.Order.Hom.Basic._hyg.1283) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1296 : AddSubmonoid.{u1} M (AddMonoid.toAddZeroClass.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3))) (x._@.Mathlib.Order.Hom.Basic._hyg.1298 : AddSubmonoid.{u1} M (AddMonoid.toAddZeroClass.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3))) => LE.le.{u1} (AddSubmonoid.{u1} M (AddMonoid.toAddZeroClass.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3))) (Preorder.toLE.{u1} (AddSubmonoid.{u1} M (AddMonoid.toAddZeroClass.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3))) (PartialOrder.toPreorder.{u1} (AddSubmonoid.{u1} M (AddMonoid.toAddZeroClass.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3))) (CompleteSemilatticeInf.toPartialOrder.{u1} (AddSubmonoid.{u1} M (AddMonoid.toAddZeroClass.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3))) (CompleteLattice.toCompleteSemilatticeInf.{u1} (AddSubmonoid.{u1} M (AddMonoid.toAddZeroClass.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3))) (AddSubmonoid.instCompleteLatticeAddSubmonoid.{u1} M (AddMonoid.toAddZeroClass.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3))))))) x._@.Mathlib.Order.Hom.Basic._hyg.1296 x._@.Mathlib.Order.Hom.Basic._hyg.1298))) (OrderIso.symm.{u1, u1} (AddSubmonoid.{u1} M (AddMonoid.toAddZeroClass.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3))) (Submodule.{0, u1} Nat M Nat.semiring _inst_3 (AddCommMonoid.natModule.{u1} M _inst_3)) (Preorder.toLE.{u1} (AddSubmonoid.{u1} M (AddMonoid.toAddZeroClass.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3))) (PartialOrder.toPreorder.{u1} (AddSubmonoid.{u1} M (AddMonoid.toAddZeroClass.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3))) (CompleteSemilatticeInf.toPartialOrder.{u1} (AddSubmonoid.{u1} M (AddMonoid.toAddZeroClass.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3))) (CompleteLattice.toCompleteSemilatticeInf.{u1} (AddSubmonoid.{u1} M (AddMonoid.toAddZeroClass.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3))) (AddSubmonoid.instCompleteLatticeAddSubmonoid.{u1} M (AddMonoid.toAddZeroClass.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3))))))) (Preorder.toLE.{u1} (Submodule.{0, u1} Nat M Nat.semiring _inst_3 (AddCommMonoid.natModule.{u1} M _inst_3)) (PartialOrder.toPreorder.{u1} (Submodule.{0, u1} Nat M Nat.semiring _inst_3 (AddCommMonoid.natModule.{u1} M _inst_3)) (CompleteSemilatticeInf.toPartialOrder.{u1} (Submodule.{0, u1} Nat M Nat.semiring _inst_3 (AddCommMonoid.natModule.{u1} M _inst_3)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (Submodule.{0, u1} Nat M Nat.semiring _inst_3 (AddCommMonoid.natModule.{u1} M _inst_3)) (Submodule.completeLattice.{0, u1} Nat M Nat.semiring _inst_3 (AddCommMonoid.natModule.{u1} M _inst_3)))))) (AddSubmonoid.toNatSubmodule.{u1} M _inst_3))) (Submodule.toAddSubmonoid.{0, u1} Nat M Nat.semiring _inst_3 (AddCommMonoid.natModule.{u1} M _inst_3))
 Case conversion may be inaccurate. Consider using '#align add_submonoid.to_nat_submodule_symm AddSubmonoid.toNatSubmodule_symmₓ'. -/
 @[simp]
 theorem AddSubmonoid.toNatSubmodule_symm :
@@ -635,7 +635,7 @@ theorem AddSubmonoid.toNatSubmodule_symm :
 lean 3 declaration is
   forall {M : Type.{u1}} [_inst_3 : AddCommMonoid.{u1} M] (S : AddSubmonoid.{u1} M (AddMonoid.toAddZeroClass.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3))), Eq.{succ u1} (Set.{u1} M) ((fun (a : Type.{u1}) (b : Type.{u1}) [self : HasLiftT.{succ u1, succ u1} a b] => self.0) (Submodule.{0, u1} Nat M Nat.semiring _inst_3 (AddCommMonoid.natModule.{u1} M _inst_3)) (Set.{u1} M) (HasLiftT.mk.{succ u1, succ u1} (Submodule.{0, u1} Nat M Nat.semiring _inst_3 (AddCommMonoid.natModule.{u1} M _inst_3)) (Set.{u1} M) (CoeTCₓ.coe.{succ u1, succ u1} (Submodule.{0, u1} Nat M Nat.semiring _inst_3 (AddCommMonoid.natModule.{u1} M _inst_3)) (Set.{u1} M) (SetLike.Set.hasCoeT.{u1, u1} (Submodule.{0, u1} Nat M Nat.semiring _inst_3 (AddCommMonoid.natModule.{u1} M _inst_3)) M (Submodule.setLike.{0, u1} Nat M Nat.semiring _inst_3 (AddCommMonoid.natModule.{u1} M _inst_3))))) (coeFn.{succ u1, succ u1} (OrderIso.{u1, u1} (AddSubmonoid.{u1} M (AddMonoid.toAddZeroClass.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3))) (Submodule.{0, u1} Nat M Nat.semiring _inst_3 (AddCommMonoid.natModule.{u1} M _inst_3)) (Preorder.toLE.{u1} (AddSubmonoid.{u1} M (AddMonoid.toAddZeroClass.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3))) (PartialOrder.toPreorder.{u1} (AddSubmonoid.{u1} M (AddMonoid.toAddZeroClass.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3))) (CompleteSemilatticeInf.toPartialOrder.{u1} (AddSubmonoid.{u1} M (AddMonoid.toAddZeroClass.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3))) (CompleteLattice.toCompleteSemilatticeInf.{u1} (AddSubmonoid.{u1} M (AddMonoid.toAddZeroClass.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3))) (AddSubmonoid.completeLattice.{u1} M (AddMonoid.toAddZeroClass.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3))))))) (Preorder.toLE.{u1} (Submodule.{0, u1} Nat M Nat.semiring _inst_3 (AddCommMonoid.natModule.{u1} M _inst_3)) (PartialOrder.toPreorder.{u1} (Submodule.{0, u1} Nat M Nat.semiring _inst_3 (AddCommMonoid.natModule.{u1} M _inst_3)) (CompleteSemilatticeInf.toPartialOrder.{u1} (Submodule.{0, u1} Nat M Nat.semiring _inst_3 (AddCommMonoid.natModule.{u1} M _inst_3)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (Submodule.{0, u1} Nat M Nat.semiring _inst_3 (AddCommMonoid.natModule.{u1} M _inst_3)) (Submodule.completeLattice.{0, u1} Nat M Nat.semiring _inst_3 (AddCommMonoid.natModule.{u1} M _inst_3))))))) (fun (_x : RelIso.{u1, u1} (AddSubmonoid.{u1} M (AddMonoid.toAddZeroClass.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3))) (Submodule.{0, u1} Nat M Nat.semiring _inst_3 (AddCommMonoid.natModule.{u1} M _inst_3)) (LE.le.{u1} (AddSubmonoid.{u1} M (AddMonoid.toAddZeroClass.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3))) (Preorder.toLE.{u1} (AddSubmonoid.{u1} M (AddMonoid.toAddZeroClass.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3))) (PartialOrder.toPreorder.{u1} (AddSubmonoid.{u1} M (AddMonoid.toAddZeroClass.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3))) (CompleteSemilatticeInf.toPartialOrder.{u1} (AddSubmonoid.{u1} M (AddMonoid.toAddZeroClass.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3))) (CompleteLattice.toCompleteSemilatticeInf.{u1} (AddSubmonoid.{u1} M (AddMonoid.toAddZeroClass.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3))) (AddSubmonoid.completeLattice.{u1} M (AddMonoid.toAddZeroClass.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3)))))))) (LE.le.{u1} (Submodule.{0, u1} Nat M Nat.semiring _inst_3 (AddCommMonoid.natModule.{u1} M _inst_3)) (Preorder.toLE.{u1} (Submodule.{0, u1} Nat M Nat.semiring _inst_3 (AddCommMonoid.natModule.{u1} M _inst_3)) (PartialOrder.toPreorder.{u1} (Submodule.{0, u1} Nat M Nat.semiring _inst_3 (AddCommMonoid.natModule.{u1} M _inst_3)) (CompleteSemilatticeInf.toPartialOrder.{u1} (Submodule.{0, u1} Nat M Nat.semiring _inst_3 (AddCommMonoid.natModule.{u1} M _inst_3)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (Submodule.{0, u1} Nat M Nat.semiring _inst_3 (AddCommMonoid.natModule.{u1} M _inst_3)) (Submodule.completeLattice.{0, u1} Nat M Nat.semiring _inst_3 (AddCommMonoid.natModule.{u1} M _inst_3)))))))) => (AddSubmonoid.{u1} M (AddMonoid.toAddZeroClass.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3))) -> (Submodule.{0, u1} Nat M Nat.semiring _inst_3 (AddCommMonoid.natModule.{u1} M _inst_3))) (RelIso.hasCoeToFun.{u1, u1} (AddSubmonoid.{u1} M (AddMonoid.toAddZeroClass.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3))) (Submodule.{0, u1} Nat M Nat.semiring _inst_3 (AddCommMonoid.natModule.{u1} M _inst_3)) (LE.le.{u1} (AddSubmonoid.{u1} M (AddMonoid.toAddZeroClass.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3))) (Preorder.toLE.{u1} (AddSubmonoid.{u1} M (AddMonoid.toAddZeroClass.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3))) (PartialOrder.toPreorder.{u1} (AddSubmonoid.{u1} M (AddMonoid.toAddZeroClass.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3))) (CompleteSemilatticeInf.toPartialOrder.{u1} (AddSubmonoid.{u1} M (AddMonoid.toAddZeroClass.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3))) (CompleteLattice.toCompleteSemilatticeInf.{u1} (AddSubmonoid.{u1} M (AddMonoid.toAddZeroClass.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3))) (AddSubmonoid.completeLattice.{u1} M (AddMonoid.toAddZeroClass.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3)))))))) (LE.le.{u1} (Submodule.{0, u1} Nat M Nat.semiring _inst_3 (AddCommMonoid.natModule.{u1} M _inst_3)) (Preorder.toLE.{u1} (Submodule.{0, u1} Nat M Nat.semiring _inst_3 (AddCommMonoid.natModule.{u1} M _inst_3)) (PartialOrder.toPreorder.{u1} (Submodule.{0, u1} Nat M Nat.semiring _inst_3 (AddCommMonoid.natModule.{u1} M _inst_3)) (CompleteSemilatticeInf.toPartialOrder.{u1} (Submodule.{0, u1} Nat M Nat.semiring _inst_3 (AddCommMonoid.natModule.{u1} M _inst_3)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (Submodule.{0, u1} Nat M Nat.semiring _inst_3 (AddCommMonoid.natModule.{u1} M _inst_3)) (Submodule.completeLattice.{0, u1} Nat M Nat.semiring _inst_3 (AddCommMonoid.natModule.{u1} M _inst_3)))))))) (AddSubmonoid.toNatSubmodule.{u1} M _inst_3) S)) ((fun (a : Type.{u1}) (b : Type.{u1}) [self : HasLiftT.{succ u1, succ u1} a b] => self.0) (AddSubmonoid.{u1} M (AddMonoid.toAddZeroClass.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3))) (Set.{u1} M) (HasLiftT.mk.{succ u1, succ u1} (AddSubmonoid.{u1} M (AddMonoid.toAddZeroClass.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3))) (Set.{u1} M) (CoeTCₓ.coe.{succ u1, succ u1} (AddSubmonoid.{u1} M (AddMonoid.toAddZeroClass.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3))) (Set.{u1} M) (SetLike.Set.hasCoeT.{u1, u1} (AddSubmonoid.{u1} M (AddMonoid.toAddZeroClass.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3))) M (AddSubmonoid.setLike.{u1} M (AddMonoid.toAddZeroClass.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3)))))) S)
 but is expected to have type
-  forall {M : Type.{u1}} [_inst_3 : AddCommMonoid.{u1} M] (S : AddSubmonoid.{u1} M (AddMonoid.toAddZeroClass.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3))), Eq.{succ u1} (Set.{u1} M) (SetLike.coe.{u1, u1} ((fun (x._@.Mathlib.Data.FunLike.Embedding._hyg.19 : AddSubmonoid.{u1} M (AddMonoid.toAddZeroClass.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3))) => Submodule.{0, u1} Nat M Nat.semiring _inst_3 (AddCommMonoid.natModule.{u1} M _inst_3)) S) M (Submodule.setLike.{0, u1} Nat M Nat.semiring _inst_3 (AddCommMonoid.natModule.{u1} M _inst_3)) (FunLike.coe.{succ u1, succ u1, succ u1} (Function.Embedding.{succ u1, succ u1} (AddSubmonoid.{u1} M (AddMonoid.toAddZeroClass.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3))) (Submodule.{0, u1} Nat M Nat.semiring _inst_3 (AddCommMonoid.natModule.{u1} M _inst_3))) (AddSubmonoid.{u1} M (AddMonoid.toAddZeroClass.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3))) (fun (_x : AddSubmonoid.{u1} M (AddMonoid.toAddZeroClass.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3))) => (fun (x._@.Mathlib.Data.FunLike.Embedding._hyg.19 : AddSubmonoid.{u1} M (AddMonoid.toAddZeroClass.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3))) => Submodule.{0, u1} Nat M Nat.semiring _inst_3 (AddCommMonoid.natModule.{u1} M _inst_3)) _x) (EmbeddingLike.toFunLike.{succ u1, succ u1, succ u1} (Function.Embedding.{succ u1, succ u1} (AddSubmonoid.{u1} M (AddMonoid.toAddZeroClass.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3))) (Submodule.{0, u1} Nat M Nat.semiring _inst_3 (AddCommMonoid.natModule.{u1} M _inst_3))) (AddSubmonoid.{u1} M (AddMonoid.toAddZeroClass.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3))) (Submodule.{0, u1} Nat M Nat.semiring _inst_3 (AddCommMonoid.natModule.{u1} M _inst_3)) (Function.instEmbeddingLikeEmbedding.{succ u1, succ u1} (AddSubmonoid.{u1} M (AddMonoid.toAddZeroClass.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3))) (Submodule.{0, u1} Nat M Nat.semiring _inst_3 (AddCommMonoid.natModule.{u1} M _inst_3)))) (RelEmbedding.toEmbedding.{u1, u1} (AddSubmonoid.{u1} M (AddMonoid.toAddZeroClass.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3))) (Submodule.{0, u1} Nat M Nat.semiring _inst_3 (AddCommMonoid.natModule.{u1} M _inst_3)) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1281 : AddSubmonoid.{u1} M (AddMonoid.toAddZeroClass.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3))) (x._@.Mathlib.Order.Hom.Basic._hyg.1283 : AddSubmonoid.{u1} M (AddMonoid.toAddZeroClass.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3))) => LE.le.{u1} (AddSubmonoid.{u1} M (AddMonoid.toAddZeroClass.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3))) (Preorder.toLE.{u1} (AddSubmonoid.{u1} M (AddMonoid.toAddZeroClass.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3))) (PartialOrder.toPreorder.{u1} (AddSubmonoid.{u1} M (AddMonoid.toAddZeroClass.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3))) (CompleteSemilatticeInf.toPartialOrder.{u1} (AddSubmonoid.{u1} M (AddMonoid.toAddZeroClass.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3))) (CompleteLattice.toCompleteSemilatticeInf.{u1} (AddSubmonoid.{u1} M (AddMonoid.toAddZeroClass.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3))) (AddSubmonoid.instCompleteLatticeAddSubmonoid.{u1} M (AddMonoid.toAddZeroClass.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3))))))) x._@.Mathlib.Order.Hom.Basic._hyg.1281 x._@.Mathlib.Order.Hom.Basic._hyg.1283) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1296 : Submodule.{0, u1} Nat M Nat.semiring _inst_3 (AddCommMonoid.natModule.{u1} M _inst_3)) (x._@.Mathlib.Order.Hom.Basic._hyg.1298 : Submodule.{0, u1} Nat M Nat.semiring _inst_3 (AddCommMonoid.natModule.{u1} M _inst_3)) => LE.le.{u1} (Submodule.{0, u1} Nat M Nat.semiring _inst_3 (AddCommMonoid.natModule.{u1} M _inst_3)) (Preorder.toLE.{u1} (Submodule.{0, u1} Nat M Nat.semiring _inst_3 (AddCommMonoid.natModule.{u1} M _inst_3)) (PartialOrder.toPreorder.{u1} (Submodule.{0, u1} Nat M Nat.semiring _inst_3 (AddCommMonoid.natModule.{u1} M _inst_3)) (CompleteSemilatticeInf.toPartialOrder.{u1} (Submodule.{0, u1} Nat M Nat.semiring _inst_3 (AddCommMonoid.natModule.{u1} M _inst_3)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (Submodule.{0, u1} Nat M Nat.semiring _inst_3 (AddCommMonoid.natModule.{u1} M _inst_3)) (Submodule.completeLattice.{0, u1} Nat M Nat.semiring _inst_3 (AddCommMonoid.natModule.{u1} M _inst_3)))))) x._@.Mathlib.Order.Hom.Basic._hyg.1296 x._@.Mathlib.Order.Hom.Basic._hyg.1298) (RelIso.toRelEmbedding.{u1, u1} (AddSubmonoid.{u1} M (AddMonoid.toAddZeroClass.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3))) (Submodule.{0, u1} Nat M Nat.semiring _inst_3 (AddCommMonoid.natModule.{u1} M _inst_3)) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1281 : AddSubmonoid.{u1} M (AddMonoid.toAddZeroClass.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3))) (x._@.Mathlib.Order.Hom.Basic._hyg.1283 : AddSubmonoid.{u1} M (AddMonoid.toAddZeroClass.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3))) => LE.le.{u1} (AddSubmonoid.{u1} M (AddMonoid.toAddZeroClass.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3))) (Preorder.toLE.{u1} (AddSubmonoid.{u1} M (AddMonoid.toAddZeroClass.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3))) (PartialOrder.toPreorder.{u1} (AddSubmonoid.{u1} M (AddMonoid.toAddZeroClass.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3))) (CompleteSemilatticeInf.toPartialOrder.{u1} (AddSubmonoid.{u1} M (AddMonoid.toAddZeroClass.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3))) (CompleteLattice.toCompleteSemilatticeInf.{u1} (AddSubmonoid.{u1} M (AddMonoid.toAddZeroClass.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3))) (AddSubmonoid.instCompleteLatticeAddSubmonoid.{u1} M (AddMonoid.toAddZeroClass.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3))))))) x._@.Mathlib.Order.Hom.Basic._hyg.1281 x._@.Mathlib.Order.Hom.Basic._hyg.1283) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1296 : Submodule.{0, u1} Nat M Nat.semiring _inst_3 (AddCommMonoid.natModule.{u1} M _inst_3)) (x._@.Mathlib.Order.Hom.Basic._hyg.1298 : Submodule.{0, u1} Nat M Nat.semiring _inst_3 (AddCommMonoid.natModule.{u1} M _inst_3)) => LE.le.{u1} (Submodule.{0, u1} Nat M Nat.semiring _inst_3 (AddCommMonoid.natModule.{u1} M _inst_3)) (Preorder.toLE.{u1} (Submodule.{0, u1} Nat M Nat.semiring _inst_3 (AddCommMonoid.natModule.{u1} M _inst_3)) (PartialOrder.toPreorder.{u1} (Submodule.{0, u1} Nat M Nat.semiring _inst_3 (AddCommMonoid.natModule.{u1} M _inst_3)) (CompleteSemilatticeInf.toPartialOrder.{u1} (Submodule.{0, u1} Nat M Nat.semiring _inst_3 (AddCommMonoid.natModule.{u1} M _inst_3)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (Submodule.{0, u1} Nat M Nat.semiring _inst_3 (AddCommMonoid.natModule.{u1} M _inst_3)) (Submodule.completeLattice.{0, u1} Nat M Nat.semiring _inst_3 (AddCommMonoid.natModule.{u1} M _inst_3)))))) x._@.Mathlib.Order.Hom.Basic._hyg.1296 x._@.Mathlib.Order.Hom.Basic._hyg.1298) (AddSubmonoid.toNatSubmodule.{u1} M _inst_3))) S)) (SetLike.coe.{u1, u1} (AddSubmonoid.{u1} M (AddMonoid.toAddZeroClass.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3))) M (AddSubmonoid.instSetLikeAddSubmonoid.{u1} M (AddMonoid.toAddZeroClass.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3))) S)
+  forall {M : Type.{u1}} [_inst_3 : AddCommMonoid.{u1} M] (S : AddSubmonoid.{u1} M (AddMonoid.toAddZeroClass.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3))), Eq.{succ u1} (Set.{u1} M) (SetLike.coe.{u1, u1} (Submodule.{0, u1} Nat M Nat.semiring _inst_3 (AddCommMonoid.natModule.{u1} M _inst_3)) M (Submodule.setLike.{0, u1} Nat M Nat.semiring _inst_3 (AddCommMonoid.natModule.{u1} M _inst_3)) (FunLike.coe.{succ u1, succ u1, succ u1} (RelIso.{u1, u1} (AddSubmonoid.{u1} M (AddMonoid.toAddZeroClass.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3))) (Submodule.{0, u1} Nat M Nat.semiring _inst_3 (AddCommMonoid.natModule.{u1} M _inst_3)) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1281 : AddSubmonoid.{u1} M (AddMonoid.toAddZeroClass.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3))) (x._@.Mathlib.Order.Hom.Basic._hyg.1283 : AddSubmonoid.{u1} M (AddMonoid.toAddZeroClass.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3))) => LE.le.{u1} (AddSubmonoid.{u1} M (AddMonoid.toAddZeroClass.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3))) (Preorder.toLE.{u1} (AddSubmonoid.{u1} M (AddMonoid.toAddZeroClass.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3))) (PartialOrder.toPreorder.{u1} (AddSubmonoid.{u1} M (AddMonoid.toAddZeroClass.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3))) (CompleteSemilatticeInf.toPartialOrder.{u1} (AddSubmonoid.{u1} M (AddMonoid.toAddZeroClass.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3))) (CompleteLattice.toCompleteSemilatticeInf.{u1} (AddSubmonoid.{u1} M (AddMonoid.toAddZeroClass.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3))) (AddSubmonoid.instCompleteLatticeAddSubmonoid.{u1} M (AddMonoid.toAddZeroClass.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3))))))) x._@.Mathlib.Order.Hom.Basic._hyg.1281 x._@.Mathlib.Order.Hom.Basic._hyg.1283) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1296 : Submodule.{0, u1} Nat M Nat.semiring _inst_3 (AddCommMonoid.natModule.{u1} M _inst_3)) (x._@.Mathlib.Order.Hom.Basic._hyg.1298 : Submodule.{0, u1} Nat M Nat.semiring _inst_3 (AddCommMonoid.natModule.{u1} M _inst_3)) => LE.le.{u1} (Submodule.{0, u1} Nat M Nat.semiring _inst_3 (AddCommMonoid.natModule.{u1} M _inst_3)) (Preorder.toLE.{u1} (Submodule.{0, u1} Nat M Nat.semiring _inst_3 (AddCommMonoid.natModule.{u1} M _inst_3)) (PartialOrder.toPreorder.{u1} (Submodule.{0, u1} Nat M Nat.semiring _inst_3 (AddCommMonoid.natModule.{u1} M _inst_3)) (CompleteSemilatticeInf.toPartialOrder.{u1} (Submodule.{0, u1} Nat M Nat.semiring _inst_3 (AddCommMonoid.natModule.{u1} M _inst_3)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (Submodule.{0, u1} Nat M Nat.semiring _inst_3 (AddCommMonoid.natModule.{u1} M _inst_3)) (Submodule.completeLattice.{0, u1} Nat M Nat.semiring _inst_3 (AddCommMonoid.natModule.{u1} M _inst_3)))))) x._@.Mathlib.Order.Hom.Basic._hyg.1296 x._@.Mathlib.Order.Hom.Basic._hyg.1298)) (AddSubmonoid.{u1} M (AddMonoid.toAddZeroClass.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3))) (fun (_x : AddSubmonoid.{u1} M (AddMonoid.toAddZeroClass.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3))) => Submodule.{0, u1} Nat M Nat.semiring _inst_3 (AddCommMonoid.natModule.{u1} M _inst_3)) (RelHomClass.toFunLike.{u1, u1, u1} (RelIso.{u1, u1} (AddSubmonoid.{u1} M (AddMonoid.toAddZeroClass.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3))) (Submodule.{0, u1} Nat M Nat.semiring _inst_3 (AddCommMonoid.natModule.{u1} M _inst_3)) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1281 : AddSubmonoid.{u1} M (AddMonoid.toAddZeroClass.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3))) (x._@.Mathlib.Order.Hom.Basic._hyg.1283 : AddSubmonoid.{u1} M (AddMonoid.toAddZeroClass.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3))) => LE.le.{u1} (AddSubmonoid.{u1} M (AddMonoid.toAddZeroClass.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3))) (Preorder.toLE.{u1} (AddSubmonoid.{u1} M (AddMonoid.toAddZeroClass.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3))) (PartialOrder.toPreorder.{u1} (AddSubmonoid.{u1} M (AddMonoid.toAddZeroClass.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3))) (CompleteSemilatticeInf.toPartialOrder.{u1} (AddSubmonoid.{u1} M (AddMonoid.toAddZeroClass.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3))) (CompleteLattice.toCompleteSemilatticeInf.{u1} (AddSubmonoid.{u1} M (AddMonoid.toAddZeroClass.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3))) (AddSubmonoid.instCompleteLatticeAddSubmonoid.{u1} M (AddMonoid.toAddZeroClass.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3))))))) x._@.Mathlib.Order.Hom.Basic._hyg.1281 x._@.Mathlib.Order.Hom.Basic._hyg.1283) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1296 : Submodule.{0, u1} Nat M Nat.semiring _inst_3 (AddCommMonoid.natModule.{u1} M _inst_3)) (x._@.Mathlib.Order.Hom.Basic._hyg.1298 : Submodule.{0, u1} Nat M Nat.semiring _inst_3 (AddCommMonoid.natModule.{u1} M _inst_3)) => LE.le.{u1} (Submodule.{0, u1} Nat M Nat.semiring _inst_3 (AddCommMonoid.natModule.{u1} M _inst_3)) (Preorder.toLE.{u1} (Submodule.{0, u1} Nat M Nat.semiring _inst_3 (AddCommMonoid.natModule.{u1} M _inst_3)) (PartialOrder.toPreorder.{u1} (Submodule.{0, u1} Nat M Nat.semiring _inst_3 (AddCommMonoid.natModule.{u1} M _inst_3)) (CompleteSemilatticeInf.toPartialOrder.{u1} (Submodule.{0, u1} Nat M Nat.semiring _inst_3 (AddCommMonoid.natModule.{u1} M _inst_3)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (Submodule.{0, u1} Nat M Nat.semiring _inst_3 (AddCommMonoid.natModule.{u1} M _inst_3)) (Submodule.completeLattice.{0, u1} Nat M Nat.semiring _inst_3 (AddCommMonoid.natModule.{u1} M _inst_3)))))) x._@.Mathlib.Order.Hom.Basic._hyg.1296 x._@.Mathlib.Order.Hom.Basic._hyg.1298)) (AddSubmonoid.{u1} M (AddMonoid.toAddZeroClass.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3))) (Submodule.{0, u1} Nat M Nat.semiring _inst_3 (AddCommMonoid.natModule.{u1} M _inst_3)) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1281 : AddSubmonoid.{u1} M (AddMonoid.toAddZeroClass.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3))) (x._@.Mathlib.Order.Hom.Basic._hyg.1283 : AddSubmonoid.{u1} M (AddMonoid.toAddZeroClass.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3))) => LE.le.{u1} (AddSubmonoid.{u1} M (AddMonoid.toAddZeroClass.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3))) (Preorder.toLE.{u1} (AddSubmonoid.{u1} M (AddMonoid.toAddZeroClass.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3))) (PartialOrder.toPreorder.{u1} (AddSubmonoid.{u1} M (AddMonoid.toAddZeroClass.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3))) (CompleteSemilatticeInf.toPartialOrder.{u1} (AddSubmonoid.{u1} M (AddMonoid.toAddZeroClass.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3))) (CompleteLattice.toCompleteSemilatticeInf.{u1} (AddSubmonoid.{u1} M (AddMonoid.toAddZeroClass.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3))) (AddSubmonoid.instCompleteLatticeAddSubmonoid.{u1} M (AddMonoid.toAddZeroClass.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3))))))) x._@.Mathlib.Order.Hom.Basic._hyg.1281 x._@.Mathlib.Order.Hom.Basic._hyg.1283) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1296 : Submodule.{0, u1} Nat M Nat.semiring _inst_3 (AddCommMonoid.natModule.{u1} M _inst_3)) (x._@.Mathlib.Order.Hom.Basic._hyg.1298 : Submodule.{0, u1} Nat M Nat.semiring _inst_3 (AddCommMonoid.natModule.{u1} M _inst_3)) => LE.le.{u1} (Submodule.{0, u1} Nat M Nat.semiring _inst_3 (AddCommMonoid.natModule.{u1} M _inst_3)) (Preorder.toLE.{u1} (Submodule.{0, u1} Nat M Nat.semiring _inst_3 (AddCommMonoid.natModule.{u1} M _inst_3)) (PartialOrder.toPreorder.{u1} (Submodule.{0, u1} Nat M Nat.semiring _inst_3 (AddCommMonoid.natModule.{u1} M _inst_3)) (CompleteSemilatticeInf.toPartialOrder.{u1} (Submodule.{0, u1} Nat M Nat.semiring _inst_3 (AddCommMonoid.natModule.{u1} M _inst_3)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (Submodule.{0, u1} Nat M Nat.semiring _inst_3 (AddCommMonoid.natModule.{u1} M _inst_3)) (Submodule.completeLattice.{0, u1} Nat M Nat.semiring _inst_3 (AddCommMonoid.natModule.{u1} M _inst_3)))))) x._@.Mathlib.Order.Hom.Basic._hyg.1296 x._@.Mathlib.Order.Hom.Basic._hyg.1298) (RelIso.instRelHomClassRelIso.{u1, u1} (AddSubmonoid.{u1} M (AddMonoid.toAddZeroClass.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3))) (Submodule.{0, u1} Nat M Nat.semiring _inst_3 (AddCommMonoid.natModule.{u1} M _inst_3)) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1281 : AddSubmonoid.{u1} M (AddMonoid.toAddZeroClass.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3))) (x._@.Mathlib.Order.Hom.Basic._hyg.1283 : AddSubmonoid.{u1} M (AddMonoid.toAddZeroClass.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3))) => LE.le.{u1} (AddSubmonoid.{u1} M (AddMonoid.toAddZeroClass.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3))) (Preorder.toLE.{u1} (AddSubmonoid.{u1} M (AddMonoid.toAddZeroClass.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3))) (PartialOrder.toPreorder.{u1} (AddSubmonoid.{u1} M (AddMonoid.toAddZeroClass.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3))) (CompleteSemilatticeInf.toPartialOrder.{u1} (AddSubmonoid.{u1} M (AddMonoid.toAddZeroClass.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3))) (CompleteLattice.toCompleteSemilatticeInf.{u1} (AddSubmonoid.{u1} M (AddMonoid.toAddZeroClass.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3))) (AddSubmonoid.instCompleteLatticeAddSubmonoid.{u1} M (AddMonoid.toAddZeroClass.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3))))))) x._@.Mathlib.Order.Hom.Basic._hyg.1281 x._@.Mathlib.Order.Hom.Basic._hyg.1283) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1296 : Submodule.{0, u1} Nat M Nat.semiring _inst_3 (AddCommMonoid.natModule.{u1} M _inst_3)) (x._@.Mathlib.Order.Hom.Basic._hyg.1298 : Submodule.{0, u1} Nat M Nat.semiring _inst_3 (AddCommMonoid.natModule.{u1} M _inst_3)) => LE.le.{u1} (Submodule.{0, u1} Nat M Nat.semiring _inst_3 (AddCommMonoid.natModule.{u1} M _inst_3)) (Preorder.toLE.{u1} (Submodule.{0, u1} Nat M Nat.semiring _inst_3 (AddCommMonoid.natModule.{u1} M _inst_3)) (PartialOrder.toPreorder.{u1} (Submodule.{0, u1} Nat M Nat.semiring _inst_3 (AddCommMonoid.natModule.{u1} M _inst_3)) (CompleteSemilatticeInf.toPartialOrder.{u1} (Submodule.{0, u1} Nat M Nat.semiring _inst_3 (AddCommMonoid.natModule.{u1} M _inst_3)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (Submodule.{0, u1} Nat M Nat.semiring _inst_3 (AddCommMonoid.natModule.{u1} M _inst_3)) (Submodule.completeLattice.{0, u1} Nat M Nat.semiring _inst_3 (AddCommMonoid.natModule.{u1} M _inst_3)))))) x._@.Mathlib.Order.Hom.Basic._hyg.1296 x._@.Mathlib.Order.Hom.Basic._hyg.1298))) (AddSubmonoid.toNatSubmodule.{u1} M _inst_3) S)) (SetLike.coe.{u1, u1} (AddSubmonoid.{u1} M (AddMonoid.toAddZeroClass.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3))) M (AddSubmonoid.instSetLikeAddSubmonoid.{u1} M (AddMonoid.toAddZeroClass.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3))) S)
 Case conversion may be inaccurate. Consider using '#align add_submonoid.coe_to_nat_submodule AddSubmonoid.coe_toNatSubmoduleₓ'. -/
 @[simp]
 theorem AddSubmonoid.coe_toNatSubmodule (S : AddSubmonoid M) : (S.toNatSubmodule : Set M) = S :=
@@ -646,7 +646,7 @@ theorem AddSubmonoid.coe_toNatSubmodule (S : AddSubmonoid M) : (S.toNatSubmodule
 lean 3 declaration is
   forall {M : Type.{u1}} [_inst_3 : AddCommMonoid.{u1} M] (S : AddSubmonoid.{u1} M (AddMonoid.toAddZeroClass.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3))), Eq.{succ u1} (AddSubmonoid.{u1} M (AddMonoid.toAddZeroClass.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3))) (Submodule.toAddSubmonoid.{0, u1} Nat M Nat.semiring _inst_3 (AddCommMonoid.natModule.{u1} M _inst_3) (coeFn.{succ u1, succ u1} (OrderIso.{u1, u1} (AddSubmonoid.{u1} M (AddMonoid.toAddZeroClass.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3))) (Submodule.{0, u1} Nat M Nat.semiring _inst_3 (AddCommMonoid.natModule.{u1} M _inst_3)) (Preorder.toLE.{u1} (AddSubmonoid.{u1} M (AddMonoid.toAddZeroClass.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3))) (PartialOrder.toPreorder.{u1} (AddSubmonoid.{u1} M (AddMonoid.toAddZeroClass.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3))) (CompleteSemilatticeInf.toPartialOrder.{u1} (AddSubmonoid.{u1} M (AddMonoid.toAddZeroClass.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3))) (CompleteLattice.toCompleteSemilatticeInf.{u1} (AddSubmonoid.{u1} M (AddMonoid.toAddZeroClass.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3))) (AddSubmonoid.completeLattice.{u1} M (AddMonoid.toAddZeroClass.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3))))))) (Preorder.toLE.{u1} (Submodule.{0, u1} Nat M Nat.semiring _inst_3 (AddCommMonoid.natModule.{u1} M _inst_3)) (PartialOrder.toPreorder.{u1} (Submodule.{0, u1} Nat M Nat.semiring _inst_3 (AddCommMonoid.natModule.{u1} M _inst_3)) (CompleteSemilatticeInf.toPartialOrder.{u1} (Submodule.{0, u1} Nat M Nat.semiring _inst_3 (AddCommMonoid.natModule.{u1} M _inst_3)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (Submodule.{0, u1} Nat M Nat.semiring _inst_3 (AddCommMonoid.natModule.{u1} M _inst_3)) (Submodule.completeLattice.{0, u1} Nat M Nat.semiring _inst_3 (AddCommMonoid.natModule.{u1} M _inst_3))))))) (fun (_x : RelIso.{u1, u1} (AddSubmonoid.{u1} M (AddMonoid.toAddZeroClass.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3))) (Submodule.{0, u1} Nat M Nat.semiring _inst_3 (AddCommMonoid.natModule.{u1} M _inst_3)) (LE.le.{u1} (AddSubmonoid.{u1} M (AddMonoid.toAddZeroClass.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3))) (Preorder.toLE.{u1} (AddSubmonoid.{u1} M (AddMonoid.toAddZeroClass.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3))) (PartialOrder.toPreorder.{u1} (AddSubmonoid.{u1} M (AddMonoid.toAddZeroClass.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3))) (CompleteSemilatticeInf.toPartialOrder.{u1} (AddSubmonoid.{u1} M (AddMonoid.toAddZeroClass.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3))) (CompleteLattice.toCompleteSemilatticeInf.{u1} (AddSubmonoid.{u1} M (AddMonoid.toAddZeroClass.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3))) (AddSubmonoid.completeLattice.{u1} M (AddMonoid.toAddZeroClass.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3)))))))) (LE.le.{u1} (Submodule.{0, u1} Nat M Nat.semiring _inst_3 (AddCommMonoid.natModule.{u1} M _inst_3)) (Preorder.toLE.{u1} (Submodule.{0, u1} Nat M Nat.semiring _inst_3 (AddCommMonoid.natModule.{u1} M _inst_3)) (PartialOrder.toPreorder.{u1} (Submodule.{0, u1} Nat M Nat.semiring _inst_3 (AddCommMonoid.natModule.{u1} M _inst_3)) (CompleteSemilatticeInf.toPartialOrder.{u1} (Submodule.{0, u1} Nat M Nat.semiring _inst_3 (AddCommMonoid.natModule.{u1} M _inst_3)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (Submodule.{0, u1} Nat M Nat.semiring _inst_3 (AddCommMonoid.natModule.{u1} M _inst_3)) (Submodule.completeLattice.{0, u1} Nat M Nat.semiring _inst_3 (AddCommMonoid.natModule.{u1} M _inst_3)))))))) => (AddSubmonoid.{u1} M (AddMonoid.toAddZeroClass.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3))) -> (Submodule.{0, u1} Nat M Nat.semiring _inst_3 (AddCommMonoid.natModule.{u1} M _inst_3))) (RelIso.hasCoeToFun.{u1, u1} (AddSubmonoid.{u1} M (AddMonoid.toAddZeroClass.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3))) (Submodule.{0, u1} Nat M Nat.semiring _inst_3 (AddCommMonoid.natModule.{u1} M _inst_3)) (LE.le.{u1} (AddSubmonoid.{u1} M (AddMonoid.toAddZeroClass.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3))) (Preorder.toLE.{u1} (AddSubmonoid.{u1} M (AddMonoid.toAddZeroClass.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3))) (PartialOrder.toPreorder.{u1} (AddSubmonoid.{u1} M (AddMonoid.toAddZeroClass.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3))) (CompleteSemilatticeInf.toPartialOrder.{u1} (AddSubmonoid.{u1} M (AddMonoid.toAddZeroClass.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3))) (CompleteLattice.toCompleteSemilatticeInf.{u1} (AddSubmonoid.{u1} M (AddMonoid.toAddZeroClass.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3))) (AddSubmonoid.completeLattice.{u1} M (AddMonoid.toAddZeroClass.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3)))))))) (LE.le.{u1} (Submodule.{0, u1} Nat M Nat.semiring _inst_3 (AddCommMonoid.natModule.{u1} M _inst_3)) (Preorder.toLE.{u1} (Submodule.{0, u1} Nat M Nat.semiring _inst_3 (AddCommMonoid.natModule.{u1} M _inst_3)) (PartialOrder.toPreorder.{u1} (Submodule.{0, u1} Nat M Nat.semiring _inst_3 (AddCommMonoid.natModule.{u1} M _inst_3)) (CompleteSemilatticeInf.toPartialOrder.{u1} (Submodule.{0, u1} Nat M Nat.semiring _inst_3 (AddCommMonoid.natModule.{u1} M _inst_3)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (Submodule.{0, u1} Nat M Nat.semiring _inst_3 (AddCommMonoid.natModule.{u1} M _inst_3)) (Submodule.completeLattice.{0, u1} Nat M Nat.semiring _inst_3 (AddCommMonoid.natModule.{u1} M _inst_3)))))))) (AddSubmonoid.toNatSubmodule.{u1} M _inst_3) S)) S
 but is expected to have type
-  forall {M : Type.{u1}} [_inst_3 : AddCommMonoid.{u1} M] (S : AddSubmonoid.{u1} M (AddMonoid.toAddZeroClass.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3))), Eq.{succ u1} (AddSubmonoid.{u1} M (AddMonoid.toAddZeroClass.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3))) (Submodule.toAddSubmonoid.{0, u1} Nat M Nat.semiring _inst_3 (AddCommMonoid.natModule.{u1} M _inst_3) (FunLike.coe.{succ u1, succ u1, succ u1} (Function.Embedding.{succ u1, succ u1} (AddSubmonoid.{u1} M (AddMonoid.toAddZeroClass.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3))) (Submodule.{0, u1} Nat M Nat.semiring _inst_3 (AddCommMonoid.natModule.{u1} M _inst_3))) (AddSubmonoid.{u1} M (AddMonoid.toAddZeroClass.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3))) (fun (_x : AddSubmonoid.{u1} M (AddMonoid.toAddZeroClass.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3))) => (fun (x._@.Mathlib.Data.FunLike.Embedding._hyg.19 : AddSubmonoid.{u1} M (AddMonoid.toAddZeroClass.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3))) => Submodule.{0, u1} Nat M Nat.semiring _inst_3 (AddCommMonoid.natModule.{u1} M _inst_3)) _x) (EmbeddingLike.toFunLike.{succ u1, succ u1, succ u1} (Function.Embedding.{succ u1, succ u1} (AddSubmonoid.{u1} M (AddMonoid.toAddZeroClass.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3))) (Submodule.{0, u1} Nat M Nat.semiring _inst_3 (AddCommMonoid.natModule.{u1} M _inst_3))) (AddSubmonoid.{u1} M (AddMonoid.toAddZeroClass.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3))) (Submodule.{0, u1} Nat M Nat.semiring _inst_3 (AddCommMonoid.natModule.{u1} M _inst_3)) (Function.instEmbeddingLikeEmbedding.{succ u1, succ u1} (AddSubmonoid.{u1} M (AddMonoid.toAddZeroClass.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3))) (Submodule.{0, u1} Nat M Nat.semiring _inst_3 (AddCommMonoid.natModule.{u1} M _inst_3)))) (RelEmbedding.toEmbedding.{u1, u1} (AddSubmonoid.{u1} M (AddMonoid.toAddZeroClass.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3))) (Submodule.{0, u1} Nat M Nat.semiring _inst_3 (AddCommMonoid.natModule.{u1} M _inst_3)) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1281 : AddSubmonoid.{u1} M (AddMonoid.toAddZeroClass.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3))) (x._@.Mathlib.Order.Hom.Basic._hyg.1283 : AddSubmonoid.{u1} M (AddMonoid.toAddZeroClass.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3))) => LE.le.{u1} (AddSubmonoid.{u1} M (AddMonoid.toAddZeroClass.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3))) (Preorder.toLE.{u1} (AddSubmonoid.{u1} M (AddMonoid.toAddZeroClass.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3))) (PartialOrder.toPreorder.{u1} (AddSubmonoid.{u1} M (AddMonoid.toAddZeroClass.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3))) (CompleteSemilatticeInf.toPartialOrder.{u1} (AddSubmonoid.{u1} M (AddMonoid.toAddZeroClass.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3))) (CompleteLattice.toCompleteSemilatticeInf.{u1} (AddSubmonoid.{u1} M (AddMonoid.toAddZeroClass.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3))) (AddSubmonoid.instCompleteLatticeAddSubmonoid.{u1} M (AddMonoid.toAddZeroClass.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3))))))) x._@.Mathlib.Order.Hom.Basic._hyg.1281 x._@.Mathlib.Order.Hom.Basic._hyg.1283) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1296 : Submodule.{0, u1} Nat M Nat.semiring _inst_3 (AddCommMonoid.natModule.{u1} M _inst_3)) (x._@.Mathlib.Order.Hom.Basic._hyg.1298 : Submodule.{0, u1} Nat M Nat.semiring _inst_3 (AddCommMonoid.natModule.{u1} M _inst_3)) => LE.le.{u1} (Submodule.{0, u1} Nat M Nat.semiring _inst_3 (AddCommMonoid.natModule.{u1} M _inst_3)) (Preorder.toLE.{u1} (Submodule.{0, u1} Nat M Nat.semiring _inst_3 (AddCommMonoid.natModule.{u1} M _inst_3)) (PartialOrder.toPreorder.{u1} (Submodule.{0, u1} Nat M Nat.semiring _inst_3 (AddCommMonoid.natModule.{u1} M _inst_3)) (CompleteSemilatticeInf.toPartialOrder.{u1} (Submodule.{0, u1} Nat M Nat.semiring _inst_3 (AddCommMonoid.natModule.{u1} M _inst_3)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (Submodule.{0, u1} Nat M Nat.semiring _inst_3 (AddCommMonoid.natModule.{u1} M _inst_3)) (Submodule.completeLattice.{0, u1} Nat M Nat.semiring _inst_3 (AddCommMonoid.natModule.{u1} M _inst_3)))))) x._@.Mathlib.Order.Hom.Basic._hyg.1296 x._@.Mathlib.Order.Hom.Basic._hyg.1298) (RelIso.toRelEmbedding.{u1, u1} (AddSubmonoid.{u1} M (AddMonoid.toAddZeroClass.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3))) (Submodule.{0, u1} Nat M Nat.semiring _inst_3 (AddCommMonoid.natModule.{u1} M _inst_3)) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1281 : AddSubmonoid.{u1} M (AddMonoid.toAddZeroClass.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3))) (x._@.Mathlib.Order.Hom.Basic._hyg.1283 : AddSubmonoid.{u1} M (AddMonoid.toAddZeroClass.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3))) => LE.le.{u1} (AddSubmonoid.{u1} M (AddMonoid.toAddZeroClass.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3))) (Preorder.toLE.{u1} (AddSubmonoid.{u1} M (AddMonoid.toAddZeroClass.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3))) (PartialOrder.toPreorder.{u1} (AddSubmonoid.{u1} M (AddMonoid.toAddZeroClass.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3))) (CompleteSemilatticeInf.toPartialOrder.{u1} (AddSubmonoid.{u1} M (AddMonoid.toAddZeroClass.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3))) (CompleteLattice.toCompleteSemilatticeInf.{u1} (AddSubmonoid.{u1} M (AddMonoid.toAddZeroClass.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3))) (AddSubmonoid.instCompleteLatticeAddSubmonoid.{u1} M (AddMonoid.toAddZeroClass.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3))))))) x._@.Mathlib.Order.Hom.Basic._hyg.1281 x._@.Mathlib.Order.Hom.Basic._hyg.1283) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1296 : Submodule.{0, u1} Nat M Nat.semiring _inst_3 (AddCommMonoid.natModule.{u1} M _inst_3)) (x._@.Mathlib.Order.Hom.Basic._hyg.1298 : Submodule.{0, u1} Nat M Nat.semiring _inst_3 (AddCommMonoid.natModule.{u1} M _inst_3)) => LE.le.{u1} (Submodule.{0, u1} Nat M Nat.semiring _inst_3 (AddCommMonoid.natModule.{u1} M _inst_3)) (Preorder.toLE.{u1} (Submodule.{0, u1} Nat M Nat.semiring _inst_3 (AddCommMonoid.natModule.{u1} M _inst_3)) (PartialOrder.toPreorder.{u1} (Submodule.{0, u1} Nat M Nat.semiring _inst_3 (AddCommMonoid.natModule.{u1} M _inst_3)) (CompleteSemilatticeInf.toPartialOrder.{u1} (Submodule.{0, u1} Nat M Nat.semiring _inst_3 (AddCommMonoid.natModule.{u1} M _inst_3)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (Submodule.{0, u1} Nat M Nat.semiring _inst_3 (AddCommMonoid.natModule.{u1} M _inst_3)) (Submodule.completeLattice.{0, u1} Nat M Nat.semiring _inst_3 (AddCommMonoid.natModule.{u1} M _inst_3)))))) x._@.Mathlib.Order.Hom.Basic._hyg.1296 x._@.Mathlib.Order.Hom.Basic._hyg.1298) (AddSubmonoid.toNatSubmodule.{u1} M _inst_3))) S)) S
+  forall {M : Type.{u1}} [_inst_3 : AddCommMonoid.{u1} M] (S : AddSubmonoid.{u1} M (AddMonoid.toAddZeroClass.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3))), Eq.{succ u1} (AddSubmonoid.{u1} M (AddMonoid.toAddZeroClass.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3))) (Submodule.toAddSubmonoid.{0, u1} Nat M Nat.semiring _inst_3 (AddCommMonoid.natModule.{u1} M _inst_3) (FunLike.coe.{succ u1, succ u1, succ u1} (RelIso.{u1, u1} (AddSubmonoid.{u1} M (AddMonoid.toAddZeroClass.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3))) (Submodule.{0, u1} Nat M Nat.semiring _inst_3 (AddCommMonoid.natModule.{u1} M _inst_3)) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1281 : AddSubmonoid.{u1} M (AddMonoid.toAddZeroClass.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3))) (x._@.Mathlib.Order.Hom.Basic._hyg.1283 : AddSubmonoid.{u1} M (AddMonoid.toAddZeroClass.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3))) => LE.le.{u1} (AddSubmonoid.{u1} M (AddMonoid.toAddZeroClass.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3))) (Preorder.toLE.{u1} (AddSubmonoid.{u1} M (AddMonoid.toAddZeroClass.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3))) (PartialOrder.toPreorder.{u1} (AddSubmonoid.{u1} M (AddMonoid.toAddZeroClass.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3))) (CompleteSemilatticeInf.toPartialOrder.{u1} (AddSubmonoid.{u1} M (AddMonoid.toAddZeroClass.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3))) (CompleteLattice.toCompleteSemilatticeInf.{u1} (AddSubmonoid.{u1} M (AddMonoid.toAddZeroClass.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3))) (AddSubmonoid.instCompleteLatticeAddSubmonoid.{u1} M (AddMonoid.toAddZeroClass.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3))))))) x._@.Mathlib.Order.Hom.Basic._hyg.1281 x._@.Mathlib.Order.Hom.Basic._hyg.1283) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1296 : Submodule.{0, u1} Nat M Nat.semiring _inst_3 (AddCommMonoid.natModule.{u1} M _inst_3)) (x._@.Mathlib.Order.Hom.Basic._hyg.1298 : Submodule.{0, u1} Nat M Nat.semiring _inst_3 (AddCommMonoid.natModule.{u1} M _inst_3)) => LE.le.{u1} (Submodule.{0, u1} Nat M Nat.semiring _inst_3 (AddCommMonoid.natModule.{u1} M _inst_3)) (Preorder.toLE.{u1} (Submodule.{0, u1} Nat M Nat.semiring _inst_3 (AddCommMonoid.natModule.{u1} M _inst_3)) (PartialOrder.toPreorder.{u1} (Submodule.{0, u1} Nat M Nat.semiring _inst_3 (AddCommMonoid.natModule.{u1} M _inst_3)) (CompleteSemilatticeInf.toPartialOrder.{u1} (Submodule.{0, u1} Nat M Nat.semiring _inst_3 (AddCommMonoid.natModule.{u1} M _inst_3)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (Submodule.{0, u1} Nat M Nat.semiring _inst_3 (AddCommMonoid.natModule.{u1} M _inst_3)) (Submodule.completeLattice.{0, u1} Nat M Nat.semiring _inst_3 (AddCommMonoid.natModule.{u1} M _inst_3)))))) x._@.Mathlib.Order.Hom.Basic._hyg.1296 x._@.Mathlib.Order.Hom.Basic._hyg.1298)) (AddSubmonoid.{u1} M (AddMonoid.toAddZeroClass.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3))) (fun (_x : AddSubmonoid.{u1} M (AddMonoid.toAddZeroClass.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3))) => Submodule.{0, u1} Nat M Nat.semiring _inst_3 (AddCommMonoid.natModule.{u1} M _inst_3)) (RelHomClass.toFunLike.{u1, u1, u1} (RelIso.{u1, u1} (AddSubmonoid.{u1} M (AddMonoid.toAddZeroClass.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3))) (Submodule.{0, u1} Nat M Nat.semiring _inst_3 (AddCommMonoid.natModule.{u1} M _inst_3)) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1281 : AddSubmonoid.{u1} M (AddMonoid.toAddZeroClass.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3))) (x._@.Mathlib.Order.Hom.Basic._hyg.1283 : AddSubmonoid.{u1} M (AddMonoid.toAddZeroClass.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3))) => LE.le.{u1} (AddSubmonoid.{u1} M (AddMonoid.toAddZeroClass.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3))) (Preorder.toLE.{u1} (AddSubmonoid.{u1} M (AddMonoid.toAddZeroClass.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3))) (PartialOrder.toPreorder.{u1} (AddSubmonoid.{u1} M (AddMonoid.toAddZeroClass.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3))) (CompleteSemilatticeInf.toPartialOrder.{u1} (AddSubmonoid.{u1} M (AddMonoid.toAddZeroClass.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3))) (CompleteLattice.toCompleteSemilatticeInf.{u1} (AddSubmonoid.{u1} M (AddMonoid.toAddZeroClass.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3))) (AddSubmonoid.instCompleteLatticeAddSubmonoid.{u1} M (AddMonoid.toAddZeroClass.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3))))))) x._@.Mathlib.Order.Hom.Basic._hyg.1281 x._@.Mathlib.Order.Hom.Basic._hyg.1283) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1296 : Submodule.{0, u1} Nat M Nat.semiring _inst_3 (AddCommMonoid.natModule.{u1} M _inst_3)) (x._@.Mathlib.Order.Hom.Basic._hyg.1298 : Submodule.{0, u1} Nat M Nat.semiring _inst_3 (AddCommMonoid.natModule.{u1} M _inst_3)) => LE.le.{u1} (Submodule.{0, u1} Nat M Nat.semiring _inst_3 (AddCommMonoid.natModule.{u1} M _inst_3)) (Preorder.toLE.{u1} (Submodule.{0, u1} Nat M Nat.semiring _inst_3 (AddCommMonoid.natModule.{u1} M _inst_3)) (PartialOrder.toPreorder.{u1} (Submodule.{0, u1} Nat M Nat.semiring _inst_3 (AddCommMonoid.natModule.{u1} M _inst_3)) (CompleteSemilatticeInf.toPartialOrder.{u1} (Submodule.{0, u1} Nat M Nat.semiring _inst_3 (AddCommMonoid.natModule.{u1} M _inst_3)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (Submodule.{0, u1} Nat M Nat.semiring _inst_3 (AddCommMonoid.natModule.{u1} M _inst_3)) (Submodule.completeLattice.{0, u1} Nat M Nat.semiring _inst_3 (AddCommMonoid.natModule.{u1} M _inst_3)))))) x._@.Mathlib.Order.Hom.Basic._hyg.1296 x._@.Mathlib.Order.Hom.Basic._hyg.1298)) (AddSubmonoid.{u1} M (AddMonoid.toAddZeroClass.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3))) (Submodule.{0, u1} Nat M Nat.semiring _inst_3 (AddCommMonoid.natModule.{u1} M _inst_3)) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1281 : AddSubmonoid.{u1} M (AddMonoid.toAddZeroClass.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3))) (x._@.Mathlib.Order.Hom.Basic._hyg.1283 : AddSubmonoid.{u1} M (AddMonoid.toAddZeroClass.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3))) => LE.le.{u1} (AddSubmonoid.{u1} M (AddMonoid.toAddZeroClass.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3))) (Preorder.toLE.{u1} (AddSubmonoid.{u1} M (AddMonoid.toAddZeroClass.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3))) (PartialOrder.toPreorder.{u1} (AddSubmonoid.{u1} M (AddMonoid.toAddZeroClass.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3))) (CompleteSemilatticeInf.toPartialOrder.{u1} (AddSubmonoid.{u1} M (AddMonoid.toAddZeroClass.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3))) (CompleteLattice.toCompleteSemilatticeInf.{u1} (AddSubmonoid.{u1} M (AddMonoid.toAddZeroClass.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3))) (AddSubmonoid.instCompleteLatticeAddSubmonoid.{u1} M (AddMonoid.toAddZeroClass.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3))))))) x._@.Mathlib.Order.Hom.Basic._hyg.1281 x._@.Mathlib.Order.Hom.Basic._hyg.1283) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1296 : Submodule.{0, u1} Nat M Nat.semiring _inst_3 (AddCommMonoid.natModule.{u1} M _inst_3)) (x._@.Mathlib.Order.Hom.Basic._hyg.1298 : Submodule.{0, u1} Nat M Nat.semiring _inst_3 (AddCommMonoid.natModule.{u1} M _inst_3)) => LE.le.{u1} (Submodule.{0, u1} Nat M Nat.semiring _inst_3 (AddCommMonoid.natModule.{u1} M _inst_3)) (Preorder.toLE.{u1} (Submodule.{0, u1} Nat M Nat.semiring _inst_3 (AddCommMonoid.natModule.{u1} M _inst_3)) (PartialOrder.toPreorder.{u1} (Submodule.{0, u1} Nat M Nat.semiring _inst_3 (AddCommMonoid.natModule.{u1} M _inst_3)) (CompleteSemilatticeInf.toPartialOrder.{u1} (Submodule.{0, u1} Nat M Nat.semiring _inst_3 (AddCommMonoid.natModule.{u1} M _inst_3)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (Submodule.{0, u1} Nat M Nat.semiring _inst_3 (AddCommMonoid.natModule.{u1} M _inst_3)) (Submodule.completeLattice.{0, u1} Nat M Nat.semiring _inst_3 (AddCommMonoid.natModule.{u1} M _inst_3)))))) x._@.Mathlib.Order.Hom.Basic._hyg.1296 x._@.Mathlib.Order.Hom.Basic._hyg.1298) (RelIso.instRelHomClassRelIso.{u1, u1} (AddSubmonoid.{u1} M (AddMonoid.toAddZeroClass.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3))) (Submodule.{0, u1} Nat M Nat.semiring _inst_3 (AddCommMonoid.natModule.{u1} M _inst_3)) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1281 : AddSubmonoid.{u1} M (AddMonoid.toAddZeroClass.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3))) (x._@.Mathlib.Order.Hom.Basic._hyg.1283 : AddSubmonoid.{u1} M (AddMonoid.toAddZeroClass.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3))) => LE.le.{u1} (AddSubmonoid.{u1} M (AddMonoid.toAddZeroClass.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3))) (Preorder.toLE.{u1} (AddSubmonoid.{u1} M (AddMonoid.toAddZeroClass.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3))) (PartialOrder.toPreorder.{u1} (AddSubmonoid.{u1} M (AddMonoid.toAddZeroClass.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3))) (CompleteSemilatticeInf.toPartialOrder.{u1} (AddSubmonoid.{u1} M (AddMonoid.toAddZeroClass.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3))) (CompleteLattice.toCompleteSemilatticeInf.{u1} (AddSubmonoid.{u1} M (AddMonoid.toAddZeroClass.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3))) (AddSubmonoid.instCompleteLatticeAddSubmonoid.{u1} M (AddMonoid.toAddZeroClass.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3))))))) x._@.Mathlib.Order.Hom.Basic._hyg.1281 x._@.Mathlib.Order.Hom.Basic._hyg.1283) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1296 : Submodule.{0, u1} Nat M Nat.semiring _inst_3 (AddCommMonoid.natModule.{u1} M _inst_3)) (x._@.Mathlib.Order.Hom.Basic._hyg.1298 : Submodule.{0, u1} Nat M Nat.semiring _inst_3 (AddCommMonoid.natModule.{u1} M _inst_3)) => LE.le.{u1} (Submodule.{0, u1} Nat M Nat.semiring _inst_3 (AddCommMonoid.natModule.{u1} M _inst_3)) (Preorder.toLE.{u1} (Submodule.{0, u1} Nat M Nat.semiring _inst_3 (AddCommMonoid.natModule.{u1} M _inst_3)) (PartialOrder.toPreorder.{u1} (Submodule.{0, u1} Nat M Nat.semiring _inst_3 (AddCommMonoid.natModule.{u1} M _inst_3)) (CompleteSemilatticeInf.toPartialOrder.{u1} (Submodule.{0, u1} Nat M Nat.semiring _inst_3 (AddCommMonoid.natModule.{u1} M _inst_3)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (Submodule.{0, u1} Nat M Nat.semiring _inst_3 (AddCommMonoid.natModule.{u1} M _inst_3)) (Submodule.completeLattice.{0, u1} Nat M Nat.semiring _inst_3 (AddCommMonoid.natModule.{u1} M _inst_3)))))) x._@.Mathlib.Order.Hom.Basic._hyg.1296 x._@.Mathlib.Order.Hom.Basic._hyg.1298))) (AddSubmonoid.toNatSubmodule.{u1} M _inst_3) S)) S
 Case conversion may be inaccurate. Consider using '#align add_submonoid.to_nat_submodule_to_add_submonoid AddSubmonoid.toNatSubmodule_toAddSubmonoidₓ'. -/
 @[simp]
 theorem AddSubmonoid.toNatSubmodule_toAddSubmonoid (S : AddSubmonoid M) :
@@ -658,7 +658,7 @@ theorem AddSubmonoid.toNatSubmodule_toAddSubmonoid (S : AddSubmonoid M) :
 lean 3 declaration is
   forall {M : Type.{u1}} [_inst_3 : AddCommMonoid.{u1} M] (S : Submodule.{0, u1} Nat M Nat.semiring _inst_3 (AddCommMonoid.natModule.{u1} M _inst_3)), Eq.{succ u1} (Submodule.{0, u1} Nat M Nat.semiring _inst_3 (AddCommMonoid.natModule.{u1} M _inst_3)) (coeFn.{succ u1, succ u1} (OrderIso.{u1, u1} (AddSubmonoid.{u1} M (AddMonoid.toAddZeroClass.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3))) (Submodule.{0, u1} Nat M Nat.semiring _inst_3 (AddCommMonoid.natModule.{u1} M _inst_3)) (Preorder.toLE.{u1} (AddSubmonoid.{u1} M (AddMonoid.toAddZeroClass.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3))) (PartialOrder.toPreorder.{u1} (AddSubmonoid.{u1} M (AddMonoid.toAddZeroClass.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3))) (CompleteSemilatticeInf.toPartialOrder.{u1} (AddSubmonoid.{u1} M (AddMonoid.toAddZeroClass.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3))) (CompleteLattice.toCompleteSemilatticeInf.{u1} (AddSubmonoid.{u1} M (AddMonoid.toAddZeroClass.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3))) (AddSubmonoid.completeLattice.{u1} M (AddMonoid.toAddZeroClass.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3))))))) (Preorder.toLE.{u1} (Submodule.{0, u1} Nat M Nat.semiring _inst_3 (AddCommMonoid.natModule.{u1} M _inst_3)) (PartialOrder.toPreorder.{u1} (Submodule.{0, u1} Nat M Nat.semiring _inst_3 (AddCommMonoid.natModule.{u1} M _inst_3)) (CompleteSemilatticeInf.toPartialOrder.{u1} (Submodule.{0, u1} Nat M Nat.semiring _inst_3 (AddCommMonoid.natModule.{u1} M _inst_3)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (Submodule.{0, u1} Nat M Nat.semiring _inst_3 (AddCommMonoid.natModule.{u1} M _inst_3)) (Submodule.completeLattice.{0, u1} Nat M Nat.semiring _inst_3 (AddCommMonoid.natModule.{u1} M _inst_3))))))) (fun (_x : RelIso.{u1, u1} (AddSubmonoid.{u1} M (AddMonoid.toAddZeroClass.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3))) (Submodule.{0, u1} Nat M Nat.semiring _inst_3 (AddCommMonoid.natModule.{u1} M _inst_3)) (LE.le.{u1} (AddSubmonoid.{u1} M (AddMonoid.toAddZeroClass.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3))) (Preorder.toLE.{u1} (AddSubmonoid.{u1} M (AddMonoid.toAddZeroClass.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3))) (PartialOrder.toPreorder.{u1} (AddSubmonoid.{u1} M (AddMonoid.toAddZeroClass.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3))) (CompleteSemilatticeInf.toPartialOrder.{u1} (AddSubmonoid.{u1} M (AddMonoid.toAddZeroClass.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3))) (CompleteLattice.toCompleteSemilatticeInf.{u1} (AddSubmonoid.{u1} M (AddMonoid.toAddZeroClass.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3))) (AddSubmonoid.completeLattice.{u1} M (AddMonoid.toAddZeroClass.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3)))))))) (LE.le.{u1} (Submodule.{0, u1} Nat M Nat.semiring _inst_3 (AddCommMonoid.natModule.{u1} M _inst_3)) (Preorder.toLE.{u1} (Submodule.{0, u1} Nat M Nat.semiring _inst_3 (AddCommMonoid.natModule.{u1} M _inst_3)) (PartialOrder.toPreorder.{u1} (Submodule.{0, u1} Nat M Nat.semiring _inst_3 (AddCommMonoid.natModule.{u1} M _inst_3)) (CompleteSemilatticeInf.toPartialOrder.{u1} (Submodule.{0, u1} Nat M Nat.semiring _inst_3 (AddCommMonoid.natModule.{u1} M _inst_3)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (Submodule.{0, u1} Nat M Nat.semiring _inst_3 (AddCommMonoid.natModule.{u1} M _inst_3)) (Submodule.completeLattice.{0, u1} Nat M Nat.semiring _inst_3 (AddCommMonoid.natModule.{u1} M _inst_3)))))))) => (AddSubmonoid.{u1} M (AddMonoid.toAddZeroClass.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3))) -> (Submodule.{0, u1} Nat M Nat.semiring _inst_3 (AddCommMonoid.natModule.{u1} M _inst_3))) (RelIso.hasCoeToFun.{u1, u1} (AddSubmonoid.{u1} M (AddMonoid.toAddZeroClass.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3))) (Submodule.{0, u1} Nat M Nat.semiring _inst_3 (AddCommMonoid.natModule.{u1} M _inst_3)) (LE.le.{u1} (AddSubmonoid.{u1} M (AddMonoid.toAddZeroClass.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3))) (Preorder.toLE.{u1} (AddSubmonoid.{u1} M (AddMonoid.toAddZeroClass.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3))) (PartialOrder.toPreorder.{u1} (AddSubmonoid.{u1} M (AddMonoid.toAddZeroClass.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3))) (CompleteSemilatticeInf.toPartialOrder.{u1} (AddSubmonoid.{u1} M (AddMonoid.toAddZeroClass.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3))) (CompleteLattice.toCompleteSemilatticeInf.{u1} (AddSubmonoid.{u1} M (AddMonoid.toAddZeroClass.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3))) (AddSubmonoid.completeLattice.{u1} M (AddMonoid.toAddZeroClass.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3)))))))) (LE.le.{u1} (Submodule.{0, u1} Nat M Nat.semiring _inst_3 (AddCommMonoid.natModule.{u1} M _inst_3)) (Preorder.toLE.{u1} (Submodule.{0, u1} Nat M Nat.semiring _inst_3 (AddCommMonoid.natModule.{u1} M _inst_3)) (PartialOrder.toPreorder.{u1} (Submodule.{0, u1} Nat M Nat.semiring _inst_3 (AddCommMonoid.natModule.{u1} M _inst_3)) (CompleteSemilatticeInf.toPartialOrder.{u1} (Submodule.{0, u1} Nat M Nat.semiring _inst_3 (AddCommMonoid.natModule.{u1} M _inst_3)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (Submodule.{0, u1} Nat M Nat.semiring _inst_3 (AddCommMonoid.natModule.{u1} M _inst_3)) (Submodule.completeLattice.{0, u1} Nat M Nat.semiring _inst_3 (AddCommMonoid.natModule.{u1} M _inst_3)))))))) (AddSubmonoid.toNatSubmodule.{u1} M _inst_3) (Submodule.toAddSubmonoid.{0, u1} Nat M Nat.semiring _inst_3 (AddCommMonoid.natModule.{u1} M _inst_3) S)) S
 but is expected to have type
-  forall {M : Type.{u1}} [_inst_3 : AddCommMonoid.{u1} M] (S : Submodule.{0, u1} Nat M Nat.semiring _inst_3 (AddCommMonoid.natModule.{u1} M _inst_3)), Eq.{succ u1} ((fun (x._@.Mathlib.Data.FunLike.Embedding._hyg.19 : AddSubmonoid.{u1} M (AddMonoid.toAddZeroClass.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3))) => Submodule.{0, u1} Nat M Nat.semiring _inst_3 (AddCommMonoid.natModule.{u1} M _inst_3)) (Submodule.toAddSubmonoid.{0, u1} Nat M Nat.semiring _inst_3 (AddCommMonoid.natModule.{u1} M _inst_3) S)) (FunLike.coe.{succ u1, succ u1, succ u1} (Function.Embedding.{succ u1, succ u1} (AddSubmonoid.{u1} M (AddMonoid.toAddZeroClass.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3))) (Submodule.{0, u1} Nat M Nat.semiring _inst_3 (AddCommMonoid.natModule.{u1} M _inst_3))) (AddSubmonoid.{u1} M (AddMonoid.toAddZeroClass.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3))) (fun (_x : AddSubmonoid.{u1} M (AddMonoid.toAddZeroClass.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3))) => (fun (x._@.Mathlib.Data.FunLike.Embedding._hyg.19 : AddSubmonoid.{u1} M (AddMonoid.toAddZeroClass.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3))) => Submodule.{0, u1} Nat M Nat.semiring _inst_3 (AddCommMonoid.natModule.{u1} M _inst_3)) _x) (EmbeddingLike.toFunLike.{succ u1, succ u1, succ u1} (Function.Embedding.{succ u1, succ u1} (AddSubmonoid.{u1} M (AddMonoid.toAddZeroClass.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3))) (Submodule.{0, u1} Nat M Nat.semiring _inst_3 (AddCommMonoid.natModule.{u1} M _inst_3))) (AddSubmonoid.{u1} M (AddMonoid.toAddZeroClass.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3))) (Submodule.{0, u1} Nat M Nat.semiring _inst_3 (AddCommMonoid.natModule.{u1} M _inst_3)) (Function.instEmbeddingLikeEmbedding.{succ u1, succ u1} (AddSubmonoid.{u1} M (AddMonoid.toAddZeroClass.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3))) (Submodule.{0, u1} Nat M Nat.semiring _inst_3 (AddCommMonoid.natModule.{u1} M _inst_3)))) (RelEmbedding.toEmbedding.{u1, u1} (AddSubmonoid.{u1} M (AddMonoid.toAddZeroClass.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3))) (Submodule.{0, u1} Nat M Nat.semiring _inst_3 (AddCommMonoid.natModule.{u1} M _inst_3)) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1281 : AddSubmonoid.{u1} M (AddMonoid.toAddZeroClass.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3))) (x._@.Mathlib.Order.Hom.Basic._hyg.1283 : AddSubmonoid.{u1} M (AddMonoid.toAddZeroClass.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3))) => LE.le.{u1} (AddSubmonoid.{u1} M (AddMonoid.toAddZeroClass.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3))) (Preorder.toLE.{u1} (AddSubmonoid.{u1} M (AddMonoid.toAddZeroClass.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3))) (PartialOrder.toPreorder.{u1} (AddSubmonoid.{u1} M (AddMonoid.toAddZeroClass.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3))) (CompleteSemilatticeInf.toPartialOrder.{u1} (AddSubmonoid.{u1} M (AddMonoid.toAddZeroClass.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3))) (CompleteLattice.toCompleteSemilatticeInf.{u1} (AddSubmonoid.{u1} M (AddMonoid.toAddZeroClass.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3))) (AddSubmonoid.instCompleteLatticeAddSubmonoid.{u1} M (AddMonoid.toAddZeroClass.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3))))))) x._@.Mathlib.Order.Hom.Basic._hyg.1281 x._@.Mathlib.Order.Hom.Basic._hyg.1283) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1296 : Submodule.{0, u1} Nat M Nat.semiring _inst_3 (AddCommMonoid.natModule.{u1} M _inst_3)) (x._@.Mathlib.Order.Hom.Basic._hyg.1298 : Submodule.{0, u1} Nat M Nat.semiring _inst_3 (AddCommMonoid.natModule.{u1} M _inst_3)) => LE.le.{u1} (Submodule.{0, u1} Nat M Nat.semiring _inst_3 (AddCommMonoid.natModule.{u1} M _inst_3)) (Preorder.toLE.{u1} (Submodule.{0, u1} Nat M Nat.semiring _inst_3 (AddCommMonoid.natModule.{u1} M _inst_3)) (PartialOrder.toPreorder.{u1} (Submodule.{0, u1} Nat M Nat.semiring _inst_3 (AddCommMonoid.natModule.{u1} M _inst_3)) (CompleteSemilatticeInf.toPartialOrder.{u1} (Submodule.{0, u1} Nat M Nat.semiring _inst_3 (AddCommMonoid.natModule.{u1} M _inst_3)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (Submodule.{0, u1} Nat M Nat.semiring _inst_3 (AddCommMonoid.natModule.{u1} M _inst_3)) (Submodule.completeLattice.{0, u1} Nat M Nat.semiring _inst_3 (AddCommMonoid.natModule.{u1} M _inst_3)))))) x._@.Mathlib.Order.Hom.Basic._hyg.1296 x._@.Mathlib.Order.Hom.Basic._hyg.1298) (RelIso.toRelEmbedding.{u1, u1} (AddSubmonoid.{u1} M (AddMonoid.toAddZeroClass.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3))) (Submodule.{0, u1} Nat M Nat.semiring _inst_3 (AddCommMonoid.natModule.{u1} M _inst_3)) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1281 : AddSubmonoid.{u1} M (AddMonoid.toAddZeroClass.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3))) (x._@.Mathlib.Order.Hom.Basic._hyg.1283 : AddSubmonoid.{u1} M (AddMonoid.toAddZeroClass.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3))) => LE.le.{u1} (AddSubmonoid.{u1} M (AddMonoid.toAddZeroClass.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3))) (Preorder.toLE.{u1} (AddSubmonoid.{u1} M (AddMonoid.toAddZeroClass.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3))) (PartialOrder.toPreorder.{u1} (AddSubmonoid.{u1} M (AddMonoid.toAddZeroClass.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3))) (CompleteSemilatticeInf.toPartialOrder.{u1} (AddSubmonoid.{u1} M (AddMonoid.toAddZeroClass.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3))) (CompleteLattice.toCompleteSemilatticeInf.{u1} (AddSubmonoid.{u1} M (AddMonoid.toAddZeroClass.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3))) (AddSubmonoid.instCompleteLatticeAddSubmonoid.{u1} M (AddMonoid.toAddZeroClass.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3))))))) x._@.Mathlib.Order.Hom.Basic._hyg.1281 x._@.Mathlib.Order.Hom.Basic._hyg.1283) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1296 : Submodule.{0, u1} Nat M Nat.semiring _inst_3 (AddCommMonoid.natModule.{u1} M _inst_3)) (x._@.Mathlib.Order.Hom.Basic._hyg.1298 : Submodule.{0, u1} Nat M Nat.semiring _inst_3 (AddCommMonoid.natModule.{u1} M _inst_3)) => LE.le.{u1} (Submodule.{0, u1} Nat M Nat.semiring _inst_3 (AddCommMonoid.natModule.{u1} M _inst_3)) (Preorder.toLE.{u1} (Submodule.{0, u1} Nat M Nat.semiring _inst_3 (AddCommMonoid.natModule.{u1} M _inst_3)) (PartialOrder.toPreorder.{u1} (Submodule.{0, u1} Nat M Nat.semiring _inst_3 (AddCommMonoid.natModule.{u1} M _inst_3)) (CompleteSemilatticeInf.toPartialOrder.{u1} (Submodule.{0, u1} Nat M Nat.semiring _inst_3 (AddCommMonoid.natModule.{u1} M _inst_3)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (Submodule.{0, u1} Nat M Nat.semiring _inst_3 (AddCommMonoid.natModule.{u1} M _inst_3)) (Submodule.completeLattice.{0, u1} Nat M Nat.semiring _inst_3 (AddCommMonoid.natModule.{u1} M _inst_3)))))) x._@.Mathlib.Order.Hom.Basic._hyg.1296 x._@.Mathlib.Order.Hom.Basic._hyg.1298) (AddSubmonoid.toNatSubmodule.{u1} M _inst_3))) (Submodule.toAddSubmonoid.{0, u1} Nat M Nat.semiring _inst_3 (AddCommMonoid.natModule.{u1} M _inst_3) S)) S
+  forall {M : Type.{u1}} [_inst_3 : AddCommMonoid.{u1} M] (S : Submodule.{0, u1} Nat M Nat.semiring _inst_3 (AddCommMonoid.natModule.{u1} M _inst_3)), Eq.{succ u1} (Submodule.{0, u1} Nat M Nat.semiring _inst_3 (AddCommMonoid.natModule.{u1} M _inst_3)) (FunLike.coe.{succ u1, succ u1, succ u1} (RelIso.{u1, u1} (AddSubmonoid.{u1} M (AddMonoid.toAddZeroClass.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3))) (Submodule.{0, u1} Nat M Nat.semiring _inst_3 (AddCommMonoid.natModule.{u1} M _inst_3)) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1281 : AddSubmonoid.{u1} M (AddMonoid.toAddZeroClass.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3))) (x._@.Mathlib.Order.Hom.Basic._hyg.1283 : AddSubmonoid.{u1} M (AddMonoid.toAddZeroClass.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3))) => LE.le.{u1} (AddSubmonoid.{u1} M (AddMonoid.toAddZeroClass.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3))) (Preorder.toLE.{u1} (AddSubmonoid.{u1} M (AddMonoid.toAddZeroClass.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3))) (PartialOrder.toPreorder.{u1} (AddSubmonoid.{u1} M (AddMonoid.toAddZeroClass.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3))) (CompleteSemilatticeInf.toPartialOrder.{u1} (AddSubmonoid.{u1} M (AddMonoid.toAddZeroClass.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3))) (CompleteLattice.toCompleteSemilatticeInf.{u1} (AddSubmonoid.{u1} M (AddMonoid.toAddZeroClass.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3))) (AddSubmonoid.instCompleteLatticeAddSubmonoid.{u1} M (AddMonoid.toAddZeroClass.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3))))))) x._@.Mathlib.Order.Hom.Basic._hyg.1281 x._@.Mathlib.Order.Hom.Basic._hyg.1283) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1296 : Submodule.{0, u1} Nat M Nat.semiring _inst_3 (AddCommMonoid.natModule.{u1} M _inst_3)) (x._@.Mathlib.Order.Hom.Basic._hyg.1298 : Submodule.{0, u1} Nat M Nat.semiring _inst_3 (AddCommMonoid.natModule.{u1} M _inst_3)) => LE.le.{u1} (Submodule.{0, u1} Nat M Nat.semiring _inst_3 (AddCommMonoid.natModule.{u1} M _inst_3)) (Preorder.toLE.{u1} (Submodule.{0, u1} Nat M Nat.semiring _inst_3 (AddCommMonoid.natModule.{u1} M _inst_3)) (PartialOrder.toPreorder.{u1} (Submodule.{0, u1} Nat M Nat.semiring _inst_3 (AddCommMonoid.natModule.{u1} M _inst_3)) (CompleteSemilatticeInf.toPartialOrder.{u1} (Submodule.{0, u1} Nat M Nat.semiring _inst_3 (AddCommMonoid.natModule.{u1} M _inst_3)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (Submodule.{0, u1} Nat M Nat.semiring _inst_3 (AddCommMonoid.natModule.{u1} M _inst_3)) (Submodule.completeLattice.{0, u1} Nat M Nat.semiring _inst_3 (AddCommMonoid.natModule.{u1} M _inst_3)))))) x._@.Mathlib.Order.Hom.Basic._hyg.1296 x._@.Mathlib.Order.Hom.Basic._hyg.1298)) (AddSubmonoid.{u1} M (AddMonoid.toAddZeroClass.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3))) (fun (_x : AddSubmonoid.{u1} M (AddMonoid.toAddZeroClass.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3))) => Submodule.{0, u1} Nat M Nat.semiring _inst_3 (AddCommMonoid.natModule.{u1} M _inst_3)) (RelHomClass.toFunLike.{u1, u1, u1} (RelIso.{u1, u1} (AddSubmonoid.{u1} M (AddMonoid.toAddZeroClass.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3))) (Submodule.{0, u1} Nat M Nat.semiring _inst_3 (AddCommMonoid.natModule.{u1} M _inst_3)) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1281 : AddSubmonoid.{u1} M (AddMonoid.toAddZeroClass.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3))) (x._@.Mathlib.Order.Hom.Basic._hyg.1283 : AddSubmonoid.{u1} M (AddMonoid.toAddZeroClass.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3))) => LE.le.{u1} (AddSubmonoid.{u1} M (AddMonoid.toAddZeroClass.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3))) (Preorder.toLE.{u1} (AddSubmonoid.{u1} M (AddMonoid.toAddZeroClass.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3))) (PartialOrder.toPreorder.{u1} (AddSubmonoid.{u1} M (AddMonoid.toAddZeroClass.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3))) (CompleteSemilatticeInf.toPartialOrder.{u1} (AddSubmonoid.{u1} M (AddMonoid.toAddZeroClass.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3))) (CompleteLattice.toCompleteSemilatticeInf.{u1} (AddSubmonoid.{u1} M (AddMonoid.toAddZeroClass.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3))) (AddSubmonoid.instCompleteLatticeAddSubmonoid.{u1} M (AddMonoid.toAddZeroClass.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3))))))) x._@.Mathlib.Order.Hom.Basic._hyg.1281 x._@.Mathlib.Order.Hom.Basic._hyg.1283) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1296 : Submodule.{0, u1} Nat M Nat.semiring _inst_3 (AddCommMonoid.natModule.{u1} M _inst_3)) (x._@.Mathlib.Order.Hom.Basic._hyg.1298 : Submodule.{0, u1} Nat M Nat.semiring _inst_3 (AddCommMonoid.natModule.{u1} M _inst_3)) => LE.le.{u1} (Submodule.{0, u1} Nat M Nat.semiring _inst_3 (AddCommMonoid.natModule.{u1} M _inst_3)) (Preorder.toLE.{u1} (Submodule.{0, u1} Nat M Nat.semiring _inst_3 (AddCommMonoid.natModule.{u1} M _inst_3)) (PartialOrder.toPreorder.{u1} (Submodule.{0, u1} Nat M Nat.semiring _inst_3 (AddCommMonoid.natModule.{u1} M _inst_3)) (CompleteSemilatticeInf.toPartialOrder.{u1} (Submodule.{0, u1} Nat M Nat.semiring _inst_3 (AddCommMonoid.natModule.{u1} M _inst_3)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (Submodule.{0, u1} Nat M Nat.semiring _inst_3 (AddCommMonoid.natModule.{u1} M _inst_3)) (Submodule.completeLattice.{0, u1} Nat M Nat.semiring _inst_3 (AddCommMonoid.natModule.{u1} M _inst_3)))))) x._@.Mathlib.Order.Hom.Basic._hyg.1296 x._@.Mathlib.Order.Hom.Basic._hyg.1298)) (AddSubmonoid.{u1} M (AddMonoid.toAddZeroClass.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3))) (Submodule.{0, u1} Nat M Nat.semiring _inst_3 (AddCommMonoid.natModule.{u1} M _inst_3)) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1281 : AddSubmonoid.{u1} M (AddMonoid.toAddZeroClass.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3))) (x._@.Mathlib.Order.Hom.Basic._hyg.1283 : AddSubmonoid.{u1} M (AddMonoid.toAddZeroClass.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3))) => LE.le.{u1} (AddSubmonoid.{u1} M (AddMonoid.toAddZeroClass.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3))) (Preorder.toLE.{u1} (AddSubmonoid.{u1} M (AddMonoid.toAddZeroClass.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3))) (PartialOrder.toPreorder.{u1} (AddSubmonoid.{u1} M (AddMonoid.toAddZeroClass.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3))) (CompleteSemilatticeInf.toPartialOrder.{u1} (AddSubmonoid.{u1} M (AddMonoid.toAddZeroClass.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3))) (CompleteLattice.toCompleteSemilatticeInf.{u1} (AddSubmonoid.{u1} M (AddMonoid.toAddZeroClass.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3))) (AddSubmonoid.instCompleteLatticeAddSubmonoid.{u1} M (AddMonoid.toAddZeroClass.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3))))))) x._@.Mathlib.Order.Hom.Basic._hyg.1281 x._@.Mathlib.Order.Hom.Basic._hyg.1283) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1296 : Submodule.{0, u1} Nat M Nat.semiring _inst_3 (AddCommMonoid.natModule.{u1} M _inst_3)) (x._@.Mathlib.Order.Hom.Basic._hyg.1298 : Submodule.{0, u1} Nat M Nat.semiring _inst_3 (AddCommMonoid.natModule.{u1} M _inst_3)) => LE.le.{u1} (Submodule.{0, u1} Nat M Nat.semiring _inst_3 (AddCommMonoid.natModule.{u1} M _inst_3)) (Preorder.toLE.{u1} (Submodule.{0, u1} Nat M Nat.semiring _inst_3 (AddCommMonoid.natModule.{u1} M _inst_3)) (PartialOrder.toPreorder.{u1} (Submodule.{0, u1} Nat M Nat.semiring _inst_3 (AddCommMonoid.natModule.{u1} M _inst_3)) (CompleteSemilatticeInf.toPartialOrder.{u1} (Submodule.{0, u1} Nat M Nat.semiring _inst_3 (AddCommMonoid.natModule.{u1} M _inst_3)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (Submodule.{0, u1} Nat M Nat.semiring _inst_3 (AddCommMonoid.natModule.{u1} M _inst_3)) (Submodule.completeLattice.{0, u1} Nat M Nat.semiring _inst_3 (AddCommMonoid.natModule.{u1} M _inst_3)))))) x._@.Mathlib.Order.Hom.Basic._hyg.1296 x._@.Mathlib.Order.Hom.Basic._hyg.1298) (RelIso.instRelHomClassRelIso.{u1, u1} (AddSubmonoid.{u1} M (AddMonoid.toAddZeroClass.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3))) (Submodule.{0, u1} Nat M Nat.semiring _inst_3 (AddCommMonoid.natModule.{u1} M _inst_3)) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1281 : AddSubmonoid.{u1} M (AddMonoid.toAddZeroClass.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3))) (x._@.Mathlib.Order.Hom.Basic._hyg.1283 : AddSubmonoid.{u1} M (AddMonoid.toAddZeroClass.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3))) => LE.le.{u1} (AddSubmonoid.{u1} M (AddMonoid.toAddZeroClass.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3))) (Preorder.toLE.{u1} (AddSubmonoid.{u1} M (AddMonoid.toAddZeroClass.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3))) (PartialOrder.toPreorder.{u1} (AddSubmonoid.{u1} M (AddMonoid.toAddZeroClass.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3))) (CompleteSemilatticeInf.toPartialOrder.{u1} (AddSubmonoid.{u1} M (AddMonoid.toAddZeroClass.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3))) (CompleteLattice.toCompleteSemilatticeInf.{u1} (AddSubmonoid.{u1} M (AddMonoid.toAddZeroClass.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3))) (AddSubmonoid.instCompleteLatticeAddSubmonoid.{u1} M (AddMonoid.toAddZeroClass.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3))))))) x._@.Mathlib.Order.Hom.Basic._hyg.1281 x._@.Mathlib.Order.Hom.Basic._hyg.1283) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1296 : Submodule.{0, u1} Nat M Nat.semiring _inst_3 (AddCommMonoid.natModule.{u1} M _inst_3)) (x._@.Mathlib.Order.Hom.Basic._hyg.1298 : Submodule.{0, u1} Nat M Nat.semiring _inst_3 (AddCommMonoid.natModule.{u1} M _inst_3)) => LE.le.{u1} (Submodule.{0, u1} Nat M Nat.semiring _inst_3 (AddCommMonoid.natModule.{u1} M _inst_3)) (Preorder.toLE.{u1} (Submodule.{0, u1} Nat M Nat.semiring _inst_3 (AddCommMonoid.natModule.{u1} M _inst_3)) (PartialOrder.toPreorder.{u1} (Submodule.{0, u1} Nat M Nat.semiring _inst_3 (AddCommMonoid.natModule.{u1} M _inst_3)) (CompleteSemilatticeInf.toPartialOrder.{u1} (Submodule.{0, u1} Nat M Nat.semiring _inst_3 (AddCommMonoid.natModule.{u1} M _inst_3)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (Submodule.{0, u1} Nat M Nat.semiring _inst_3 (AddCommMonoid.natModule.{u1} M _inst_3)) (Submodule.completeLattice.{0, u1} Nat M Nat.semiring _inst_3 (AddCommMonoid.natModule.{u1} M _inst_3)))))) x._@.Mathlib.Order.Hom.Basic._hyg.1296 x._@.Mathlib.Order.Hom.Basic._hyg.1298))) (AddSubmonoid.toNatSubmodule.{u1} M _inst_3) (Submodule.toAddSubmonoid.{0, u1} Nat M Nat.semiring _inst_3 (AddCommMonoid.natModule.{u1} M _inst_3) S)) S
 Case conversion may be inaccurate. Consider using '#align submodule.to_add_submonoid_to_nat_submodule Submodule.toAddSubmonoid_toNatSubmoduleₓ'. -/
 @[simp]
 theorem Submodule.toAddSubmonoid_toNatSubmodule (S : Submodule ℕ M) :
@@ -694,7 +694,7 @@ def AddSubgroup.toIntSubmodule : AddSubgroup M ≃o Submodule ℤ M
 lean 3 declaration is
   forall {M : Type.{u1}} [_inst_1 : AddCommGroup.{u1} M], Eq.{succ u1} ((Submodule.{0, u1} Int M Int.semiring (AddCommGroup.toAddCommMonoid.{u1} M _inst_1) (AddCommGroup.intModule.{u1} M _inst_1)) -> (AddSubgroup.{u1} M (AddCommGroup.toAddGroup.{u1} M _inst_1))) (coeFn.{succ u1, succ u1} (OrderIso.{u1, u1} (Submodule.{0, u1} Int M Int.semiring (AddCommGroup.toAddCommMonoid.{u1} M _inst_1) (AddCommGroup.intModule.{u1} M _inst_1)) (AddSubgroup.{u1} M (AddCommGroup.toAddGroup.{u1} M _inst_1)) (Preorder.toLE.{u1} (Submodule.{0, u1} Int M Int.semiring (AddCommGroup.toAddCommMonoid.{u1} M _inst_1) (AddCommGroup.intModule.{u1} M _inst_1)) (PartialOrder.toPreorder.{u1} (Submodule.{0, u1} Int M Int.semiring (AddCommGroup.toAddCommMonoid.{u1} M _inst_1) (AddCommGroup.intModule.{u1} M _inst_1)) (CompleteSemilatticeInf.toPartialOrder.{u1} (Submodule.{0, u1} Int M Int.semiring (AddCommGroup.toAddCommMonoid.{u1} M _inst_1) (AddCommGroup.intModule.{u1} M _inst_1)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (Submodule.{0, u1} Int M Int.semiring (AddCommGroup.toAddCommMonoid.{u1} M _inst_1) (AddCommGroup.intModule.{u1} M _inst_1)) (Submodule.completeLattice.{0, u1} Int M Int.semiring (AddCommGroup.toAddCommMonoid.{u1} M _inst_1) (AddCommGroup.intModule.{u1} M _inst_1)))))) (Preorder.toLE.{u1} (AddSubgroup.{u1} M (AddCommGroup.toAddGroup.{u1} M _inst_1)) (PartialOrder.toPreorder.{u1} (AddSubgroup.{u1} M (AddCommGroup.toAddGroup.{u1} M _inst_1)) (CompleteSemilatticeInf.toPartialOrder.{u1} (AddSubgroup.{u1} M (AddCommGroup.toAddGroup.{u1} M _inst_1)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (AddSubgroup.{u1} M (AddCommGroup.toAddGroup.{u1} M _inst_1)) (AddSubgroup.completeLattice.{u1} M (AddCommGroup.toAddGroup.{u1} M _inst_1))))))) (fun (_x : RelIso.{u1, u1} (Submodule.{0, u1} Int M Int.semiring (AddCommGroup.toAddCommMonoid.{u1} M _inst_1) (AddCommGroup.intModule.{u1} M _inst_1)) (AddSubgroup.{u1} M (AddCommGroup.toAddGroup.{u1} M _inst_1)) (LE.le.{u1} (Submodule.{0, u1} Int M Int.semiring (AddCommGroup.toAddCommMonoid.{u1} M _inst_1) (AddCommGroup.intModule.{u1} M _inst_1)) (Preorder.toLE.{u1} (Submodule.{0, u1} Int M Int.semiring (AddCommGroup.toAddCommMonoid.{u1} M _inst_1) (AddCommGroup.intModule.{u1} M _inst_1)) (PartialOrder.toPreorder.{u1} (Submodule.{0, u1} Int M Int.semiring (AddCommGroup.toAddCommMonoid.{u1} M _inst_1) (AddCommGroup.intModule.{u1} M _inst_1)) (CompleteSemilatticeInf.toPartialOrder.{u1} (Submodule.{0, u1} Int M Int.semiring (AddCommGroup.toAddCommMonoid.{u1} M _inst_1) (AddCommGroup.intModule.{u1} M _inst_1)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (Submodule.{0, u1} Int M Int.semiring (AddCommGroup.toAddCommMonoid.{u1} M _inst_1) (AddCommGroup.intModule.{u1} M _inst_1)) (Submodule.completeLattice.{0, u1} Int M Int.semiring (AddCommGroup.toAddCommMonoid.{u1} M _inst_1) (AddCommGroup.intModule.{u1} M _inst_1))))))) (LE.le.{u1} (AddSubgroup.{u1} M (AddCommGroup.toAddGroup.{u1} M _inst_1)) (Preorder.toLE.{u1} (AddSubgroup.{u1} M (AddCommGroup.toAddGroup.{u1} M _inst_1)) (PartialOrder.toPreorder.{u1} (AddSubgroup.{u1} M (AddCommGroup.toAddGroup.{u1} M _inst_1)) (CompleteSemilatticeInf.toPartialOrder.{u1} (AddSubgroup.{u1} M (AddCommGroup.toAddGroup.{u1} M _inst_1)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (AddSubgroup.{u1} M (AddCommGroup.toAddGroup.{u1} M _inst_1)) (AddSubgroup.completeLattice.{u1} M (AddCommGroup.toAddGroup.{u1} M _inst_1)))))))) => (Submodule.{0, u1} Int M Int.semiring (AddCommGroup.toAddCommMonoid.{u1} M _inst_1) (AddCommGroup.intModule.{u1} M _inst_1)) -> (AddSubgroup.{u1} M (AddCommGroup.toAddGroup.{u1} M _inst_1))) (RelIso.hasCoeToFun.{u1, u1} (Submodule.{0, u1} Int M Int.semiring (AddCommGroup.toAddCommMonoid.{u1} M _inst_1) (AddCommGroup.intModule.{u1} M _inst_1)) (AddSubgroup.{u1} M (AddCommGroup.toAddGroup.{u1} M _inst_1)) (LE.le.{u1} (Submodule.{0, u1} Int M Int.semiring (AddCommGroup.toAddCommMonoid.{u1} M _inst_1) (AddCommGroup.intModule.{u1} M _inst_1)) (Preorder.toLE.{u1} (Submodule.{0, u1} Int M Int.semiring (AddCommGroup.toAddCommMonoid.{u1} M _inst_1) (AddCommGroup.intModule.{u1} M _inst_1)) (PartialOrder.toPreorder.{u1} (Submodule.{0, u1} Int M Int.semiring (AddCommGroup.toAddCommMonoid.{u1} M _inst_1) (AddCommGroup.intModule.{u1} M _inst_1)) (CompleteSemilatticeInf.toPartialOrder.{u1} (Submodule.{0, u1} Int M Int.semiring (AddCommGroup.toAddCommMonoid.{u1} M _inst_1) (AddCommGroup.intModule.{u1} M _inst_1)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (Submodule.{0, u1} Int M Int.semiring (AddCommGroup.toAddCommMonoid.{u1} M _inst_1) (AddCommGroup.intModule.{u1} M _inst_1)) (Submodule.completeLattice.{0, u1} Int M Int.semiring (AddCommGroup.toAddCommMonoid.{u1} M _inst_1) (AddCommGroup.intModule.{u1} M _inst_1))))))) (LE.le.{u1} (AddSubgroup.{u1} M (AddCommGroup.toAddGroup.{u1} M _inst_1)) (Preorder.toLE.{u1} (AddSubgroup.{u1} M (AddCommGroup.toAddGroup.{u1} M _inst_1)) (PartialOrder.toPreorder.{u1} (AddSubgroup.{u1} M (AddCommGroup.toAddGroup.{u1} M _inst_1)) (CompleteSemilatticeInf.toPartialOrder.{u1} (AddSubgroup.{u1} M (AddCommGroup.toAddGroup.{u1} M _inst_1)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (AddSubgroup.{u1} M (AddCommGroup.toAddGroup.{u1} M _inst_1)) (AddSubgroup.completeLattice.{u1} M (AddCommGroup.toAddGroup.{u1} M _inst_1)))))))) (OrderIso.symm.{u1, u1} (AddSubgroup.{u1} M (AddCommGroup.toAddGroup.{u1} M _inst_1)) (Submodule.{0, u1} Int M Int.semiring (AddCommGroup.toAddCommMonoid.{u1} M _inst_1) (AddCommGroup.intModule.{u1} M _inst_1)) (Preorder.toLE.{u1} (AddSubgroup.{u1} M (AddCommGroup.toAddGroup.{u1} M _inst_1)) (PartialOrder.toPreorder.{u1} (AddSubgroup.{u1} M (AddCommGroup.toAddGroup.{u1} M _inst_1)) (CompleteSemilatticeInf.toPartialOrder.{u1} (AddSubgroup.{u1} M (AddCommGroup.toAddGroup.{u1} M _inst_1)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (AddSubgroup.{u1} M (AddCommGroup.toAddGroup.{u1} M _inst_1)) (AddSubgroup.completeLattice.{u1} M (AddCommGroup.toAddGroup.{u1} M _inst_1)))))) (Preorder.toLE.{u1} (Submodule.{0, u1} Int M Int.semiring (AddCommGroup.toAddCommMonoid.{u1} M _inst_1) (AddCommGroup.intModule.{u1} M _inst_1)) (PartialOrder.toPreorder.{u1} (Submodule.{0, u1} Int M Int.semiring (AddCommGroup.toAddCommMonoid.{u1} M _inst_1) (AddCommGroup.intModule.{u1} M _inst_1)) (CompleteSemilatticeInf.toPartialOrder.{u1} (Submodule.{0, u1} Int M Int.semiring (AddCommGroup.toAddCommMonoid.{u1} M _inst_1) (AddCommGroup.intModule.{u1} M _inst_1)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (Submodule.{0, u1} Int M Int.semiring (AddCommGroup.toAddCommMonoid.{u1} M _inst_1) (AddCommGroup.intModule.{u1} M _inst_1)) (Submodule.completeLattice.{0, u1} Int M Int.semiring (AddCommGroup.toAddCommMonoid.{u1} M _inst_1) (AddCommGroup.intModule.{u1} M _inst_1)))))) (AddSubgroup.toIntSubmodule.{u1} M _inst_1))) (Submodule.toAddSubgroup.{0, u1} Int M Int.ring _inst_1 (AddCommGroup.intModule.{u1} M _inst_1))
 but is expected to have type
-  forall {M : Type.{u1}} [_inst_1 : AddCommGroup.{u1} M], Eq.{succ u1} (forall (ᾰ : Submodule.{0, u1} Int M Int.instSemiringInt (AddCommGroup.toAddCommMonoid.{u1} M _inst_1) (AddCommGroup.intModule.{u1} M _inst_1)), (fun (x._@.Mathlib.Data.FunLike.Embedding._hyg.19 : Submodule.{0, u1} Int M Int.instSemiringInt (AddCommGroup.toAddCommMonoid.{u1} M _inst_1) (AddCommGroup.intModule.{u1} M _inst_1)) => AddSubgroup.{u1} M (AddCommGroup.toAddGroup.{u1} M _inst_1)) ᾰ) (FunLike.coe.{succ u1, succ u1, succ u1} (Function.Embedding.{succ u1, succ u1} (Submodule.{0, u1} Int M Int.instSemiringInt (AddCommGroup.toAddCommMonoid.{u1} M _inst_1) (AddCommGroup.intModule.{u1} M _inst_1)) (AddSubgroup.{u1} M (AddCommGroup.toAddGroup.{u1} M _inst_1))) (Submodule.{0, u1} Int M Int.instSemiringInt (AddCommGroup.toAddCommMonoid.{u1} M _inst_1) (AddCommGroup.intModule.{u1} M _inst_1)) (fun (_x : Submodule.{0, u1} Int M Int.instSemiringInt (AddCommGroup.toAddCommMonoid.{u1} M _inst_1) (AddCommGroup.intModule.{u1} M _inst_1)) => (fun (x._@.Mathlib.Data.FunLike.Embedding._hyg.19 : Submodule.{0, u1} Int M Int.instSemiringInt (AddCommGroup.toAddCommMonoid.{u1} M _inst_1) (AddCommGroup.intModule.{u1} M _inst_1)) => AddSubgroup.{u1} M (AddCommGroup.toAddGroup.{u1} M _inst_1)) _x) (EmbeddingLike.toFunLike.{succ u1, succ u1, succ u1} (Function.Embedding.{succ u1, succ u1} (Submodule.{0, u1} Int M Int.instSemiringInt (AddCommGroup.toAddCommMonoid.{u1} M _inst_1) (AddCommGroup.intModule.{u1} M _inst_1)) (AddSubgroup.{u1} M (AddCommGroup.toAddGroup.{u1} M _inst_1))) (Submodule.{0, u1} Int M Int.instSemiringInt (AddCommGroup.toAddCommMonoid.{u1} M _inst_1) (AddCommGroup.intModule.{u1} M _inst_1)) (AddSubgroup.{u1} M (AddCommGroup.toAddGroup.{u1} M _inst_1)) (Function.instEmbeddingLikeEmbedding.{succ u1, succ u1} (Submodule.{0, u1} Int M Int.instSemiringInt (AddCommGroup.toAddCommMonoid.{u1} M _inst_1) (AddCommGroup.intModule.{u1} M _inst_1)) (AddSubgroup.{u1} M (AddCommGroup.toAddGroup.{u1} M _inst_1)))) (RelEmbedding.toEmbedding.{u1, u1} (Submodule.{0, u1} Int M Int.instSemiringInt (AddCommGroup.toAddCommMonoid.{u1} M _inst_1) (AddCommGroup.intModule.{u1} M _inst_1)) (AddSubgroup.{u1} M (AddCommGroup.toAddGroup.{u1} M _inst_1)) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1281 : Submodule.{0, u1} Int M Int.instSemiringInt (AddCommGroup.toAddCommMonoid.{u1} M _inst_1) (AddCommGroup.intModule.{u1} M _inst_1)) (x._@.Mathlib.Order.Hom.Basic._hyg.1283 : Submodule.{0, u1} Int M Int.instSemiringInt (AddCommGroup.toAddCommMonoid.{u1} M _inst_1) (AddCommGroup.intModule.{u1} M _inst_1)) => LE.le.{u1} (Submodule.{0, u1} Int M Int.instSemiringInt (AddCommGroup.toAddCommMonoid.{u1} M _inst_1) (AddCommGroup.intModule.{u1} M _inst_1)) (Preorder.toLE.{u1} (Submodule.{0, u1} Int M Int.instSemiringInt (AddCommGroup.toAddCommMonoid.{u1} M _inst_1) (AddCommGroup.intModule.{u1} M _inst_1)) (PartialOrder.toPreorder.{u1} (Submodule.{0, u1} Int M Int.instSemiringInt (AddCommGroup.toAddCommMonoid.{u1} M _inst_1) (AddCommGroup.intModule.{u1} M _inst_1)) (CompleteSemilatticeInf.toPartialOrder.{u1} (Submodule.{0, u1} Int M Int.instSemiringInt (AddCommGroup.toAddCommMonoid.{u1} M _inst_1) (AddCommGroup.intModule.{u1} M _inst_1)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (Submodule.{0, u1} Int M Int.instSemiringInt (AddCommGroup.toAddCommMonoid.{u1} M _inst_1) (AddCommGroup.intModule.{u1} M _inst_1)) (Submodule.completeLattice.{0, u1} Int M Int.instSemiringInt (AddCommGroup.toAddCommMonoid.{u1} M _inst_1) (AddCommGroup.intModule.{u1} M _inst_1)))))) x._@.Mathlib.Order.Hom.Basic._hyg.1281 x._@.Mathlib.Order.Hom.Basic._hyg.1283) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1296 : AddSubgroup.{u1} M (AddCommGroup.toAddGroup.{u1} M _inst_1)) (x._@.Mathlib.Order.Hom.Basic._hyg.1298 : AddSubgroup.{u1} M (AddCommGroup.toAddGroup.{u1} M _inst_1)) => LE.le.{u1} (AddSubgroup.{u1} M (AddCommGroup.toAddGroup.{u1} M _inst_1)) (Preorder.toLE.{u1} (AddSubgroup.{u1} M (AddCommGroup.toAddGroup.{u1} M _inst_1)) (PartialOrder.toPreorder.{u1} (AddSubgroup.{u1} M (AddCommGroup.toAddGroup.{u1} M _inst_1)) (CompleteSemilatticeInf.toPartialOrder.{u1} (AddSubgroup.{u1} M (AddCommGroup.toAddGroup.{u1} M _inst_1)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (AddSubgroup.{u1} M (AddCommGroup.toAddGroup.{u1} M _inst_1)) (AddSubgroup.instCompleteLatticeAddSubgroup.{u1} M (AddCommGroup.toAddGroup.{u1} M _inst_1)))))) x._@.Mathlib.Order.Hom.Basic._hyg.1296 x._@.Mathlib.Order.Hom.Basic._hyg.1298) (RelIso.toRelEmbedding.{u1, u1} (Submodule.{0, u1} Int M Int.instSemiringInt (AddCommGroup.toAddCommMonoid.{u1} M _inst_1) (AddCommGroup.intModule.{u1} M _inst_1)) (AddSubgroup.{u1} M (AddCommGroup.toAddGroup.{u1} M _inst_1)) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1281 : Submodule.{0, u1} Int M Int.instSemiringInt (AddCommGroup.toAddCommMonoid.{u1} M _inst_1) (AddCommGroup.intModule.{u1} M _inst_1)) (x._@.Mathlib.Order.Hom.Basic._hyg.1283 : Submodule.{0, u1} Int M Int.instSemiringInt (AddCommGroup.toAddCommMonoid.{u1} M _inst_1) (AddCommGroup.intModule.{u1} M _inst_1)) => LE.le.{u1} (Submodule.{0, u1} Int M Int.instSemiringInt (AddCommGroup.toAddCommMonoid.{u1} M _inst_1) (AddCommGroup.intModule.{u1} M _inst_1)) (Preorder.toLE.{u1} (Submodule.{0, u1} Int M Int.instSemiringInt (AddCommGroup.toAddCommMonoid.{u1} M _inst_1) (AddCommGroup.intModule.{u1} M _inst_1)) (PartialOrder.toPreorder.{u1} (Submodule.{0, u1} Int M Int.instSemiringInt (AddCommGroup.toAddCommMonoid.{u1} M _inst_1) (AddCommGroup.intModule.{u1} M _inst_1)) (CompleteSemilatticeInf.toPartialOrder.{u1} (Submodule.{0, u1} Int M Int.instSemiringInt (AddCommGroup.toAddCommMonoid.{u1} M _inst_1) (AddCommGroup.intModule.{u1} M _inst_1)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (Submodule.{0, u1} Int M Int.instSemiringInt (AddCommGroup.toAddCommMonoid.{u1} M _inst_1) (AddCommGroup.intModule.{u1} M _inst_1)) (Submodule.completeLattice.{0, u1} Int M Int.instSemiringInt (AddCommGroup.toAddCommMonoid.{u1} M _inst_1) (AddCommGroup.intModule.{u1} M _inst_1)))))) x._@.Mathlib.Order.Hom.Basic._hyg.1281 x._@.Mathlib.Order.Hom.Basic._hyg.1283) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1296 : AddSubgroup.{u1} M (AddCommGroup.toAddGroup.{u1} M _inst_1)) (x._@.Mathlib.Order.Hom.Basic._hyg.1298 : AddSubgroup.{u1} M (AddCommGroup.toAddGroup.{u1} M _inst_1)) => LE.le.{u1} (AddSubgroup.{u1} M (AddCommGroup.toAddGroup.{u1} M _inst_1)) (Preorder.toLE.{u1} (AddSubgroup.{u1} M (AddCommGroup.toAddGroup.{u1} M _inst_1)) (PartialOrder.toPreorder.{u1} (AddSubgroup.{u1} M (AddCommGroup.toAddGroup.{u1} M _inst_1)) (CompleteSemilatticeInf.toPartialOrder.{u1} (AddSubgroup.{u1} M (AddCommGroup.toAddGroup.{u1} M _inst_1)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (AddSubgroup.{u1} M (AddCommGroup.toAddGroup.{u1} M _inst_1)) (AddSubgroup.instCompleteLatticeAddSubgroup.{u1} M (AddCommGroup.toAddGroup.{u1} M _inst_1)))))) x._@.Mathlib.Order.Hom.Basic._hyg.1296 x._@.Mathlib.Order.Hom.Basic._hyg.1298) (OrderIso.symm.{u1, u1} (AddSubgroup.{u1} M (AddCommGroup.toAddGroup.{u1} M _inst_1)) (Submodule.{0, u1} Int M Int.instSemiringInt (AddCommGroup.toAddCommMonoid.{u1} M _inst_1) (AddCommGroup.intModule.{u1} M _inst_1)) (Preorder.toLE.{u1} (AddSubgroup.{u1} M (AddCommGroup.toAddGroup.{u1} M _inst_1)) (PartialOrder.toPreorder.{u1} (AddSubgroup.{u1} M (AddCommGroup.toAddGroup.{u1} M _inst_1)) (CompleteSemilatticeInf.toPartialOrder.{u1} (AddSubgroup.{u1} M (AddCommGroup.toAddGroup.{u1} M _inst_1)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (AddSubgroup.{u1} M (AddCommGroup.toAddGroup.{u1} M _inst_1)) (AddSubgroup.instCompleteLatticeAddSubgroup.{u1} M (AddCommGroup.toAddGroup.{u1} M _inst_1)))))) (Preorder.toLE.{u1} (Submodule.{0, u1} Int M Int.instSemiringInt (AddCommGroup.toAddCommMonoid.{u1} M _inst_1) (AddCommGroup.intModule.{u1} M _inst_1)) (PartialOrder.toPreorder.{u1} (Submodule.{0, u1} Int M Int.instSemiringInt (AddCommGroup.toAddCommMonoid.{u1} M _inst_1) (AddCommGroup.intModule.{u1} M _inst_1)) (CompleteSemilatticeInf.toPartialOrder.{u1} (Submodule.{0, u1} Int M Int.instSemiringInt (AddCommGroup.toAddCommMonoid.{u1} M _inst_1) (AddCommGroup.intModule.{u1} M _inst_1)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (Submodule.{0, u1} Int M Int.instSemiringInt (AddCommGroup.toAddCommMonoid.{u1} M _inst_1) (AddCommGroup.intModule.{u1} M _inst_1)) (Submodule.completeLattice.{0, u1} Int M Int.instSemiringInt (AddCommGroup.toAddCommMonoid.{u1} M _inst_1) (AddCommGroup.intModule.{u1} M _inst_1)))))) (AddSubgroup.toIntSubmodule.{u1} M _inst_1))))) (Submodule.toAddSubgroup.{0, u1} Int M Int.instRingInt _inst_1 (AddCommGroup.intModule.{u1} M _inst_1))
+  forall {M : Type.{u1}} [_inst_1 : AddCommGroup.{u1} M], Eq.{succ u1} ((Submodule.{0, u1} Int M Int.instSemiringInt (AddCommGroup.toAddCommMonoid.{u1} M _inst_1) (AddCommGroup.intModule.{u1} M _inst_1)) -> (AddSubgroup.{u1} M (AddCommGroup.toAddGroup.{u1} M _inst_1))) (FunLike.coe.{succ u1, succ u1, succ u1} (RelIso.{u1, u1} (Submodule.{0, u1} Int M Int.instSemiringInt (AddCommGroup.toAddCommMonoid.{u1} M _inst_1) (AddCommGroup.intModule.{u1} M _inst_1)) (AddSubgroup.{u1} M (AddCommGroup.toAddGroup.{u1} M _inst_1)) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1281 : Submodule.{0, u1} Int M Int.instSemiringInt (AddCommGroup.toAddCommMonoid.{u1} M _inst_1) (AddCommGroup.intModule.{u1} M _inst_1)) (x._@.Mathlib.Order.Hom.Basic._hyg.1283 : Submodule.{0, u1} Int M Int.instSemiringInt (AddCommGroup.toAddCommMonoid.{u1} M _inst_1) (AddCommGroup.intModule.{u1} M _inst_1)) => LE.le.{u1} (Submodule.{0, u1} Int M Int.instSemiringInt (AddCommGroup.toAddCommMonoid.{u1} M _inst_1) (AddCommGroup.intModule.{u1} M _inst_1)) (Preorder.toLE.{u1} (Submodule.{0, u1} Int M Int.instSemiringInt (AddCommGroup.toAddCommMonoid.{u1} M _inst_1) (AddCommGroup.intModule.{u1} M _inst_1)) (PartialOrder.toPreorder.{u1} (Submodule.{0, u1} Int M Int.instSemiringInt (AddCommGroup.toAddCommMonoid.{u1} M _inst_1) (AddCommGroup.intModule.{u1} M _inst_1)) (CompleteSemilatticeInf.toPartialOrder.{u1} (Submodule.{0, u1} Int M Int.instSemiringInt (AddCommGroup.toAddCommMonoid.{u1} M _inst_1) (AddCommGroup.intModule.{u1} M _inst_1)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (Submodule.{0, u1} Int M Int.instSemiringInt (AddCommGroup.toAddCommMonoid.{u1} M _inst_1) (AddCommGroup.intModule.{u1} M _inst_1)) (Submodule.completeLattice.{0, u1} Int M Int.instSemiringInt (AddCommGroup.toAddCommMonoid.{u1} M _inst_1) (AddCommGroup.intModule.{u1} M _inst_1)))))) x._@.Mathlib.Order.Hom.Basic._hyg.1281 x._@.Mathlib.Order.Hom.Basic._hyg.1283) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1296 : AddSubgroup.{u1} M (AddCommGroup.toAddGroup.{u1} M _inst_1)) (x._@.Mathlib.Order.Hom.Basic._hyg.1298 : AddSubgroup.{u1} M (AddCommGroup.toAddGroup.{u1} M _inst_1)) => LE.le.{u1} (AddSubgroup.{u1} M (AddCommGroup.toAddGroup.{u1} M _inst_1)) (Preorder.toLE.{u1} (AddSubgroup.{u1} M (AddCommGroup.toAddGroup.{u1} M _inst_1)) (PartialOrder.toPreorder.{u1} (AddSubgroup.{u1} M (AddCommGroup.toAddGroup.{u1} M _inst_1)) (CompleteSemilatticeInf.toPartialOrder.{u1} (AddSubgroup.{u1} M (AddCommGroup.toAddGroup.{u1} M _inst_1)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (AddSubgroup.{u1} M (AddCommGroup.toAddGroup.{u1} M _inst_1)) (AddSubgroup.instCompleteLatticeAddSubgroup.{u1} M (AddCommGroup.toAddGroup.{u1} M _inst_1)))))) x._@.Mathlib.Order.Hom.Basic._hyg.1296 x._@.Mathlib.Order.Hom.Basic._hyg.1298)) (Submodule.{0, u1} Int M Int.instSemiringInt (AddCommGroup.toAddCommMonoid.{u1} M _inst_1) (AddCommGroup.intModule.{u1} M _inst_1)) (fun (_x : Submodule.{0, u1} Int M Int.instSemiringInt (AddCommGroup.toAddCommMonoid.{u1} M _inst_1) (AddCommGroup.intModule.{u1} M _inst_1)) => AddSubgroup.{u1} M (AddCommGroup.toAddGroup.{u1} M _inst_1)) (RelHomClass.toFunLike.{u1, u1, u1} (RelIso.{u1, u1} (Submodule.{0, u1} Int M Int.instSemiringInt (AddCommGroup.toAddCommMonoid.{u1} M _inst_1) (AddCommGroup.intModule.{u1} M _inst_1)) (AddSubgroup.{u1} M (AddCommGroup.toAddGroup.{u1} M _inst_1)) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1281 : Submodule.{0, u1} Int M Int.instSemiringInt (AddCommGroup.toAddCommMonoid.{u1} M _inst_1) (AddCommGroup.intModule.{u1} M _inst_1)) (x._@.Mathlib.Order.Hom.Basic._hyg.1283 : Submodule.{0, u1} Int M Int.instSemiringInt (AddCommGroup.toAddCommMonoid.{u1} M _inst_1) (AddCommGroup.intModule.{u1} M _inst_1)) => LE.le.{u1} (Submodule.{0, u1} Int M Int.instSemiringInt (AddCommGroup.toAddCommMonoid.{u1} M _inst_1) (AddCommGroup.intModule.{u1} M _inst_1)) (Preorder.toLE.{u1} (Submodule.{0, u1} Int M Int.instSemiringInt (AddCommGroup.toAddCommMonoid.{u1} M _inst_1) (AddCommGroup.intModule.{u1} M _inst_1)) (PartialOrder.toPreorder.{u1} (Submodule.{0, u1} Int M Int.instSemiringInt (AddCommGroup.toAddCommMonoid.{u1} M _inst_1) (AddCommGroup.intModule.{u1} M _inst_1)) (CompleteSemilatticeInf.toPartialOrder.{u1} (Submodule.{0, u1} Int M Int.instSemiringInt (AddCommGroup.toAddCommMonoid.{u1} M _inst_1) (AddCommGroup.intModule.{u1} M _inst_1)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (Submodule.{0, u1} Int M Int.instSemiringInt (AddCommGroup.toAddCommMonoid.{u1} M _inst_1) (AddCommGroup.intModule.{u1} M _inst_1)) (Submodule.completeLattice.{0, u1} Int M Int.instSemiringInt (AddCommGroup.toAddCommMonoid.{u1} M _inst_1) (AddCommGroup.intModule.{u1} M _inst_1)))))) x._@.Mathlib.Order.Hom.Basic._hyg.1281 x._@.Mathlib.Order.Hom.Basic._hyg.1283) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1296 : AddSubgroup.{u1} M (AddCommGroup.toAddGroup.{u1} M _inst_1)) (x._@.Mathlib.Order.Hom.Basic._hyg.1298 : AddSubgroup.{u1} M (AddCommGroup.toAddGroup.{u1} M _inst_1)) => LE.le.{u1} (AddSubgroup.{u1} M (AddCommGroup.toAddGroup.{u1} M _inst_1)) (Preorder.toLE.{u1} (AddSubgroup.{u1} M (AddCommGroup.toAddGroup.{u1} M _inst_1)) (PartialOrder.toPreorder.{u1} (AddSubgroup.{u1} M (AddCommGroup.toAddGroup.{u1} M _inst_1)) (CompleteSemilatticeInf.toPartialOrder.{u1} (AddSubgroup.{u1} M (AddCommGroup.toAddGroup.{u1} M _inst_1)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (AddSubgroup.{u1} M (AddCommGroup.toAddGroup.{u1} M _inst_1)) (AddSubgroup.instCompleteLatticeAddSubgroup.{u1} M (AddCommGroup.toAddGroup.{u1} M _inst_1)))))) x._@.Mathlib.Order.Hom.Basic._hyg.1296 x._@.Mathlib.Order.Hom.Basic._hyg.1298)) (Submodule.{0, u1} Int M Int.instSemiringInt (AddCommGroup.toAddCommMonoid.{u1} M _inst_1) (AddCommGroup.intModule.{u1} M _inst_1)) (AddSubgroup.{u1} M (AddCommGroup.toAddGroup.{u1} M _inst_1)) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1281 : Submodule.{0, u1} Int M Int.instSemiringInt (AddCommGroup.toAddCommMonoid.{u1} M _inst_1) (AddCommGroup.intModule.{u1} M _inst_1)) (x._@.Mathlib.Order.Hom.Basic._hyg.1283 : Submodule.{0, u1} Int M Int.instSemiringInt (AddCommGroup.toAddCommMonoid.{u1} M _inst_1) (AddCommGroup.intModule.{u1} M _inst_1)) => LE.le.{u1} (Submodule.{0, u1} Int M Int.instSemiringInt (AddCommGroup.toAddCommMonoid.{u1} M _inst_1) (AddCommGroup.intModule.{u1} M _inst_1)) (Preorder.toLE.{u1} (Submodule.{0, u1} Int M Int.instSemiringInt (AddCommGroup.toAddCommMonoid.{u1} M _inst_1) (AddCommGroup.intModule.{u1} M _inst_1)) (PartialOrder.toPreorder.{u1} (Submodule.{0, u1} Int M Int.instSemiringInt (AddCommGroup.toAddCommMonoid.{u1} M _inst_1) (AddCommGroup.intModule.{u1} M _inst_1)) (CompleteSemilatticeInf.toPartialOrder.{u1} (Submodule.{0, u1} Int M Int.instSemiringInt (AddCommGroup.toAddCommMonoid.{u1} M _inst_1) (AddCommGroup.intModule.{u1} M _inst_1)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (Submodule.{0, u1} Int M Int.instSemiringInt (AddCommGroup.toAddCommMonoid.{u1} M _inst_1) (AddCommGroup.intModule.{u1} M _inst_1)) (Submodule.completeLattice.{0, u1} Int M Int.instSemiringInt (AddCommGroup.toAddCommMonoid.{u1} M _inst_1) (AddCommGroup.intModule.{u1} M _inst_1)))))) x._@.Mathlib.Order.Hom.Basic._hyg.1281 x._@.Mathlib.Order.Hom.Basic._hyg.1283) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1296 : AddSubgroup.{u1} M (AddCommGroup.toAddGroup.{u1} M _inst_1)) (x._@.Mathlib.Order.Hom.Basic._hyg.1298 : AddSubgroup.{u1} M (AddCommGroup.toAddGroup.{u1} M _inst_1)) => LE.le.{u1} (AddSubgroup.{u1} M (AddCommGroup.toAddGroup.{u1} M _inst_1)) (Preorder.toLE.{u1} (AddSubgroup.{u1} M (AddCommGroup.toAddGroup.{u1} M _inst_1)) (PartialOrder.toPreorder.{u1} (AddSubgroup.{u1} M (AddCommGroup.toAddGroup.{u1} M _inst_1)) (CompleteSemilatticeInf.toPartialOrder.{u1} (AddSubgroup.{u1} M (AddCommGroup.toAddGroup.{u1} M _inst_1)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (AddSubgroup.{u1} M (AddCommGroup.toAddGroup.{u1} M _inst_1)) (AddSubgroup.instCompleteLatticeAddSubgroup.{u1} M (AddCommGroup.toAddGroup.{u1} M _inst_1)))))) x._@.Mathlib.Order.Hom.Basic._hyg.1296 x._@.Mathlib.Order.Hom.Basic._hyg.1298) (RelIso.instRelHomClassRelIso.{u1, u1} (Submodule.{0, u1} Int M Int.instSemiringInt (AddCommGroup.toAddCommMonoid.{u1} M _inst_1) (AddCommGroup.intModule.{u1} M _inst_1)) (AddSubgroup.{u1} M (AddCommGroup.toAddGroup.{u1} M _inst_1)) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1281 : Submodule.{0, u1} Int M Int.instSemiringInt (AddCommGroup.toAddCommMonoid.{u1} M _inst_1) (AddCommGroup.intModule.{u1} M _inst_1)) (x._@.Mathlib.Order.Hom.Basic._hyg.1283 : Submodule.{0, u1} Int M Int.instSemiringInt (AddCommGroup.toAddCommMonoid.{u1} M _inst_1) (AddCommGroup.intModule.{u1} M _inst_1)) => LE.le.{u1} (Submodule.{0, u1} Int M Int.instSemiringInt (AddCommGroup.toAddCommMonoid.{u1} M _inst_1) (AddCommGroup.intModule.{u1} M _inst_1)) (Preorder.toLE.{u1} (Submodule.{0, u1} Int M Int.instSemiringInt (AddCommGroup.toAddCommMonoid.{u1} M _inst_1) (AddCommGroup.intModule.{u1} M _inst_1)) (PartialOrder.toPreorder.{u1} (Submodule.{0, u1} Int M Int.instSemiringInt (AddCommGroup.toAddCommMonoid.{u1} M _inst_1) (AddCommGroup.intModule.{u1} M _inst_1)) (CompleteSemilatticeInf.toPartialOrder.{u1} (Submodule.{0, u1} Int M Int.instSemiringInt (AddCommGroup.toAddCommMonoid.{u1} M _inst_1) (AddCommGroup.intModule.{u1} M _inst_1)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (Submodule.{0, u1} Int M Int.instSemiringInt (AddCommGroup.toAddCommMonoid.{u1} M _inst_1) (AddCommGroup.intModule.{u1} M _inst_1)) (Submodule.completeLattice.{0, u1} Int M Int.instSemiringInt (AddCommGroup.toAddCommMonoid.{u1} M _inst_1) (AddCommGroup.intModule.{u1} M _inst_1)))))) x._@.Mathlib.Order.Hom.Basic._hyg.1281 x._@.Mathlib.Order.Hom.Basic._hyg.1283) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1296 : AddSubgroup.{u1} M (AddCommGroup.toAddGroup.{u1} M _inst_1)) (x._@.Mathlib.Order.Hom.Basic._hyg.1298 : AddSubgroup.{u1} M (AddCommGroup.toAddGroup.{u1} M _inst_1)) => LE.le.{u1} (AddSubgroup.{u1} M (AddCommGroup.toAddGroup.{u1} M _inst_1)) (Preorder.toLE.{u1} (AddSubgroup.{u1} M (AddCommGroup.toAddGroup.{u1} M _inst_1)) (PartialOrder.toPreorder.{u1} (AddSubgroup.{u1} M (AddCommGroup.toAddGroup.{u1} M _inst_1)) (CompleteSemilatticeInf.toPartialOrder.{u1} (AddSubgroup.{u1} M (AddCommGroup.toAddGroup.{u1} M _inst_1)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (AddSubgroup.{u1} M (AddCommGroup.toAddGroup.{u1} M _inst_1)) (AddSubgroup.instCompleteLatticeAddSubgroup.{u1} M (AddCommGroup.toAddGroup.{u1} M _inst_1)))))) x._@.Mathlib.Order.Hom.Basic._hyg.1296 x._@.Mathlib.Order.Hom.Basic._hyg.1298))) (OrderIso.symm.{u1, u1} (AddSubgroup.{u1} M (AddCommGroup.toAddGroup.{u1} M _inst_1)) (Submodule.{0, u1} Int M Int.instSemiringInt (AddCommGroup.toAddCommMonoid.{u1} M _inst_1) (AddCommGroup.intModule.{u1} M _inst_1)) (Preorder.toLE.{u1} (AddSubgroup.{u1} M (AddCommGroup.toAddGroup.{u1} M _inst_1)) (PartialOrder.toPreorder.{u1} (AddSubgroup.{u1} M (AddCommGroup.toAddGroup.{u1} M _inst_1)) (CompleteSemilatticeInf.toPartialOrder.{u1} (AddSubgroup.{u1} M (AddCommGroup.toAddGroup.{u1} M _inst_1)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (AddSubgroup.{u1} M (AddCommGroup.toAddGroup.{u1} M _inst_1)) (AddSubgroup.instCompleteLatticeAddSubgroup.{u1} M (AddCommGroup.toAddGroup.{u1} M _inst_1)))))) (Preorder.toLE.{u1} (Submodule.{0, u1} Int M Int.instSemiringInt (AddCommGroup.toAddCommMonoid.{u1} M _inst_1) (AddCommGroup.intModule.{u1} M _inst_1)) (PartialOrder.toPreorder.{u1} (Submodule.{0, u1} Int M Int.instSemiringInt (AddCommGroup.toAddCommMonoid.{u1} M _inst_1) (AddCommGroup.intModule.{u1} M _inst_1)) (CompleteSemilatticeInf.toPartialOrder.{u1} (Submodule.{0, u1} Int M Int.instSemiringInt (AddCommGroup.toAddCommMonoid.{u1} M _inst_1) (AddCommGroup.intModule.{u1} M _inst_1)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (Submodule.{0, u1} Int M Int.instSemiringInt (AddCommGroup.toAddCommMonoid.{u1} M _inst_1) (AddCommGroup.intModule.{u1} M _inst_1)) (Submodule.completeLattice.{0, u1} Int M Int.instSemiringInt (AddCommGroup.toAddCommMonoid.{u1} M _inst_1) (AddCommGroup.intModule.{u1} M _inst_1)))))) (AddSubgroup.toIntSubmodule.{u1} M _inst_1))) (Submodule.toAddSubgroup.{0, u1} Int M Int.instRingInt _inst_1 (AddCommGroup.intModule.{u1} M _inst_1))
 Case conversion may be inaccurate. Consider using '#align add_subgroup.to_int_submodule_symm AddSubgroup.toIntSubmodule_symmₓ'. -/
 @[simp]
 theorem AddSubgroup.toIntSubmodule_symm :
@@ -706,7 +706,7 @@ theorem AddSubgroup.toIntSubmodule_symm :
 lean 3 declaration is
   forall {M : Type.{u1}} [_inst_1 : AddCommGroup.{u1} M] (S : AddSubgroup.{u1} M (AddCommGroup.toAddGroup.{u1} M _inst_1)), Eq.{succ u1} (Set.{u1} M) ((fun (a : Type.{u1}) (b : Type.{u1}) [self : HasLiftT.{succ u1, succ u1} a b] => self.0) (Submodule.{0, u1} Int M Int.semiring (AddCommGroup.toAddCommMonoid.{u1} M _inst_1) (AddCommGroup.intModule.{u1} M _inst_1)) (Set.{u1} M) (HasLiftT.mk.{succ u1, succ u1} (Submodule.{0, u1} Int M Int.semiring (AddCommGroup.toAddCommMonoid.{u1} M _inst_1) (AddCommGroup.intModule.{u1} M _inst_1)) (Set.{u1} M) (CoeTCₓ.coe.{succ u1, succ u1} (Submodule.{0, u1} Int M Int.semiring (AddCommGroup.toAddCommMonoid.{u1} M _inst_1) (AddCommGroup.intModule.{u1} M _inst_1)) (Set.{u1} M) (SetLike.Set.hasCoeT.{u1, u1} (Submodule.{0, u1} Int M Int.semiring (AddCommGroup.toAddCommMonoid.{u1} M _inst_1) (AddCommGroup.intModule.{u1} M _inst_1)) M (Submodule.setLike.{0, u1} Int M Int.semiring (AddCommGroup.toAddCommMonoid.{u1} M _inst_1) (AddCommGroup.intModule.{u1} M _inst_1))))) (coeFn.{succ u1, succ u1} (OrderIso.{u1, u1} (AddSubgroup.{u1} M (AddCommGroup.toAddGroup.{u1} M _inst_1)) (Submodule.{0, u1} Int M Int.semiring (AddCommGroup.toAddCommMonoid.{u1} M _inst_1) (AddCommGroup.intModule.{u1} M _inst_1)) (Preorder.toLE.{u1} (AddSubgroup.{u1} M (AddCommGroup.toAddGroup.{u1} M _inst_1)) (PartialOrder.toPreorder.{u1} (AddSubgroup.{u1} M (AddCommGroup.toAddGroup.{u1} M _inst_1)) (CompleteSemilatticeInf.toPartialOrder.{u1} (AddSubgroup.{u1} M (AddCommGroup.toAddGroup.{u1} M _inst_1)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (AddSubgroup.{u1} M (AddCommGroup.toAddGroup.{u1} M _inst_1)) (AddSubgroup.completeLattice.{u1} M (AddCommGroup.toAddGroup.{u1} M _inst_1)))))) (Preorder.toLE.{u1} (Submodule.{0, u1} Int M Int.semiring (AddCommGroup.toAddCommMonoid.{u1} M _inst_1) (AddCommGroup.intModule.{u1} M _inst_1)) (PartialOrder.toPreorder.{u1} (Submodule.{0, u1} Int M Int.semiring (AddCommGroup.toAddCommMonoid.{u1} M _inst_1) (AddCommGroup.intModule.{u1} M _inst_1)) (CompleteSemilatticeInf.toPartialOrder.{u1} (Submodule.{0, u1} Int M Int.semiring (AddCommGroup.toAddCommMonoid.{u1} M _inst_1) (AddCommGroup.intModule.{u1} M _inst_1)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (Submodule.{0, u1} Int M Int.semiring (AddCommGroup.toAddCommMonoid.{u1} M _inst_1) (AddCommGroup.intModule.{u1} M _inst_1)) (Submodule.completeLattice.{0, u1} Int M Int.semiring (AddCommGroup.toAddCommMonoid.{u1} M _inst_1) (AddCommGroup.intModule.{u1} M _inst_1))))))) (fun (_x : RelIso.{u1, u1} (AddSubgroup.{u1} M (AddCommGroup.toAddGroup.{u1} M _inst_1)) (Submodule.{0, u1} Int M Int.semiring (AddCommGroup.toAddCommMonoid.{u1} M _inst_1) (AddCommGroup.intModule.{u1} M _inst_1)) (LE.le.{u1} (AddSubgroup.{u1} M (AddCommGroup.toAddGroup.{u1} M _inst_1)) (Preorder.toLE.{u1} (AddSubgroup.{u1} M (AddCommGroup.toAddGroup.{u1} M _inst_1)) (PartialOrder.toPreorder.{u1} (AddSubgroup.{u1} M (AddCommGroup.toAddGroup.{u1} M _inst_1)) (CompleteSemilatticeInf.toPartialOrder.{u1} (AddSubgroup.{u1} M (AddCommGroup.toAddGroup.{u1} M _inst_1)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (AddSubgroup.{u1} M (AddCommGroup.toAddGroup.{u1} M _inst_1)) (AddSubgroup.completeLattice.{u1} M (AddCommGroup.toAddGroup.{u1} M _inst_1))))))) (LE.le.{u1} (Submodule.{0, u1} Int M Int.semiring (AddCommGroup.toAddCommMonoid.{u1} M _inst_1) (AddCommGroup.intModule.{u1} M _inst_1)) (Preorder.toLE.{u1} (Submodule.{0, u1} Int M Int.semiring (AddCommGroup.toAddCommMonoid.{u1} M _inst_1) (AddCommGroup.intModule.{u1} M _inst_1)) (PartialOrder.toPreorder.{u1} (Submodule.{0, u1} Int M Int.semiring (AddCommGroup.toAddCommMonoid.{u1} M _inst_1) (AddCommGroup.intModule.{u1} M _inst_1)) (CompleteSemilatticeInf.toPartialOrder.{u1} (Submodule.{0, u1} Int M Int.semiring (AddCommGroup.toAddCommMonoid.{u1} M _inst_1) (AddCommGroup.intModule.{u1} M _inst_1)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (Submodule.{0, u1} Int M Int.semiring (AddCommGroup.toAddCommMonoid.{u1} M _inst_1) (AddCommGroup.intModule.{u1} M _inst_1)) (Submodule.completeLattice.{0, u1} Int M Int.semiring (AddCommGroup.toAddCommMonoid.{u1} M _inst_1) (AddCommGroup.intModule.{u1} M _inst_1)))))))) => (AddSubgroup.{u1} M (AddCommGroup.toAddGroup.{u1} M _inst_1)) -> (Submodule.{0, u1} Int M Int.semiring (AddCommGroup.toAddCommMonoid.{u1} M _inst_1) (AddCommGroup.intModule.{u1} M _inst_1))) (RelIso.hasCoeToFun.{u1, u1} (AddSubgroup.{u1} M (AddCommGroup.toAddGroup.{u1} M _inst_1)) (Submodule.{0, u1} Int M Int.semiring (AddCommGroup.toAddCommMonoid.{u1} M _inst_1) (AddCommGroup.intModule.{u1} M _inst_1)) (LE.le.{u1} (AddSubgroup.{u1} M (AddCommGroup.toAddGroup.{u1} M _inst_1)) (Preorder.toLE.{u1} (AddSubgroup.{u1} M (AddCommGroup.toAddGroup.{u1} M _inst_1)) (PartialOrder.toPreorder.{u1} (AddSubgroup.{u1} M (AddCommGroup.toAddGroup.{u1} M _inst_1)) (CompleteSemilatticeInf.toPartialOrder.{u1} (AddSubgroup.{u1} M (AddCommGroup.toAddGroup.{u1} M _inst_1)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (AddSubgroup.{u1} M (AddCommGroup.toAddGroup.{u1} M _inst_1)) (AddSubgroup.completeLattice.{u1} M (AddCommGroup.toAddGroup.{u1} M _inst_1))))))) (LE.le.{u1} (Submodule.{0, u1} Int M Int.semiring (AddCommGroup.toAddCommMonoid.{u1} M _inst_1) (AddCommGroup.intModule.{u1} M _inst_1)) (Preorder.toLE.{u1} (Submodule.{0, u1} Int M Int.semiring (AddCommGroup.toAddCommMonoid.{u1} M _inst_1) (AddCommGroup.intModule.{u1} M _inst_1)) (PartialOrder.toPreorder.{u1} (Submodule.{0, u1} Int M Int.semiring (AddCommGroup.toAddCommMonoid.{u1} M _inst_1) (AddCommGroup.intModule.{u1} M _inst_1)) (CompleteSemilatticeInf.toPartialOrder.{u1} (Submodule.{0, u1} Int M Int.semiring (AddCommGroup.toAddCommMonoid.{u1} M _inst_1) (AddCommGroup.intModule.{u1} M _inst_1)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (Submodule.{0, u1} Int M Int.semiring (AddCommGroup.toAddCommMonoid.{u1} M _inst_1) (AddCommGroup.intModule.{u1} M _inst_1)) (Submodule.completeLattice.{0, u1} Int M Int.semiring (AddCommGroup.toAddCommMonoid.{u1} M _inst_1) (AddCommGroup.intModule.{u1} M _inst_1)))))))) (AddSubgroup.toIntSubmodule.{u1} M _inst_1) S)) ((fun (a : Type.{u1}) (b : Type.{u1}) [self : HasLiftT.{succ u1, succ u1} a b] => self.0) (AddSubgroup.{u1} M (AddCommGroup.toAddGroup.{u1} M _inst_1)) (Set.{u1} M) (HasLiftT.mk.{succ u1, succ u1} (AddSubgroup.{u1} M (AddCommGroup.toAddGroup.{u1} M _inst_1)) (Set.{u1} M) (CoeTCₓ.coe.{succ u1, succ u1} (AddSubgroup.{u1} M (AddCommGroup.toAddGroup.{u1} M _inst_1)) (Set.{u1} M) (SetLike.Set.hasCoeT.{u1, u1} (AddSubgroup.{u1} M (AddCommGroup.toAddGroup.{u1} M _inst_1)) M (AddSubgroup.setLike.{u1} M (AddCommGroup.toAddGroup.{u1} M _inst_1))))) S)
 but is expected to have type
-  forall {M : Type.{u1}} [_inst_1 : AddCommGroup.{u1} M] (S : AddSubgroup.{u1} M (AddCommGroup.toAddGroup.{u1} M _inst_1)), Eq.{succ u1} (Set.{u1} M) (SetLike.coe.{u1, u1} ((fun (x._@.Mathlib.Data.FunLike.Embedding._hyg.19 : AddSubgroup.{u1} M (AddCommGroup.toAddGroup.{u1} M _inst_1)) => Submodule.{0, u1} Int M Int.instSemiringInt (AddCommGroup.toAddCommMonoid.{u1} M _inst_1) (AddCommGroup.intModule.{u1} M _inst_1)) S) M (Submodule.setLike.{0, u1} Int M Int.instSemiringInt (AddCommGroup.toAddCommMonoid.{u1} M _inst_1) (AddCommGroup.intModule.{u1} M _inst_1)) (FunLike.coe.{succ u1, succ u1, succ u1} (Function.Embedding.{succ u1, succ u1} (AddSubgroup.{u1} M (AddCommGroup.toAddGroup.{u1} M _inst_1)) (Submodule.{0, u1} Int M Int.instSemiringInt (AddCommGroup.toAddCommMonoid.{u1} M _inst_1) (AddCommGroup.intModule.{u1} M _inst_1))) (AddSubgroup.{u1} M (AddCommGroup.toAddGroup.{u1} M _inst_1)) (fun (_x : AddSubgroup.{u1} M (AddCommGroup.toAddGroup.{u1} M _inst_1)) => (fun (x._@.Mathlib.Data.FunLike.Embedding._hyg.19 : AddSubgroup.{u1} M (AddCommGroup.toAddGroup.{u1} M _inst_1)) => Submodule.{0, u1} Int M Int.instSemiringInt (AddCommGroup.toAddCommMonoid.{u1} M _inst_1) (AddCommGroup.intModule.{u1} M _inst_1)) _x) (EmbeddingLike.toFunLike.{succ u1, succ u1, succ u1} (Function.Embedding.{succ u1, succ u1} (AddSubgroup.{u1} M (AddCommGroup.toAddGroup.{u1} M _inst_1)) (Submodule.{0, u1} Int M Int.instSemiringInt (AddCommGroup.toAddCommMonoid.{u1} M _inst_1) (AddCommGroup.intModule.{u1} M _inst_1))) (AddSubgroup.{u1} M (AddCommGroup.toAddGroup.{u1} M _inst_1)) (Submodule.{0, u1} Int M Int.instSemiringInt (AddCommGroup.toAddCommMonoid.{u1} M _inst_1) (AddCommGroup.intModule.{u1} M _inst_1)) (Function.instEmbeddingLikeEmbedding.{succ u1, succ u1} (AddSubgroup.{u1} M (AddCommGroup.toAddGroup.{u1} M _inst_1)) (Submodule.{0, u1} Int M Int.instSemiringInt (AddCommGroup.toAddCommMonoid.{u1} M _inst_1) (AddCommGroup.intModule.{u1} M _inst_1)))) (RelEmbedding.toEmbedding.{u1, u1} (AddSubgroup.{u1} M (AddCommGroup.toAddGroup.{u1} M _inst_1)) (Submodule.{0, u1} Int M Int.instSemiringInt (AddCommGroup.toAddCommMonoid.{u1} M _inst_1) (AddCommGroup.intModule.{u1} M _inst_1)) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1281 : AddSubgroup.{u1} M (AddCommGroup.toAddGroup.{u1} M _inst_1)) (x._@.Mathlib.Order.Hom.Basic._hyg.1283 : AddSubgroup.{u1} M (AddCommGroup.toAddGroup.{u1} M _inst_1)) => LE.le.{u1} (AddSubgroup.{u1} M (AddCommGroup.toAddGroup.{u1} M _inst_1)) (Preorder.toLE.{u1} (AddSubgroup.{u1} M (AddCommGroup.toAddGroup.{u1} M _inst_1)) (PartialOrder.toPreorder.{u1} (AddSubgroup.{u1} M (AddCommGroup.toAddGroup.{u1} M _inst_1)) (CompleteSemilatticeInf.toPartialOrder.{u1} (AddSubgroup.{u1} M (AddCommGroup.toAddGroup.{u1} M _inst_1)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (AddSubgroup.{u1} M (AddCommGroup.toAddGroup.{u1} M _inst_1)) (AddSubgroup.instCompleteLatticeAddSubgroup.{u1} M (AddCommGroup.toAddGroup.{u1} M _inst_1)))))) x._@.Mathlib.Order.Hom.Basic._hyg.1281 x._@.Mathlib.Order.Hom.Basic._hyg.1283) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1296 : Submodule.{0, u1} Int M Int.instSemiringInt (AddCommGroup.toAddCommMonoid.{u1} M _inst_1) (AddCommGroup.intModule.{u1} M _inst_1)) (x._@.Mathlib.Order.Hom.Basic._hyg.1298 : Submodule.{0, u1} Int M Int.instSemiringInt (AddCommGroup.toAddCommMonoid.{u1} M _inst_1) (AddCommGroup.intModule.{u1} M _inst_1)) => LE.le.{u1} (Submodule.{0, u1} Int M Int.instSemiringInt (AddCommGroup.toAddCommMonoid.{u1} M _inst_1) (AddCommGroup.intModule.{u1} M _inst_1)) (Preorder.toLE.{u1} (Submodule.{0, u1} Int M Int.instSemiringInt (AddCommGroup.toAddCommMonoid.{u1} M _inst_1) (AddCommGroup.intModule.{u1} M _inst_1)) (PartialOrder.toPreorder.{u1} (Submodule.{0, u1} Int M Int.instSemiringInt (AddCommGroup.toAddCommMonoid.{u1} M _inst_1) (AddCommGroup.intModule.{u1} M _inst_1)) (CompleteSemilatticeInf.toPartialOrder.{u1} (Submodule.{0, u1} Int M Int.instSemiringInt (AddCommGroup.toAddCommMonoid.{u1} M _inst_1) (AddCommGroup.intModule.{u1} M _inst_1)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (Submodule.{0, u1} Int M Int.instSemiringInt (AddCommGroup.toAddCommMonoid.{u1} M _inst_1) (AddCommGroup.intModule.{u1} M _inst_1)) (Submodule.completeLattice.{0, u1} Int M Int.instSemiringInt (AddCommGroup.toAddCommMonoid.{u1} M _inst_1) (AddCommGroup.intModule.{u1} M _inst_1)))))) x._@.Mathlib.Order.Hom.Basic._hyg.1296 x._@.Mathlib.Order.Hom.Basic._hyg.1298) (RelIso.toRelEmbedding.{u1, u1} (AddSubgroup.{u1} M (AddCommGroup.toAddGroup.{u1} M _inst_1)) (Submodule.{0, u1} Int M Int.instSemiringInt (AddCommGroup.toAddCommMonoid.{u1} M _inst_1) (AddCommGroup.intModule.{u1} M _inst_1)) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1281 : AddSubgroup.{u1} M (AddCommGroup.toAddGroup.{u1} M _inst_1)) (x._@.Mathlib.Order.Hom.Basic._hyg.1283 : AddSubgroup.{u1} M (AddCommGroup.toAddGroup.{u1} M _inst_1)) => LE.le.{u1} (AddSubgroup.{u1} M (AddCommGroup.toAddGroup.{u1} M _inst_1)) (Preorder.toLE.{u1} (AddSubgroup.{u1} M (AddCommGroup.toAddGroup.{u1} M _inst_1)) (PartialOrder.toPreorder.{u1} (AddSubgroup.{u1} M (AddCommGroup.toAddGroup.{u1} M _inst_1)) (CompleteSemilatticeInf.toPartialOrder.{u1} (AddSubgroup.{u1} M (AddCommGroup.toAddGroup.{u1} M _inst_1)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (AddSubgroup.{u1} M (AddCommGroup.toAddGroup.{u1} M _inst_1)) (AddSubgroup.instCompleteLatticeAddSubgroup.{u1} M (AddCommGroup.toAddGroup.{u1} M _inst_1)))))) x._@.Mathlib.Order.Hom.Basic._hyg.1281 x._@.Mathlib.Order.Hom.Basic._hyg.1283) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1296 : Submodule.{0, u1} Int M Int.instSemiringInt (AddCommGroup.toAddCommMonoid.{u1} M _inst_1) (AddCommGroup.intModule.{u1} M _inst_1)) (x._@.Mathlib.Order.Hom.Basic._hyg.1298 : Submodule.{0, u1} Int M Int.instSemiringInt (AddCommGroup.toAddCommMonoid.{u1} M _inst_1) (AddCommGroup.intModule.{u1} M _inst_1)) => LE.le.{u1} (Submodule.{0, u1} Int M Int.instSemiringInt (AddCommGroup.toAddCommMonoid.{u1} M _inst_1) (AddCommGroup.intModule.{u1} M _inst_1)) (Preorder.toLE.{u1} (Submodule.{0, u1} Int M Int.instSemiringInt (AddCommGroup.toAddCommMonoid.{u1} M _inst_1) (AddCommGroup.intModule.{u1} M _inst_1)) (PartialOrder.toPreorder.{u1} (Submodule.{0, u1} Int M Int.instSemiringInt (AddCommGroup.toAddCommMonoid.{u1} M _inst_1) (AddCommGroup.intModule.{u1} M _inst_1)) (CompleteSemilatticeInf.toPartialOrder.{u1} (Submodule.{0, u1} Int M Int.instSemiringInt (AddCommGroup.toAddCommMonoid.{u1} M _inst_1) (AddCommGroup.intModule.{u1} M _inst_1)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (Submodule.{0, u1} Int M Int.instSemiringInt (AddCommGroup.toAddCommMonoid.{u1} M _inst_1) (AddCommGroup.intModule.{u1} M _inst_1)) (Submodule.completeLattice.{0, u1} Int M Int.instSemiringInt (AddCommGroup.toAddCommMonoid.{u1} M _inst_1) (AddCommGroup.intModule.{u1} M _inst_1)))))) x._@.Mathlib.Order.Hom.Basic._hyg.1296 x._@.Mathlib.Order.Hom.Basic._hyg.1298) (AddSubgroup.toIntSubmodule.{u1} M _inst_1))) S)) (SetLike.coe.{u1, u1} (AddSubgroup.{u1} M (AddCommGroup.toAddGroup.{u1} M _inst_1)) M (AddSubgroup.instSetLikeAddSubgroup.{u1} M (AddCommGroup.toAddGroup.{u1} M _inst_1)) S)
+  forall {M : Type.{u1}} [_inst_1 : AddCommGroup.{u1} M] (S : AddSubgroup.{u1} M (AddCommGroup.toAddGroup.{u1} M _inst_1)), Eq.{succ u1} (Set.{u1} M) (SetLike.coe.{u1, u1} (Submodule.{0, u1} Int M Int.instSemiringInt (AddCommGroup.toAddCommMonoid.{u1} M _inst_1) (AddCommGroup.intModule.{u1} M _inst_1)) M (Submodule.setLike.{0, u1} Int M Int.instSemiringInt (AddCommGroup.toAddCommMonoid.{u1} M _inst_1) (AddCommGroup.intModule.{u1} M _inst_1)) (FunLike.coe.{succ u1, succ u1, succ u1} (RelIso.{u1, u1} (AddSubgroup.{u1} M (AddCommGroup.toAddGroup.{u1} M _inst_1)) (Submodule.{0, u1} Int M Int.instSemiringInt (AddCommGroup.toAddCommMonoid.{u1} M _inst_1) (AddCommGroup.intModule.{u1} M _inst_1)) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1281 : AddSubgroup.{u1} M (AddCommGroup.toAddGroup.{u1} M _inst_1)) (x._@.Mathlib.Order.Hom.Basic._hyg.1283 : AddSubgroup.{u1} M (AddCommGroup.toAddGroup.{u1} M _inst_1)) => LE.le.{u1} (AddSubgroup.{u1} M (AddCommGroup.toAddGroup.{u1} M _inst_1)) (Preorder.toLE.{u1} (AddSubgroup.{u1} M (AddCommGroup.toAddGroup.{u1} M _inst_1)) (PartialOrder.toPreorder.{u1} (AddSubgroup.{u1} M (AddCommGroup.toAddGroup.{u1} M _inst_1)) (CompleteSemilatticeInf.toPartialOrder.{u1} (AddSubgroup.{u1} M (AddCommGroup.toAddGroup.{u1} M _inst_1)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (AddSubgroup.{u1} M (AddCommGroup.toAddGroup.{u1} M _inst_1)) (AddSubgroup.instCompleteLatticeAddSubgroup.{u1} M (AddCommGroup.toAddGroup.{u1} M _inst_1)))))) x._@.Mathlib.Order.Hom.Basic._hyg.1281 x._@.Mathlib.Order.Hom.Basic._hyg.1283) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1296 : Submodule.{0, u1} Int M Int.instSemiringInt (AddCommGroup.toAddCommMonoid.{u1} M _inst_1) (AddCommGroup.intModule.{u1} M _inst_1)) (x._@.Mathlib.Order.Hom.Basic._hyg.1298 : Submodule.{0, u1} Int M Int.instSemiringInt (AddCommGroup.toAddCommMonoid.{u1} M _inst_1) (AddCommGroup.intModule.{u1} M _inst_1)) => LE.le.{u1} (Submodule.{0, u1} Int M Int.instSemiringInt (AddCommGroup.toAddCommMonoid.{u1} M _inst_1) (AddCommGroup.intModule.{u1} M _inst_1)) (Preorder.toLE.{u1} (Submodule.{0, u1} Int M Int.instSemiringInt (AddCommGroup.toAddCommMonoid.{u1} M _inst_1) (AddCommGroup.intModule.{u1} M _inst_1)) (PartialOrder.toPreorder.{u1} (Submodule.{0, u1} Int M Int.instSemiringInt (AddCommGroup.toAddCommMonoid.{u1} M _inst_1) (AddCommGroup.intModule.{u1} M _inst_1)) (CompleteSemilatticeInf.toPartialOrder.{u1} (Submodule.{0, u1} Int M Int.instSemiringInt (AddCommGroup.toAddCommMonoid.{u1} M _inst_1) (AddCommGroup.intModule.{u1} M _inst_1)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (Submodule.{0, u1} Int M Int.instSemiringInt (AddCommGroup.toAddCommMonoid.{u1} M _inst_1) (AddCommGroup.intModule.{u1} M _inst_1)) (Submodule.completeLattice.{0, u1} Int M Int.instSemiringInt (AddCommGroup.toAddCommMonoid.{u1} M _inst_1) (AddCommGroup.intModule.{u1} M _inst_1)))))) x._@.Mathlib.Order.Hom.Basic._hyg.1296 x._@.Mathlib.Order.Hom.Basic._hyg.1298)) (AddSubgroup.{u1} M (AddCommGroup.toAddGroup.{u1} M _inst_1)) (fun (_x : AddSubgroup.{u1} M (AddCommGroup.toAddGroup.{u1} M _inst_1)) => Submodule.{0, u1} Int M Int.instSemiringInt (AddCommGroup.toAddCommMonoid.{u1} M _inst_1) (AddCommGroup.intModule.{u1} M _inst_1)) (RelHomClass.toFunLike.{u1, u1, u1} (RelIso.{u1, u1} (AddSubgroup.{u1} M (AddCommGroup.toAddGroup.{u1} M _inst_1)) (Submodule.{0, u1} Int M Int.instSemiringInt (AddCommGroup.toAddCommMonoid.{u1} M _inst_1) (AddCommGroup.intModule.{u1} M _inst_1)) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1281 : AddSubgroup.{u1} M (AddCommGroup.toAddGroup.{u1} M _inst_1)) (x._@.Mathlib.Order.Hom.Basic._hyg.1283 : AddSubgroup.{u1} M (AddCommGroup.toAddGroup.{u1} M _inst_1)) => LE.le.{u1} (AddSubgroup.{u1} M (AddCommGroup.toAddGroup.{u1} M _inst_1)) (Preorder.toLE.{u1} (AddSubgroup.{u1} M (AddCommGroup.toAddGroup.{u1} M _inst_1)) (PartialOrder.toPreorder.{u1} (AddSubgroup.{u1} M (AddCommGroup.toAddGroup.{u1} M _inst_1)) (CompleteSemilatticeInf.toPartialOrder.{u1} (AddSubgroup.{u1} M (AddCommGroup.toAddGroup.{u1} M _inst_1)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (AddSubgroup.{u1} M (AddCommGroup.toAddGroup.{u1} M _inst_1)) (AddSubgroup.instCompleteLatticeAddSubgroup.{u1} M (AddCommGroup.toAddGroup.{u1} M _inst_1)))))) x._@.Mathlib.Order.Hom.Basic._hyg.1281 x._@.Mathlib.Order.Hom.Basic._hyg.1283) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1296 : Submodule.{0, u1} Int M Int.instSemiringInt (AddCommGroup.toAddCommMonoid.{u1} M _inst_1) (AddCommGroup.intModule.{u1} M _inst_1)) (x._@.Mathlib.Order.Hom.Basic._hyg.1298 : Submodule.{0, u1} Int M Int.instSemiringInt (AddCommGroup.toAddCommMonoid.{u1} M _inst_1) (AddCommGroup.intModule.{u1} M _inst_1)) => LE.le.{u1} (Submodule.{0, u1} Int M Int.instSemiringInt (AddCommGroup.toAddCommMonoid.{u1} M _inst_1) (AddCommGroup.intModule.{u1} M _inst_1)) (Preorder.toLE.{u1} (Submodule.{0, u1} Int M Int.instSemiringInt (AddCommGroup.toAddCommMonoid.{u1} M _inst_1) (AddCommGroup.intModule.{u1} M _inst_1)) (PartialOrder.toPreorder.{u1} (Submodule.{0, u1} Int M Int.instSemiringInt (AddCommGroup.toAddCommMonoid.{u1} M _inst_1) (AddCommGroup.intModule.{u1} M _inst_1)) (CompleteSemilatticeInf.toPartialOrder.{u1} (Submodule.{0, u1} Int M Int.instSemiringInt (AddCommGroup.toAddCommMonoid.{u1} M _inst_1) (AddCommGroup.intModule.{u1} M _inst_1)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (Submodule.{0, u1} Int M Int.instSemiringInt (AddCommGroup.toAddCommMonoid.{u1} M _inst_1) (AddCommGroup.intModule.{u1} M _inst_1)) (Submodule.completeLattice.{0, u1} Int M Int.instSemiringInt (AddCommGroup.toAddCommMonoid.{u1} M _inst_1) (AddCommGroup.intModule.{u1} M _inst_1)))))) x._@.Mathlib.Order.Hom.Basic._hyg.1296 x._@.Mathlib.Order.Hom.Basic._hyg.1298)) (AddSubgroup.{u1} M (AddCommGroup.toAddGroup.{u1} M _inst_1)) (Submodule.{0, u1} Int M Int.instSemiringInt (AddCommGroup.toAddCommMonoid.{u1} M _inst_1) (AddCommGroup.intModule.{u1} M _inst_1)) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1281 : AddSubgroup.{u1} M (AddCommGroup.toAddGroup.{u1} M _inst_1)) (x._@.Mathlib.Order.Hom.Basic._hyg.1283 : AddSubgroup.{u1} M (AddCommGroup.toAddGroup.{u1} M _inst_1)) => LE.le.{u1} (AddSubgroup.{u1} M (AddCommGroup.toAddGroup.{u1} M _inst_1)) (Preorder.toLE.{u1} (AddSubgroup.{u1} M (AddCommGroup.toAddGroup.{u1} M _inst_1)) (PartialOrder.toPreorder.{u1} (AddSubgroup.{u1} M (AddCommGroup.toAddGroup.{u1} M _inst_1)) (CompleteSemilatticeInf.toPartialOrder.{u1} (AddSubgroup.{u1} M (AddCommGroup.toAddGroup.{u1} M _inst_1)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (AddSubgroup.{u1} M (AddCommGroup.toAddGroup.{u1} M _inst_1)) (AddSubgroup.instCompleteLatticeAddSubgroup.{u1} M (AddCommGroup.toAddGroup.{u1} M _inst_1)))))) x._@.Mathlib.Order.Hom.Basic._hyg.1281 x._@.Mathlib.Order.Hom.Basic._hyg.1283) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1296 : Submodule.{0, u1} Int M Int.instSemiringInt (AddCommGroup.toAddCommMonoid.{u1} M _inst_1) (AddCommGroup.intModule.{u1} M _inst_1)) (x._@.Mathlib.Order.Hom.Basic._hyg.1298 : Submodule.{0, u1} Int M Int.instSemiringInt (AddCommGroup.toAddCommMonoid.{u1} M _inst_1) (AddCommGroup.intModule.{u1} M _inst_1)) => LE.le.{u1} (Submodule.{0, u1} Int M Int.instSemiringInt (AddCommGroup.toAddCommMonoid.{u1} M _inst_1) (AddCommGroup.intModule.{u1} M _inst_1)) (Preorder.toLE.{u1} (Submodule.{0, u1} Int M Int.instSemiringInt (AddCommGroup.toAddCommMonoid.{u1} M _inst_1) (AddCommGroup.intModule.{u1} M _inst_1)) (PartialOrder.toPreorder.{u1} (Submodule.{0, u1} Int M Int.instSemiringInt (AddCommGroup.toAddCommMonoid.{u1} M _inst_1) (AddCommGroup.intModule.{u1} M _inst_1)) (CompleteSemilatticeInf.toPartialOrder.{u1} (Submodule.{0, u1} Int M Int.instSemiringInt (AddCommGroup.toAddCommMonoid.{u1} M _inst_1) (AddCommGroup.intModule.{u1} M _inst_1)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (Submodule.{0, u1} Int M Int.instSemiringInt (AddCommGroup.toAddCommMonoid.{u1} M _inst_1) (AddCommGroup.intModule.{u1} M _inst_1)) (Submodule.completeLattice.{0, u1} Int M Int.instSemiringInt (AddCommGroup.toAddCommMonoid.{u1} M _inst_1) (AddCommGroup.intModule.{u1} M _inst_1)))))) x._@.Mathlib.Order.Hom.Basic._hyg.1296 x._@.Mathlib.Order.Hom.Basic._hyg.1298) (RelIso.instRelHomClassRelIso.{u1, u1} (AddSubgroup.{u1} M (AddCommGroup.toAddGroup.{u1} M _inst_1)) (Submodule.{0, u1} Int M Int.instSemiringInt (AddCommGroup.toAddCommMonoid.{u1} M _inst_1) (AddCommGroup.intModule.{u1} M _inst_1)) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1281 : AddSubgroup.{u1} M (AddCommGroup.toAddGroup.{u1} M _inst_1)) (x._@.Mathlib.Order.Hom.Basic._hyg.1283 : AddSubgroup.{u1} M (AddCommGroup.toAddGroup.{u1} M _inst_1)) => LE.le.{u1} (AddSubgroup.{u1} M (AddCommGroup.toAddGroup.{u1} M _inst_1)) (Preorder.toLE.{u1} (AddSubgroup.{u1} M (AddCommGroup.toAddGroup.{u1} M _inst_1)) (PartialOrder.toPreorder.{u1} (AddSubgroup.{u1} M (AddCommGroup.toAddGroup.{u1} M _inst_1)) (CompleteSemilatticeInf.toPartialOrder.{u1} (AddSubgroup.{u1} M (AddCommGroup.toAddGroup.{u1} M _inst_1)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (AddSubgroup.{u1} M (AddCommGroup.toAddGroup.{u1} M _inst_1)) (AddSubgroup.instCompleteLatticeAddSubgroup.{u1} M (AddCommGroup.toAddGroup.{u1} M _inst_1)))))) x._@.Mathlib.Order.Hom.Basic._hyg.1281 x._@.Mathlib.Order.Hom.Basic._hyg.1283) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1296 : Submodule.{0, u1} Int M Int.instSemiringInt (AddCommGroup.toAddCommMonoid.{u1} M _inst_1) (AddCommGroup.intModule.{u1} M _inst_1)) (x._@.Mathlib.Order.Hom.Basic._hyg.1298 : Submodule.{0, u1} Int M Int.instSemiringInt (AddCommGroup.toAddCommMonoid.{u1} M _inst_1) (AddCommGroup.intModule.{u1} M _inst_1)) => LE.le.{u1} (Submodule.{0, u1} Int M Int.instSemiringInt (AddCommGroup.toAddCommMonoid.{u1} M _inst_1) (AddCommGroup.intModule.{u1} M _inst_1)) (Preorder.toLE.{u1} (Submodule.{0, u1} Int M Int.instSemiringInt (AddCommGroup.toAddCommMonoid.{u1} M _inst_1) (AddCommGroup.intModule.{u1} M _inst_1)) (PartialOrder.toPreorder.{u1} (Submodule.{0, u1} Int M Int.instSemiringInt (AddCommGroup.toAddCommMonoid.{u1} M _inst_1) (AddCommGroup.intModule.{u1} M _inst_1)) (CompleteSemilatticeInf.toPartialOrder.{u1} (Submodule.{0, u1} Int M Int.instSemiringInt (AddCommGroup.toAddCommMonoid.{u1} M _inst_1) (AddCommGroup.intModule.{u1} M _inst_1)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (Submodule.{0, u1} Int M Int.instSemiringInt (AddCommGroup.toAddCommMonoid.{u1} M _inst_1) (AddCommGroup.intModule.{u1} M _inst_1)) (Submodule.completeLattice.{0, u1} Int M Int.instSemiringInt (AddCommGroup.toAddCommMonoid.{u1} M _inst_1) (AddCommGroup.intModule.{u1} M _inst_1)))))) x._@.Mathlib.Order.Hom.Basic._hyg.1296 x._@.Mathlib.Order.Hom.Basic._hyg.1298))) (AddSubgroup.toIntSubmodule.{u1} M _inst_1) S)) (SetLike.coe.{u1, u1} (AddSubgroup.{u1} M (AddCommGroup.toAddGroup.{u1} M _inst_1)) M (AddSubgroup.instSetLikeAddSubgroup.{u1} M (AddCommGroup.toAddGroup.{u1} M _inst_1)) S)
 Case conversion may be inaccurate. Consider using '#align add_subgroup.coe_to_int_submodule AddSubgroup.coe_toIntSubmoduleₓ'. -/
 @[simp]
 theorem AddSubgroup.coe_toIntSubmodule (S : AddSubgroup M) : (S.toIntSubmodule : Set M) = S :=
@@ -717,7 +717,7 @@ theorem AddSubgroup.coe_toIntSubmodule (S : AddSubgroup M) : (S.toIntSubmodule :
 lean 3 declaration is
   forall {M : Type.{u1}} [_inst_1 : AddCommGroup.{u1} M] (S : AddSubgroup.{u1} M (AddCommGroup.toAddGroup.{u1} M _inst_1)), Eq.{succ u1} (AddSubgroup.{u1} M (AddCommGroup.toAddGroup.{u1} M _inst_1)) (Submodule.toAddSubgroup.{0, u1} Int M Int.ring _inst_1 (AddCommGroup.intModule.{u1} M _inst_1) (coeFn.{succ u1, succ u1} (OrderIso.{u1, u1} (AddSubgroup.{u1} M (AddCommGroup.toAddGroup.{u1} M _inst_1)) (Submodule.{0, u1} Int M Int.semiring (AddCommGroup.toAddCommMonoid.{u1} M _inst_1) (AddCommGroup.intModule.{u1} M _inst_1)) (Preorder.toLE.{u1} (AddSubgroup.{u1} M (AddCommGroup.toAddGroup.{u1} M _inst_1)) (PartialOrder.toPreorder.{u1} (AddSubgroup.{u1} M (AddCommGroup.toAddGroup.{u1} M _inst_1)) (CompleteSemilatticeInf.toPartialOrder.{u1} (AddSubgroup.{u1} M (AddCommGroup.toAddGroup.{u1} M _inst_1)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (AddSubgroup.{u1} M (AddCommGroup.toAddGroup.{u1} M _inst_1)) (AddSubgroup.completeLattice.{u1} M (AddCommGroup.toAddGroup.{u1} M _inst_1)))))) (Preorder.toLE.{u1} (Submodule.{0, u1} Int M Int.semiring (AddCommGroup.toAddCommMonoid.{u1} M _inst_1) (AddCommGroup.intModule.{u1} M _inst_1)) (PartialOrder.toPreorder.{u1} (Submodule.{0, u1} Int M Int.semiring (AddCommGroup.toAddCommMonoid.{u1} M _inst_1) (AddCommGroup.intModule.{u1} M _inst_1)) (CompleteSemilatticeInf.toPartialOrder.{u1} (Submodule.{0, u1} Int M Int.semiring (AddCommGroup.toAddCommMonoid.{u1} M _inst_1) (AddCommGroup.intModule.{u1} M _inst_1)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (Submodule.{0, u1} Int M Int.semiring (AddCommGroup.toAddCommMonoid.{u1} M _inst_1) (AddCommGroup.intModule.{u1} M _inst_1)) (Submodule.completeLattice.{0, u1} Int M Int.semiring (AddCommGroup.toAddCommMonoid.{u1} M _inst_1) (AddCommGroup.intModule.{u1} M _inst_1))))))) (fun (_x : RelIso.{u1, u1} (AddSubgroup.{u1} M (AddCommGroup.toAddGroup.{u1} M _inst_1)) (Submodule.{0, u1} Int M Int.semiring (AddCommGroup.toAddCommMonoid.{u1} M _inst_1) (AddCommGroup.intModule.{u1} M _inst_1)) (LE.le.{u1} (AddSubgroup.{u1} M (AddCommGroup.toAddGroup.{u1} M _inst_1)) (Preorder.toLE.{u1} (AddSubgroup.{u1} M (AddCommGroup.toAddGroup.{u1} M _inst_1)) (PartialOrder.toPreorder.{u1} (AddSubgroup.{u1} M (AddCommGroup.toAddGroup.{u1} M _inst_1)) (CompleteSemilatticeInf.toPartialOrder.{u1} (AddSubgroup.{u1} M (AddCommGroup.toAddGroup.{u1} M _inst_1)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (AddSubgroup.{u1} M (AddCommGroup.toAddGroup.{u1} M _inst_1)) (AddSubgroup.completeLattice.{u1} M (AddCommGroup.toAddGroup.{u1} M _inst_1))))))) (LE.le.{u1} (Submodule.{0, u1} Int M Int.semiring (AddCommGroup.toAddCommMonoid.{u1} M _inst_1) (AddCommGroup.intModule.{u1} M _inst_1)) (Preorder.toLE.{u1} (Submodule.{0, u1} Int M Int.semiring (AddCommGroup.toAddCommMonoid.{u1} M _inst_1) (AddCommGroup.intModule.{u1} M _inst_1)) (PartialOrder.toPreorder.{u1} (Submodule.{0, u1} Int M Int.semiring (AddCommGroup.toAddCommMonoid.{u1} M _inst_1) (AddCommGroup.intModule.{u1} M _inst_1)) (CompleteSemilatticeInf.toPartialOrder.{u1} (Submodule.{0, u1} Int M Int.semiring (AddCommGroup.toAddCommMonoid.{u1} M _inst_1) (AddCommGroup.intModule.{u1} M _inst_1)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (Submodule.{0, u1} Int M Int.semiring (AddCommGroup.toAddCommMonoid.{u1} M _inst_1) (AddCommGroup.intModule.{u1} M _inst_1)) (Submodule.completeLattice.{0, u1} Int M Int.semiring (AddCommGroup.toAddCommMonoid.{u1} M _inst_1) (AddCommGroup.intModule.{u1} M _inst_1)))))))) => (AddSubgroup.{u1} M (AddCommGroup.toAddGroup.{u1} M _inst_1)) -> (Submodule.{0, u1} Int M Int.semiring (AddCommGroup.toAddCommMonoid.{u1} M _inst_1) (AddCommGroup.intModule.{u1} M _inst_1))) (RelIso.hasCoeToFun.{u1, u1} (AddSubgroup.{u1} M (AddCommGroup.toAddGroup.{u1} M _inst_1)) (Submodule.{0, u1} Int M Int.semiring (AddCommGroup.toAddCommMonoid.{u1} M _inst_1) (AddCommGroup.intModule.{u1} M _inst_1)) (LE.le.{u1} (AddSubgroup.{u1} M (AddCommGroup.toAddGroup.{u1} M _inst_1)) (Preorder.toLE.{u1} (AddSubgroup.{u1} M (AddCommGroup.toAddGroup.{u1} M _inst_1)) (PartialOrder.toPreorder.{u1} (AddSubgroup.{u1} M (AddCommGroup.toAddGroup.{u1} M _inst_1)) (CompleteSemilatticeInf.toPartialOrder.{u1} (AddSubgroup.{u1} M (AddCommGroup.toAddGroup.{u1} M _inst_1)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (AddSubgroup.{u1} M (AddCommGroup.toAddGroup.{u1} M _inst_1)) (AddSubgroup.completeLattice.{u1} M (AddCommGroup.toAddGroup.{u1} M _inst_1))))))) (LE.le.{u1} (Submodule.{0, u1} Int M Int.semiring (AddCommGroup.toAddCommMonoid.{u1} M _inst_1) (AddCommGroup.intModule.{u1} M _inst_1)) (Preorder.toLE.{u1} (Submodule.{0, u1} Int M Int.semiring (AddCommGroup.toAddCommMonoid.{u1} M _inst_1) (AddCommGroup.intModule.{u1} M _inst_1)) (PartialOrder.toPreorder.{u1} (Submodule.{0, u1} Int M Int.semiring (AddCommGroup.toAddCommMonoid.{u1} M _inst_1) (AddCommGroup.intModule.{u1} M _inst_1)) (CompleteSemilatticeInf.toPartialOrder.{u1} (Submodule.{0, u1} Int M Int.semiring (AddCommGroup.toAddCommMonoid.{u1} M _inst_1) (AddCommGroup.intModule.{u1} M _inst_1)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (Submodule.{0, u1} Int M Int.semiring (AddCommGroup.toAddCommMonoid.{u1} M _inst_1) (AddCommGroup.intModule.{u1} M _inst_1)) (Submodule.completeLattice.{0, u1} Int M Int.semiring (AddCommGroup.toAddCommMonoid.{u1} M _inst_1) (AddCommGroup.intModule.{u1} M _inst_1)))))))) (AddSubgroup.toIntSubmodule.{u1} M _inst_1) S)) S
 but is expected to have type
-  forall {M : Type.{u1}} [_inst_1 : AddCommGroup.{u1} M] (S : AddSubgroup.{u1} M (AddCommGroup.toAddGroup.{u1} M _inst_1)), Eq.{succ u1} (AddSubgroup.{u1} M (AddCommGroup.toAddGroup.{u1} M _inst_1)) (Submodule.toAddSubgroup.{0, u1} Int M Int.instRingInt _inst_1 (AddCommGroup.intModule.{u1} M _inst_1) (FunLike.coe.{succ u1, succ u1, succ u1} (Function.Embedding.{succ u1, succ u1} (AddSubgroup.{u1} M (AddCommGroup.toAddGroup.{u1} M _inst_1)) (Submodule.{0, u1} Int M Int.instSemiringInt (AddCommGroup.toAddCommMonoid.{u1} M _inst_1) (AddCommGroup.intModule.{u1} M _inst_1))) (AddSubgroup.{u1} M (AddCommGroup.toAddGroup.{u1} M _inst_1)) (fun (_x : AddSubgroup.{u1} M (AddCommGroup.toAddGroup.{u1} M _inst_1)) => (fun (x._@.Mathlib.Data.FunLike.Embedding._hyg.19 : AddSubgroup.{u1} M (AddCommGroup.toAddGroup.{u1} M _inst_1)) => Submodule.{0, u1} Int M Int.instSemiringInt (AddCommGroup.toAddCommMonoid.{u1} M _inst_1) (AddCommGroup.intModule.{u1} M _inst_1)) _x) (EmbeddingLike.toFunLike.{succ u1, succ u1, succ u1} (Function.Embedding.{succ u1, succ u1} (AddSubgroup.{u1} M (AddCommGroup.toAddGroup.{u1} M _inst_1)) (Submodule.{0, u1} Int M Int.instSemiringInt (AddCommGroup.toAddCommMonoid.{u1} M _inst_1) (AddCommGroup.intModule.{u1} M _inst_1))) (AddSubgroup.{u1} M (AddCommGroup.toAddGroup.{u1} M _inst_1)) (Submodule.{0, u1} Int M Int.instSemiringInt (AddCommGroup.toAddCommMonoid.{u1} M _inst_1) (AddCommGroup.intModule.{u1} M _inst_1)) (Function.instEmbeddingLikeEmbedding.{succ u1, succ u1} (AddSubgroup.{u1} M (AddCommGroup.toAddGroup.{u1} M _inst_1)) (Submodule.{0, u1} Int M Int.instSemiringInt (AddCommGroup.toAddCommMonoid.{u1} M _inst_1) (AddCommGroup.intModule.{u1} M _inst_1)))) (RelEmbedding.toEmbedding.{u1, u1} (AddSubgroup.{u1} M (AddCommGroup.toAddGroup.{u1} M _inst_1)) (Submodule.{0, u1} Int M Int.instSemiringInt (AddCommGroup.toAddCommMonoid.{u1} M _inst_1) (AddCommGroup.intModule.{u1} M _inst_1)) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1281 : AddSubgroup.{u1} M (AddCommGroup.toAddGroup.{u1} M _inst_1)) (x._@.Mathlib.Order.Hom.Basic._hyg.1283 : AddSubgroup.{u1} M (AddCommGroup.toAddGroup.{u1} M _inst_1)) => LE.le.{u1} (AddSubgroup.{u1} M (AddCommGroup.toAddGroup.{u1} M _inst_1)) (Preorder.toLE.{u1} (AddSubgroup.{u1} M (AddCommGroup.toAddGroup.{u1} M _inst_1)) (PartialOrder.toPreorder.{u1} (AddSubgroup.{u1} M (AddCommGroup.toAddGroup.{u1} M _inst_1)) (CompleteSemilatticeInf.toPartialOrder.{u1} (AddSubgroup.{u1} M (AddCommGroup.toAddGroup.{u1} M _inst_1)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (AddSubgroup.{u1} M (AddCommGroup.toAddGroup.{u1} M _inst_1)) (AddSubgroup.instCompleteLatticeAddSubgroup.{u1} M (AddCommGroup.toAddGroup.{u1} M _inst_1)))))) x._@.Mathlib.Order.Hom.Basic._hyg.1281 x._@.Mathlib.Order.Hom.Basic._hyg.1283) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1296 : Submodule.{0, u1} Int M Int.instSemiringInt (AddCommGroup.toAddCommMonoid.{u1} M _inst_1) (AddCommGroup.intModule.{u1} M _inst_1)) (x._@.Mathlib.Order.Hom.Basic._hyg.1298 : Submodule.{0, u1} Int M Int.instSemiringInt (AddCommGroup.toAddCommMonoid.{u1} M _inst_1) (AddCommGroup.intModule.{u1} M _inst_1)) => LE.le.{u1} (Submodule.{0, u1} Int M Int.instSemiringInt (AddCommGroup.toAddCommMonoid.{u1} M _inst_1) (AddCommGroup.intModule.{u1} M _inst_1)) (Preorder.toLE.{u1} (Submodule.{0, u1} Int M Int.instSemiringInt (AddCommGroup.toAddCommMonoid.{u1} M _inst_1) (AddCommGroup.intModule.{u1} M _inst_1)) (PartialOrder.toPreorder.{u1} (Submodule.{0, u1} Int M Int.instSemiringInt (AddCommGroup.toAddCommMonoid.{u1} M _inst_1) (AddCommGroup.intModule.{u1} M _inst_1)) (CompleteSemilatticeInf.toPartialOrder.{u1} (Submodule.{0, u1} Int M Int.instSemiringInt (AddCommGroup.toAddCommMonoid.{u1} M _inst_1) (AddCommGroup.intModule.{u1} M _inst_1)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (Submodule.{0, u1} Int M Int.instSemiringInt (AddCommGroup.toAddCommMonoid.{u1} M _inst_1) (AddCommGroup.intModule.{u1} M _inst_1)) (Submodule.completeLattice.{0, u1} Int M Int.instSemiringInt (AddCommGroup.toAddCommMonoid.{u1} M _inst_1) (AddCommGroup.intModule.{u1} M _inst_1)))))) x._@.Mathlib.Order.Hom.Basic._hyg.1296 x._@.Mathlib.Order.Hom.Basic._hyg.1298) (RelIso.toRelEmbedding.{u1, u1} (AddSubgroup.{u1} M (AddCommGroup.toAddGroup.{u1} M _inst_1)) (Submodule.{0, u1} Int M Int.instSemiringInt (AddCommGroup.toAddCommMonoid.{u1} M _inst_1) (AddCommGroup.intModule.{u1} M _inst_1)) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1281 : AddSubgroup.{u1} M (AddCommGroup.toAddGroup.{u1} M _inst_1)) (x._@.Mathlib.Order.Hom.Basic._hyg.1283 : AddSubgroup.{u1} M (AddCommGroup.toAddGroup.{u1} M _inst_1)) => LE.le.{u1} (AddSubgroup.{u1} M (AddCommGroup.toAddGroup.{u1} M _inst_1)) (Preorder.toLE.{u1} (AddSubgroup.{u1} M (AddCommGroup.toAddGroup.{u1} M _inst_1)) (PartialOrder.toPreorder.{u1} (AddSubgroup.{u1} M (AddCommGroup.toAddGroup.{u1} M _inst_1)) (CompleteSemilatticeInf.toPartialOrder.{u1} (AddSubgroup.{u1} M (AddCommGroup.toAddGroup.{u1} M _inst_1)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (AddSubgroup.{u1} M (AddCommGroup.toAddGroup.{u1} M _inst_1)) (AddSubgroup.instCompleteLatticeAddSubgroup.{u1} M (AddCommGroup.toAddGroup.{u1} M _inst_1)))))) x._@.Mathlib.Order.Hom.Basic._hyg.1281 x._@.Mathlib.Order.Hom.Basic._hyg.1283) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1296 : Submodule.{0, u1} Int M Int.instSemiringInt (AddCommGroup.toAddCommMonoid.{u1} M _inst_1) (AddCommGroup.intModule.{u1} M _inst_1)) (x._@.Mathlib.Order.Hom.Basic._hyg.1298 : Submodule.{0, u1} Int M Int.instSemiringInt (AddCommGroup.toAddCommMonoid.{u1} M _inst_1) (AddCommGroup.intModule.{u1} M _inst_1)) => LE.le.{u1} (Submodule.{0, u1} Int M Int.instSemiringInt (AddCommGroup.toAddCommMonoid.{u1} M _inst_1) (AddCommGroup.intModule.{u1} M _inst_1)) (Preorder.toLE.{u1} (Submodule.{0, u1} Int M Int.instSemiringInt (AddCommGroup.toAddCommMonoid.{u1} M _inst_1) (AddCommGroup.intModule.{u1} M _inst_1)) (PartialOrder.toPreorder.{u1} (Submodule.{0, u1} Int M Int.instSemiringInt (AddCommGroup.toAddCommMonoid.{u1} M _inst_1) (AddCommGroup.intModule.{u1} M _inst_1)) (CompleteSemilatticeInf.toPartialOrder.{u1} (Submodule.{0, u1} Int M Int.instSemiringInt (AddCommGroup.toAddCommMonoid.{u1} M _inst_1) (AddCommGroup.intModule.{u1} M _inst_1)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (Submodule.{0, u1} Int M Int.instSemiringInt (AddCommGroup.toAddCommMonoid.{u1} M _inst_1) (AddCommGroup.intModule.{u1} M _inst_1)) (Submodule.completeLattice.{0, u1} Int M Int.instSemiringInt (AddCommGroup.toAddCommMonoid.{u1} M _inst_1) (AddCommGroup.intModule.{u1} M _inst_1)))))) x._@.Mathlib.Order.Hom.Basic._hyg.1296 x._@.Mathlib.Order.Hom.Basic._hyg.1298) (AddSubgroup.toIntSubmodule.{u1} M _inst_1))) S)) S
+  forall {M : Type.{u1}} [_inst_1 : AddCommGroup.{u1} M] (S : AddSubgroup.{u1} M (AddCommGroup.toAddGroup.{u1} M _inst_1)), Eq.{succ u1} (AddSubgroup.{u1} M (AddCommGroup.toAddGroup.{u1} M _inst_1)) (Submodule.toAddSubgroup.{0, u1} Int M Int.instRingInt _inst_1 (AddCommGroup.intModule.{u1} M _inst_1) (FunLike.coe.{succ u1, succ u1, succ u1} (RelIso.{u1, u1} (AddSubgroup.{u1} M (AddCommGroup.toAddGroup.{u1} M _inst_1)) (Submodule.{0, u1} Int M Int.instSemiringInt (AddCommGroup.toAddCommMonoid.{u1} M _inst_1) (AddCommGroup.intModule.{u1} M _inst_1)) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1281 : AddSubgroup.{u1} M (AddCommGroup.toAddGroup.{u1} M _inst_1)) (x._@.Mathlib.Order.Hom.Basic._hyg.1283 : AddSubgroup.{u1} M (AddCommGroup.toAddGroup.{u1} M _inst_1)) => LE.le.{u1} (AddSubgroup.{u1} M (AddCommGroup.toAddGroup.{u1} M _inst_1)) (Preorder.toLE.{u1} (AddSubgroup.{u1} M (AddCommGroup.toAddGroup.{u1} M _inst_1)) (PartialOrder.toPreorder.{u1} (AddSubgroup.{u1} M (AddCommGroup.toAddGroup.{u1} M _inst_1)) (CompleteSemilatticeInf.toPartialOrder.{u1} (AddSubgroup.{u1} M (AddCommGroup.toAddGroup.{u1} M _inst_1)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (AddSubgroup.{u1} M (AddCommGroup.toAddGroup.{u1} M _inst_1)) (AddSubgroup.instCompleteLatticeAddSubgroup.{u1} M (AddCommGroup.toAddGroup.{u1} M _inst_1)))))) x._@.Mathlib.Order.Hom.Basic._hyg.1281 x._@.Mathlib.Order.Hom.Basic._hyg.1283) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1296 : Submodule.{0, u1} Int M Int.instSemiringInt (AddCommGroup.toAddCommMonoid.{u1} M _inst_1) (AddCommGroup.intModule.{u1} M _inst_1)) (x._@.Mathlib.Order.Hom.Basic._hyg.1298 : Submodule.{0, u1} Int M Int.instSemiringInt (AddCommGroup.toAddCommMonoid.{u1} M _inst_1) (AddCommGroup.intModule.{u1} M _inst_1)) => LE.le.{u1} (Submodule.{0, u1} Int M Int.instSemiringInt (AddCommGroup.toAddCommMonoid.{u1} M _inst_1) (AddCommGroup.intModule.{u1} M _inst_1)) (Preorder.toLE.{u1} (Submodule.{0, u1} Int M Int.instSemiringInt (AddCommGroup.toAddCommMonoid.{u1} M _inst_1) (AddCommGroup.intModule.{u1} M _inst_1)) (PartialOrder.toPreorder.{u1} (Submodule.{0, u1} Int M Int.instSemiringInt (AddCommGroup.toAddCommMonoid.{u1} M _inst_1) (AddCommGroup.intModule.{u1} M _inst_1)) (CompleteSemilatticeInf.toPartialOrder.{u1} (Submodule.{0, u1} Int M Int.instSemiringInt (AddCommGroup.toAddCommMonoid.{u1} M _inst_1) (AddCommGroup.intModule.{u1} M _inst_1)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (Submodule.{0, u1} Int M Int.instSemiringInt (AddCommGroup.toAddCommMonoid.{u1} M _inst_1) (AddCommGroup.intModule.{u1} M _inst_1)) (Submodule.completeLattice.{0, u1} Int M Int.instSemiringInt (AddCommGroup.toAddCommMonoid.{u1} M _inst_1) (AddCommGroup.intModule.{u1} M _inst_1)))))) x._@.Mathlib.Order.Hom.Basic._hyg.1296 x._@.Mathlib.Order.Hom.Basic._hyg.1298)) (AddSubgroup.{u1} M (AddCommGroup.toAddGroup.{u1} M _inst_1)) (fun (_x : AddSubgroup.{u1} M (AddCommGroup.toAddGroup.{u1} M _inst_1)) => Submodule.{0, u1} Int M Int.instSemiringInt (AddCommGroup.toAddCommMonoid.{u1} M _inst_1) (AddCommGroup.intModule.{u1} M _inst_1)) (RelHomClass.toFunLike.{u1, u1, u1} (RelIso.{u1, u1} (AddSubgroup.{u1} M (AddCommGroup.toAddGroup.{u1} M _inst_1)) (Submodule.{0, u1} Int M Int.instSemiringInt (AddCommGroup.toAddCommMonoid.{u1} M _inst_1) (AddCommGroup.intModule.{u1} M _inst_1)) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1281 : AddSubgroup.{u1} M (AddCommGroup.toAddGroup.{u1} M _inst_1)) (x._@.Mathlib.Order.Hom.Basic._hyg.1283 : AddSubgroup.{u1} M (AddCommGroup.toAddGroup.{u1} M _inst_1)) => LE.le.{u1} (AddSubgroup.{u1} M (AddCommGroup.toAddGroup.{u1} M _inst_1)) (Preorder.toLE.{u1} (AddSubgroup.{u1} M (AddCommGroup.toAddGroup.{u1} M _inst_1)) (PartialOrder.toPreorder.{u1} (AddSubgroup.{u1} M (AddCommGroup.toAddGroup.{u1} M _inst_1)) (CompleteSemilatticeInf.toPartialOrder.{u1} (AddSubgroup.{u1} M (AddCommGroup.toAddGroup.{u1} M _inst_1)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (AddSubgroup.{u1} M (AddCommGroup.toAddGroup.{u1} M _inst_1)) (AddSubgroup.instCompleteLatticeAddSubgroup.{u1} M (AddCommGroup.toAddGroup.{u1} M _inst_1)))))) x._@.Mathlib.Order.Hom.Basic._hyg.1281 x._@.Mathlib.Order.Hom.Basic._hyg.1283) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1296 : Submodule.{0, u1} Int M Int.instSemiringInt (AddCommGroup.toAddCommMonoid.{u1} M _inst_1) (AddCommGroup.intModule.{u1} M _inst_1)) (x._@.Mathlib.Order.Hom.Basic._hyg.1298 : Submodule.{0, u1} Int M Int.instSemiringInt (AddCommGroup.toAddCommMonoid.{u1} M _inst_1) (AddCommGroup.intModule.{u1} M _inst_1)) => LE.le.{u1} (Submodule.{0, u1} Int M Int.instSemiringInt (AddCommGroup.toAddCommMonoid.{u1} M _inst_1) (AddCommGroup.intModule.{u1} M _inst_1)) (Preorder.toLE.{u1} (Submodule.{0, u1} Int M Int.instSemiringInt (AddCommGroup.toAddCommMonoid.{u1} M _inst_1) (AddCommGroup.intModule.{u1} M _inst_1)) (PartialOrder.toPreorder.{u1} (Submodule.{0, u1} Int M Int.instSemiringInt (AddCommGroup.toAddCommMonoid.{u1} M _inst_1) (AddCommGroup.intModule.{u1} M _inst_1)) (CompleteSemilatticeInf.toPartialOrder.{u1} (Submodule.{0, u1} Int M Int.instSemiringInt (AddCommGroup.toAddCommMonoid.{u1} M _inst_1) (AddCommGroup.intModule.{u1} M _inst_1)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (Submodule.{0, u1} Int M Int.instSemiringInt (AddCommGroup.toAddCommMonoid.{u1} M _inst_1) (AddCommGroup.intModule.{u1} M _inst_1)) (Submodule.completeLattice.{0, u1} Int M Int.instSemiringInt (AddCommGroup.toAddCommMonoid.{u1} M _inst_1) (AddCommGroup.intModule.{u1} M _inst_1)))))) x._@.Mathlib.Order.Hom.Basic._hyg.1296 x._@.Mathlib.Order.Hom.Basic._hyg.1298)) (AddSubgroup.{u1} M (AddCommGroup.toAddGroup.{u1} M _inst_1)) (Submodule.{0, u1} Int M Int.instSemiringInt (AddCommGroup.toAddCommMonoid.{u1} M _inst_1) (AddCommGroup.intModule.{u1} M _inst_1)) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1281 : AddSubgroup.{u1} M (AddCommGroup.toAddGroup.{u1} M _inst_1)) (x._@.Mathlib.Order.Hom.Basic._hyg.1283 : AddSubgroup.{u1} M (AddCommGroup.toAddGroup.{u1} M _inst_1)) => LE.le.{u1} (AddSubgroup.{u1} M (AddCommGroup.toAddGroup.{u1} M _inst_1)) (Preorder.toLE.{u1} (AddSubgroup.{u1} M (AddCommGroup.toAddGroup.{u1} M _inst_1)) (PartialOrder.toPreorder.{u1} (AddSubgroup.{u1} M (AddCommGroup.toAddGroup.{u1} M _inst_1)) (CompleteSemilatticeInf.toPartialOrder.{u1} (AddSubgroup.{u1} M (AddCommGroup.toAddGroup.{u1} M _inst_1)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (AddSubgroup.{u1} M (AddCommGroup.toAddGroup.{u1} M _inst_1)) (AddSubgroup.instCompleteLatticeAddSubgroup.{u1} M (AddCommGroup.toAddGroup.{u1} M _inst_1)))))) x._@.Mathlib.Order.Hom.Basic._hyg.1281 x._@.Mathlib.Order.Hom.Basic._hyg.1283) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1296 : Submodule.{0, u1} Int M Int.instSemiringInt (AddCommGroup.toAddCommMonoid.{u1} M _inst_1) (AddCommGroup.intModule.{u1} M _inst_1)) (x._@.Mathlib.Order.Hom.Basic._hyg.1298 : Submodule.{0, u1} Int M Int.instSemiringInt (AddCommGroup.toAddCommMonoid.{u1} M _inst_1) (AddCommGroup.intModule.{u1} M _inst_1)) => LE.le.{u1} (Submodule.{0, u1} Int M Int.instSemiringInt (AddCommGroup.toAddCommMonoid.{u1} M _inst_1) (AddCommGroup.intModule.{u1} M _inst_1)) (Preorder.toLE.{u1} (Submodule.{0, u1} Int M Int.instSemiringInt (AddCommGroup.toAddCommMonoid.{u1} M _inst_1) (AddCommGroup.intModule.{u1} M _inst_1)) (PartialOrder.toPreorder.{u1} (Submodule.{0, u1} Int M Int.instSemiringInt (AddCommGroup.toAddCommMonoid.{u1} M _inst_1) (AddCommGroup.intModule.{u1} M _inst_1)) (CompleteSemilatticeInf.toPartialOrder.{u1} (Submodule.{0, u1} Int M Int.instSemiringInt (AddCommGroup.toAddCommMonoid.{u1} M _inst_1) (AddCommGroup.intModule.{u1} M _inst_1)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (Submodule.{0, u1} Int M Int.instSemiringInt (AddCommGroup.toAddCommMonoid.{u1} M _inst_1) (AddCommGroup.intModule.{u1} M _inst_1)) (Submodule.completeLattice.{0, u1} Int M Int.instSemiringInt (AddCommGroup.toAddCommMonoid.{u1} M _inst_1) (AddCommGroup.intModule.{u1} M _inst_1)))))) x._@.Mathlib.Order.Hom.Basic._hyg.1296 x._@.Mathlib.Order.Hom.Basic._hyg.1298) (RelIso.instRelHomClassRelIso.{u1, u1} (AddSubgroup.{u1} M (AddCommGroup.toAddGroup.{u1} M _inst_1)) (Submodule.{0, u1} Int M Int.instSemiringInt (AddCommGroup.toAddCommMonoid.{u1} M _inst_1) (AddCommGroup.intModule.{u1} M _inst_1)) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1281 : AddSubgroup.{u1} M (AddCommGroup.toAddGroup.{u1} M _inst_1)) (x._@.Mathlib.Order.Hom.Basic._hyg.1283 : AddSubgroup.{u1} M (AddCommGroup.toAddGroup.{u1} M _inst_1)) => LE.le.{u1} (AddSubgroup.{u1} M (AddCommGroup.toAddGroup.{u1} M _inst_1)) (Preorder.toLE.{u1} (AddSubgroup.{u1} M (AddCommGroup.toAddGroup.{u1} M _inst_1)) (PartialOrder.toPreorder.{u1} (AddSubgroup.{u1} M (AddCommGroup.toAddGroup.{u1} M _inst_1)) (CompleteSemilatticeInf.toPartialOrder.{u1} (AddSubgroup.{u1} M (AddCommGroup.toAddGroup.{u1} M _inst_1)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (AddSubgroup.{u1} M (AddCommGroup.toAddGroup.{u1} M _inst_1)) (AddSubgroup.instCompleteLatticeAddSubgroup.{u1} M (AddCommGroup.toAddGroup.{u1} M _inst_1)))))) x._@.Mathlib.Order.Hom.Basic._hyg.1281 x._@.Mathlib.Order.Hom.Basic._hyg.1283) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1296 : Submodule.{0, u1} Int M Int.instSemiringInt (AddCommGroup.toAddCommMonoid.{u1} M _inst_1) (AddCommGroup.intModule.{u1} M _inst_1)) (x._@.Mathlib.Order.Hom.Basic._hyg.1298 : Submodule.{0, u1} Int M Int.instSemiringInt (AddCommGroup.toAddCommMonoid.{u1} M _inst_1) (AddCommGroup.intModule.{u1} M _inst_1)) => LE.le.{u1} (Submodule.{0, u1} Int M Int.instSemiringInt (AddCommGroup.toAddCommMonoid.{u1} M _inst_1) (AddCommGroup.intModule.{u1} M _inst_1)) (Preorder.toLE.{u1} (Submodule.{0, u1} Int M Int.instSemiringInt (AddCommGroup.toAddCommMonoid.{u1} M _inst_1) (AddCommGroup.intModule.{u1} M _inst_1)) (PartialOrder.toPreorder.{u1} (Submodule.{0, u1} Int M Int.instSemiringInt (AddCommGroup.toAddCommMonoid.{u1} M _inst_1) (AddCommGroup.intModule.{u1} M _inst_1)) (CompleteSemilatticeInf.toPartialOrder.{u1} (Submodule.{0, u1} Int M Int.instSemiringInt (AddCommGroup.toAddCommMonoid.{u1} M _inst_1) (AddCommGroup.intModule.{u1} M _inst_1)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (Submodule.{0, u1} Int M Int.instSemiringInt (AddCommGroup.toAddCommMonoid.{u1} M _inst_1) (AddCommGroup.intModule.{u1} M _inst_1)) (Submodule.completeLattice.{0, u1} Int M Int.instSemiringInt (AddCommGroup.toAddCommMonoid.{u1} M _inst_1) (AddCommGroup.intModule.{u1} M _inst_1)))))) x._@.Mathlib.Order.Hom.Basic._hyg.1296 x._@.Mathlib.Order.Hom.Basic._hyg.1298))) (AddSubgroup.toIntSubmodule.{u1} M _inst_1) S)) S
 Case conversion may be inaccurate. Consider using '#align add_subgroup.to_int_submodule_to_add_subgroup AddSubgroup.toIntSubmodule_toAddSubgroupₓ'. -/
 @[simp]
 theorem AddSubgroup.toIntSubmodule_toAddSubgroup (S : AddSubgroup M) :
@@ -729,7 +729,7 @@ theorem AddSubgroup.toIntSubmodule_toAddSubgroup (S : AddSubgroup M) :
 lean 3 declaration is
   forall {M : Type.{u1}} [_inst_1 : AddCommGroup.{u1} M] (S : Submodule.{0, u1} Int M Int.semiring (AddCommGroup.toAddCommMonoid.{u1} M _inst_1) (AddCommGroup.intModule.{u1} M _inst_1)), Eq.{succ u1} (Submodule.{0, u1} Int M Int.semiring (AddCommGroup.toAddCommMonoid.{u1} M _inst_1) (AddCommGroup.intModule.{u1} M _inst_1)) (coeFn.{succ u1, succ u1} (OrderIso.{u1, u1} (AddSubgroup.{u1} M (AddCommGroup.toAddGroup.{u1} M _inst_1)) (Submodule.{0, u1} Int M Int.semiring (AddCommGroup.toAddCommMonoid.{u1} M _inst_1) (AddCommGroup.intModule.{u1} M _inst_1)) (Preorder.toLE.{u1} (AddSubgroup.{u1} M (AddCommGroup.toAddGroup.{u1} M _inst_1)) (PartialOrder.toPreorder.{u1} (AddSubgroup.{u1} M (AddCommGroup.toAddGroup.{u1} M _inst_1)) (CompleteSemilatticeInf.toPartialOrder.{u1} (AddSubgroup.{u1} M (AddCommGroup.toAddGroup.{u1} M _inst_1)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (AddSubgroup.{u1} M (AddCommGroup.toAddGroup.{u1} M _inst_1)) (AddSubgroup.completeLattice.{u1} M (AddCommGroup.toAddGroup.{u1} M _inst_1)))))) (Preorder.toLE.{u1} (Submodule.{0, u1} Int M Int.semiring (AddCommGroup.toAddCommMonoid.{u1} M _inst_1) (AddCommGroup.intModule.{u1} M _inst_1)) (PartialOrder.toPreorder.{u1} (Submodule.{0, u1} Int M Int.semiring (AddCommGroup.toAddCommMonoid.{u1} M _inst_1) (AddCommGroup.intModule.{u1} M _inst_1)) (CompleteSemilatticeInf.toPartialOrder.{u1} (Submodule.{0, u1} Int M Int.semiring (AddCommGroup.toAddCommMonoid.{u1} M _inst_1) (AddCommGroup.intModule.{u1} M _inst_1)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (Submodule.{0, u1} Int M Int.semiring (AddCommGroup.toAddCommMonoid.{u1} M _inst_1) (AddCommGroup.intModule.{u1} M _inst_1)) (Submodule.completeLattice.{0, u1} Int M Int.semiring (AddCommGroup.toAddCommMonoid.{u1} M _inst_1) (AddCommGroup.intModule.{u1} M _inst_1))))))) (fun (_x : RelIso.{u1, u1} (AddSubgroup.{u1} M (AddCommGroup.toAddGroup.{u1} M _inst_1)) (Submodule.{0, u1} Int M Int.semiring (AddCommGroup.toAddCommMonoid.{u1} M _inst_1) (AddCommGroup.intModule.{u1} M _inst_1)) (LE.le.{u1} (AddSubgroup.{u1} M (AddCommGroup.toAddGroup.{u1} M _inst_1)) (Preorder.toLE.{u1} (AddSubgroup.{u1} M (AddCommGroup.toAddGroup.{u1} M _inst_1)) (PartialOrder.toPreorder.{u1} (AddSubgroup.{u1} M (AddCommGroup.toAddGroup.{u1} M _inst_1)) (CompleteSemilatticeInf.toPartialOrder.{u1} (AddSubgroup.{u1} M (AddCommGroup.toAddGroup.{u1} M _inst_1)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (AddSubgroup.{u1} M (AddCommGroup.toAddGroup.{u1} M _inst_1)) (AddSubgroup.completeLattice.{u1} M (AddCommGroup.toAddGroup.{u1} M _inst_1))))))) (LE.le.{u1} (Submodule.{0, u1} Int M Int.semiring (AddCommGroup.toAddCommMonoid.{u1} M _inst_1) (AddCommGroup.intModule.{u1} M _inst_1)) (Preorder.toLE.{u1} (Submodule.{0, u1} Int M Int.semiring (AddCommGroup.toAddCommMonoid.{u1} M _inst_1) (AddCommGroup.intModule.{u1} M _inst_1)) (PartialOrder.toPreorder.{u1} (Submodule.{0, u1} Int M Int.semiring (AddCommGroup.toAddCommMonoid.{u1} M _inst_1) (AddCommGroup.intModule.{u1} M _inst_1)) (CompleteSemilatticeInf.toPartialOrder.{u1} (Submodule.{0, u1} Int M Int.semiring (AddCommGroup.toAddCommMonoid.{u1} M _inst_1) (AddCommGroup.intModule.{u1} M _inst_1)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (Submodule.{0, u1} Int M Int.semiring (AddCommGroup.toAddCommMonoid.{u1} M _inst_1) (AddCommGroup.intModule.{u1} M _inst_1)) (Submodule.completeLattice.{0, u1} Int M Int.semiring (AddCommGroup.toAddCommMonoid.{u1} M _inst_1) (AddCommGroup.intModule.{u1} M _inst_1)))))))) => (AddSubgroup.{u1} M (AddCommGroup.toAddGroup.{u1} M _inst_1)) -> (Submodule.{0, u1} Int M Int.semiring (AddCommGroup.toAddCommMonoid.{u1} M _inst_1) (AddCommGroup.intModule.{u1} M _inst_1))) (RelIso.hasCoeToFun.{u1, u1} (AddSubgroup.{u1} M (AddCommGroup.toAddGroup.{u1} M _inst_1)) (Submodule.{0, u1} Int M Int.semiring (AddCommGroup.toAddCommMonoid.{u1} M _inst_1) (AddCommGroup.intModule.{u1} M _inst_1)) (LE.le.{u1} (AddSubgroup.{u1} M (AddCommGroup.toAddGroup.{u1} M _inst_1)) (Preorder.toLE.{u1} (AddSubgroup.{u1} M (AddCommGroup.toAddGroup.{u1} M _inst_1)) (PartialOrder.toPreorder.{u1} (AddSubgroup.{u1} M (AddCommGroup.toAddGroup.{u1} M _inst_1)) (CompleteSemilatticeInf.toPartialOrder.{u1} (AddSubgroup.{u1} M (AddCommGroup.toAddGroup.{u1} M _inst_1)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (AddSubgroup.{u1} M (AddCommGroup.toAddGroup.{u1} M _inst_1)) (AddSubgroup.completeLattice.{u1} M (AddCommGroup.toAddGroup.{u1} M _inst_1))))))) (LE.le.{u1} (Submodule.{0, u1} Int M Int.semiring (AddCommGroup.toAddCommMonoid.{u1} M _inst_1) (AddCommGroup.intModule.{u1} M _inst_1)) (Preorder.toLE.{u1} (Submodule.{0, u1} Int M Int.semiring (AddCommGroup.toAddCommMonoid.{u1} M _inst_1) (AddCommGroup.intModule.{u1} M _inst_1)) (PartialOrder.toPreorder.{u1} (Submodule.{0, u1} Int M Int.semiring (AddCommGroup.toAddCommMonoid.{u1} M _inst_1) (AddCommGroup.intModule.{u1} M _inst_1)) (CompleteSemilatticeInf.toPartialOrder.{u1} (Submodule.{0, u1} Int M Int.semiring (AddCommGroup.toAddCommMonoid.{u1} M _inst_1) (AddCommGroup.intModule.{u1} M _inst_1)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (Submodule.{0, u1} Int M Int.semiring (AddCommGroup.toAddCommMonoid.{u1} M _inst_1) (AddCommGroup.intModule.{u1} M _inst_1)) (Submodule.completeLattice.{0, u1} Int M Int.semiring (AddCommGroup.toAddCommMonoid.{u1} M _inst_1) (AddCommGroup.intModule.{u1} M _inst_1)))))))) (AddSubgroup.toIntSubmodule.{u1} M _inst_1) (Submodule.toAddSubgroup.{0, u1} Int M Int.ring _inst_1 (AddCommGroup.intModule.{u1} M _inst_1) S)) S
 but is expected to have type
-  forall {M : Type.{u1}} [_inst_1 : AddCommGroup.{u1} M] (S : Submodule.{0, u1} Int M Int.instSemiringInt (AddCommGroup.toAddCommMonoid.{u1} M _inst_1) (AddCommGroup.intModule.{u1} M _inst_1)), Eq.{succ u1} ((fun (x._@.Mathlib.Data.FunLike.Embedding._hyg.19 : AddSubgroup.{u1} M (AddCommGroup.toAddGroup.{u1} M _inst_1)) => Submodule.{0, u1} Int M Int.instSemiringInt (AddCommGroup.toAddCommMonoid.{u1} M _inst_1) (AddCommGroup.intModule.{u1} M _inst_1)) (Submodule.toAddSubgroup.{0, u1} Int M Int.instRingInt _inst_1 (AddCommGroup.intModule.{u1} M _inst_1) S)) (FunLike.coe.{succ u1, succ u1, succ u1} (Function.Embedding.{succ u1, succ u1} (AddSubgroup.{u1} M (AddCommGroup.toAddGroup.{u1} M _inst_1)) (Submodule.{0, u1} Int M Int.instSemiringInt (AddCommGroup.toAddCommMonoid.{u1} M _inst_1) (AddCommGroup.intModule.{u1} M _inst_1))) (AddSubgroup.{u1} M (AddCommGroup.toAddGroup.{u1} M _inst_1)) (fun (_x : AddSubgroup.{u1} M (AddCommGroup.toAddGroup.{u1} M _inst_1)) => (fun (x._@.Mathlib.Data.FunLike.Embedding._hyg.19 : AddSubgroup.{u1} M (AddCommGroup.toAddGroup.{u1} M _inst_1)) => Submodule.{0, u1} Int M Int.instSemiringInt (AddCommGroup.toAddCommMonoid.{u1} M _inst_1) (AddCommGroup.intModule.{u1} M _inst_1)) _x) (EmbeddingLike.toFunLike.{succ u1, succ u1, succ u1} (Function.Embedding.{succ u1, succ u1} (AddSubgroup.{u1} M (AddCommGroup.toAddGroup.{u1} M _inst_1)) (Submodule.{0, u1} Int M Int.instSemiringInt (AddCommGroup.toAddCommMonoid.{u1} M _inst_1) (AddCommGroup.intModule.{u1} M _inst_1))) (AddSubgroup.{u1} M (AddCommGroup.toAddGroup.{u1} M _inst_1)) (Submodule.{0, u1} Int M Int.instSemiringInt (AddCommGroup.toAddCommMonoid.{u1} M _inst_1) (AddCommGroup.intModule.{u1} M _inst_1)) (Function.instEmbeddingLikeEmbedding.{succ u1, succ u1} (AddSubgroup.{u1} M (AddCommGroup.toAddGroup.{u1} M _inst_1)) (Submodule.{0, u1} Int M Int.instSemiringInt (AddCommGroup.toAddCommMonoid.{u1} M _inst_1) (AddCommGroup.intModule.{u1} M _inst_1)))) (RelEmbedding.toEmbedding.{u1, u1} (AddSubgroup.{u1} M (AddCommGroup.toAddGroup.{u1} M _inst_1)) (Submodule.{0, u1} Int M Int.instSemiringInt (AddCommGroup.toAddCommMonoid.{u1} M _inst_1) (AddCommGroup.intModule.{u1} M _inst_1)) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1281 : AddSubgroup.{u1} M (AddCommGroup.toAddGroup.{u1} M _inst_1)) (x._@.Mathlib.Order.Hom.Basic._hyg.1283 : AddSubgroup.{u1} M (AddCommGroup.toAddGroup.{u1} M _inst_1)) => LE.le.{u1} (AddSubgroup.{u1} M (AddCommGroup.toAddGroup.{u1} M _inst_1)) (Preorder.toLE.{u1} (AddSubgroup.{u1} M (AddCommGroup.toAddGroup.{u1} M _inst_1)) (PartialOrder.toPreorder.{u1} (AddSubgroup.{u1} M (AddCommGroup.toAddGroup.{u1} M _inst_1)) (CompleteSemilatticeInf.toPartialOrder.{u1} (AddSubgroup.{u1} M (AddCommGroup.toAddGroup.{u1} M _inst_1)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (AddSubgroup.{u1} M (AddCommGroup.toAddGroup.{u1} M _inst_1)) (AddSubgroup.instCompleteLatticeAddSubgroup.{u1} M (AddCommGroup.toAddGroup.{u1} M _inst_1)))))) x._@.Mathlib.Order.Hom.Basic._hyg.1281 x._@.Mathlib.Order.Hom.Basic._hyg.1283) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1296 : Submodule.{0, u1} Int M Int.instSemiringInt (AddCommGroup.toAddCommMonoid.{u1} M _inst_1) (AddCommGroup.intModule.{u1} M _inst_1)) (x._@.Mathlib.Order.Hom.Basic._hyg.1298 : Submodule.{0, u1} Int M Int.instSemiringInt (AddCommGroup.toAddCommMonoid.{u1} M _inst_1) (AddCommGroup.intModule.{u1} M _inst_1)) => LE.le.{u1} (Submodule.{0, u1} Int M Int.instSemiringInt (AddCommGroup.toAddCommMonoid.{u1} M _inst_1) (AddCommGroup.intModule.{u1} M _inst_1)) (Preorder.toLE.{u1} (Submodule.{0, u1} Int M Int.instSemiringInt (AddCommGroup.toAddCommMonoid.{u1} M _inst_1) (AddCommGroup.intModule.{u1} M _inst_1)) (PartialOrder.toPreorder.{u1} (Submodule.{0, u1} Int M Int.instSemiringInt (AddCommGroup.toAddCommMonoid.{u1} M _inst_1) (AddCommGroup.intModule.{u1} M _inst_1)) (CompleteSemilatticeInf.toPartialOrder.{u1} (Submodule.{0, u1} Int M Int.instSemiringInt (AddCommGroup.toAddCommMonoid.{u1} M _inst_1) (AddCommGroup.intModule.{u1} M _inst_1)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (Submodule.{0, u1} Int M Int.instSemiringInt (AddCommGroup.toAddCommMonoid.{u1} M _inst_1) (AddCommGroup.intModule.{u1} M _inst_1)) (Submodule.completeLattice.{0, u1} Int M Int.instSemiringInt (AddCommGroup.toAddCommMonoid.{u1} M _inst_1) (AddCommGroup.intModule.{u1} M _inst_1)))))) x._@.Mathlib.Order.Hom.Basic._hyg.1296 x._@.Mathlib.Order.Hom.Basic._hyg.1298) (RelIso.toRelEmbedding.{u1, u1} (AddSubgroup.{u1} M (AddCommGroup.toAddGroup.{u1} M _inst_1)) (Submodule.{0, u1} Int M Int.instSemiringInt (AddCommGroup.toAddCommMonoid.{u1} M _inst_1) (AddCommGroup.intModule.{u1} M _inst_1)) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1281 : AddSubgroup.{u1} M (AddCommGroup.toAddGroup.{u1} M _inst_1)) (x._@.Mathlib.Order.Hom.Basic._hyg.1283 : AddSubgroup.{u1} M (AddCommGroup.toAddGroup.{u1} M _inst_1)) => LE.le.{u1} (AddSubgroup.{u1} M (AddCommGroup.toAddGroup.{u1} M _inst_1)) (Preorder.toLE.{u1} (AddSubgroup.{u1} M (AddCommGroup.toAddGroup.{u1} M _inst_1)) (PartialOrder.toPreorder.{u1} (AddSubgroup.{u1} M (AddCommGroup.toAddGroup.{u1} M _inst_1)) (CompleteSemilatticeInf.toPartialOrder.{u1} (AddSubgroup.{u1} M (AddCommGroup.toAddGroup.{u1} M _inst_1)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (AddSubgroup.{u1} M (AddCommGroup.toAddGroup.{u1} M _inst_1)) (AddSubgroup.instCompleteLatticeAddSubgroup.{u1} M (AddCommGroup.toAddGroup.{u1} M _inst_1)))))) x._@.Mathlib.Order.Hom.Basic._hyg.1281 x._@.Mathlib.Order.Hom.Basic._hyg.1283) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1296 : Submodule.{0, u1} Int M Int.instSemiringInt (AddCommGroup.toAddCommMonoid.{u1} M _inst_1) (AddCommGroup.intModule.{u1} M _inst_1)) (x._@.Mathlib.Order.Hom.Basic._hyg.1298 : Submodule.{0, u1} Int M Int.instSemiringInt (AddCommGroup.toAddCommMonoid.{u1} M _inst_1) (AddCommGroup.intModule.{u1} M _inst_1)) => LE.le.{u1} (Submodule.{0, u1} Int M Int.instSemiringInt (AddCommGroup.toAddCommMonoid.{u1} M _inst_1) (AddCommGroup.intModule.{u1} M _inst_1)) (Preorder.toLE.{u1} (Submodule.{0, u1} Int M Int.instSemiringInt (AddCommGroup.toAddCommMonoid.{u1} M _inst_1) (AddCommGroup.intModule.{u1} M _inst_1)) (PartialOrder.toPreorder.{u1} (Submodule.{0, u1} Int M Int.instSemiringInt (AddCommGroup.toAddCommMonoid.{u1} M _inst_1) (AddCommGroup.intModule.{u1} M _inst_1)) (CompleteSemilatticeInf.toPartialOrder.{u1} (Submodule.{0, u1} Int M Int.instSemiringInt (AddCommGroup.toAddCommMonoid.{u1} M _inst_1) (AddCommGroup.intModule.{u1} M _inst_1)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (Submodule.{0, u1} Int M Int.instSemiringInt (AddCommGroup.toAddCommMonoid.{u1} M _inst_1) (AddCommGroup.intModule.{u1} M _inst_1)) (Submodule.completeLattice.{0, u1} Int M Int.instSemiringInt (AddCommGroup.toAddCommMonoid.{u1} M _inst_1) (AddCommGroup.intModule.{u1} M _inst_1)))))) x._@.Mathlib.Order.Hom.Basic._hyg.1296 x._@.Mathlib.Order.Hom.Basic._hyg.1298) (AddSubgroup.toIntSubmodule.{u1} M _inst_1))) (Submodule.toAddSubgroup.{0, u1} Int M Int.instRingInt _inst_1 (AddCommGroup.intModule.{u1} M _inst_1) S)) S
+  forall {M : Type.{u1}} [_inst_1 : AddCommGroup.{u1} M] (S : Submodule.{0, u1} Int M Int.instSemiringInt (AddCommGroup.toAddCommMonoid.{u1} M _inst_1) (AddCommGroup.intModule.{u1} M _inst_1)), Eq.{succ u1} (Submodule.{0, u1} Int M Int.instSemiringInt (AddCommGroup.toAddCommMonoid.{u1} M _inst_1) (AddCommGroup.intModule.{u1} M _inst_1)) (FunLike.coe.{succ u1, succ u1, succ u1} (RelIso.{u1, u1} (AddSubgroup.{u1} M (AddCommGroup.toAddGroup.{u1} M _inst_1)) (Submodule.{0, u1} Int M Int.instSemiringInt (AddCommGroup.toAddCommMonoid.{u1} M _inst_1) (AddCommGroup.intModule.{u1} M _inst_1)) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1281 : AddSubgroup.{u1} M (AddCommGroup.toAddGroup.{u1} M _inst_1)) (x._@.Mathlib.Order.Hom.Basic._hyg.1283 : AddSubgroup.{u1} M (AddCommGroup.toAddGroup.{u1} M _inst_1)) => LE.le.{u1} (AddSubgroup.{u1} M (AddCommGroup.toAddGroup.{u1} M _inst_1)) (Preorder.toLE.{u1} (AddSubgroup.{u1} M (AddCommGroup.toAddGroup.{u1} M _inst_1)) (PartialOrder.toPreorder.{u1} (AddSubgroup.{u1} M (AddCommGroup.toAddGroup.{u1} M _inst_1)) (CompleteSemilatticeInf.toPartialOrder.{u1} (AddSubgroup.{u1} M (AddCommGroup.toAddGroup.{u1} M _inst_1)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (AddSubgroup.{u1} M (AddCommGroup.toAddGroup.{u1} M _inst_1)) (AddSubgroup.instCompleteLatticeAddSubgroup.{u1} M (AddCommGroup.toAddGroup.{u1} M _inst_1)))))) x._@.Mathlib.Order.Hom.Basic._hyg.1281 x._@.Mathlib.Order.Hom.Basic._hyg.1283) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1296 : Submodule.{0, u1} Int M Int.instSemiringInt (AddCommGroup.toAddCommMonoid.{u1} M _inst_1) (AddCommGroup.intModule.{u1} M _inst_1)) (x._@.Mathlib.Order.Hom.Basic._hyg.1298 : Submodule.{0, u1} Int M Int.instSemiringInt (AddCommGroup.toAddCommMonoid.{u1} M _inst_1) (AddCommGroup.intModule.{u1} M _inst_1)) => LE.le.{u1} (Submodule.{0, u1} Int M Int.instSemiringInt (AddCommGroup.toAddCommMonoid.{u1} M _inst_1) (AddCommGroup.intModule.{u1} M _inst_1)) (Preorder.toLE.{u1} (Submodule.{0, u1} Int M Int.instSemiringInt (AddCommGroup.toAddCommMonoid.{u1} M _inst_1) (AddCommGroup.intModule.{u1} M _inst_1)) (PartialOrder.toPreorder.{u1} (Submodule.{0, u1} Int M Int.instSemiringInt (AddCommGroup.toAddCommMonoid.{u1} M _inst_1) (AddCommGroup.intModule.{u1} M _inst_1)) (CompleteSemilatticeInf.toPartialOrder.{u1} (Submodule.{0, u1} Int M Int.instSemiringInt (AddCommGroup.toAddCommMonoid.{u1} M _inst_1) (AddCommGroup.intModule.{u1} M _inst_1)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (Submodule.{0, u1} Int M Int.instSemiringInt (AddCommGroup.toAddCommMonoid.{u1} M _inst_1) (AddCommGroup.intModule.{u1} M _inst_1)) (Submodule.completeLattice.{0, u1} Int M Int.instSemiringInt (AddCommGroup.toAddCommMonoid.{u1} M _inst_1) (AddCommGroup.intModule.{u1} M _inst_1)))))) x._@.Mathlib.Order.Hom.Basic._hyg.1296 x._@.Mathlib.Order.Hom.Basic._hyg.1298)) (AddSubgroup.{u1} M (AddCommGroup.toAddGroup.{u1} M _inst_1)) (fun (_x : AddSubgroup.{u1} M (AddCommGroup.toAddGroup.{u1} M _inst_1)) => Submodule.{0, u1} Int M Int.instSemiringInt (AddCommGroup.toAddCommMonoid.{u1} M _inst_1) (AddCommGroup.intModule.{u1} M _inst_1)) (RelHomClass.toFunLike.{u1, u1, u1} (RelIso.{u1, u1} (AddSubgroup.{u1} M (AddCommGroup.toAddGroup.{u1} M _inst_1)) (Submodule.{0, u1} Int M Int.instSemiringInt (AddCommGroup.toAddCommMonoid.{u1} M _inst_1) (AddCommGroup.intModule.{u1} M _inst_1)) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1281 : AddSubgroup.{u1} M (AddCommGroup.toAddGroup.{u1} M _inst_1)) (x._@.Mathlib.Order.Hom.Basic._hyg.1283 : AddSubgroup.{u1} M (AddCommGroup.toAddGroup.{u1} M _inst_1)) => LE.le.{u1} (AddSubgroup.{u1} M (AddCommGroup.toAddGroup.{u1} M _inst_1)) (Preorder.toLE.{u1} (AddSubgroup.{u1} M (AddCommGroup.toAddGroup.{u1} M _inst_1)) (PartialOrder.toPreorder.{u1} (AddSubgroup.{u1} M (AddCommGroup.toAddGroup.{u1} M _inst_1)) (CompleteSemilatticeInf.toPartialOrder.{u1} (AddSubgroup.{u1} M (AddCommGroup.toAddGroup.{u1} M _inst_1)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (AddSubgroup.{u1} M (AddCommGroup.toAddGroup.{u1} M _inst_1)) (AddSubgroup.instCompleteLatticeAddSubgroup.{u1} M (AddCommGroup.toAddGroup.{u1} M _inst_1)))))) x._@.Mathlib.Order.Hom.Basic._hyg.1281 x._@.Mathlib.Order.Hom.Basic._hyg.1283) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1296 : Submodule.{0, u1} Int M Int.instSemiringInt (AddCommGroup.toAddCommMonoid.{u1} M _inst_1) (AddCommGroup.intModule.{u1} M _inst_1)) (x._@.Mathlib.Order.Hom.Basic._hyg.1298 : Submodule.{0, u1} Int M Int.instSemiringInt (AddCommGroup.toAddCommMonoid.{u1} M _inst_1) (AddCommGroup.intModule.{u1} M _inst_1)) => LE.le.{u1} (Submodule.{0, u1} Int M Int.instSemiringInt (AddCommGroup.toAddCommMonoid.{u1} M _inst_1) (AddCommGroup.intModule.{u1} M _inst_1)) (Preorder.toLE.{u1} (Submodule.{0, u1} Int M Int.instSemiringInt (AddCommGroup.toAddCommMonoid.{u1} M _inst_1) (AddCommGroup.intModule.{u1} M _inst_1)) (PartialOrder.toPreorder.{u1} (Submodule.{0, u1} Int M Int.instSemiringInt (AddCommGroup.toAddCommMonoid.{u1} M _inst_1) (AddCommGroup.intModule.{u1} M _inst_1)) (CompleteSemilatticeInf.toPartialOrder.{u1} (Submodule.{0, u1} Int M Int.instSemiringInt (AddCommGroup.toAddCommMonoid.{u1} M _inst_1) (AddCommGroup.intModule.{u1} M _inst_1)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (Submodule.{0, u1} Int M Int.instSemiringInt (AddCommGroup.toAddCommMonoid.{u1} M _inst_1) (AddCommGroup.intModule.{u1} M _inst_1)) (Submodule.completeLattice.{0, u1} Int M Int.instSemiringInt (AddCommGroup.toAddCommMonoid.{u1} M _inst_1) (AddCommGroup.intModule.{u1} M _inst_1)))))) x._@.Mathlib.Order.Hom.Basic._hyg.1296 x._@.Mathlib.Order.Hom.Basic._hyg.1298)) (AddSubgroup.{u1} M (AddCommGroup.toAddGroup.{u1} M _inst_1)) (Submodule.{0, u1} Int M Int.instSemiringInt (AddCommGroup.toAddCommMonoid.{u1} M _inst_1) (AddCommGroup.intModule.{u1} M _inst_1)) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1281 : AddSubgroup.{u1} M (AddCommGroup.toAddGroup.{u1} M _inst_1)) (x._@.Mathlib.Order.Hom.Basic._hyg.1283 : AddSubgroup.{u1} M (AddCommGroup.toAddGroup.{u1} M _inst_1)) => LE.le.{u1} (AddSubgroup.{u1} M (AddCommGroup.toAddGroup.{u1} M _inst_1)) (Preorder.toLE.{u1} (AddSubgroup.{u1} M (AddCommGroup.toAddGroup.{u1} M _inst_1)) (PartialOrder.toPreorder.{u1} (AddSubgroup.{u1} M (AddCommGroup.toAddGroup.{u1} M _inst_1)) (CompleteSemilatticeInf.toPartialOrder.{u1} (AddSubgroup.{u1} M (AddCommGroup.toAddGroup.{u1} M _inst_1)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (AddSubgroup.{u1} M (AddCommGroup.toAddGroup.{u1} M _inst_1)) (AddSubgroup.instCompleteLatticeAddSubgroup.{u1} M (AddCommGroup.toAddGroup.{u1} M _inst_1)))))) x._@.Mathlib.Order.Hom.Basic._hyg.1281 x._@.Mathlib.Order.Hom.Basic._hyg.1283) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1296 : Submodule.{0, u1} Int M Int.instSemiringInt (AddCommGroup.toAddCommMonoid.{u1} M _inst_1) (AddCommGroup.intModule.{u1} M _inst_1)) (x._@.Mathlib.Order.Hom.Basic._hyg.1298 : Submodule.{0, u1} Int M Int.instSemiringInt (AddCommGroup.toAddCommMonoid.{u1} M _inst_1) (AddCommGroup.intModule.{u1} M _inst_1)) => LE.le.{u1} (Submodule.{0, u1} Int M Int.instSemiringInt (AddCommGroup.toAddCommMonoid.{u1} M _inst_1) (AddCommGroup.intModule.{u1} M _inst_1)) (Preorder.toLE.{u1} (Submodule.{0, u1} Int M Int.instSemiringInt (AddCommGroup.toAddCommMonoid.{u1} M _inst_1) (AddCommGroup.intModule.{u1} M _inst_1)) (PartialOrder.toPreorder.{u1} (Submodule.{0, u1} Int M Int.instSemiringInt (AddCommGroup.toAddCommMonoid.{u1} M _inst_1) (AddCommGroup.intModule.{u1} M _inst_1)) (CompleteSemilatticeInf.toPartialOrder.{u1} (Submodule.{0, u1} Int M Int.instSemiringInt (AddCommGroup.toAddCommMonoid.{u1} M _inst_1) (AddCommGroup.intModule.{u1} M _inst_1)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (Submodule.{0, u1} Int M Int.instSemiringInt (AddCommGroup.toAddCommMonoid.{u1} M _inst_1) (AddCommGroup.intModule.{u1} M _inst_1)) (Submodule.completeLattice.{0, u1} Int M Int.instSemiringInt (AddCommGroup.toAddCommMonoid.{u1} M _inst_1) (AddCommGroup.intModule.{u1} M _inst_1)))))) x._@.Mathlib.Order.Hom.Basic._hyg.1296 x._@.Mathlib.Order.Hom.Basic._hyg.1298) (RelIso.instRelHomClassRelIso.{u1, u1} (AddSubgroup.{u1} M (AddCommGroup.toAddGroup.{u1} M _inst_1)) (Submodule.{0, u1} Int M Int.instSemiringInt (AddCommGroup.toAddCommMonoid.{u1} M _inst_1) (AddCommGroup.intModule.{u1} M _inst_1)) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1281 : AddSubgroup.{u1} M (AddCommGroup.toAddGroup.{u1} M _inst_1)) (x._@.Mathlib.Order.Hom.Basic._hyg.1283 : AddSubgroup.{u1} M (AddCommGroup.toAddGroup.{u1} M _inst_1)) => LE.le.{u1} (AddSubgroup.{u1} M (AddCommGroup.toAddGroup.{u1} M _inst_1)) (Preorder.toLE.{u1} (AddSubgroup.{u1} M (AddCommGroup.toAddGroup.{u1} M _inst_1)) (PartialOrder.toPreorder.{u1} (AddSubgroup.{u1} M (AddCommGroup.toAddGroup.{u1} M _inst_1)) (CompleteSemilatticeInf.toPartialOrder.{u1} (AddSubgroup.{u1} M (AddCommGroup.toAddGroup.{u1} M _inst_1)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (AddSubgroup.{u1} M (AddCommGroup.toAddGroup.{u1} M _inst_1)) (AddSubgroup.instCompleteLatticeAddSubgroup.{u1} M (AddCommGroup.toAddGroup.{u1} M _inst_1)))))) x._@.Mathlib.Order.Hom.Basic._hyg.1281 x._@.Mathlib.Order.Hom.Basic._hyg.1283) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1296 : Submodule.{0, u1} Int M Int.instSemiringInt (AddCommGroup.toAddCommMonoid.{u1} M _inst_1) (AddCommGroup.intModule.{u1} M _inst_1)) (x._@.Mathlib.Order.Hom.Basic._hyg.1298 : Submodule.{0, u1} Int M Int.instSemiringInt (AddCommGroup.toAddCommMonoid.{u1} M _inst_1) (AddCommGroup.intModule.{u1} M _inst_1)) => LE.le.{u1} (Submodule.{0, u1} Int M Int.instSemiringInt (AddCommGroup.toAddCommMonoid.{u1} M _inst_1) (AddCommGroup.intModule.{u1} M _inst_1)) (Preorder.toLE.{u1} (Submodule.{0, u1} Int M Int.instSemiringInt (AddCommGroup.toAddCommMonoid.{u1} M _inst_1) (AddCommGroup.intModule.{u1} M _inst_1)) (PartialOrder.toPreorder.{u1} (Submodule.{0, u1} Int M Int.instSemiringInt (AddCommGroup.toAddCommMonoid.{u1} M _inst_1) (AddCommGroup.intModule.{u1} M _inst_1)) (CompleteSemilatticeInf.toPartialOrder.{u1} (Submodule.{0, u1} Int M Int.instSemiringInt (AddCommGroup.toAddCommMonoid.{u1} M _inst_1) (AddCommGroup.intModule.{u1} M _inst_1)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (Submodule.{0, u1} Int M Int.instSemiringInt (AddCommGroup.toAddCommMonoid.{u1} M _inst_1) (AddCommGroup.intModule.{u1} M _inst_1)) (Submodule.completeLattice.{0, u1} Int M Int.instSemiringInt (AddCommGroup.toAddCommMonoid.{u1} M _inst_1) (AddCommGroup.intModule.{u1} M _inst_1)))))) x._@.Mathlib.Order.Hom.Basic._hyg.1296 x._@.Mathlib.Order.Hom.Basic._hyg.1298))) (AddSubgroup.toIntSubmodule.{u1} M _inst_1) (Submodule.toAddSubgroup.{0, u1} Int M Int.instRingInt _inst_1 (AddCommGroup.intModule.{u1} M _inst_1) S)) S
 Case conversion may be inaccurate. Consider using '#align submodule.to_add_subgroup_to_int_submodule Submodule.toAddSubgroup_toIntSubmoduleₓ'. -/
 @[simp]
 theorem Submodule.toAddSubgroup_toIntSubmodule (S : Submodule ℤ M) :

mathlib commit https://github.com/leanprover-community/mathlib/commit/02ba8949f486ebecf93fe7460f1ed0564b5e442c

@@ -60,7 +60,7 @@ instance inhabited' : Inhabited (Submodule R M) :=
 lean 3 declaration is
   forall {R : Type.{u1}} {M : Type.{u2}} [_inst_1 : Semiring.{u1} R] [_inst_3 : AddCommMonoid.{u2} M] [_inst_4 : Module.{u1, u2} R M _inst_1 _inst_3], Eq.{succ u2} (Set.{u2} M) ((fun (a : Type.{u2}) (b : Type.{u2}) [self : HasLiftT.{succ u2, succ u2} a b] => self.0) (Submodule.{u1, u2} R M _inst_1 _inst_3 _inst_4) (Set.{u2} M) (HasLiftT.mk.{succ u2, succ u2} (Submodule.{u1, u2} R M _inst_1 _inst_3 _inst_4) (Set.{u2} M) (CoeTCₓ.coe.{succ u2, succ u2} (Submodule.{u1, u2} R M _inst_1 _inst_3 _inst_4) (Set.{u2} M) (SetLike.Set.hasCoeT.{u2, u2} (Submodule.{u1, u2} R M _inst_1 _inst_3 _inst_4) M (Submodule.setLike.{u1, u2} R M _inst_1 _inst_3 _inst_4)))) (Bot.bot.{u2} (Submodule.{u1, u2} R M _inst_1 _inst_3 _inst_4) (Submodule.hasBot.{u1, u2} R M _inst_1 _inst_3 _inst_4))) (Singleton.singleton.{u2, u2} M (Set.{u2} M) (Set.hasSingleton.{u2} M) (OfNat.ofNat.{u2} M 0 (OfNat.mk.{u2} M 0 (Zero.zero.{u2} M (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3)))))))
 but is expected to have type
-  forall {R : Type.{u1}} {M : Type.{u2}} [_inst_1 : Semiring.{u1} R] [_inst_3 : AddCommMonoid.{u2} M] [_inst_4 : Module.{u1, u2} R M _inst_1 _inst_3], Eq.{succ u2} (Set.{u2} M) (SetLike.coe.{u2, u2} (Submodule.{u1, u2} R M _inst_1 _inst_3 _inst_4) M (Submodule.instSetLikeSubmodule.{u1, u2} R M _inst_1 _inst_3 _inst_4) (Bot.bot.{u2} (Submodule.{u1, u2} R M _inst_1 _inst_3 _inst_4) (Submodule.instBotSubmodule.{u1, u2} R M _inst_1 _inst_3 _inst_4))) (Singleton.singleton.{u2, u2} M (Set.{u2} M) (Set.instSingletonSet.{u2} M) (OfNat.ofNat.{u2} M 0 (Zero.toOfNat0.{u2} M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3)))))
+  forall {R : Type.{u1}} {M : Type.{u2}} [_inst_1 : Semiring.{u1} R] [_inst_3 : AddCommMonoid.{u2} M] [_inst_4 : Module.{u1, u2} R M _inst_1 _inst_3], Eq.{succ u2} (Set.{u2} M) (SetLike.coe.{u2, u2} (Submodule.{u1, u2} R M _inst_1 _inst_3 _inst_4) M (Submodule.setLike.{u1, u2} R M _inst_1 _inst_3 _inst_4) (Bot.bot.{u2} (Submodule.{u1, u2} R M _inst_1 _inst_3 _inst_4) (Submodule.instBotSubmodule.{u1, u2} R M _inst_1 _inst_3 _inst_4))) (Singleton.singleton.{u2, u2} M (Set.{u2} M) (Set.instSingletonSet.{u2} M) (OfNat.ofNat.{u2} M 0 (Zero.toOfNat0.{u2} M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3)))))
 Case conversion may be inaccurate. Consider using '#align submodule.bot_coe Submodule.bot_coeₓ'. -/
 @[simp]
 theorem bot_coe : ((⊥ : Submodule R M) : Set M) = {0} :=
@@ -97,7 +97,7 @@ theorem restrictScalars_bot : restrictScalars S (⊥ : Submodule R M) = ⊥ :=
 lean 3 declaration is
   forall (R : Type.{u1}) {M : Type.{u2}} [_inst_1 : Semiring.{u1} R] [_inst_3 : AddCommMonoid.{u2} M] [_inst_4 : Module.{u1, u2} R M _inst_1 _inst_3] {x : M}, Iff (Membership.Mem.{u2, u2} M (Submodule.{u1, u2} R M _inst_1 _inst_3 _inst_4) (SetLike.hasMem.{u2, u2} (Submodule.{u1, u2} R M _inst_1 _inst_3 _inst_4) M (Submodule.setLike.{u1, u2} R M _inst_1 _inst_3 _inst_4)) x (Bot.bot.{u2} (Submodule.{u1, u2} R M _inst_1 _inst_3 _inst_4) (Submodule.hasBot.{u1, u2} R M _inst_1 _inst_3 _inst_4))) (Eq.{succ u2} M x (OfNat.ofNat.{u2} M 0 (OfNat.mk.{u2} M 0 (Zero.zero.{u2} M (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3)))))))
 but is expected to have type
-  forall (R : Type.{u1}) {M : Type.{u2}} [_inst_1 : Semiring.{u1} R] [_inst_3 : AddCommMonoid.{u2} M] [_inst_4 : Module.{u1, u2} R M _inst_1 _inst_3] {x : M}, Iff (Membership.mem.{u2, u2} M (Submodule.{u1, u2} R M _inst_1 _inst_3 _inst_4) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} R M _inst_1 _inst_3 _inst_4) M (Submodule.instSetLikeSubmodule.{u1, u2} R M _inst_1 _inst_3 _inst_4)) x (Bot.bot.{u2} (Submodule.{u1, u2} R M _inst_1 _inst_3 _inst_4) (Submodule.instBotSubmodule.{u1, u2} R M _inst_1 _inst_3 _inst_4))) (Eq.{succ u2} M x (OfNat.ofNat.{u2} M 0 (Zero.toOfNat0.{u2} M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3)))))
+  forall (R : Type.{u1}) {M : Type.{u2}} [_inst_1 : Semiring.{u1} R] [_inst_3 : AddCommMonoid.{u2} M] [_inst_4 : Module.{u1, u2} R M _inst_1 _inst_3] {x : M}, Iff (Membership.mem.{u2, u2} M (Submodule.{u1, u2} R M _inst_1 _inst_3 _inst_4) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} R M _inst_1 _inst_3 _inst_4) M (Submodule.setLike.{u1, u2} R M _inst_1 _inst_3 _inst_4)) x (Bot.bot.{u2} (Submodule.{u1, u2} R M _inst_1 _inst_3 _inst_4) (Submodule.instBotSubmodule.{u1, u2} R M _inst_1 _inst_3 _inst_4))) (Eq.{succ u2} M x (OfNat.ofNat.{u2} M 0 (Zero.toOfNat0.{u2} M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3)))))
 Case conversion may be inaccurate. Consider using '#align submodule.mem_bot Submodule.mem_botₓ'. -/
 @[simp]
 theorem mem_bot {x : M} : x ∈ (⊥ : Submodule R M) ↔ x = 0 :=
@@ -121,7 +121,7 @@ theorem restrictScalars_eq_bot_iff {p : Submodule R M} : restrictScalars S p = 
 lean 3 declaration is
   forall {R : Type.{u1}} {M : Type.{u2}} [_inst_1 : Semiring.{u1} R] [_inst_3 : AddCommMonoid.{u2} M] [_inst_4 : Module.{u1, u2} R M _inst_1 _inst_3], Unique.{succ u2} (coeSort.{succ u2, succ (succ u2)} (Submodule.{u1, u2} R M _inst_1 _inst_3 _inst_4) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Submodule.{u1, u2} R M _inst_1 _inst_3 _inst_4) M (Submodule.setLike.{u1, u2} R M _inst_1 _inst_3 _inst_4)) (Bot.bot.{u2} (Submodule.{u1, u2} R M _inst_1 _inst_3 _inst_4) (Submodule.hasBot.{u1, u2} R M _inst_1 _inst_3 _inst_4)))
 but is expected to have type
-  forall {R : Type.{u1}} {M : Type.{u2}} [_inst_1 : Semiring.{u1} R] [_inst_3 : AddCommMonoid.{u2} M] [_inst_4 : Module.{u1, u2} R M _inst_1 _inst_3], Unique.{succ u2} (Subtype.{succ u2} M (fun (x : M) => Membership.mem.{u2, u2} M (Submodule.{u1, u2} R M _inst_1 _inst_3 _inst_4) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} R M _inst_1 _inst_3 _inst_4) M (Submodule.instSetLikeSubmodule.{u1, u2} R M _inst_1 _inst_3 _inst_4)) x (Bot.bot.{u2} (Submodule.{u1, u2} R M _inst_1 _inst_3 _inst_4) (Submodule.instBotSubmodule.{u1, u2} R M _inst_1 _inst_3 _inst_4))))
+  forall {R : Type.{u1}} {M : Type.{u2}} [_inst_1 : Semiring.{u1} R] [_inst_3 : AddCommMonoid.{u2} M] [_inst_4 : Module.{u1, u2} R M _inst_1 _inst_3], Unique.{succ u2} (Subtype.{succ u2} M (fun (x : M) => Membership.mem.{u2, u2} M (Submodule.{u1, u2} R M _inst_1 _inst_3 _inst_4) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} R M _inst_1 _inst_3 _inst_4) M (Submodule.setLike.{u1, u2} R M _inst_1 _inst_3 _inst_4)) x (Bot.bot.{u2} (Submodule.{u1, u2} R M _inst_1 _inst_3 _inst_4) (Submodule.instBotSubmodule.{u1, u2} R M _inst_1 _inst_3 _inst_4))))
 Case conversion may be inaccurate. Consider using '#align submodule.unique_bot Submodule.uniqueBotₓ'. -/
 instance uniqueBot : Unique (⊥ : Submodule R M) :=
   ⟨inferInstance, fun x => Subtype.ext <| (mem_bot R).1 x.Mem⟩
@@ -135,7 +135,7 @@ instance : OrderBot (Submodule R M) where
 lean 3 declaration is
   forall {R : Type.{u1}} {M : Type.{u2}} [_inst_1 : Semiring.{u1} R] [_inst_3 : AddCommMonoid.{u2} M] [_inst_4 : Module.{u1, u2} R M _inst_1 _inst_3] (p : Submodule.{u1, u2} R M _inst_1 _inst_3 _inst_4), Iff (Eq.{succ u2} (Submodule.{u1, u2} R M _inst_1 _inst_3 _inst_4) p (Bot.bot.{u2} (Submodule.{u1, u2} R M _inst_1 _inst_3 _inst_4) (Submodule.hasBot.{u1, u2} R M _inst_1 _inst_3 _inst_4))) (forall (x : M), (Membership.Mem.{u2, u2} M (Submodule.{u1, u2} R M _inst_1 _inst_3 _inst_4) (SetLike.hasMem.{u2, u2} (Submodule.{u1, u2} R M _inst_1 _inst_3 _inst_4) M (Submodule.setLike.{u1, u2} R M _inst_1 _inst_3 _inst_4)) x p) -> (Eq.{succ u2} M x (OfNat.ofNat.{u2} M 0 (OfNat.mk.{u2} M 0 (Zero.zero.{u2} M (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))))))))
 but is expected to have type
-  forall {R : Type.{u2}} {M : Type.{u1}} [_inst_1 : Semiring.{u2} R] [_inst_3 : AddCommMonoid.{u1} M] [_inst_4 : Module.{u2, u1} R M _inst_1 _inst_3] (p : Submodule.{u2, u1} R M _inst_1 _inst_3 _inst_4), Iff (Eq.{succ u1} (Submodule.{u2, u1} R M _inst_1 _inst_3 _inst_4) p (Bot.bot.{u1} (Submodule.{u2, u1} R M _inst_1 _inst_3 _inst_4) (Submodule.instBotSubmodule.{u2, u1} R M _inst_1 _inst_3 _inst_4))) (forall (x : M), (Membership.mem.{u1, u1} M (Submodule.{u2, u1} R M _inst_1 _inst_3 _inst_4) (SetLike.instMembership.{u1, u1} (Submodule.{u2, u1} R M _inst_1 _inst_3 _inst_4) M (Submodule.instSetLikeSubmodule.{u2, u1} R M _inst_1 _inst_3 _inst_4)) x p) -> (Eq.{succ u1} M x (OfNat.ofNat.{u1} M 0 (Zero.toOfNat0.{u1} M (AddMonoid.toZero.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3))))))
+  forall {R : Type.{u2}} {M : Type.{u1}} [_inst_1 : Semiring.{u2} R] [_inst_3 : AddCommMonoid.{u1} M] [_inst_4 : Module.{u2, u1} R M _inst_1 _inst_3] (p : Submodule.{u2, u1} R M _inst_1 _inst_3 _inst_4), Iff (Eq.{succ u1} (Submodule.{u2, u1} R M _inst_1 _inst_3 _inst_4) p (Bot.bot.{u1} (Submodule.{u2, u1} R M _inst_1 _inst_3 _inst_4) (Submodule.instBotSubmodule.{u2, u1} R M _inst_1 _inst_3 _inst_4))) (forall (x : M), (Membership.mem.{u1, u1} M (Submodule.{u2, u1} R M _inst_1 _inst_3 _inst_4) (SetLike.instMembership.{u1, u1} (Submodule.{u2, u1} R M _inst_1 _inst_3 _inst_4) M (Submodule.setLike.{u2, u1} R M _inst_1 _inst_3 _inst_4)) x p) -> (Eq.{succ u1} M x (OfNat.ofNat.{u1} M 0 (Zero.toOfNat0.{u1} M (AddMonoid.toZero.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3))))))
 Case conversion may be inaccurate. Consider using '#align submodule.eq_bot_iff Submodule.eq_bot_iffₓ'. -/
 protected theorem eq_bot_iff (p : Submodule R M) : p = ⊥ ↔ ∀ x ∈ p, x = (0 : M) :=
   ⟨fun h => h.symm ▸ fun x hx => (mem_bot R).mp hx, fun h =>
@@ -146,7 +146,7 @@ protected theorem eq_bot_iff (p : Submodule R M) : p = ⊥ ↔ ∀ x ∈ p, x =
 lean 3 declaration is
   forall {R : Type.{u1}} {M : Type.{u2}} [_inst_1 : Semiring.{u1} R] [_inst_3 : AddCommMonoid.{u2} M] [_inst_4 : Module.{u1, u2} R M _inst_1 _inst_3] (x : coeSort.{succ u2, succ (succ u2)} (Submodule.{u1, u2} R M _inst_1 _inst_3 _inst_4) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Submodule.{u1, u2} R M _inst_1 _inst_3 _inst_4) M (Submodule.setLike.{u1, u2} R M _inst_1 _inst_3 _inst_4)) (Bot.bot.{u2} (Submodule.{u1, u2} R M _inst_1 _inst_3 _inst_4) (Submodule.hasBot.{u1, u2} R M _inst_1 _inst_3 _inst_4))) (y : coeSort.{succ u2, succ (succ u2)} (Submodule.{u1, u2} R M _inst_1 _inst_3 _inst_4) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Submodule.{u1, u2} R M _inst_1 _inst_3 _inst_4) M (Submodule.setLike.{u1, u2} R M _inst_1 _inst_3 _inst_4)) (Bot.bot.{u2} (Submodule.{u1, u2} R M _inst_1 _inst_3 _inst_4) (Submodule.hasBot.{u1, u2} R M _inst_1 _inst_3 _inst_4))), Eq.{succ u2} (coeSort.{succ u2, succ (succ u2)} (Submodule.{u1, u2} R M _inst_1 _inst_3 _inst_4) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Submodule.{u1, u2} R M _inst_1 _inst_3 _inst_4) M (Submodule.setLike.{u1, u2} R M _inst_1 _inst_3 _inst_4)) (Bot.bot.{u2} (Submodule.{u1, u2} R M _inst_1 _inst_3 _inst_4) (Submodule.hasBot.{u1, u2} R M _inst_1 _inst_3 _inst_4))) x y
 but is expected to have type
-  forall {R : Type.{u1}} {M : Type.{u2}} [_inst_1 : Semiring.{u1} R] [_inst_3 : AddCommMonoid.{u2} M] [_inst_4 : Module.{u1, u2} R M _inst_1 _inst_3] (x : Subtype.{succ u2} M (fun (x : M) => Membership.mem.{u2, u2} M (Submodule.{u1, u2} R M _inst_1 _inst_3 _inst_4) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} R M _inst_1 _inst_3 _inst_4) M (Submodule.instSetLikeSubmodule.{u1, u2} R M _inst_1 _inst_3 _inst_4)) x (Bot.bot.{u2} (Submodule.{u1, u2} R M _inst_1 _inst_3 _inst_4) (Submodule.instBotSubmodule.{u1, u2} R M _inst_1 _inst_3 _inst_4)))) (y : Subtype.{succ u2} M (fun (x : M) => Membership.mem.{u2, u2} M (Submodule.{u1, u2} R M _inst_1 _inst_3 _inst_4) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} R M _inst_1 _inst_3 _inst_4) M (Submodule.instSetLikeSubmodule.{u1, u2} R M _inst_1 _inst_3 _inst_4)) x (Bot.bot.{u2} (Submodule.{u1, u2} R M _inst_1 _inst_3 _inst_4) (Submodule.instBotSubmodule.{u1, u2} R M _inst_1 _inst_3 _inst_4)))), Eq.{succ u2} (Subtype.{succ u2} M (fun (x : M) => Membership.mem.{u2, u2} M (Submodule.{u1, u2} R M _inst_1 _inst_3 _inst_4) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} R M _inst_1 _inst_3 _inst_4) M (Submodule.instSetLikeSubmodule.{u1, u2} R M _inst_1 _inst_3 _inst_4)) x (Bot.bot.{u2} (Submodule.{u1, u2} R M _inst_1 _inst_3 _inst_4) (Submodule.instBotSubmodule.{u1, u2} R M _inst_1 _inst_3 _inst_4)))) x y
+  forall {R : Type.{u1}} {M : Type.{u2}} [_inst_1 : Semiring.{u1} R] [_inst_3 : AddCommMonoid.{u2} M] [_inst_4 : Module.{u1, u2} R M _inst_1 _inst_3] (x : Subtype.{succ u2} M (fun (x : M) => Membership.mem.{u2, u2} M (Submodule.{u1, u2} R M _inst_1 _inst_3 _inst_4) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} R M _inst_1 _inst_3 _inst_4) M (Submodule.setLike.{u1, u2} R M _inst_1 _inst_3 _inst_4)) x (Bot.bot.{u2} (Submodule.{u1, u2} R M _inst_1 _inst_3 _inst_4) (Submodule.instBotSubmodule.{u1, u2} R M _inst_1 _inst_3 _inst_4)))) (y : Subtype.{succ u2} M (fun (x : M) => Membership.mem.{u2, u2} M (Submodule.{u1, u2} R M _inst_1 _inst_3 _inst_4) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} R M _inst_1 _inst_3 _inst_4) M (Submodule.setLike.{u1, u2} R M _inst_1 _inst_3 _inst_4)) x (Bot.bot.{u2} (Submodule.{u1, u2} R M _inst_1 _inst_3 _inst_4) (Submodule.instBotSubmodule.{u1, u2} R M _inst_1 _inst_3 _inst_4)))), Eq.{succ u2} (Subtype.{succ u2} M (fun (x : M) => Membership.mem.{u2, u2} M (Submodule.{u1, u2} R M _inst_1 _inst_3 _inst_4) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} R M _inst_1 _inst_3 _inst_4) M (Submodule.setLike.{u1, u2} R M _inst_1 _inst_3 _inst_4)) x (Bot.bot.{u2} (Submodule.{u1, u2} R M _inst_1 _inst_3 _inst_4) (Submodule.instBotSubmodule.{u1, u2} R M _inst_1 _inst_3 _inst_4)))) x y
 Case conversion may be inaccurate. Consider using '#align submodule.bot_ext Submodule.bot_extₓ'. -/
 @[ext]
 protected theorem bot_ext (x y : (⊥ : Submodule R M)) : x = y :=
@@ -160,7 +160,7 @@ protected theorem bot_ext (x y : (⊥ : Submodule R M)) : x = y :=
 lean 3 declaration is
   forall {R : Type.{u1}} {M : Type.{u2}} [_inst_1 : Semiring.{u1} R] [_inst_3 : AddCommMonoid.{u2} M] [_inst_4 : Module.{u1, u2} R M _inst_1 _inst_3] (p : Submodule.{u1, u2} R M _inst_1 _inst_3 _inst_4), Iff (Ne.{succ u2} (Submodule.{u1, u2} R M _inst_1 _inst_3 _inst_4) p (Bot.bot.{u2} (Submodule.{u1, u2} R M _inst_1 _inst_3 _inst_4) (Submodule.hasBot.{u1, u2} R M _inst_1 _inst_3 _inst_4))) (Exists.{succ u2} M (fun (x : M) => Exists.{0} (Membership.Mem.{u2, u2} M (Submodule.{u1, u2} R M _inst_1 _inst_3 _inst_4) (SetLike.hasMem.{u2, u2} (Submodule.{u1, u2} R M _inst_1 _inst_3 _inst_4) M (Submodule.setLike.{u1, u2} R M _inst_1 _inst_3 _inst_4)) x p) (fun (H : Membership.Mem.{u2, u2} M (Submodule.{u1, u2} R M _inst_1 _inst_3 _inst_4) (SetLike.hasMem.{u2, u2} (Submodule.{u1, u2} R M _inst_1 _inst_3 _inst_4) M (Submodule.setLike.{u1, u2} R M _inst_1 _inst_3 _inst_4)) x p) => Ne.{succ u2} M x (OfNat.ofNat.{u2} M 0 (OfNat.mk.{u2} M 0 (Zero.zero.{u2} M (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3)))))))))
 but is expected to have type
-  forall {R : Type.{u2}} {M : Type.{u1}} [_inst_1 : Semiring.{u2} R] [_inst_3 : AddCommMonoid.{u1} M] [_inst_4 : Module.{u2, u1} R M _inst_1 _inst_3] (p : Submodule.{u2, u1} R M _inst_1 _inst_3 _inst_4), Iff (Ne.{succ u1} (Submodule.{u2, u1} R M _inst_1 _inst_3 _inst_4) p (Bot.bot.{u1} (Submodule.{u2, u1} R M _inst_1 _inst_3 _inst_4) (Submodule.instBotSubmodule.{u2, u1} R M _inst_1 _inst_3 _inst_4))) (Exists.{succ u1} M (fun (x : M) => And (Membership.mem.{u1, u1} M (Submodule.{u2, u1} R M _inst_1 _inst_3 _inst_4) (SetLike.instMembership.{u1, u1} (Submodule.{u2, u1} R M _inst_1 _inst_3 _inst_4) M (Submodule.instSetLikeSubmodule.{u2, u1} R M _inst_1 _inst_3 _inst_4)) x p) (Ne.{succ u1} M x (OfNat.ofNat.{u1} M 0 (Zero.toOfNat0.{u1} M (AddMonoid.toZero.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3)))))))
+  forall {R : Type.{u2}} {M : Type.{u1}} [_inst_1 : Semiring.{u2} R] [_inst_3 : AddCommMonoid.{u1} M] [_inst_4 : Module.{u2, u1} R M _inst_1 _inst_3] (p : Submodule.{u2, u1} R M _inst_1 _inst_3 _inst_4), Iff (Ne.{succ u1} (Submodule.{u2, u1} R M _inst_1 _inst_3 _inst_4) p (Bot.bot.{u1} (Submodule.{u2, u1} R M _inst_1 _inst_3 _inst_4) (Submodule.instBotSubmodule.{u2, u1} R M _inst_1 _inst_3 _inst_4))) (Exists.{succ u1} M (fun (x : M) => And (Membership.mem.{u1, u1} M (Submodule.{u2, u1} R M _inst_1 _inst_3 _inst_4) (SetLike.instMembership.{u1, u1} (Submodule.{u2, u1} R M _inst_1 _inst_3 _inst_4) M (Submodule.setLike.{u2, u1} R M _inst_1 _inst_3 _inst_4)) x p) (Ne.{succ u1} M x (OfNat.ofNat.{u1} M 0 (Zero.toOfNat0.{u1} M (AddMonoid.toZero.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3)))))))
 Case conversion may be inaccurate. Consider using '#align submodule.ne_bot_iff Submodule.ne_bot_iffₓ'. -/
 protected theorem ne_bot_iff (p : Submodule R M) : p ≠ ⊥ ↔ ∃ x ∈ p, x ≠ (0 : M) :=
   by
@@ -170,9 +170,9 @@ protected theorem ne_bot_iff (p : Submodule R M) : p ≠ ⊥ ↔ ∃ x ∈ p, x
 
 /- warning: submodule.nonzero_mem_of_bot_lt -> Submodule.nonzero_mem_of_bot_lt is a dubious translation:
 lean 3 declaration is
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+  forall {R : Type.{u1}} {M : Type.{u2}} [_inst_1 : Semiring.{u1} R] [_inst_3 : AddCommMonoid.{u2} M] [_inst_4 : Module.{u1, u2} R M _inst_1 _inst_3] {p : Submodule.{u1, u2} R M _inst_1 _inst_3 _inst_4}, (LT.lt.{u2} (Submodule.{u1, u2} R M _inst_1 _inst_3 _inst_4) (Preorder.toLT.{u2} (Submodule.{u1, u2} R M _inst_1 _inst_3 _inst_4) (PartialOrder.toPreorder.{u2} (Submodule.{u1, u2} R M _inst_1 _inst_3 _inst_4) (SetLike.partialOrder.{u2, u2} (Submodule.{u1, u2} R M _inst_1 _inst_3 _inst_4) M (Submodule.setLike.{u1, u2} R M _inst_1 _inst_3 _inst_4)))) (Bot.bot.{u2} (Submodule.{u1, u2} R M _inst_1 _inst_3 _inst_4) (Submodule.hasBot.{u1, u2} R M _inst_1 _inst_3 _inst_4)) p) -> (Exists.{succ u2} (coeSort.{succ u2, succ (succ u2)} (Submodule.{u1, u2} R M _inst_1 _inst_3 _inst_4) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Submodule.{u1, u2} R M _inst_1 _inst_3 _inst_4) M (Submodule.setLike.{u1, u2} R M _inst_1 _inst_3 _inst_4)) p) (fun (a : coeSort.{succ u2, succ (succ u2)} (Submodule.{u1, u2} R M _inst_1 _inst_3 _inst_4) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Submodule.{u1, u2} R M _inst_1 _inst_3 _inst_4) M (Submodule.setLike.{u1, u2} R M _inst_1 _inst_3 _inst_4)) p) => Ne.{succ u2} (coeSort.{succ u2, succ (succ u2)} (Submodule.{u1, u2} R M _inst_1 _inst_3 _inst_4) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Submodule.{u1, u2} R M _inst_1 _inst_3 _inst_4) M (Submodule.setLike.{u1, u2} R M _inst_1 _inst_3 _inst_4)) p) a (OfNat.ofNat.{u2} (coeSort.{succ u2, succ (succ u2)} (Submodule.{u1, u2} R M _inst_1 _inst_3 _inst_4) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Submodule.{u1, u2} R M _inst_1 _inst_3 _inst_4) M (Submodule.setLike.{u1, u2} R M _inst_1 _inst_3 _inst_4)) p) 0 (OfNat.mk.{u2} (coeSort.{succ u2, succ (succ u2)} (Submodule.{u1, u2} R M _inst_1 _inst_3 _inst_4) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Submodule.{u1, u2} R M _inst_1 _inst_3 _inst_4) M (Submodule.setLike.{u1, u2} R M _inst_1 _inst_3 _inst_4)) p) 0 (Zero.zero.{u2} (coeSort.{succ u2, succ (succ u2)} (Submodule.{u1, u2} R M _inst_1 _inst_3 _inst_4) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Submodule.{u1, u2} R M _inst_1 _inst_3 _inst_4) M (Submodule.setLike.{u1, u2} R M _inst_1 _inst_3 _inst_4)) p) (Submodule.zero.{u1, u2} R M _inst_1 _inst_3 _inst_4 p))))))
 but is expected to have type
-  forall {R : Type.{u2}} {M : Type.{u1}} [_inst_1 : Semiring.{u2} R] [_inst_3 : AddCommMonoid.{u1} M] [_inst_4 : Module.{u2, u1} R M _inst_1 _inst_3] {p : Submodule.{u2, u1} R M _inst_1 _inst_3 _inst_4}, (LT.lt.{u1} (Submodule.{u2, u1} R M _inst_1 _inst_3 _inst_4) (Preorder.toLT.{u1} (Submodule.{u2, u1} R M _inst_1 _inst_3 _inst_4) (PartialOrder.toPreorder.{u1} (Submodule.{u2, u1} R M _inst_1 _inst_3 _inst_4) (SetLike.instPartialOrder.{u1, u1} (Submodule.{u2, u1} R M _inst_1 _inst_3 _inst_4) M (Submodule.instSetLikeSubmodule.{u2, u1} R M _inst_1 _inst_3 _inst_4)))) (Bot.bot.{u1} (Submodule.{u2, u1} R M _inst_1 _inst_3 _inst_4) (Submodule.instBotSubmodule.{u2, u1} R M _inst_1 _inst_3 _inst_4)) p) -> (Exists.{succ u1} (Subtype.{succ u1} M (fun (x : M) => Membership.mem.{u1, u1} M (Submodule.{u2, u1} R M _inst_1 _inst_3 _inst_4) (SetLike.instMembership.{u1, u1} (Submodule.{u2, u1} R M _inst_1 _inst_3 _inst_4) M (Submodule.instSetLikeSubmodule.{u2, u1} R M _inst_1 _inst_3 _inst_4)) x p)) (fun (a : Subtype.{succ u1} M (fun (x : M) => Membership.mem.{u1, u1} M (Submodule.{u2, u1} R M _inst_1 _inst_3 _inst_4) (SetLike.instMembership.{u1, u1} (Submodule.{u2, u1} R M _inst_1 _inst_3 _inst_4) M (Submodule.instSetLikeSubmodule.{u2, u1} R M _inst_1 _inst_3 _inst_4)) x p)) => Ne.{succ u1} (Subtype.{succ u1} M (fun (x : M) => Membership.mem.{u1, u1} M (Submodule.{u2, u1} R M _inst_1 _inst_3 _inst_4) (SetLike.instMembership.{u1, u1} (Submodule.{u2, u1} R M _inst_1 _inst_3 _inst_4) M (Submodule.instSetLikeSubmodule.{u2, u1} R M _inst_1 _inst_3 _inst_4)) x p)) a (OfNat.ofNat.{u1} (Subtype.{succ u1} M (fun (x : M) => Membership.mem.{u1, u1} M (Submodule.{u2, u1} R M _inst_1 _inst_3 _inst_4) (SetLike.instMembership.{u1, u1} (Submodule.{u2, u1} R M _inst_1 _inst_3 _inst_4) M (Submodule.instSetLikeSubmodule.{u2, u1} R M _inst_1 _inst_3 _inst_4)) x p)) 0 (Zero.toOfNat0.{u1} (Subtype.{succ u1} M (fun (x : M) => Membership.mem.{u1, u1} M (Submodule.{u2, u1} R M _inst_1 _inst_3 _inst_4) (SetLike.instMembership.{u1, u1} (Submodule.{u2, u1} R M _inst_1 _inst_3 _inst_4) M (Submodule.instSetLikeSubmodule.{u2, u1} R M _inst_1 _inst_3 _inst_4)) x p)) (Submodule.instZeroSubtypeMemSubmoduleInstMembershipInstSetLikeSubmodule.{u2, u1} R M _inst_1 _inst_3 _inst_4 p)))))
+  forall {R : Type.{u2}} {M : Type.{u1}} [_inst_1 : Semiring.{u2} R] [_inst_3 : AddCommMonoid.{u1} M] [_inst_4 : Module.{u2, u1} R M _inst_1 _inst_3] {p : Submodule.{u2, u1} R M _inst_1 _inst_3 _inst_4}, (LT.lt.{u1} (Submodule.{u2, u1} R M _inst_1 _inst_3 _inst_4) (Preorder.toLT.{u1} (Submodule.{u2, u1} R M _inst_1 _inst_3 _inst_4) (PartialOrder.toPreorder.{u1} (Submodule.{u2, u1} R M _inst_1 _inst_3 _inst_4) (SetLike.instPartialOrder.{u1, u1} (Submodule.{u2, u1} R M _inst_1 _inst_3 _inst_4) M (Submodule.setLike.{u2, u1} R M _inst_1 _inst_3 _inst_4)))) (Bot.bot.{u1} (Submodule.{u2, u1} R M _inst_1 _inst_3 _inst_4) (Submodule.instBotSubmodule.{u2, u1} R M _inst_1 _inst_3 _inst_4)) p) -> (Exists.{succ u1} (Subtype.{succ u1} M (fun (x : M) => Membership.mem.{u1, u1} M (Submodule.{u2, u1} R M _inst_1 _inst_3 _inst_4) (SetLike.instMembership.{u1, u1} (Submodule.{u2, u1} R M _inst_1 _inst_3 _inst_4) M (Submodule.setLike.{u2, u1} R M _inst_1 _inst_3 _inst_4)) x p)) (fun (a : Subtype.{succ u1} M (fun (x : M) => Membership.mem.{u1, u1} M (Submodule.{u2, u1} R M _inst_1 _inst_3 _inst_4) (SetLike.instMembership.{u1, u1} (Submodule.{u2, u1} R M _inst_1 _inst_3 _inst_4) M (Submodule.setLike.{u2, u1} R M _inst_1 _inst_3 _inst_4)) x p)) => Ne.{succ u1} (Subtype.{succ u1} M (fun (x : M) => Membership.mem.{u1, u1} M (Submodule.{u2, u1} R M _inst_1 _inst_3 _inst_4) (SetLike.instMembership.{u1, u1} (Submodule.{u2, u1} R M _inst_1 _inst_3 _inst_4) M (Submodule.setLike.{u2, u1} R M _inst_1 _inst_3 _inst_4)) x p)) a (OfNat.ofNat.{u1} (Subtype.{succ u1} M (fun (x : M) => Membership.mem.{u1, u1} M (Submodule.{u2, u1} R M _inst_1 _inst_3 _inst_4) (SetLike.instMembership.{u1, u1} (Submodule.{u2, u1} R M _inst_1 _inst_3 _inst_4) M (Submodule.setLike.{u2, u1} R M _inst_1 _inst_3 _inst_4)) x p)) 0 (Zero.toOfNat0.{u1} (Subtype.{succ u1} M (fun (x : M) => Membership.mem.{u1, u1} M (Submodule.{u2, u1} R M _inst_1 _inst_3 _inst_4) (SetLike.instMembership.{u1, u1} (Submodule.{u2, u1} R M _inst_1 _inst_3 _inst_4) M (Submodule.setLike.{u2, u1} R M _inst_1 _inst_3 _inst_4)) x p)) (Submodule.zero.{u2, u1} R M _inst_1 _inst_3 _inst_4 p)))))
 Case conversion may be inaccurate. Consider using '#align submodule.nonzero_mem_of_bot_lt Submodule.nonzero_mem_of_bot_ltₓ'. -/
 theorem nonzero_mem_of_bot_lt {p : Submodule R M} (bot_lt : ⊥ < p) : ∃ a : p, a ≠ 0 :=
   let ⟨b, hb₁, hb₂⟩ := p.ne_bot_iff.mp bot_lt.ne'
@@ -183,7 +183,7 @@ theorem nonzero_mem_of_bot_lt {p : Submodule R M} (bot_lt : ⊥ < p) : ∃ a : p
 lean 3 declaration is
   forall {R : Type.{u1}} {M : Type.{u2}} [_inst_1 : Semiring.{u1} R] [_inst_3 : AddCommMonoid.{u2} M] [_inst_4 : Module.{u1, u2} R M _inst_1 _inst_3] {p : Submodule.{u1, u2} R M _inst_1 _inst_3 _inst_4}, (Ne.{succ u2} (Submodule.{u1, u2} R M _inst_1 _inst_3 _inst_4) p (Bot.bot.{u2} (Submodule.{u1, u2} R M _inst_1 _inst_3 _inst_4) (Submodule.hasBot.{u1, u2} R M _inst_1 _inst_3 _inst_4))) -> (Exists.{succ u2} M (fun (b : M) => And (Membership.Mem.{u2, u2} M (Submodule.{u1, u2} R M _inst_1 _inst_3 _inst_4) (SetLike.hasMem.{u2, u2} (Submodule.{u1, u2} R M _inst_1 _inst_3 _inst_4) M (Submodule.setLike.{u1, u2} R M _inst_1 _inst_3 _inst_4)) b p) (Ne.{succ u2} M b (OfNat.ofNat.{u2} M 0 (OfNat.mk.{u2} M 0 (Zero.zero.{u2} M (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3)))))))))
 but is expected to have type
-  forall {R : Type.{u2}} {M : Type.{u1}} [_inst_1 : Semiring.{u2} R] [_inst_3 : AddCommMonoid.{u1} M] [_inst_4 : Module.{u2, u1} R M _inst_1 _inst_3] {p : Submodule.{u2, u1} R M _inst_1 _inst_3 _inst_4}, (Ne.{succ u1} (Submodule.{u2, u1} R M _inst_1 _inst_3 _inst_4) p (Bot.bot.{u1} (Submodule.{u2, u1} R M _inst_1 _inst_3 _inst_4) (Submodule.instBotSubmodule.{u2, u1} R M _inst_1 _inst_3 _inst_4))) -> (Exists.{succ u1} M (fun (b : M) => And (Membership.mem.{u1, u1} M (Submodule.{u2, u1} R M _inst_1 _inst_3 _inst_4) (SetLike.instMembership.{u1, u1} (Submodule.{u2, u1} R M _inst_1 _inst_3 _inst_4) M (Submodule.instSetLikeSubmodule.{u2, u1} R M _inst_1 _inst_3 _inst_4)) b p) (Ne.{succ u1} M b (OfNat.ofNat.{u1} M 0 (Zero.toOfNat0.{u1} M (AddMonoid.toZero.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3)))))))
+  forall {R : Type.{u2}} {M : Type.{u1}} [_inst_1 : Semiring.{u2} R] [_inst_3 : AddCommMonoid.{u1} M] [_inst_4 : Module.{u2, u1} R M _inst_1 _inst_3] {p : Submodule.{u2, u1} R M _inst_1 _inst_3 _inst_4}, (Ne.{succ u1} (Submodule.{u2, u1} R M _inst_1 _inst_3 _inst_4) p (Bot.bot.{u1} (Submodule.{u2, u1} R M _inst_1 _inst_3 _inst_4) (Submodule.instBotSubmodule.{u2, u1} R M _inst_1 _inst_3 _inst_4))) -> (Exists.{succ u1} M (fun (b : M) => And (Membership.mem.{u1, u1} M (Submodule.{u2, u1} R M _inst_1 _inst_3 _inst_4) (SetLike.instMembership.{u1, u1} (Submodule.{u2, u1} R M _inst_1 _inst_3 _inst_4) M (Submodule.setLike.{u2, u1} R M _inst_1 _inst_3 _inst_4)) b p) (Ne.{succ u1} M b (OfNat.ofNat.{u1} M 0 (Zero.toOfNat0.{u1} M (AddMonoid.toZero.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3)))))))
 Case conversion may be inaccurate. Consider using '#align submodule.exists_mem_ne_zero_of_ne_bot Submodule.exists_mem_ne_zero_of_ne_botₓ'. -/
 theorem exists_mem_ne_zero_of_ne_bot {p : Submodule R M} (h : p ≠ ⊥) : ∃ b : M, b ∈ p ∧ b ≠ 0 :=
   let ⟨b, hb₁, hb₂⟩ := p.ne_bot_iff.mp h
@@ -194,7 +194,7 @@ theorem exists_mem_ne_zero_of_ne_bot {p : Submodule R M} (h : p ≠ ⊥) : ∃ b
 lean 3 declaration is
   forall {R : Type.{u1}} {M : Type.{u2}} [_inst_1 : Semiring.{u1} R] [_inst_3 : AddCommMonoid.{u2} M] [_inst_4 : Module.{u1, u2} R M _inst_1 _inst_3], LinearEquiv.{u1, u1, u2, u3} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R _inst_1) (RingHomInvPair.ids.{u1} R _inst_1) (coeSort.{succ u2, succ (succ u2)} (Submodule.{u1, u2} R M _inst_1 _inst_3 _inst_4) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Submodule.{u1, u2} R M _inst_1 _inst_3 _inst_4) M (Submodule.setLike.{u1, u2} R M _inst_1 _inst_3 _inst_4)) (Bot.bot.{u2} (Submodule.{u1, u2} R M _inst_1 _inst_3 _inst_4) (Submodule.hasBot.{u1, u2} R M _inst_1 _inst_3 _inst_4))) PUnit.{succ u3} (Submodule.addCommMonoid.{u1, u2} R M _inst_1 _inst_3 _inst_4 (Bot.bot.{u2} (Submodule.{u1, u2} R M _inst_1 _inst_3 _inst_4) (Submodule.hasBot.{u1, u2} R M _inst_1 _inst_3 _inst_4))) (AddCommGroup.toAddCommMonoid.{u3} PUnit.{succ u3} PUnit.addCommGroup.{u3}) (Submodule.module.{u1, u2} R M _inst_1 _inst_3 _inst_4 (Bot.bot.{u2} (Submodule.{u1, u2} R M _inst_1 _inst_3 _inst_4) (Submodule.hasBot.{u1, u2} R M _inst_1 _inst_3 _inst_4))) (PUnit.module.{u1, u3} R _inst_1)
 but is expected to have type
-  forall {R : Type.{u1}} {M : Type.{u2}} [_inst_1 : Semiring.{u1} R] [_inst_3 : AddCommMonoid.{u2} M] [_inst_4 : Module.{u1, u2} R M _inst_1 _inst_3], LinearEquiv.{u1, u1, u2, u3} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R _inst_1) (RingHomInvPair.ids.{u1} R _inst_1) (Subtype.{succ u2} M (fun (x : M) => Membership.mem.{u2, u2} M (Submodule.{u1, u2} R M _inst_1 _inst_3 _inst_4) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} R M _inst_1 _inst_3 _inst_4) M (Submodule.instSetLikeSubmodule.{u1, u2} R M _inst_1 _inst_3 _inst_4)) x (Bot.bot.{u2} (Submodule.{u1, u2} R M _inst_1 _inst_3 _inst_4) (Submodule.instBotSubmodule.{u1, u2} R M _inst_1 _inst_3 _inst_4)))) PUnit.{succ u3} (Submodule.instAddCommMonoidSubtypeMemSubmoduleInstMembershipInstSetLikeSubmodule.{u1, u2} R M _inst_1 _inst_3 _inst_4 (Bot.bot.{u2} (Submodule.{u1, u2} R M _inst_1 _inst_3 _inst_4) (Submodule.instBotSubmodule.{u1, u2} R M _inst_1 _inst_3 _inst_4))) (OrderedCancelAddCommMonoid.toAddCommMonoid.{u3} PUnit.{succ u3} (LinearOrderedCancelAddCommMonoid.toOrderedCancelAddCommMonoid.{u3} PUnit.{succ u3} PUnit.linearOrderedCancelAddCommMonoid.{u3})) (Submodule.instModuleSubtypeMemSubmoduleInstMembershipInstSetLikeSubmoduleInstAddCommMonoidSubtypeMemSubmoduleInstMembershipInstSetLikeSubmodule.{u1, u2} R M _inst_1 _inst_3 _inst_4 (Bot.bot.{u2} (Submodule.{u1, u2} R M _inst_1 _inst_3 _inst_4) (Submodule.instBotSubmodule.{u1, u2} R M _inst_1 _inst_3 _inst_4))) (PUnit.module.{u1, u3} R _inst_1)
+  forall {R : Type.{u1}} {M : Type.{u2}} [_inst_1 : Semiring.{u1} R] [_inst_3 : AddCommMonoid.{u2} M] [_inst_4 : Module.{u1, u2} R M _inst_1 _inst_3], LinearEquiv.{u1, u1, u2, u3} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R _inst_1) (RingHomInvPair.ids.{u1} R _inst_1) (Subtype.{succ u2} M (fun (x : M) => Membership.mem.{u2, u2} M (Submodule.{u1, u2} R M _inst_1 _inst_3 _inst_4) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} R M _inst_1 _inst_3 _inst_4) M (Submodule.setLike.{u1, u2} R M _inst_1 _inst_3 _inst_4)) x (Bot.bot.{u2} (Submodule.{u1, u2} R M _inst_1 _inst_3 _inst_4) (Submodule.instBotSubmodule.{u1, u2} R M _inst_1 _inst_3 _inst_4)))) PUnit.{succ u3} (Submodule.addCommMonoid.{u1, u2} R M _inst_1 _inst_3 _inst_4 (Bot.bot.{u2} (Submodule.{u1, u2} R M _inst_1 _inst_3 _inst_4) (Submodule.instBotSubmodule.{u1, u2} R M _inst_1 _inst_3 _inst_4))) (OrderedCancelAddCommMonoid.toAddCommMonoid.{u3} PUnit.{succ u3} (LinearOrderedCancelAddCommMonoid.toOrderedCancelAddCommMonoid.{u3} PUnit.{succ u3} PUnit.linearOrderedCancelAddCommMonoid.{u3})) (Submodule.module.{u1, u2} R M _inst_1 _inst_3 _inst_4 (Bot.bot.{u2} (Submodule.{u1, u2} R M _inst_1 _inst_3 _inst_4) (Submodule.instBotSubmodule.{u1, u2} R M _inst_1 _inst_3 _inst_4))) (PUnit.module.{u1, u3} R _inst_1)
 Case conversion may be inaccurate. Consider using '#align submodule.bot_equiv_punit Submodule.botEquivPUnitₓ'. -/
 /-- The bottom submodule is linearly equivalent to punit as an `R`-module. -/
 @[simps]
@@ -220,7 +220,7 @@ def botEquivPUnit : (⊥ : Submodule R M) ≃ₗ[R] PUnit
 lean 3 declaration is
   forall {R : Type.{u1}} {M : Type.{u2}} [_inst_1 : Semiring.{u1} R] [_inst_3 : AddCommMonoid.{u2} M] [_inst_4 : Module.{u1, u2} R M _inst_1 _inst_3] (p : Submodule.{u1, u2} R M _inst_1 _inst_3 _inst_4) [_inst_8 : Subsingleton.{succ u2} (coeSort.{succ u2, succ (succ u2)} (Submodule.{u1, u2} R M _inst_1 _inst_3 _inst_4) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Submodule.{u1, u2} R M _inst_1 _inst_3 _inst_4) M (Submodule.setLike.{u1, u2} R M _inst_1 _inst_3 _inst_4)) p)], Eq.{succ u2} (Submodule.{u1, u2} R M _inst_1 _inst_3 _inst_4) p (Bot.bot.{u2} (Submodule.{u1, u2} R M _inst_1 _inst_3 _inst_4) (Submodule.hasBot.{u1, u2} R M _inst_1 _inst_3 _inst_4))
 but is expected to have type
-  forall {R : Type.{u2}} {M : Type.{u1}} [_inst_1 : Semiring.{u2} R] [_inst_3 : AddCommMonoid.{u1} M] [_inst_4 : Module.{u2, u1} R M _inst_1 _inst_3] (p : Submodule.{u2, u1} R M _inst_1 _inst_3 _inst_4) [_inst_8 : Subsingleton.{succ u1} (Subtype.{succ u1} M (fun (x : M) => Membership.mem.{u1, u1} M (Submodule.{u2, u1} R M _inst_1 _inst_3 _inst_4) (SetLike.instMembership.{u1, u1} (Submodule.{u2, u1} R M _inst_1 _inst_3 _inst_4) M (Submodule.instSetLikeSubmodule.{u2, u1} R M _inst_1 _inst_3 _inst_4)) x p))], Eq.{succ u1} (Submodule.{u2, u1} R M _inst_1 _inst_3 _inst_4) p (Bot.bot.{u1} (Submodule.{u2, u1} R M _inst_1 _inst_3 _inst_4) (Submodule.instBotSubmodule.{u2, u1} R M _inst_1 _inst_3 _inst_4))
+  forall {R : Type.{u2}} {M : Type.{u1}} [_inst_1 : Semiring.{u2} R] [_inst_3 : AddCommMonoid.{u1} M] [_inst_4 : Module.{u2, u1} R M _inst_1 _inst_3] (p : Submodule.{u2, u1} R M _inst_1 _inst_3 _inst_4) [_inst_8 : Subsingleton.{succ u1} (Subtype.{succ u1} M (fun (x : M) => Membership.mem.{u1, u1} M (Submodule.{u2, u1} R M _inst_1 _inst_3 _inst_4) (SetLike.instMembership.{u1, u1} (Submodule.{u2, u1} R M _inst_1 _inst_3 _inst_4) M (Submodule.setLike.{u2, u1} R M _inst_1 _inst_3 _inst_4)) x p))], Eq.{succ u1} (Submodule.{u2, u1} R M _inst_1 _inst_3 _inst_4) p (Bot.bot.{u1} (Submodule.{u2, u1} R M _inst_1 _inst_3 _inst_4) (Submodule.instBotSubmodule.{u2, u1} R M _inst_1 _inst_3 _inst_4))
 Case conversion may be inaccurate. Consider using '#align submodule.eq_bot_of_subsingleton Submodule.eq_bot_of_subsingletonₓ'. -/
 theorem eq_bot_of_subsingleton (p : Submodule R M) [Subsingleton p] : p = ⊥ :=
   by
@@ -239,7 +239,7 @@ instance : Top (Submodule R M) :=
 lean 3 declaration is
   forall {R : Type.{u1}} {M : Type.{u2}} [_inst_1 : Semiring.{u1} R] [_inst_3 : AddCommMonoid.{u2} M] [_inst_4 : Module.{u1, u2} R M _inst_1 _inst_3], Eq.{succ u2} (Set.{u2} M) ((fun (a : Type.{u2}) (b : Type.{u2}) [self : HasLiftT.{succ u2, succ u2} a b] => self.0) (Submodule.{u1, u2} R M _inst_1 _inst_3 _inst_4) (Set.{u2} M) (HasLiftT.mk.{succ u2, succ u2} (Submodule.{u1, u2} R M _inst_1 _inst_3 _inst_4) (Set.{u2} M) (CoeTCₓ.coe.{succ u2, succ u2} (Submodule.{u1, u2} R M _inst_1 _inst_3 _inst_4) (Set.{u2} M) (SetLike.Set.hasCoeT.{u2, u2} (Submodule.{u1, u2} R M _inst_1 _inst_3 _inst_4) M (Submodule.setLike.{u1, u2} R M _inst_1 _inst_3 _inst_4)))) (Top.top.{u2} (Submodule.{u1, u2} R M _inst_1 _inst_3 _inst_4) (Submodule.hasTop.{u1, u2} R M _inst_1 _inst_3 _inst_4))) (Set.univ.{u2} M)
 but is expected to have type
-  forall {R : Type.{u1}} {M : Type.{u2}} [_inst_1 : Semiring.{u1} R] [_inst_3 : AddCommMonoid.{u2} M] [_inst_4 : Module.{u1, u2} R M _inst_1 _inst_3], Eq.{succ u2} (Set.{u2} M) (SetLike.coe.{u2, u2} (Submodule.{u1, u2} R M _inst_1 _inst_3 _inst_4) M (Submodule.instSetLikeSubmodule.{u1, u2} R M _inst_1 _inst_3 _inst_4) (Top.top.{u2} (Submodule.{u1, u2} R M _inst_1 _inst_3 _inst_4) (Submodule.instTopSubmodule.{u1, u2} R M _inst_1 _inst_3 _inst_4))) (Set.univ.{u2} M)
+  forall {R : Type.{u1}} {M : Type.{u2}} [_inst_1 : Semiring.{u1} R] [_inst_3 : AddCommMonoid.{u2} M] [_inst_4 : Module.{u1, u2} R M _inst_1 _inst_3], Eq.{succ u2} (Set.{u2} M) (SetLike.coe.{u2, u2} (Submodule.{u1, u2} R M _inst_1 _inst_3 _inst_4) M (Submodule.setLike.{u1, u2} R M _inst_1 _inst_3 _inst_4) (Top.top.{u2} (Submodule.{u1, u2} R M _inst_1 _inst_3 _inst_4) (Submodule.instTopSubmodule.{u1, u2} R M _inst_1 _inst_3 _inst_4))) (Set.univ.{u2} M)
 Case conversion may be inaccurate. Consider using '#align submodule.top_coe Submodule.top_coeₓ'. -/
 @[simp]
 theorem top_coe : ((⊤ : Submodule R M) : Set M) = Set.univ :=
@@ -261,7 +261,7 @@ theorem top_toAddSubmonoid : (⊤ : Submodule R M).toAddSubmonoid = ⊤ :=
 lean 3 declaration is
   forall {R : Type.{u1}} {M : Type.{u2}} [_inst_1 : Semiring.{u1} R] [_inst_3 : AddCommMonoid.{u2} M] [_inst_4 : Module.{u1, u2} R M _inst_1 _inst_3] {x : M}, Membership.Mem.{u2, u2} M (Submodule.{u1, u2} R M _inst_1 _inst_3 _inst_4) (SetLike.hasMem.{u2, u2} (Submodule.{u1, u2} R M _inst_1 _inst_3 _inst_4) M (Submodule.setLike.{u1, u2} R M _inst_1 _inst_3 _inst_4)) x (Top.top.{u2} (Submodule.{u1, u2} R M _inst_1 _inst_3 _inst_4) (Submodule.hasTop.{u1, u2} R M _inst_1 _inst_3 _inst_4))
 but is expected to have type
-  forall {R : Type.{u1}} {M : Type.{u2}} [_inst_1 : Semiring.{u1} R] [_inst_3 : AddCommMonoid.{u2} M] [_inst_4 : Module.{u1, u2} R M _inst_1 _inst_3] {x : M}, Membership.mem.{u2, u2} M (Submodule.{u1, u2} R M _inst_1 _inst_3 _inst_4) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} R M _inst_1 _inst_3 _inst_4) M (Submodule.instSetLikeSubmodule.{u1, u2} R M _inst_1 _inst_3 _inst_4)) x (Top.top.{u2} (Submodule.{u1, u2} R M _inst_1 _inst_3 _inst_4) (Submodule.instTopSubmodule.{u1, u2} R M _inst_1 _inst_3 _inst_4))
+  forall {R : Type.{u1}} {M : Type.{u2}} [_inst_1 : Semiring.{u1} R] [_inst_3 : AddCommMonoid.{u2} M] [_inst_4 : Module.{u1, u2} R M _inst_1 _inst_3] {x : M}, Membership.mem.{u2, u2} M (Submodule.{u1, u2} R M _inst_1 _inst_3 _inst_4) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} R M _inst_1 _inst_3 _inst_4) M (Submodule.setLike.{u1, u2} R M _inst_1 _inst_3 _inst_4)) x (Top.top.{u2} (Submodule.{u1, u2} R M _inst_1 _inst_3 _inst_4) (Submodule.instTopSubmodule.{u1, u2} R M _inst_1 _inst_3 _inst_4))
 Case conversion may be inaccurate. Consider using '#align submodule.mem_top Submodule.mem_topₓ'. -/
 @[simp]
 theorem mem_top {x : M} : x ∈ (⊤ : Submodule R M) :=
@@ -304,7 +304,7 @@ instance : OrderTop (Submodule R M) where
 lean 3 declaration is
   forall {R : Type.{u1}} {M : Type.{u2}} [_inst_1 : Semiring.{u1} R] [_inst_3 : AddCommMonoid.{u2} M] [_inst_4 : Module.{u1, u2} R M _inst_1 _inst_3] {p : Submodule.{u1, u2} R M _inst_1 _inst_3 _inst_4}, Iff (Eq.{succ u2} (Submodule.{u1, u2} R M _inst_1 _inst_3 _inst_4) p (Top.top.{u2} (Submodule.{u1, u2} R M _inst_1 _inst_3 _inst_4) (Submodule.hasTop.{u1, u2} R M _inst_1 _inst_3 _inst_4))) (forall (x : M), Membership.Mem.{u2, u2} M (Submodule.{u1, u2} R M _inst_1 _inst_3 _inst_4) (SetLike.hasMem.{u2, u2} (Submodule.{u1, u2} R M _inst_1 _inst_3 _inst_4) M (Submodule.setLike.{u1, u2} R M _inst_1 _inst_3 _inst_4)) x p)
 but is expected to have type
-  forall {R : Type.{u2}} {M : Type.{u1}} [_inst_1 : Semiring.{u2} R] [_inst_3 : AddCommMonoid.{u1} M] [_inst_4 : Module.{u2, u1} R M _inst_1 _inst_3] {p : Submodule.{u2, u1} R M _inst_1 _inst_3 _inst_4}, Iff (Eq.{succ u1} (Submodule.{u2, u1} R M _inst_1 _inst_3 _inst_4) p (Top.top.{u1} (Submodule.{u2, u1} R M _inst_1 _inst_3 _inst_4) (Submodule.instTopSubmodule.{u2, u1} R M _inst_1 _inst_3 _inst_4))) (forall (x : M), Membership.mem.{u1, u1} M (Submodule.{u2, u1} R M _inst_1 _inst_3 _inst_4) (SetLike.instMembership.{u1, u1} (Submodule.{u2, u1} R M _inst_1 _inst_3 _inst_4) M (Submodule.instSetLikeSubmodule.{u2, u1} R M _inst_1 _inst_3 _inst_4)) x p)
+  forall {R : Type.{u2}} {M : Type.{u1}} [_inst_1 : Semiring.{u2} R] [_inst_3 : AddCommMonoid.{u1} M] [_inst_4 : Module.{u2, u1} R M _inst_1 _inst_3] {p : Submodule.{u2, u1} R M _inst_1 _inst_3 _inst_4}, Iff (Eq.{succ u1} (Submodule.{u2, u1} R M _inst_1 _inst_3 _inst_4) p (Top.top.{u1} (Submodule.{u2, u1} R M _inst_1 _inst_3 _inst_4) (Submodule.instTopSubmodule.{u2, u1} R M _inst_1 _inst_3 _inst_4))) (forall (x : M), Membership.mem.{u1, u1} M (Submodule.{u2, u1} R M _inst_1 _inst_3 _inst_4) (SetLike.instMembership.{u1, u1} (Submodule.{u2, u1} R M _inst_1 _inst_3 _inst_4) M (Submodule.setLike.{u2, u1} R M _inst_1 _inst_3 _inst_4)) x p)
 Case conversion may be inaccurate. Consider using '#align submodule.eq_top_iff' Submodule.eq_top_iff'ₓ'. -/
 theorem eq_top_iff' {p : Submodule R M} : p = ⊤ ↔ ∀ x, x ∈ p :=
   eq_top_iff.trans ⟨fun h x => h trivial, fun h x _ => h x⟩
@@ -314,7 +314,7 @@ theorem eq_top_iff' {p : Submodule R M} : p = ⊤ ↔ ∀ x, x ∈ p :=
 lean 3 declaration is
   forall {R : Type.{u1}} {M : Type.{u2}} [_inst_1 : Semiring.{u1} R] [_inst_3 : AddCommMonoid.{u2} M] [_inst_4 : Module.{u1, u2} R M _inst_1 _inst_3], LinearEquiv.{u1, u1, u2, u2} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R _inst_1) (RingHomInvPair.ids.{u1} R _inst_1) (coeSort.{succ u2, succ (succ u2)} (Submodule.{u1, u2} R M _inst_1 _inst_3 _inst_4) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Submodule.{u1, u2} R M _inst_1 _inst_3 _inst_4) M (Submodule.setLike.{u1, u2} R M _inst_1 _inst_3 _inst_4)) (Top.top.{u2} (Submodule.{u1, u2} R M _inst_1 _inst_3 _inst_4) (Submodule.hasTop.{u1, u2} R M _inst_1 _inst_3 _inst_4))) M (Submodule.addCommMonoid.{u1, u2} R M _inst_1 _inst_3 _inst_4 (Top.top.{u2} (Submodule.{u1, u2} R M _inst_1 _inst_3 _inst_4) (Submodule.hasTop.{u1, u2} R M _inst_1 _inst_3 _inst_4))) _inst_3 (Submodule.module.{u1, u2} R M _inst_1 _inst_3 _inst_4 (Top.top.{u2} (Submodule.{u1, u2} R M _inst_1 _inst_3 _inst_4) (Submodule.hasTop.{u1, u2} R M _inst_1 _inst_3 _inst_4))) _inst_4
 but is expected to have type
-  forall {R : Type.{u1}} {M : Type.{u2}} [_inst_1 : Semiring.{u1} R] [_inst_3 : AddCommMonoid.{u2} M] [_inst_4 : Module.{u1, u2} R M _inst_1 _inst_3], LinearEquiv.{u1, u1, u2, u2} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R _inst_1) (RingHomInvPair.ids.{u1} R _inst_1) (Subtype.{succ u2} M (fun (x : M) => Membership.mem.{u2, u2} M (Submodule.{u1, u2} R M _inst_1 _inst_3 _inst_4) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} R M _inst_1 _inst_3 _inst_4) M (Submodule.instSetLikeSubmodule.{u1, u2} R M _inst_1 _inst_3 _inst_4)) x (Top.top.{u2} (Submodule.{u1, u2} R M _inst_1 _inst_3 _inst_4) (Submodule.instTopSubmodule.{u1, u2} R M _inst_1 _inst_3 _inst_4)))) M (Submodule.instAddCommMonoidSubtypeMemSubmoduleInstMembershipInstSetLikeSubmodule.{u1, u2} R M _inst_1 _inst_3 _inst_4 (Top.top.{u2} (Submodule.{u1, u2} R M _inst_1 _inst_3 _inst_4) (Submodule.instTopSubmodule.{u1, u2} R M _inst_1 _inst_3 _inst_4))) _inst_3 (Submodule.instModuleSubtypeMemSubmoduleInstMembershipInstSetLikeSubmoduleInstAddCommMonoidSubtypeMemSubmoduleInstMembershipInstSetLikeSubmodule.{u1, u2} R M _inst_1 _inst_3 _inst_4 (Top.top.{u2} (Submodule.{u1, u2} R M _inst_1 _inst_3 _inst_4) (Submodule.instTopSubmodule.{u1, u2} R M _inst_1 _inst_3 _inst_4))) _inst_4
+  forall {R : Type.{u1}} {M : Type.{u2}} [_inst_1 : Semiring.{u1} R] [_inst_3 : AddCommMonoid.{u2} M] [_inst_4 : Module.{u1, u2} R M _inst_1 _inst_3], LinearEquiv.{u1, u1, u2, u2} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R _inst_1) (RingHomInvPair.ids.{u1} R _inst_1) (Subtype.{succ u2} M (fun (x : M) => Membership.mem.{u2, u2} M (Submodule.{u1, u2} R M _inst_1 _inst_3 _inst_4) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} R M _inst_1 _inst_3 _inst_4) M (Submodule.setLike.{u1, u2} R M _inst_1 _inst_3 _inst_4)) x (Top.top.{u2} (Submodule.{u1, u2} R M _inst_1 _inst_3 _inst_4) (Submodule.instTopSubmodule.{u1, u2} R M _inst_1 _inst_3 _inst_4)))) M (Submodule.addCommMonoid.{u1, u2} R M _inst_1 _inst_3 _inst_4 (Top.top.{u2} (Submodule.{u1, u2} R M _inst_1 _inst_3 _inst_4) (Submodule.instTopSubmodule.{u1, u2} R M _inst_1 _inst_3 _inst_4))) _inst_3 (Submodule.module.{u1, u2} R M _inst_1 _inst_3 _inst_4 (Top.top.{u2} (Submodule.{u1, u2} R M _inst_1 _inst_3 _inst_4) (Submodule.instTopSubmodule.{u1, u2} R M _inst_1 _inst_3 _inst_4))) _inst_4
 Case conversion may be inaccurate. Consider using '#align submodule.top_equiv Submodule.topEquivₓ'. -/
 /-- The top submodule is linearly equivalent to the module.
 
@@ -383,7 +383,7 @@ instance : CompleteLattice (Submodule R M) :=
 lean 3 declaration is
   forall {R : Type.{u1}} {M : Type.{u2}} [_inst_1 : Semiring.{u1} R] [_inst_3 : AddCommMonoid.{u2} M] [_inst_4 : Module.{u1, u2} R M _inst_1 _inst_3] {p : Submodule.{u1, u2} R M _inst_1 _inst_3 _inst_4} {q : Submodule.{u1, u2} R M _inst_1 _inst_3 _inst_4}, Eq.{succ u2} (Set.{u2} M) ((fun (a : Type.{u2}) (b : Type.{u2}) [self : HasLiftT.{succ u2, succ u2} a b] => self.0) (Submodule.{u1, u2} R M _inst_1 _inst_3 _inst_4) (Set.{u2} M) (HasLiftT.mk.{succ u2, succ u2} (Submodule.{u1, u2} R M _inst_1 _inst_3 _inst_4) (Set.{u2} M) (CoeTCₓ.coe.{succ u2, succ u2} (Submodule.{u1, u2} R M _inst_1 _inst_3 _inst_4) (Set.{u2} M) (SetLike.Set.hasCoeT.{u2, u2} (Submodule.{u1, u2} R M _inst_1 _inst_3 _inst_4) M (Submodule.setLike.{u1, u2} R M _inst_1 _inst_3 _inst_4)))) (Inf.inf.{u2} (Submodule.{u1, u2} R M _inst_1 _inst_3 _inst_4) (Submodule.hasInf.{u1, u2} R M _inst_1 _inst_3 _inst_4) p q)) (Inter.inter.{u2} (Set.{u2} M) (Set.hasInter.{u2} M) ((fun (a : Type.{u2}) (b : Type.{u2}) [self : HasLiftT.{succ u2, succ u2} a b] => self.0) (Submodule.{u1, u2} R M _inst_1 _inst_3 _inst_4) (Set.{u2} M) (HasLiftT.mk.{succ u2, succ u2} (Submodule.{u1, u2} R M _inst_1 _inst_3 _inst_4) (Set.{u2} M) (CoeTCₓ.coe.{succ u2, succ u2} (Submodule.{u1, u2} R M _inst_1 _inst_3 _inst_4) (Set.{u2} M) (SetLike.Set.hasCoeT.{u2, u2} (Submodule.{u1, u2} R M _inst_1 _inst_3 _inst_4) M (Submodule.setLike.{u1, u2} R M _inst_1 _inst_3 _inst_4)))) p) ((fun (a : Type.{u2}) (b : Type.{u2}) [self : HasLiftT.{succ u2, succ u2} a b] => self.0) (Submodule.{u1, u2} R M _inst_1 _inst_3 _inst_4) (Set.{u2} M) (HasLiftT.mk.{succ u2, succ u2} (Submodule.{u1, u2} R M _inst_1 _inst_3 _inst_4) (Set.{u2} M) (CoeTCₓ.coe.{succ u2, succ u2} (Submodule.{u1, u2} R M _inst_1 _inst_3 _inst_4) (Set.{u2} M) (SetLike.Set.hasCoeT.{u2, u2} (Submodule.{u1, u2} R M _inst_1 _inst_3 _inst_4) M (Submodule.setLike.{u1, u2} R M _inst_1 _inst_3 _inst_4)))) q))
 but is expected to have type
-  forall {R : Type.{u1}} {M : Type.{u2}} [_inst_1 : Semiring.{u1} R] [_inst_3 : AddCommMonoid.{u2} M] [_inst_4 : Module.{u1, u2} R M _inst_1 _inst_3] {p : Submodule.{u1, u2} R M _inst_1 _inst_3 _inst_4} {q : Submodule.{u1, u2} R M _inst_1 _inst_3 _inst_4}, Eq.{succ u2} (Set.{u2} M) (SetLike.coe.{u2, u2} (Submodule.{u1, u2} R M _inst_1 _inst_3 _inst_4) M (Submodule.instSetLikeSubmodule.{u1, u2} R M _inst_1 _inst_3 _inst_4) (Inf.inf.{u2} (Submodule.{u1, u2} R M _inst_1 _inst_3 _inst_4) (Submodule.instInfSubmodule.{u1, u2} R M _inst_1 _inst_3 _inst_4) p q)) (Inter.inter.{u2} (Set.{u2} M) (Set.instInterSet.{u2} M) (SetLike.coe.{u2, u2} (Submodule.{u1, u2} R M _inst_1 _inst_3 _inst_4) M (Submodule.instSetLikeSubmodule.{u1, u2} R M _inst_1 _inst_3 _inst_4) p) (SetLike.coe.{u2, u2} (Submodule.{u1, u2} R M _inst_1 _inst_3 _inst_4) M (Submodule.instSetLikeSubmodule.{u1, u2} R M _inst_1 _inst_3 _inst_4) q))
+  forall {R : Type.{u1}} {M : Type.{u2}} [_inst_1 : Semiring.{u1} R] [_inst_3 : AddCommMonoid.{u2} M] [_inst_4 : Module.{u1, u2} R M _inst_1 _inst_3] {p : Submodule.{u1, u2} R M _inst_1 _inst_3 _inst_4} {q : Submodule.{u1, u2} R M _inst_1 _inst_3 _inst_4}, Eq.{succ u2} (Set.{u2} M) (SetLike.coe.{u2, u2} (Submodule.{u1, u2} R M _inst_1 _inst_3 _inst_4) M (Submodule.setLike.{u1, u2} R M _inst_1 _inst_3 _inst_4) (Inf.inf.{u2} (Submodule.{u1, u2} R M _inst_1 _inst_3 _inst_4) (Submodule.instInfSubmodule.{u1, u2} R M _inst_1 _inst_3 _inst_4) p q)) (Inter.inter.{u2} (Set.{u2} M) (Set.instInterSet.{u2} M) (SetLike.coe.{u2, u2} (Submodule.{u1, u2} R M _inst_1 _inst_3 _inst_4) M (Submodule.setLike.{u1, u2} R M _inst_1 _inst_3 _inst_4) p) (SetLike.coe.{u2, u2} (Submodule.{u1, u2} R M _inst_1 _inst_3 _inst_4) M (Submodule.setLike.{u1, u2} R M _inst_1 _inst_3 _inst_4) q))
 Case conversion may be inaccurate. Consider using '#align submodule.inf_coe Submodule.inf_coeₓ'. -/
 @[simp]
 theorem inf_coe : ↑(p ⊓ q) = (p ∩ q : Set M) :=
@@ -394,7 +394,7 @@ theorem inf_coe : ↑(p ⊓ q) = (p ∩ q : Set M) :=
 lean 3 declaration is
   forall {R : Type.{u1}} {M : Type.{u2}} [_inst_1 : Semiring.{u1} R] [_inst_3 : AddCommMonoid.{u2} M] [_inst_4 : Module.{u1, u2} R M _inst_1 _inst_3] {p : Submodule.{u1, u2} R M _inst_1 _inst_3 _inst_4} {q : Submodule.{u1, u2} R M _inst_1 _inst_3 _inst_4} {x : M}, Iff (Membership.Mem.{u2, u2} M (Submodule.{u1, u2} R M _inst_1 _inst_3 _inst_4) (SetLike.hasMem.{u2, u2} (Submodule.{u1, u2} R M _inst_1 _inst_3 _inst_4) M (Submodule.setLike.{u1, u2} R M _inst_1 _inst_3 _inst_4)) x (Inf.inf.{u2} (Submodule.{u1, u2} R M _inst_1 _inst_3 _inst_4) (Submodule.hasInf.{u1, u2} R M _inst_1 _inst_3 _inst_4) p q)) (And (Membership.Mem.{u2, u2} M (Submodule.{u1, u2} R M _inst_1 _inst_3 _inst_4) (SetLike.hasMem.{u2, u2} (Submodule.{u1, u2} R M _inst_1 _inst_3 _inst_4) M (Submodule.setLike.{u1, u2} R M _inst_1 _inst_3 _inst_4)) x p) (Membership.Mem.{u2, u2} M (Submodule.{u1, u2} R M _inst_1 _inst_3 _inst_4) (SetLike.hasMem.{u2, u2} (Submodule.{u1, u2} R M _inst_1 _inst_3 _inst_4) M (Submodule.setLike.{u1, u2} R M _inst_1 _inst_3 _inst_4)) x q))
 but is expected to have type
-  forall {R : Type.{u2}} {M : Type.{u1}} [_inst_1 : Semiring.{u2} R] [_inst_3 : AddCommMonoid.{u1} M] [_inst_4 : Module.{u2, u1} R M _inst_1 _inst_3] {p : Submodule.{u2, u1} R M _inst_1 _inst_3 _inst_4} {q : Submodule.{u2, u1} R M _inst_1 _inst_3 _inst_4} {x : M}, Iff (Membership.mem.{u1, u1} M (Submodule.{u2, u1} R M _inst_1 _inst_3 _inst_4) (SetLike.instMembership.{u1, u1} (Submodule.{u2, u1} R M _inst_1 _inst_3 _inst_4) M (Submodule.instSetLikeSubmodule.{u2, u1} R M _inst_1 _inst_3 _inst_4)) x (Inf.inf.{u1} (Submodule.{u2, u1} R M _inst_1 _inst_3 _inst_4) (Submodule.instInfSubmodule.{u2, u1} R M _inst_1 _inst_3 _inst_4) p q)) (And (Membership.mem.{u1, u1} M (Submodule.{u2, u1} R M _inst_1 _inst_3 _inst_4) (SetLike.instMembership.{u1, u1} (Submodule.{u2, u1} R M _inst_1 _inst_3 _inst_4) M (Submodule.instSetLikeSubmodule.{u2, u1} R M _inst_1 _inst_3 _inst_4)) x p) (Membership.mem.{u1, u1} M (Submodule.{u2, u1} R M _inst_1 _inst_3 _inst_4) (SetLike.instMembership.{u1, u1} (Submodule.{u2, u1} R M _inst_1 _inst_3 _inst_4) M (Submodule.instSetLikeSubmodule.{u2, u1} R M _inst_1 _inst_3 _inst_4)) x q))
+  forall {R : Type.{u2}} {M : Type.{u1}} [_inst_1 : Semiring.{u2} R] [_inst_3 : AddCommMonoid.{u1} M] [_inst_4 : Module.{u2, u1} R M _inst_1 _inst_3] {p : Submodule.{u2, u1} R M _inst_1 _inst_3 _inst_4} {q : Submodule.{u2, u1} R M _inst_1 _inst_3 _inst_4} {x : M}, Iff (Membership.mem.{u1, u1} M (Submodule.{u2, u1} R M _inst_1 _inst_3 _inst_4) (SetLike.instMembership.{u1, u1} (Submodule.{u2, u1} R M _inst_1 _inst_3 _inst_4) M (Submodule.setLike.{u2, u1} R M _inst_1 _inst_3 _inst_4)) x (Inf.inf.{u1} (Submodule.{u2, u1} R M _inst_1 _inst_3 _inst_4) (Submodule.instInfSubmodule.{u2, u1} R M _inst_1 _inst_3 _inst_4) p q)) (And (Membership.mem.{u1, u1} M (Submodule.{u2, u1} R M _inst_1 _inst_3 _inst_4) (SetLike.instMembership.{u1, u1} (Submodule.{u2, u1} R M _inst_1 _inst_3 _inst_4) M (Submodule.setLike.{u2, u1} R M _inst_1 _inst_3 _inst_4)) x p) (Membership.mem.{u1, u1} M (Submodule.{u2, u1} R M _inst_1 _inst_3 _inst_4) (SetLike.instMembership.{u1, u1} (Submodule.{u2, u1} R M _inst_1 _inst_3 _inst_4) M (Submodule.setLike.{u2, u1} R M _inst_1 _inst_3 _inst_4)) x q))
 Case conversion may be inaccurate. Consider using '#align submodule.mem_inf Submodule.mem_infₓ'. -/
 @[simp]
 theorem mem_inf {p q : Submodule R M} {x : M} : x ∈ p ⊓ q ↔ x ∈ p ∧ x ∈ q :=
@@ -405,7 +405,7 @@ theorem mem_inf {p q : Submodule R M} {x : M} : x ∈ p ⊓ q ↔ x ∈ p ∧ x
 lean 3 declaration is
   forall {R : Type.{u1}} {M : Type.{u2}} [_inst_1 : Semiring.{u1} R] [_inst_3 : AddCommMonoid.{u2} M] [_inst_4 : Module.{u1, u2} R M _inst_1 _inst_3] (P : Set.{u2} (Submodule.{u1, u2} R M _inst_1 _inst_3 _inst_4)), Eq.{succ u2} (Set.{u2} M) ((fun (a : Type.{u2}) (b : Type.{u2}) [self : HasLiftT.{succ u2, succ u2} a b] => self.0) (Submodule.{u1, u2} R M _inst_1 _inst_3 _inst_4) (Set.{u2} M) (HasLiftT.mk.{succ u2, succ u2} (Submodule.{u1, u2} R M _inst_1 _inst_3 _inst_4) (Set.{u2} M) (CoeTCₓ.coe.{succ u2, succ u2} (Submodule.{u1, u2} R M _inst_1 _inst_3 _inst_4) (Set.{u2} M) (SetLike.Set.hasCoeT.{u2, u2} (Submodule.{u1, u2} R M _inst_1 _inst_3 _inst_4) M (Submodule.setLike.{u1, u2} R M _inst_1 _inst_3 _inst_4)))) (InfSet.infₛ.{u2} (Submodule.{u1, u2} R M _inst_1 _inst_3 _inst_4) (Submodule.hasInf.{u1, u2} R M _inst_1 _inst_3 _inst_4) P)) (Set.interᵢ.{u2, succ u2} M (Submodule.{u1, u2} R M _inst_1 _inst_3 _inst_4) (fun (p : Submodule.{u1, u2} R M _inst_1 _inst_3 _inst_4) => Set.interᵢ.{u2, 0} M (Membership.Mem.{u2, u2} (Submodule.{u1, u2} R M _inst_1 _inst_3 _inst_4) (Set.{u2} (Submodule.{u1, u2} R M _inst_1 _inst_3 _inst_4)) (Set.hasMem.{u2} (Submodule.{u1, u2} R M _inst_1 _inst_3 _inst_4)) p P) (fun (H : Membership.Mem.{u2, u2} (Submodule.{u1, u2} R M _inst_1 _inst_3 _inst_4) (Set.{u2} (Submodule.{u1, u2} R M _inst_1 _inst_3 _inst_4)) (Set.hasMem.{u2} (Submodule.{u1, u2} R M _inst_1 _inst_3 _inst_4)) p P) => (fun (a : Type.{u2}) (b : Type.{u2}) [self : HasLiftT.{succ u2, succ u2} a b] => self.0) (Submodule.{u1, u2} R M _inst_1 _inst_3 _inst_4) (Set.{u2} M) (HasLiftT.mk.{succ u2, succ u2} (Submodule.{u1, u2} R M _inst_1 _inst_3 _inst_4) (Set.{u2} M) (CoeTCₓ.coe.{succ u2, succ u2} (Submodule.{u1, u2} R M _inst_1 _inst_3 _inst_4) (Set.{u2} M) (SetLike.Set.hasCoeT.{u2, u2} (Submodule.{u1, u2} R M _inst_1 _inst_3 _inst_4) M (Submodule.setLike.{u1, u2} R M _inst_1 _inst_3 _inst_4)))) p)))
 but is expected to have type
-  forall {R : Type.{u1}} {M : Type.{u2}} [_inst_1 : Semiring.{u1} R] [_inst_3 : AddCommMonoid.{u2} M] [_inst_4 : Module.{u1, u2} R M _inst_1 _inst_3] (P : Set.{u2} (Submodule.{u1, u2} R M _inst_1 _inst_3 _inst_4)), Eq.{succ u2} (Set.{u2} M) (SetLike.coe.{u2, u2} (Submodule.{u1, u2} R M _inst_1 _inst_3 _inst_4) M (Submodule.instSetLikeSubmodule.{u1, u2} R M _inst_1 _inst_3 _inst_4) (InfSet.infₛ.{u2} (Submodule.{u1, u2} R M _inst_1 _inst_3 _inst_4) (Submodule.instInfSetSubmodule.{u1, u2} R M _inst_1 _inst_3 _inst_4) P)) (Set.interᵢ.{u2, succ u2} M (Submodule.{u1, u2} R M _inst_1 _inst_3 _inst_4) (fun (p : Submodule.{u1, u2} R M _inst_1 _inst_3 _inst_4) => Set.interᵢ.{u2, 0} M (Membership.mem.{u2, u2} (Submodule.{u1, u2} R M _inst_1 _inst_3 _inst_4) (Set.{u2} (Submodule.{u1, u2} R M _inst_1 _inst_3 _inst_4)) (Set.instMembershipSet.{u2} (Submodule.{u1, u2} R M _inst_1 _inst_3 _inst_4)) p P) (fun (H : Membership.mem.{u2, u2} (Submodule.{u1, u2} R M _inst_1 _inst_3 _inst_4) (Set.{u2} (Submodule.{u1, u2} R M _inst_1 _inst_3 _inst_4)) (Set.instMembershipSet.{u2} (Submodule.{u1, u2} R M _inst_1 _inst_3 _inst_4)) p P) => SetLike.coe.{u2, u2} (Submodule.{u1, u2} R M _inst_1 _inst_3 _inst_4) M (Submodule.instSetLikeSubmodule.{u1, u2} R M _inst_1 _inst_3 _inst_4) p)))
+  forall {R : Type.{u1}} {M : Type.{u2}} [_inst_1 : Semiring.{u1} R] [_inst_3 : AddCommMonoid.{u2} M] [_inst_4 : Module.{u1, u2} R M _inst_1 _inst_3] (P : Set.{u2} (Submodule.{u1, u2} R M _inst_1 _inst_3 _inst_4)), Eq.{succ u2} (Set.{u2} M) (SetLike.coe.{u2, u2} (Submodule.{u1, u2} R M _inst_1 _inst_3 _inst_4) M (Submodule.setLike.{u1, u2} R M _inst_1 _inst_3 _inst_4) (InfSet.infₛ.{u2} (Submodule.{u1, u2} R M _inst_1 _inst_3 _inst_4) (Submodule.instInfSetSubmodule.{u1, u2} R M _inst_1 _inst_3 _inst_4) P)) (Set.interᵢ.{u2, succ u2} M (Submodule.{u1, u2} R M _inst_1 _inst_3 _inst_4) (fun (p : Submodule.{u1, u2} R M _inst_1 _inst_3 _inst_4) => Set.interᵢ.{u2, 0} M (Membership.mem.{u2, u2} (Submodule.{u1, u2} R M _inst_1 _inst_3 _inst_4) (Set.{u2} (Submodule.{u1, u2} R M _inst_1 _inst_3 _inst_4)) (Set.instMembershipSet.{u2} (Submodule.{u1, u2} R M _inst_1 _inst_3 _inst_4)) p P) (fun (H : Membership.mem.{u2, u2} (Submodule.{u1, u2} R M _inst_1 _inst_3 _inst_4) (Set.{u2} (Submodule.{u1, u2} R M _inst_1 _inst_3 _inst_4)) (Set.instMembershipSet.{u2} (Submodule.{u1, u2} R M _inst_1 _inst_3 _inst_4)) p P) => SetLike.coe.{u2, u2} (Submodule.{u1, u2} R M _inst_1 _inst_3 _inst_4) M (Submodule.setLike.{u1, u2} R M _inst_1 _inst_3 _inst_4) p)))
 Case conversion may be inaccurate. Consider using '#align submodule.Inf_coe Submodule.infₛ_coeₓ'. -/
 @[simp]
 theorem infₛ_coe (P : Set (Submodule R M)) : (↑(infₛ P) : Set M) = ⋂ p ∈ P, ↑p :=
@@ -416,7 +416,7 @@ theorem infₛ_coe (P : Set (Submodule R M)) : (↑(infₛ P) : Set M) = ⋂ p 
 lean 3 declaration is
   forall {R : Type.{u1}} {M : Type.{u2}} [_inst_1 : Semiring.{u1} R] [_inst_3 : AddCommMonoid.{u2} M] [_inst_4 : Module.{u1, u2} R M _inst_1 _inst_3] {ι : Type.{u3}} (s : Finset.{u3} ι) (p : ι -> (Submodule.{u1, u2} R M _inst_1 _inst_3 _inst_4)), Eq.{succ u2} (Set.{u2} M) ((fun (a : Type.{u2}) (b : Type.{u2}) [self : HasLiftT.{succ u2, succ u2} a b] => self.0) (Submodule.{u1, u2} R M _inst_1 _inst_3 _inst_4) (Set.{u2} M) (HasLiftT.mk.{succ u2, succ u2} (Submodule.{u1, u2} R M _inst_1 _inst_3 _inst_4) (Set.{u2} M) (CoeTCₓ.coe.{succ u2, succ u2} (Submodule.{u1, u2} R M _inst_1 _inst_3 _inst_4) (Set.{u2} M) (SetLike.Set.hasCoeT.{u2, u2} (Submodule.{u1, u2} R M _inst_1 _inst_3 _inst_4) M (Submodule.setLike.{u1, u2} R M _inst_1 _inst_3 _inst_4)))) (Finset.inf.{u2, u3} (Submodule.{u1, u2} R M _inst_1 _inst_3 _inst_4) ι (Lattice.toSemilatticeInf.{u2} (Submodule.{u1, u2} R M _inst_1 _inst_3 _inst_4) (CompleteLattice.toLattice.{u2} (Submodule.{u1, u2} R M _inst_1 _inst_3 _inst_4) (Submodule.completeLattice.{u1, u2} R M _inst_1 _inst_3 _inst_4))) (Submodule.orderTop.{u1, u2} R M _inst_1 _inst_3 _inst_4) s p)) (Set.interᵢ.{u2, succ u3} M ι (fun (i : ι) => Set.interᵢ.{u2, 0} M (Membership.Mem.{u3, u3} ι (Finset.{u3} ι) (Finset.hasMem.{u3} ι) i s) (fun (H : Membership.Mem.{u3, u3} ι (Finset.{u3} ι) (Finset.hasMem.{u3} ι) i s) => (fun (a : Type.{u2}) (b : Type.{u2}) [self : HasLiftT.{succ u2, succ u2} a b] => self.0) (Submodule.{u1, u2} R M _inst_1 _inst_3 _inst_4) (Set.{u2} M) (HasLiftT.mk.{succ u2, succ u2} (Submodule.{u1, u2} R M _inst_1 _inst_3 _inst_4) (Set.{u2} M) (CoeTCₓ.coe.{succ u2, succ u2} (Submodule.{u1, u2} R M _inst_1 _inst_3 _inst_4) (Set.{u2} M) (SetLike.Set.hasCoeT.{u2, u2} (Submodule.{u1, u2} R M _inst_1 _inst_3 _inst_4) M (Submodule.setLike.{u1, u2} R M _inst_1 _inst_3 _inst_4)))) (p i))))
 but is expected to have type
-  forall {R : Type.{u2}} {M : Type.{u1}} [_inst_1 : Semiring.{u2} R] [_inst_3 : AddCommMonoid.{u1} M] [_inst_4 : Module.{u2, u1} R M _inst_1 _inst_3] {ι : Type.{u3}} (s : Finset.{u3} ι) (p : ι -> (Submodule.{u2, u1} R M _inst_1 _inst_3 _inst_4)), Eq.{succ u1} (Set.{u1} M) (SetLike.coe.{u1, u1} (Submodule.{u2, u1} R M _inst_1 _inst_3 _inst_4) M (Submodule.instSetLikeSubmodule.{u2, u1} R M _inst_1 _inst_3 _inst_4) (Finset.inf.{u1, u3} (Submodule.{u2, u1} R M _inst_1 _inst_3 _inst_4) ι (Lattice.toSemilatticeInf.{u1} (Submodule.{u2, u1} R M _inst_1 _inst_3 _inst_4) (CompleteLattice.toLattice.{u1} (Submodule.{u2, u1} R M _inst_1 _inst_3 _inst_4) (Submodule.completeLattice.{u2, u1} R M _inst_1 _inst_3 _inst_4))) (Submodule.instOrderTopSubmoduleToLEToPreorderInstPartialOrderInstSetLikeSubmodule.{u2, u1} R M _inst_1 _inst_3 _inst_4) s p)) (Set.interᵢ.{u1, succ u3} M ι (fun (i : ι) => Set.interᵢ.{u1, 0} M (Membership.mem.{u3, u3} ι (Finset.{u3} ι) (Finset.instMembershipFinset.{u3} ι) i s) (fun (H : Membership.mem.{u3, u3} ι (Finset.{u3} ι) (Finset.instMembershipFinset.{u3} ι) i s) => SetLike.coe.{u1, u1} (Submodule.{u2, u1} R M _inst_1 _inst_3 _inst_4) M (Submodule.instSetLikeSubmodule.{u2, u1} R M _inst_1 _inst_3 _inst_4) (p i))))
+  forall {R : Type.{u2}} {M : Type.{u1}} [_inst_1 : Semiring.{u2} R] [_inst_3 : AddCommMonoid.{u1} M] [_inst_4 : Module.{u2, u1} R M _inst_1 _inst_3] {ι : Type.{u3}} (s : Finset.{u3} ι) (p : ι -> (Submodule.{u2, u1} R M _inst_1 _inst_3 _inst_4)), Eq.{succ u1} (Set.{u1} M) (SetLike.coe.{u1, u1} (Submodule.{u2, u1} R M _inst_1 _inst_3 _inst_4) M (Submodule.setLike.{u2, u1} R M _inst_1 _inst_3 _inst_4) (Finset.inf.{u1, u3} (Submodule.{u2, u1} R M _inst_1 _inst_3 _inst_4) ι (Lattice.toSemilatticeInf.{u1} (Submodule.{u2, u1} R M _inst_1 _inst_3 _inst_4) (CompleteLattice.toLattice.{u1} (Submodule.{u2, u1} R M _inst_1 _inst_3 _inst_4) (Submodule.completeLattice.{u2, u1} R M _inst_1 _inst_3 _inst_4))) (Submodule.instOrderTopSubmoduleToLEToPreorderInstPartialOrderSetLike.{u2, u1} R M _inst_1 _inst_3 _inst_4) s p)) (Set.interᵢ.{u1, succ u3} M ι (fun (i : ι) => Set.interᵢ.{u1, 0} M (Membership.mem.{u3, u3} ι (Finset.{u3} ι) (Finset.instMembershipFinset.{u3} ι) i s) (fun (H : Membership.mem.{u3, u3} ι (Finset.{u3} ι) (Finset.instMembershipFinset.{u3} ι) i s) => SetLike.coe.{u1, u1} (Submodule.{u2, u1} R M _inst_1 _inst_3 _inst_4) M (Submodule.setLike.{u2, u1} R M _inst_1 _inst_3 _inst_4) (p i))))
 Case conversion may be inaccurate. Consider using '#align submodule.finset_inf_coe Submodule.finset_inf_coeₓ'. -/
 @[simp]
 theorem finset_inf_coe {ι} (s : Finset ι) (p : ι → Submodule R M) :
@@ -433,7 +433,7 @@ theorem finset_inf_coe {ι} (s : Finset ι) (p : ι → Submodule R M) :
 lean 3 declaration is
   forall {R : Type.{u1}} {M : Type.{u2}} [_inst_1 : Semiring.{u1} R] [_inst_3 : AddCommMonoid.{u2} M] [_inst_4 : Module.{u1, u2} R M _inst_1 _inst_3] {ι : Sort.{u3}} (p : ι -> (Submodule.{u1, u2} R M _inst_1 _inst_3 _inst_4)), Eq.{succ u2} (Set.{u2} M) ((fun (a : Type.{u2}) (b : Type.{u2}) [self : HasLiftT.{succ u2, succ u2} a b] => self.0) (Submodule.{u1, u2} R M _inst_1 _inst_3 _inst_4) (Set.{u2} M) (HasLiftT.mk.{succ u2, succ u2} (Submodule.{u1, u2} R M _inst_1 _inst_3 _inst_4) (Set.{u2} M) (CoeTCₓ.coe.{succ u2, succ u2} (Submodule.{u1, u2} R M _inst_1 _inst_3 _inst_4) (Set.{u2} M) (SetLike.Set.hasCoeT.{u2, u2} (Submodule.{u1, u2} R M _inst_1 _inst_3 _inst_4) M (Submodule.setLike.{u1, u2} R M _inst_1 _inst_3 _inst_4)))) (infᵢ.{u2, u3} (Submodule.{u1, u2} R M _inst_1 _inst_3 _inst_4) (Submodule.hasInf.{u1, u2} R M _inst_1 _inst_3 _inst_4) ι (fun (i : ι) => p i))) (Set.interᵢ.{u2, u3} M ι (fun (i : ι) => (fun (a : Type.{u2}) (b : Type.{u2}) [self : HasLiftT.{succ u2, succ u2} a b] => self.0) (Submodule.{u1, u2} R M _inst_1 _inst_3 _inst_4) (Set.{u2} M) (HasLiftT.mk.{succ u2, succ u2} (Submodule.{u1, u2} R M _inst_1 _inst_3 _inst_4) (Set.{u2} M) (CoeTCₓ.coe.{succ u2, succ u2} (Submodule.{u1, u2} R M _inst_1 _inst_3 _inst_4) (Set.{u2} M) (SetLike.Set.hasCoeT.{u2, u2} (Submodule.{u1, u2} R M _inst_1 _inst_3 _inst_4) M (Submodule.setLike.{u1, u2} R M _inst_1 _inst_3 _inst_4)))) (p i)))
 but is expected to have type
-  forall {R : Type.{u2}} {M : Type.{u1}} [_inst_1 : Semiring.{u2} R] [_inst_3 : AddCommMonoid.{u1} M] [_inst_4 : Module.{u2, u1} R M _inst_1 _inst_3] {ι : Sort.{u3}} (p : ι -> (Submodule.{u2, u1} R M _inst_1 _inst_3 _inst_4)), Eq.{succ u1} (Set.{u1} M) (SetLike.coe.{u1, u1} (Submodule.{u2, u1} R M _inst_1 _inst_3 _inst_4) M (Submodule.instSetLikeSubmodule.{u2, u1} R M _inst_1 _inst_3 _inst_4) (infᵢ.{u1, u3} (Submodule.{u2, u1} R M _inst_1 _inst_3 _inst_4) (Submodule.instInfSetSubmodule.{u2, u1} R M _inst_1 _inst_3 _inst_4) ι (fun (i : ι) => p i))) (Set.interᵢ.{u1, u3} M ι (fun (i : ι) => SetLike.coe.{u1, u1} (Submodule.{u2, u1} R M _inst_1 _inst_3 _inst_4) M (Submodule.instSetLikeSubmodule.{u2, u1} R M _inst_1 _inst_3 _inst_4) (p i)))
+  forall {R : Type.{u2}} {M : Type.{u1}} [_inst_1 : Semiring.{u2} R] [_inst_3 : AddCommMonoid.{u1} M] [_inst_4 : Module.{u2, u1} R M _inst_1 _inst_3] {ι : Sort.{u3}} (p : ι -> (Submodule.{u2, u1} R M _inst_1 _inst_3 _inst_4)), Eq.{succ u1} (Set.{u1} M) (SetLike.coe.{u1, u1} (Submodule.{u2, u1} R M _inst_1 _inst_3 _inst_4) M (Submodule.setLike.{u2, u1} R M _inst_1 _inst_3 _inst_4) (infᵢ.{u1, u3} (Submodule.{u2, u1} R M _inst_1 _inst_3 _inst_4) (Submodule.instInfSetSubmodule.{u2, u1} R M _inst_1 _inst_3 _inst_4) ι (fun (i : ι) => p i))) (Set.interᵢ.{u1, u3} M ι (fun (i : ι) => SetLike.coe.{u1, u1} (Submodule.{u2, u1} R M _inst_1 _inst_3 _inst_4) M (Submodule.setLike.{u2, u1} R M _inst_1 _inst_3 _inst_4) (p i)))
 Case conversion may be inaccurate. Consider using '#align submodule.infi_coe Submodule.infᵢ_coeₓ'. -/
 @[simp]
 theorem infᵢ_coe {ι} (p : ι → Submodule R M) : (↑(⨅ i, p i) : Set M) = ⋂ i, ↑(p i) := by
@@ -444,7 +444,7 @@ theorem infᵢ_coe {ι} (p : ι → Submodule R M) : (↑(⨅ i, p i) : Set M) =
 lean 3 declaration is
   forall {R : Type.{u1}} {M : Type.{u2}} [_inst_1 : Semiring.{u1} R] [_inst_3 : AddCommMonoid.{u2} M] [_inst_4 : Module.{u1, u2} R M _inst_1 _inst_3] {S : Set.{u2} (Submodule.{u1, u2} R M _inst_1 _inst_3 _inst_4)} {x : M}, Iff (Membership.Mem.{u2, u2} M (Submodule.{u1, u2} R M _inst_1 _inst_3 _inst_4) (SetLike.hasMem.{u2, u2} (Submodule.{u1, u2} R M _inst_1 _inst_3 _inst_4) M (Submodule.setLike.{u1, u2} R M _inst_1 _inst_3 _inst_4)) x (InfSet.infₛ.{u2} (Submodule.{u1, u2} R M _inst_1 _inst_3 _inst_4) (Submodule.hasInf.{u1, u2} R M _inst_1 _inst_3 _inst_4) S)) (forall (p : Submodule.{u1, u2} R M _inst_1 _inst_3 _inst_4), (Membership.Mem.{u2, u2} (Submodule.{u1, u2} R M _inst_1 _inst_3 _inst_4) (Set.{u2} (Submodule.{u1, u2} R M _inst_1 _inst_3 _inst_4)) (Set.hasMem.{u2} (Submodule.{u1, u2} R M _inst_1 _inst_3 _inst_4)) p S) -> (Membership.Mem.{u2, u2} M (Submodule.{u1, u2} R M _inst_1 _inst_3 _inst_4) (SetLike.hasMem.{u2, u2} (Submodule.{u1, u2} R M _inst_1 _inst_3 _inst_4) M (Submodule.setLike.{u1, u2} R M _inst_1 _inst_3 _inst_4)) x p))
 but is expected to have type
-  forall {R : Type.{u1}} {M : Type.{u2}} [_inst_1 : Semiring.{u1} R] [_inst_3 : AddCommMonoid.{u2} M] [_inst_4 : Module.{u1, u2} R M _inst_1 _inst_3] {S : Set.{u2} (Submodule.{u1, u2} R M _inst_1 _inst_3 _inst_4)} {x : M}, Iff (Membership.mem.{u2, u2} M (Submodule.{u1, u2} R M _inst_1 _inst_3 _inst_4) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} R M _inst_1 _inst_3 _inst_4) M (Submodule.instSetLikeSubmodule.{u1, u2} R M _inst_1 _inst_3 _inst_4)) x (InfSet.infₛ.{u2} (Submodule.{u1, u2} R M _inst_1 _inst_3 _inst_4) (Submodule.instInfSetSubmodule.{u1, u2} R M _inst_1 _inst_3 _inst_4) S)) (forall (p : Submodule.{u1, u2} R M _inst_1 _inst_3 _inst_4), (Membership.mem.{u2, u2} (Submodule.{u1, u2} R M _inst_1 _inst_3 _inst_4) (Set.{u2} (Submodule.{u1, u2} R M _inst_1 _inst_3 _inst_4)) (Set.instMembershipSet.{u2} (Submodule.{u1, u2} R M _inst_1 _inst_3 _inst_4)) p S) -> (Membership.mem.{u2, u2} M (Submodule.{u1, u2} R M _inst_1 _inst_3 _inst_4) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} R M _inst_1 _inst_3 _inst_4) M (Submodule.instSetLikeSubmodule.{u1, u2} R M _inst_1 _inst_3 _inst_4)) x p))
+  forall {R : Type.{u1}} {M : Type.{u2}} [_inst_1 : Semiring.{u1} R] [_inst_3 : AddCommMonoid.{u2} M] [_inst_4 : Module.{u1, u2} R M _inst_1 _inst_3] {S : Set.{u2} (Submodule.{u1, u2} R M _inst_1 _inst_3 _inst_4)} {x : M}, Iff (Membership.mem.{u2, u2} M (Submodule.{u1, u2} R M _inst_1 _inst_3 _inst_4) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} R M _inst_1 _inst_3 _inst_4) M (Submodule.setLike.{u1, u2} R M _inst_1 _inst_3 _inst_4)) x (InfSet.infₛ.{u2} (Submodule.{u1, u2} R M _inst_1 _inst_3 _inst_4) (Submodule.instInfSetSubmodule.{u1, u2} R M _inst_1 _inst_3 _inst_4) S)) (forall (p : Submodule.{u1, u2} R M _inst_1 _inst_3 _inst_4), (Membership.mem.{u2, u2} (Submodule.{u1, u2} R M _inst_1 _inst_3 _inst_4) (Set.{u2} (Submodule.{u1, u2} R M _inst_1 _inst_3 _inst_4)) (Set.instMembershipSet.{u2} (Submodule.{u1, u2} R M _inst_1 _inst_3 _inst_4)) p S) -> (Membership.mem.{u2, u2} M (Submodule.{u1, u2} R M _inst_1 _inst_3 _inst_4) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} R M _inst_1 _inst_3 _inst_4) M (Submodule.setLike.{u1, u2} R M _inst_1 _inst_3 _inst_4)) x p))
 Case conversion may be inaccurate. Consider using '#align submodule.mem_Inf Submodule.mem_infₛₓ'. -/
 @[simp]
 theorem mem_infₛ {S : Set (Submodule R M)} {x : M} : x ∈ infₛ S ↔ ∀ p ∈ S, x ∈ p :=
@@ -455,7 +455,7 @@ theorem mem_infₛ {S : Set (Submodule R M)} {x : M} : x ∈ infₛ S ↔ ∀ p
 lean 3 declaration is
   forall {R : Type.{u1}} {M : Type.{u2}} [_inst_1 : Semiring.{u1} R] [_inst_3 : AddCommMonoid.{u2} M] [_inst_4 : Module.{u1, u2} R M _inst_1 _inst_3] {ι : Sort.{u3}} (p : ι -> (Submodule.{u1, u2} R M _inst_1 _inst_3 _inst_4)) {x : M}, Iff (Membership.Mem.{u2, u2} M (Submodule.{u1, u2} R M _inst_1 _inst_3 _inst_4) (SetLike.hasMem.{u2, u2} (Submodule.{u1, u2} R M _inst_1 _inst_3 _inst_4) M (Submodule.setLike.{u1, u2} R M _inst_1 _inst_3 _inst_4)) x (infᵢ.{u2, u3} (Submodule.{u1, u2} R M _inst_1 _inst_3 _inst_4) (Submodule.hasInf.{u1, u2} R M _inst_1 _inst_3 _inst_4) ι (fun (i : ι) => p i))) (forall (i : ι), Membership.Mem.{u2, u2} M (Submodule.{u1, u2} R M _inst_1 _inst_3 _inst_4) (SetLike.hasMem.{u2, u2} (Submodule.{u1, u2} R M _inst_1 _inst_3 _inst_4) M (Submodule.setLike.{u1, u2} R M _inst_1 _inst_3 _inst_4)) x (p i))
 but is expected to have type
-  forall {R : Type.{u2}} {M : Type.{u1}} [_inst_1 : Semiring.{u2} R] [_inst_3 : AddCommMonoid.{u1} M] [_inst_4 : Module.{u2, u1} R M _inst_1 _inst_3] {ι : Sort.{u3}} (p : ι -> (Submodule.{u2, u1} R M _inst_1 _inst_3 _inst_4)) {x : M}, Iff (Membership.mem.{u1, u1} M (Submodule.{u2, u1} R M _inst_1 _inst_3 _inst_4) (SetLike.instMembership.{u1, u1} (Submodule.{u2, u1} R M _inst_1 _inst_3 _inst_4) M (Submodule.instSetLikeSubmodule.{u2, u1} R M _inst_1 _inst_3 _inst_4)) x (infᵢ.{u1, u3} (Submodule.{u2, u1} R M _inst_1 _inst_3 _inst_4) (Submodule.instInfSetSubmodule.{u2, u1} R M _inst_1 _inst_3 _inst_4) ι (fun (i : ι) => p i))) (forall (i : ι), Membership.mem.{u1, u1} M (Submodule.{u2, u1} R M _inst_1 _inst_3 _inst_4) (SetLike.instMembership.{u1, u1} (Submodule.{u2, u1} R M _inst_1 _inst_3 _inst_4) M (Submodule.instSetLikeSubmodule.{u2, u1} R M _inst_1 _inst_3 _inst_4)) x (p i))
+  forall {R : Type.{u2}} {M : Type.{u1}} [_inst_1 : Semiring.{u2} R] [_inst_3 : AddCommMonoid.{u1} M] [_inst_4 : Module.{u2, u1} R M _inst_1 _inst_3] {ι : Sort.{u3}} (p : ι -> (Submodule.{u2, u1} R M _inst_1 _inst_3 _inst_4)) {x : M}, Iff (Membership.mem.{u1, u1} M (Submodule.{u2, u1} R M _inst_1 _inst_3 _inst_4) (SetLike.instMembership.{u1, u1} (Submodule.{u2, u1} R M _inst_1 _inst_3 _inst_4) M (Submodule.setLike.{u2, u1} R M _inst_1 _inst_3 _inst_4)) x (infᵢ.{u1, u3} (Submodule.{u2, u1} R M _inst_1 _inst_3 _inst_4) (Submodule.instInfSetSubmodule.{u2, u1} R M _inst_1 _inst_3 _inst_4) ι (fun (i : ι) => p i))) (forall (i : ι), Membership.mem.{u1, u1} M (Submodule.{u2, u1} R M _inst_1 _inst_3 _inst_4) (SetLike.instMembership.{u1, u1} (Submodule.{u2, u1} R M _inst_1 _inst_3 _inst_4) M (Submodule.setLike.{u2, u1} R M _inst_1 _inst_3 _inst_4)) x (p i))
 Case conversion may be inaccurate. Consider using '#align submodule.mem_infi Submodule.mem_infᵢₓ'. -/
 @[simp]
 theorem mem_infᵢ {ι} (p : ι → Submodule R M) {x} : (x ∈ ⨅ i, p i) ↔ ∀ i, x ∈ p i := by
@@ -466,7 +466,7 @@ theorem mem_infᵢ {ι} (p : ι → Submodule R M) {x} : (x ∈ ⨅ i, p i) ↔
 lean 3 declaration is
   forall {R : Type.{u1}} {M : Type.{u2}} [_inst_1 : Semiring.{u1} R] [_inst_3 : AddCommMonoid.{u2} M] [_inst_4 : Module.{u1, u2} R M _inst_1 _inst_3] {ι : Type.{u3}} {s : Finset.{u3} ι} {p : ι -> (Submodule.{u1, u2} R M _inst_1 _inst_3 _inst_4)} {x : M}, Iff (Membership.Mem.{u2, u2} M (Submodule.{u1, u2} R M _inst_1 _inst_3 _inst_4) (SetLike.hasMem.{u2, u2} (Submodule.{u1, u2} R M _inst_1 _inst_3 _inst_4) M (Submodule.setLike.{u1, u2} R M _inst_1 _inst_3 _inst_4)) x (Finset.inf.{u2, u3} (Submodule.{u1, u2} R M _inst_1 _inst_3 _inst_4) ι (Lattice.toSemilatticeInf.{u2} (Submodule.{u1, u2} R M _inst_1 _inst_3 _inst_4) (CompleteLattice.toLattice.{u2} (Submodule.{u1, u2} R M _inst_1 _inst_3 _inst_4) (Submodule.completeLattice.{u1, u2} R M _inst_1 _inst_3 _inst_4))) (Submodule.orderTop.{u1, u2} R M _inst_1 _inst_3 _inst_4) s p)) (forall (i : ι), (Membership.Mem.{u3, u3} ι (Finset.{u3} ι) (Finset.hasMem.{u3} ι) i s) -> (Membership.Mem.{u2, u2} M (Submodule.{u1, u2} R M _inst_1 _inst_3 _inst_4) (SetLike.hasMem.{u2, u2} (Submodule.{u1, u2} R M _inst_1 _inst_3 _inst_4) M (Submodule.setLike.{u1, u2} R M _inst_1 _inst_3 _inst_4)) x (p i)))
 but is expected to have type
-  forall {R : Type.{u2}} {M : Type.{u1}} [_inst_1 : Semiring.{u2} R] [_inst_3 : AddCommMonoid.{u1} M] [_inst_4 : Module.{u2, u1} R M _inst_1 _inst_3] {ι : Type.{u3}} {s : Finset.{u3} ι} {p : ι -> (Submodule.{u2, u1} R M _inst_1 _inst_3 _inst_4)} {x : M}, Iff (Membership.mem.{u1, u1} M (Submodule.{u2, u1} R M _inst_1 _inst_3 _inst_4) (SetLike.instMembership.{u1, u1} (Submodule.{u2, u1} R M _inst_1 _inst_3 _inst_4) M (Submodule.instSetLikeSubmodule.{u2, u1} R M _inst_1 _inst_3 _inst_4)) x (Finset.inf.{u1, u3} (Submodule.{u2, u1} R M _inst_1 _inst_3 _inst_4) ι (Lattice.toSemilatticeInf.{u1} (Submodule.{u2, u1} R M _inst_1 _inst_3 _inst_4) (CompleteLattice.toLattice.{u1} (Submodule.{u2, u1} R M _inst_1 _inst_3 _inst_4) (Submodule.completeLattice.{u2, u1} R M _inst_1 _inst_3 _inst_4))) (Submodule.instOrderTopSubmoduleToLEToPreorderInstPartialOrderInstSetLikeSubmodule.{u2, u1} R M _inst_1 _inst_3 _inst_4) s p)) (forall (i : ι), (Membership.mem.{u3, u3} ι (Finset.{u3} ι) (Finset.instMembershipFinset.{u3} ι) i s) -> (Membership.mem.{u1, u1} M (Submodule.{u2, u1} R M _inst_1 _inst_3 _inst_4) (SetLike.instMembership.{u1, u1} (Submodule.{u2, u1} R M _inst_1 _inst_3 _inst_4) M (Submodule.instSetLikeSubmodule.{u2, u1} R M _inst_1 _inst_3 _inst_4)) x (p i)))
+  forall {R : Type.{u2}} {M : Type.{u1}} [_inst_1 : Semiring.{u2} R] [_inst_3 : AddCommMonoid.{u1} M] [_inst_4 : Module.{u2, u1} R M _inst_1 _inst_3] {ι : Type.{u3}} {s : Finset.{u3} ι} {p : ι -> (Submodule.{u2, u1} R M _inst_1 _inst_3 _inst_4)} {x : M}, Iff (Membership.mem.{u1, u1} M (Submodule.{u2, u1} R M _inst_1 _inst_3 _inst_4) (SetLike.instMembership.{u1, u1} (Submodule.{u2, u1} R M _inst_1 _inst_3 _inst_4) M (Submodule.setLike.{u2, u1} R M _inst_1 _inst_3 _inst_4)) x (Finset.inf.{u1, u3} (Submodule.{u2, u1} R M _inst_1 _inst_3 _inst_4) ι (Lattice.toSemilatticeInf.{u1} (Submodule.{u2, u1} R M _inst_1 _inst_3 _inst_4) (CompleteLattice.toLattice.{u1} (Submodule.{u2, u1} R M _inst_1 _inst_3 _inst_4) (Submodule.completeLattice.{u2, u1} R M _inst_1 _inst_3 _inst_4))) (Submodule.instOrderTopSubmoduleToLEToPreorderInstPartialOrderSetLike.{u2, u1} R M _inst_1 _inst_3 _inst_4) s p)) (forall (i : ι), (Membership.mem.{u3, u3} ι (Finset.{u3} ι) (Finset.instMembershipFinset.{u3} ι) i s) -> (Membership.mem.{u1, u1} M (Submodule.{u2, u1} R M _inst_1 _inst_3 _inst_4) (SetLike.instMembership.{u1, u1} (Submodule.{u2, u1} R M _inst_1 _inst_3 _inst_4) M (Submodule.setLike.{u2, u1} R M _inst_1 _inst_3 _inst_4)) x (p i)))
 Case conversion may be inaccurate. Consider using '#align submodule.mem_finset_inf Submodule.mem_finset_infₓ'. -/
 @[simp]
 theorem mem_finset_inf {ι} {s : Finset ι} {p : ι → Submodule R M} {x : M} :
@@ -478,7 +478,7 @@ theorem mem_finset_inf {ι} {s : Finset ι} {p : ι → Submodule R M} {x : M} :
 lean 3 declaration is
   forall {R : Type.{u1}} {M : Type.{u2}} [_inst_1 : Semiring.{u1} R] [_inst_3 : AddCommMonoid.{u2} M] [_inst_4 : Module.{u1, u2} R M _inst_1 _inst_3] {S : Submodule.{u1, u2} R M _inst_1 _inst_3 _inst_4} {T : Submodule.{u1, u2} R M _inst_1 _inst_3 _inst_4} {x : M}, (Membership.Mem.{u2, u2} M (Submodule.{u1, u2} R M _inst_1 _inst_3 _inst_4) (SetLike.hasMem.{u2, u2} (Submodule.{u1, u2} R M _inst_1 _inst_3 _inst_4) M (Submodule.setLike.{u1, u2} R M _inst_1 _inst_3 _inst_4)) x S) -> (Membership.Mem.{u2, u2} M (Submodule.{u1, u2} R M _inst_1 _inst_3 _inst_4) (SetLike.hasMem.{u2, u2} (Submodule.{u1, u2} R M _inst_1 _inst_3 _inst_4) M (Submodule.setLike.{u1, u2} R M _inst_1 _inst_3 _inst_4)) x (Sup.sup.{u2} (Submodule.{u1, u2} R M _inst_1 _inst_3 _inst_4) (SemilatticeSup.toHasSup.{u2} (Submodule.{u1, u2} R M _inst_1 _inst_3 _inst_4) (Lattice.toSemilatticeSup.{u2} (Submodule.{u1, u2} R M _inst_1 _inst_3 _inst_4) (CompleteLattice.toLattice.{u2} (Submodule.{u1, u2} R M _inst_1 _inst_3 _inst_4) (Submodule.completeLattice.{u1, u2} R M _inst_1 _inst_3 _inst_4)))) S T))
 but is expected to have type
-  forall {R : Type.{u2}} {M : Type.{u1}} [_inst_1 : Semiring.{u2} R] [_inst_3 : AddCommMonoid.{u1} M] [_inst_4 : Module.{u2, u1} R M _inst_1 _inst_3] {S : Submodule.{u2, u1} R M _inst_1 _inst_3 _inst_4} {T : Submodule.{u2, u1} R M _inst_1 _inst_3 _inst_4} {x : M}, (Membership.mem.{u1, u1} M (Submodule.{u2, u1} R M _inst_1 _inst_3 _inst_4) (SetLike.instMembership.{u1, u1} (Submodule.{u2, u1} R M _inst_1 _inst_3 _inst_4) M (Submodule.instSetLikeSubmodule.{u2, u1} R M _inst_1 _inst_3 _inst_4)) x S) -> (Membership.mem.{u1, u1} M (Submodule.{u2, u1} R M _inst_1 _inst_3 _inst_4) (SetLike.instMembership.{u1, u1} (Submodule.{u2, u1} R M _inst_1 _inst_3 _inst_4) M (Submodule.instSetLikeSubmodule.{u2, u1} R M _inst_1 _inst_3 _inst_4)) x (Sup.sup.{u1} (Submodule.{u2, u1} R M _inst_1 _inst_3 _inst_4) (SemilatticeSup.toSup.{u1} (Submodule.{u2, u1} R M _inst_1 _inst_3 _inst_4) (Lattice.toSemilatticeSup.{u1} (Submodule.{u2, u1} R M _inst_1 _inst_3 _inst_4) (CompleteLattice.toLattice.{u1} (Submodule.{u2, u1} R M _inst_1 _inst_3 _inst_4) (Submodule.completeLattice.{u2, u1} R M _inst_1 _inst_3 _inst_4)))) S T))
+  forall {R : Type.{u2}} {M : Type.{u1}} [_inst_1 : Semiring.{u2} R] [_inst_3 : AddCommMonoid.{u1} M] [_inst_4 : Module.{u2, u1} R M _inst_1 _inst_3] {S : Submodule.{u2, u1} R M _inst_1 _inst_3 _inst_4} {T : Submodule.{u2, u1} R M _inst_1 _inst_3 _inst_4} {x : M}, (Membership.mem.{u1, u1} M (Submodule.{u2, u1} R M _inst_1 _inst_3 _inst_4) (SetLike.instMembership.{u1, u1} (Submodule.{u2, u1} R M _inst_1 _inst_3 _inst_4) M (Submodule.setLike.{u2, u1} R M _inst_1 _inst_3 _inst_4)) x S) -> (Membership.mem.{u1, u1} M (Submodule.{u2, u1} R M _inst_1 _inst_3 _inst_4) (SetLike.instMembership.{u1, u1} (Submodule.{u2, u1} R M _inst_1 _inst_3 _inst_4) M (Submodule.setLike.{u2, u1} R M _inst_1 _inst_3 _inst_4)) x (Sup.sup.{u1} (Submodule.{u2, u1} R M _inst_1 _inst_3 _inst_4) (SemilatticeSup.toSup.{u1} (Submodule.{u2, u1} R M _inst_1 _inst_3 _inst_4) (Lattice.toSemilatticeSup.{u1} (Submodule.{u2, u1} R M _inst_1 _inst_3 _inst_4) (CompleteLattice.toLattice.{u1} (Submodule.{u2, u1} R M _inst_1 _inst_3 _inst_4) (Submodule.completeLattice.{u2, u1} R M _inst_1 _inst_3 _inst_4)))) S T))
 Case conversion may be inaccurate. Consider using '#align submodule.mem_sup_left Submodule.mem_sup_leftₓ'. -/
 theorem mem_sup_left {S T : Submodule R M} : ∀ {x : M}, x ∈ S → x ∈ S ⊔ T :=
   show S ≤ S ⊔ T from le_sup_left
@@ -488,7 +488,7 @@ theorem mem_sup_left {S T : Submodule R M} : ∀ {x : M}, x ∈ S → x ∈ S 
 lean 3 declaration is
   forall {R : Type.{u1}} {M : Type.{u2}} [_inst_1 : Semiring.{u1} R] [_inst_3 : AddCommMonoid.{u2} M] [_inst_4 : Module.{u1, u2} R M _inst_1 _inst_3] {S : Submodule.{u1, u2} R M _inst_1 _inst_3 _inst_4} {T : Submodule.{u1, u2} R M _inst_1 _inst_3 _inst_4} {x : M}, (Membership.Mem.{u2, u2} M (Submodule.{u1, u2} R M _inst_1 _inst_3 _inst_4) (SetLike.hasMem.{u2, u2} (Submodule.{u1, u2} R M _inst_1 _inst_3 _inst_4) M (Submodule.setLike.{u1, u2} R M _inst_1 _inst_3 _inst_4)) x T) -> (Membership.Mem.{u2, u2} M (Submodule.{u1, u2} R M _inst_1 _inst_3 _inst_4) (SetLike.hasMem.{u2, u2} (Submodule.{u1, u2} R M _inst_1 _inst_3 _inst_4) M (Submodule.setLike.{u1, u2} R M _inst_1 _inst_3 _inst_4)) x (Sup.sup.{u2} (Submodule.{u1, u2} R M _inst_1 _inst_3 _inst_4) (SemilatticeSup.toHasSup.{u2} (Submodule.{u1, u2} R M _inst_1 _inst_3 _inst_4) (Lattice.toSemilatticeSup.{u2} (Submodule.{u1, u2} R M _inst_1 _inst_3 _inst_4) (CompleteLattice.toLattice.{u2} (Submodule.{u1, u2} R M _inst_1 _inst_3 _inst_4) (Submodule.completeLattice.{u1, u2} R M _inst_1 _inst_3 _inst_4)))) S T))
 but is expected to have type
-  forall {R : Type.{u2}} {M : Type.{u1}} [_inst_1 : Semiring.{u2} R] [_inst_3 : AddCommMonoid.{u1} M] [_inst_4 : Module.{u2, u1} R M _inst_1 _inst_3] {S : Submodule.{u2, u1} R M _inst_1 _inst_3 _inst_4} {T : Submodule.{u2, u1} R M _inst_1 _inst_3 _inst_4} {x : M}, (Membership.mem.{u1, u1} M (Submodule.{u2, u1} R M _inst_1 _inst_3 _inst_4) (SetLike.instMembership.{u1, u1} (Submodule.{u2, u1} R M _inst_1 _inst_3 _inst_4) M (Submodule.instSetLikeSubmodule.{u2, u1} R M _inst_1 _inst_3 _inst_4)) x T) -> (Membership.mem.{u1, u1} M (Submodule.{u2, u1} R M _inst_1 _inst_3 _inst_4) (SetLike.instMembership.{u1, u1} (Submodule.{u2, u1} R M _inst_1 _inst_3 _inst_4) M (Submodule.instSetLikeSubmodule.{u2, u1} R M _inst_1 _inst_3 _inst_4)) x (Sup.sup.{u1} (Submodule.{u2, u1} R M _inst_1 _inst_3 _inst_4) (SemilatticeSup.toSup.{u1} (Submodule.{u2, u1} R M _inst_1 _inst_3 _inst_4) (Lattice.toSemilatticeSup.{u1} (Submodule.{u2, u1} R M _inst_1 _inst_3 _inst_4) (CompleteLattice.toLattice.{u1} (Submodule.{u2, u1} R M _inst_1 _inst_3 _inst_4) (Submodule.completeLattice.{u2, u1} R M _inst_1 _inst_3 _inst_4)))) S T))
+  forall {R : Type.{u2}} {M : Type.{u1}} [_inst_1 : Semiring.{u2} R] [_inst_3 : AddCommMonoid.{u1} M] [_inst_4 : Module.{u2, u1} R M _inst_1 _inst_3] {S : Submodule.{u2, u1} R M _inst_1 _inst_3 _inst_4} {T : Submodule.{u2, u1} R M _inst_1 _inst_3 _inst_4} {x : M}, (Membership.mem.{u1, u1} M (Submodule.{u2, u1} R M _inst_1 _inst_3 _inst_4) (SetLike.instMembership.{u1, u1} (Submodule.{u2, u1} R M _inst_1 _inst_3 _inst_4) M (Submodule.setLike.{u2, u1} R M _inst_1 _inst_3 _inst_4)) x T) -> (Membership.mem.{u1, u1} M (Submodule.{u2, u1} R M _inst_1 _inst_3 _inst_4) (SetLike.instMembership.{u1, u1} (Submodule.{u2, u1} R M _inst_1 _inst_3 _inst_4) M (Submodule.setLike.{u2, u1} R M _inst_1 _inst_3 _inst_4)) x (Sup.sup.{u1} (Submodule.{u2, u1} R M _inst_1 _inst_3 _inst_4) (SemilatticeSup.toSup.{u1} (Submodule.{u2, u1} R M _inst_1 _inst_3 _inst_4) (Lattice.toSemilatticeSup.{u1} (Submodule.{u2, u1} R M _inst_1 _inst_3 _inst_4) (CompleteLattice.toLattice.{u1} (Submodule.{u2, u1} R M _inst_1 _inst_3 _inst_4) (Submodule.completeLattice.{u2, u1} R M _inst_1 _inst_3 _inst_4)))) S T))
 Case conversion may be inaccurate. Consider using '#align submodule.mem_sup_right Submodule.mem_sup_rightₓ'. -/
 theorem mem_sup_right {S T : Submodule R M} : ∀ {x : M}, x ∈ T → x ∈ S ⊔ T :=
   show T ≤ S ⊔ T from le_sup_right
@@ -498,7 +498,7 @@ theorem mem_sup_right {S T : Submodule R M} : ∀ {x : M}, x ∈ T → x ∈ S 
 lean 3 declaration is
   forall {R : Type.{u1}} {M : Type.{u2}} [_inst_1 : Semiring.{u1} R] [_inst_3 : AddCommMonoid.{u2} M] [_inst_4 : Module.{u1, u2} R M _inst_1 _inst_3] {S : Submodule.{u1, u2} R M _inst_1 _inst_3 _inst_4} {T : Submodule.{u1, u2} R M _inst_1 _inst_3 _inst_4} {s : M} {t : M}, (Membership.Mem.{u2, u2} M (Submodule.{u1, u2} R M _inst_1 _inst_3 _inst_4) (SetLike.hasMem.{u2, u2} (Submodule.{u1, u2} R M _inst_1 _inst_3 _inst_4) M (Submodule.setLike.{u1, u2} R M _inst_1 _inst_3 _inst_4)) s S) -> (Membership.Mem.{u2, u2} M (Submodule.{u1, u2} R M _inst_1 _inst_3 _inst_4) (SetLike.hasMem.{u2, u2} (Submodule.{u1, u2} R M _inst_1 _inst_3 _inst_4) M (Submodule.setLike.{u1, u2} R M _inst_1 _inst_3 _inst_4)) t T) -> (Membership.Mem.{u2, u2} M (Submodule.{u1, u2} R M _inst_1 _inst_3 _inst_4) (SetLike.hasMem.{u2, u2} (Submodule.{u1, u2} R M _inst_1 _inst_3 _inst_4) M (Submodule.setLike.{u1, u2} R M _inst_1 _inst_3 _inst_4)) (HAdd.hAdd.{u2, u2, u2} M M M (instHAdd.{u2} M (AddZeroClass.toHasAdd.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3)))) s t) (Sup.sup.{u2} (Submodule.{u1, u2} R M _inst_1 _inst_3 _inst_4) (SemilatticeSup.toHasSup.{u2} (Submodule.{u1, u2} R M _inst_1 _inst_3 _inst_4) (Lattice.toSemilatticeSup.{u2} (Submodule.{u1, u2} R M _inst_1 _inst_3 _inst_4) (CompleteLattice.toLattice.{u2} (Submodule.{u1, u2} R M _inst_1 _inst_3 _inst_4) (Submodule.completeLattice.{u1, u2} R M _inst_1 _inst_3 _inst_4)))) S T))
 but is expected to have type
-  forall {R : Type.{u2}} {M : Type.{u1}} [_inst_1 : Semiring.{u2} R] [_inst_3 : AddCommMonoid.{u1} M] [_inst_4 : Module.{u2, u1} R M _inst_1 _inst_3] {S : Submodule.{u2, u1} R M _inst_1 _inst_3 _inst_4} {T : Submodule.{u2, u1} R M _inst_1 _inst_3 _inst_4} {s : M} {t : M}, (Membership.mem.{u1, u1} M (Submodule.{u2, u1} R M _inst_1 _inst_3 _inst_4) (SetLike.instMembership.{u1, u1} (Submodule.{u2, u1} R M _inst_1 _inst_3 _inst_4) M (Submodule.instSetLikeSubmodule.{u2, u1} R M _inst_1 _inst_3 _inst_4)) s S) -> (Membership.mem.{u1, u1} M (Submodule.{u2, u1} R M _inst_1 _inst_3 _inst_4) (SetLike.instMembership.{u1, u1} (Submodule.{u2, u1} R M _inst_1 _inst_3 _inst_4) M (Submodule.instSetLikeSubmodule.{u2, u1} R M _inst_1 _inst_3 _inst_4)) t T) -> (Membership.mem.{u1, u1} M (Submodule.{u2, u1} R M _inst_1 _inst_3 _inst_4) (SetLike.instMembership.{u1, u1} (Submodule.{u2, u1} R M _inst_1 _inst_3 _inst_4) M (Submodule.instSetLikeSubmodule.{u2, u1} R M _inst_1 _inst_3 _inst_4)) (HAdd.hAdd.{u1, u1, u1} M M M (instHAdd.{u1} M (AddZeroClass.toAdd.{u1} M (AddMonoid.toAddZeroClass.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3)))) s t) (Sup.sup.{u1} (Submodule.{u2, u1} R M _inst_1 _inst_3 _inst_4) (SemilatticeSup.toSup.{u1} (Submodule.{u2, u1} R M _inst_1 _inst_3 _inst_4) (Lattice.toSemilatticeSup.{u1} (Submodule.{u2, u1} R M _inst_1 _inst_3 _inst_4) (CompleteLattice.toLattice.{u1} (Submodule.{u2, u1} R M _inst_1 _inst_3 _inst_4) (Submodule.completeLattice.{u2, u1} R M _inst_1 _inst_3 _inst_4)))) S T))
+  forall {R : Type.{u2}} {M : Type.{u1}} [_inst_1 : Semiring.{u2} R] [_inst_3 : AddCommMonoid.{u1} M] [_inst_4 : Module.{u2, u1} R M _inst_1 _inst_3] {S : Submodule.{u2, u1} R M _inst_1 _inst_3 _inst_4} {T : Submodule.{u2, u1} R M _inst_1 _inst_3 _inst_4} {s : M} {t : M}, (Membership.mem.{u1, u1} M (Submodule.{u2, u1} R M _inst_1 _inst_3 _inst_4) (SetLike.instMembership.{u1, u1} (Submodule.{u2, u1} R M _inst_1 _inst_3 _inst_4) M (Submodule.setLike.{u2, u1} R M _inst_1 _inst_3 _inst_4)) s S) -> (Membership.mem.{u1, u1} M (Submodule.{u2, u1} R M _inst_1 _inst_3 _inst_4) (SetLike.instMembership.{u1, u1} (Submodule.{u2, u1} R M _inst_1 _inst_3 _inst_4) M (Submodule.setLike.{u2, u1} R M _inst_1 _inst_3 _inst_4)) t T) -> (Membership.mem.{u1, u1} M (Submodule.{u2, u1} R M _inst_1 _inst_3 _inst_4) (SetLike.instMembership.{u1, u1} (Submodule.{u2, u1} R M _inst_1 _inst_3 _inst_4) M (Submodule.setLike.{u2, u1} R M _inst_1 _inst_3 _inst_4)) (HAdd.hAdd.{u1, u1, u1} M M M (instHAdd.{u1} M (AddZeroClass.toAdd.{u1} M (AddMonoid.toAddZeroClass.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3)))) s t) (Sup.sup.{u1} (Submodule.{u2, u1} R M _inst_1 _inst_3 _inst_4) (SemilatticeSup.toSup.{u1} (Submodule.{u2, u1} R M _inst_1 _inst_3 _inst_4) (Lattice.toSemilatticeSup.{u1} (Submodule.{u2, u1} R M _inst_1 _inst_3 _inst_4) (CompleteLattice.toLattice.{u1} (Submodule.{u2, u1} R M _inst_1 _inst_3 _inst_4) (Submodule.completeLattice.{u2, u1} R M _inst_1 _inst_3 _inst_4)))) S T))
 Case conversion may be inaccurate. Consider using '#align submodule.add_mem_sup Submodule.add_mem_supₓ'. -/
 theorem add_mem_sup {S T : Submodule R M} {s t : M} (hs : s ∈ S) (ht : t ∈ T) : s + t ∈ S ⊔ T :=
   add_mem (mem_sup_left hs) (mem_sup_right ht)
@@ -508,7 +508,7 @@ theorem add_mem_sup {S T : Submodule R M} {s t : M} (hs : s ∈ S) (ht : t ∈ T
 lean 3 declaration is
   forall {R' : Type.{u1}} {M' : Type.{u2}} [_inst_8 : Ring.{u1} R'] [_inst_9 : AddCommGroup.{u2} M'] [_inst_10 : Module.{u1, u2} R' M' (Ring.toSemiring.{u1} R' _inst_8) (AddCommGroup.toAddCommMonoid.{u2} M' _inst_9)] {S : Submodule.{u1, u2} R' M' (Ring.toSemiring.{u1} R' _inst_8) (AddCommGroup.toAddCommMonoid.{u2} M' _inst_9) _inst_10} {T : Submodule.{u1, u2} R' M' (Ring.toSemiring.{u1} R' _inst_8) (AddCommGroup.toAddCommMonoid.{u2} M' _inst_9) _inst_10} {s : M'} {t : M'}, (Membership.Mem.{u2, u2} M' (Submodule.{u1, u2} R' M' (Ring.toSemiring.{u1} R' _inst_8) (AddCommGroup.toAddCommMonoid.{u2} M' _inst_9) _inst_10) (SetLike.hasMem.{u2, u2} (Submodule.{u1, u2} R' M' (Ring.toSemiring.{u1} R' _inst_8) (AddCommGroup.toAddCommMonoid.{u2} M' _inst_9) _inst_10) M' (Submodule.setLike.{u1, u2} R' M' (Ring.toSemiring.{u1} R' _inst_8) (AddCommGroup.toAddCommMonoid.{u2} M' _inst_9) _inst_10)) s S) -> (Membership.Mem.{u2, u2} M' (Submodule.{u1, u2} R' M' (Ring.toSemiring.{u1} R' _inst_8) (AddCommGroup.toAddCommMonoid.{u2} M' _inst_9) _inst_10) (SetLike.hasMem.{u2, u2} (Submodule.{u1, u2} R' M' (Ring.toSemiring.{u1} R' _inst_8) (AddCommGroup.toAddCommMonoid.{u2} M' _inst_9) _inst_10) M' (Submodule.setLike.{u1, u2} R' M' (Ring.toSemiring.{u1} R' _inst_8) (AddCommGroup.toAddCommMonoid.{u2} M' _inst_9) _inst_10)) t T) -> (Membership.Mem.{u2, u2} M' (Submodule.{u1, u2} R' M' (Ring.toSemiring.{u1} R' _inst_8) (AddCommGroup.toAddCommMonoid.{u2} M' _inst_9) _inst_10) (SetLike.hasMem.{u2, u2} (Submodule.{u1, u2} R' M' (Ring.toSemiring.{u1} R' _inst_8) (AddCommGroup.toAddCommMonoid.{u2} M' _inst_9) _inst_10) M' (Submodule.setLike.{u1, u2} R' M' (Ring.toSemiring.{u1} R' _inst_8) (AddCommGroup.toAddCommMonoid.{u2} M' _inst_9) _inst_10)) (HSub.hSub.{u2, u2, u2} M' M' M' (instHSub.{u2} M' (SubNegMonoid.toHasSub.{u2} M' (AddGroup.toSubNegMonoid.{u2} M' (AddCommGroup.toAddGroup.{u2} M' _inst_9)))) s t) (Sup.sup.{u2} (Submodule.{u1, u2} R' M' (Ring.toSemiring.{u1} R' _inst_8) (AddCommGroup.toAddCommMonoid.{u2} M' _inst_9) _inst_10) (SemilatticeSup.toHasSup.{u2} (Submodule.{u1, u2} R' M' (Ring.toSemiring.{u1} R' _inst_8) (AddCommGroup.toAddCommMonoid.{u2} M' _inst_9) _inst_10) (Lattice.toSemilatticeSup.{u2} (Submodule.{u1, u2} R' M' (Ring.toSemiring.{u1} R' _inst_8) (AddCommGroup.toAddCommMonoid.{u2} M' _inst_9) _inst_10) (CompleteLattice.toLattice.{u2} (Submodule.{u1, u2} R' M' (Ring.toSemiring.{u1} R' _inst_8) (AddCommGroup.toAddCommMonoid.{u2} M' _inst_9) _inst_10) (Submodule.completeLattice.{u1, u2} R' M' (Ring.toSemiring.{u1} R' _inst_8) (AddCommGroup.toAddCommMonoid.{u2} M' _inst_9) _inst_10)))) S T))
 but is expected to have type
-  forall {R' : Type.{u2}} {M' : Type.{u1}} [_inst_8 : Ring.{u2} R'] [_inst_9 : AddCommGroup.{u1} M'] [_inst_10 : Module.{u2, u1} R' M' (Ring.toSemiring.{u2} R' _inst_8) (AddCommGroup.toAddCommMonoid.{u1} M' _inst_9)] {S : Submodule.{u2, u1} R' M' (Ring.toSemiring.{u2} R' _inst_8) (AddCommGroup.toAddCommMonoid.{u1} M' _inst_9) _inst_10} {T : Submodule.{u2, u1} R' M' (Ring.toSemiring.{u2} R' _inst_8) (AddCommGroup.toAddCommMonoid.{u1} M' _inst_9) _inst_10} {s : M'} {t : M'}, (Membership.mem.{u1, u1} M' (Submodule.{u2, u1} R' M' (Ring.toSemiring.{u2} R' _inst_8) (AddCommGroup.toAddCommMonoid.{u1} M' _inst_9) _inst_10) (SetLike.instMembership.{u1, u1} (Submodule.{u2, u1} R' M' (Ring.toSemiring.{u2} R' _inst_8) (AddCommGroup.toAddCommMonoid.{u1} M' _inst_9) _inst_10) M' (Submodule.instSetLikeSubmodule.{u2, u1} R' M' (Ring.toSemiring.{u2} R' _inst_8) (AddCommGroup.toAddCommMonoid.{u1} M' _inst_9) _inst_10)) s S) -> (Membership.mem.{u1, u1} M' (Submodule.{u2, u1} R' M' (Ring.toSemiring.{u2} R' _inst_8) (AddCommGroup.toAddCommMonoid.{u1} M' _inst_9) _inst_10) (SetLike.instMembership.{u1, u1} (Submodule.{u2, u1} R' M' (Ring.toSemiring.{u2} R' _inst_8) (AddCommGroup.toAddCommMonoid.{u1} M' _inst_9) _inst_10) M' (Submodule.instSetLikeSubmodule.{u2, u1} R' M' (Ring.toSemiring.{u2} R' _inst_8) (AddCommGroup.toAddCommMonoid.{u1} M' _inst_9) _inst_10)) t T) -> (Membership.mem.{u1, u1} M' (Submodule.{u2, u1} R' M' (Ring.toSemiring.{u2} R' _inst_8) (AddCommGroup.toAddCommMonoid.{u1} M' _inst_9) _inst_10) (SetLike.instMembership.{u1, u1} (Submodule.{u2, u1} R' M' (Ring.toSemiring.{u2} R' _inst_8) (AddCommGroup.toAddCommMonoid.{u1} M' _inst_9) _inst_10) M' (Submodule.instSetLikeSubmodule.{u2, u1} R' M' (Ring.toSemiring.{u2} R' _inst_8) (AddCommGroup.toAddCommMonoid.{u1} M' _inst_9) _inst_10)) (HSub.hSub.{u1, u1, u1} M' M' M' (instHSub.{u1} M' (SubNegMonoid.toSub.{u1} M' (AddGroup.toSubNegMonoid.{u1} M' (AddCommGroup.toAddGroup.{u1} M' _inst_9)))) s t) (Sup.sup.{u1} (Submodule.{u2, u1} R' M' (Ring.toSemiring.{u2} R' _inst_8) (AddCommGroup.toAddCommMonoid.{u1} M' _inst_9) _inst_10) (SemilatticeSup.toSup.{u1} (Submodule.{u2, u1} R' M' (Ring.toSemiring.{u2} R' _inst_8) (AddCommGroup.toAddCommMonoid.{u1} M' _inst_9) _inst_10) (Lattice.toSemilatticeSup.{u1} (Submodule.{u2, u1} R' M' (Ring.toSemiring.{u2} R' _inst_8) (AddCommGroup.toAddCommMonoid.{u1} M' _inst_9) _inst_10) (CompleteLattice.toLattice.{u1} (Submodule.{u2, u1} R' M' (Ring.toSemiring.{u2} R' _inst_8) (AddCommGroup.toAddCommMonoid.{u1} M' _inst_9) _inst_10) (Submodule.completeLattice.{u2, u1} R' M' (Ring.toSemiring.{u2} R' _inst_8) (AddCommGroup.toAddCommMonoid.{u1} M' _inst_9) _inst_10)))) S T))
+  forall {R' : Type.{u2}} {M' : Type.{u1}} [_inst_8 : Ring.{u2} R'] [_inst_9 : AddCommGroup.{u1} M'] [_inst_10 : Module.{u2, u1} R' M' (Ring.toSemiring.{u2} R' _inst_8) (AddCommGroup.toAddCommMonoid.{u1} M' _inst_9)] {S : Submodule.{u2, u1} R' M' (Ring.toSemiring.{u2} R' _inst_8) (AddCommGroup.toAddCommMonoid.{u1} M' _inst_9) _inst_10} {T : Submodule.{u2, u1} R' M' (Ring.toSemiring.{u2} R' _inst_8) (AddCommGroup.toAddCommMonoid.{u1} M' _inst_9) _inst_10} {s : M'} {t : M'}, (Membership.mem.{u1, u1} M' (Submodule.{u2, u1} R' M' (Ring.toSemiring.{u2} R' _inst_8) (AddCommGroup.toAddCommMonoid.{u1} M' _inst_9) _inst_10) (SetLike.instMembership.{u1, u1} (Submodule.{u2, u1} R' M' (Ring.toSemiring.{u2} R' _inst_8) (AddCommGroup.toAddCommMonoid.{u1} M' _inst_9) _inst_10) M' (Submodule.setLike.{u2, u1} R' M' (Ring.toSemiring.{u2} R' _inst_8) (AddCommGroup.toAddCommMonoid.{u1} M' _inst_9) _inst_10)) s S) -> (Membership.mem.{u1, u1} M' (Submodule.{u2, u1} R' M' (Ring.toSemiring.{u2} R' _inst_8) (AddCommGroup.toAddCommMonoid.{u1} M' _inst_9) _inst_10) (SetLike.instMembership.{u1, u1} (Submodule.{u2, u1} R' M' (Ring.toSemiring.{u2} R' _inst_8) (AddCommGroup.toAddCommMonoid.{u1} M' _inst_9) _inst_10) M' (Submodule.setLike.{u2, u1} R' M' (Ring.toSemiring.{u2} R' _inst_8) (AddCommGroup.toAddCommMonoid.{u1} M' _inst_9) _inst_10)) t T) -> (Membership.mem.{u1, u1} M' (Submodule.{u2, u1} R' M' (Ring.toSemiring.{u2} R' _inst_8) (AddCommGroup.toAddCommMonoid.{u1} M' _inst_9) _inst_10) (SetLike.instMembership.{u1, u1} (Submodule.{u2, u1} R' M' (Ring.toSemiring.{u2} R' _inst_8) (AddCommGroup.toAddCommMonoid.{u1} M' _inst_9) _inst_10) M' (Submodule.setLike.{u2, u1} R' M' (Ring.toSemiring.{u2} R' _inst_8) (AddCommGroup.toAddCommMonoid.{u1} M' _inst_9) _inst_10)) (HSub.hSub.{u1, u1, u1} M' M' M' (instHSub.{u1} M' (SubNegMonoid.toSub.{u1} M' (AddGroup.toSubNegMonoid.{u1} M' (AddCommGroup.toAddGroup.{u1} M' _inst_9)))) s t) (Sup.sup.{u1} (Submodule.{u2, u1} R' M' (Ring.toSemiring.{u2} R' _inst_8) (AddCommGroup.toAddCommMonoid.{u1} M' _inst_9) _inst_10) (SemilatticeSup.toSup.{u1} (Submodule.{u2, u1} R' M' (Ring.toSemiring.{u2} R' _inst_8) (AddCommGroup.toAddCommMonoid.{u1} M' _inst_9) _inst_10) (Lattice.toSemilatticeSup.{u1} (Submodule.{u2, u1} R' M' (Ring.toSemiring.{u2} R' _inst_8) (AddCommGroup.toAddCommMonoid.{u1} M' _inst_9) _inst_10) (CompleteLattice.toLattice.{u1} (Submodule.{u2, u1} R' M' (Ring.toSemiring.{u2} R' _inst_8) (AddCommGroup.toAddCommMonoid.{u1} M' _inst_9) _inst_10) (Submodule.completeLattice.{u2, u1} R' M' (Ring.toSemiring.{u2} R' _inst_8) (AddCommGroup.toAddCommMonoid.{u1} M' _inst_9) _inst_10)))) S T))
 Case conversion may be inaccurate. Consider using '#align submodule.sub_mem_sup Submodule.sub_mem_supₓ'. -/
 theorem sub_mem_sup {R' M' : Type _} [Ring R'] [AddCommGroup M'] [Module R' M']
     {S T : Submodule R' M'} {s t : M'} (hs : s ∈ S) (ht : t ∈ T) : s - t ∈ S ⊔ T :=
@@ -521,7 +521,7 @@ theorem sub_mem_sup {R' M' : Type _} [Ring R'] [AddCommGroup M'] [Module R' M']
 lean 3 declaration is
   forall {R : Type.{u1}} {M : Type.{u2}} [_inst_1 : Semiring.{u1} R] [_inst_3 : AddCommMonoid.{u2} M] [_inst_4 : Module.{u1, u2} R M _inst_1 _inst_3] {ι : Sort.{u3}} {b : M} {p : ι -> (Submodule.{u1, u2} R M _inst_1 _inst_3 _inst_4)} (i : ι), (Membership.Mem.{u2, u2} M (Submodule.{u1, u2} R M _inst_1 _inst_3 _inst_4) (SetLike.hasMem.{u2, u2} (Submodule.{u1, u2} R M _inst_1 _inst_3 _inst_4) M (Submodule.setLike.{u1, u2} R M _inst_1 _inst_3 _inst_4)) b (p i)) -> (Membership.Mem.{u2, u2} M (Submodule.{u1, u2} R M _inst_1 _inst_3 _inst_4) (SetLike.hasMem.{u2, u2} (Submodule.{u1, u2} R M _inst_1 _inst_3 _inst_4) M (Submodule.setLike.{u1, u2} R M _inst_1 _inst_3 _inst_4)) b (supᵢ.{u2, u3} (Submodule.{u1, u2} R M _inst_1 _inst_3 _inst_4) (CompleteSemilatticeSup.toHasSup.{u2} (Submodule.{u1, u2} R M _inst_1 _inst_3 _inst_4) (CompleteLattice.toCompleteSemilatticeSup.{u2} (Submodule.{u1, u2} R M _inst_1 _inst_3 _inst_4) (Submodule.completeLattice.{u1, u2} R M _inst_1 _inst_3 _inst_4))) ι (fun (i : ι) => p i)))
 but is expected to have type
-  forall {R : Type.{u2}} {M : Type.{u1}} [_inst_1 : Semiring.{u2} R] [_inst_3 : AddCommMonoid.{u1} M] [_inst_4 : Module.{u2, u1} R M _inst_1 _inst_3] {ι : Sort.{u3}} {b : M} {p : ι -> (Submodule.{u2, u1} R M _inst_1 _inst_3 _inst_4)} (i : ι), (Membership.mem.{u1, u1} M (Submodule.{u2, u1} R M _inst_1 _inst_3 _inst_4) (SetLike.instMembership.{u1, u1} (Submodule.{u2, u1} R M _inst_1 _inst_3 _inst_4) M (Submodule.instSetLikeSubmodule.{u2, u1} R M _inst_1 _inst_3 _inst_4)) b (p i)) -> (Membership.mem.{u1, u1} M (Submodule.{u2, u1} R M _inst_1 _inst_3 _inst_4) (SetLike.instMembership.{u1, u1} (Submodule.{u2, u1} R M _inst_1 _inst_3 _inst_4) M (Submodule.instSetLikeSubmodule.{u2, u1} R M _inst_1 _inst_3 _inst_4)) b (supᵢ.{u1, u3} (Submodule.{u2, u1} R M _inst_1 _inst_3 _inst_4) (CompleteLattice.toSupSet.{u1} (Submodule.{u2, u1} R M _inst_1 _inst_3 _inst_4) (Submodule.completeLattice.{u2, u1} R M _inst_1 _inst_3 _inst_4)) ι (fun (i : ι) => p i)))
+  forall {R : Type.{u2}} {M : Type.{u1}} [_inst_1 : Semiring.{u2} R] [_inst_3 : AddCommMonoid.{u1} M] [_inst_4 : Module.{u2, u1} R M _inst_1 _inst_3] {ι : Sort.{u3}} {b : M} {p : ι -> (Submodule.{u2, u1} R M _inst_1 _inst_3 _inst_4)} (i : ι), (Membership.mem.{u1, u1} M (Submodule.{u2, u1} R M _inst_1 _inst_3 _inst_4) (SetLike.instMembership.{u1, u1} (Submodule.{u2, u1} R M _inst_1 _inst_3 _inst_4) M (Submodule.setLike.{u2, u1} R M _inst_1 _inst_3 _inst_4)) b (p i)) -> (Membership.mem.{u1, u1} M (Submodule.{u2, u1} R M _inst_1 _inst_3 _inst_4) (SetLike.instMembership.{u1, u1} (Submodule.{u2, u1} R M _inst_1 _inst_3 _inst_4) M (Submodule.setLike.{u2, u1} R M _inst_1 _inst_3 _inst_4)) b (supᵢ.{u1, u3} (Submodule.{u2, u1} R M _inst_1 _inst_3 _inst_4) (CompleteLattice.toSupSet.{u1} (Submodule.{u2, u1} R M _inst_1 _inst_3 _inst_4) (Submodule.completeLattice.{u2, u1} R M _inst_1 _inst_3 _inst_4)) ι (fun (i : ι) => p i)))
 Case conversion may be inaccurate. Consider using '#align submodule.mem_supr_of_mem Submodule.mem_supᵢ_of_memₓ'. -/
 theorem mem_supᵢ_of_mem {ι : Sort _} {b : M} {p : ι → Submodule R M} (i : ι) (h : b ∈ p i) :
     b ∈ ⨆ i, p i :=
@@ -535,7 +535,7 @@ open BigOperators
 lean 3 declaration is
   forall {R : Type.{u1}} {M : Type.{u2}} [_inst_1 : Semiring.{u1} R] [_inst_3 : AddCommMonoid.{u2} M] [_inst_4 : Module.{u1, u2} R M _inst_1 _inst_3] {ι : Type.{u3}} [_inst_8 : Fintype.{u3} ι] {f : ι -> M} {p : ι -> (Submodule.{u1, u2} R M _inst_1 _inst_3 _inst_4)}, (forall (i : ι), Membership.Mem.{u2, u2} M (Submodule.{u1, u2} R M _inst_1 _inst_3 _inst_4) (SetLike.hasMem.{u2, u2} (Submodule.{u1, u2} R M _inst_1 _inst_3 _inst_4) M (Submodule.setLike.{u1, u2} R M _inst_1 _inst_3 _inst_4)) (f i) (p i)) -> (Membership.Mem.{u2, u2} M (Submodule.{u1, u2} R M _inst_1 _inst_3 _inst_4) (SetLike.hasMem.{u2, u2} (Submodule.{u1, u2} R M _inst_1 _inst_3 _inst_4) M (Submodule.setLike.{u1, u2} R M _inst_1 _inst_3 _inst_4)) (Finset.sum.{u2, u3} M ι _inst_3 (Finset.univ.{u3} ι _inst_8) (fun (i : ι) => f i)) (supᵢ.{u2, succ u3} (Submodule.{u1, u2} R M _inst_1 _inst_3 _inst_4) (CompleteSemilatticeSup.toHasSup.{u2} (Submodule.{u1, u2} R M _inst_1 _inst_3 _inst_4) (CompleteLattice.toCompleteSemilatticeSup.{u2} (Submodule.{u1, u2} R M _inst_1 _inst_3 _inst_4) (Submodule.completeLattice.{u1, u2} R M _inst_1 _inst_3 _inst_4))) ι (fun (i : ι) => p i)))
 but is expected to have type
-  forall {R : Type.{u2}} {M : Type.{u1}} [_inst_1 : Semiring.{u2} R] [_inst_3 : AddCommMonoid.{u1} M] [_inst_4 : Module.{u2, u1} R M _inst_1 _inst_3] {ι : Type.{u3}} [_inst_8 : Fintype.{u3} ι] {f : ι -> M} {p : ι -> (Submodule.{u2, u1} R M _inst_1 _inst_3 _inst_4)}, (forall (i : ι), Membership.mem.{u1, u1} M (Submodule.{u2, u1} R M _inst_1 _inst_3 _inst_4) (SetLike.instMembership.{u1, u1} (Submodule.{u2, u1} R M _inst_1 _inst_3 _inst_4) M (Submodule.instSetLikeSubmodule.{u2, u1} R M _inst_1 _inst_3 _inst_4)) (f i) (p i)) -> (Membership.mem.{u1, u1} M (Submodule.{u2, u1} R M _inst_1 _inst_3 _inst_4) (SetLike.instMembership.{u1, u1} (Submodule.{u2, u1} R M _inst_1 _inst_3 _inst_4) M (Submodule.instSetLikeSubmodule.{u2, u1} R M _inst_1 _inst_3 _inst_4)) (Finset.sum.{u1, u3} M ι _inst_3 (Finset.univ.{u3} ι _inst_8) (fun (i : ι) => f i)) (supᵢ.{u1, succ u3} (Submodule.{u2, u1} R M _inst_1 _inst_3 _inst_4) (CompleteLattice.toSupSet.{u1} (Submodule.{u2, u1} R M _inst_1 _inst_3 _inst_4) (Submodule.completeLattice.{u2, u1} R M _inst_1 _inst_3 _inst_4)) ι (fun (i : ι) => p i)))
+  forall {R : Type.{u2}} {M : Type.{u1}} [_inst_1 : Semiring.{u2} R] [_inst_3 : AddCommMonoid.{u1} M] [_inst_4 : Module.{u2, u1} R M _inst_1 _inst_3] {ι : Type.{u3}} [_inst_8 : Fintype.{u3} ι] {f : ι -> M} {p : ι -> (Submodule.{u2, u1} R M _inst_1 _inst_3 _inst_4)}, (forall (i : ι), Membership.mem.{u1, u1} M (Submodule.{u2, u1} R M _inst_1 _inst_3 _inst_4) (SetLike.instMembership.{u1, u1} (Submodule.{u2, u1} R M _inst_1 _inst_3 _inst_4) M (Submodule.setLike.{u2, u1} R M _inst_1 _inst_3 _inst_4)) (f i) (p i)) -> (Membership.mem.{u1, u1} M (Submodule.{u2, u1} R M _inst_1 _inst_3 _inst_4) (SetLike.instMembership.{u1, u1} (Submodule.{u2, u1} R M _inst_1 _inst_3 _inst_4) M (Submodule.setLike.{u2, u1} R M _inst_1 _inst_3 _inst_4)) (Finset.sum.{u1, u3} M ι _inst_3 (Finset.univ.{u3} ι _inst_8) (fun (i : ι) => f i)) (supᵢ.{u1, succ u3} (Submodule.{u2, u1} R M _inst_1 _inst_3 _inst_4) (CompleteLattice.toSupSet.{u1} (Submodule.{u2, u1} R M _inst_1 _inst_3 _inst_4) (Submodule.completeLattice.{u2, u1} R M _inst_1 _inst_3 _inst_4)) ι (fun (i : ι) => p i)))
 Case conversion may be inaccurate. Consider using '#align submodule.sum_mem_supr Submodule.sum_mem_supᵢₓ'. -/
 theorem sum_mem_supᵢ {ι : Type _} [Fintype ι] {f : ι → M} {p : ι → Submodule R M}
     (h : ∀ i, f i ∈ p i) : (∑ i, f i) ∈ ⨆ i, p i :=
@@ -546,7 +546,7 @@ theorem sum_mem_supᵢ {ι : Type _} [Fintype ι] {f : ι → M} {p : ι → Sub
 lean 3 declaration is
   forall {R : Type.{u1}} {M : Type.{u2}} [_inst_1 : Semiring.{u1} R] [_inst_3 : AddCommMonoid.{u2} M] [_inst_4 : Module.{u1, u2} R M _inst_1 _inst_3] {ι : Type.{u3}} {s : Finset.{u3} ι} {f : ι -> M} {p : ι -> (Submodule.{u1, u2} R M _inst_1 _inst_3 _inst_4)}, (forall (i : ι), (Membership.Mem.{u3, u3} ι (Finset.{u3} ι) (Finset.hasMem.{u3} ι) i s) -> (Membership.Mem.{u2, u2} M (Submodule.{u1, u2} R M _inst_1 _inst_3 _inst_4) (SetLike.hasMem.{u2, u2} (Submodule.{u1, u2} R M _inst_1 _inst_3 _inst_4) M (Submodule.setLike.{u1, u2} R M _inst_1 _inst_3 _inst_4)) (f i) (p i))) -> (Membership.Mem.{u2, u2} M (Submodule.{u1, u2} R M _inst_1 _inst_3 _inst_4) (SetLike.hasMem.{u2, u2} (Submodule.{u1, u2} R M _inst_1 _inst_3 _inst_4) M (Submodule.setLike.{u1, u2} R M _inst_1 _inst_3 _inst_4)) (Finset.sum.{u2, u3} M ι _inst_3 s (fun (i : ι) => f i)) (supᵢ.{u2, succ u3} (Submodule.{u1, u2} R M _inst_1 _inst_3 _inst_4) (CompleteSemilatticeSup.toHasSup.{u2} (Submodule.{u1, u2} R M _inst_1 _inst_3 _inst_4) (CompleteLattice.toCompleteSemilatticeSup.{u2} (Submodule.{u1, u2} R M _inst_1 _inst_3 _inst_4) (Submodule.completeLattice.{u1, u2} R M _inst_1 _inst_3 _inst_4))) ι (fun (i : ι) => supᵢ.{u2, 0} (Submodule.{u1, u2} R M _inst_1 _inst_3 _inst_4) (CompleteSemilatticeSup.toHasSup.{u2} (Submodule.{u1, u2} R M _inst_1 _inst_3 _inst_4) (CompleteLattice.toCompleteSemilatticeSup.{u2} (Submodule.{u1, u2} R M _inst_1 _inst_3 _inst_4) (Submodule.completeLattice.{u1, u2} R M _inst_1 _inst_3 _inst_4))) (Membership.Mem.{u3, u3} ι (Finset.{u3} ι) (Finset.hasMem.{u3} ι) i s) (fun (H : Membership.Mem.{u3, u3} ι (Finset.{u3} ι) (Finset.hasMem.{u3} ι) i s) => p i))))
 but is expected to have type
-  forall {R : Type.{u2}} {M : Type.{u1}} [_inst_1 : Semiring.{u2} R] [_inst_3 : AddCommMonoid.{u1} M] [_inst_4 : Module.{u2, u1} R M _inst_1 _inst_3] {ι : Type.{u3}} {s : Finset.{u3} ι} {f : ι -> M} {p : ι -> (Submodule.{u2, u1} R M _inst_1 _inst_3 _inst_4)}, (forall (i : ι), (Membership.mem.{u3, u3} ι (Finset.{u3} ι) (Finset.instMembershipFinset.{u3} ι) i s) -> (Membership.mem.{u1, u1} M (Submodule.{u2, u1} R M _inst_1 _inst_3 _inst_4) (SetLike.instMembership.{u1, u1} (Submodule.{u2, u1} R M _inst_1 _inst_3 _inst_4) M (Submodule.instSetLikeSubmodule.{u2, u1} R M _inst_1 _inst_3 _inst_4)) (f i) (p i))) -> (Membership.mem.{u1, u1} M (Submodule.{u2, u1} R M _inst_1 _inst_3 _inst_4) (SetLike.instMembership.{u1, u1} (Submodule.{u2, u1} R M _inst_1 _inst_3 _inst_4) M (Submodule.instSetLikeSubmodule.{u2, u1} R M _inst_1 _inst_3 _inst_4)) (Finset.sum.{u1, u3} M ι _inst_3 s (fun (i : ι) => f i)) (supᵢ.{u1, succ u3} (Submodule.{u2, u1} R M _inst_1 _inst_3 _inst_4) (CompleteLattice.toSupSet.{u1} (Submodule.{u2, u1} R M _inst_1 _inst_3 _inst_4) (Submodule.completeLattice.{u2, u1} R M _inst_1 _inst_3 _inst_4)) ι (fun (i : ι) => supᵢ.{u1, 0} (Submodule.{u2, u1} R M _inst_1 _inst_3 _inst_4) (CompleteLattice.toSupSet.{u1} (Submodule.{u2, u1} R M _inst_1 _inst_3 _inst_4) (Submodule.completeLattice.{u2, u1} R M _inst_1 _inst_3 _inst_4)) (Membership.mem.{u3, u3} ι (Finset.{u3} ι) (Finset.instMembershipFinset.{u3} ι) i s) (fun (H : Membership.mem.{u3, u3} ι (Finset.{u3} ι) (Finset.instMembershipFinset.{u3} ι) i s) => p i))))
+  forall {R : Type.{u2}} {M : Type.{u1}} [_inst_1 : Semiring.{u2} R] [_inst_3 : AddCommMonoid.{u1} M] [_inst_4 : Module.{u2, u1} R M _inst_1 _inst_3] {ι : Type.{u3}} {s : Finset.{u3} ι} {f : ι -> M} {p : ι -> (Submodule.{u2, u1} R M _inst_1 _inst_3 _inst_4)}, (forall (i : ι), (Membership.mem.{u3, u3} ι (Finset.{u3} ι) (Finset.instMembershipFinset.{u3} ι) i s) -> (Membership.mem.{u1, u1} M (Submodule.{u2, u1} R M _inst_1 _inst_3 _inst_4) (SetLike.instMembership.{u1, u1} (Submodule.{u2, u1} R M _inst_1 _inst_3 _inst_4) M (Submodule.setLike.{u2, u1} R M _inst_1 _inst_3 _inst_4)) (f i) (p i))) -> (Membership.mem.{u1, u1} M (Submodule.{u2, u1} R M _inst_1 _inst_3 _inst_4) (SetLike.instMembership.{u1, u1} (Submodule.{u2, u1} R M _inst_1 _inst_3 _inst_4) M (Submodule.setLike.{u2, u1} R M _inst_1 _inst_3 _inst_4)) (Finset.sum.{u1, u3} M ι _inst_3 s (fun (i : ι) => f i)) (supᵢ.{u1, succ u3} (Submodule.{u2, u1} R M _inst_1 _inst_3 _inst_4) (CompleteLattice.toSupSet.{u1} (Submodule.{u2, u1} R M _inst_1 _inst_3 _inst_4) (Submodule.completeLattice.{u2, u1} R M _inst_1 _inst_3 _inst_4)) ι (fun (i : ι) => supᵢ.{u1, 0} (Submodule.{u2, u1} R M _inst_1 _inst_3 _inst_4) (CompleteLattice.toSupSet.{u1} (Submodule.{u2, u1} R M _inst_1 _inst_3 _inst_4) (Submodule.completeLattice.{u2, u1} R M _inst_1 _inst_3 _inst_4)) (Membership.mem.{u3, u3} ι (Finset.{u3} ι) (Finset.instMembershipFinset.{u3} ι) i s) (fun (H : Membership.mem.{u3, u3} ι (Finset.{u3} ι) (Finset.instMembershipFinset.{u3} ι) i s) => p i))))
 Case conversion may be inaccurate. Consider using '#align submodule.sum_mem_bsupr Submodule.sum_mem_bsupᵢₓ'. -/
 theorem sum_mem_bsupᵢ {ι : Type _} {s : Finset ι} {f : ι → M} {p : ι → Submodule R M}
     (h : ∀ i ∈ s, f i ∈ p i) : (∑ i in s, f i) ∈ ⨆ i ∈ s, p i :=
@@ -560,7 +560,7 @@ theorem sum_mem_bsupᵢ {ι : Type _} {s : Finset ι} {f : ι → M} {p : ι →
 lean 3 declaration is
   forall {R : Type.{u1}} {M : Type.{u2}} [_inst_1 : Semiring.{u1} R] [_inst_3 : AddCommMonoid.{u2} M] [_inst_4 : Module.{u1, u2} R M _inst_1 _inst_3] {S : Set.{u2} (Submodule.{u1, u2} R M _inst_1 _inst_3 _inst_4)} {s : Submodule.{u1, u2} R M _inst_1 _inst_3 _inst_4}, (Membership.Mem.{u2, u2} (Submodule.{u1, u2} R M _inst_1 _inst_3 _inst_4) (Set.{u2} (Submodule.{u1, u2} R M _inst_1 _inst_3 _inst_4)) (Set.hasMem.{u2} (Submodule.{u1, u2} R M _inst_1 _inst_3 _inst_4)) s S) -> (forall {x : M}, (Membership.Mem.{u2, u2} M (Submodule.{u1, u2} R M _inst_1 _inst_3 _inst_4) (SetLike.hasMem.{u2, u2} (Submodule.{u1, u2} R M _inst_1 _inst_3 _inst_4) M (Submodule.setLike.{u1, u2} R M _inst_1 _inst_3 _inst_4)) x s) -> (Membership.Mem.{u2, u2} M (Submodule.{u1, u2} R M _inst_1 _inst_3 _inst_4) (SetLike.hasMem.{u2, u2} (Submodule.{u1, u2} R M _inst_1 _inst_3 _inst_4) M (Submodule.setLike.{u1, u2} R M _inst_1 _inst_3 _inst_4)) x (SupSet.supₛ.{u2} (Submodule.{u1, u2} R M _inst_1 _inst_3 _inst_4) (CompleteSemilatticeSup.toHasSup.{u2} (Submodule.{u1, u2} R M _inst_1 _inst_3 _inst_4) (CompleteLattice.toCompleteSemilatticeSup.{u2} (Submodule.{u1, u2} R M _inst_1 _inst_3 _inst_4) (Submodule.completeLattice.{u1, u2} R M _inst_1 _inst_3 _inst_4))) S)))
 but is expected to have type
-  forall {R : Type.{u1}} {M : Type.{u2}} [_inst_1 : Semiring.{u1} R] [_inst_3 : AddCommMonoid.{u2} M] [_inst_4 : Module.{u1, u2} R M _inst_1 _inst_3] {S : Set.{u2} (Submodule.{u1, u2} R M _inst_1 _inst_3 _inst_4)} {s : Submodule.{u1, u2} R M _inst_1 _inst_3 _inst_4}, (Membership.mem.{u2, u2} (Submodule.{u1, u2} R M _inst_1 _inst_3 _inst_4) (Set.{u2} (Submodule.{u1, u2} R M _inst_1 _inst_3 _inst_4)) (Set.instMembershipSet.{u2} (Submodule.{u1, u2} R M _inst_1 _inst_3 _inst_4)) s S) -> (forall {x : M}, (Membership.mem.{u2, u2} M (Submodule.{u1, u2} R M _inst_1 _inst_3 _inst_4) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} R M _inst_1 _inst_3 _inst_4) M (Submodule.instSetLikeSubmodule.{u1, u2} R M _inst_1 _inst_3 _inst_4)) x s) -> (Membership.mem.{u2, u2} M (Submodule.{u1, u2} R M _inst_1 _inst_3 _inst_4) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} R M _inst_1 _inst_3 _inst_4) M (Submodule.instSetLikeSubmodule.{u1, u2} R M _inst_1 _inst_3 _inst_4)) x (SupSet.supₛ.{u2} (Submodule.{u1, u2} R M _inst_1 _inst_3 _inst_4) (CompleteLattice.toSupSet.{u2} (Submodule.{u1, u2} R M _inst_1 _inst_3 _inst_4) (Submodule.completeLattice.{u1, u2} R M _inst_1 _inst_3 _inst_4)) S)))
+  forall {R : Type.{u1}} {M : Type.{u2}} [_inst_1 : Semiring.{u1} R] [_inst_3 : AddCommMonoid.{u2} M] [_inst_4 : Module.{u1, u2} R M _inst_1 _inst_3] {S : Set.{u2} (Submodule.{u1, u2} R M _inst_1 _inst_3 _inst_4)} {s : Submodule.{u1, u2} R M _inst_1 _inst_3 _inst_4}, (Membership.mem.{u2, u2} (Submodule.{u1, u2} R M _inst_1 _inst_3 _inst_4) (Set.{u2} (Submodule.{u1, u2} R M _inst_1 _inst_3 _inst_4)) (Set.instMembershipSet.{u2} (Submodule.{u1, u2} R M _inst_1 _inst_3 _inst_4)) s S) -> (forall {x : M}, (Membership.mem.{u2, u2} M (Submodule.{u1, u2} R M _inst_1 _inst_3 _inst_4) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} R M _inst_1 _inst_3 _inst_4) M (Submodule.setLike.{u1, u2} R M _inst_1 _inst_3 _inst_4)) x s) -> (Membership.mem.{u2, u2} M (Submodule.{u1, u2} R M _inst_1 _inst_3 _inst_4) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} R M _inst_1 _inst_3 _inst_4) M (Submodule.setLike.{u1, u2} R M _inst_1 _inst_3 _inst_4)) x (SupSet.supₛ.{u2} (Submodule.{u1, u2} R M _inst_1 _inst_3 _inst_4) (CompleteLattice.toSupSet.{u2} (Submodule.{u1, u2} R M _inst_1 _inst_3 _inst_4) (Submodule.completeLattice.{u1, u2} R M _inst_1 _inst_3 _inst_4)) S)))
 Case conversion may be inaccurate. Consider using '#align submodule.mem_Sup_of_mem Submodule.mem_supₛ_of_memₓ'. -/
 theorem mem_supₛ_of_mem {S : Set (Submodule R M)} {s : Submodule R M} (hs : s ∈ S) :
     ∀ {x : M}, x ∈ s → x ∈ supₛ S :=
@@ -571,7 +571,7 @@ theorem mem_supₛ_of_mem {S : Set (Submodule R M)} {s : Submodule R M} (hs : s
 lean 3 declaration is
   forall {R : Type.{u1}} {M : Type.{u2}} [_inst_1 : Semiring.{u1} R] [_inst_3 : AddCommMonoid.{u2} M] [_inst_4 : Module.{u1, u2} R M _inst_1 _inst_3] {p : Submodule.{u1, u2} R M _inst_1 _inst_3 _inst_4} {p' : Submodule.{u1, u2} R M _inst_1 _inst_3 _inst_4}, Iff (Disjoint.{u2} (Submodule.{u1, u2} R M _inst_1 _inst_3 _inst_4) (CompleteSemilatticeInf.toPartialOrder.{u2} (Submodule.{u1, u2} R M _inst_1 _inst_3 _inst_4) (CompleteLattice.toCompleteSemilatticeInf.{u2} (Submodule.{u1, u2} R M _inst_1 _inst_3 _inst_4) (Submodule.completeLattice.{u1, u2} R M _inst_1 _inst_3 _inst_4))) (Submodule.orderBot.{u1, u2} R M _inst_1 _inst_3 _inst_4) p p') (forall (x : M), (Membership.Mem.{u2, u2} M (Submodule.{u1, u2} R M _inst_1 _inst_3 _inst_4) (SetLike.hasMem.{u2, u2} (Submodule.{u1, u2} R M _inst_1 _inst_3 _inst_4) M (Submodule.setLike.{u1, u2} R M _inst_1 _inst_3 _inst_4)) x p) -> (Membership.Mem.{u2, u2} M (Submodule.{u1, u2} R M _inst_1 _inst_3 _inst_4) (SetLike.hasMem.{u2, u2} (Submodule.{u1, u2} R M _inst_1 _inst_3 _inst_4) M (Submodule.setLike.{u1, u2} R M _inst_1 _inst_3 _inst_4)) x p') -> (Eq.{succ u2} M x (OfNat.ofNat.{u2} M 0 (OfNat.mk.{u2} M 0 (Zero.zero.{u2} M (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3))))))))
 but is expected to have type
-  forall {R : Type.{u2}} {M : Type.{u1}} [_inst_1 : Semiring.{u2} R] [_inst_3 : AddCommMonoid.{u1} M] [_inst_4 : Module.{u2, u1} R M _inst_1 _inst_3] {p : Submodule.{u2, u1} R M _inst_1 _inst_3 _inst_4} {p' : Submodule.{u2, u1} R M _inst_1 _inst_3 _inst_4}, Iff (Disjoint.{u1} (Submodule.{u2, u1} R M _inst_1 _inst_3 _inst_4) (CompleteSemilatticeInf.toPartialOrder.{u1} (Submodule.{u2, u1} R M _inst_1 _inst_3 _inst_4) (CompleteLattice.toCompleteSemilatticeInf.{u1} (Submodule.{u2, u1} R M _inst_1 _inst_3 _inst_4) (Submodule.completeLattice.{u2, u1} R M _inst_1 _inst_3 _inst_4))) (Submodule.instOrderBotSubmoduleToLEToPreorderInstPartialOrderInstSetLikeSubmodule.{u2, u1} R M _inst_1 _inst_3 _inst_4) p p') (forall (x : M), (Membership.mem.{u1, u1} M (Submodule.{u2, u1} R M _inst_1 _inst_3 _inst_4) (SetLike.instMembership.{u1, u1} (Submodule.{u2, u1} R M _inst_1 _inst_3 _inst_4) M (Submodule.instSetLikeSubmodule.{u2, u1} R M _inst_1 _inst_3 _inst_4)) x p) -> (Membership.mem.{u1, u1} M (Submodule.{u2, u1} R M _inst_1 _inst_3 _inst_4) (SetLike.instMembership.{u1, u1} (Submodule.{u2, u1} R M _inst_1 _inst_3 _inst_4) M (Submodule.instSetLikeSubmodule.{u2, u1} R M _inst_1 _inst_3 _inst_4)) x p') -> (Eq.{succ u1} M x (OfNat.ofNat.{u1} M 0 (Zero.toOfNat0.{u1} M (AddMonoid.toZero.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3))))))
+  forall {R : Type.{u2}} {M : Type.{u1}} [_inst_1 : Semiring.{u2} R] [_inst_3 : AddCommMonoid.{u1} M] [_inst_4 : Module.{u2, u1} R M _inst_1 _inst_3] {p : Submodule.{u2, u1} R M _inst_1 _inst_3 _inst_4} {p' : Submodule.{u2, u1} R M _inst_1 _inst_3 _inst_4}, Iff (Disjoint.{u1} (Submodule.{u2, u1} R M _inst_1 _inst_3 _inst_4) (CompleteSemilatticeInf.toPartialOrder.{u1} (Submodule.{u2, u1} R M _inst_1 _inst_3 _inst_4) (CompleteLattice.toCompleteSemilatticeInf.{u1} (Submodule.{u2, u1} R M _inst_1 _inst_3 _inst_4) (Submodule.completeLattice.{u2, u1} R M _inst_1 _inst_3 _inst_4))) (Submodule.instOrderBotSubmoduleToLEToPreorderInstPartialOrderSetLike.{u2, u1} R M _inst_1 _inst_3 _inst_4) p p') (forall (x : M), (Membership.mem.{u1, u1} M (Submodule.{u2, u1} R M _inst_1 _inst_3 _inst_4) (SetLike.instMembership.{u1, u1} (Submodule.{u2, u1} R M _inst_1 _inst_3 _inst_4) M (Submodule.setLike.{u2, u1} R M _inst_1 _inst_3 _inst_4)) x p) -> (Membership.mem.{u1, u1} M (Submodule.{u2, u1} R M _inst_1 _inst_3 _inst_4) (SetLike.instMembership.{u1, u1} (Submodule.{u2, u1} R M _inst_1 _inst_3 _inst_4) M (Submodule.setLike.{u2, u1} R M _inst_1 _inst_3 _inst_4)) x p') -> (Eq.{succ u1} M x (OfNat.ofNat.{u1} M 0 (Zero.toOfNat0.{u1} M (AddMonoid.toZero.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3))))))
 Case conversion may be inaccurate. Consider using '#align submodule.disjoint_def Submodule.disjoint_defₓ'. -/
 theorem disjoint_def {p p' : Submodule R M} : Disjoint p p' ↔ ∀ x ∈ p, x ∈ p' → x = (0 : M) :=
   disjoint_iff_inf_le.trans <| show (∀ x, x ∈ p ∧ x ∈ p' → x ∈ ({0} : Set M)) ↔ _ by simp
@@ -581,7 +581,7 @@ theorem disjoint_def {p p' : Submodule R M} : Disjoint p p' ↔ ∀ x ∈ p, x 
 lean 3 declaration is
   forall {R : Type.{u1}} {M : Type.{u2}} [_inst_1 : Semiring.{u1} R] [_inst_3 : AddCommMonoid.{u2} M] [_inst_4 : Module.{u1, u2} R M _inst_1 _inst_3] {p : Submodule.{u1, u2} R M _inst_1 _inst_3 _inst_4} {p' : Submodule.{u1, u2} R M _inst_1 _inst_3 _inst_4}, Iff (Disjoint.{u2} (Submodule.{u1, u2} R M _inst_1 _inst_3 _inst_4) (CompleteSemilatticeInf.toPartialOrder.{u2} (Submodule.{u1, u2} R M _inst_1 _inst_3 _inst_4) (CompleteLattice.toCompleteSemilatticeInf.{u2} (Submodule.{u1, u2} R M _inst_1 _inst_3 _inst_4) (Submodule.completeLattice.{u1, u2} R M _inst_1 _inst_3 _inst_4))) (Submodule.orderBot.{u1, u2} R M _inst_1 _inst_3 _inst_4) p p') (forall (x : M), (Membership.Mem.{u2, u2} M (Submodule.{u1, u2} R M _inst_1 _inst_3 _inst_4) (SetLike.hasMem.{u2, u2} (Submodule.{u1, u2} R M _inst_1 _inst_3 _inst_4) M (Submodule.setLike.{u1, u2} R M _inst_1 _inst_3 _inst_4)) x p) -> (forall (y : M), (Membership.Mem.{u2, u2} M (Submodule.{u1, u2} R M _inst_1 _inst_3 _inst_4) (SetLike.hasMem.{u2, u2} (Submodule.{u1, u2} R M _inst_1 _inst_3 _inst_4) M (Submodule.setLike.{u1, u2} R M _inst_1 _inst_3 _inst_4)) y p') -> (Eq.{succ u2} M x y) -> (Eq.{succ u2} M x (OfNat.ofNat.{u2} M 0 (OfNat.mk.{u2} M 0 (Zero.zero.{u2} M (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3)))))))))
 but is expected to have type
-  forall {R : Type.{u2}} {M : Type.{u1}} [_inst_1 : Semiring.{u2} R] [_inst_3 : AddCommMonoid.{u1} M] [_inst_4 : Module.{u2, u1} R M _inst_1 _inst_3] {p : Submodule.{u2, u1} R M _inst_1 _inst_3 _inst_4} {p' : Submodule.{u2, u1} R M _inst_1 _inst_3 _inst_4}, Iff (Disjoint.{u1} (Submodule.{u2, u1} R M _inst_1 _inst_3 _inst_4) (CompleteSemilatticeInf.toPartialOrder.{u1} (Submodule.{u2, u1} R M _inst_1 _inst_3 _inst_4) (CompleteLattice.toCompleteSemilatticeInf.{u1} (Submodule.{u2, u1} R M _inst_1 _inst_3 _inst_4) (Submodule.completeLattice.{u2, u1} R M _inst_1 _inst_3 _inst_4))) (Submodule.instOrderBotSubmoduleToLEToPreorderInstPartialOrderInstSetLikeSubmodule.{u2, u1} R M _inst_1 _inst_3 _inst_4) p p') (forall (x : M), (Membership.mem.{u1, u1} M (Submodule.{u2, u1} R M _inst_1 _inst_3 _inst_4) (SetLike.instMembership.{u1, u1} (Submodule.{u2, u1} R M _inst_1 _inst_3 _inst_4) M (Submodule.instSetLikeSubmodule.{u2, u1} R M _inst_1 _inst_3 _inst_4)) x p) -> (forall (y : M), (Membership.mem.{u1, u1} M (Submodule.{u2, u1} R M _inst_1 _inst_3 _inst_4) (SetLike.instMembership.{u1, u1} (Submodule.{u2, u1} R M _inst_1 _inst_3 _inst_4) M (Submodule.instSetLikeSubmodule.{u2, u1} R M _inst_1 _inst_3 _inst_4)) y p') -> (Eq.{succ u1} M x y) -> (Eq.{succ u1} M x (OfNat.ofNat.{u1} M 0 (Zero.toOfNat0.{u1} M (AddMonoid.toZero.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3)))))))
+  forall {R : Type.{u2}} {M : Type.{u1}} [_inst_1 : Semiring.{u2} R] [_inst_3 : AddCommMonoid.{u1} M] [_inst_4 : Module.{u2, u1} R M _inst_1 _inst_3] {p : Submodule.{u2, u1} R M _inst_1 _inst_3 _inst_4} {p' : Submodule.{u2, u1} R M _inst_1 _inst_3 _inst_4}, Iff (Disjoint.{u1} (Submodule.{u2, u1} R M _inst_1 _inst_3 _inst_4) (CompleteSemilatticeInf.toPartialOrder.{u1} (Submodule.{u2, u1} R M _inst_1 _inst_3 _inst_4) (CompleteLattice.toCompleteSemilatticeInf.{u1} (Submodule.{u2, u1} R M _inst_1 _inst_3 _inst_4) (Submodule.completeLattice.{u2, u1} R M _inst_1 _inst_3 _inst_4))) (Submodule.instOrderBotSubmoduleToLEToPreorderInstPartialOrderSetLike.{u2, u1} R M _inst_1 _inst_3 _inst_4) p p') (forall (x : M), (Membership.mem.{u1, u1} M (Submodule.{u2, u1} R M _inst_1 _inst_3 _inst_4) (SetLike.instMembership.{u1, u1} (Submodule.{u2, u1} R M _inst_1 _inst_3 _inst_4) M (Submodule.setLike.{u2, u1} R M _inst_1 _inst_3 _inst_4)) x p) -> (forall (y : M), (Membership.mem.{u1, u1} M (Submodule.{u2, u1} R M _inst_1 _inst_3 _inst_4) (SetLike.instMembership.{u1, u1} (Submodule.{u2, u1} R M _inst_1 _inst_3 _inst_4) M (Submodule.setLike.{u2, u1} R M _inst_1 _inst_3 _inst_4)) y p') -> (Eq.{succ u1} M x y) -> (Eq.{succ u1} M x (OfNat.ofNat.{u1} M 0 (Zero.toOfNat0.{u1} M (AddMonoid.toZero.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3)))))))
 Case conversion may be inaccurate. Consider using '#align submodule.disjoint_def' Submodule.disjoint_def'ₓ'. -/
 theorem disjoint_def' {p p' : Submodule R M} :
     Disjoint p p' ↔ ∀ x ∈ p, ∀ y ∈ p', x = y → x = (0 : M) :=
@@ -591,9 +591,9 @@ theorem disjoint_def' {p p' : Submodule R M} :
 
 /- warning: submodule.eq_zero_of_coe_mem_of_disjoint -> Submodule.eq_zero_of_coe_mem_of_disjoint is a dubious translation:
 lean 3 declaration is
-  forall {R : Type.{u1}} {M : Type.{u2}} [_inst_1 : Semiring.{u1} R] [_inst_3 : AddCommMonoid.{u2} M] [_inst_4 : Module.{u1, u2} R M _inst_1 _inst_3] {p : Submodule.{u1, u2} R M _inst_1 _inst_3 _inst_4} {q : Submodule.{u1, u2} R M _inst_1 _inst_3 _inst_4}, (Disjoint.{u2} (Submodule.{u1, u2} R M _inst_1 _inst_3 _inst_4) (CompleteSemilatticeInf.toPartialOrder.{u2} (Submodule.{u1, u2} R M _inst_1 _inst_3 _inst_4) (CompleteLattice.toCompleteSemilatticeInf.{u2} (Submodule.{u1, u2} R M _inst_1 _inst_3 _inst_4) (Submodule.completeLattice.{u1, u2} R M _inst_1 _inst_3 _inst_4))) (Submodule.orderBot.{u1, u2} R M _inst_1 _inst_3 _inst_4) p q) -> (forall {a : coeSort.{succ u2, succ (succ u2)} (Submodule.{u1, u2} R M _inst_1 _inst_3 _inst_4) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Submodule.{u1, u2} R M _inst_1 _inst_3 _inst_4) M (Submodule.setLike.{u1, u2} R M _inst_1 _inst_3 _inst_4)) p}, (Membership.Mem.{u2, u2} M (Submodule.{u1, u2} R M _inst_1 _inst_3 _inst_4) (SetLike.hasMem.{u2, u2} (Submodule.{u1, u2} R M _inst_1 _inst_3 _inst_4) M (Submodule.setLike.{u1, u2} R M _inst_1 _inst_3 _inst_4)) ((fun (a : Type.{u2}) (b : Type.{u2}) [self : HasLiftT.{succ u2, succ u2} a b] => self.0) (coeSort.{succ u2, succ (succ u2)} (Submodule.{u1, u2} R M _inst_1 _inst_3 _inst_4) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Submodule.{u1, u2} R M _inst_1 _inst_3 _inst_4) M (Submodule.setLike.{u1, u2} R M _inst_1 _inst_3 _inst_4)) p) M (HasLiftT.mk.{succ u2, succ u2} (coeSort.{succ u2, succ (succ u2)} (Submodule.{u1, u2} R M _inst_1 _inst_3 _inst_4) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Submodule.{u1, u2} R M _inst_1 _inst_3 _inst_4) M (Submodule.setLike.{u1, u2} R M _inst_1 _inst_3 _inst_4)) p) M (CoeTCₓ.coe.{succ u2, succ u2} (coeSort.{succ u2, succ (succ u2)} (Submodule.{u1, u2} R M _inst_1 _inst_3 _inst_4) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Submodule.{u1, u2} R M _inst_1 _inst_3 _inst_4) M (Submodule.setLike.{u1, u2} R M _inst_1 _inst_3 _inst_4)) p) M (coeBase.{succ u2, succ u2} (coeSort.{succ u2, succ (succ u2)} (Submodule.{u1, u2} R M _inst_1 _inst_3 _inst_4) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Submodule.{u1, u2} R M _inst_1 _inst_3 _inst_4) M (Submodule.setLike.{u1, u2} R M _inst_1 _inst_3 _inst_4)) p) M (coeSubtype.{succ u2} M (fun (x : M) => Membership.Mem.{u2, u2} M (Submodule.{u1, u2} R M _inst_1 _inst_3 _inst_4) (SetLike.hasMem.{u2, u2} (Submodule.{u1, u2} R M _inst_1 _inst_3 _inst_4) M (Submodule.setLike.{u1, u2} R M _inst_1 _inst_3 _inst_4)) x p))))) a) q) -> (Eq.{succ u2} (coeSort.{succ u2, succ (succ u2)} (Submodule.{u1, u2} R M _inst_1 _inst_3 _inst_4) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Submodule.{u1, u2} R M _inst_1 _inst_3 _inst_4) M (Submodule.setLike.{u1, u2} R M _inst_1 _inst_3 _inst_4)) p) a (OfNat.ofNat.{u2} (coeSort.{succ u2, succ (succ u2)} (Submodule.{u1, u2} R M _inst_1 _inst_3 _inst_4) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Submodule.{u1, u2} R M _inst_1 _inst_3 _inst_4) M (Submodule.setLike.{u1, u2} R M _inst_1 _inst_3 _inst_4)) p) 0 (OfNat.mk.{u2} (coeSort.{succ u2, succ (succ u2)} (Submodule.{u1, u2} R M _inst_1 _inst_3 _inst_4) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Submodule.{u1, u2} R M _inst_1 _inst_3 _inst_4) M (Submodule.setLike.{u1, u2} R M _inst_1 _inst_3 _inst_4)) p) 0 (Zero.zero.{u2} (coeSort.{succ u2, succ (succ u2)} (Submodule.{u1, u2} R M _inst_1 _inst_3 _inst_4) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Submodule.{u1, u2} R M _inst_1 _inst_3 _inst_4) M (Submodule.setLike.{u1, u2} R M _inst_1 _inst_3 _inst_4)) p) (Submodule.hasZero.{u1, u2} R M _inst_1 _inst_3 _inst_4 p))))))
+  forall {R : Type.{u1}} {M : Type.{u2}} [_inst_1 : Semiring.{u1} R] [_inst_3 : AddCommMonoid.{u2} M] [_inst_4 : Module.{u1, u2} R M _inst_1 _inst_3] {p : Submodule.{u1, u2} R M _inst_1 _inst_3 _inst_4} {q : Submodule.{u1, u2} R M _inst_1 _inst_3 _inst_4}, (Disjoint.{u2} (Submodule.{u1, u2} R M _inst_1 _inst_3 _inst_4) (CompleteSemilatticeInf.toPartialOrder.{u2} (Submodule.{u1, u2} R M _inst_1 _inst_3 _inst_4) (CompleteLattice.toCompleteSemilatticeInf.{u2} (Submodule.{u1, u2} R M _inst_1 _inst_3 _inst_4) (Submodule.completeLattice.{u1, u2} R M _inst_1 _inst_3 _inst_4))) (Submodule.orderBot.{u1, u2} R M _inst_1 _inst_3 _inst_4) p q) -> (forall {a : coeSort.{succ u2, succ (succ u2)} (Submodule.{u1, u2} R M _inst_1 _inst_3 _inst_4) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Submodule.{u1, u2} R M _inst_1 _inst_3 _inst_4) M (Submodule.setLike.{u1, u2} R M _inst_1 _inst_3 _inst_4)) p}, (Membership.Mem.{u2, u2} M (Submodule.{u1, u2} R M _inst_1 _inst_3 _inst_4) (SetLike.hasMem.{u2, u2} (Submodule.{u1, u2} R M _inst_1 _inst_3 _inst_4) M (Submodule.setLike.{u1, u2} R M _inst_1 _inst_3 _inst_4)) ((fun (a : Type.{u2}) (b : Type.{u2}) [self : HasLiftT.{succ u2, succ u2} a b] => self.0) (coeSort.{succ u2, succ (succ u2)} (Submodule.{u1, u2} R M _inst_1 _inst_3 _inst_4) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Submodule.{u1, u2} R M _inst_1 _inst_3 _inst_4) M (Submodule.setLike.{u1, u2} R M _inst_1 _inst_3 _inst_4)) p) M (HasLiftT.mk.{succ u2, succ u2} (coeSort.{succ u2, succ (succ u2)} (Submodule.{u1, u2} R M _inst_1 _inst_3 _inst_4) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Submodule.{u1, u2} R M _inst_1 _inst_3 _inst_4) M (Submodule.setLike.{u1, u2} R M _inst_1 _inst_3 _inst_4)) p) M (CoeTCₓ.coe.{succ u2, succ u2} (coeSort.{succ u2, succ (succ u2)} (Submodule.{u1, u2} R M _inst_1 _inst_3 _inst_4) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Submodule.{u1, u2} R M _inst_1 _inst_3 _inst_4) M (Submodule.setLike.{u1, u2} R M _inst_1 _inst_3 _inst_4)) p) M (coeBase.{succ u2, succ u2} (coeSort.{succ u2, succ (succ u2)} (Submodule.{u1, u2} R M _inst_1 _inst_3 _inst_4) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Submodule.{u1, u2} R M _inst_1 _inst_3 _inst_4) M (Submodule.setLike.{u1, u2} R M _inst_1 _inst_3 _inst_4)) p) M (coeSubtype.{succ u2} M (fun (x : M) => Membership.Mem.{u2, u2} M (Submodule.{u1, u2} R M _inst_1 _inst_3 _inst_4) (SetLike.hasMem.{u2, u2} (Submodule.{u1, u2} R M _inst_1 _inst_3 _inst_4) M (Submodule.setLike.{u1, u2} R M _inst_1 _inst_3 _inst_4)) x p))))) a) q) -> (Eq.{succ u2} (coeSort.{succ u2, succ (succ u2)} (Submodule.{u1, u2} R M _inst_1 _inst_3 _inst_4) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Submodule.{u1, u2} R M _inst_1 _inst_3 _inst_4) M (Submodule.setLike.{u1, u2} R M _inst_1 _inst_3 _inst_4)) p) a (OfNat.ofNat.{u2} (coeSort.{succ u2, succ (succ u2)} (Submodule.{u1, u2} R M _inst_1 _inst_3 _inst_4) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Submodule.{u1, u2} R M _inst_1 _inst_3 _inst_4) M (Submodule.setLike.{u1, u2} R M _inst_1 _inst_3 _inst_4)) p) 0 (OfNat.mk.{u2} (coeSort.{succ u2, succ (succ u2)} (Submodule.{u1, u2} R M _inst_1 _inst_3 _inst_4) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Submodule.{u1, u2} R M _inst_1 _inst_3 _inst_4) M (Submodule.setLike.{u1, u2} R M _inst_1 _inst_3 _inst_4)) p) 0 (Zero.zero.{u2} (coeSort.{succ u2, succ (succ u2)} (Submodule.{u1, u2} R M _inst_1 _inst_3 _inst_4) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Submodule.{u1, u2} R M _inst_1 _inst_3 _inst_4) M (Submodule.setLike.{u1, u2} R M _inst_1 _inst_3 _inst_4)) p) (Submodule.zero.{u1, u2} R M _inst_1 _inst_3 _inst_4 p))))))
 but is expected to have type
-  forall {R : Type.{u1}} {M : Type.{u2}} [_inst_1 : Semiring.{u1} R] [_inst_3 : AddCommMonoid.{u2} M] [_inst_4 : Module.{u1, u2} R M _inst_1 _inst_3] {p : Submodule.{u1, u2} R M _inst_1 _inst_3 _inst_4} {q : Submodule.{u1, u2} R M _inst_1 _inst_3 _inst_4}, (Disjoint.{u2} (Submodule.{u1, u2} R M _inst_1 _inst_3 _inst_4) (CompleteSemilatticeInf.toPartialOrder.{u2} (Submodule.{u1, u2} R M _inst_1 _inst_3 _inst_4) (CompleteLattice.toCompleteSemilatticeInf.{u2} (Submodule.{u1, u2} R M _inst_1 _inst_3 _inst_4) (Submodule.completeLattice.{u1, u2} R M _inst_1 _inst_3 _inst_4))) (Submodule.instOrderBotSubmoduleToLEToPreorderInstPartialOrderInstSetLikeSubmodule.{u1, u2} R M _inst_1 _inst_3 _inst_4) p q) -> (forall {a : Subtype.{succ u2} M (fun (x : M) => Membership.mem.{u2, u2} M (Submodule.{u1, u2} R M _inst_1 _inst_3 _inst_4) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} R M _inst_1 _inst_3 _inst_4) M (Submodule.instSetLikeSubmodule.{u1, u2} R M _inst_1 _inst_3 _inst_4)) x p)}, (Membership.mem.{u2, u2} M (Submodule.{u1, u2} R M _inst_1 _inst_3 _inst_4) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} R M _inst_1 _inst_3 _inst_4) M (Submodule.instSetLikeSubmodule.{u1, u2} R M _inst_1 _inst_3 _inst_4)) (Subtype.val.{succ u2} M (fun (x : M) => Membership.mem.{u2, u2} M (Set.{u2} M) (Set.instMembershipSet.{u2} M) x (SetLike.coe.{u2, u2} (Submodule.{u1, u2} R M _inst_1 _inst_3 _inst_4) M (Submodule.instSetLikeSubmodule.{u1, u2} R M _inst_1 _inst_3 _inst_4) p)) a) q) -> (Eq.{succ u2} (Subtype.{succ u2} M (fun (x : M) => Membership.mem.{u2, u2} M (Submodule.{u1, u2} R M _inst_1 _inst_3 _inst_4) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} R M _inst_1 _inst_3 _inst_4) M (Submodule.instSetLikeSubmodule.{u1, u2} R M _inst_1 _inst_3 _inst_4)) x p)) a (OfNat.ofNat.{u2} (Subtype.{succ u2} M (fun (x : M) => Membership.mem.{u2, u2} M (Submodule.{u1, u2} R M _inst_1 _inst_3 _inst_4) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} R M _inst_1 _inst_3 _inst_4) M (Submodule.instSetLikeSubmodule.{u1, u2} R M _inst_1 _inst_3 _inst_4)) x p)) 0 (Zero.toOfNat0.{u2} (Subtype.{succ u2} M (fun (x : M) => Membership.mem.{u2, u2} M (Submodule.{u1, u2} R M _inst_1 _inst_3 _inst_4) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} R M _inst_1 _inst_3 _inst_4) M (Submodule.instSetLikeSubmodule.{u1, u2} R M _inst_1 _inst_3 _inst_4)) x p)) (Submodule.instZeroSubtypeMemSubmoduleInstMembershipInstSetLikeSubmodule.{u1, u2} R M _inst_1 _inst_3 _inst_4 p)))))
+  forall {R : Type.{u1}} {M : Type.{u2}} [_inst_1 : Semiring.{u1} R] [_inst_3 : AddCommMonoid.{u2} M] [_inst_4 : Module.{u1, u2} R M _inst_1 _inst_3] {p : Submodule.{u1, u2} R M _inst_1 _inst_3 _inst_4} {q : Submodule.{u1, u2} R M _inst_1 _inst_3 _inst_4}, (Disjoint.{u2} (Submodule.{u1, u2} R M _inst_1 _inst_3 _inst_4) (CompleteSemilatticeInf.toPartialOrder.{u2} (Submodule.{u1, u2} R M _inst_1 _inst_3 _inst_4) (CompleteLattice.toCompleteSemilatticeInf.{u2} (Submodule.{u1, u2} R M _inst_1 _inst_3 _inst_4) (Submodule.completeLattice.{u1, u2} R M _inst_1 _inst_3 _inst_4))) (Submodule.instOrderBotSubmoduleToLEToPreorderInstPartialOrderSetLike.{u1, u2} R M _inst_1 _inst_3 _inst_4) p q) -> (forall {a : Subtype.{succ u2} M (fun (x : M) => Membership.mem.{u2, u2} M (Submodule.{u1, u2} R M _inst_1 _inst_3 _inst_4) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} R M _inst_1 _inst_3 _inst_4) M (Submodule.setLike.{u1, u2} R M _inst_1 _inst_3 _inst_4)) x p)}, (Membership.mem.{u2, u2} M (Submodule.{u1, u2} R M _inst_1 _inst_3 _inst_4) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} R M _inst_1 _inst_3 _inst_4) M (Submodule.setLike.{u1, u2} R M _inst_1 _inst_3 _inst_4)) (Subtype.val.{succ u2} M (fun (x : M) => Membership.mem.{u2, u2} M (Set.{u2} M) (Set.instMembershipSet.{u2} M) x (SetLike.coe.{u2, u2} (Submodule.{u1, u2} R M _inst_1 _inst_3 _inst_4) M (Submodule.setLike.{u1, u2} R M _inst_1 _inst_3 _inst_4) p)) a) q) -> (Eq.{succ u2} (Subtype.{succ u2} M (fun (x : M) => Membership.mem.{u2, u2} M (Submodule.{u1, u2} R M _inst_1 _inst_3 _inst_4) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} R M _inst_1 _inst_3 _inst_4) M (Submodule.setLike.{u1, u2} R M _inst_1 _inst_3 _inst_4)) x p)) a (OfNat.ofNat.{u2} (Subtype.{succ u2} M (fun (x : M) => Membership.mem.{u2, u2} M (Submodule.{u1, u2} R M _inst_1 _inst_3 _inst_4) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} R M _inst_1 _inst_3 _inst_4) M (Submodule.setLike.{u1, u2} R M _inst_1 _inst_3 _inst_4)) x p)) 0 (Zero.toOfNat0.{u2} (Subtype.{succ u2} M (fun (x : M) => Membership.mem.{u2, u2} M (Submodule.{u1, u2} R M _inst_1 _inst_3 _inst_4) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} R M _inst_1 _inst_3 _inst_4) M (Submodule.setLike.{u1, u2} R M _inst_1 _inst_3 _inst_4)) x p)) (Submodule.zero.{u1, u2} R M _inst_1 _inst_3 _inst_4 p)))))
 Case conversion may be inaccurate. Consider using '#align submodule.eq_zero_of_coe_mem_of_disjoint Submodule.eq_zero_of_coe_mem_of_disjointₓ'. -/
 theorem eq_zero_of_coe_mem_of_disjoint (hpq : Disjoint p q) {a : p} (ha : (a : M) ∈ q) : a = 0 := by
   exact_mod_cast disjoint_def.mp hpq a (coe_mem a) ha
@@ -635,7 +635,7 @@ theorem AddSubmonoid.toNatSubmodule_symm :
 lean 3 declaration is
   forall {M : Type.{u1}} [_inst_3 : AddCommMonoid.{u1} M] (S : AddSubmonoid.{u1} M (AddMonoid.toAddZeroClass.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3))), Eq.{succ u1} (Set.{u1} M) ((fun (a : Type.{u1}) (b : Type.{u1}) [self : HasLiftT.{succ u1, succ u1} a b] => self.0) (Submodule.{0, u1} Nat M Nat.semiring _inst_3 (AddCommMonoid.natModule.{u1} M _inst_3)) (Set.{u1} M) (HasLiftT.mk.{succ u1, succ u1} (Submodule.{0, u1} Nat M Nat.semiring _inst_3 (AddCommMonoid.natModule.{u1} M _inst_3)) (Set.{u1} M) (CoeTCₓ.coe.{succ u1, succ u1} (Submodule.{0, u1} Nat M Nat.semiring _inst_3 (AddCommMonoid.natModule.{u1} M _inst_3)) (Set.{u1} M) (SetLike.Set.hasCoeT.{u1, u1} (Submodule.{0, u1} Nat M Nat.semiring _inst_3 (AddCommMonoid.natModule.{u1} M _inst_3)) M (Submodule.setLike.{0, u1} Nat M Nat.semiring _inst_3 (AddCommMonoid.natModule.{u1} M _inst_3))))) (coeFn.{succ u1, succ u1} (OrderIso.{u1, u1} (AddSubmonoid.{u1} M (AddMonoid.toAddZeroClass.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3))) (Submodule.{0, u1} Nat M Nat.semiring _inst_3 (AddCommMonoid.natModule.{u1} M _inst_3)) (Preorder.toLE.{u1} (AddSubmonoid.{u1} M (AddMonoid.toAddZeroClass.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3))) (PartialOrder.toPreorder.{u1} (AddSubmonoid.{u1} M (AddMonoid.toAddZeroClass.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3))) (CompleteSemilatticeInf.toPartialOrder.{u1} (AddSubmonoid.{u1} M (AddMonoid.toAddZeroClass.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3))) (CompleteLattice.toCompleteSemilatticeInf.{u1} (AddSubmonoid.{u1} M (AddMonoid.toAddZeroClass.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3))) (AddSubmonoid.completeLattice.{u1} M (AddMonoid.toAddZeroClass.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3))))))) (Preorder.toLE.{u1} (Submodule.{0, u1} Nat M Nat.semiring _inst_3 (AddCommMonoid.natModule.{u1} M _inst_3)) (PartialOrder.toPreorder.{u1} (Submodule.{0, u1} Nat M Nat.semiring _inst_3 (AddCommMonoid.natModule.{u1} M _inst_3)) (CompleteSemilatticeInf.toPartialOrder.{u1} (Submodule.{0, u1} Nat M Nat.semiring _inst_3 (AddCommMonoid.natModule.{u1} M _inst_3)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (Submodule.{0, u1} Nat M Nat.semiring _inst_3 (AddCommMonoid.natModule.{u1} M _inst_3)) (Submodule.completeLattice.{0, u1} Nat M Nat.semiring _inst_3 (AddCommMonoid.natModule.{u1} M _inst_3))))))) (fun (_x : RelIso.{u1, u1} (AddSubmonoid.{u1} M (AddMonoid.toAddZeroClass.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3))) (Submodule.{0, u1} Nat M Nat.semiring _inst_3 (AddCommMonoid.natModule.{u1} M _inst_3)) (LE.le.{u1} (AddSubmonoid.{u1} M (AddMonoid.toAddZeroClass.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3))) (Preorder.toLE.{u1} (AddSubmonoid.{u1} M (AddMonoid.toAddZeroClass.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3))) (PartialOrder.toPreorder.{u1} (AddSubmonoid.{u1} M (AddMonoid.toAddZeroClass.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3))) (CompleteSemilatticeInf.toPartialOrder.{u1} (AddSubmonoid.{u1} M (AddMonoid.toAddZeroClass.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3))) (CompleteLattice.toCompleteSemilatticeInf.{u1} (AddSubmonoid.{u1} M (AddMonoid.toAddZeroClass.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3))) (AddSubmonoid.completeLattice.{u1} M (AddMonoid.toAddZeroClass.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3)))))))) (LE.le.{u1} (Submodule.{0, u1} Nat M Nat.semiring _inst_3 (AddCommMonoid.natModule.{u1} M _inst_3)) (Preorder.toLE.{u1} (Submodule.{0, u1} Nat M Nat.semiring _inst_3 (AddCommMonoid.natModule.{u1} M _inst_3)) (PartialOrder.toPreorder.{u1} (Submodule.{0, u1} Nat M Nat.semiring _inst_3 (AddCommMonoid.natModule.{u1} M _inst_3)) (CompleteSemilatticeInf.toPartialOrder.{u1} (Submodule.{0, u1} Nat M Nat.semiring _inst_3 (AddCommMonoid.natModule.{u1} M _inst_3)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (Submodule.{0, u1} Nat M Nat.semiring _inst_3 (AddCommMonoid.natModule.{u1} M _inst_3)) (Submodule.completeLattice.{0, u1} Nat M Nat.semiring _inst_3 (AddCommMonoid.natModule.{u1} M _inst_3)))))))) => (AddSubmonoid.{u1} M (AddMonoid.toAddZeroClass.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3))) -> (Submodule.{0, u1} Nat M Nat.semiring _inst_3 (AddCommMonoid.natModule.{u1} M _inst_3))) (RelIso.hasCoeToFun.{u1, u1} (AddSubmonoid.{u1} M (AddMonoid.toAddZeroClass.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3))) (Submodule.{0, u1} Nat M Nat.semiring _inst_3 (AddCommMonoid.natModule.{u1} M _inst_3)) (LE.le.{u1} (AddSubmonoid.{u1} M (AddMonoid.toAddZeroClass.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3))) (Preorder.toLE.{u1} (AddSubmonoid.{u1} M (AddMonoid.toAddZeroClass.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3))) (PartialOrder.toPreorder.{u1} (AddSubmonoid.{u1} M (AddMonoid.toAddZeroClass.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3))) (CompleteSemilatticeInf.toPartialOrder.{u1} (AddSubmonoid.{u1} M (AddMonoid.toAddZeroClass.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3))) (CompleteLattice.toCompleteSemilatticeInf.{u1} (AddSubmonoid.{u1} M (AddMonoid.toAddZeroClass.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3))) (AddSubmonoid.completeLattice.{u1} M (AddMonoid.toAddZeroClass.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3)))))))) (LE.le.{u1} (Submodule.{0, u1} Nat M Nat.semiring _inst_3 (AddCommMonoid.natModule.{u1} M _inst_3)) (Preorder.toLE.{u1} (Submodule.{0, u1} Nat M Nat.semiring _inst_3 (AddCommMonoid.natModule.{u1} M _inst_3)) (PartialOrder.toPreorder.{u1} (Submodule.{0, u1} Nat M Nat.semiring _inst_3 (AddCommMonoid.natModule.{u1} M _inst_3)) (CompleteSemilatticeInf.toPartialOrder.{u1} (Submodule.{0, u1} Nat M Nat.semiring _inst_3 (AddCommMonoid.natModule.{u1} M _inst_3)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (Submodule.{0, u1} Nat M Nat.semiring _inst_3 (AddCommMonoid.natModule.{u1} M _inst_3)) (Submodule.completeLattice.{0, u1} Nat M Nat.semiring _inst_3 (AddCommMonoid.natModule.{u1} M _inst_3)))))))) (AddSubmonoid.toNatSubmodule.{u1} M _inst_3) S)) ((fun (a : Type.{u1}) (b : Type.{u1}) [self : HasLiftT.{succ u1, succ u1} a b] => self.0) (AddSubmonoid.{u1} M (AddMonoid.toAddZeroClass.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3))) (Set.{u1} M) (HasLiftT.mk.{succ u1, succ u1} (AddSubmonoid.{u1} M (AddMonoid.toAddZeroClass.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3))) (Set.{u1} M) (CoeTCₓ.coe.{succ u1, succ u1} (AddSubmonoid.{u1} M (AddMonoid.toAddZeroClass.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3))) (Set.{u1} M) (SetLike.Set.hasCoeT.{u1, u1} (AddSubmonoid.{u1} M (AddMonoid.toAddZeroClass.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3))) M (AddSubmonoid.setLike.{u1} M (AddMonoid.toAddZeroClass.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3)))))) S)
 but is expected to have type
-  forall {M : Type.{u1}} [_inst_3 : AddCommMonoid.{u1} M] (S : AddSubmonoid.{u1} M (AddMonoid.toAddZeroClass.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3))), Eq.{succ u1} (Set.{u1} M) (SetLike.coe.{u1, u1} ((fun (x._@.Mathlib.Data.FunLike.Embedding._hyg.19 : AddSubmonoid.{u1} M (AddMonoid.toAddZeroClass.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3))) => Submodule.{0, u1} Nat M Nat.semiring _inst_3 (AddCommMonoid.natModule.{u1} M _inst_3)) S) M (Submodule.instSetLikeSubmodule.{0, u1} Nat M Nat.semiring _inst_3 (AddCommMonoid.natModule.{u1} M _inst_3)) (FunLike.coe.{succ u1, succ u1, succ u1} (Function.Embedding.{succ u1, succ u1} (AddSubmonoid.{u1} M (AddMonoid.toAddZeroClass.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3))) (Submodule.{0, u1} Nat M Nat.semiring _inst_3 (AddCommMonoid.natModule.{u1} M _inst_3))) (AddSubmonoid.{u1} M (AddMonoid.toAddZeroClass.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3))) (fun (_x : AddSubmonoid.{u1} M (AddMonoid.toAddZeroClass.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3))) => (fun (x._@.Mathlib.Data.FunLike.Embedding._hyg.19 : AddSubmonoid.{u1} M (AddMonoid.toAddZeroClass.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3))) => Submodule.{0, u1} Nat M Nat.semiring _inst_3 (AddCommMonoid.natModule.{u1} M _inst_3)) _x) (EmbeddingLike.toFunLike.{succ u1, succ u1, succ u1} (Function.Embedding.{succ u1, succ u1} (AddSubmonoid.{u1} M (AddMonoid.toAddZeroClass.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3))) (Submodule.{0, u1} Nat M Nat.semiring _inst_3 (AddCommMonoid.natModule.{u1} M _inst_3))) (AddSubmonoid.{u1} M (AddMonoid.toAddZeroClass.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3))) (Submodule.{0, u1} Nat M Nat.semiring _inst_3 (AddCommMonoid.natModule.{u1} M _inst_3)) (Function.instEmbeddingLikeEmbedding.{succ u1, succ u1} (AddSubmonoid.{u1} M (AddMonoid.toAddZeroClass.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3))) (Submodule.{0, u1} Nat M Nat.semiring _inst_3 (AddCommMonoid.natModule.{u1} M _inst_3)))) (RelEmbedding.toEmbedding.{u1, u1} (AddSubmonoid.{u1} M (AddMonoid.toAddZeroClass.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3))) (Submodule.{0, u1} Nat M Nat.semiring _inst_3 (AddCommMonoid.natModule.{u1} M _inst_3)) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1281 : AddSubmonoid.{u1} M (AddMonoid.toAddZeroClass.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3))) (x._@.Mathlib.Order.Hom.Basic._hyg.1283 : AddSubmonoid.{u1} M (AddMonoid.toAddZeroClass.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3))) => LE.le.{u1} (AddSubmonoid.{u1} M (AddMonoid.toAddZeroClass.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3))) (Preorder.toLE.{u1} (AddSubmonoid.{u1} M (AddMonoid.toAddZeroClass.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3))) (PartialOrder.toPreorder.{u1} (AddSubmonoid.{u1} M (AddMonoid.toAddZeroClass.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3))) (CompleteSemilatticeInf.toPartialOrder.{u1} (AddSubmonoid.{u1} M (AddMonoid.toAddZeroClass.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3))) (CompleteLattice.toCompleteSemilatticeInf.{u1} (AddSubmonoid.{u1} M (AddMonoid.toAddZeroClass.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3))) (AddSubmonoid.instCompleteLatticeAddSubmonoid.{u1} M (AddMonoid.toAddZeroClass.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3))))))) x._@.Mathlib.Order.Hom.Basic._hyg.1281 x._@.Mathlib.Order.Hom.Basic._hyg.1283) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1296 : Submodule.{0, u1} Nat M Nat.semiring _inst_3 (AddCommMonoid.natModule.{u1} M _inst_3)) (x._@.Mathlib.Order.Hom.Basic._hyg.1298 : Submodule.{0, u1} Nat M Nat.semiring _inst_3 (AddCommMonoid.natModule.{u1} M _inst_3)) => LE.le.{u1} (Submodule.{0, u1} Nat M Nat.semiring _inst_3 (AddCommMonoid.natModule.{u1} M _inst_3)) (Preorder.toLE.{u1} (Submodule.{0, u1} Nat M Nat.semiring _inst_3 (AddCommMonoid.natModule.{u1} M _inst_3)) (PartialOrder.toPreorder.{u1} (Submodule.{0, u1} Nat M Nat.semiring _inst_3 (AddCommMonoid.natModule.{u1} M _inst_3)) (CompleteSemilatticeInf.toPartialOrder.{u1} (Submodule.{0, u1} Nat M Nat.semiring _inst_3 (AddCommMonoid.natModule.{u1} M _inst_3)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (Submodule.{0, u1} Nat M Nat.semiring _inst_3 (AddCommMonoid.natModule.{u1} M _inst_3)) (Submodule.completeLattice.{0, u1} Nat M Nat.semiring _inst_3 (AddCommMonoid.natModule.{u1} M _inst_3)))))) x._@.Mathlib.Order.Hom.Basic._hyg.1296 x._@.Mathlib.Order.Hom.Basic._hyg.1298) (RelIso.toRelEmbedding.{u1, u1} (AddSubmonoid.{u1} M (AddMonoid.toAddZeroClass.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3))) (Submodule.{0, u1} Nat M Nat.semiring _inst_3 (AddCommMonoid.natModule.{u1} M _inst_3)) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1281 : AddSubmonoid.{u1} M (AddMonoid.toAddZeroClass.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3))) (x._@.Mathlib.Order.Hom.Basic._hyg.1283 : AddSubmonoid.{u1} M (AddMonoid.toAddZeroClass.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3))) => LE.le.{u1} (AddSubmonoid.{u1} M (AddMonoid.toAddZeroClass.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3))) (Preorder.toLE.{u1} (AddSubmonoid.{u1} M (AddMonoid.toAddZeroClass.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3))) (PartialOrder.toPreorder.{u1} (AddSubmonoid.{u1} M (AddMonoid.toAddZeroClass.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3))) (CompleteSemilatticeInf.toPartialOrder.{u1} (AddSubmonoid.{u1} M (AddMonoid.toAddZeroClass.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3))) (CompleteLattice.toCompleteSemilatticeInf.{u1} (AddSubmonoid.{u1} M (AddMonoid.toAddZeroClass.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3))) (AddSubmonoid.instCompleteLatticeAddSubmonoid.{u1} M (AddMonoid.toAddZeroClass.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3))))))) x._@.Mathlib.Order.Hom.Basic._hyg.1281 x._@.Mathlib.Order.Hom.Basic._hyg.1283) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1296 : Submodule.{0, u1} Nat M Nat.semiring _inst_3 (AddCommMonoid.natModule.{u1} M _inst_3)) (x._@.Mathlib.Order.Hom.Basic._hyg.1298 : Submodule.{0, u1} Nat M Nat.semiring _inst_3 (AddCommMonoid.natModule.{u1} M _inst_3)) => LE.le.{u1} (Submodule.{0, u1} Nat M Nat.semiring _inst_3 (AddCommMonoid.natModule.{u1} M _inst_3)) (Preorder.toLE.{u1} (Submodule.{0, u1} Nat M Nat.semiring _inst_3 (AddCommMonoid.natModule.{u1} M _inst_3)) (PartialOrder.toPreorder.{u1} (Submodule.{0, u1} Nat M Nat.semiring _inst_3 (AddCommMonoid.natModule.{u1} M _inst_3)) (CompleteSemilatticeInf.toPartialOrder.{u1} (Submodule.{0, u1} Nat M Nat.semiring _inst_3 (AddCommMonoid.natModule.{u1} M _inst_3)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (Submodule.{0, u1} Nat M Nat.semiring _inst_3 (AddCommMonoid.natModule.{u1} M _inst_3)) (Submodule.completeLattice.{0, u1} Nat M Nat.semiring _inst_3 (AddCommMonoid.natModule.{u1} M _inst_3)))))) x._@.Mathlib.Order.Hom.Basic._hyg.1296 x._@.Mathlib.Order.Hom.Basic._hyg.1298) (AddSubmonoid.toNatSubmodule.{u1} M _inst_3))) S)) (SetLike.coe.{u1, u1} (AddSubmonoid.{u1} M (AddMonoid.toAddZeroClass.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3))) M (AddSubmonoid.instSetLikeAddSubmonoid.{u1} M (AddMonoid.toAddZeroClass.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3))) S)
+  forall {M : Type.{u1}} [_inst_3 : AddCommMonoid.{u1} M] (S : AddSubmonoid.{u1} M (AddMonoid.toAddZeroClass.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3))), Eq.{succ u1} (Set.{u1} M) (SetLike.coe.{u1, u1} ((fun (x._@.Mathlib.Data.FunLike.Embedding._hyg.19 : AddSubmonoid.{u1} M (AddMonoid.toAddZeroClass.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3))) => Submodule.{0, u1} Nat M Nat.semiring _inst_3 (AddCommMonoid.natModule.{u1} M _inst_3)) S) M (Submodule.setLike.{0, u1} Nat M Nat.semiring _inst_3 (AddCommMonoid.natModule.{u1} M _inst_3)) (FunLike.coe.{succ u1, succ u1, succ u1} (Function.Embedding.{succ u1, succ u1} (AddSubmonoid.{u1} M (AddMonoid.toAddZeroClass.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3))) (Submodule.{0, u1} Nat M Nat.semiring _inst_3 (AddCommMonoid.natModule.{u1} M _inst_3))) (AddSubmonoid.{u1} M (AddMonoid.toAddZeroClass.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3))) (fun (_x : AddSubmonoid.{u1} M (AddMonoid.toAddZeroClass.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3))) => (fun (x._@.Mathlib.Data.FunLike.Embedding._hyg.19 : AddSubmonoid.{u1} M (AddMonoid.toAddZeroClass.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3))) => Submodule.{0, u1} Nat M Nat.semiring _inst_3 (AddCommMonoid.natModule.{u1} M _inst_3)) _x) (EmbeddingLike.toFunLike.{succ u1, succ u1, succ u1} (Function.Embedding.{succ u1, succ u1} (AddSubmonoid.{u1} M (AddMonoid.toAddZeroClass.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3))) (Submodule.{0, u1} Nat M Nat.semiring _inst_3 (AddCommMonoid.natModule.{u1} M _inst_3))) (AddSubmonoid.{u1} M (AddMonoid.toAddZeroClass.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3))) (Submodule.{0, u1} Nat M Nat.semiring _inst_3 (AddCommMonoid.natModule.{u1} M _inst_3)) (Function.instEmbeddingLikeEmbedding.{succ u1, succ u1} (AddSubmonoid.{u1} M (AddMonoid.toAddZeroClass.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3))) (Submodule.{0, u1} Nat M Nat.semiring _inst_3 (AddCommMonoid.natModule.{u1} M _inst_3)))) (RelEmbedding.toEmbedding.{u1, u1} (AddSubmonoid.{u1} M (AddMonoid.toAddZeroClass.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3))) (Submodule.{0, u1} Nat M Nat.semiring _inst_3 (AddCommMonoid.natModule.{u1} M _inst_3)) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1281 : AddSubmonoid.{u1} M (AddMonoid.toAddZeroClass.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3))) (x._@.Mathlib.Order.Hom.Basic._hyg.1283 : AddSubmonoid.{u1} M (AddMonoid.toAddZeroClass.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3))) => LE.le.{u1} (AddSubmonoid.{u1} M (AddMonoid.toAddZeroClass.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3))) (Preorder.toLE.{u1} (AddSubmonoid.{u1} M (AddMonoid.toAddZeroClass.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3))) (PartialOrder.toPreorder.{u1} (AddSubmonoid.{u1} M (AddMonoid.toAddZeroClass.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3))) (CompleteSemilatticeInf.toPartialOrder.{u1} (AddSubmonoid.{u1} M (AddMonoid.toAddZeroClass.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3))) (CompleteLattice.toCompleteSemilatticeInf.{u1} (AddSubmonoid.{u1} M (AddMonoid.toAddZeroClass.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3))) (AddSubmonoid.instCompleteLatticeAddSubmonoid.{u1} M (AddMonoid.toAddZeroClass.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3))))))) x._@.Mathlib.Order.Hom.Basic._hyg.1281 x._@.Mathlib.Order.Hom.Basic._hyg.1283) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1296 : Submodule.{0, u1} Nat M Nat.semiring _inst_3 (AddCommMonoid.natModule.{u1} M _inst_3)) (x._@.Mathlib.Order.Hom.Basic._hyg.1298 : Submodule.{0, u1} Nat M Nat.semiring _inst_3 (AddCommMonoid.natModule.{u1} M _inst_3)) => LE.le.{u1} (Submodule.{0, u1} Nat M Nat.semiring _inst_3 (AddCommMonoid.natModule.{u1} M _inst_3)) (Preorder.toLE.{u1} (Submodule.{0, u1} Nat M Nat.semiring _inst_3 (AddCommMonoid.natModule.{u1} M _inst_3)) (PartialOrder.toPreorder.{u1} (Submodule.{0, u1} Nat M Nat.semiring _inst_3 (AddCommMonoid.natModule.{u1} M _inst_3)) (CompleteSemilatticeInf.toPartialOrder.{u1} (Submodule.{0, u1} Nat M Nat.semiring _inst_3 (AddCommMonoid.natModule.{u1} M _inst_3)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (Submodule.{0, u1} Nat M Nat.semiring _inst_3 (AddCommMonoid.natModule.{u1} M _inst_3)) (Submodule.completeLattice.{0, u1} Nat M Nat.semiring _inst_3 (AddCommMonoid.natModule.{u1} M _inst_3)))))) x._@.Mathlib.Order.Hom.Basic._hyg.1296 x._@.Mathlib.Order.Hom.Basic._hyg.1298) (RelIso.toRelEmbedding.{u1, u1} (AddSubmonoid.{u1} M (AddMonoid.toAddZeroClass.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3))) (Submodule.{0, u1} Nat M Nat.semiring _inst_3 (AddCommMonoid.natModule.{u1} M _inst_3)) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1281 : AddSubmonoid.{u1} M (AddMonoid.toAddZeroClass.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3))) (x._@.Mathlib.Order.Hom.Basic._hyg.1283 : AddSubmonoid.{u1} M (AddMonoid.toAddZeroClass.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3))) => LE.le.{u1} (AddSubmonoid.{u1} M (AddMonoid.toAddZeroClass.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3))) (Preorder.toLE.{u1} (AddSubmonoid.{u1} M (AddMonoid.toAddZeroClass.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3))) (PartialOrder.toPreorder.{u1} (AddSubmonoid.{u1} M (AddMonoid.toAddZeroClass.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3))) (CompleteSemilatticeInf.toPartialOrder.{u1} (AddSubmonoid.{u1} M (AddMonoid.toAddZeroClass.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3))) (CompleteLattice.toCompleteSemilatticeInf.{u1} (AddSubmonoid.{u1} M (AddMonoid.toAddZeroClass.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3))) (AddSubmonoid.instCompleteLatticeAddSubmonoid.{u1} M (AddMonoid.toAddZeroClass.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3))))))) x._@.Mathlib.Order.Hom.Basic._hyg.1281 x._@.Mathlib.Order.Hom.Basic._hyg.1283) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1296 : Submodule.{0, u1} Nat M Nat.semiring _inst_3 (AddCommMonoid.natModule.{u1} M _inst_3)) (x._@.Mathlib.Order.Hom.Basic._hyg.1298 : Submodule.{0, u1} Nat M Nat.semiring _inst_3 (AddCommMonoid.natModule.{u1} M _inst_3)) => LE.le.{u1} (Submodule.{0, u1} Nat M Nat.semiring _inst_3 (AddCommMonoid.natModule.{u1} M _inst_3)) (Preorder.toLE.{u1} (Submodule.{0, u1} Nat M Nat.semiring _inst_3 (AddCommMonoid.natModule.{u1} M _inst_3)) (PartialOrder.toPreorder.{u1} (Submodule.{0, u1} Nat M Nat.semiring _inst_3 (AddCommMonoid.natModule.{u1} M _inst_3)) (CompleteSemilatticeInf.toPartialOrder.{u1} (Submodule.{0, u1} Nat M Nat.semiring _inst_3 (AddCommMonoid.natModule.{u1} M _inst_3)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (Submodule.{0, u1} Nat M Nat.semiring _inst_3 (AddCommMonoid.natModule.{u1} M _inst_3)) (Submodule.completeLattice.{0, u1} Nat M Nat.semiring _inst_3 (AddCommMonoid.natModule.{u1} M _inst_3)))))) x._@.Mathlib.Order.Hom.Basic._hyg.1296 x._@.Mathlib.Order.Hom.Basic._hyg.1298) (AddSubmonoid.toNatSubmodule.{u1} M _inst_3))) S)) (SetLike.coe.{u1, u1} (AddSubmonoid.{u1} M (AddMonoid.toAddZeroClass.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3))) M (AddSubmonoid.instSetLikeAddSubmonoid.{u1} M (AddMonoid.toAddZeroClass.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3))) S)
 Case conversion may be inaccurate. Consider using '#align add_submonoid.coe_to_nat_submodule AddSubmonoid.coe_toNatSubmoduleₓ'. -/
 @[simp]
 theorem AddSubmonoid.coe_toNatSubmodule (S : AddSubmonoid M) : (S.toNatSubmodule : Set M) = S :=
@@ -706,7 +706,7 @@ theorem AddSubgroup.toIntSubmodule_symm :
 lean 3 declaration is
   forall {M : Type.{u1}} [_inst_1 : AddCommGroup.{u1} M] (S : AddSubgroup.{u1} M (AddCommGroup.toAddGroup.{u1} M _inst_1)), Eq.{succ u1} (Set.{u1} M) ((fun (a : Type.{u1}) (b : Type.{u1}) [self : HasLiftT.{succ u1, succ u1} a b] => self.0) (Submodule.{0, u1} Int M Int.semiring (AddCommGroup.toAddCommMonoid.{u1} M _inst_1) (AddCommGroup.intModule.{u1} M _inst_1)) (Set.{u1} M) (HasLiftT.mk.{succ u1, succ u1} (Submodule.{0, u1} Int M Int.semiring (AddCommGroup.toAddCommMonoid.{u1} M _inst_1) (AddCommGroup.intModule.{u1} M _inst_1)) (Set.{u1} M) (CoeTCₓ.coe.{succ u1, succ u1} (Submodule.{0, u1} Int M Int.semiring (AddCommGroup.toAddCommMonoid.{u1} M _inst_1) (AddCommGroup.intModule.{u1} M _inst_1)) (Set.{u1} M) (SetLike.Set.hasCoeT.{u1, u1} (Submodule.{0, u1} Int M Int.semiring (AddCommGroup.toAddCommMonoid.{u1} M _inst_1) (AddCommGroup.intModule.{u1} M _inst_1)) M (Submodule.setLike.{0, u1} Int M Int.semiring (AddCommGroup.toAddCommMonoid.{u1} M _inst_1) (AddCommGroup.intModule.{u1} M _inst_1))))) (coeFn.{succ u1, succ u1} (OrderIso.{u1, u1} (AddSubgroup.{u1} M (AddCommGroup.toAddGroup.{u1} M _inst_1)) (Submodule.{0, u1} Int M Int.semiring (AddCommGroup.toAddCommMonoid.{u1} M _inst_1) (AddCommGroup.intModule.{u1} M _inst_1)) (Preorder.toLE.{u1} (AddSubgroup.{u1} M (AddCommGroup.toAddGroup.{u1} M _inst_1)) (PartialOrder.toPreorder.{u1} (AddSubgroup.{u1} M (AddCommGroup.toAddGroup.{u1} M _inst_1)) (CompleteSemilatticeInf.toPartialOrder.{u1} (AddSubgroup.{u1} M (AddCommGroup.toAddGroup.{u1} M _inst_1)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (AddSubgroup.{u1} M (AddCommGroup.toAddGroup.{u1} M _inst_1)) (AddSubgroup.completeLattice.{u1} M (AddCommGroup.toAddGroup.{u1} M _inst_1)))))) (Preorder.toLE.{u1} (Submodule.{0, u1} Int M Int.semiring (AddCommGroup.toAddCommMonoid.{u1} M _inst_1) (AddCommGroup.intModule.{u1} M _inst_1)) (PartialOrder.toPreorder.{u1} (Submodule.{0, u1} Int M Int.semiring (AddCommGroup.toAddCommMonoid.{u1} M _inst_1) (AddCommGroup.intModule.{u1} M _inst_1)) (CompleteSemilatticeInf.toPartialOrder.{u1} (Submodule.{0, u1} Int M Int.semiring (AddCommGroup.toAddCommMonoid.{u1} M _inst_1) (AddCommGroup.intModule.{u1} M _inst_1)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (Submodule.{0, u1} Int M Int.semiring (AddCommGroup.toAddCommMonoid.{u1} M _inst_1) (AddCommGroup.intModule.{u1} M _inst_1)) (Submodule.completeLattice.{0, u1} Int M Int.semiring (AddCommGroup.toAddCommMonoid.{u1} M _inst_1) (AddCommGroup.intModule.{u1} M _inst_1))))))) (fun (_x : RelIso.{u1, u1} (AddSubgroup.{u1} M (AddCommGroup.toAddGroup.{u1} M _inst_1)) (Submodule.{0, u1} Int M Int.semiring (AddCommGroup.toAddCommMonoid.{u1} M _inst_1) (AddCommGroup.intModule.{u1} M _inst_1)) (LE.le.{u1} (AddSubgroup.{u1} M (AddCommGroup.toAddGroup.{u1} M _inst_1)) (Preorder.toLE.{u1} (AddSubgroup.{u1} M (AddCommGroup.toAddGroup.{u1} M _inst_1)) (PartialOrder.toPreorder.{u1} (AddSubgroup.{u1} M (AddCommGroup.toAddGroup.{u1} M _inst_1)) (CompleteSemilatticeInf.toPartialOrder.{u1} (AddSubgroup.{u1} M (AddCommGroup.toAddGroup.{u1} M _inst_1)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (AddSubgroup.{u1} M (AddCommGroup.toAddGroup.{u1} M _inst_1)) (AddSubgroup.completeLattice.{u1} M (AddCommGroup.toAddGroup.{u1} M _inst_1))))))) (LE.le.{u1} (Submodule.{0, u1} Int M Int.semiring (AddCommGroup.toAddCommMonoid.{u1} M _inst_1) (AddCommGroup.intModule.{u1} M _inst_1)) (Preorder.toLE.{u1} (Submodule.{0, u1} Int M Int.semiring (AddCommGroup.toAddCommMonoid.{u1} M _inst_1) (AddCommGroup.intModule.{u1} M _inst_1)) (PartialOrder.toPreorder.{u1} (Submodule.{0, u1} Int M Int.semiring (AddCommGroup.toAddCommMonoid.{u1} M _inst_1) (AddCommGroup.intModule.{u1} M _inst_1)) (CompleteSemilatticeInf.toPartialOrder.{u1} (Submodule.{0, u1} Int M Int.semiring (AddCommGroup.toAddCommMonoid.{u1} M _inst_1) (AddCommGroup.intModule.{u1} M _inst_1)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (Submodule.{0, u1} Int M Int.semiring (AddCommGroup.toAddCommMonoid.{u1} M _inst_1) (AddCommGroup.intModule.{u1} M _inst_1)) (Submodule.completeLattice.{0, u1} Int M Int.semiring (AddCommGroup.toAddCommMonoid.{u1} M _inst_1) (AddCommGroup.intModule.{u1} M _inst_1)))))))) => (AddSubgroup.{u1} M (AddCommGroup.toAddGroup.{u1} M _inst_1)) -> (Submodule.{0, u1} Int M Int.semiring (AddCommGroup.toAddCommMonoid.{u1} M _inst_1) (AddCommGroup.intModule.{u1} M _inst_1))) (RelIso.hasCoeToFun.{u1, u1} (AddSubgroup.{u1} M (AddCommGroup.toAddGroup.{u1} M _inst_1)) (Submodule.{0, u1} Int M Int.semiring (AddCommGroup.toAddCommMonoid.{u1} M _inst_1) (AddCommGroup.intModule.{u1} M _inst_1)) (LE.le.{u1} (AddSubgroup.{u1} M (AddCommGroup.toAddGroup.{u1} M _inst_1)) (Preorder.toLE.{u1} (AddSubgroup.{u1} M (AddCommGroup.toAddGroup.{u1} M _inst_1)) (PartialOrder.toPreorder.{u1} (AddSubgroup.{u1} M (AddCommGroup.toAddGroup.{u1} M _inst_1)) (CompleteSemilatticeInf.toPartialOrder.{u1} (AddSubgroup.{u1} M (AddCommGroup.toAddGroup.{u1} M _inst_1)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (AddSubgroup.{u1} M (AddCommGroup.toAddGroup.{u1} M _inst_1)) (AddSubgroup.completeLattice.{u1} M (AddCommGroup.toAddGroup.{u1} M _inst_1))))))) (LE.le.{u1} (Submodule.{0, u1} Int M Int.semiring (AddCommGroup.toAddCommMonoid.{u1} M _inst_1) (AddCommGroup.intModule.{u1} M _inst_1)) (Preorder.toLE.{u1} (Submodule.{0, u1} Int M Int.semiring (AddCommGroup.toAddCommMonoid.{u1} M _inst_1) (AddCommGroup.intModule.{u1} M _inst_1)) (PartialOrder.toPreorder.{u1} (Submodule.{0, u1} Int M Int.semiring (AddCommGroup.toAddCommMonoid.{u1} M _inst_1) (AddCommGroup.intModule.{u1} M _inst_1)) (CompleteSemilatticeInf.toPartialOrder.{u1} (Submodule.{0, u1} Int M Int.semiring (AddCommGroup.toAddCommMonoid.{u1} M _inst_1) (AddCommGroup.intModule.{u1} M _inst_1)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (Submodule.{0, u1} Int M Int.semiring (AddCommGroup.toAddCommMonoid.{u1} M _inst_1) (AddCommGroup.intModule.{u1} M _inst_1)) (Submodule.completeLattice.{0, u1} Int M Int.semiring (AddCommGroup.toAddCommMonoid.{u1} M _inst_1) (AddCommGroup.intModule.{u1} M _inst_1)))))))) (AddSubgroup.toIntSubmodule.{u1} M _inst_1) S)) ((fun (a : Type.{u1}) (b : Type.{u1}) [self : HasLiftT.{succ u1, succ u1} a b] => self.0) (AddSubgroup.{u1} M (AddCommGroup.toAddGroup.{u1} M _inst_1)) (Set.{u1} M) (HasLiftT.mk.{succ u1, succ u1} (AddSubgroup.{u1} M (AddCommGroup.toAddGroup.{u1} M _inst_1)) (Set.{u1} M) (CoeTCₓ.coe.{succ u1, succ u1} (AddSubgroup.{u1} M (AddCommGroup.toAddGroup.{u1} M _inst_1)) (Set.{u1} M) (SetLike.Set.hasCoeT.{u1, u1} (AddSubgroup.{u1} M (AddCommGroup.toAddGroup.{u1} M _inst_1)) M (AddSubgroup.setLike.{u1} M (AddCommGroup.toAddGroup.{u1} M _inst_1))))) S)
 but is expected to have type
-  forall {M : Type.{u1}} [_inst_1 : AddCommGroup.{u1} M] (S : AddSubgroup.{u1} M (AddCommGroup.toAddGroup.{u1} M _inst_1)), Eq.{succ u1} (Set.{u1} M) (SetLike.coe.{u1, u1} ((fun (x._@.Mathlib.Data.FunLike.Embedding._hyg.19 : AddSubgroup.{u1} M (AddCommGroup.toAddGroup.{u1} M _inst_1)) => Submodule.{0, u1} Int M Int.instSemiringInt (AddCommGroup.toAddCommMonoid.{u1} M _inst_1) (AddCommGroup.intModule.{u1} M _inst_1)) S) M (Submodule.instSetLikeSubmodule.{0, u1} Int M Int.instSemiringInt (AddCommGroup.toAddCommMonoid.{u1} M _inst_1) (AddCommGroup.intModule.{u1} M _inst_1)) (FunLike.coe.{succ u1, succ u1, succ u1} (Function.Embedding.{succ u1, succ u1} (AddSubgroup.{u1} M (AddCommGroup.toAddGroup.{u1} M _inst_1)) (Submodule.{0, u1} Int M Int.instSemiringInt (AddCommGroup.toAddCommMonoid.{u1} M _inst_1) (AddCommGroup.intModule.{u1} M _inst_1))) (AddSubgroup.{u1} M (AddCommGroup.toAddGroup.{u1} M _inst_1)) (fun (_x : AddSubgroup.{u1} M (AddCommGroup.toAddGroup.{u1} M _inst_1)) => (fun (x._@.Mathlib.Data.FunLike.Embedding._hyg.19 : AddSubgroup.{u1} M (AddCommGroup.toAddGroup.{u1} M _inst_1)) => Submodule.{0, u1} Int M Int.instSemiringInt (AddCommGroup.toAddCommMonoid.{u1} M _inst_1) (AddCommGroup.intModule.{u1} M _inst_1)) _x) (EmbeddingLike.toFunLike.{succ u1, succ u1, succ u1} (Function.Embedding.{succ u1, succ u1} (AddSubgroup.{u1} M (AddCommGroup.toAddGroup.{u1} M _inst_1)) (Submodule.{0, u1} Int M Int.instSemiringInt (AddCommGroup.toAddCommMonoid.{u1} M _inst_1) (AddCommGroup.intModule.{u1} M _inst_1))) (AddSubgroup.{u1} M (AddCommGroup.toAddGroup.{u1} M _inst_1)) (Submodule.{0, u1} Int M Int.instSemiringInt (AddCommGroup.toAddCommMonoid.{u1} M _inst_1) (AddCommGroup.intModule.{u1} M _inst_1)) (Function.instEmbeddingLikeEmbedding.{succ u1, succ u1} (AddSubgroup.{u1} M (AddCommGroup.toAddGroup.{u1} M _inst_1)) (Submodule.{0, u1} Int M Int.instSemiringInt (AddCommGroup.toAddCommMonoid.{u1} M _inst_1) (AddCommGroup.intModule.{u1} M _inst_1)))) (RelEmbedding.toEmbedding.{u1, u1} (AddSubgroup.{u1} M (AddCommGroup.toAddGroup.{u1} M _inst_1)) (Submodule.{0, u1} Int M Int.instSemiringInt (AddCommGroup.toAddCommMonoid.{u1} M _inst_1) (AddCommGroup.intModule.{u1} M _inst_1)) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1281 : AddSubgroup.{u1} M (AddCommGroup.toAddGroup.{u1} M _inst_1)) (x._@.Mathlib.Order.Hom.Basic._hyg.1283 : AddSubgroup.{u1} M (AddCommGroup.toAddGroup.{u1} M _inst_1)) => LE.le.{u1} (AddSubgroup.{u1} M (AddCommGroup.toAddGroup.{u1} M _inst_1)) (Preorder.toLE.{u1} (AddSubgroup.{u1} M (AddCommGroup.toAddGroup.{u1} M _inst_1)) (PartialOrder.toPreorder.{u1} (AddSubgroup.{u1} M (AddCommGroup.toAddGroup.{u1} M _inst_1)) (CompleteSemilatticeInf.toPartialOrder.{u1} (AddSubgroup.{u1} M (AddCommGroup.toAddGroup.{u1} M _inst_1)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (AddSubgroup.{u1} M (AddCommGroup.toAddGroup.{u1} M _inst_1)) (AddSubgroup.instCompleteLatticeAddSubgroup.{u1} M (AddCommGroup.toAddGroup.{u1} M _inst_1)))))) x._@.Mathlib.Order.Hom.Basic._hyg.1281 x._@.Mathlib.Order.Hom.Basic._hyg.1283) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1296 : Submodule.{0, u1} Int M Int.instSemiringInt (AddCommGroup.toAddCommMonoid.{u1} M _inst_1) (AddCommGroup.intModule.{u1} M _inst_1)) (x._@.Mathlib.Order.Hom.Basic._hyg.1298 : Submodule.{0, u1} Int M Int.instSemiringInt (AddCommGroup.toAddCommMonoid.{u1} M _inst_1) (AddCommGroup.intModule.{u1} M _inst_1)) => LE.le.{u1} (Submodule.{0, u1} Int M Int.instSemiringInt (AddCommGroup.toAddCommMonoid.{u1} M _inst_1) (AddCommGroup.intModule.{u1} M _inst_1)) (Preorder.toLE.{u1} (Submodule.{0, u1} Int M Int.instSemiringInt (AddCommGroup.toAddCommMonoid.{u1} M _inst_1) (AddCommGroup.intModule.{u1} M _inst_1)) (PartialOrder.toPreorder.{u1} (Submodule.{0, u1} Int M Int.instSemiringInt (AddCommGroup.toAddCommMonoid.{u1} M _inst_1) (AddCommGroup.intModule.{u1} M _inst_1)) (CompleteSemilatticeInf.toPartialOrder.{u1} (Submodule.{0, u1} Int M Int.instSemiringInt (AddCommGroup.toAddCommMonoid.{u1} M _inst_1) (AddCommGroup.intModule.{u1} M _inst_1)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (Submodule.{0, u1} Int M Int.instSemiringInt (AddCommGroup.toAddCommMonoid.{u1} M _inst_1) (AddCommGroup.intModule.{u1} M _inst_1)) (Submodule.completeLattice.{0, u1} Int M Int.instSemiringInt (AddCommGroup.toAddCommMonoid.{u1} M _inst_1) (AddCommGroup.intModule.{u1} M _inst_1)))))) x._@.Mathlib.Order.Hom.Basic._hyg.1296 x._@.Mathlib.Order.Hom.Basic._hyg.1298) (RelIso.toRelEmbedding.{u1, u1} (AddSubgroup.{u1} M (AddCommGroup.toAddGroup.{u1} M _inst_1)) (Submodule.{0, u1} Int M Int.instSemiringInt (AddCommGroup.toAddCommMonoid.{u1} M _inst_1) (AddCommGroup.intModule.{u1} M _inst_1)) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1281 : AddSubgroup.{u1} M (AddCommGroup.toAddGroup.{u1} M _inst_1)) (x._@.Mathlib.Order.Hom.Basic._hyg.1283 : AddSubgroup.{u1} M (AddCommGroup.toAddGroup.{u1} M _inst_1)) => LE.le.{u1} (AddSubgroup.{u1} M (AddCommGroup.toAddGroup.{u1} M _inst_1)) (Preorder.toLE.{u1} (AddSubgroup.{u1} M (AddCommGroup.toAddGroup.{u1} M _inst_1)) (PartialOrder.toPreorder.{u1} (AddSubgroup.{u1} M (AddCommGroup.toAddGroup.{u1} M _inst_1)) (CompleteSemilatticeInf.toPartialOrder.{u1} (AddSubgroup.{u1} M (AddCommGroup.toAddGroup.{u1} M _inst_1)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (AddSubgroup.{u1} M (AddCommGroup.toAddGroup.{u1} M _inst_1)) (AddSubgroup.instCompleteLatticeAddSubgroup.{u1} M (AddCommGroup.toAddGroup.{u1} M _inst_1)))))) x._@.Mathlib.Order.Hom.Basic._hyg.1281 x._@.Mathlib.Order.Hom.Basic._hyg.1283) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1296 : Submodule.{0, u1} Int M Int.instSemiringInt (AddCommGroup.toAddCommMonoid.{u1} M _inst_1) (AddCommGroup.intModule.{u1} M _inst_1)) (x._@.Mathlib.Order.Hom.Basic._hyg.1298 : Submodule.{0, u1} Int M Int.instSemiringInt (AddCommGroup.toAddCommMonoid.{u1} M _inst_1) (AddCommGroup.intModule.{u1} M _inst_1)) => LE.le.{u1} (Submodule.{0, u1} Int M Int.instSemiringInt (AddCommGroup.toAddCommMonoid.{u1} M _inst_1) (AddCommGroup.intModule.{u1} M _inst_1)) (Preorder.toLE.{u1} (Submodule.{0, u1} Int M Int.instSemiringInt (AddCommGroup.toAddCommMonoid.{u1} M _inst_1) (AddCommGroup.intModule.{u1} M _inst_1)) (PartialOrder.toPreorder.{u1} (Submodule.{0, u1} Int M Int.instSemiringInt (AddCommGroup.toAddCommMonoid.{u1} M _inst_1) (AddCommGroup.intModule.{u1} M _inst_1)) (CompleteSemilatticeInf.toPartialOrder.{u1} (Submodule.{0, u1} Int M Int.instSemiringInt (AddCommGroup.toAddCommMonoid.{u1} M _inst_1) (AddCommGroup.intModule.{u1} M _inst_1)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (Submodule.{0, u1} Int M Int.instSemiringInt (AddCommGroup.toAddCommMonoid.{u1} M _inst_1) (AddCommGroup.intModule.{u1} M _inst_1)) (Submodule.completeLattice.{0, u1} Int M Int.instSemiringInt (AddCommGroup.toAddCommMonoid.{u1} M _inst_1) (AddCommGroup.intModule.{u1} M _inst_1)))))) x._@.Mathlib.Order.Hom.Basic._hyg.1296 x._@.Mathlib.Order.Hom.Basic._hyg.1298) (AddSubgroup.toIntSubmodule.{u1} M _inst_1))) S)) (SetLike.coe.{u1, u1} (AddSubgroup.{u1} M (AddCommGroup.toAddGroup.{u1} M _inst_1)) M (AddSubgroup.instSetLikeAddSubgroup.{u1} M (AddCommGroup.toAddGroup.{u1} M _inst_1)) S)
+  forall {M : Type.{u1}} [_inst_1 : AddCommGroup.{u1} M] (S : AddSubgroup.{u1} M (AddCommGroup.toAddGroup.{u1} M _inst_1)), Eq.{succ u1} (Set.{u1} M) (SetLike.coe.{u1, u1} ((fun (x._@.Mathlib.Data.FunLike.Embedding._hyg.19 : AddSubgroup.{u1} M (AddCommGroup.toAddGroup.{u1} M _inst_1)) => Submodule.{0, u1} Int M Int.instSemiringInt (AddCommGroup.toAddCommMonoid.{u1} M _inst_1) (AddCommGroup.intModule.{u1} M _inst_1)) S) M (Submodule.setLike.{0, u1} Int M Int.instSemiringInt (AddCommGroup.toAddCommMonoid.{u1} M _inst_1) (AddCommGroup.intModule.{u1} M _inst_1)) (FunLike.coe.{succ u1, succ u1, succ u1} (Function.Embedding.{succ u1, succ u1} (AddSubgroup.{u1} M (AddCommGroup.toAddGroup.{u1} M _inst_1)) (Submodule.{0, u1} Int M Int.instSemiringInt (AddCommGroup.toAddCommMonoid.{u1} M _inst_1) (AddCommGroup.intModule.{u1} M _inst_1))) (AddSubgroup.{u1} M (AddCommGroup.toAddGroup.{u1} M _inst_1)) (fun (_x : AddSubgroup.{u1} M (AddCommGroup.toAddGroup.{u1} M _inst_1)) => (fun (x._@.Mathlib.Data.FunLike.Embedding._hyg.19 : AddSubgroup.{u1} M (AddCommGroup.toAddGroup.{u1} M _inst_1)) => Submodule.{0, u1} Int M Int.instSemiringInt (AddCommGroup.toAddCommMonoid.{u1} M _inst_1) (AddCommGroup.intModule.{u1} M _inst_1)) _x) (EmbeddingLike.toFunLike.{succ u1, succ u1, succ u1} (Function.Embedding.{succ u1, succ u1} (AddSubgroup.{u1} M (AddCommGroup.toAddGroup.{u1} M _inst_1)) (Submodule.{0, u1} Int M Int.instSemiringInt (AddCommGroup.toAddCommMonoid.{u1} M _inst_1) (AddCommGroup.intModule.{u1} M _inst_1))) (AddSubgroup.{u1} M (AddCommGroup.toAddGroup.{u1} M _inst_1)) (Submodule.{0, u1} Int M Int.instSemiringInt (AddCommGroup.toAddCommMonoid.{u1} M _inst_1) (AddCommGroup.intModule.{u1} M _inst_1)) (Function.instEmbeddingLikeEmbedding.{succ u1, succ u1} (AddSubgroup.{u1} M (AddCommGroup.toAddGroup.{u1} M _inst_1)) (Submodule.{0, u1} Int M Int.instSemiringInt (AddCommGroup.toAddCommMonoid.{u1} M _inst_1) (AddCommGroup.intModule.{u1} M _inst_1)))) (RelEmbedding.toEmbedding.{u1, u1} (AddSubgroup.{u1} M (AddCommGroup.toAddGroup.{u1} M _inst_1)) (Submodule.{0, u1} Int M Int.instSemiringInt (AddCommGroup.toAddCommMonoid.{u1} M _inst_1) (AddCommGroup.intModule.{u1} M _inst_1)) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1281 : AddSubgroup.{u1} M (AddCommGroup.toAddGroup.{u1} M _inst_1)) (x._@.Mathlib.Order.Hom.Basic._hyg.1283 : AddSubgroup.{u1} M (AddCommGroup.toAddGroup.{u1} M _inst_1)) => LE.le.{u1} (AddSubgroup.{u1} M (AddCommGroup.toAddGroup.{u1} M _inst_1)) (Preorder.toLE.{u1} (AddSubgroup.{u1} M (AddCommGroup.toAddGroup.{u1} M _inst_1)) (PartialOrder.toPreorder.{u1} (AddSubgroup.{u1} M (AddCommGroup.toAddGroup.{u1} M _inst_1)) (CompleteSemilatticeInf.toPartialOrder.{u1} (AddSubgroup.{u1} M (AddCommGroup.toAddGroup.{u1} M _inst_1)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (AddSubgroup.{u1} M (AddCommGroup.toAddGroup.{u1} M _inst_1)) (AddSubgroup.instCompleteLatticeAddSubgroup.{u1} M (AddCommGroup.toAddGroup.{u1} M _inst_1)))))) x._@.Mathlib.Order.Hom.Basic._hyg.1281 x._@.Mathlib.Order.Hom.Basic._hyg.1283) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1296 : Submodule.{0, u1} Int M Int.instSemiringInt (AddCommGroup.toAddCommMonoid.{u1} M _inst_1) (AddCommGroup.intModule.{u1} M _inst_1)) (x._@.Mathlib.Order.Hom.Basic._hyg.1298 : Submodule.{0, u1} Int M Int.instSemiringInt (AddCommGroup.toAddCommMonoid.{u1} M _inst_1) (AddCommGroup.intModule.{u1} M _inst_1)) => LE.le.{u1} (Submodule.{0, u1} Int M Int.instSemiringInt (AddCommGroup.toAddCommMonoid.{u1} M _inst_1) (AddCommGroup.intModule.{u1} M _inst_1)) (Preorder.toLE.{u1} (Submodule.{0, u1} Int M Int.instSemiringInt (AddCommGroup.toAddCommMonoid.{u1} M _inst_1) (AddCommGroup.intModule.{u1} M _inst_1)) (PartialOrder.toPreorder.{u1} (Submodule.{0, u1} Int M Int.instSemiringInt (AddCommGroup.toAddCommMonoid.{u1} M _inst_1) (AddCommGroup.intModule.{u1} M _inst_1)) (CompleteSemilatticeInf.toPartialOrder.{u1} (Submodule.{0, u1} Int M Int.instSemiringInt (AddCommGroup.toAddCommMonoid.{u1} M _inst_1) (AddCommGroup.intModule.{u1} M _inst_1)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (Submodule.{0, u1} Int M Int.instSemiringInt (AddCommGroup.toAddCommMonoid.{u1} M _inst_1) (AddCommGroup.intModule.{u1} M _inst_1)) (Submodule.completeLattice.{0, u1} Int M Int.instSemiringInt (AddCommGroup.toAddCommMonoid.{u1} M _inst_1) (AddCommGroup.intModule.{u1} M _inst_1)))))) x._@.Mathlib.Order.Hom.Basic._hyg.1296 x._@.Mathlib.Order.Hom.Basic._hyg.1298) (RelIso.toRelEmbedding.{u1, u1} (AddSubgroup.{u1} M (AddCommGroup.toAddGroup.{u1} M _inst_1)) (Submodule.{0, u1} Int M Int.instSemiringInt (AddCommGroup.toAddCommMonoid.{u1} M _inst_1) (AddCommGroup.intModule.{u1} M _inst_1)) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1281 : AddSubgroup.{u1} M (AddCommGroup.toAddGroup.{u1} M _inst_1)) (x._@.Mathlib.Order.Hom.Basic._hyg.1283 : AddSubgroup.{u1} M (AddCommGroup.toAddGroup.{u1} M _inst_1)) => LE.le.{u1} (AddSubgroup.{u1} M (AddCommGroup.toAddGroup.{u1} M _inst_1)) (Preorder.toLE.{u1} (AddSubgroup.{u1} M (AddCommGroup.toAddGroup.{u1} M _inst_1)) (PartialOrder.toPreorder.{u1} (AddSubgroup.{u1} M (AddCommGroup.toAddGroup.{u1} M _inst_1)) (CompleteSemilatticeInf.toPartialOrder.{u1} (AddSubgroup.{u1} M (AddCommGroup.toAddGroup.{u1} M _inst_1)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (AddSubgroup.{u1} M (AddCommGroup.toAddGroup.{u1} M _inst_1)) (AddSubgroup.instCompleteLatticeAddSubgroup.{u1} M (AddCommGroup.toAddGroup.{u1} M _inst_1)))))) x._@.Mathlib.Order.Hom.Basic._hyg.1281 x._@.Mathlib.Order.Hom.Basic._hyg.1283) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1296 : Submodule.{0, u1} Int M Int.instSemiringInt (AddCommGroup.toAddCommMonoid.{u1} M _inst_1) (AddCommGroup.intModule.{u1} M _inst_1)) (x._@.Mathlib.Order.Hom.Basic._hyg.1298 : Submodule.{0, u1} Int M Int.instSemiringInt (AddCommGroup.toAddCommMonoid.{u1} M _inst_1) (AddCommGroup.intModule.{u1} M _inst_1)) => LE.le.{u1} (Submodule.{0, u1} Int M Int.instSemiringInt (AddCommGroup.toAddCommMonoid.{u1} M _inst_1) (AddCommGroup.intModule.{u1} M _inst_1)) (Preorder.toLE.{u1} (Submodule.{0, u1} Int M Int.instSemiringInt (AddCommGroup.toAddCommMonoid.{u1} M _inst_1) (AddCommGroup.intModule.{u1} M _inst_1)) (PartialOrder.toPreorder.{u1} (Submodule.{0, u1} Int M Int.instSemiringInt (AddCommGroup.toAddCommMonoid.{u1} M _inst_1) (AddCommGroup.intModule.{u1} M _inst_1)) (CompleteSemilatticeInf.toPartialOrder.{u1} (Submodule.{0, u1} Int M Int.instSemiringInt (AddCommGroup.toAddCommMonoid.{u1} M _inst_1) (AddCommGroup.intModule.{u1} M _inst_1)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (Submodule.{0, u1} Int M Int.instSemiringInt (AddCommGroup.toAddCommMonoid.{u1} M _inst_1) (AddCommGroup.intModule.{u1} M _inst_1)) (Submodule.completeLattice.{0, u1} Int M Int.instSemiringInt (AddCommGroup.toAddCommMonoid.{u1} M _inst_1) (AddCommGroup.intModule.{u1} M _inst_1)))))) x._@.Mathlib.Order.Hom.Basic._hyg.1296 x._@.Mathlib.Order.Hom.Basic._hyg.1298) (AddSubgroup.toIntSubmodule.{u1} M _inst_1))) S)) (SetLike.coe.{u1, u1} (AddSubgroup.{u1} M (AddCommGroup.toAddGroup.{u1} M _inst_1)) M (AddSubgroup.instSetLikeAddSubgroup.{u1} M (AddCommGroup.toAddGroup.{u1} M _inst_1)) S)
 Case conversion may be inaccurate. Consider using '#align add_subgroup.coe_to_int_submodule AddSubgroup.coe_toIntSubmoduleₓ'. -/
 @[simp]
 theorem AddSubgroup.coe_toIntSubmodule (S : AddSubgroup M) : (S.toIntSubmodule : Set M) = S :=

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

@@ -354,7 +354,7 @@ private theorem le_Inf' {S : Set (Submodule R M)} {p} : (∀ q ∈ S, p ≤ q) 
   Set.subset_interᵢ₂
 #align submodule.le_Inf' submodule.le_Inf'
 
-instance : HasInf (Submodule R M) :=
+instance : Inf (Submodule R M) :=
   ⟨fun p q =>
     { carrier := p ∩ q
       zero_mem' := by simp [zero_mem]
@@ -381,9 +381,9 @@ instance : CompleteLattice (Submodule R M) :=
 
 /- warning: submodule.inf_coe -> Submodule.inf_coe is a dubious translation:
 lean 3 declaration is
-  forall {R : Type.{u1}} {M : Type.{u2}} [_inst_1 : Semiring.{u1} R] [_inst_3 : AddCommMonoid.{u2} M] [_inst_4 : Module.{u1, u2} R M _inst_1 _inst_3] {p : Submodule.{u1, u2} R M _inst_1 _inst_3 _inst_4} {q : Submodule.{u1, u2} R M _inst_1 _inst_3 _inst_4}, Eq.{succ u2} (Set.{u2} M) ((fun (a : Type.{u2}) (b : Type.{u2}) [self : HasLiftT.{succ u2, succ u2} a b] => self.0) (Submodule.{u1, u2} R M _inst_1 _inst_3 _inst_4) (Set.{u2} M) (HasLiftT.mk.{succ u2, succ u2} (Submodule.{u1, u2} R M _inst_1 _inst_3 _inst_4) (Set.{u2} M) (CoeTCₓ.coe.{succ u2, succ u2} (Submodule.{u1, u2} R M _inst_1 _inst_3 _inst_4) (Set.{u2} M) (SetLike.Set.hasCoeT.{u2, u2} (Submodule.{u1, u2} R M _inst_1 _inst_3 _inst_4) M (Submodule.setLike.{u1, u2} R M _inst_1 _inst_3 _inst_4)))) (HasInf.inf.{u2} (Submodule.{u1, u2} R M _inst_1 _inst_3 _inst_4) (Submodule.hasInf.{u1, u2} R M _inst_1 _inst_3 _inst_4) p q)) (Inter.inter.{u2} (Set.{u2} M) (Set.hasInter.{u2} M) ((fun (a : Type.{u2}) (b : Type.{u2}) [self : HasLiftT.{succ u2, succ u2} a b] => self.0) (Submodule.{u1, u2} R M _inst_1 _inst_3 _inst_4) (Set.{u2} M) (HasLiftT.mk.{succ u2, succ u2} (Submodule.{u1, u2} R M _inst_1 _inst_3 _inst_4) (Set.{u2} M) (CoeTCₓ.coe.{succ u2, succ u2} (Submodule.{u1, u2} R M _inst_1 _inst_3 _inst_4) (Set.{u2} M) (SetLike.Set.hasCoeT.{u2, u2} (Submodule.{u1, u2} R M _inst_1 _inst_3 _inst_4) M (Submodule.setLike.{u1, u2} R M _inst_1 _inst_3 _inst_4)))) p) ((fun (a : Type.{u2}) (b : Type.{u2}) [self : HasLiftT.{succ u2, succ u2} a b] => self.0) (Submodule.{u1, u2} R M _inst_1 _inst_3 _inst_4) (Set.{u2} M) (HasLiftT.mk.{succ u2, succ u2} (Submodule.{u1, u2} R M _inst_1 _inst_3 _inst_4) (Set.{u2} M) (CoeTCₓ.coe.{succ u2, succ u2} (Submodule.{u1, u2} R M _inst_1 _inst_3 _inst_4) (Set.{u2} M) (SetLike.Set.hasCoeT.{u2, u2} (Submodule.{u1, u2} R M _inst_1 _inst_3 _inst_4) M (Submodule.setLike.{u1, u2} R M _inst_1 _inst_3 _inst_4)))) q))
+  forall {R : Type.{u1}} {M : Type.{u2}} [_inst_1 : Semiring.{u1} R] [_inst_3 : AddCommMonoid.{u2} M] [_inst_4 : Module.{u1, u2} R M _inst_1 _inst_3] {p : Submodule.{u1, u2} R M _inst_1 _inst_3 _inst_4} {q : Submodule.{u1, u2} R M _inst_1 _inst_3 _inst_4}, Eq.{succ u2} (Set.{u2} M) ((fun (a : Type.{u2}) (b : Type.{u2}) [self : HasLiftT.{succ u2, succ u2} a b] => self.0) (Submodule.{u1, u2} R M _inst_1 _inst_3 _inst_4) (Set.{u2} M) (HasLiftT.mk.{succ u2, succ u2} (Submodule.{u1, u2} R M _inst_1 _inst_3 _inst_4) (Set.{u2} M) (CoeTCₓ.coe.{succ u2, succ u2} (Submodule.{u1, u2} R M _inst_1 _inst_3 _inst_4) (Set.{u2} M) (SetLike.Set.hasCoeT.{u2, u2} (Submodule.{u1, u2} R M _inst_1 _inst_3 _inst_4) M (Submodule.setLike.{u1, u2} R M _inst_1 _inst_3 _inst_4)))) (Inf.inf.{u2} (Submodule.{u1, u2} R M _inst_1 _inst_3 _inst_4) (Submodule.hasInf.{u1, u2} R M _inst_1 _inst_3 _inst_4) p q)) (Inter.inter.{u2} (Set.{u2} M) (Set.hasInter.{u2} M) ((fun (a : Type.{u2}) (b : Type.{u2}) [self : HasLiftT.{succ u2, succ u2} a b] => self.0) (Submodule.{u1, u2} R M _inst_1 _inst_3 _inst_4) (Set.{u2} M) (HasLiftT.mk.{succ u2, succ u2} (Submodule.{u1, u2} R M _inst_1 _inst_3 _inst_4) (Set.{u2} M) (CoeTCₓ.coe.{succ u2, succ u2} (Submodule.{u1, u2} R M _inst_1 _inst_3 _inst_4) (Set.{u2} M) (SetLike.Set.hasCoeT.{u2, u2} (Submodule.{u1, u2} R M _inst_1 _inst_3 _inst_4) M (Submodule.setLike.{u1, u2} R M _inst_1 _inst_3 _inst_4)))) p) ((fun (a : Type.{u2}) (b : Type.{u2}) [self : HasLiftT.{succ u2, succ u2} a b] => self.0) (Submodule.{u1, u2} R M _inst_1 _inst_3 _inst_4) (Set.{u2} M) (HasLiftT.mk.{succ u2, succ u2} (Submodule.{u1, u2} R M _inst_1 _inst_3 _inst_4) (Set.{u2} M) (CoeTCₓ.coe.{succ u2, succ u2} (Submodule.{u1, u2} R M _inst_1 _inst_3 _inst_4) (Set.{u2} M) (SetLike.Set.hasCoeT.{u2, u2} (Submodule.{u1, u2} R M _inst_1 _inst_3 _inst_4) M (Submodule.setLike.{u1, u2} R M _inst_1 _inst_3 _inst_4)))) q))
 but is expected to have type
-  forall {R : Type.{u1}} {M : Type.{u2}} [_inst_1 : Semiring.{u1} R] [_inst_3 : AddCommMonoid.{u2} M] [_inst_4 : Module.{u1, u2} R M _inst_1 _inst_3] {p : Submodule.{u1, u2} R M _inst_1 _inst_3 _inst_4} {q : Submodule.{u1, u2} R M _inst_1 _inst_3 _inst_4}, Eq.{succ u2} (Set.{u2} M) (SetLike.coe.{u2, u2} (Submodule.{u1, u2} R M _inst_1 _inst_3 _inst_4) M (Submodule.instSetLikeSubmodule.{u1, u2} R M _inst_1 _inst_3 _inst_4) (HasInf.inf.{u2} (Submodule.{u1, u2} R M _inst_1 _inst_3 _inst_4) (Submodule.instHasInfSubmodule.{u1, u2} R M _inst_1 _inst_3 _inst_4) p q)) (Inter.inter.{u2} (Set.{u2} M) (Set.instInterSet.{u2} M) (SetLike.coe.{u2, u2} (Submodule.{u1, u2} R M _inst_1 _inst_3 _inst_4) M (Submodule.instSetLikeSubmodule.{u1, u2} R M _inst_1 _inst_3 _inst_4) p) (SetLike.coe.{u2, u2} (Submodule.{u1, u2} R M _inst_1 _inst_3 _inst_4) M (Submodule.instSetLikeSubmodule.{u1, u2} R M _inst_1 _inst_3 _inst_4) q))
+  forall {R : Type.{u1}} {M : Type.{u2}} [_inst_1 : Semiring.{u1} R] [_inst_3 : AddCommMonoid.{u2} M] [_inst_4 : Module.{u1, u2} R M _inst_1 _inst_3] {p : Submodule.{u1, u2} R M _inst_1 _inst_3 _inst_4} {q : Submodule.{u1, u2} R M _inst_1 _inst_3 _inst_4}, Eq.{succ u2} (Set.{u2} M) (SetLike.coe.{u2, u2} (Submodule.{u1, u2} R M _inst_1 _inst_3 _inst_4) M (Submodule.instSetLikeSubmodule.{u1, u2} R M _inst_1 _inst_3 _inst_4) (Inf.inf.{u2} (Submodule.{u1, u2} R M _inst_1 _inst_3 _inst_4) (Submodule.instInfSubmodule.{u1, u2} R M _inst_1 _inst_3 _inst_4) p q)) (Inter.inter.{u2} (Set.{u2} M) (Set.instInterSet.{u2} M) (SetLike.coe.{u2, u2} (Submodule.{u1, u2} R M _inst_1 _inst_3 _inst_4) M (Submodule.instSetLikeSubmodule.{u1, u2} R M _inst_1 _inst_3 _inst_4) p) (SetLike.coe.{u2, u2} (Submodule.{u1, u2} R M _inst_1 _inst_3 _inst_4) M (Submodule.instSetLikeSubmodule.{u1, u2} R M _inst_1 _inst_3 _inst_4) q))
 Case conversion may be inaccurate. Consider using '#align submodule.inf_coe Submodule.inf_coeₓ'. -/
 @[simp]
 theorem inf_coe : ↑(p ⊓ q) = (p ∩ q : Set M) :=
@@ -392,9 +392,9 @@ theorem inf_coe : ↑(p ⊓ q) = (p ∩ q : Set M) :=
 
 /- warning: submodule.mem_inf -> Submodule.mem_inf is a dubious translation:
 lean 3 declaration is
-  forall {R : Type.{u1}} {M : Type.{u2}} [_inst_1 : Semiring.{u1} R] [_inst_3 : AddCommMonoid.{u2} M] [_inst_4 : Module.{u1, u2} R M _inst_1 _inst_3] {p : Submodule.{u1, u2} R M _inst_1 _inst_3 _inst_4} {q : Submodule.{u1, u2} R M _inst_1 _inst_3 _inst_4} {x : M}, Iff (Membership.Mem.{u2, u2} M (Submodule.{u1, u2} R M _inst_1 _inst_3 _inst_4) (SetLike.hasMem.{u2, u2} (Submodule.{u1, u2} R M _inst_1 _inst_3 _inst_4) M (Submodule.setLike.{u1, u2} R M _inst_1 _inst_3 _inst_4)) x (HasInf.inf.{u2} (Submodule.{u1, u2} R M _inst_1 _inst_3 _inst_4) (Submodule.hasInf.{u1, u2} R M _inst_1 _inst_3 _inst_4) p q)) (And (Membership.Mem.{u2, u2} M (Submodule.{u1, u2} R M _inst_1 _inst_3 _inst_4) (SetLike.hasMem.{u2, u2} (Submodule.{u1, u2} R M _inst_1 _inst_3 _inst_4) M (Submodule.setLike.{u1, u2} R M _inst_1 _inst_3 _inst_4)) x p) (Membership.Mem.{u2, u2} M (Submodule.{u1, u2} R M _inst_1 _inst_3 _inst_4) (SetLike.hasMem.{u2, u2} (Submodule.{u1, u2} R M _inst_1 _inst_3 _inst_4) M (Submodule.setLike.{u1, u2} R M _inst_1 _inst_3 _inst_4)) x q))
+  forall {R : Type.{u1}} {M : Type.{u2}} [_inst_1 : Semiring.{u1} R] [_inst_3 : AddCommMonoid.{u2} M] [_inst_4 : Module.{u1, u2} R M _inst_1 _inst_3] {p : Submodule.{u1, u2} R M _inst_1 _inst_3 _inst_4} {q : Submodule.{u1, u2} R M _inst_1 _inst_3 _inst_4} {x : M}, Iff (Membership.Mem.{u2, u2} M (Submodule.{u1, u2} R M _inst_1 _inst_3 _inst_4) (SetLike.hasMem.{u2, u2} (Submodule.{u1, u2} R M _inst_1 _inst_3 _inst_4) M (Submodule.setLike.{u1, u2} R M _inst_1 _inst_3 _inst_4)) x (Inf.inf.{u2} (Submodule.{u1, u2} R M _inst_1 _inst_3 _inst_4) (Submodule.hasInf.{u1, u2} R M _inst_1 _inst_3 _inst_4) p q)) (And (Membership.Mem.{u2, u2} M (Submodule.{u1, u2} R M _inst_1 _inst_3 _inst_4) (SetLike.hasMem.{u2, u2} (Submodule.{u1, u2} R M _inst_1 _inst_3 _inst_4) M (Submodule.setLike.{u1, u2} R M _inst_1 _inst_3 _inst_4)) x p) (Membership.Mem.{u2, u2} M (Submodule.{u1, u2} R M _inst_1 _inst_3 _inst_4) (SetLike.hasMem.{u2, u2} (Submodule.{u1, u2} R M _inst_1 _inst_3 _inst_4) M (Submodule.setLike.{u1, u2} R M _inst_1 _inst_3 _inst_4)) x q))
 but is expected to have type
-  forall {R : Type.{u2}} {M : Type.{u1}} [_inst_1 : Semiring.{u2} R] [_inst_3 : AddCommMonoid.{u1} M] [_inst_4 : Module.{u2, u1} R M _inst_1 _inst_3] {p : Submodule.{u2, u1} R M _inst_1 _inst_3 _inst_4} {q : Submodule.{u2, u1} R M _inst_1 _inst_3 _inst_4} {x : M}, Iff (Membership.mem.{u1, u1} M (Submodule.{u2, u1} R M _inst_1 _inst_3 _inst_4) (SetLike.instMembership.{u1, u1} (Submodule.{u2, u1} R M _inst_1 _inst_3 _inst_4) M (Submodule.instSetLikeSubmodule.{u2, u1} R M _inst_1 _inst_3 _inst_4)) x (HasInf.inf.{u1} (Submodule.{u2, u1} R M _inst_1 _inst_3 _inst_4) (Submodule.instHasInfSubmodule.{u2, u1} R M _inst_1 _inst_3 _inst_4) p q)) (And (Membership.mem.{u1, u1} M (Submodule.{u2, u1} R M _inst_1 _inst_3 _inst_4) (SetLike.instMembership.{u1, u1} (Submodule.{u2, u1} R M _inst_1 _inst_3 _inst_4) M (Submodule.instSetLikeSubmodule.{u2, u1} R M _inst_1 _inst_3 _inst_4)) x p) (Membership.mem.{u1, u1} M (Submodule.{u2, u1} R M _inst_1 _inst_3 _inst_4) (SetLike.instMembership.{u1, u1} (Submodule.{u2, u1} R M _inst_1 _inst_3 _inst_4) M (Submodule.instSetLikeSubmodule.{u2, u1} R M _inst_1 _inst_3 _inst_4)) x q))
+  forall {R : Type.{u2}} {M : Type.{u1}} [_inst_1 : Semiring.{u2} R] [_inst_3 : AddCommMonoid.{u1} M] [_inst_4 : Module.{u2, u1} R M _inst_1 _inst_3] {p : Submodule.{u2, u1} R M _inst_1 _inst_3 _inst_4} {q : Submodule.{u2, u1} R M _inst_1 _inst_3 _inst_4} {x : M}, Iff (Membership.mem.{u1, u1} M (Submodule.{u2, u1} R M _inst_1 _inst_3 _inst_4) (SetLike.instMembership.{u1, u1} (Submodule.{u2, u1} R M _inst_1 _inst_3 _inst_4) M (Submodule.instSetLikeSubmodule.{u2, u1} R M _inst_1 _inst_3 _inst_4)) x (Inf.inf.{u1} (Submodule.{u2, u1} R M _inst_1 _inst_3 _inst_4) (Submodule.instInfSubmodule.{u2, u1} R M _inst_1 _inst_3 _inst_4) p q)) (And (Membership.mem.{u1, u1} M (Submodule.{u2, u1} R M _inst_1 _inst_3 _inst_4) (SetLike.instMembership.{u1, u1} (Submodule.{u2, u1} R M _inst_1 _inst_3 _inst_4) M (Submodule.instSetLikeSubmodule.{u2, u1} R M _inst_1 _inst_3 _inst_4)) x p) (Membership.mem.{u1, u1} M (Submodule.{u2, u1} R M _inst_1 _inst_3 _inst_4) (SetLike.instMembership.{u1, u1} (Submodule.{u2, u1} R M _inst_1 _inst_3 _inst_4) M (Submodule.instSetLikeSubmodule.{u2, u1} R M _inst_1 _inst_3 _inst_4)) x q))
 Case conversion may be inaccurate. Consider using '#align submodule.mem_inf Submodule.mem_infₓ'. -/
 @[simp]
 theorem mem_inf {p q : Submodule R M} {x : M} : x ∈ p ⊓ q ↔ x ∈ p ∧ x ∈ q :=
@@ -476,9 +476,9 @@ theorem mem_finset_inf {ι} {s : Finset ι} {p : ι → Submodule R M} {x : M} :
 
 /- warning: submodule.mem_sup_left -> Submodule.mem_sup_left is a dubious translation:
 lean 3 declaration is
-  forall {R : Type.{u1}} {M : Type.{u2}} [_inst_1 : Semiring.{u1} R] [_inst_3 : AddCommMonoid.{u2} M] [_inst_4 : Module.{u1, u2} R M _inst_1 _inst_3] {S : Submodule.{u1, u2} R M _inst_1 _inst_3 _inst_4} {T : Submodule.{u1, u2} R M _inst_1 _inst_3 _inst_4} {x : M}, (Membership.Mem.{u2, u2} M (Submodule.{u1, u2} R M _inst_1 _inst_3 _inst_4) (SetLike.hasMem.{u2, u2} (Submodule.{u1, u2} R M _inst_1 _inst_3 _inst_4) M (Submodule.setLike.{u1, u2} R M _inst_1 _inst_3 _inst_4)) x S) -> (Membership.Mem.{u2, u2} M (Submodule.{u1, u2} R M _inst_1 _inst_3 _inst_4) (SetLike.hasMem.{u2, u2} (Submodule.{u1, u2} R M _inst_1 _inst_3 _inst_4) M (Submodule.setLike.{u1, u2} R M _inst_1 _inst_3 _inst_4)) x (HasSup.sup.{u2} (Submodule.{u1, u2} R M _inst_1 _inst_3 _inst_4) (SemilatticeSup.toHasSup.{u2} (Submodule.{u1, u2} R M _inst_1 _inst_3 _inst_4) (Lattice.toSemilatticeSup.{u2} (Submodule.{u1, u2} R M _inst_1 _inst_3 _inst_4) (CompleteLattice.toLattice.{u2} (Submodule.{u1, u2} R M _inst_1 _inst_3 _inst_4) (Submodule.completeLattice.{u1, u2} R M _inst_1 _inst_3 _inst_4)))) S T))
+  forall {R : Type.{u1}} {M : Type.{u2}} [_inst_1 : Semiring.{u1} R] [_inst_3 : AddCommMonoid.{u2} M] [_inst_4 : Module.{u1, u2} R M _inst_1 _inst_3] {S : Submodule.{u1, u2} R M _inst_1 _inst_3 _inst_4} {T : Submodule.{u1, u2} R M _inst_1 _inst_3 _inst_4} {x : M}, (Membership.Mem.{u2, u2} M (Submodule.{u1, u2} R M _inst_1 _inst_3 _inst_4) (SetLike.hasMem.{u2, u2} (Submodule.{u1, u2} R M _inst_1 _inst_3 _inst_4) M (Submodule.setLike.{u1, u2} R M _inst_1 _inst_3 _inst_4)) x S) -> (Membership.Mem.{u2, u2} M (Submodule.{u1, u2} R M _inst_1 _inst_3 _inst_4) (SetLike.hasMem.{u2, u2} (Submodule.{u1, u2} R M _inst_1 _inst_3 _inst_4) M (Submodule.setLike.{u1, u2} R M _inst_1 _inst_3 _inst_4)) x (Sup.sup.{u2} (Submodule.{u1, u2} R M _inst_1 _inst_3 _inst_4) (SemilatticeSup.toHasSup.{u2} (Submodule.{u1, u2} R M _inst_1 _inst_3 _inst_4) (Lattice.toSemilatticeSup.{u2} (Submodule.{u1, u2} R M _inst_1 _inst_3 _inst_4) (CompleteLattice.toLattice.{u2} (Submodule.{u1, u2} R M _inst_1 _inst_3 _inst_4) (Submodule.completeLattice.{u1, u2} R M _inst_1 _inst_3 _inst_4)))) S T))
 but is expected to have type
-  forall {R : Type.{u2}} {M : Type.{u1}} [_inst_1 : Semiring.{u2} R] [_inst_3 : AddCommMonoid.{u1} M] [_inst_4 : Module.{u2, u1} R M _inst_1 _inst_3] {S : Submodule.{u2, u1} R M _inst_1 _inst_3 _inst_4} {T : Submodule.{u2, u1} R M _inst_1 _inst_3 _inst_4} {x : M}, (Membership.mem.{u1, u1} M (Submodule.{u2, u1} R M _inst_1 _inst_3 _inst_4) (SetLike.instMembership.{u1, u1} (Submodule.{u2, u1} R M _inst_1 _inst_3 _inst_4) M (Submodule.instSetLikeSubmodule.{u2, u1} R M _inst_1 _inst_3 _inst_4)) x S) -> (Membership.mem.{u1, u1} M (Submodule.{u2, u1} R M _inst_1 _inst_3 _inst_4) (SetLike.instMembership.{u1, u1} (Submodule.{u2, u1} R M _inst_1 _inst_3 _inst_4) M (Submodule.instSetLikeSubmodule.{u2, u1} R M _inst_1 _inst_3 _inst_4)) x (HasSup.sup.{u1} (Submodule.{u2, u1} R M _inst_1 _inst_3 _inst_4) (SemilatticeSup.toHasSup.{u1} (Submodule.{u2, u1} R M _inst_1 _inst_3 _inst_4) (Lattice.toSemilatticeSup.{u1} (Submodule.{u2, u1} R M _inst_1 _inst_3 _inst_4) (CompleteLattice.toLattice.{u1} (Submodule.{u2, u1} R M _inst_1 _inst_3 _inst_4) (Submodule.completeLattice.{u2, u1} R M _inst_1 _inst_3 _inst_4)))) S T))
+  forall {R : Type.{u2}} {M : Type.{u1}} [_inst_1 : Semiring.{u2} R] [_inst_3 : AddCommMonoid.{u1} M] [_inst_4 : Module.{u2, u1} R M _inst_1 _inst_3] {S : Submodule.{u2, u1} R M _inst_1 _inst_3 _inst_4} {T : Submodule.{u2, u1} R M _inst_1 _inst_3 _inst_4} {x : M}, (Membership.mem.{u1, u1} M (Submodule.{u2, u1} R M _inst_1 _inst_3 _inst_4) (SetLike.instMembership.{u1, u1} (Submodule.{u2, u1} R M _inst_1 _inst_3 _inst_4) M (Submodule.instSetLikeSubmodule.{u2, u1} R M _inst_1 _inst_3 _inst_4)) x S) -> (Membership.mem.{u1, u1} M (Submodule.{u2, u1} R M _inst_1 _inst_3 _inst_4) (SetLike.instMembership.{u1, u1} (Submodule.{u2, u1} R M _inst_1 _inst_3 _inst_4) M (Submodule.instSetLikeSubmodule.{u2, u1} R M _inst_1 _inst_3 _inst_4)) x (Sup.sup.{u1} (Submodule.{u2, u1} R M _inst_1 _inst_3 _inst_4) (SemilatticeSup.toSup.{u1} (Submodule.{u2, u1} R M _inst_1 _inst_3 _inst_4) (Lattice.toSemilatticeSup.{u1} (Submodule.{u2, u1} R M _inst_1 _inst_3 _inst_4) (CompleteLattice.toLattice.{u1} (Submodule.{u2, u1} R M _inst_1 _inst_3 _inst_4) (Submodule.completeLattice.{u2, u1} R M _inst_1 _inst_3 _inst_4)))) S T))
 Case conversion may be inaccurate. Consider using '#align submodule.mem_sup_left Submodule.mem_sup_leftₓ'. -/
 theorem mem_sup_left {S T : Submodule R M} : ∀ {x : M}, x ∈ S → x ∈ S ⊔ T :=
   show S ≤ S ⊔ T from le_sup_left
@@ -486,9 +486,9 @@ theorem mem_sup_left {S T : Submodule R M} : ∀ {x : M}, x ∈ S → x ∈ S 
 
 /- warning: submodule.mem_sup_right -> Submodule.mem_sup_right is a dubious translation:
 lean 3 declaration is
-  forall {R : Type.{u1}} {M : Type.{u2}} [_inst_1 : Semiring.{u1} R] [_inst_3 : AddCommMonoid.{u2} M] [_inst_4 : Module.{u1, u2} R M _inst_1 _inst_3] {S : Submodule.{u1, u2} R M _inst_1 _inst_3 _inst_4} {T : Submodule.{u1, u2} R M _inst_1 _inst_3 _inst_4} {x : M}, (Membership.Mem.{u2, u2} M (Submodule.{u1, u2} R M _inst_1 _inst_3 _inst_4) (SetLike.hasMem.{u2, u2} (Submodule.{u1, u2} R M _inst_1 _inst_3 _inst_4) M (Submodule.setLike.{u1, u2} R M _inst_1 _inst_3 _inst_4)) x T) -> (Membership.Mem.{u2, u2} M (Submodule.{u1, u2} R M _inst_1 _inst_3 _inst_4) (SetLike.hasMem.{u2, u2} (Submodule.{u1, u2} R M _inst_1 _inst_3 _inst_4) M (Submodule.setLike.{u1, u2} R M _inst_1 _inst_3 _inst_4)) x (HasSup.sup.{u2} (Submodule.{u1, u2} R M _inst_1 _inst_3 _inst_4) (SemilatticeSup.toHasSup.{u2} (Submodule.{u1, u2} R M _inst_1 _inst_3 _inst_4) (Lattice.toSemilatticeSup.{u2} (Submodule.{u1, u2} R M _inst_1 _inst_3 _inst_4) (CompleteLattice.toLattice.{u2} (Submodule.{u1, u2} R M _inst_1 _inst_3 _inst_4) (Submodule.completeLattice.{u1, u2} R M _inst_1 _inst_3 _inst_4)))) S T))
+  forall {R : Type.{u1}} {M : Type.{u2}} [_inst_1 : Semiring.{u1} R] [_inst_3 : AddCommMonoid.{u2} M] [_inst_4 : Module.{u1, u2} R M _inst_1 _inst_3] {S : Submodule.{u1, u2} R M _inst_1 _inst_3 _inst_4} {T : Submodule.{u1, u2} R M _inst_1 _inst_3 _inst_4} {x : M}, (Membership.Mem.{u2, u2} M (Submodule.{u1, u2} R M _inst_1 _inst_3 _inst_4) (SetLike.hasMem.{u2, u2} (Submodule.{u1, u2} R M _inst_1 _inst_3 _inst_4) M (Submodule.setLike.{u1, u2} R M _inst_1 _inst_3 _inst_4)) x T) -> (Membership.Mem.{u2, u2} M (Submodule.{u1, u2} R M _inst_1 _inst_3 _inst_4) (SetLike.hasMem.{u2, u2} (Submodule.{u1, u2} R M _inst_1 _inst_3 _inst_4) M (Submodule.setLike.{u1, u2} R M _inst_1 _inst_3 _inst_4)) x (Sup.sup.{u2} (Submodule.{u1, u2} R M _inst_1 _inst_3 _inst_4) (SemilatticeSup.toHasSup.{u2} (Submodule.{u1, u2} R M _inst_1 _inst_3 _inst_4) (Lattice.toSemilatticeSup.{u2} (Submodule.{u1, u2} R M _inst_1 _inst_3 _inst_4) (CompleteLattice.toLattice.{u2} (Submodule.{u1, u2} R M _inst_1 _inst_3 _inst_4) (Submodule.completeLattice.{u1, u2} R M _inst_1 _inst_3 _inst_4)))) S T))
 but is expected to have type
-  forall {R : Type.{u2}} {M : Type.{u1}} [_inst_1 : Semiring.{u2} R] [_inst_3 : AddCommMonoid.{u1} M] [_inst_4 : Module.{u2, u1} R M _inst_1 _inst_3] {S : Submodule.{u2, u1} R M _inst_1 _inst_3 _inst_4} {T : Submodule.{u2, u1} R M _inst_1 _inst_3 _inst_4} {x : M}, (Membership.mem.{u1, u1} M (Submodule.{u2, u1} R M _inst_1 _inst_3 _inst_4) (SetLike.instMembership.{u1, u1} (Submodule.{u2, u1} R M _inst_1 _inst_3 _inst_4) M (Submodule.instSetLikeSubmodule.{u2, u1} R M _inst_1 _inst_3 _inst_4)) x T) -> (Membership.mem.{u1, u1} M (Submodule.{u2, u1} R M _inst_1 _inst_3 _inst_4) (SetLike.instMembership.{u1, u1} (Submodule.{u2, u1} R M _inst_1 _inst_3 _inst_4) M (Submodule.instSetLikeSubmodule.{u2, u1} R M _inst_1 _inst_3 _inst_4)) x (HasSup.sup.{u1} (Submodule.{u2, u1} R M _inst_1 _inst_3 _inst_4) (SemilatticeSup.toHasSup.{u1} (Submodule.{u2, u1} R M _inst_1 _inst_3 _inst_4) (Lattice.toSemilatticeSup.{u1} (Submodule.{u2, u1} R M _inst_1 _inst_3 _inst_4) (CompleteLattice.toLattice.{u1} (Submodule.{u2, u1} R M _inst_1 _inst_3 _inst_4) (Submodule.completeLattice.{u2, u1} R M _inst_1 _inst_3 _inst_4)))) S T))
+  forall {R : Type.{u2}} {M : Type.{u1}} [_inst_1 : Semiring.{u2} R] [_inst_3 : AddCommMonoid.{u1} M] [_inst_4 : Module.{u2, u1} R M _inst_1 _inst_3] {S : Submodule.{u2, u1} R M _inst_1 _inst_3 _inst_4} {T : Submodule.{u2, u1} R M _inst_1 _inst_3 _inst_4} {x : M}, (Membership.mem.{u1, u1} M (Submodule.{u2, u1} R M _inst_1 _inst_3 _inst_4) (SetLike.instMembership.{u1, u1} (Submodule.{u2, u1} R M _inst_1 _inst_3 _inst_4) M (Submodule.instSetLikeSubmodule.{u2, u1} R M _inst_1 _inst_3 _inst_4)) x T) -> (Membership.mem.{u1, u1} M (Submodule.{u2, u1} R M _inst_1 _inst_3 _inst_4) (SetLike.instMembership.{u1, u1} (Submodule.{u2, u1} R M _inst_1 _inst_3 _inst_4) M (Submodule.instSetLikeSubmodule.{u2, u1} R M _inst_1 _inst_3 _inst_4)) x (Sup.sup.{u1} (Submodule.{u2, u1} R M _inst_1 _inst_3 _inst_4) (SemilatticeSup.toSup.{u1} (Submodule.{u2, u1} R M _inst_1 _inst_3 _inst_4) (Lattice.toSemilatticeSup.{u1} (Submodule.{u2, u1} R M _inst_1 _inst_3 _inst_4) (CompleteLattice.toLattice.{u1} (Submodule.{u2, u1} R M _inst_1 _inst_3 _inst_4) (Submodule.completeLattice.{u2, u1} R M _inst_1 _inst_3 _inst_4)))) S T))
 Case conversion may be inaccurate. Consider using '#align submodule.mem_sup_right Submodule.mem_sup_rightₓ'. -/
 theorem mem_sup_right {S T : Submodule R M} : ∀ {x : M}, x ∈ T → x ∈ S ⊔ T :=
   show T ≤ S ⊔ T from le_sup_right
@@ -496,9 +496,9 @@ theorem mem_sup_right {S T : Submodule R M} : ∀ {x : M}, x ∈ T → x ∈ S 
 
 /- warning: submodule.add_mem_sup -> Submodule.add_mem_sup is a dubious translation:
 lean 3 declaration is
-  forall {R : Type.{u1}} {M : Type.{u2}} [_inst_1 : Semiring.{u1} R] [_inst_3 : AddCommMonoid.{u2} M] [_inst_4 : Module.{u1, u2} R M _inst_1 _inst_3] {S : Submodule.{u1, u2} R M _inst_1 _inst_3 _inst_4} {T : Submodule.{u1, u2} R M _inst_1 _inst_3 _inst_4} {s : M} {t : M}, (Membership.Mem.{u2, u2} M (Submodule.{u1, u2} R M _inst_1 _inst_3 _inst_4) (SetLike.hasMem.{u2, u2} (Submodule.{u1, u2} R M _inst_1 _inst_3 _inst_4) M (Submodule.setLike.{u1, u2} R M _inst_1 _inst_3 _inst_4)) s S) -> (Membership.Mem.{u2, u2} M (Submodule.{u1, u2} R M _inst_1 _inst_3 _inst_4) (SetLike.hasMem.{u2, u2} (Submodule.{u1, u2} R M _inst_1 _inst_3 _inst_4) M (Submodule.setLike.{u1, u2} R M _inst_1 _inst_3 _inst_4)) t T) -> (Membership.Mem.{u2, u2} M (Submodule.{u1, u2} R M _inst_1 _inst_3 _inst_4) (SetLike.hasMem.{u2, u2} (Submodule.{u1, u2} R M _inst_1 _inst_3 _inst_4) M (Submodule.setLike.{u1, u2} R M _inst_1 _inst_3 _inst_4)) (HAdd.hAdd.{u2, u2, u2} M M M (instHAdd.{u2} M (AddZeroClass.toHasAdd.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3)))) s t) (HasSup.sup.{u2} (Submodule.{u1, u2} R M _inst_1 _inst_3 _inst_4) (SemilatticeSup.toHasSup.{u2} (Submodule.{u1, u2} R M _inst_1 _inst_3 _inst_4) (Lattice.toSemilatticeSup.{u2} (Submodule.{u1, u2} R M _inst_1 _inst_3 _inst_4) (CompleteLattice.toLattice.{u2} (Submodule.{u1, u2} R M _inst_1 _inst_3 _inst_4) (Submodule.completeLattice.{u1, u2} R M _inst_1 _inst_3 _inst_4)))) S T))
+  forall {R : Type.{u1}} {M : Type.{u2}} [_inst_1 : Semiring.{u1} R] [_inst_3 : AddCommMonoid.{u2} M] [_inst_4 : Module.{u1, u2} R M _inst_1 _inst_3] {S : Submodule.{u1, u2} R M _inst_1 _inst_3 _inst_4} {T : Submodule.{u1, u2} R M _inst_1 _inst_3 _inst_4} {s : M} {t : M}, (Membership.Mem.{u2, u2} M (Submodule.{u1, u2} R M _inst_1 _inst_3 _inst_4) (SetLike.hasMem.{u2, u2} (Submodule.{u1, u2} R M _inst_1 _inst_3 _inst_4) M (Submodule.setLike.{u1, u2} R M _inst_1 _inst_3 _inst_4)) s S) -> (Membership.Mem.{u2, u2} M (Submodule.{u1, u2} R M _inst_1 _inst_3 _inst_4) (SetLike.hasMem.{u2, u2} (Submodule.{u1, u2} R M _inst_1 _inst_3 _inst_4) M (Submodule.setLike.{u1, u2} R M _inst_1 _inst_3 _inst_4)) t T) -> (Membership.Mem.{u2, u2} M (Submodule.{u1, u2} R M _inst_1 _inst_3 _inst_4) (SetLike.hasMem.{u2, u2} (Submodule.{u1, u2} R M _inst_1 _inst_3 _inst_4) M (Submodule.setLike.{u1, u2} R M _inst_1 _inst_3 _inst_4)) (HAdd.hAdd.{u2, u2, u2} M M M (instHAdd.{u2} M (AddZeroClass.toHasAdd.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3)))) s t) (Sup.sup.{u2} (Submodule.{u1, u2} R M _inst_1 _inst_3 _inst_4) (SemilatticeSup.toHasSup.{u2} (Submodule.{u1, u2} R M _inst_1 _inst_3 _inst_4) (Lattice.toSemilatticeSup.{u2} (Submodule.{u1, u2} R M _inst_1 _inst_3 _inst_4) (CompleteLattice.toLattice.{u2} (Submodule.{u1, u2} R M _inst_1 _inst_3 _inst_4) (Submodule.completeLattice.{u1, u2} R M _inst_1 _inst_3 _inst_4)))) S T))
 but is expected to have type
-  forall {R : Type.{u2}} {M : Type.{u1}} [_inst_1 : Semiring.{u2} R] [_inst_3 : AddCommMonoid.{u1} M] [_inst_4 : Module.{u2, u1} R M _inst_1 _inst_3] {S : Submodule.{u2, u1} R M _inst_1 _inst_3 _inst_4} {T : Submodule.{u2, u1} R M _inst_1 _inst_3 _inst_4} {s : M} {t : M}, (Membership.mem.{u1, u1} M (Submodule.{u2, u1} R M _inst_1 _inst_3 _inst_4) (SetLike.instMembership.{u1, u1} (Submodule.{u2, u1} R M _inst_1 _inst_3 _inst_4) M (Submodule.instSetLikeSubmodule.{u2, u1} R M _inst_1 _inst_3 _inst_4)) s S) -> (Membership.mem.{u1, u1} M (Submodule.{u2, u1} R M _inst_1 _inst_3 _inst_4) (SetLike.instMembership.{u1, u1} (Submodule.{u2, u1} R M _inst_1 _inst_3 _inst_4) M (Submodule.instSetLikeSubmodule.{u2, u1} R M _inst_1 _inst_3 _inst_4)) t T) -> (Membership.mem.{u1, u1} M (Submodule.{u2, u1} R M _inst_1 _inst_3 _inst_4) (SetLike.instMembership.{u1, u1} (Submodule.{u2, u1} R M _inst_1 _inst_3 _inst_4) M (Submodule.instSetLikeSubmodule.{u2, u1} R M _inst_1 _inst_3 _inst_4)) (HAdd.hAdd.{u1, u1, u1} M M M (instHAdd.{u1} M (AddZeroClass.toAdd.{u1} M (AddMonoid.toAddZeroClass.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3)))) s t) (HasSup.sup.{u1} (Submodule.{u2, u1} R M _inst_1 _inst_3 _inst_4) (SemilatticeSup.toHasSup.{u1} (Submodule.{u2, u1} R M _inst_1 _inst_3 _inst_4) (Lattice.toSemilatticeSup.{u1} (Submodule.{u2, u1} R M _inst_1 _inst_3 _inst_4) (CompleteLattice.toLattice.{u1} (Submodule.{u2, u1} R M _inst_1 _inst_3 _inst_4) (Submodule.completeLattice.{u2, u1} R M _inst_1 _inst_3 _inst_4)))) S T))
+  forall {R : Type.{u2}} {M : Type.{u1}} [_inst_1 : Semiring.{u2} R] [_inst_3 : AddCommMonoid.{u1} M] [_inst_4 : Module.{u2, u1} R M _inst_1 _inst_3] {S : Submodule.{u2, u1} R M _inst_1 _inst_3 _inst_4} {T : Submodule.{u2, u1} R M _inst_1 _inst_3 _inst_4} {s : M} {t : M}, (Membership.mem.{u1, u1} M (Submodule.{u2, u1} R M _inst_1 _inst_3 _inst_4) (SetLike.instMembership.{u1, u1} (Submodule.{u2, u1} R M _inst_1 _inst_3 _inst_4) M (Submodule.instSetLikeSubmodule.{u2, u1} R M _inst_1 _inst_3 _inst_4)) s S) -> (Membership.mem.{u1, u1} M (Submodule.{u2, u1} R M _inst_1 _inst_3 _inst_4) (SetLike.instMembership.{u1, u1} (Submodule.{u2, u1} R M _inst_1 _inst_3 _inst_4) M (Submodule.instSetLikeSubmodule.{u2, u1} R M _inst_1 _inst_3 _inst_4)) t T) -> (Membership.mem.{u1, u1} M (Submodule.{u2, u1} R M _inst_1 _inst_3 _inst_4) (SetLike.instMembership.{u1, u1} (Submodule.{u2, u1} R M _inst_1 _inst_3 _inst_4) M (Submodule.instSetLikeSubmodule.{u2, u1} R M _inst_1 _inst_3 _inst_4)) (HAdd.hAdd.{u1, u1, u1} M M M (instHAdd.{u1} M (AddZeroClass.toAdd.{u1} M (AddMonoid.toAddZeroClass.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3)))) s t) (Sup.sup.{u1} (Submodule.{u2, u1} R M _inst_1 _inst_3 _inst_4) (SemilatticeSup.toSup.{u1} (Submodule.{u2, u1} R M _inst_1 _inst_3 _inst_4) (Lattice.toSemilatticeSup.{u1} (Submodule.{u2, u1} R M _inst_1 _inst_3 _inst_4) (CompleteLattice.toLattice.{u1} (Submodule.{u2, u1} R M _inst_1 _inst_3 _inst_4) (Submodule.completeLattice.{u2, u1} R M _inst_1 _inst_3 _inst_4)))) S T))
 Case conversion may be inaccurate. Consider using '#align submodule.add_mem_sup Submodule.add_mem_supₓ'. -/
 theorem add_mem_sup {S T : Submodule R M} {s t : M} (hs : s ∈ S) (ht : t ∈ T) : s + t ∈ S ⊔ T :=
   add_mem (mem_sup_left hs) (mem_sup_right ht)
@@ -506,9 +506,9 @@ theorem add_mem_sup {S T : Submodule R M} {s t : M} (hs : s ∈ S) (ht : t ∈ T
 
 /- warning: submodule.sub_mem_sup -> Submodule.sub_mem_sup is a dubious translation:
 lean 3 declaration is
-  forall {R' : Type.{u1}} {M' : Type.{u2}} [_inst_8 : Ring.{u1} R'] [_inst_9 : AddCommGroup.{u2} M'] [_inst_10 : Module.{u1, u2} R' M' (Ring.toSemiring.{u1} R' _inst_8) (AddCommGroup.toAddCommMonoid.{u2} M' _inst_9)] {S : Submodule.{u1, u2} R' M' (Ring.toSemiring.{u1} R' _inst_8) (AddCommGroup.toAddCommMonoid.{u2} M' _inst_9) _inst_10} {T : Submodule.{u1, u2} R' M' (Ring.toSemiring.{u1} R' _inst_8) (AddCommGroup.toAddCommMonoid.{u2} M' _inst_9) _inst_10} {s : M'} {t : M'}, (Membership.Mem.{u2, u2} M' (Submodule.{u1, u2} R' M' (Ring.toSemiring.{u1} R' _inst_8) (AddCommGroup.toAddCommMonoid.{u2} M' _inst_9) _inst_10) (SetLike.hasMem.{u2, u2} (Submodule.{u1, u2} R' M' (Ring.toSemiring.{u1} R' _inst_8) (AddCommGroup.toAddCommMonoid.{u2} M' _inst_9) _inst_10) M' (Submodule.setLike.{u1, u2} R' M' (Ring.toSemiring.{u1} R' _inst_8) (AddCommGroup.toAddCommMonoid.{u2} M' _inst_9) _inst_10)) s S) -> (Membership.Mem.{u2, u2} M' (Submodule.{u1, u2} R' M' (Ring.toSemiring.{u1} R' _inst_8) (AddCommGroup.toAddCommMonoid.{u2} M' _inst_9) _inst_10) (SetLike.hasMem.{u2, u2} (Submodule.{u1, u2} R' M' (Ring.toSemiring.{u1} R' _inst_8) (AddCommGroup.toAddCommMonoid.{u2} M' _inst_9) _inst_10) M' (Submodule.setLike.{u1, u2} R' M' (Ring.toSemiring.{u1} R' _inst_8) (AddCommGroup.toAddCommMonoid.{u2} M' _inst_9) _inst_10)) t T) -> (Membership.Mem.{u2, u2} M' (Submodule.{u1, u2} R' M' (Ring.toSemiring.{u1} R' _inst_8) (AddCommGroup.toAddCommMonoid.{u2} M' _inst_9) _inst_10) (SetLike.hasMem.{u2, u2} (Submodule.{u1, u2} R' M' (Ring.toSemiring.{u1} R' _inst_8) (AddCommGroup.toAddCommMonoid.{u2} M' _inst_9) _inst_10) M' (Submodule.setLike.{u1, u2} R' M' (Ring.toSemiring.{u1} R' _inst_8) (AddCommGroup.toAddCommMonoid.{u2} M' _inst_9) _inst_10)) (HSub.hSub.{u2, u2, u2} M' M' M' (instHSub.{u2} M' (SubNegMonoid.toHasSub.{u2} M' (AddGroup.toSubNegMonoid.{u2} M' (AddCommGroup.toAddGroup.{u2} M' _inst_9)))) s t) (HasSup.sup.{u2} (Submodule.{u1, u2} R' M' (Ring.toSemiring.{u1} R' _inst_8) (AddCommGroup.toAddCommMonoid.{u2} M' _inst_9) _inst_10) (SemilatticeSup.toHasSup.{u2} (Submodule.{u1, u2} R' M' (Ring.toSemiring.{u1} R' _inst_8) (AddCommGroup.toAddCommMonoid.{u2} M' _inst_9) _inst_10) (Lattice.toSemilatticeSup.{u2} (Submodule.{u1, u2} R' M' (Ring.toSemiring.{u1} R' _inst_8) (AddCommGroup.toAddCommMonoid.{u2} M' _inst_9) _inst_10) (CompleteLattice.toLattice.{u2} (Submodule.{u1, u2} R' M' (Ring.toSemiring.{u1} R' _inst_8) (AddCommGroup.toAddCommMonoid.{u2} M' _inst_9) _inst_10) (Submodule.completeLattice.{u1, u2} R' M' (Ring.toSemiring.{u1} R' _inst_8) (AddCommGroup.toAddCommMonoid.{u2} M' _inst_9) _inst_10)))) S T))
+  forall {R' : Type.{u1}} {M' : Type.{u2}} [_inst_8 : Ring.{u1} R'] [_inst_9 : AddCommGroup.{u2} M'] [_inst_10 : Module.{u1, u2} R' M' (Ring.toSemiring.{u1} R' _inst_8) (AddCommGroup.toAddCommMonoid.{u2} M' _inst_9)] {S : Submodule.{u1, u2} R' M' (Ring.toSemiring.{u1} R' _inst_8) (AddCommGroup.toAddCommMonoid.{u2} M' _inst_9) _inst_10} {T : Submodule.{u1, u2} R' M' (Ring.toSemiring.{u1} R' _inst_8) (AddCommGroup.toAddCommMonoid.{u2} M' _inst_9) _inst_10} {s : M'} {t : M'}, (Membership.Mem.{u2, u2} M' (Submodule.{u1, u2} R' M' (Ring.toSemiring.{u1} R' _inst_8) (AddCommGroup.toAddCommMonoid.{u2} M' _inst_9) _inst_10) (SetLike.hasMem.{u2, u2} (Submodule.{u1, u2} R' M' (Ring.toSemiring.{u1} R' _inst_8) (AddCommGroup.toAddCommMonoid.{u2} M' _inst_9) _inst_10) M' (Submodule.setLike.{u1, u2} R' M' (Ring.toSemiring.{u1} R' _inst_8) (AddCommGroup.toAddCommMonoid.{u2} M' _inst_9) _inst_10)) s S) -> (Membership.Mem.{u2, u2} M' (Submodule.{u1, u2} R' M' (Ring.toSemiring.{u1} R' _inst_8) (AddCommGroup.toAddCommMonoid.{u2} M' _inst_9) _inst_10) (SetLike.hasMem.{u2, u2} (Submodule.{u1, u2} R' M' (Ring.toSemiring.{u1} R' _inst_8) (AddCommGroup.toAddCommMonoid.{u2} M' _inst_9) _inst_10) M' (Submodule.setLike.{u1, u2} R' M' (Ring.toSemiring.{u1} R' _inst_8) (AddCommGroup.toAddCommMonoid.{u2} M' _inst_9) _inst_10)) t T) -> (Membership.Mem.{u2, u2} M' (Submodule.{u1, u2} R' M' (Ring.toSemiring.{u1} R' _inst_8) (AddCommGroup.toAddCommMonoid.{u2} M' _inst_9) _inst_10) (SetLike.hasMem.{u2, u2} (Submodule.{u1, u2} R' M' (Ring.toSemiring.{u1} R' _inst_8) (AddCommGroup.toAddCommMonoid.{u2} M' _inst_9) _inst_10) M' (Submodule.setLike.{u1, u2} R' M' (Ring.toSemiring.{u1} R' _inst_8) (AddCommGroup.toAddCommMonoid.{u2} M' _inst_9) _inst_10)) (HSub.hSub.{u2, u2, u2} M' M' M' (instHSub.{u2} M' (SubNegMonoid.toHasSub.{u2} M' (AddGroup.toSubNegMonoid.{u2} M' (AddCommGroup.toAddGroup.{u2} M' _inst_9)))) s t) (Sup.sup.{u2} (Submodule.{u1, u2} R' M' (Ring.toSemiring.{u1} R' _inst_8) (AddCommGroup.toAddCommMonoid.{u2} M' _inst_9) _inst_10) (SemilatticeSup.toHasSup.{u2} (Submodule.{u1, u2} R' M' (Ring.toSemiring.{u1} R' _inst_8) (AddCommGroup.toAddCommMonoid.{u2} M' _inst_9) _inst_10) (Lattice.toSemilatticeSup.{u2} (Submodule.{u1, u2} R' M' (Ring.toSemiring.{u1} R' _inst_8) (AddCommGroup.toAddCommMonoid.{u2} M' _inst_9) _inst_10) (CompleteLattice.toLattice.{u2} (Submodule.{u1, u2} R' M' (Ring.toSemiring.{u1} R' _inst_8) (AddCommGroup.toAddCommMonoid.{u2} M' _inst_9) _inst_10) (Submodule.completeLattice.{u1, u2} R' M' (Ring.toSemiring.{u1} R' _inst_8) (AddCommGroup.toAddCommMonoid.{u2} M' _inst_9) _inst_10)))) S T))
 but is expected to have type
-  forall {R' : Type.{u2}} {M' : Type.{u1}} [_inst_8 : Ring.{u2} R'] [_inst_9 : AddCommGroup.{u1} M'] [_inst_10 : Module.{u2, u1} R' M' (Ring.toSemiring.{u2} R' _inst_8) (AddCommGroup.toAddCommMonoid.{u1} M' _inst_9)] {S : Submodule.{u2, u1} R' M' (Ring.toSemiring.{u2} R' _inst_8) (AddCommGroup.toAddCommMonoid.{u1} M' _inst_9) _inst_10} {T : Submodule.{u2, u1} R' M' (Ring.toSemiring.{u2} R' _inst_8) (AddCommGroup.toAddCommMonoid.{u1} M' _inst_9) _inst_10} {s : M'} {t : M'}, (Membership.mem.{u1, u1} M' (Submodule.{u2, u1} R' M' (Ring.toSemiring.{u2} R' _inst_8) (AddCommGroup.toAddCommMonoid.{u1} M' _inst_9) _inst_10) (SetLike.instMembership.{u1, u1} (Submodule.{u2, u1} R' M' (Ring.toSemiring.{u2} R' _inst_8) (AddCommGroup.toAddCommMonoid.{u1} M' _inst_9) _inst_10) M' (Submodule.instSetLikeSubmodule.{u2, u1} R' M' (Ring.toSemiring.{u2} R' _inst_8) (AddCommGroup.toAddCommMonoid.{u1} M' _inst_9) _inst_10)) s S) -> (Membership.mem.{u1, u1} M' (Submodule.{u2, u1} R' M' (Ring.toSemiring.{u2} R' _inst_8) (AddCommGroup.toAddCommMonoid.{u1} M' _inst_9) _inst_10) (SetLike.instMembership.{u1, u1} (Submodule.{u2, u1} R' M' (Ring.toSemiring.{u2} R' _inst_8) (AddCommGroup.toAddCommMonoid.{u1} M' _inst_9) _inst_10) M' (Submodule.instSetLikeSubmodule.{u2, u1} R' M' (Ring.toSemiring.{u2} R' _inst_8) (AddCommGroup.toAddCommMonoid.{u1} M' _inst_9) _inst_10)) t T) -> (Membership.mem.{u1, u1} M' (Submodule.{u2, u1} R' M' (Ring.toSemiring.{u2} R' _inst_8) (AddCommGroup.toAddCommMonoid.{u1} M' _inst_9) _inst_10) (SetLike.instMembership.{u1, u1} (Submodule.{u2, u1} R' M' (Ring.toSemiring.{u2} R' _inst_8) (AddCommGroup.toAddCommMonoid.{u1} M' _inst_9) _inst_10) M' (Submodule.instSetLikeSubmodule.{u2, u1} R' M' (Ring.toSemiring.{u2} R' _inst_8) (AddCommGroup.toAddCommMonoid.{u1} M' _inst_9) _inst_10)) (HSub.hSub.{u1, u1, u1} M' M' M' (instHSub.{u1} M' (SubNegMonoid.toSub.{u1} M' (AddGroup.toSubNegMonoid.{u1} M' (AddCommGroup.toAddGroup.{u1} M' _inst_9)))) s t) (HasSup.sup.{u1} (Submodule.{u2, u1} R' M' (Ring.toSemiring.{u2} R' _inst_8) (AddCommGroup.toAddCommMonoid.{u1} M' _inst_9) _inst_10) (SemilatticeSup.toHasSup.{u1} (Submodule.{u2, u1} R' M' (Ring.toSemiring.{u2} R' _inst_8) (AddCommGroup.toAddCommMonoid.{u1} M' _inst_9) _inst_10) (Lattice.toSemilatticeSup.{u1} (Submodule.{u2, u1} R' M' (Ring.toSemiring.{u2} R' _inst_8) (AddCommGroup.toAddCommMonoid.{u1} M' _inst_9) _inst_10) (CompleteLattice.toLattice.{u1} (Submodule.{u2, u1} R' M' (Ring.toSemiring.{u2} R' _inst_8) (AddCommGroup.toAddCommMonoid.{u1} M' _inst_9) _inst_10) (Submodule.completeLattice.{u2, u1} R' M' (Ring.toSemiring.{u2} R' _inst_8) (AddCommGroup.toAddCommMonoid.{u1} M' _inst_9) _inst_10)))) S T))
+  forall {R' : Type.{u2}} {M' : Type.{u1}} [_inst_8 : Ring.{u2} R'] [_inst_9 : AddCommGroup.{u1} M'] [_inst_10 : Module.{u2, u1} R' M' (Ring.toSemiring.{u2} R' _inst_8) (AddCommGroup.toAddCommMonoid.{u1} M' _inst_9)] {S : Submodule.{u2, u1} R' M' (Ring.toSemiring.{u2} R' _inst_8) (AddCommGroup.toAddCommMonoid.{u1} M' _inst_9) _inst_10} {T : Submodule.{u2, u1} R' M' (Ring.toSemiring.{u2} R' _inst_8) (AddCommGroup.toAddCommMonoid.{u1} M' _inst_9) _inst_10} {s : M'} {t : M'}, (Membership.mem.{u1, u1} M' (Submodule.{u2, u1} R' M' (Ring.toSemiring.{u2} R' _inst_8) (AddCommGroup.toAddCommMonoid.{u1} M' _inst_9) _inst_10) (SetLike.instMembership.{u1, u1} (Submodule.{u2, u1} R' M' (Ring.toSemiring.{u2} R' _inst_8) (AddCommGroup.toAddCommMonoid.{u1} M' _inst_9) _inst_10) M' (Submodule.instSetLikeSubmodule.{u2, u1} R' M' (Ring.toSemiring.{u2} R' _inst_8) (AddCommGroup.toAddCommMonoid.{u1} M' _inst_9) _inst_10)) s S) -> (Membership.mem.{u1, u1} M' (Submodule.{u2, u1} R' M' (Ring.toSemiring.{u2} R' _inst_8) (AddCommGroup.toAddCommMonoid.{u1} M' _inst_9) _inst_10) (SetLike.instMembership.{u1, u1} (Submodule.{u2, u1} R' M' (Ring.toSemiring.{u2} R' _inst_8) (AddCommGroup.toAddCommMonoid.{u1} M' _inst_9) _inst_10) M' (Submodule.instSetLikeSubmodule.{u2, u1} R' M' (Ring.toSemiring.{u2} R' _inst_8) (AddCommGroup.toAddCommMonoid.{u1} M' _inst_9) _inst_10)) t T) -> (Membership.mem.{u1, u1} M' (Submodule.{u2, u1} R' M' (Ring.toSemiring.{u2} R' _inst_8) (AddCommGroup.toAddCommMonoid.{u1} M' _inst_9) _inst_10) (SetLike.instMembership.{u1, u1} (Submodule.{u2, u1} R' M' (Ring.toSemiring.{u2} R' _inst_8) (AddCommGroup.toAddCommMonoid.{u1} M' _inst_9) _inst_10) M' (Submodule.instSetLikeSubmodule.{u2, u1} R' M' (Ring.toSemiring.{u2} R' _inst_8) (AddCommGroup.toAddCommMonoid.{u1} M' _inst_9) _inst_10)) (HSub.hSub.{u1, u1, u1} M' M' M' (instHSub.{u1} M' (SubNegMonoid.toSub.{u1} M' (AddGroup.toSubNegMonoid.{u1} M' (AddCommGroup.toAddGroup.{u1} M' _inst_9)))) s t) (Sup.sup.{u1} (Submodule.{u2, u1} R' M' (Ring.toSemiring.{u2} R' _inst_8) (AddCommGroup.toAddCommMonoid.{u1} M' _inst_9) _inst_10) (SemilatticeSup.toSup.{u1} (Submodule.{u2, u1} R' M' (Ring.toSemiring.{u2} R' _inst_8) (AddCommGroup.toAddCommMonoid.{u1} M' _inst_9) _inst_10) (Lattice.toSemilatticeSup.{u1} (Submodule.{u2, u1} R' M' (Ring.toSemiring.{u2} R' _inst_8) (AddCommGroup.toAddCommMonoid.{u1} M' _inst_9) _inst_10) (CompleteLattice.toLattice.{u1} (Submodule.{u2, u1} R' M' (Ring.toSemiring.{u2} R' _inst_8) (AddCommGroup.toAddCommMonoid.{u1} M' _inst_9) _inst_10) (Submodule.completeLattice.{u2, u1} R' M' (Ring.toSemiring.{u2} R' _inst_8) (AddCommGroup.toAddCommMonoid.{u1} M' _inst_9) _inst_10)))) S T))
 Case conversion may be inaccurate. Consider using '#align submodule.sub_mem_sup Submodule.sub_mem_supₓ'. -/
 theorem sub_mem_sup {R' M' : Type _} [Ring R'] [AddCommGroup M'] [Module R' M']
     {S T : Submodule R' M'} {s t : M'} (hs : s ∈ S) (ht : t ∈ T) : s - t ∈ S ⊔ T :=

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

Moves definition of and lemmas related to Set.Subsingleton and Set.Nontrivial to a new file, so that Basic can be shorter.

@@ -6,7 +6,7 @@ Authors: Johannes Hölzl, Mario Carneiro, Kevin Buzzard, Yury Kudryashov
 import Mathlib.Algebra.Module.Equiv
 import Mathlib.Algebra.Module.Submodule.Basic
 import Mathlib.Algebra.PUnitInstances
-import Mathlib.Data.Set.Basic
+import Mathlib.Data.Set.Subsingleton
 
 #align_import algebra.module.submodule.lattice from "leanprover-community/mathlib"@"f7fc89d5d5ff1db2d1242c7bb0e9062ce47ef47c"
 

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)

@@ -34,9 +34,7 @@ variable {R S M : Type*}
 section AddCommMonoid
 
 variable [Semiring R] [Semiring S] [AddCommMonoid M] [Module R M] [Module S M]
-
 variable [SMul S R] [IsScalarTower S R M]
-
 variable {p q : Submodule R M}
 
 namespace Submodule

• 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.

@@ -6,6 +6,7 @@ Authors: Johannes Hölzl, Mario Carneiro, Kevin Buzzard, Yury Kudryashov
 import Mathlib.Algebra.Module.Equiv
 import Mathlib.Algebra.Module.Submodule.Basic
 import Mathlib.Algebra.PUnitInstances
+import Mathlib.Data.Set.Basic
 
 #align_import algebra.module.submodule.lattice from "leanprover-community/mathlib"@"f7fc89d5d5ff1db2d1242c7bb0e9062ce47ef47c"
 

This uses the improved shake script from #9772 to reduce imports across mathlib. The corresponding noshake.json file has been added to #9772.

Co-authored-by: Mario Carneiro <di.gama@gmail.com>

@@ -3,7 +3,8 @@ Copyright (c) 2017 Johannes Hölzl. All rights reserved.
 Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Johannes Hölzl, Mario Carneiro, Kevin Buzzard, Yury Kudryashov
 -/
-import Mathlib.Algebra.Module.Submodule.LinearMap
+import Mathlib.Algebra.Module.Equiv
+import Mathlib.Algebra.Module.Submodule.Basic
 import Mathlib.Algebra.PUnitInstances
 
 #align_import algebra.module.submodule.lattice from "leanprover-community/mathlib"@"f7fc89d5d5ff1db2d1242c7bb0e9062ce47ef47c"

@@ -317,6 +317,28 @@ theorem mem_sSup_of_mem {S : Set (Submodule R M)} {s : Submodule R M} (hs : s 
   exact this
 #align submodule.mem_Sup_of_mem Submodule.mem_sSup_of_mem
 
+@[simp]
+theorem toAddSubmonoid_sSup (s : Set (Submodule R M)) :
+    (sSup s).toAddSubmonoid = sSup (toAddSubmonoid '' s) := by
+  let p : Submodule R M :=
+    { toAddSubmonoid := sSup (toAddSubmonoid '' s)
+      smul_mem' := fun t {m} h ↦ by
+        simp_rw [AddSubsemigroup.mem_carrier, AddSubmonoid.mem_toSubsemigroup, sSup_eq_iSup'] at h ⊢
+        refine AddSubmonoid.iSup_induction'
+          (C := fun x _ ↦ t • x ∈ ⨆ p : toAddSubmonoid '' s, (p : AddSubmonoid M)) ?_ ?_
+          (fun x y _ _ ↦ ?_) h
+        · rintro ⟨-, ⟨p : Submodule R M, hp : p ∈ s, rfl⟩⟩ x (hx : x ∈ p)
+          suffices p.toAddSubmonoid ≤ ⨆ q : toAddSubmonoid '' s, (q : AddSubmonoid M) by
+            exact this (smul_mem p t hx)
+          apply le_sSup
+          rw [Subtype.range_coe_subtype]
+          exact ⟨p, hp, rfl⟩
+        · simpa only [smul_zero] using zero_mem _
+        · simp_rw [smul_add]; exact add_mem }
+  refine le_antisymm (?_ : sSup s ≤ p) ?_
+  · exact sSup_le fun q hq ↦ le_sSup <| Set.mem_image_of_mem toAddSubmonoid hq
+  · exact sSup_le fun _ ⟨q, hq, hq'⟩ ↦ hq'.symm ▸ le_sSup hq
+
 variable (R)
 
 @[simp]

This is a straight copy-paste: there are no new lemmas and nothing has been removed or renamed. The only changes are a few lemmas where argument explicitness or ordering has changed (and where it did not seem to make sense to replicate the old argument explicitness or ordering).

@@ -67,27 +67,12 @@ theorem bot_toAddSubmonoid : (⊥ : Submodule R M).toAddSubmonoid = ⊥ :=
 lemma bot_toAddSubgroup {R M} [Ring R] [AddCommGroup M] [Module R M] :
     (⊥ : Submodule R M).toAddSubgroup = ⊥ := rfl
 
-section
-
-variable (R)
-
-@[simp]
-theorem restrictScalars_bot : restrictScalars S (⊥ : Submodule R M) = ⊥ :=
-  rfl
-#align submodule.restrict_scalars_bot Submodule.restrictScalars_bot
-
+variable (R) in
 @[simp]
 theorem mem_bot {x : M} : x ∈ (⊥ : Submodule R M) ↔ x = 0 :=
   Set.mem_singleton_iff
 #align submodule.mem_bot Submodule.mem_bot
 
-end
-
-@[simp]
-theorem restrictScalars_eq_bot_iff {p : Submodule R M} : restrictScalars S p = ⊥ ↔ p = ⊥ := by
-  simp [SetLike.ext_iff]
-#align submodule.restrict_scalars_eq_bot_iff Submodule.restrictScalars_eq_bot_iff
-
 instance uniqueBot : Unique (⊥ : Submodule R M) :=
   ⟨inferInstance, fun x ↦ Subtype.ext <| (mem_bot R).1 x.mem⟩
 #align submodule.unique_bot Submodule.uniqueBot
@@ -175,22 +160,6 @@ theorem mem_top {x : M} : x ∈ (⊤ : Submodule R M) :=
   trivial
 #align submodule.mem_top Submodule.mem_top
 
-section
-
-variable (R)
-
-@[simp]
-theorem restrictScalars_top : restrictScalars S (⊤ : Submodule R M) = ⊤ :=
-  rfl
-#align submodule.restrict_scalars_top Submodule.restrictScalars_top
-
-end
-
-@[simp]
-theorem restrictScalars_eq_top_iff {p : Submodule R M} : restrictScalars S p = ⊤ ↔ p = ⊤ := by
-  simp [SetLike.ext_iff]
-#align submodule.restrict_scalars_eq_top_iff Submodule.restrictScalars_eq_top_iff
-
 instance : OrderTop (Submodule R M) where
   top := ⊤
   le_top _ _ _ := trivial

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

@@ -63,6 +63,10 @@ theorem bot_toAddSubmonoid : (⊥ : Submodule R M).toAddSubmonoid = ⊥ :=
   rfl
 #align submodule.bot_to_add_submonoid Submodule.bot_toAddSubmonoid
 
+@[simp]
+lemma bot_toAddSubgroup {R M} [Ring R] [AddCommGroup M] [Module R M] :
+    (⊥ : Submodule R M).toAddSubgroup = ⊥ := rfl
+
 section
 
 variable (R)
@@ -162,6 +166,10 @@ theorem top_toAddSubmonoid : (⊤ : Submodule R M).toAddSubmonoid = ⊤ :=
   rfl
 #align submodule.top_to_add_submonoid Submodule.top_toAddSubmonoid
 
+@[simp]
+lemma top_toAddSubgroup {R M} [Ring R] [AddCommGroup M] [Module R M] :
+    (⊤ : Submodule R M).toAddSubgroup = ⊤ := rfl
+
 @[simp]
 theorem mem_top {x : M} : x ∈ (⊤ : Submodule R M) :=
   trivial

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>

@@ -383,8 +383,8 @@ theorem disjoint_def' {p p' : Submodule R M} :
     ⟨fun h x hx _ hy hxy ↦ h x hx <| hxy.symm ▸ hy, fun h x hx hx' ↦ h _ hx x hx' rfl⟩
 #align submodule.disjoint_def' Submodule.disjoint_def'
 
-theorem eq_zero_of_coe_mem_of_disjoint (hpq : Disjoint p q) {a : p} (ha : (a : M) ∈ q) : a = 0 := by
-  exact_mod_cast disjoint_def.mp hpq a (coe_mem a) ha
+theorem eq_zero_of_coe_mem_of_disjoint (hpq : Disjoint p q) {a : p} (ha : (a : M) ∈ q) : a = 0 :=
+  mod_cast disjoint_def.mp hpq a (coe_mem a) ha
 #align submodule.eq_zero_of_coe_mem_of_disjoint Submodule.eq_zero_of_coe_mem_of_disjoint
 
 theorem mem_right_iff_eq_zero_of_disjoint {p p' : Submodule R M} (h : Disjoint p p') {x : p} :

This reduces the file from ~2600 lines to ~1600 lines.

Co-authored-by: Vierkantor <vierkantor@vierkantor.com> Co-authored-by: Floris van Doorn <fpvdoorn@gmail.com>

@@ -3,7 +3,7 @@ Copyright (c) 2017 Johannes Hölzl. All rights reserved.
 Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Johannes Hölzl, Mario Carneiro, Kevin Buzzard, Yury Kudryashov
 -/
-import Mathlib.Algebra.Module.Submodule.Basic
+import Mathlib.Algebra.Module.Submodule.LinearMap
 import Mathlib.Algebra.PUnitInstances
 
 #align_import algebra.module.submodule.lattice from "leanprover-community/mathlib"@"f7fc89d5d5ff1db2d1242c7bb0e9062ce47ef47c"

@@ -130,12 +130,18 @@ def botEquivPUnit : (⊥ : Submodule R M) ≃ₗ[R] PUnit.{v+1} where
   right_inv _ := rfl
 #align submodule.bot_equiv_punit Submodule.botEquivPUnit
 
-theorem eq_bot_of_subsingleton (p : Submodule R M) [Subsingleton p] : p = ⊥ := by
-  rw [eq_bot_iff]
-  intro v hv
-  exact congr_arg Subtype.val (Subsingleton.elim (⟨v, hv⟩ : p) 0)
+theorem subsingleton_iff_eq_bot : Subsingleton p ↔ p = ⊥ := by
+  rw [subsingleton_iff, Submodule.eq_bot_iff]
+  refine ⟨fun h x hx ↦ by simpa using h ⟨x, hx⟩ ⟨0, p.zero_mem⟩,
+    fun h ⟨x, hx⟩ ⟨y, hy⟩ ↦ by simp [h x hx, h y hy]⟩
+
+theorem eq_bot_of_subsingleton [Subsingleton p] : p = ⊥ :=
+  subsingleton_iff_eq_bot.mp inferInstance
 #align submodule.eq_bot_of_subsingleton Submodule.eq_bot_of_subsingleton
 
+theorem nontrivial_iff_ne_bot : Nontrivial p ↔ p ≠ ⊥ := by
+  rw [iff_not_comm, not_nontrivial_iff_subsingleton, subsingleton_iff_eq_bot]
+
 /-!
 ## Top element of a submodule
 -/

@@ -25,8 +25,7 @@ to unify the APIs where possible.
 
 -/
 
-set_option autoImplicit true
-
+universe v
 
 variable {R S M : Type*}
 
@@ -40,6 +39,10 @@ variable {p q : Submodule R M}
 
 namespace Submodule
 
+/-!
+## Bottom element of a submodule
+-/
+
 /-- The set `{0}` is the bottom element of the lattice of submodules. -/
 instance : Bot (Submodule R M) :=
   ⟨{ (⊥ : AddSubmonoid M) with
@@ -133,6 +136,10 @@ theorem eq_bot_of_subsingleton (p : Submodule R M) [Subsingleton p] : p = ⊥ :=
   exact congr_arg Subtype.val (Subsingleton.elim (⟨v, hv⟩ : p) 0)
 #align submodule.eq_bot_of_subsingleton Submodule.eq_bot_of_subsingleton
 
+/-!
+## Top element of a submodule
+-/
+
 /-- The universal set is the top element of the lattice of submodules. -/
 instance : Top (Submodule R M) :=
   ⟨{ (⊤ : AddSubmonoid M) with
@@ -191,6 +198,10 @@ def topEquiv : (⊤ : Submodule R M) ≃ₗ[R] M where
   right_inv _ := rfl
 #align submodule.top_equiv Submodule.topEquiv
 
+/-!
+## Infima & suprema in a submodule
+-/
+
 instance : InfSet (Submodule R M) :=
   ⟨fun S ↦
     { carrier := ⋂ s ∈ S, (s : Set M)
@@ -313,7 +324,7 @@ theorem sum_mem_biSup {ι : Type*} {s : Finset ι} {f : ι → M} {p : ι → Su
   sum_mem fun i hi ↦ mem_iSup_of_mem i <| mem_iSup_of_mem hi (h i hi)
 #align submodule.sum_mem_bsupr Submodule.sum_mem_biSup
 
-/-! Note that `Submodule.mem_iSup` is provided in `LinearAlgebra/Span.lean`. -/
+/-! Note that `Submodule.mem_iSup` is provided in `Mathlib/LinearAlgebra/Span.lean`. -/
 
 
 theorem mem_sSup_of_mem {S : Set (Submodule R M)} {s : Submodule R M} (hs : s ∈ S) :
@@ -323,6 +334,39 @@ theorem mem_sSup_of_mem {S : Set (Submodule R M)} {s : Submodule R M} (hs : s 
   exact this
 #align submodule.mem_Sup_of_mem Submodule.mem_sSup_of_mem
 
+variable (R)
+
+@[simp]
+theorem subsingleton_iff : Subsingleton (Submodule R M) ↔ Subsingleton M :=
+  have h : Subsingleton (Submodule R M) ↔ Subsingleton (AddSubmonoid M) := by
+    rw [← subsingleton_iff_bot_eq_top, ← subsingleton_iff_bot_eq_top, ← toAddSubmonoid_eq,
+      bot_toAddSubmonoid, top_toAddSubmonoid]
+  h.trans AddSubmonoid.subsingleton_iff
+#align submodule.subsingleton_iff Submodule.subsingleton_iff
+
+@[simp]
+theorem nontrivial_iff : Nontrivial (Submodule R M) ↔ Nontrivial M :=
+  not_iff_not.mp
+    ((not_nontrivial_iff_subsingleton.trans <| subsingleton_iff R).trans
+      not_nontrivial_iff_subsingleton.symm)
+#align submodule.nontrivial_iff Submodule.nontrivial_iff
+
+variable {R}
+
+instance [Subsingleton M] : Unique (Submodule R M) :=
+  ⟨⟨⊥⟩, fun a => @Subsingleton.elim _ ((subsingleton_iff R).mpr ‹_›) a _⟩
+
+instance unique' [Subsingleton R] : Unique (Submodule R M) := by
+  haveI := Module.subsingleton R M; infer_instance
+#align submodule.unique' Submodule.unique'
+
+instance [Nontrivial M] : Nontrivial (Submodule R M) :=
+  (nontrivial_iff R).mpr ‹_›
+
+/-!
+## Disjointness of submodules
+-/
+
 theorem disjoint_def {p p' : Submodule R M} : Disjoint p p' ↔ ∀ x ∈ p, x ∈ p' → x = (0 : M) :=
   disjoint_iff_inf_le.trans <| show (∀ x, x ∈ p ∧ x ∈ p' → x ∈ ({0} : Set M)) ↔ _ by simp
 #align submodule.disjoint_def Submodule.disjoint_def
@@ -337,10 +381,24 @@ theorem eq_zero_of_coe_mem_of_disjoint (hpq : Disjoint p q) {a : p} (ha : (a : M
   exact_mod_cast disjoint_def.mp hpq a (coe_mem a) ha
 #align submodule.eq_zero_of_coe_mem_of_disjoint Submodule.eq_zero_of_coe_mem_of_disjoint
 
+theorem mem_right_iff_eq_zero_of_disjoint {p p' : Submodule R M} (h : Disjoint p p') {x : p} :
+    (x : M) ∈ p' ↔ x = 0 :=
+  ⟨fun hx => coe_eq_zero.1 <| disjoint_def.1 h x x.2 hx, fun h => h.symm ▸ p'.zero_mem⟩
+#align submodule.mem_right_iff_eq_zero_of_disjoint Submodule.mem_right_iff_eq_zero_of_disjoint
+
+theorem mem_left_iff_eq_zero_of_disjoint {p p' : Submodule R M} (h : Disjoint p p') {x : p'} :
+    (x : M) ∈ p ↔ x = 0 :=
+  ⟨fun hx => coe_eq_zero.1 <| disjoint_def.1 h x hx x.2, fun h => h.symm ▸ p.zero_mem⟩
+#align submodule.mem_left_iff_eq_zero_of_disjoint Submodule.mem_left_iff_eq_zero_of_disjoint
+
 end Submodule
 
 section NatSubmodule
 
+/-!
+## ℕ-submodules
+-/
+
 -- Porting note: `S.toNatSubmodule` doesn't work. I used `AddSubmonoid.toNatSubmodule S` instead.
 /-- An additive submonoid is equivalent to a ℕ-submodule. -/
 def AddSubmonoid.toNatSubmodule : AddSubmonoid M ≃o Submodule ℕ M where
@@ -381,6 +439,10 @@ end AddCommMonoid
 
 section IntSubmodule
 
+/-!
+## ℤ-submodules
+-/
+
 variable [AddCommGroup M]
 
 -- Porting note: `S.toIntSubmodule` doesn't work. I used `AddSubgroup.toIntSubmodule S` instead.

Autoimplicits are highly controversial and also defeat the performance-improving work in #6474.

The intent of this PR is to make autoImplicit opt-in on a per-file basis, by disabling it in the lakefile and enabling it again with set_option autoImplicit true in the few files that rely on it.

That also keeps this PR small, as opposed to attempting to "fix" files to not need it any more.

I claim that many of the uses of autoImplicit in these files are accidental; situations such as:

• Assuming variables are in scope, but pasting the lemma in the wrong section
• Pasting in a lemma from a scratch file without checking to see if the variable names are consistent with the rest of the file
• Making a copy-paste error between lemmas and forgetting to add an explicit arguments.

Having set_option autoImplicit false as the default prevents these types of mistake being made in the 90% of files where autoImplicits are not used at all, and causes them to be caught by CI during review.

I think there were various points during the port where we encouraged porters to delete the universes u v lines; I think having autoparams for universe variables only would cover a lot of the cases we actually use them, while avoiding any real shortcomings.

A Zulip poll (after combining overlapping votes accordingly) was in favor of this change with 5:5:18 as the no:dontcare:yes vote ratio.

While this PR was being reviewed, a handful of files gained some more likely-accidental autoImplicits. In these places, set_option autoImplicit true has been placed locally within a section, rather than at the top of the file.

@@ -25,6 +25,8 @@ to unify the APIs where possible.
 
 -/
 
+set_option autoImplicit true
+
 
 variable {R S M : Type*}
 

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

This has nice performance benefits.

@@ -26,7 +26,7 @@ to unify the APIs where possible.
 -/
 
 
-variable {R S M : Type _}
+variable {R S M : Type*}
 
 section AddCommMonoid
 
@@ -288,25 +288,25 @@ theorem add_mem_sup {S T : Submodule R M} {s t : M} (hs : s ∈ S) (ht : t ∈ T
   add_mem (mem_sup_left hs) (mem_sup_right ht)
 #align submodule.add_mem_sup Submodule.add_mem_sup
 
-theorem sub_mem_sup {R' M' : Type _} [Ring R'] [AddCommGroup M'] [Module R' M']
+theorem sub_mem_sup {R' M' : Type*} [Ring R'] [AddCommGroup M'] [Module R' M']
     {S T : Submodule R' M'} {s t : M'} (hs : s ∈ S) (ht : t ∈ T) : s - t ∈ S ⊔ T := by
   rw [sub_eq_add_neg]
   exact add_mem_sup hs (neg_mem ht)
 #align submodule.sub_mem_sup Submodule.sub_mem_sup
 
-theorem mem_iSup_of_mem {ι : Sort _} {b : M} {p : ι → Submodule R M} (i : ι) (h : b ∈ p i) :
+theorem mem_iSup_of_mem {ι : Sort*} {b : M} {p : ι → Submodule R M} (i : ι) (h : b ∈ p i) :
     b ∈ ⨆ i, p i :=
   (le_iSup p i) h
 #align submodule.mem_supr_of_mem Submodule.mem_iSup_of_mem
 
 open BigOperators
 
-theorem sum_mem_iSup {ι : Type _} [Fintype ι] {f : ι → M} {p : ι → Submodule R M}
+theorem sum_mem_iSup {ι : Type*} [Fintype ι] {f : ι → M} {p : ι → Submodule R M}
     (h : ∀ i, f i ∈ p i) : (∑ i, f i) ∈ ⨆ i, p i :=
   sum_mem fun i _ ↦ mem_iSup_of_mem i (h i)
 #align submodule.sum_mem_supr Submodule.sum_mem_iSup
 
-theorem sum_mem_biSup {ι : Type _} {s : Finset ι} {f : ι → M} {p : ι → Submodule R M}
+theorem sum_mem_biSup {ι : Type*} {s : Finset ι} {f : ι → M} {p : ι → Submodule R M}
     (h : ∀ i ∈ s, f i ∈ p i) : (∑ i in s, f i) ∈ ⨆ i ∈ s, p i :=
   sum_mem fun i hi ↦ mem_iSup_of_mem i <| mem_iSup_of_mem hi (h i hi)
 #align submodule.sum_mem_bsupr Submodule.sum_mem_biSup

• depends on: #5966

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

@@ -2,15 +2,12 @@
 Copyright (c) 2017 Johannes Hölzl. All rights reserved.
 Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Johannes Hölzl, Mario Carneiro, Kevin Buzzard, Yury Kudryashov
-
-! This file was ported from Lean 3 source module algebra.module.submodule.lattice
-! leanprover-community/mathlib commit f7fc89d5d5ff1db2d1242c7bb0e9062ce47ef47c
-! Please do not edit these lines, except to modify the commit id
-! if you have ported upstream changes.
 -/
 import Mathlib.Algebra.Module.Submodule.Basic
 import Mathlib.Algebra.PUnitInstances
 
+#align_import algebra.module.submodule.lattice from "leanprover-community/mathlib"@"f7fc89d5d5ff1db2d1242c7bb0e9062ce47ef47c"
+
 /-!
 # The lattice structure on `Submodule`s
 

This is the second half of the changes originally in #5699, removing all occurrences of ; after a space and implementing a linter rule to enforce it.

In most cases this 2-character substring has a space after it, so the following command was run first:

find . -type f -name "*.lean" -exec sed -i -E 's/ ; /; /g' {} \;

The remaining cases were few enough in number that they were done manually.

@@ -256,7 +256,7 @@ theorem finset_inf_coe {ι} (s : Finset ι) (p : ι → Submodule R M) :
 
 @[simp]
 theorem iInf_coe {ι} (p : ι → Submodule R M) : (↑(⨅ i, p i) : Set M) = ⋂ i, ↑(p i) := by
-  rw [iInf, sInf_coe] ; simp only [Set.mem_range, Set.iInter_exists, Set.iInter_iInter_eq']
+  rw [iInf, sInf_coe]; simp only [Set.mem_range, Set.iInter_exists, Set.iInter_iInter_eq']
 #align submodule.infi_coe Submodule.iInf_coe
 
 @[simp]
@@ -266,7 +266,7 @@ theorem mem_sInf {S : Set (Submodule R M)} {x : M} : x ∈ sInf S ↔ ∀ p ∈
 
 @[simp]
 theorem mem_iInf {ι} (p : ι → Submodule R M) {x} : (x ∈ ⨅ i, p i) ↔ ∀ i, x ∈ p i := by
-  rw [← SetLike.mem_coe, iInf_coe, Set.mem_iInter] ; rfl
+  rw [← SetLike.mem_coe, iInf_coe, Set.mem_iInter]; rfl
 #align submodule.mem_infi Submodule.mem_iInf
 
 @[simp]

This PR also increase the priority of Submodule.bot_ext.

Co-authored-by: Jireh Loreaux <loreaujy@gmail.com>

@@ -95,7 +95,7 @@ protected theorem eq_bot_iff (p : Submodule R M) : p = ⊥ ↔ ∀ x ∈ p, x =
     fun h ↦ eq_bot_iff.mpr fun x hx ↦ (mem_bot R).mpr (h x hx)⟩
 #align submodule.eq_bot_iff Submodule.eq_bot_iff
 
-@[ext]
+@[ext high]
 protected theorem bot_ext (x y : (⊥ : Submodule R M)) : x = y := by
   rcases x with ⟨x, xm⟩; rcases y with ⟨y, ym⟩; congr
   rw [(Submodule.eq_bot_iff _).mp rfl x xm]

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>

@@ -116,9 +116,10 @@ theorem exists_mem_ne_zero_of_ne_bot {p : Submodule R M} (h : p ≠ ⊥) : ∃ b
   ⟨b, hb₁, hb₂⟩
 #align submodule.exists_mem_ne_zero_of_ne_bot Submodule.exists_mem_ne_zero_of_ne_bot
 
+-- FIXME: we default PUnit to PUnit.{1} here without the explicit universe annotation
 /-- The bottom submodule is linearly equivalent to punit as an `R`-module. -/
 @[simps]
-def botEquivPUnit : (⊥ : Submodule R M) ≃ₗ[R] PUnit where
+def botEquivPUnit : (⊥ : Submodule R M) ≃ₗ[R] PUnit.{v+1} where
   toFun _ := PUnit.unit
   invFun _ := 0
   map_add' _ _ := rfl

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>

@@ -198,11 +198,11 @@ instance : InfSet (Submodule R M) :=
       add_mem' := by simp (config := { contextual := true }) [add_mem]
       smul_mem' := by simp (config := { contextual := true }) [smul_mem] }⟩
 
-private theorem infₛ_le' {S : Set (Submodule R M)} {p} : p ∈ S → infₛ S ≤ p :=
-  Set.binterᵢ_subset_of_mem
+private theorem sInf_le' {S : Set (Submodule R M)} {p} : p ∈ S → sInf S ≤ p :=
+  Set.biInter_subset_of_mem
 
-private theorem le_infₛ' {S : Set (Submodule R M)} {p} : (∀ q ∈ S, p ≤ q) → p ≤ infₛ S :=
-  Set.subset_interᵢ₂
+private theorem le_sInf' {S : Set (Submodule R M)} {p} : (∀ q ∈ S, p ≤ q) → p ≤ sInf S :=
+  Set.subset_iInter₂
 
 instance : Inf (Submodule R M) :=
   ⟨fun p q ↦
@@ -214,18 +214,18 @@ instance : Inf (Submodule R M) :=
 instance completeLattice : CompleteLattice (Submodule R M) :=
   { (inferInstance : OrderTop (Submodule R M)),
     (inferInstance : OrderBot (Submodule R M)) with
-    sup := fun a b ↦ infₛ { x | a ≤ x ∧ b ≤ x }
-    le_sup_left := fun _ _ ↦ le_infₛ' fun _ ⟨h, _⟩ ↦ h
-    le_sup_right := fun _ _ ↦ le_infₛ' fun _ ⟨_, h⟩ ↦ h
-    sup_le := fun _ _ _ h₁ h₂ ↦ infₛ_le' ⟨h₁, h₂⟩
+    sup := fun a b ↦ sInf { x | a ≤ x ∧ b ≤ x }
+    le_sup_left := fun _ _ ↦ le_sInf' fun _ ⟨h, _⟩ ↦ h
+    le_sup_right := fun _ _ ↦ le_sInf' fun _ ⟨_, h⟩ ↦ h
+    sup_le := fun _ _ _ h₁ h₂ ↦ sInf_le' ⟨h₁, h₂⟩
     inf := (· ⊓ ·)
     le_inf := fun _ _ _ ↦ Set.subset_inter
     inf_le_left := fun _ _ ↦ Set.inter_subset_left _ _
     inf_le_right := fun _ _ ↦ Set.inter_subset_right _ _
-    le_supₛ := fun _ _ hs ↦ le_infₛ' fun _ hq ↦ by exact hq _ hs
-    supₛ_le := fun _ _ hs ↦ infₛ_le' hs
-    le_infₛ := fun _ _ ↦ le_infₛ'
-    infₛ_le := fun _ _ ↦ infₛ_le' }
+    le_sSup := fun _ _ hs ↦ le_sInf' fun _ hq ↦ by exact hq _ hs
+    sSup_le := fun _ _ hs ↦ sInf_le' hs
+    le_sInf := fun _ _ ↦ le_sInf'
+    sInf_le := fun _ _ ↦ sInf_le' }
 #align submodule.complete_lattice Submodule.completeLattice
 
 @[simp]
@@ -239,9 +239,9 @@ theorem mem_inf {p q : Submodule R M} {x : M} : x ∈ p ⊓ q ↔ x ∈ p ∧ x
 #align submodule.mem_inf Submodule.mem_inf
 
 @[simp]
-theorem infₛ_coe (P : Set (Submodule R M)) : (↑(infₛ P) : Set M) = ⋂ p ∈ P, ↑p :=
+theorem sInf_coe (P : Set (Submodule R M)) : (↑(sInf P) : Set M) = ⋂ p ∈ P, ↑p :=
   rfl
-#align submodule.Inf_coe Submodule.infₛ_coe
+#align submodule.Inf_coe Submodule.sInf_coe
 
 @[simp]
 theorem finset_inf_coe {ι} (s : Finset ι) (p : ι → Submodule R M) :
@@ -254,24 +254,24 @@ theorem finset_inf_coe {ι} (s : Finset ι) (p : ι → Submodule R M) :
 #align submodule.finset_inf_coe Submodule.finset_inf_coe
 
 @[simp]
-theorem infᵢ_coe {ι} (p : ι → Submodule R M) : (↑(⨅ i, p i) : Set M) = ⋂ i, ↑(p i) := by
-  rw [infᵢ, infₛ_coe] ; simp only [Set.mem_range, Set.interᵢ_exists, Set.interᵢ_interᵢ_eq']
-#align submodule.infi_coe Submodule.infᵢ_coe
+theorem iInf_coe {ι} (p : ι → Submodule R M) : (↑(⨅ i, p i) : Set M) = ⋂ i, ↑(p i) := by
+  rw [iInf, sInf_coe] ; simp only [Set.mem_range, Set.iInter_exists, Set.iInter_iInter_eq']
+#align submodule.infi_coe Submodule.iInf_coe
 
 @[simp]
-theorem mem_infₛ {S : Set (Submodule R M)} {x : M} : x ∈ infₛ S ↔ ∀ p ∈ S, x ∈ p :=
-  Set.mem_interᵢ₂
-#align submodule.mem_Inf Submodule.mem_infₛ
+theorem mem_sInf {S : Set (Submodule R M)} {x : M} : x ∈ sInf S ↔ ∀ p ∈ S, x ∈ p :=
+  Set.mem_iInter₂
+#align submodule.mem_Inf Submodule.mem_sInf
 
 @[simp]
-theorem mem_infᵢ {ι} (p : ι → Submodule R M) {x} : (x ∈ ⨅ i, p i) ↔ ∀ i, x ∈ p i := by
-  rw [← SetLike.mem_coe, infᵢ_coe, Set.mem_interᵢ] ; rfl
-#align submodule.mem_infi Submodule.mem_infᵢ
+theorem mem_iInf {ι} (p : ι → Submodule R M) {x} : (x ∈ ⨅ i, p i) ↔ ∀ i, x ∈ p i := by
+  rw [← SetLike.mem_coe, iInf_coe, Set.mem_iInter] ; rfl
+#align submodule.mem_infi Submodule.mem_iInf
 
 @[simp]
 theorem mem_finset_inf {ι} {s : Finset ι} {p : ι → Submodule R M} {x : M} :
     x ∈ s.inf p ↔ ∀ i ∈ s, x ∈ p i := by
-  simp only [← SetLike.mem_coe, finset_inf_coe, Set.mem_interᵢ]
+  simp only [← SetLike.mem_coe, finset_inf_coe, Set.mem_iInter]
 #align submodule.mem_finset_inf Submodule.mem_finset_inf
 
 theorem mem_sup_left {S T : Submodule R M} : ∀ {x : M}, x ∈ S → x ∈ S ⊔ T := by
@@ -296,32 +296,32 @@ theorem sub_mem_sup {R' M' : Type _} [Ring R'] [AddCommGroup M'] [Module R' M']
   exact add_mem_sup hs (neg_mem ht)
 #align submodule.sub_mem_sup Submodule.sub_mem_sup
 
-theorem mem_supᵢ_of_mem {ι : Sort _} {b : M} {p : ι → Submodule R M} (i : ι) (h : b ∈ p i) :
+theorem mem_iSup_of_mem {ι : Sort _} {b : M} {p : ι → Submodule R M} (i : ι) (h : b ∈ p i) :
     b ∈ ⨆ i, p i :=
-  (le_supᵢ p i) h
-#align submodule.mem_supr_of_mem Submodule.mem_supᵢ_of_mem
+  (le_iSup p i) h
+#align submodule.mem_supr_of_mem Submodule.mem_iSup_of_mem
 
 open BigOperators
 
-theorem sum_mem_supᵢ {ι : Type _} [Fintype ι] {f : ι → M} {p : ι → Submodule R M}
+theorem sum_mem_iSup {ι : Type _} [Fintype ι] {f : ι → M} {p : ι → Submodule R M}
     (h : ∀ i, f i ∈ p i) : (∑ i, f i) ∈ ⨆ i, p i :=
-  sum_mem fun i _ ↦ mem_supᵢ_of_mem i (h i)
-#align submodule.sum_mem_supr Submodule.sum_mem_supᵢ
+  sum_mem fun i _ ↦ mem_iSup_of_mem i (h i)
+#align submodule.sum_mem_supr Submodule.sum_mem_iSup
 
-theorem sum_mem_bsupᵢ {ι : Type _} {s : Finset ι} {f : ι → M} {p : ι → Submodule R M}
+theorem sum_mem_biSup {ι : Type _} {s : Finset ι} {f : ι → M} {p : ι → Submodule R M}
     (h : ∀ i ∈ s, f i ∈ p i) : (∑ i in s, f i) ∈ ⨆ i ∈ s, p i :=
-  sum_mem fun i hi ↦ mem_supᵢ_of_mem i <| mem_supᵢ_of_mem hi (h i hi)
-#align submodule.sum_mem_bsupr Submodule.sum_mem_bsupᵢ
+  sum_mem fun i hi ↦ mem_iSup_of_mem i <| mem_iSup_of_mem hi (h i hi)
+#align submodule.sum_mem_bsupr Submodule.sum_mem_biSup
 
-/-! Note that `Submodule.mem_supᵢ` is provided in `LinearAlgebra/Span.lean`. -/
+/-! Note that `Submodule.mem_iSup` is provided in `LinearAlgebra/Span.lean`. -/
 
 
-theorem mem_supₛ_of_mem {S : Set (Submodule R M)} {s : Submodule R M} (hs : s ∈ S) :
-    ∀ {x : M}, x ∈ s → x ∈ supₛ S := by
-  have := le_supₛ hs
+theorem mem_sSup_of_mem {S : Set (Submodule R M)} {s : Submodule R M} (hs : s ∈ S) :
+    ∀ {x : M}, x ∈ s → x ∈ sSup S := by
+  have := le_sSup hs
   rw [LE.le] at this
   exact this
-#align submodule.mem_Sup_of_mem Submodule.mem_supₛ_of_mem
+#align submodule.mem_Sup_of_mem Submodule.mem_sSup_of_mem
 
 theorem disjoint_def {p p' : Submodule R M} : Disjoint p p' ↔ ∀ x ∈ p, x ∈ p' → x = (0 : M) :=
   disjoint_iff_inf_le.trans <| show (∀ x, x ∈ p ∧ x ∈ p' → x ∈ ({0} : Set M)) ↔ _ by simp

Co-authored-by: Yury G. Kudryashov <urkud@urkud.name>

@@ -204,7 +204,7 @@ private theorem infₛ_le' {S : Set (Submodule R M)} {p} : p ∈ S → infₛ S
 private theorem le_infₛ' {S : Set (Submodule R M)} {p} : (∀ q ∈ S, p ≤ q) → p ≤ infₛ S :=
   Set.subset_interᵢ₂
 
-instance : HasInf (Submodule R M) :=
+instance : Inf (Submodule R M) :=
   ⟨fun p q ↦
     { carrier := p ∩ q
       zero_mem' := by simp [zero_mem]

@@ -211,7 +211,7 @@ instance : HasInf (Submodule R M) :=
       add_mem' := by simp (config := { contextual := true }) [add_mem]
       smul_mem' := by simp (config := { contextual := true }) [smul_mem] }⟩
 
-instance : CompleteLattice (Submodule R M) :=
+instance completeLattice : CompleteLattice (Submodule R M) :=
   { (inferInstance : OrderTop (Submodule R M)),
     (inferInstance : OrderBot (Submodule R M)) with
     sup := fun a b ↦ infₛ { x | a ≤ x ∧ b ≤ x }
@@ -226,6 +226,7 @@ instance : CompleteLattice (Submodule R M) :=
     supₛ_le := fun _ _ hs ↦ infₛ_le' hs
     le_infₛ := fun _ _ ↦ le_infₛ'
     infₛ_le := fun _ _ ↦ infₛ_le' }
+#align submodule.complete_lattice Submodule.completeLattice
 
 @[simp]
 theorem inf_coe : ↑(p ⊓ q) = (p ∩ q : Set M) :=

@@ -118,14 +118,13 @@ theorem exists_mem_ne_zero_of_ne_bot {p : Submodule R M} (h : p ≠ ⊥) : ∃ b
 
 /-- The bottom submodule is linearly equivalent to punit as an `R`-module. -/
 @[simps]
-def botEquivPUnit : (⊥ : Submodule R M) ≃ₗ[R] PUnit
-    where
+def botEquivPUnit : (⊥ : Submodule R M) ≃ₗ[R] PUnit where
   toFun _ := PUnit.unit
   invFun _ := 0
-  map_add' := fun _ _ ↦ rfl
-  map_smul' := fun _ _ ↦ rfl
-  left_inv := by intro ; simp only [eq_iff_true_of_subsingleton]
-  right_inv := fun _ ↦ rfl
+  map_add' _ _ := rfl
+  map_smul' _ _ := rfl
+  left_inv _ := Subsingleton.elim _ _
+  right_inv _ := rfl
 #align submodule.bot_equiv_punit Submodule.botEquivPUnit
 
 theorem eq_bot_of_subsingleton (p : Submodule R M) [Subsingleton p] : p = ⊥ := by
@@ -183,14 +182,13 @@ theorem eq_top_iff' {p : Submodule R M} : p = ⊤ ↔ ∀ x, x ∈ p :=
 
 This is the module version of `AddSubmonoid.topEquiv`. -/
 @[simps]
-def topEquiv : (⊤ : Submodule R M) ≃ₗ[R] M
-    where
+def topEquiv : (⊤ : Submodule R M) ≃ₗ[R] M where
   toFun x := x
   invFun x := ⟨x, mem_top⟩
-  map_add' := fun _ _ ↦ rfl
-  map_smul' := fun _ _ ↦ rfl
-  left_inv := fun _ ↦ rfl
-  right_inv := fun _ ↦ rfl
+  map_add' _ _ := rfl
+  map_smul' _ _ := rfl
+  left_inv _ := rfl
+  right_inv _ := rfl
 #align submodule.top_equiv Submodule.topEquiv
 
 instance : InfSet (Submodule R M) :=
@@ -200,10 +198,10 @@ instance : InfSet (Submodule R M) :=
       add_mem' := by simp (config := { contextual := true }) [add_mem]
       smul_mem' := by simp (config := { contextual := true }) [smul_mem] }⟩
 
-private theorem Inf_le' {S : Set (Submodule R M)} {p} : p ∈ S → infₛ S ≤ p :=
+private theorem infₛ_le' {S : Set (Submodule R M)} {p} : p ∈ S → infₛ S ≤ p :=
   Set.binterᵢ_subset_of_mem
 
-private theorem le_Inf' {S : Set (Submodule R M)} {p} : (∀ q ∈ S, p ≤ q) → p ≤ infₛ S :=
+private theorem le_infₛ' {S : Set (Submodule R M)} {p} : (∀ q ∈ S, p ≤ q) → p ≤ infₛ S :=
   Set.subset_interᵢ₂
 
 instance : HasInf (Submodule R M) :=
@@ -217,17 +215,17 @@ instance : CompleteLattice (Submodule R M) :=
   { (inferInstance : OrderTop (Submodule R M)),
     (inferInstance : OrderBot (Submodule R M)) with
     sup := fun a b ↦ infₛ { x | a ≤ x ∧ b ≤ x }
-    le_sup_left := fun _ _ ↦ le_Inf' fun _ ⟨h, _⟩ ↦ h
-    le_sup_right := fun _ _ ↦ le_Inf' fun _ ⟨_, h⟩ ↦ h
-    sup_le := fun _ _ _ h₁ h₂ ↦ Inf_le' ⟨h₁, h₂⟩
+    le_sup_left := fun _ _ ↦ le_infₛ' fun _ ⟨h, _⟩ ↦ h
+    le_sup_right := fun _ _ ↦ le_infₛ' fun _ ⟨_, h⟩ ↦ h
+    sup_le := fun _ _ _ h₁ h₂ ↦ infₛ_le' ⟨h₁, h₂⟩
     inf := (· ⊓ ·)
     le_inf := fun _ _ _ ↦ Set.subset_inter
     inf_le_left := fun _ _ ↦ Set.inter_subset_left _ _
     inf_le_right := fun _ _ ↦ Set.inter_subset_right _ _
-    le_supₛ := fun _ _ hs ↦ le_Inf' fun _ hq ↦ by exact hq _ hs
-    supₛ_le := fun _ _ hs ↦ Inf_le' hs
-    le_infₛ := fun _ _ ↦ le_Inf'
-    infₛ_le := fun _ _ ↦ Inf_le' }
+    le_supₛ := fun _ _ hs ↦ le_infₛ' fun _ hq ↦ by exact hq _ hs
+    supₛ_le := fun _ _ hs ↦ infₛ_le' hs
+    le_infₛ := fun _ _ ↦ le_infₛ'
+    infₛ_le := fun _ _ ↦ infₛ_le' }
 
 @[simp]
 theorem inf_coe : ↑(p ⊓ q) = (p ∩ q : Set M) :=
@@ -309,12 +307,12 @@ theorem sum_mem_supᵢ {ι : Type _} [Fintype ι] {f : ι → M} {p : ι → Sub
   sum_mem fun i _ ↦ mem_supᵢ_of_mem i (h i)
 #align submodule.sum_mem_supr Submodule.sum_mem_supᵢ
 
-theorem sum_mem_bsupr {ι : Type _} {s : Finset ι} {f : ι → M} {p : ι → Submodule R M}
+theorem sum_mem_bsupᵢ {ι : Type _} {s : Finset ι} {f : ι → M} {p : ι → Submodule R M}
     (h : ∀ i ∈ s, f i ∈ p i) : (∑ i in s, f i) ∈ ⨆ i ∈ s, p i :=
   sum_mem fun i hi ↦ mem_supᵢ_of_mem i <| mem_supᵢ_of_mem hi (h i hi)
-#align submodule.sum_mem_bsupr Submodule.sum_mem_bsupr
+#align submodule.sum_mem_bsupr Submodule.sum_mem_bsupᵢ
 
-/-! Note that `Submodule.mem_supr` is provided in `LinearAlgebra/Span.lean`. -/
+/-! Note that `Submodule.mem_supᵢ` is provided in `LinearAlgebra/Span.lean`. -/
 
 
 theorem mem_supₛ_of_mem {S : Set (Submodule R M)} {s : Submodule R M} (hs : s ∈ S) :
@@ -344,12 +342,11 @@ section NatSubmodule
 
 -- Porting note: `S.toNatSubmodule` doesn't work. I used `AddSubmonoid.toNatSubmodule S` instead.
 /-- An additive submonoid is equivalent to a ℕ-submodule. -/
-def AddSubmonoid.toNatSubmodule : AddSubmonoid M ≃o Submodule ℕ M
-    where
+def AddSubmonoid.toNatSubmodule : AddSubmonoid M ≃o Submodule ℕ M where
   toFun S := { S with smul_mem' := fun r s hs ↦ show r • s ∈ S from nsmul_mem hs _ }
   invFun := Submodule.toAddSubmonoid
-  left_inv := fun _ ↦ rfl
-  right_inv := fun _ ↦ rfl
+  left_inv _ := rfl
+  right_inv _ := rfl
   map_rel_iff' := Iff.rfl
 #align add_submonoid.to_nat_submodule AddSubmonoid.toNatSubmodule
 
@@ -387,12 +384,11 @@ variable [AddCommGroup M]
 
 -- Porting note: `S.toIntSubmodule` doesn't work. I used `AddSubgroup.toIntSubmodule S` instead.
 /-- An additive subgroup is equivalent to a ℤ-submodule. -/
-def AddSubgroup.toIntSubmodule : AddSubgroup M ≃o Submodule ℤ M
-    where
+def AddSubgroup.toIntSubmodule : AddSubgroup M ≃o Submodule ℤ M where
   toFun S := { S with smul_mem' := fun _ _ hs ↦ S.zsmul_mem hs _ }
   invFun := Submodule.toAddSubgroup
-  left_inv := fun _ ↦ rfl
-  right_inv := fun _ ↦ rfl
+  left_inv _ := rfl
+  right_inv _ := rfl
   map_rel_iff' := Iff.rfl
 #align add_subgroup.to_int_submodule AddSubgroup.toIntSubmodule
 

@@ -302,8 +302,7 @@ theorem mem_supᵢ_of_mem {ι : Sort _} {b : M} {p : ι → Submodule R M} (i :
   (le_supᵢ p i) h
 #align submodule.mem_supr_of_mem Submodule.mem_supᵢ_of_mem
 
--- Porting note: commented out
--- open BigOperators
+open BigOperators
 
 theorem sum_mem_supᵢ {ι : Type _} [Fintype ι] {f : ι → M} {p : ι → Submodule R M}
     (h : ∀ i, f i ∈ p i) : (∑ i, f i) ∈ ⨆ i, p i :=

Co-authored-by: Johan Commelin <johan@commelin.net>